i MECHANICS OF THE URINARY BLADDER IN HEALTH AND DISEASE By Tyler Glenn Tuttle A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of Mechanical Engineering Doctor of Philosophy 202 1 ii ABSTRACT MECHANICS OF THE URINARY BLADDER IN HEALTH AND DISEASE By Tyler G lenn Tuttle The urinary bladder stores and voids urine through relaxation and contraction. The ability of the bladder to drastically increase in size while maintaining minimal pressure is key to proper organ function, making the study of bladder tissue mechanical characteristics crucial. Several diseases and disabilities that lead to bladder dysfunction are accompanied by pa thological remodeling of the bladder wall that can dramatically impact its mechanical behavior. Before we can understand pathological changes, we must understand the healthy characteristics of the bladder. To this end, we must identify the relevancy of dif ferent animals as models of human bladder mechanics. Several studies exist that characterize either the human bladder or pig bladder. However, differences in mechanical testing protocols between studies leads to high variation in observed mechanical prope rties within the same species. This makes it difficult to infer the utility of the pig bladder as an effective model for human bladder mechanics. The first goal of this dissertation is to directly compare the mechanics of the human and pig bladder tested u nder identical conditions. To do this we have employed constitutive modeling of uniaxial tensile data from human and pig bladder specimens, and shown anisotropic behavior and comparable mechanical behavior between pig and human bladders. The second goal of this dissertation is to assess the viscoelastic properties of the porcine bladder wall, and how they are affected by anatomical location and osmotic swelling. In certain pathological conditions degradation of the urothelium can expose the bladder wall t o osmotic challenge from urine, changing the hydration level, and consequently, viscoelastic behavior of the iii tissue. Through osmotic swelling of pig bladder tissue, stress - relaxation testing, and viscoelastic constitutive modeling we have shown that high l evels of urine osmolarity may lead to increased relaxation times that could increase the stress state of the bladder wall and be a driving factor in pathological remodeling. The final goal of this dissertation is to identify how a pathological condition, i.e., spinal cord injury, can affect bladder extracellular matrix morphology and compliance in the long - term. Prior studies on rat bladder mechanics after spinal cord injury have shown increased capacity and compliance of the bladder post - injury in the sh ort - term. Through imaging, histological analysis, mechanical testing, and constitutive modeling of the long - term spinal cord injured rat bladder extracellular matrix, we have shown profound remodeling of collagen in the bladder wall after spinal cord injur y, leading to an increase in capacity, and compliance. It is likely that increase in compliance is a result of the increase in fiber waviness that is seen in our histological analysis, which was predicted by our structural fiber - recruitment constitutive mo del. iv TABLE OF CONTENTS LIST OF TABLES ................................ ................................ ................................ ................... vii LIST OF FIGURES ................................ ................................ ................................ ................ viii CHAPTER 1 - L I T ERATURE REVIEW ................................ ................................ .................... 1 1.1. Background ................................ ................................ ................................ ...................... 1 1.1.1. Anatomy & physiology ................................ ................................ .............................. 1 1.1.2. Mechanical properties ................................ ................................ ................................ 2 1.1.2.1 Viscoelasticity ................................ ................................ ................................ ...... 3 1.1.2.2 Hyperelasticity ................................ ................................ ................................ ...... 4 1.1.2.2 Fiber reinforced composite ................................ ................................ .................... 5 1.1.3. Neurogenic bladder ................................ ................................ ................................ .... 6 1.2. Experimental studies ................................ ................................ ................................ ......... 8 1.2.1 In vivo studies ................................ ................................ ................................ .............. 9 1.2.2. Ex vivo studies ................................ ................................ ................................ .......... 10 1.2.2.1. Ex vivo small - animal studies ................................ ................................ .............. 10 1.2.2.2. Ex vivo large - animal studies ................................ ................................ ............... 12 1.2.2.3. Ex vivo animal studies of the bladder extracellular matrix ................................ .. 14 1.2.2.4. Ex vivo human studies ................................ ................................ ........................ 16 1.3. Viscoelastic modeling ................................ ................................ ................................ ..... 17 1.3.1. Animal models of health and disease ................................ ................................ ........ 18 1.3.1.1. Models informed by data collected in vivo ................................ ......................... 18 1.3.1.2. Models informed by data collected in vitro ................................ ......................... 19 1.3.1.3. Models informed by data collected both in vivo & in vitro ................................ .. 20 1.3.2. Human models of health and disease ................................ ................................ ........ 21 1.3.2.1. Models informed by data collected in vitro ................................ ......................... 21 1.3.2.2. Models informed by data collected both in vivo and in vitro ............................... 22 1.4. Hyperelastic modeling ................................ ................................ ................................ .... 22 1.4.1. Continuum/exponential models ................................ ................................ ................ 23 1.4.2. Fiber recruitment models ................................ ................................ .......................... 26 1.4.2.1. Quantification of fiber waviness ................................ ................................ ......... 27 1.4.2.2. Fiber recruitment model structural theory ................................ ........................... 27 1.4.2.3. Fiber recruitment models of the bladder ................................ ............................. 28 1.5 Objectives of this dissertation ................................ ................................ .......................... 28 CHAPTER 2 - DIRECT COMPARISON OF HEALTHY HUMAN AND PIG BLADDER TISSUE MECHANI CAL PROPERTIES ................................ ................................ .................. 30 2.1. Overview ................................ ................................ ................................ ........................ 30 2.2. Methods ................................ ................................ ................................ .......................... 31 2.2.1. Tissue prepar ation ................................ ................................ ................................ .... 31 2.2.2. Mechanical testing ................................ ................................ ................................ .... 33 2.2.2.1. Uniaxial testing ................................ ................................ ................................ .. 33 v 2.2.2.2. Compression testing ................................ ................................ ........................... 35 2.2.3. Constitutive modeling ................................ ................................ .............................. 35 2.2.3.1. Fiber recruitment (M1) ................................ ................................ ....................... 35 2.2.3.2. Continuum model (M2) ................................ ................................ ...................... 37 2.2.3.3. Material parameter estimation ................................ ................................ ............ 39 2.2.4. Statistical analysis ................................ ................................ ................................ .... 41 2.3. R esults ................................ ................................ ................................ ............................ 42 2.3.1. Collagen recruitment model (M1) ................................ ................................ ............. 42 2.3.2. Continuum model (M2) ................................ ................................ ............................ 43 2.3.3. Modeling of compression tests ................................ ................................ ................. 47 2.4. Discussion ................................ ................................ ................................ ...................... 48 2.4.1. Validation of model M2 using compression data ................................ ...................... 48 2.4.2. High stress, orthotropic contribution to mechanical behavior ................................ .... 49 2.4.3. Species - specific mechanical behavior ................................ ................................ ....... 50 2.4.4. Porcine tissue anisotropy ................................ ................................ .......................... 50 2.4.5. Limitations ................................ ................................ ................................ ............... 52 2.5 Acknowledgements ................................ ................................ ................................ .......... 54 APPENDIX ................................ ................................ ................................ ........................... 55 CHAPTER 3 - EFFECTS OF SWELLING ON THE VISCOELASTIC BEHAVIOR OF THE PORCINE URINARY BLADDER WALL ................................ ................................ ............... 58 3.1. Overview ................................ ................................ ................................ ........................ 58 3.2. Methods ................................ ................................ ................................ .......................... 60 3.2.1. Tissue procurement ................................ ................................ ................................ .. 60 3.2.2. E xperimental protocols ................................ ................................ ............................. 60 3.2.2.1. Tissue swelling ................................ ................................ ................................ .. 60 3.2.2.2. Stress - relaxation ................................ ................................ ................................ . 63 3.2.3. Data analysis ................................ ................................ ................................ ............ 65 3.2.3.1. Tis sue swelling ................................ ................................ ................................ .. 65 3.2.3.2. Stress - relaxation ................................ ................................ ................................ . 66 3.2.4 Modeling ................................ ................................ ................................ ................... 67 3.2.4.1 Modified Maxwell - Wiechert model ................................ ................................ .... 67 3.2.4.2 Parameter estimation ................................ ................................ ........................... 69 3.2.5 Statistical analysis ................................ ................................ ................................ ..... 69 3.3. Results ................................ ................................ ................................ ............................ 70 3.3.1. Tissue swelling ................................ ................................ ................................ ......... 70 3.3.2. Stress relaxation experimental data ................................ ................................ ........... 71 3.3.3. Modeling results ................................ ................................ ................................ ....... 74 3.4. Discussion ................................ ................................ ................................ ...................... 77 3.4.1. Tissue swelling ................................ ................................ ................................ ......... 77 3.4.2. Stress - relaxation ................................ ................................ ................................ ....... 78 3.4.3. Modeling ................................ ................................ ................................ .................. 79 3.4.4. Limitations ................................ ................................ ................................ ............... 81 3.5 Conclusions ................................ ................................ ................................ ..................... 82 APPENDIX ................................ ................................ ................................ ........................... 84 vi CHAPTER 4 - CHANGES IN MORPHOLOGY AND COMPLIANCE IN THE LONG - TERM SPINAL CORD INJURED RAT BLADDER EXTRACELLULAR MATRIX .......................... 86 4.1. Overview ................................ ................................ ................................ ........................ 86 4.2. Methods ................................ ................................ ................................ .......................... 87 4.2.1. Animal groups and tissue preparation ................................ ................................ ....... 87 4.2.2. Geometry estimation ................................ ................................ ................................ 88 4.2.3. Histology ................................ ................................ ................................ .................. 88 4.2.4. Mechanical testing ................................ ................................ ................................ .... 89 4.2.4. Constitutive modeling ................................ ................................ .............................. 91 4.2.5.1. Fiber recruitment model ................................ ................................ ..................... 91 4.2.5.2. Exponential model ................................ ................................ ............................. 94 4.2.6. Statistical analysis ................................ ................................ ................................ .... 94 4.3. Results ................................ ................................ ................................ ............................ 95 4.3.1. Ring circumference ................................ ................................ ................................ .. 95 4.3.2. Histology ................................ ................................ ................................ .................. 95 4.3.3. Mechanica l testing ................................ ................................ ................................ .... 99 4.3.4. Constitutive modeling ................................ ................................ ............................ 100 4.4. Discussion ................................ ................................ ................................ .................... 102 4.5 Limitations ................................ ................................ ................................ .................... 107 4.6 Conclusions ................................ ................................ ................................ ................... 108 APPENDIX ................................ ................................ ................................ ......................... 110 CHAPTER 5 - CONCLUSIONS AND FUTURE WORK ................................ ....................... 112 5.1 Conclusions ................................ ................................ ................................ ................... 112 5.2 Future work ................................ ................................ ................................ ................... 113 BIBLIOGRAPHY ................................ ................................ ................................ ................... 114 vii LIST OF TABLES Table 2.1 Donor demographic information: age, sex, and cause of death ................................ ... 33 Table 2.2 Parameter estimates for M1, NRMSE for each supraphysiologic loading fit, and representing stretch for 5% collagen recruitment for each group. ................................ ............... 42 Table 4.1 Parameter estimates for the fiber recruitment and exponential continuum models for all samples ................................ ................................ ................................ ................................ ... 111 viii LIST OF FIGURES Figure 1.1 Anatomy of the human bladder [6]. ................................ ................................ ............ 2 Figure 1.2 (a) Schematic of the bladder in the sagittal plane, and (b) image of a cut open porcine bladder with anatomical regions labeled [7]. ................................ ................................ ................ 3 Figure 1.3 Uniaxial stress - relaxation curves for porcine bladder strips in the longitudinal and circumferential directions for strains of (a) 0.2, (b) 0.5, (c) 1.0, and (d) 2.0 [16] .......................... 4 Figure 1.4 Stress - strain curves from uniaxial tensile tests if bladder from (a) dorsal, (b) ventral, (c) lateral, (d) lower body, and (e) trigone regions, showing consistently stiffer behavior in the apex - to - base direction [7]. ................................ ................................ ................................ ........... 5 Figure 1.5 Multiphoton images of collagen in the bladder during loading in the (a) toe regime and (b) transition regime [9]. ................................ ................................ ................................ ....... 6 Figure 1.6 Histological images of normal (A, C) and spinal cord injured (B, D) rat bladders. The top images show increased thickness in the SCI bladder compared to controls. In the bottom images, more elastin fibers are present in the SCI bladder than the control [21]. .......................... 8 Figure 1.7 Depiction of cystometric test and resulting pressure/volume relationships for filling and voiding [23]. ................................ ................................ ................................ ......................... 9 Figure 1.8 (a) Maximum stretches and (b) maximum areal strains obtained from stress mediated biaxial tensile tests for healthy and SCI rat bladders with different durations of SCI [31]. ......... 12 Figure 1.9 Maxwell - Wiechert viscoelastic model with two Maxwell elements [56]. .................. 18 Figure 1.10 Pressure - volume cystometric data from dogs, along with pressure - volume predictions for (a) prolate, and (b) oblate spheroidal bladder models with varying eccentricities [76]. ................................ ................................ ................................ ................................ .......... 26 Figure 2.1 Sample orientation schematic and uniaxial sample preparation. a) The trigone is removed from whole bladder and a steel die produce dumbbell specimens (inset). Also shown are the transverse and longitudinal directions, as well as schematics of orientations of specimens. b) Pictured is a representat ive tissue specimen mounted in the uniaxial tester. ........................... 33 Figure 2.2 Testing protocol for tissue specimens and representative data - mod el prediction results. a) Stretch versus time graph showing three load - unload cycles and the timing of those cycles, and b) stress versus stretch graph showing loading data (symbols) of a single specimen and its corresponding model prediction curves (lines ) for Pulls 1, 2, and 3. ............................... 34 Figure 2.3 Schematic diagram of collagen recruitment model. Gradual engagement of collagen fibers (top row) are modeled by spring elements (bottom row). As the model/tissue is stretched ix (left to right), the hooks engaging the bar is mirrored by the straightening of t he collagen fibers, and the stretching of the springs represents the stretching of the individual collagen fibers. ....... 36 Figure 2.4 Mul ti - step parameter estimation approach. a) Representative plot demonstrates the regions used for parameter estimation of the isotropic and orthotropic strain energy functions and , respectively, as well as representative sample data and M2 model output. b) Collagen fiber recruitment model, M1, used to estimate fiber recruitment distribution. c) Representative supraphysiologic data ( ) and M1 model output after parameter estimation. d) Plot of fiber recruitment distribution that shows is calculated as the stretch at which 5% of collagen fibers are recruited. is used as the cutoff point for the stretch range used for parameter estimation of . ................................ ................................ ..................... 41 Figure 2.5 Normalized root mean square error (NRMSE) and standardized residuals for all data. Histograms of (a) NRMSE for all fitted curves, where represents number of fitted curves, and (b) standardiz ed residuals for all data points included in the fitting process, where represents number of residuals. ................................ ................................ ................................ .................. 45 Figure 2.6 Human and porcine fitted curves under different treatment conditions. M2 model output using median parameter values (lines) and interquartile range of experimental data (shaded) for a) untreated (un) and oxybutynin treated (ox) specimens in humans, and b) untreated (un), oxybutynin treated (ox), and untreated transverse (un) specimens in pigs. Plot titles represent treatment, with superscript denoting direction ( for longitudinal, for transverse), and subsc ript denoting number of samples. Only groups containing 4 or more samples are shown. ................................ ................................ ................................ ................... 45 Figure 2.7 Parameter Estimates. Estimated v alues for (a), (b), (c) are displayed in box plots (median line, box first quartile - third quartile, error bar 0th and fourth quartiles). The results shown include parameter values estimated for both humans (left) and pigs (right). Only groups containing 4 or more samples are shown, all parameter estimates can be found in an open source online repository. ................................ ................................ ................................ ........... 46 Figure 2.8 Calculated values of stress at Box plots representing the experimentally recorded stress values at for humans (left) and pigs (right). Only groups containing 4 or more samples are shown. ................................ ................................ ................................ ........... 47 Figure 2.9 Comparison of compressive behavior experimentally measured and predicted by model M2. Symbols represent the experimental data f rom compression tests in untreated pig samples (testing data - set). The line represent the model prediction for a compression test calculated using median parameter values estimated from uniaxial experiments for untreated pig tissue (training data - set). ................................ ................................ ................................ ........... 47 Figure 2.10 Fiber orientation assessment. a) Photomicrographs of Verhoff Van Gieson (VVG) stained regions human and pig, tested and untested specimens at 400x (scale bar 100 µm). In VVG stain, elastin and cell nuclei are dark blue/black, collagen is red/magenta, and other tissue elements are light brown/yellow. b) Bladder specimens were sectioned at 5µm along the axis of pull to maximi ze fiber orientation analysis. Fibrous regions were selected within specimens (shaded, center) and fiber orientation determined within selections (right, n=4 selections per x specimen). Hue corresponds to the fiber angle (right, inset). c) Fiber orientation distributions (averaged over section) relative to the pulled direction in longitudinal pig and human specimens. ................................ ................................ ................................ ................................ ................. 57 Figure 3.1 Representative bladder after being dissected and flattened. Schematic representations of the locations and number of samples taken from each bladder for (a) the swelling study (9mm diameter punch samples), (b) the anatomical location and (c) the variable - solution osmolarity stress - relaxation experiments. The rectangular punch measured 10mm × 30mm for the samples shown in both (b) and (c). ................................ ................................ ................................ .......... 62 Figure 3.2 Side view (a) and top view (b) of representative 9mm diameter punch sample for the swelling experiment, before (left) and after (right) manual thresholding. Top view (c) and side view (d) of repres entative 10mm × 30mm rectangular punch sample for the stress - relaxation experiments, before (left) and after (right) manual thresholding. Binary images (left column) show a schematic of all relevant geometric definitions for the evaluation of volume and cr oss - sectional area, see Equations ( 3. 1) - ( 3. 3). ................................ ................................ ................... 62 Figure 3.3 Stress - relaxation protocol for a representative sample. Applied strain (top) and recorded force (bottom) data, as a function of test time. This protocol was employed in all stress - relaxation experiments (i.e., anatomical location and variable solution osmolarity). .................. 64 Figure 3.4 Schematic of the modified Maxwell - stiffness increases exponentially with strain ( ), while the springs in the three Maxwell elements have stiffnesses that increase linearly with strain ( ). The dashpots are standard linear dampers ( ). ................................ ................................ ................................ ............................ 69 Figure 3.5 Relative mass ( , top) and relative volume ( , bottom) for the different solution osmolarities and anatomical locations, namely dorsal (D), ventral (V), lateral (L), lower body (LB), and trigone (T). Each bar represents the mean and standard deviation f rom 5 bladders. For 100 mOsm/L, all samples have a and almost all samples (24 of 25, 96%) have . For 300 mOsm/L, all samples have , D and V samples all have , but some L (1 of 5), LB (2 of 5), and T (1 of 5) samples have . For 600 mOsm /L some D (2 of 5) and L (1 of 5) samples have and about half of all samples show (13 of 25, 52%). For 900 mOsm/L some D (2 of 5), V (2 of 5), and L (1 of 5) samples have and over half of all samples show (16 of 25, 64%). ................................ ................................ ...................... 71 Figure 3.6 Stress - relaxation curves as a function of time relative to the start of each loading step for a rep resentative sample. The same data is shown for a linear timescale (top) and logarithmic timescale (bottom). The number of data points in each curve is 200 and have been identified by using a customized logarithmic - like spacing. A grey - scale color gradient has been employed to represent the different values of applied strain, from the lightest representing the smallest strain in the protocol ( ) to the darkest representing the largest strain in the protocol ( ). ................................ ................................ ................................ ................................ .......... 73 Figure 3.7 S tress - relaxation results for all samples showing peak stresses ( , left) and relaxed stresses ( , right) for different anatomical locations (top) and osmolarities (bottom). Open symbols are used to identify the anatomical location experiments and closed symbols to identify xi the varying solution osmolarity experiments. A grey - scale color gradient has been employed to represent the different valu es of applied strain, from the lightest representing the smallest strain in the protocol ( ) to the darkest representing the largest strain in the protocol ( ). An asterisk represents a statistically significant difference (p<0.05) and the relevant comparison is represented by an arrow. ................................ ................................ ..................... 74 Figure 3.8 Estimated values of the parameters for the modified Maxwell - Wiechert mo del when considering the anatomic location experiment. Open symbols are used to identify the different anatomical locations (as specified in the legend). An asterisk represents a statistically significant difference (p<0.05) and the relevant comparison is represented by an arrow. ............................. 76 Figure 3.9 Estimated values of the parameters for the modified Maxwell - Wiechert model when considering t he variable solution osmolarity experiment. Closed symbols are used to identify the different solution osmolarities (as specified in the legend). An asterisk represents a statistically significant difference (p<0.05) and the relevant comparison is represen ted by an arrow. ........... 77 Figure 3.10 Model description for a representative dataset. All plots show the same experimental data (solid cir cles) and model description (solid line), each with a different timescale representation. The top represented the consecutive loading steps as a function of testing time. The bottom figures represent the loading steps as a function of time relative to the start of each loading step shown for a linear timescale (left) and logarithmic timescale (right). The normalized root mean squared error (NRMSE) averaged between all samples is 0.0222 for the exponential spring parameter estimation step and 0.0377 for the entire stress - relaxation curve. .................... 85 Figure 4.1 Visual representation of the fiber recruitment model. As deformation is applied, springs engage, increasing the stiffness of the response. ................................ ............................ 93 Figure 4.2 Representative stress - stretch data with model fit from the fiber - recruitment model (top) and exponential continuum model (bottom). For the fiber - recruitment model, is initial slope, is final slope, and is the mean recruit ment stretch defined by the intersection of the initial and final slope lines. ................................ ................................ ................................ ........ 93 Figure 4.3 (a) Ring images before and after decell ularization and traced edges, and (b) mean ± standard deviation for ring circumference before and after decellularization for control, sham, and paraplegic groups. ................................ ................................ ................................ ............... 95 Figure 4.4 PSR (left two columns) and VVG (right two columns) stained bladders in the plane normal to the longitudinal direction from control (left) and paraplegic (right) rats in the lamina propria (top), detrusor (middle), and adventitia (bottom) ................................ ........................... 97 Figure 4.5 Regions of interest from a 14 - week paraplegic rat bladder showing an area of high col lagen density (PSR, left) and high amounts of elastin (VVG, right) ................................ ...... 97 Figure 4.6 Planar images from control (left) and 1 - week parapl egic (right) rat bladders in the lamina propria (top) and detrusor (bottom) ................................ ................................ ................ 98 Figure 4.7 Mean fiber orientation distributions for co ntrol and 1 - week paraplegic rat bladders in the lamina propria (top) and detrusor (bottom) with different local fiber angle weighting. xii Coherency weighting (left) give high weight to formerly muscular regions as well as collagenous regions. Weighting by the product of energy and intensity (right) gives lower weighting to previously muscular areas, while keeping high weighting in collagenous regions. ..................... 98 Figure 4.8 Stress - stretch curves (mean ± standard deviation) from control, sham, and paraplegic groups. Stretch values at different levels of stress are significantly higher in the paraplegic group when compared to the sham gr oup (arrow) and the sham and control groups combined (bracket). ................................ ................................ ................................ ................................ ................. 99 Figure 4.9 Mean ± standard deviation of stretch values at 100 kPa stress for control, sham, and paraplegic groups. The paraplegic group shows significantly higher stretch than the sham group (arrow) and the sham and control groups combined (bracket). ................................ ................. 100 Figure 4.10 Opening angle images at (a) 0 minutes and (b) 90 minutes post - cut, and (c) mean ± standard deviation of opening angle vs time from control and paraplegic groups ..................... 100 Figure 4.11 Mean ± standard deviation parameter values for the fiber - recruitment model ( , , , , , ), and exponential continuum model ( , ) ................................ ....................... 101 1 CHAPTER 1 - LI T ERATURE REVIEW 1.1. Background 1.1.1. Anatomy & p hysiology The lower urinary tract is composed of the urinary bladder , internal and external urethral sphincters, and urethra. Figure 1.1 shows a diagram of the basic anatomy of the bladder , as well as the structure of the bladder wall. Th e bladder wall has multiple layers. The inner layers, consisting of the transitional epithelium, lamina propria, and submucosa, act as a barrier between urine and the middle layer, which consists of muscle. The muscle of the bladder is the detrusor. The ou termost layer is the adventitia, which is a layer of fibrous connective tissue surrounding the organ. The bladder wall consists of smooth muscle cells (SMCs) and extracellular matrix (ECM) . The ECM, which is comprised of proteins, proteoglycans, and glycos aminoglycans, acts as a support structure that gives strength and compliance to the bladder . Collagen I and III make up the majority of the ECM, and accounts for approximately 30% of intact bladder dry - weight in humans [1 3] . Elastin in the bladder is thought to allow the tissue to recover to its original configuration after being stretched [4] . The lower urinary tract functions in two stages: storage, and voiding. During storage, a healthy bladder m aintains a low, relatively constant, pressure. This is achieved through relaxation of the bladder wall as the organ fills. During voiding, contraction of the detrusor and relaxation of the urethral sphincters must occur simultaneously. This is accomplished through a combination of somatic and autonomic innervation. The detrusor and internal urinary sphincter contain SMCs and are under involuntary control (autonomic inn ervation), whereas the external urinary sphincter is composed of skeletal muscle and is under voluntary control (somatic innervation) [5] . 2 Figure 1 . 1 Anatomy of the human bladder [6] . 1.1.2. Mechanical prope rties The bladder is one of the most physically dynamics structures in the body. The ability to drastically increase in size while maintaining low pressure makes the mechanical properties of the bladder wall an interesting research topic. Because of the pr evalence of lower urinary tract pathologies that correlate with tissue mechanical dysfunction, it is important to understand the mechanical characteristics of the bladder wall, both in healthy and pathological conditions. The mechanical behavior of the bladder wall can be described as viscoelastic, however hyperelastic models have been successfully used to describe the preconditioned behavior of the bladder wall. The mecha nical characteristics of the bladder differ between different anatomical locations (i.e. , dorsal, ventral, lateral, lower - body, trigone) [7,8] and orientations (i.e . , longitudinal/apex - to - base and circumferential/transverse) [7 15] . Figure 1 . 2 shows anatomical regions of the bladder that have been studied previously [7] . An effective way of analyzing mechanical behavior is through the use of constitutive models. Constitutive models, which can be either phenomenological or microstructurally 3 motivated, can give insight into mechanical behavior that is not possible to observe from purely experimental data. Three types of constitutive models are of interest: viscoelastic, hyperelastic, and fiber recruitment models, which are a particular type of hyperelastic model. Figure 1 . 2 (a) Schematic of the bladder in the sagittal plane, and (b) image of a cut open porcine bladder with anatomical regions labeled [7] . 1.1.2.1 Visc oelasticity When a material behaves in both a viscous and an elastic manner, it is termed viscoelastic. When a viscoelastic material undergoes deformation, the resultant stress depends on both the amount of strain and the strain rate (or more generally, th e strain history as a whole). Viscoelastic behavior of materials is commonly modeled using spring - damper models, where springs and dampers represent the elastic and viscous behavior, respectively. Common experiments used to measure viscoelastic behavior in clude stress - relaxation, creep tests, and dynamic mechanical analysis (DMA) . A stress - relaxation test involves rapidly deforming a sample and measuring the resulting stress over time at a constant level of stretch. Figure 1 . 3 shows sample stress - relaxation data for porcine bladder strips at various levels of stretch [16] . Creep tests involve rapidly deforming a sample to a s pecified level of stress, and continu ously deforming the sample to maintain that level 4 of stress. DMA involves applying a sinusoidal stress in order to estimate a storage modulus and loss modulus that describe the elastic and viscous behavior of the materi al, respectively. Figure 1 . 3 Uniaxial stress - relaxation curves for porcine bladder strips in the longitudinal and circumferential directions for strains of (a) 0.2 , (b) 0.5, (c) 1.0, and (d) 2.0 [16] 1.1.2.2 Hyperelasticity For a material to be considered hyperelastic, its stress - strain curve must be repeatable and independent of strain rate. Hyperelastic material models are derived from strai n energy functions, and are generally used when linear elastic models do not accurately describe the material behavior. For biological tissues, hyperelastic models are used when tissue is deformed at rates low enough that viscous effects are negligible. Th e most common experiments used to estimate material parameters within hyperelastic models are uniaxial and biaxial tensile tests with multiple loading and unloading cycles, applied at a constant strain rate. Figure 1 . 4 shows stress - strain curves for one loading cycle of uniaxial tensile tests on porcine bladder strips. 5 Figure 1 . 4 Stress - strain curves from uniaxial tensile tests if bladder from (a) dorsal, (b) ventral, (c) lateral, (d) lower body, and (e) trigone regions, showing consistently stiffer behavior in the apex - to - base direction [7] . 1.1.2.2 Fiber reinforced composite Soft tissues that contain collagen and elastin fibers, which are generally coiled or wavy, can be considered as fiber reinforced composites. When a tissue within this category under goes deformation, the fibers begin to straighten and cause the tissue stiffness to increase. Figure 1 . 5 shows multiphoton images of rat bladder at different levels of stretch, clearly showing the recruitment of collagen fibers with increased stretch. This type of material can be described using a fiber recruitment model, which is a subcategory of hyperelastic models that takes this phenomenon into account. In a fiber recruitment model, it is assumed that there are a large number 6 of wavy collagen fibers. When the tissue is stretched, the fibers be gin to straighten and engage. If one assumes that fibers have a distribution of waviness values that can be described by a probability density function, and each individual fiber is linearly elastic after it has straightened, then the resulting stress - str e tch curve will have a nonlinear quality to it. The resulting shape matches what has been observed in many soft collagenous tissues. Figure 1 . 5 Multiphoton images of collagen in the bladder during loading i n the (a) toe regime and (b) transition regime [9] . 1.1.3. Neurogenic bladder Because the function of the bladder relies heavily on neurological pathways, loss of neurological connection can be detrimental to the bladder and lower urinary tract as a whole. A bladder with decreased or absent neurological con neurogenic bladder can lead to many lower urinary tract symptoms, as well as hydronephrosis, renal damage, urinary tract infections (UTIs) , calculus disease, bladder cancer, and sexual dysfunction [17] . Neurogenic bladders are seen in a high percentage of individuals with various neurological conditions. Voiding dysfuncti on is seen in 80% of persons with multiple sclerosis [18] , and 70 - 84% with spinal cord injury (SCI) [19] . Manack et al. showed over the course of 1 7 year (data collected in a group of 46,271 patients with a neurogenic bladder), patients averaged 16 office visits and 0.5 emergency room visits, 39% of patients visited a urologist, and UTI diagnosis comprised over 20% of the recorded hospitalizations [19] . Neurogenic bladder pathology can present itself in different forms, based on several factors including specific neurological disorder and location of neurologic lesion [20] . Neurogenic bladder behavior can include healthy, spastic, or flaccid behavior of the detrusor and/or the urethral sp hincters, leading to high/low storage volumes and storage pressures. Furthermore, a pathological change in storage volume and storage pressure in the bladder is associated with a change in the stress/stretch experienced by the bladder wall. Subsequently, a s seen in many load bearing biological tissues, deviation from the homeostatic stress/stretch state of a tissue for an extended period of time results in remodeling, and thus a change in material properties of that tissue. Figure 1 . 6 shows histological ima ges of healthy and SCI rat bladder wall [21] . It is clear that remodeling of the SCI bladder has led to increase d wall thickness and increased concentration of smooth muscle and elastin fibers. It has been shown that in the SCI rat bladder , SMCs are oriented both longitudinally and circumferentially, whereas healthy rat bladder s show SMC orientation predominantly in the longitudinal direction, which validates the more isotropic mechanical behavior seen in the SCI rat bladder [22] . 8 Figure 1 . 6 Histological images of normal (A, C) and spinal cord injured (B, D) rat bladder s. The top images show increased thickness in the SCI bladder compared to controls. In the bottom images, more elastin fibers are present in the SCI bladder than the control [21] . 1.2. Experimental studies Experimental studies are essential for understanding how the bladder wall mechanics change in response to pathological conditions. Experimental data generally allows for both qualitative and quantitative observations of the behavior of healthy and pathological tissue. In addition to the types of in vitro experiments that w ere previously mentioned, in vivo and in vitro cystometric tests are also common in the bladder . Cystometry involves filling the bladder and recording pressure - volume data. Figure 1 . 7 shows a diagram of a cystometric experiment for filling and voiding along with sample data [23] . These tests can be stepwise cysto metry (viscoelastic) or slow and constant fill rate (hyperelastic). Some studies incorporate a combination of experiments and constitutive modeling. The following sub - sections will describe in vivo and in vitro studies that are purely 9 experimental in natur e, while studies with a combination of experiments and modeling will be discussed in later Sections (1.3 - 1. 4 ). Figure 1 . 7 Depiction of cystometric test and resulting pressure/volume relationships for filling and voiding [23] . 1.2.1 In vivo studies Cystometry is the most common in viv o mechanical test for the bladder . Cystometric studies are used clinically as diagnostic tests [23] and are a way to asses bladder compliance and capacity in humans. Therefore, it is useful to run cystometric studies on animals to compare compliance and capacity between species. This information can provide insight into the utility of different animal models as models for humans. Usi ng medium fill cystometry , Wyndaele showed strong correlation between desire to void and bladder volume and pressure in healthy young humans [24] . Klevmark showed that bladder pre ssure during filling is more dependent on rate of filling than on volume. These results were shown in both cats and humans [25,26] . Wang et al. ran in vivo cystometric experiments and in vitro biaxial tensile tests on diuretic rat bladder s; they found increased weight, capacity, and compliance in the diuretic rat bladder comp ared to controls. The purpose of this study was to isolate the diuretic effects on the bladder from the neuropathic effects induced by 10 diabetes [27] . Watanabe et al. used cystometry to ev aluate the effect of oxybutynin on rat bladder wall stiffness and found significant decrease in bladder stiffness and increase in compliance with oxybutynin compared to controls [28] . 1.2.2. Ex vivo studie s When compared to in vivo studies, in vitro studies have an advantage in terms of performing more precisely controlled mechanical manipulations, allowing for quantification of isotropy and homogeneity of mechanical properties . Additionally, in vitro testing aids in the understanding of what is happening microstructurally, which would not be possible with whole organ in vivo testing. Most in vitro experimental studies on the bladder focus on animal models . S tudies that focused on human tissues are few, due to difficulties of obtaining tissue . Ex vivo animal studies are generally conducted on either small animals (i.e. , rats, guinea pigs, rabbits), or large animals (i.e. , dogs, pigs, cows). 1.2.2.1. Ex vivo small - animal studies Small animals are attractive biological models to use due to the availability, lower cost of caring, and the ability to study mutations, diseases, and injuries more easily than in large animals. Some experimental studies on small animal bladder s are described in this secti on . Passive mechanical behavior will be discussed first, followed by active mechanical behavior. Finkbeiner et al. showed the passive mechanical response of rat and guinea pig bladder strips at various strain rates using uniaxial tensile tests with strain rates ranging from 0.5 cm/hr to 3 cm/hr, and found no difference in response of the tension - length curves [29] . These results suggest that at low stretch rates, viscoelastic effects a re minimal. This is an important finding that supports the use of hyperelastic models for mechanical testing of rodent bladder s. Gloeckner et al. employed biaxial tensile tests to measure the increase in compliance in bladder s of rats 10 and 14 11 days after SCI from [30] . Toosi et al. measured changes in compliance of the bladder of rats 3, 6, and 10 weeks post SCI using biaxial tensile tests, and found that compliance increases from 3 to 6 weeks but returns close to healthy compliance 10 weeks after the injury. Compliance was determined based on the maximum stretch and maximum are al strain reached during stress - mediated equibiaxial tensile tests. Areal strain was defined as, (1.1 ) where and are the longitudinal and circumferential stretches, respectively. Figure 1 . 8 shows the maximum strains and maximum areal stretches at time points after induced SCI. The authors suggest that compliance may decrease further for remodeling times longer than 10 weeks post - injury [31] . Parekh et al . ran in vitro pressure - volume tests on rat bladder s while measuring wall strain by tracking positions of surface markers. Results showed the bladder to be stiffer in the circumferential direction than the longitudinal direction [32] . Eika et al. ran tensile tests and chemical pr ocesses to extract collagen content on diabetic rat bladder strips and showed a decrease in collagen content and an increase in compliance of the bladder in diabetic rats, which was not observed in rats treated with insulin [33] . Mattiasson et al. ran active and passive uniaxial tensile tests on feline bladder strips subjected to 12 weeks of parasympathetic sacral decentralization, and found hypertrophy of the detrusor, decreased force production, but no change in active length - tension relations [34] . Ghoniem et al. evaluated the effect of moderate and severe urethral outlet obstruc tion on the active and passive properties of the rabbit bladder wall and found decreased contractility and increased stiffness in obstructed groups [35] . Levin et al. performed in vitro cystometric experiments on whole rabbit bladder s to determine the effect of hypoxia, alterations of calcium concentration, and muscarinic agonists and antagonists on bladder capacity and compliance. Results showed increase 12 in bladder capacity and com pliance with hypoxia and calcium concentration, and a decrease in in capacity and compliance with carbachol. Overall conclusions are that alterations in smooth muscle tone in the bladder can ha ve a significant impact on its mechanical behavior [36] . Figure 1 . 8 (a) Maximum stretches and (b) maximum areal strains obtained from stress mediated biaxial tensile tests for healthy and SCI rat bladder s with different durations of SCI [31] . 1.2.2.2. Ex vivo large - animal studies Large animals are closer to size and anatomical structure to humans but present higher cost for caring and less availability, particularly for animals with mutations, diseases, or injuries. Some experimental studies on the mechanics of large animal bladder s are described in this section. Viscoelastic behavior will be disc ussed first, followed by passive, and finally active mechanical behavior. Barnes et al. used DMA to analyze the viscoelastic response of pig urinary bladder strips and loops and found storage modulus (i.e., elastic response) to be markedly greater than los s modulus (i.e., viscous response) [37] . 13 Jokandan et al. provided extensive experimental results for uniaxial tensile, ball - burst, and DMA tests in the porcine bladder . They found the porcine bladder to be stiffer longitudinally than circumferentially at high levels of strain (>200%), and storage modulus to be higher than loss modulus, showing the highly elastic behavior of the bladder [16] , agreeing with the findings of Barnes et al. b all - burst tests [37] , which more closely mimic physiological loading conditions, showed ultimate stresses ~5 times higher than with uniaxial tensile tests, but with similar ruptur e strains. Korossis et al. ran uniaxial tensile tests on porcine bladder strips to look for differences in mechanical behavior based on anatomical region and direction. Results showed that region differences were only evident in apex - to - base direction, wit h dorsal and ventral samples being more distensible than lower - body and trigone regions. Directional differences were seen in all regions, but most notably in lower - body and trigone. Trends showed higher stiffness in the apex - to - base direction than transve rse direction [7] . Baskin et al. ran biaxial pressure driven mechanical tests on fetal bovine bladder tissue and found that elastic modulus decreases with gestational age, and i ncreased in adult bovine bladders compared to newborn [38] . Dean et al. ran uniaxial mechanical tests on fetal bovine bladders and found passive compliance to be greatest in younger fetal bladders, which decreased with fetal age, and active compliance to be lowest in younger fetal bladders, which increased with fet al age [39] . Griffiths et al. looked at the active and passive properties of pig bladder strips and found that active isometric force increa ses linearly with extension until it reaches a maximum where it is similar in size to the passive force [40] . Coplen et al. performed a cystometric study of in vitro bovine fetal bladder s and found increase in compliance with elimination of active smooth muscle tension and surgical removal of the detrusor muscle [41] . 14 1.2.2.3. Ex vivo animal s tudies of the bladder extracellular matrix In addition to smooth muscle tone, extracellular matrix (ECM) plays an important role in the compliance of the bladder . The bladder ECM is of interest not only for its contribution to mechanical response, but also for its potential in tissue engineering. Tissue engineering is the use of several branches of science including materials science, biochemistry, and biomechanics, to form ne w tissue that can be used to replace dysfunctional tissue s or organs in the body. Organ specific ECM is an attractive material which has been studied for use as a scaffold for growing new functional tissue. ECM is attractive because of its biocompatibility and mechanical properties that are close to that of the tissue they are being used to replace. The bladder ECM is a frequently studied grafting material because of its unique distensibility, which is difficult to mimic with manufactured materials, and t he frequent necessity of partial or whole bladder replacement due to pathological conditions. Some experimental studies of bladder ECM are as follows. Freytes et al. looked at the effect of different storage conditions [42] , lyophilization [43] , and sterilization methods [44] on the mechanical response of porcine bladder ECM through uniaxial tensile and ball - burst tests. Storage of lyophilized porcine bladder ECM for one year in both room temperature and refrigerated conditions resulted in alterations of material properties. No changes in ball - burst streng th were observed, but maximum tangential stiffness increased in room temperature samples, while maximum elongation increased in refrigerated samples [42] . When comparing hydrated and lyophilized pig bladder ECM, lyophilized ECM showed irreversible microstructural damage, but little change in observed mechanical properties. Interestin gly, lyophilized ECM showed more cells present than hydrated ECM seven days after seeding with NIH 3T3 cells [43] . Freytes et a l. showed different sterilization methods, including ethylene oxide, gamma irradiation, and electron beam irradiation, all had effects on the observed 15 structural properties of the pig bladder ECM. Ethylene oxide had the least effect on properties, while ga mma and electron beam irradiation decreased uniaxial and biaxial strength, maximum tangential stiffness, and energy dissipation [44] . Rosario et al. decellularized and sterilized pig bladder s for uniaxial mechanical testing and found sterilization with ethylene oxide resulted in stiffening of the ECM [45] . Bolland et al. ran uniaxial tensile tests on decellularized porcine bladder strips and found no decrease in ultimate tensile strength, but a decrease in extensibility compared to native tissu e [46] . Farhat et al. compared the mechanical properties of decellularized and intact porcine bladder and found no difference in stiffness (i.e. , force vs strain), but a significant increase in elastic modulus (i.e. , stress vs strain) for the decellularized tissue. They concluded that the increase in elastic modulus is due to the decrease in the cross - sectional area of the samples after decellulari zation, and not a change in mechanical response of the tissue [47] . Dahms et al. developed bladder ECM grafts for rats, pigs, and humans, which were tested in tension and compared to native tissue. Results showed that the bladder ECM grafts behaved similarly mechanically to the native tissue, and that pig and human tissue showed higher levels of type III collagen and elastin, whereas rats showed higher levels of type I collagen [48] . Gilbert et al. looked at fiber alignment and biaxial mechanical behavior of pig bladder E CM layers. The submucosa was scraped in either longitudinal or circumferential direction , and observed fiber alignment was skewed towards direction of scraping. Longer toe - regions and lower modulus were present in the submucosa, and samples were generally stiffer longitudinally than in the transverse direction [13] . Liu et al. tested tissue ECM from pig small intestine, urinary bladder, skin, gallbladder, and pericardium. The bladder ECM showed better water uptake, anti - biodegradation, antimicrobial activity, and stem cell attachment when compared to the ECMs of other tissues, and showed high levels of both elasticity and strength [49] . 16 Some studies have assessed tissue engineered bladder grafts after surgical implementation. Brown et al. performed anterior bladder cystectomy a nd bladder reconstruction on pigs using pig bladder ECM allografts. Results showed extensive cellular repopulation, but lack of smooth muscle bundles and urothelium. Collagen amount and organization was different in the graft region, as well as the rupture strain and elastic modulus from uniaxial tensile tests of the graft region compared to the native tissue region [50] . Oberpenning et al. created bladder neo - organs from dog urothelial and smooth muscle cells seeded onto bladder - shaped polymers. Dog bladders were removed and replaced with the neo - organs, and showed normal capacity, elastic properties, and histological ar chitecture after 11 months [51] . 1.2.2. 4 . Ex vivo human studies As previously stated, human data is hard to come by, largely due to the difficulty of obtaining tissue. However, several studies have been conducted where mechanical testing of human bladder tissue was performed. Rubod et al. performed uniaxial tensile tes ts on the bladder , vagina, and rectum obtained from human cadavers and found the bladder to be the least rigid tissue, and saw a Mullins effect as a result of straining the tissue [52] . Mullins effect is the dependen ce of the stress - strain curve on the previous maximum strain when performing cyclical tests with increasing strain. Chantereau et al. ran uniaxial tensile tests on pelvic floor ligaments and organs from young and old human cadavers and found the bladder to be more compliant than the rectum, vagina, and ligaments. Additionally, bladder s from the old group were stiffer in the low stress range than the young group [53] . As described in the previous section, Dahms et al. compared rat hum an and pig intact bladder and bladder ECM and found bladder ECM to behave similarly to native bladder tissue, and human tissue to have the highest levels of elastin and type III collagen [48] . Ewalt et al. used immunohistochemistry to imag e collagen and elastin in normal - compliance (patients with 17 vesicoureteral r eflux, or obstructive megaureter) and noncompliant (patients with myelodysplasia, neurogenic bladder , or extrophy) human bladders and found no change in fiber content in the lamina propria, but large increase in collagen and elastin in the detrusor with no ncompliant bladders, suggesting that stiffening of the detrusor prevents unfolding of the lamina propria, and thus prevents the usual high compliance seen in healthy bladders [54] . Finally, Martins et al. ran uniaxial tensile tests on female human bladders and found bladder stiffness to decrease with age, but neither stiffness nor maximum stress was correlated with body mass index nor menopausal status [55] . 1.3. Viscoelastic modeling Generally speaking, viscoelastic constitutive models of the bladder are presented along with experimental data. The most common constitutive model that will be seen in the following sections is the Maxwell - Wiechert model . This model incorporates a linear s pring in parallel with Maxwell elements, represented by a series combination of a linear spring and a damper. Figure 1 . 9 shows a Maxwell - Wiechert model w ith two Maxwell elements. For number of Maxwell elements, the relaxation function, , takes the following form, ( 1.2 ) where has dimensions of stress and is a function of time , is the spring constant of the standalone spring, is the spring constant for the i - th Maxwell element, is the time constant of the i - th Maxwell element, defined by , where is the viscous damper constant, and is the total number o f Maxwell elements. The Maxwell - Wiechert model can be generalized for an effectively infinite number of Maxwell elements, where is a function of , defined by a chosen 18 probability density function (PDF). This type of model will be described in grea ter detail in a later Section. Figure 1 . 9 Maxwell - Wiechert viscoelastic model with two Maxwell elements [56] . 1.3.1. Animal mo dels of health and disease 1.3.1.1. Models informed by data collected in vivo In this section, in vivo viscoelastic constitutive modeling studies based on data collected from bladder tissue from animal models are described. Coolsaet et al. used in vivo stepwise cystometry bladder - Wiechert model with 2 Maxwell elements was fit to the pressure - time data. Results showed that clinical cystometry fill rates are too rapid to accurately measure the relaxed response of the bladder [56] . Venegas used small - amplitude oscillatory perturbations to measure the in vivo active and passive viscoelastic properties of dog bladder s. These experiments are similar to DMA, but use cystometric volume 19 and pressure, as opposed to tensile strain and stre ss. Three configurations of singular spring - damper - mass systems, where spring and damper constants increase linearly with force, were used. The only model configuration that correctly described the observed tissue behavior was elastic and viscous component s in series, with mass in parallel [5 7,58] . 1.3.1.2. Models informed by data collected in vitro In this section, in vitro viscoelastic constitutive modeling studies based on data collected from bladder tissue from animal models are described. Glerum et al. ran uniaxial stress - relaxation te sts , consisting of multiple approximately step - wise elongations, on single pig detrusor cells . The peak forces (i.e. , immediately following step - wise elongations) appeared to be linearly dependent on the applied elongation. While being held at constant elo ngation, an exponential decay of force (i.e. , relaxation) with respect to time was seen . An exponential function, identical to the output from a Maxwell - Wiechert model with one Maxwell element, was fit to the data. Elastic modulus and relaxation times were found to be different between isolated SMCs and intact tissue [59] . These results could support the idea that, for a Maxwell - Wiechert model with multiple Maxwell elements, each element could correspond to the relaxation times of specific tissue constituents. Mastrigt & Nagtegaal ran stress - relaxation ex periments at different strain rates on pig bladder strips. A Maxwell - Wiechert model with 3 Maxwell elements, consisting of nonlinear spring and dashpot elements, was used to fit the data. Parameters were found to depend on strain rate. Authors developed a relation to predict the change in stress - time response based on applied strain rate [60] . This relation could prove useful when comparing stress - relaxation data from experiments with different protocols. Alexander ran creep experiments on rat bladder s and found time c onstants ranging from 186 seconds to 6 hours. Ex vivo cystometric experiments were then performed on rat bladder s at fill rates slow enough to assume negligible viscoelasticity based on the observed time 20 constants from previous experiments. Significant hys teresis is seen at all of the tested fill rates, suggesting that visco - plastic models are better suited for modeling the mechanical response of the bladder than viscoelastic models [61] . N agatomi et al. used a quasi - linear viscoelastic (QLV) reduced relaxation function to fit biaxial stress - relaxation data from SCI rat bladder s. The reduced relaxation function, , is as follows , (1.3) w here is the index for overall relaxation, and are the beginning and end of the linear portion of the relaxation spectrum, and is the exponential integral function. Results showed slower relaxation in SCI bladder s when compared to controls, and bioch emical assays showed decreased collagen content and increased elastin content in SCI bladder s compared to controls [21] . Nagatomi et al. used a QLV reduced relaxation function defined by a continuous relaxation spectrum of the following form (1.4) where is the continuous relaxation spectrum defined as a bimodal log - scale normal distribution for the ECM, and inversely proportional to for smooth muscle cells. Fitting this equation to normal and SCI rat bladder biaxial stress - relaxation data at different initial stress values showed the initial stress level had no impact on the relaxation response, and that SCI rat bladder s showed significantly less relaxation than controls [62] . 1.3.1.3. Models informed by data collected both in vivo & in vitro In this section, we describe viscoelastic constitutive modeling studies based on data collected both in vivo and in vitro from tissues for animal models. Mastrigt et al. present a model that incorporates 21 a viscoelastic portion (Max well - Weichart model with 3 Maxwell elements), a hyperelastic portion (exponential function), and a plastic element. The model provided good fits to pseudostatic cystometric data from pigs and dogs [11] . Kondo & Susset ran whole organ in vivo and in vitro stress relaxation experiments on dog bladder s using intermittent cystometry. A modified Maxwell - Wiechert model with 3 Maxwell elements (2 with delayed engagement) was fit to the stress relaxation data. Results showed that the elastic behavior of the bladder is much more prominent during in vitro exp eriments when compared to in vivo [63] . Coolsaet et al. ran step - wise cystometry experiments on mongrel dogs in vivo under anesthesia, and dog cadavers, as well as in vitro with intact bladders and bladder strips. Viscoelastic response was fit with a Maxwell - Weichart model with 2 Maxwell elements. Time constants (i.e. , ratio of model parameters) appeared to be independent injected bladder volume, but model parameters varied depending on injected bladder volume, suggesting a nonlinear viscoel astic model is likely needed to fully capture tissue behavior [64] . Alexander ran pressure mediated cystometric tests in vivo on cat bladder s, and in vitro on rat, rabbit and kitten whole bladder s, as well as uniaxial stress - relaxation tests on rat bladder strips. Using observations on tissue behavior from experimental data, a model was developed that incorporated viscoelastic, plasto - elastic, and irreversible creep elements. In vivo experiments s howed that while keeping the bladder at high levels of pressure for extended periods of time, irreversible creep of bladder circumference was seen, even after allowing for an 8 hour recovery period at low pressure for the animal [65] . 1.3.2. Human models of health and disease 1.3.2.1. Models informed by data collected in vitro In this section, in vitro viscoelastic constitutive modeling studies based on data collected from human tissue are described . Susset & Reignier separated the mucosa from the detrusor in human 22 bladder tissue and conducted stress - relaxation experiments. A Maxwell - Wiechart model with 3 Maxwell elements in series with a plastic element was used to model the viscoelastic behavior of the samples. Results showed that the viscoelastic coefficients of the mucosa were markedly higher than that of the detrusor [66] . Van Duyl proposed a viscoelastic/plastic model for both passive and active bladder wall mechanics which includes elastic springs and viscous dampers along with plastic and contractile elements. Two model configurations are proposed. The first is a Maxwell - Weichart model in series with a plastic/contractile element, and the second is a Maxwell - Weichart model with a plastic/contractile element in series with the standalone spring but in parallel with the Maxwell elements. The models are not fit to data and th us no prediction of which model more accurately depict tissue behavior is made [67] . 1.3.2.2. Models informed by data collected both in vivo and in vitro In this section, visc oelastic constitutive modeling studies based on data collected from human tissue both in vivo and in vitro are described. Mastrigt et al. evaluated the viscoelastic response of human bladder tissue using in vivo stepwise cystometry in living patients, and in vitro stress - relaxation of bladder strips obtained from children when the bladder needed to be opened. Data was fit with the Maxwell representation of the standard linear solid model, as well as a Maxwell - Weichart model with 3 Maxwell elements [68] . When compared to previously published data [11] , human bladders were found to be stiffer than pig bladders, but showed similar viscoelastic constants compared to pigs and do gs [68] . 1.4. Hyperelastic modeling Hyperelastic constitutive models are useful to describe the behavior of the bladder wall when the loading can be considered slow enough to make viscoelastic ef fects negligible. Many studies that 23 use hyperelastic models are interested in the mechanical behavior of the bladder at or near physiological fill rates. This can be done through cystometry, or approximating a strain rate that mimics physiological fill rat es. 1.4.1. Continuum/exponential models In this section, we describe hyperelastic continuum constitutive models employed to describe the mechanics of the bladder . Mastrigt and Griffiths looked at active mechanical properties of complete pig bladders and m odeled the active response with a classical hill equation and the passive response as depending exponentially on tissue extension [69] . Mastrigt evaluated active and passive mechanical response of pig bladder strips and fit the force - velocity response with a hyperbolic hill equation . Results showed that active bladder pressure decreased with increasing exit flow rate [70] . Reignier et al. used in vivo cystometry and in vitro uniaxial tensile tests in dog bladder s to evaluate the mechanical response of the bladder during filling. The following strain energy function, , was derived from finite strain theory for hollow spherical structures and used to fit the experimental data (1.5) (1.6) (1.7) where is the spherical stretch , is the initial intravesical pressure and is the rate of exponential increase in pressure during bladder filling. Results showed that the bladder behaves markedly different than rubber balloons [71] . Cheng et al. modeled the loading curves for biaxial tensile testing of rat bladder s by assuming an incompressible, isotropic, hyperelastic material with the following Cauchy stress tensor . 24 (1.8) Where is the Lagrange multipli er used to enforce incompressibility, is the first invariant of the left Cauchy - Green deformation tensor and F is the deformation gradient , is the shear modulus, and controls the exponential dependence on . Model fitting in conjunction with imaging led to the conclusions that large bladder distensibility is due to folds in the wall, and distensibility decreases with age due to premature recruitment of fibers on the outer wall [9] . Damaser proposed two models for analyzing the effect of increased bla dder mass as a result of urethral outlet obstruction. The first model assumes no change in the zero - pressure capacity of the bladder , and is given by the following equation, (1.9 ) where , , , and are constitutive parameters, and represents the change in wall stress that depends on radial position, , within the bladder wall. The second model assumes that mass and zero - pressure capacity increase proportionally, and is given by the following equation, (1.10 ) where , , , and are constitutive parameters. The first model predicts increased pressure and decreased compliance, consistent with experiments on animals with mild urethral outlet obstru ction. The second model predicts unchanged pressures, but increased compliance and capacity, consistent with experiments on animals with severe urethral outlet obstruction [72] . Watanabe et al. applied the following hyperelastic strain energy function, previously used for rubber, to uniaxially deformed dog bladder and modeled bladder filling as a thin walled sphere, (1.11 ) (1.12 ) 25 where and are material parameters. Model results show a relatively constant pressure while wall stress increases. This suggests that the ability of the bladder to maintain low pressures during filling is due to geometry and material properties, rather than reflex i nhibitory relaxation [73] . Habteyes et al. used the Watanabe and Ogden hyperelastic models to fit uniaxial tensile data from rabbit bladders. Results indicated that acute changes in bladder elasticity could change wall tension and lead to urgency [74] . Korkmaz and Rogg used a model for predicting the stress - stretch response of the bladder without the need for a material model by assuming the shape to be a sphere, and using previously published data to make assumptions on the volume, radius, and pressure differential between the inner and outer wall [75] . A similar approach was previously used by Damaser and Lehman to determine the effect of bladder shape on filling mechanics. Results showed that an oblate spheroid is more compliant than a sphere or prolate spheroid . Figure 1 . 10 shows cystometric pressure - volume data, along with model fit to the data for prolate and oblate spheroids with varying eccentricities [76] . 26 Figure 1 . 10 Pressure - volume cystometric data from dogs, along with pressure - volume predictions for (a) prolate, and (b) oblate spheroidal bladder models with varying eccentricities [76] . 1.4.2. Fiber recruitment models It is commonly accepted that collagen fibers in tissues, including the bladder , are highly wavy, or coiled, and the compliance of a tissue is heavily influence by the degree of waviness of these fibers. Therefore, it is important to be able to directly view and measure the waviness of fibers, and to cre ate structurally motivated constitutive models that take this waviness into account. The following sections will describe the quantification of collagen fiber waviness and the constitutive modeling of fiber recruitment. 27 1.4.2.1. Quantification of fiber wav iness Collagen fiber waviness and/or recruitment during tissue loading has been studied in various tissues including rat tail tendon [77] , rabbit achilles tendons [78,79] , human skin [80] , human vena cava [81] , pig coronary adventitia [82] , rabbit carotid arteries [83,84] , and p ig thoracic aortas [85] . Chang et al. used immunohistochemistry and confocal microscopy to image fetal bovine bladder s and found that the high compliance in the bladder is due to tightly coiled collagen fibers [86] . Cheng et al. was able to measure collagen fiber waviness at different amounts of strain by tracing fibers from images taken from a custom biaxial tensile testing setup that is compatible with a multiphoton microscope. As previously stated, results of this work showed that distensibility was decreased in samples that showed premature recruitment of fibers on the outer wall of the bladder , which seemed to be correlated with aging. 1.4.2.2. Fiber recruitment model structural theory La nir developed the structural theory for fiber recruitment and orientation distributions for fibrous tissues [87,88] and later incorpo rated fiber recruitment in a growth and remodeling model [89] . For tissues with low density of cross - l inks and wavy collagen fibers, an abbreviated structural theory of fiber recruitment models is as follows. It is assumed that individual elastin and collagen fibers are linearly elastic in tension, and are oriented with angular distributions, and . Elastin fibers are assumed be straight in the unloaded configuration, while collagen fibers are wavy. Collagen fiber waviness follows a probability density function, , where is the stretch it takes to straighten a given fiber. The force as a function of stretch for elastin and collagen fibers are, respectively, ( 1.13 ) 28 ( 1.14 ) where and are the elastin and collagen fiber elastic constants, and is the stretch of a fiber based on applied deformation and fiber orientation, . The strain energy function for this material is therefore, ( 1.15 ) Since this formulation, collagen fiber recruitment models have been used for various tissues including, but not limited to, rat carotid arteries [90] , rabbit carotid arteries [83] , [91] , rabbit skin [92] , and sheep digital tendon [93,94] . 1.4.2.3. Fiber recruitment models of the bladder Collagen fiber recruitment has been quantified and modeled previously in the bladder . Robertson et al. was able to measure the recruitment of collagen fibers in various layers of the rat bladder at different levels of stretch using multiphoton microscopy [9] . Wognum et al. used a fiber recruitment model that assumed a bimodal beta distribution of collagen fiber recruitment during biaxial loading of rat bladder s, and found evidence that de novo elastin fibers in the SCI rat bladder may play a role in crimping the collagen fiber network, thus changing the recruitment distribution and resulting mechanical properties [14] . 1.5 Objectives of this dissertation The information gathered from this literature review highlight areas in the field of bladder mechanics where further research is needed. Thus, the objectives of this dissertation are the following. 29 1. Understand the healthy mechanical behavior of the human bladder, and analyze the validity of the pig bladder as a model of the human bladder. This is done by comparing the response of human and pig bladder mechanical behavior tested under identical conditions. Due to high variability in tensile testi ng protocols and tissue conditions, no previous studies adequately compare the mechanical response of the bladder between humans and pigs. 2. Determine how pathological conditions can alter the stress in the bladder wall. This is accomplished by e valuat ing th e changes in viscoelastic response of the porcine bladder at various states of swelling to gain insight into the effects of degradation of the urothelium and/or acute inflammation. Urothelial degradation and/or acute inflammation may lead to osmotic swelli ng of the bladder wall, and may alter the stress state of cells and act as a driving force behind remodeling. 3. Evaluate the remodeling of the bladder wall under long - term pathological conditions. This is facilitated by mechanical testing and imaging of the long - term SCI rat bladder ECM . It has been hypothesized that the mechanical response of the SCI rat bladder may return to normal levels of compliance or result in hypocompliance for recovery times greater than 10 weeks [31] . 30 CHAPTER 2 - DIRECT COMPARISON OF HEALTHY HUMAN AND PIG BLADDER TISSUE MECHANICAL PROPERTIES The results in this chapter are presented in [95] . 2.1. Overview E fforts to understand bladder mechanics in humans have been limited by access to human tissue [48,68,96,97] and restricted largely to in vivo measurements in awake hu mans, which limits the ability to apply controlled manipulations. Ex vivo studies on the mechanical properties of bladder tissue have been primarily performed on animals. L arge discrepancies exist in the mechanical behavior of bladder tissue reported in li terature, even within the same species. This is likely due to the differences in testing and tissue preparation protocols between different studies. These differences make it challenging to meaningfully compare mechanical behavior, across species and acros s pathologies. Additionally, there has not been a direct experimental comparison between pig and human fresh bladder tissue mechanical behavior to evaluate the appropriateness of the pig as a model for the human bladder. To date, the only study comparing h uman and non - human bladders tested under similar, but not identical, conditions suggests comparable mechanical behavior across pig, dog, and human samples, but the analysis of differences in stiffness was inconclusive [68] . Further, no structural foundation for the observed differences is explored. Here we present the first direct comparison of healthy human and pig bladder tissue mechanically tested under identical conditions. Moreover, constitut ive modeling is used to isolate the contribution of isotropic components (i.e., ground matrix, elastin, and low - stress response of smooth muscle cells) and orthotropic components (i.e., collagen fibers and high - stress response of smooth muscle cells) to th e overall mechanical behavior of the tissue. W e tested the effect of two 31 treatments on tissue mechanical properties. Namely, elastase to digest elastin fibers, and oxybutynin to reduce smooth muscle cell spasticity. We implemented two different material m odels to aid in the interpretation of the experimental results. We found that human tissue behaves similarly to pig tissue at high deformations (collagen - dominated behavior) while we detected differences between the species at low deformations (amorphous m atrix - dominated behavior). Our results also suggest that elastin could play a role in determining the behavior of the fiber network. Finally, we confirmed the anisotropy of the tissue, which reached higher stresses in the transverse direction when compared to the longitudinal direction. This work establishes a framework for the development of future models to describe fibrotic/dysfunctional bladders as well as to aid in the development of tissue engineering solutions for this complex and remarkable organ. 2.2. Methods All tissue preparation and mechanical testing was performed by Duncan Morhardt in Ellen ratory at Michigan State University (East Lansing, Michigan). 2.2.1. Tissue preparation Bladders from six female Yorkshire pigs (6 - 9 months old) were harvested at the time of sacrifice and transported to the lab at 25 - 30°C in calcium - free and magnesium - fr ee phosphate buffered saline (PBS) pH 7.4 (Gibco), based on [98] . Human bladders (n=4) were obtained at time of organ transplant procurement and transported similarly. Age, sex, and cause of death for human donors are provided in Table 2. 1. Testing commenced within 12 hours of procurement. Tissue was kept at 37°C until specimen preparation. The bladder was divided just above the trigone leaving the 32 dome, and cut along the anterior surface and dome to allow flat preparation while maintaining the longi tudinal and transverse orientations ( see Figure 2. 1 ). A stainless - steel die was used to create dumbbell - shaped specimens by cutting from the urothelium to the serosa. Samples were collected from both the longitudinal and transverse orientations (longitudinal samples identified with a superscript , and transverse samples with moving forward). Most bl adders provided 6 - 8 specimens, specifically we collected and tested 22 longitudinal tissue samples from pig and 13 from human, and 12 transverse tissue samples from pig and 3 from human. The individual specimens were transferred to separate wells and maint ained at 37°C until testing. A subset of samples was treated with elastase an enzyme that degrades elastin fibers (4 from pig and 3 from human tissue). Samples were treated with 200 units of elastase (Worthington, NJ) for three hours (following what was reported in [98] ), but with this concentration the overall structure was compromised and mechanical testing was not possible. When treated with 50 units of elastase for the same treatment time, the samples maintained enough tissue consistency to withstand testing and elastin was significantly degraded ( elastin loss was confirmed by histology). Another subset of samples was treated with oxybutynin, an anticholinergic drug that reduces spasticity in muscle cells (11 from pig and 5 from human tissue, in addition 3 samples from pig tissue where treated with both oxybutynin and elastase). We used a concentration of 150µM oxybutynin (Sigma - Aldrich, St Louis, MI), based on in vitro studies [99,100] . Samples were randomly allocated into each treatment. Specimen dimensions were measured with calipers before testing, and were statistically unchanged after treatments . Due to a need to reduce potential contamination of reagents, we tested untreated tissue first, then oxybutynin treated tissue (pharmacologically diluted), and lastly elastase treated 33 tissue (enzymatic treatment, not dilutable). All tests from the same sp ecimen were performed within three hours of each other. The tissue procured and experiments performed were deemed exempt by the University of Michigan Institutional Review Board. Table 2 . 1 Donor demographic information: age, sex, and cause of death Donor Age Sex Cause of death A 25 Male Head trauma B 28 Male Anoxia C 44 Male Anoxia D 51 Female Anoxia 2.2.2. Mechanical testing 2.2.2.1. Uniaxial testing Individual specimens were tested on a custom uniaxial tensile loading/unloading device with screw in grips ( Figure 2. 1b ). The force was determined with a voltage converting 100mN load cell (World Precision Instruments, Sarasota, FL). The testing bath was m aintained at 37°C with a modified temperature controller (Harvard Apparatus, Cambridge, MA). Specimens were floated Figure 2 . 1 Sample orientation schematic and uniaxial s ample preparation. a) The trigone is removed from whole bladder and a steel die produce dumbbell specimens (inset). Also shown are the transverse and longitudinal directions, as well as schematics of orientations of specimens. b) Pictured is a representati ve tissue specimen mounted in the uniaxial tester. 34 into grips to minimize tare load. After placing in grips, the zero - load state was verified by advancing and retracting the grips (+/ - 1mm) while monitoring the load. The gage length for stretch (nominally 12mm) was determined by this positioning . Specimens were subjected to three load - unload cycles to a maximum stretch of 1.8 (Pull 1, Pull 2, Pull 3, without preconditioning prior) at a rate o f 0.01 s - 1 . The physiologic stretch level is approximated to be equal to 1.8, based on the average stretch experienced by a human bladder containing 400 milliliters of urine . Figure 2. 2 sh ows a plot of the physiologic loading strain history during testing. A fourth load - unload cycle (Pull 4) was performed on a subset of samples up to a maximum stretch of 2.6 (supraphysiologic loading test, same loading rate). Figure 2 . 2 Testing protocol for tissue specimens and representative data - model prediction results. a) Stretch versus time graph showing three load - unload cycles and the timing of those cycles, and b) stress versus stretch graph showing loading data (symbols) of a single specimen and its corre sponding model prediction curves (lines) for Pulls 1, 2, and 3. 35 2.2.2.2. Compression testing Orthogonal tissue specimens were prepared using a six - millimeter biopsy punch and placed in 37°C PBS buffer in a clear chamber in a Dynamic Mechanical Analyzer ( T A Instruments RSA - G2 ). After zeroing at contact, untreated pig samples (n=2) underwent compressive loading up to 0.99 kPa for one sample and 1.9 kPa for the other. 2.2.3. Constitutive modeling 2.2.3.1. F iber recruitment (M1) Collagen constitutes the largest extracellular matrix component in the human bladder at approximately 30% of the intact - tissue dry - weight [1 3] . The collagen fiber network significantly contributes to the mechanical behavior of soft tissues and has been previously modeled [101] . Collagen fibers are coiled in the unloaded configuration, but straighten and begin to bear load as the tissue is stretched ( Figure 2. 3 ). This peculiar behavior has been shown in rat tail tendon [77] , rabbit Achilles tendon [78,79] , human skin [80] , human vena cava [81] , pig coronary adventitia [82] , rabbit carotid arteries [83,91] , pig thoracic aortas [84] , and rat bladder [85] . A collagen fiber recruitment model, describing the characteristic uncoiling of collagen fibers and its mechanical consequences, was first developed by Viidik [78] , with the corresponding structural theory later described by Lanir [87] . These types of models have been used to describe several soft tissues, including rat carotid arteries [90] , rabbit skin [92] , rabbit carotid arteries [83,91] , sheep digital tendon [93,94] , and rat bladder [14] . Here, a fiber recruitment model was used to estimate the recruitment distribution of collagen fibers during uniaxial loading of pig bladder tissue ( Figure 2. 4b - d ). For this model, the percentage of recruited collagen fibers is assumed to follow a normal cu mulative distribution function ( ), 36 ( 2. 1) where is the stretch, and and are the mean and standard deviation of collagen fiber recruitment stretch, respectively. Individual collagen fibers are assumed to behave linearly in tension once straightened, as previously shown [102,103] . The recruitment distribution of linearly behaving fibers causes the global tissue response (i.e., stress - stretch curve) to behave in a nonlinear fashion. The following differential equation was used to describes uniaxial tensile behavior ( 2. 2) where is stress and is the slope of the stress - stretch curve when 100% of the collagen fibers are recruited (linear portion of the stress - stretch curve). Limitations of this model are that it ignores the contribution of all tissue components except for collagen fibers, and t hat it uses the assumption that collagen fibers are only aligned in the direction of the stretch. This model was used as an estimation of fiber recruitment, and was not used as a constitutive description of the bulk of the mechanical data. This model was o nly applied to Pull 4 (supraphysiologic loading), which was performed on a selected few samples (see 2. 2.3.3 Material parameter estimation for details). Figure 2 . 3 Schematic diagram of collagen recruitment model. Gradual engagement of collagen fibers (top row) are modeled by spring elements (bottom row). As the model/tissue is stretched (left to right), the hooks engaging the bar is mirrored by the straightening of the collagen fibers, and the stretching of the springs represents the stretching of the individual collagen fibers. 37 2.2.3.2. Continuum model (M2) A 2 - fiber family nonlinear elastic model (M2), similar to what has been previously described by Roccabianca et al. [104] , was used in this study to describe the stress - stretch behavior of the human and pig bladder tissue ( Figure 2. 4a ). Given the applied uniaxial stretch, , the deformation gradient tensor, , and right Cauchy - Green tensor, , are defined as follows, ( 2. 3) where , and are the principal stretch directions. Using these finite deformation theory descriptions, the strain energy function, , takes the following form, ( 2. 4) where is the strain energy function that describes the isotropic behavior of the tissue at low - stress, dominated by amorphous matrix, elastin fibers, and low - stress behavior of muscle cells, and is the strain energy function that describes the orthotrop ic behavior of the tissue, dominated by collagen fibers but also including the high - stress behavior of smooth muscle cells. The orthotropic components of the tissue are considered to be morphologically organized in two families, defined by the superscript . The isotropic strain energy function is defined as follows, ( 2. 5) where is the material parameter with the dimension of stress, and is the first invariant of the right Cauchy - Green deformation tensor. The orthotropic strain energy function is defined as follows, 38 ( 2. 6) where and are the material parameters for th fiber family, the first with the dimension of stress and the second dimensionless. The fibers are assumed to fold in compression and provide little to no resistance to deformation. Because the orthotropic behavior is a ssumed to be dominated by the collagen fiber response, we considered to be zero in compression (i.e., ), an assumption made in relevant previously published models [105 108] . However, we acknowledge that in bladder tissue there is likely some orthotropic contribution from smooth muscle cell bundles when compressed, which could influence the value of Lagrange multiplier and that may not be captured by the neo - Hookean component . For this reason, the assumption of in compression, while reasonable, represents a limitation of the model. The first and second fiber families are separated by 90° and oriented in the longitudinal and transverse tissue directions, respectively. is the fourth invariant of the right Cauchy - Green tensor, defined in the direction of the - th fiber family. The undeformed orientation tensor is defined as where is the fiber direction in the undeformed configuration. Here, describes the longitudinal fiber family ( ) and describes the transverse fiber family ( ), as shown in [8] . From the strain energy function, the stress - stretch relationship is obtained as follows , ( 2. 7) where is the Cauchy stress, is the identity matrix, and is a Lagrange multiplier that enforces incompressibility. This model was applied to the physiologic loading test curves for every sample in both pigs and humans (see 2.3.3 Material parameter estimation for details). 39 2.2.3.3. Material parameter estimation A key feature of the structural model M1 is that the stress - stretch curve will approach a linear relationship as the percentage of recruited fibers approaches 100%. It follows that, to estimate the material parameters with reasonable confidence, the experi mental data used to inform model M1 must reach the high - stress, linear portion of the stress - stretch curve. If the stretch applied to the sample during the mechanical testing is not sufficiently large, then uncertainty in parameter estimates for M1 would b e high. This prohibits the use of M1 to describe the data from the physiologic loading experiments ( ). For this reason, we employed the phenomenological model M2 to describe the physiologic loading data. On the other hand, to confidently estimate the parameter describing the isotropic region in M2, there is a need to define a toe - region of the stress - stretch curve ( ). The toe - region is defined as the range of stretch where collagen fibers provide negligible resistance and the mechanical behavior is isotropic, dominated by amorphous matrix, elastin, and behavior of smooth muscle cell at low - stress. The model M1 is introduced to calculate a value for that has structural relevance, as opposed to being arbitrarily chosen. The follo wing paragraphs describe the entire two - steps parameter estimation process in greater detail, starting with (1) using M1 to estimate , and (2) using in the parameter estimation process for M2. Figure 2. 4 represents a schematic of the overa ll parameter estimation process. The result of the parameter estimation for the model M1 is a cumulative distribution, ( E quation 2. 1 ), which represents an estimate of the percentage of fibers that are recruited at a given stretch (supraphysiologic loading data used). Using the cumulative distribution from M1, the toe - region ( ) was calculated, with defined as the value of stretch needed to reach 5% of fibers recruited. This method was implemented for data fro m oxybutynin treated samples (n=2), 40 elastase treated samples (n=2), and one sample treated with both oxybutynin and elastase (n=1), all of which were from pig tissue in the longitudinal direction. Due to the limited dataset available for the supraphysiolog ic loading, approximations were made in the definition of toe - region for some groups. Specifically, calculated for oxybutynin was also used for untreated samples (under the assumption that oxybutynin has the least effect on the configuration of th e collagen fiber matrix when compared to elastase), calculated for pigs was also used for the corresponding treatment groups in humans, and calculated for the longitudinal direction was also used for the transverse direction for all treat ments. This is a limitation of this study. The parameter estimation process for M2 was divided into two steps. This was done to reduce the number of parameters being calculated simultaneously, which lessens the impact of the correlation between sensitiviti es of the parameters describing the isotropic and orthotropic behavior. First, the isotropic portion of M2 was used to describe the toe - region of the stress - stretch curves ( ), resulting in a value for ( E quation 2. 5 ). Second, using the full form of the model M2 ( E quation 2. 4 ) and the estimated parameter, the full stress - stretch physiologic loading curve ( ) was employed to calculate and . Specifically, for each sample, we estimated only the set of parameters d escribing the fibers in the direction of applied stretch. This was a direct result of two hypotheses made in the model: (1) the fiber directions in M2 were defined as parallel and perpendicular to the direction of applied stretch, and (2) the fibers were n ot contributing to the mechanical behavior in compression (i.e. as shown in E quation 2. 6 , the strain energy is zero if ). 41 In all steps, the nonlinear least squares solver lsqnonlin in MATLAB was used for parameter estimation. A sensitivity study wa s performed with chosen at 2.5%, 5%, and 10% collagen recruitment. Observed statistical differences were generally conserved across all percentages. Figure 2 . 4 Multi - step parameter estimation approach. a) Representative plot demonstrates the regions used for parameter estimation of the isotropic and orthotropic strain energy functions and , respectively, as well as representative sample data and M2 model output. b) Collag en fiber recruitment model, M1, used to estimate fiber recruitment distribution. c) Representative supraphysiologic data ( ) and M1 model output after parameter estimation. d) Plot of fiber recruitment distribution that shows is calculate d as the stretch at which 5% of collagen fibers are recruited. is used as the cutoff point for the stretch range used for parameter estimation of . 2.2.4. Statistical analysis Statistical analysis was performed with JMP 14Pro (Cary, NC). Est imated material parameters were compared among treatments, between species, and between tissue orientations. The unit of measurement was pull. Due to the different distributions among groups, Wilcoxen or Kruskal - Wallis were performed with a predetermined p <0.05 to reach significance. The Steel - Dwass test, a nonparametric test for pair - wise comparisons, was employed to further examine differences 42 among subgroups when Kruskal - Wallis was <0.05. We performed a MANOVA for repeated measures (with recommended cor rections for sphericity) by pull under each condition, direction, and species but cautiously avoided stronger conclusions in these sub - analyses. With similar restrictions, we utilized a least squares model to examine pairwise differences of pulls among dif ferent conditions. 2.3. Results 2.3.1. Collagen recruitment model (M1) We used the data collected for the supraphysiologic loading test protocols ( ) to estimate the parameters of the M1 model. This resulted in three sets of approximate fibers recruitment distributions, namely as defined in E quation 2. 1 , one for each treatment group. The distribution parameters within each group were averaged, if necessary, and the stretch corresponding to the recruitment of 5% of fibers, , was estimated for each group to be used in M2 ( see Section 2 .2 .3.3 Material parameter estimation ). Table 2. 2 shows the parameters for the model M1 and the normalized root - mean - square error (NRMSE) for each sample, as well as the value of for each group. Because of the limited number of supraphysiologic loading protocol samples, no statistical analysis was performed on the M1 parameter values. T able 2 . 2 Parameter estimates for M1, NRMSE for each supraphysiologic loading fit, and representing stretch for 5% collagen recruitment for each group. Treatment elastase 195.73 2.48 0.34 0.020 1.65 elastase 16.35 1.88 0.31 0.031 oxybutynin 64.84 2.10 0.44 0.016 1.43 oxybutynin 54.76 2.26 0.47 0.016 oxy/ela 205.55 2.05 0.22 0.006 1.68 43 2.3.2. Continuum model (M2) Figure 2. 2b shows a set of data for one representative pig sample (3 loading curves) represented by symbols, and the corresponding model estimation for each pull, represented by lines. The average NRMSE for all parameter estimations was 0. 046. Figure 2. 5 shows a hist ogram of NRMSE and standardized concatenated residuals for all curves. Standardized residuals appeared to be normally distributed with a mean of - 0.2015. A negative value was expected due to the nature of the additive 2 - step parameter estimation process. Figure 2. 6 gives a representation of the stress - stretch response data and M2 model prediction for different pulls, treatments, and direction; data collected in both human ( Figure 2. 6a ) and pig ( Figure 2. 6b ) tissue. Only groups containing 4 or more samples are shown in the figure, however all estimated material parameters are available in an open source repository as described in the APPENDIX . The mechanical data suggest that, given equal deformation, the transverse direction tends to reach higher stresses than the longitudinal direction for all pulls (data shown only for pigs). The stress - stretch curve for Pull 1 is markedly different than that of both Pull 2 and Pull 3. No differences are observed between Pull 2 and 3, regardless of treatment or direction (supported by top level MANOVA ). This suggests sufficient preconditioning after only one load - unload cycle. Similar behavior has been seen in biaxially tested ra t bladder, where the second and 12 th loading curves were nearly identical [109] . Figure 2. 7 shows box plots of parameter estimates for the same groups shown in Figure 2. 6 . For both human and porcine tissue, values were higher and values were lower for Pull 1 when compared to Pull 2 and Pull 3. Furthermore, statistical analysis showed was not affected by tissue treatment, whereas and were affected by elastase (data available in the Supplementary Materials ) but n ot by oxybutynin, for both human and pig tissue. This result was 44 also supported by the fact that peak stresses at each pull had higher consistency in oxybutynin treated specimens (coefficient of variation 0.09, 0.07, 0.16 for Pulls 1, 2, and 3, respectivel y) when compared to untreated specimens (coefficient of variation 0.42, 0.37, and 0.38 for Pulls 1, 2, and 3, respectively), in human. In addition, c onsistent with Figure 2. 6 , each transverse parameter exceeded its longitudinal counterpart. Finally, values for tended to be higher in pigs than in humans, across treatments. Statistical analysis confirmed the differences observed in Figure 2. 7 . Specifically, differed little among treatments, whereas it differed significantly by direction (p < 0.0001) and by species (p < 0.001). Parameter differed by direction (p < 0.0001) and between human and pig specimens (p = 0.011); parameter was statistically different between transverse and longitudinal specim ens (p = 0.0043), however it was similar across treatments and between species. Furthermore, the parameters and differed between oxybutynin and elastase treated specimens (p < 0.0001 for , p=0.008 for ) and untreated and elastase treated specimens (p < 0.0001 for , p=0.005 for ), but did not differ between oxybutynin and untreated samples. A strong pull effect was seen in by direction (p=0.0008) but not by condition (p=0.55) or species (p=0.49). Similarly, a pu ll effect was seen in direction for (p=0.035) and (p=0.003). To aid in the interpretation of these observations, we examined the Cauchy stress at for each group ( Figure 2. 8 ). When looking at Pull 1 in humans, oxybutynin treated sampl es showed higher stresses at , whereas in pigs, untreated samples showed higher stresses at ; pigs showed higher stresses at than humans (p=0.0028); samples tested in the transverse direction showed higher stresses at than those tested in the longitudinal direction (p=0.0005, data collected in pigs). 45 Figure 2 . 5 N ormalized root mean square error (NRMSE) and standardized residuals for all data. Histograms of (a) NRMSE for all fitted curves , where represents number of fitted curves, and (b) standardized residuals for all data points included in the fitting process , where represents number of residuals. Figure 2 . 6 Human and porcine fitted curves under different treatment conditions. M2 model output using median parameter values (lines) and interquartile range of experimental data (shaded) for a) untreated (un) and oxybutynin treated (ox) s pecimens in humans, and b) untreated (un), oxybutynin treated (ox), and untreated transverse (un) specimens in pigs. Plot titles represent treatment, with superscript denoting direction ( for longitudinal, for transverse), and subscript denoting number of samples. Only groups containing 4 or more samples are shown. 46 Figure 2 . 7 Parameter Estimates. Estimated values for (a), (b), (c) are di splayed in box plots (median line, box first quartile - third quartile, error bar 0th and fourth quartiles). The results shown include parameter values estimated for both humans (left) and pigs (right). Only groups containing 4 or more samples are shown , a ll parameter estimates can be found in an open source online repository . 47 Figure 2 . 8 Calculated values of stress at Box plots representing the experimentally recorded stress values at for humans (left) and pigs (right). Only groups containing 4 or more samples are shown. 2.3.3. Modeling of compression tests We performed compression studies in the direction normal to the bladder surface in two untreated pig bladder specimens. Fig ure 2. 9 sh ows the experimental compression data (testing set) along with the model M2 prediction using median parameter values estimated employing uniaxial tests (training set). Figure 2 . 9 Comparison of co mpressive behavior experimentally measured and predicted by model M2. Symbols represent the experimental data from compression tests in untreated pig samples (testing data - set). The line represent the model prediction for a compression test calculated usin g median parameter values estimated from uniaxial experiments for untreated pig tissue (training data - set). 48 2.4. Discussion Pig tissue has provided the standard for comparison with human tissue since [48] suggested that human bladder and pig bladder have the same mechanical pr operties. Pigs have also been extensively used as a large animal model in the fields of tissue engineering and disease models [110] . This study presents constitutive mo deling of fresh human and porcine bladder tested under identical tensile - testing protocols. It includes species - specific mechanical behavior for the bladder wall, including the effect of elastase and oxybutynin treatment and testing direction. In our revie w, we found no studies that were designed with the purpose of comparing mechanical behavior of fresh human and pig bladder tissue tested under identical conditions or that have compared human and pig collagen microstructure in bladder histology. Thus, to o ur knowledge, this is the first study which can offer a direct comparison of mechanical parameters describing the fiber network between human and pig tissue. We have also performed a microscopic examination of a limited number of Van Geisen - stained human a nd porcine sectioned specimens that revealed similar structural elements of muscle, vessels, elastin, and fibrous matrix ( Figure 2.10a , APPENDIX ) supporting our choice of using a combination of fiber - based constitutive models. More in depth quantitative co mparison of microstructure from a histological standpoint is necessary to better understand the similarities and differences in these tissues, and represents an important topic for future studies to address. 2.4.1. Validation of model M2 using compression data To verify the predictive capabilities of the M2 model, stress values were generated for compression using median parameter estimates for Pull 1 from the untreated pig samples and compared to experimental data collected during compression test ( Figure 2. 9 ). Desp ite having been optimized with uniaxial tensile data (training data - set), the model predicts quite accurately the experimental 49 response of the tissue in compression (testing data - set), a deformation mode that is similar to biaxial tension. This gives us confidence in looking at the model parameters to draw conclusions about (1) the contribution of different constituents to the overall behavior of the tissue, and (2) identify possible differences between the different groups analyzed here. 2.4.2. High stress, orthotropic contribution to mechanical behavior We first focused on isolating the orthotropic contribution to the overall tissue behavior, dominated by the collagen fiber network and by high - stress behavior of smooth muscle cells, by an alyzing and . We also aimed to interpret the effect of elastase and oxybutynin treatment on tissue behavior. First, there are no significant differences when comparing untreated to oxybutynin treated samples, where oxybutynin is a clinically relevant drug with pharmacological result of reducing spasticity and cholinergic drive [99] . This suggests that smooth muscle cells are engaged pa ssively and have limited spontaneous contractions and residual muscle tone at high stresses, in both humans and pigs. Moreover, the differences we observed in and between elastase treated specimens and both oxybutynin treated and untreated sp ecimens, suggest a change in the engagement of collagen fibers as a result of elastin loss, which is potentially independent of smooth muscle cell engagement on the extracellular matrix. Taken together, these results suggest that elastin could play a role in altering the mechanical response of the collagen fiber network by affecting its waviness and, ultimately, its recruitment. These conclusions support previous reports in the spinal cord injured rat bladder, where de novo elastin fibers were thought to increase crimp of the collagen fiber network and consequently increase compliance of the tissue [14] . Interes tingly, we do observe differences between untreated and oxybutynin treated samples when comparing the Cauchy stress evaluated at for Pull 1, which results in higher stresses for 50 oxybutynin treatment in humans compared to pigs. This result could ha ve been affected, however, by the use of the same values for both untreated and oxybutynin treated samples. 2.4.3. Species - specific mechanical behavior We observed species - specific differences for the material parameter , and for parameter (differences for had low statistical relevance), while was independent of the species. Furthermore, porcine samples seemed to reach higher stresses at . These results suggest that the differences in mechanical behavior of the tissue between species stems primarily from dissimilarities in the elements contributing to the low - stress, isotropic behavior, such as elastin, amorphous matrix, and low - stress behavior of smooth muscle cells. The lack of differences in collagen network paramete rs supports the use of porcine bladder extracellular matrix as a viable scaffold material for tissue engineering of the human bladder, as suggested in previous studies [45,46,111] . 2.4.4. Porcine tissue anisotropy A difference in both the material parameter and the stress at based on direction, especially in Pull 1, suggests that elements contributing to the low - stress behavior, such elastin fibers and smooth muscle cells, may have preferential orientation in the transverse direction. Higher values for the parameters and in the transverse direction ( ) observed here could be interpreted as a dominant orthotropic behavior dictated by collagen fiber orientation or high - stress behavior of muscle cells. Previous studies have found preferential orientation in the longi tudinal direction for collagen fibers in decellularized matrix [13] (confirmed by our findings) and preferential orientation in the transverse direction for elastin fibers in the intact pig bladder [7] . Furthermore, in [8] , the authors report that the fiber distribution varies by location and across the thickne ss of the bladder wall, changing from mostly longitudinally oriented at the luminal side to mostly 51 transversely oriented close to the serosa. This is also supported by our fiber orientation analysis ( Figure 2.10 c , APPENDIX ) where we analyzed a limited number of pig and human bladder histological images. The analysis shows that the bulk of fibers are oriented in the longitudinal direction in a plane close to the lamina propria (i.e., at the luminal side of the tissue). In our analy sis, , a parameter associated with elastin fibers and low - stress muscle response, assumes a high value in the transverse direction for the first pull, suggesting a high contribution of elastin and muscle in the transverse as compared to the longitud inal direction. In the second and third pull, however, the decrease in difference of between directions is accompanied by a conserved or increase difference in and , which could be due to a preferential orientation of fibers at the outermost side of the tissue (as suggested by [8] ) or to a fiber realignment mechanism. Another possibility relates to the coiling mechanism described in model M1 the collagen fibers oriented in the longitudinal direction could be more coiled, yet more numerous, than in the transverse direction. Thus, the supraphysiologic loading seen in other studies, as opposed to the physiologically relevant loading applied in this study, could yield higher stiffness in the longitudinal direction. Lastly, testing conditions play a large role in these results. It has been shown that choice of reference configuration when defining the stress - stretch relationship can change the observed tissue anisotropy in rat bladders [14] . Several studies have reported differences in longitudinal and transverse directions in intact bladder tissue. In rodents, the longitudinal direction has been shown to be stiffer in preconditioned or tared conditions [9,10] but not under in vitro non - preloaded conditions [32] . In pig, only marginal differences have been found favoring either a softer longitudinal response with preload [11] or with supraphysiologic pulls [12] in contrast to a stiffer longitudin al response with preconditioning and loading under biaxial conditions [8] . In decellularized extracellular matrix, it 52 has been shown that the longitudinal direction is stiffer after preconditioning [13] , at very high strains [7] , and under reference state - conscious biaxial testing conditions [14] . However , the decellularization process may affect mechanical properties [47] by altering the amorphous elements described in our model. Interestingly, human bladders undergoing cystogram have appeared to be stiffer in th e transverse direction [15] , in agreement with clinical observations where the longitudinal direction experiences the greatest deformation. The experimental method describ ed here attempts to provide a near - physiologic reference state during uniaxial testing, and may reflect an un - tared state in bladder, and thus recapitulate studies where the transverse direction appears stiffer. 2.4.5. Limitations One limitation of the stu dy is the type of testing performed (uniaxial tensile testing). While biaxial testing has being employed often to characterize other soft tissues, that cannot be said for most bladder studies. For this reason, performing uniaxial tests in both longitudinal and transverse directions allowed us to explore the 2D kinematic space, while providing the best possible comparison to prior studies, especially those that have explored constitutive modeling in pig bladder [12] . To choose the protocol that offered the largest opportunity for comparison with prior literature was also particularly important given the scarcity of human tissue. Furthermore, uniaxial compression, which provides a biaxial tensile deformation state in the transverse plane, was predicted accurately by our model using parameters informed by uniaxial experiments supporting the efficacy of the experiments and modeling performed in this study ( Figure 2. 9 ). Assumptions were made in the implementation of M1 th at limit the validity of the estimated fiber recruitment distributions, which in turn could affect the value of the material parameters within M2 (see Section 2.3.1 for details). Specifically, values for evaluated from 53 pigs were used for M2 parameter estimation in both pigs and humans; this could have an effect on the parameter values as well as on the statistical differences that were observed. We contend, however, that the differences we see in some parameters confirm our observations are not a forgone conclusion (support this is approach is not circular). Similarly, oxybutynin treated values were used for untreated samples, and longitudinal values were used for transverse samples, which could also aff ect the results. Of course, relatively small sample size used here for modeling have been reported in other respected studies but still presents issues with regard to our statistical analysis. Unfortunately, obtaining more human tissue was logistically imp ossible. In the model presented here, smooth muscle cells are considered to be contributing to both the isotropic description, which dominates the low - stress response, as well as th e orthotropic description, which dominates the high - stress response. Because of this, the assumption of to be zero in compression (i.e., ) may not be accurate. This assumption has been made in several relevant models in literature when describing a collagen fiber network [105 108] . On one hand, we acknowledge that this constitutive approach is continuum in nature (i.e., a s opposed to microstructural) and the parameters estimated must be considered descriptive of the tissue behavior at a continuum level, more than a precise characterization of the network. Therefore, this model does not have the capability of separa ting the contribution of collagen fibers from other fiber - like constituents, such as smooth muscle cells, that engage in the same orthotropic fashion. As muscle fibers contain and connect with collagen, teasing out this relationship would yield useful insi ghts into the mechanical behavior of bladder tissue. On the other hand, it seems unlikely that a symmetric strain energy function is accurate in describing the behavior of any kind of fiber - like constituent when compressed. A prior study in arterial mechan ics has shown how the contribution of the fiber - like constituents (both collagen and smooth muscle cells) in compression 54 can be represented by the same strain energy function , but with parameters much lower in value (i.e., a reduction of 98% for the parameter and 72% for the parameter when in compression) [108] . Unfortunately, bladder tissue has not been as widely characterized as arterial tissue, so we do not have enough information to make a similar evaluation and for this reason we decided to assume no contribution of the fibers in compression. However, we acknowledge that in bladder tissue there is likely some orthotropic contribution from smooth muscle cell bundles when compressed , which could influence the value of Lagrange multiplier and that is not captured by the neo - Hookean component. For these reasons, the assumption of in compression, while reasonable, represents a limitation of the model. 2.5 Acknowledgement s We would like to thank the generous individuals who donated their bodies to science whi ch made this research possible, as well as Gift of Life Michigan for coordinating to procure the tissue. For the porcine bladders, we thank the generous and timely tissue sharing from Bartlett Lab in General Surgery at University of Michigan and the Michig an Center for Integrated Research in Critical Care. This work was funded in part with help from the American Urological Association Care Foundation (Russell Scott Jr. Urology Research Fund). 55 APPENDIX 56 Histological analysis Mechanically tested and untested tissue specimens were fixed in 10% formalin ( Fisher Scientific) and stored at 4°C. Specimens were dehydrated, embedded in paraffin, cut transversely ( Figure 2.10a with Verho ff Van Gieson stain (PolySciences, Warrington, PA). In Verhoff Van Gieson stain, elastin and cell nuclei are dark blue/black, collagen is red/magenta, and other tissue elements are light brown/yellow. In order to analyze specimen - wide orientation, we first captured sub - images of tissue at 400x magnification. We then compiled sub - images (up to 50 per specimen) into a single full resolution image (300dpi) using Photoshop (Adobe Systems, Mountain View, CA). Using the compiled image, four regions that traversed more than two sub - images were selected for analysis that 1) did not have muscle, 2) were central in the specimen to avoid processing artifacts, and 3) did not include blood vessels or absent space ( Figure 2.10 b ). One specimen was analyzed per condition (h umans and pigs) except in the human untreated specimen where three specimens were analyzed and averaged. Regions were analyzed for fiber orientation using OrientationJ (ImageJ plugin), tiling edge artifacts removed at 0 and 90 degrees, and normalized to to tal fiber measurements ( Figure 2.10 c ). 57 Figure 2 . 10 Fiber orientation assessment. a) Photomicrographs of Verhoff Van Gieson (VVG) stained regions human and pig, tested and untested specimens at 400x (scale bar 100 µm). In VVG stain, elastin and cell nuclei are dark blue/black, collagen is red/magenta, and other tissue elements are light brown/yellow. b) Bladder specimens were sectioned at 5µm along the axis of pull to maximize fiber orientation analys is. Fibrous regions were selected within specimens (shaded, center) and fiber orientation determined within selections (right, n=4 selections per specimen). Hue corresponds to the fiber angle (right, inset). c) Fiber orientation distributions (averaged ove r section) relative to the pulled direction in longitudinal pig and human specimens. 58 CHAPTER 3 - EFFECTS OF SWELLING ON THE VISCOELASTIC BEHAVIOR OF THE PORCINE URINARY BLADDER WALL The results in this chapter are presented in [112] . 3.1. Overview Several pathological conditions that affect the mechanical characteristics of soft tissues, including the bladder, are associated with increased inflammatory response [113 115] . Inflammation has been associated with altered mechanical properties in several tissues, including mouse pancreatic islets [116] , rat myocardium [117] , mouse brain [118] , and cartilaginous cells and tissues [119] . Moreover, tissue swelling, whether inflammatory or osmotically induced, can have profound impact on tissue mechanical response. For example, osmotically induced swelling has been shown to alter mechanical properties in human adipose tissue [120] , as well as bovine intervertebral disks [121] and aorta [122] . The dynamic mechanical r esponse of elastin from porcine thoracic aorta [123] and bovine ligamentum nuchae [124] have also been shown to change based on hydration level. Several studies have uncovered how the mechanical properties of soft tissues can be dependent on the level of hydration, such as in the human stratum corneum [125] , human osteoarthritic cartilage [126] , rat intervertebral disks [127] , and avian keratin [128] . Not only in vitro , but also in vivo studies have highlighted a similar dependency. Dittmann et al. found that the mechanical properties of in vivo human spleen, pancreas, and liver can change after consumption of 1 liter of water [129] . Additionally, theoretical modeling of inflated spheres and fiber - re inforced tubes subjected to swelling show altered mechanical response [130 132] . Yet, to date no study h as evaluated the effect of tissue hydration/swelling on the mechanical properties of the bladder. This could play a crucial role in defining the viscoelastic behavior of the organ wall due to the known 59 involvement of inflammation response in several urolog ical pathological conditions [113 115] and the wide range of urine osmolarities [133] . In a healthy mammalian bladder, the organ wall is protected from urologic constituents by the urothelium [134,135] . However, acute injury or inflammation can lead to changes in permeabilit y of the urothelium [135] . It has been shown that spinal cord injury in rats leads to increased urothelial permeability shortly after injury [136] , and bacteria and positively charged proteins (i.e., from eosinophils or sperm) can increase permeability in the urothelium and lead to cell swelling and cell lysis [134,137] . Osmotic gradients have been shown to decrease tissue electrical resistance and increase mucosal permeability in toad bladders [138,139] . Finally, while the quasi - static mechanical characteristics of the bladder have been shown to differ between orientations [7 15] and anatomical locations [7,8] , no study has evaluated differences in viscoelastic behavior based on anatomical l ocation in the bladder. In this study, we tested porcine bladder to identify if anatomical locations and osmotic using a series of stress - relaxation exper iments as well as a modified Maxwell - Wiechert model to aid in the interpretation of the experimental data. Our results highlight how tissue located near the neck of the bladder seems to present significantly different viscoelastic characteristics than the body of the organ. This supports what was previously observed and is a valuable contribution to the understanding of the location - specific properties of the bladder. We also tested the effect of ehavior is mostly independent of solution osmolarity in hypoosmotic solutions, but the use of a hyperosmotic solution can significantly affect its behavior. This is significant, since several urinary tract pathologies can disrupt the urothelial barrier cau sing increased urothelial permeability, thus subjecting the bladder wall to non - physiologic osmotic challenge. This could have implication in determining changes in 60 cellular stress states during acute inflammation and/or increased urothelium permeability, which may be a contributing factor in driving tissue remodeling (such as fibrosis). 3.2. Methods 3.2.1. Tissue procurement Porcine bladders were obtained at time of slaughter from a local slaughterhouse, and transported to the lab in airtight bags in an insulated container. Bladders were stored in the airtight bags in a refrigerator at 2 °C until tissue preparation for the experiments was performed 3.2.2. Experimental protocols 3.2.2.1. Tissue swelling Bladder tissue was soaked in a modified Krebs - Hense leit buffer solution (Sigma - Aldrich, calcium - free) of varying osmolarity to induce tissue swelling. The values of osmolarity tested were 100, 300, 600, and 900 mOsm/L. The isosmotic solution (300 mOsm/L) consisted of 2.0 g/L D - Glucose, 0.141 g/L Magnesium Sulfate [Anhydrous], 0.16 g/L Potassium Phosphate Monobasic, 0.35 g/L Potassium Chloride, 6.9 g/L Sodium Chloride, and 2.1 g/L Sodium Bicarbonate. Other osmolarities were created by simply increasing or decreasing the concentration of the aforementioned co ntents. All solutions were adjusted to pH 7.4 with 1M hydrochloric acid. The specific osmolarity levels tested in the study were chosen for the following reasons. Human plasma has a natural osmolarity near 300 mOsm/L [140] , making 300 mOsm/L a reasonable value to use to mimic physiological conditions of the healthy bladder wall. To induce swelling, we chose 100 mOsm/L which represents the low end of urine osmolarity [133] . Additionally, a pilot study showed that 100 mOsm/L is the most hypo - osmotic s olution with no evidence of cell lysis. Since urine can 61 have osmolarities ranging from 100 - 1200 mOsm/L [133] , we also included 6 00 and 900 mOsm/L solutions as examples of hyperosmotic solutions. Tissue preparation for the swelling experiment was performed within 6 hours of animal slaughter. Bladders (n=5) were cut along the lateral edge and flattened (see Figure 3. 1 for images of a representative flattened bladder). A 9 mm diameter circular punch was used to create cylindrical samples from the bladder wall. Five samples were taken from each of the five anatomical locations of interest (dorsal, ventral, lateral, lower body, and trigo ne). Figure 3. 1a depicts all samples taken from a representative bladder for the swelling study. All samples were soaked for 18 hours in 5 mL of modified Krebs - Henseleit buffer solution with an osmolarity of 300 mOsm/L at 2 °C . Samples were removed, dabb ed on delicate task wipers (Kimtech Science) to remove extraneous solution, then weighed (Acculab AL - 64) and imaged (Dual Pixel 12MP OIS, F1.7). Figure 3. 2a - b shows representative top and side view images of samples for the swelling experiment. Samples wer e then switched from the initial 300 mOsm/L solution to a new solution (5 mL) with an osmolarity of 100, 300, 600, or 900 mOsm/L, for 18 hours (i.e., one sample per location per solution for each bladder). Samples were again removed, dabbed on delicate tas k wipers to remove extraneous solution, then weighed and imaged. 62 Figure 3 . 1 Representative bladder after being dissected and flattened. Schematic representations of the locations and number of samples taken from each bladder for (a) the swelling study (9mm diameter punch samples), (b) the anatomical location and (c) the variable - solution osmolarity stress - relaxation experiments. The rectangular punch measured 10mm × 30mm for the samples shown in both (b) and (c). Figure 3 . 2 Side view (a) and top view (b) of representative 9mm diameter punch sample for the swelling experiment, before (left) and after (right) manual thresholding. Top view (c) and side view (d) of representative 10mm × 30mm rectangular punch sample for the stress - relaxation experiments, before (left) and after (right) manual thresholding. Binary images (left column) show a schematic of all relevant geometric definitions for the evaluati on of volume and cross - sectional area, see Equations ( 3. 1) - ( 3. 3). 63 3.2.2.2. Stress - relaxation Tissue preparation for the stress - relaxation experiment was performed 1 - 6 hours after animal slaughter. Bladders (n=6) were cut along the lateral edge and flattene d. A 10mm × 30mm rectangular punch was used to create rectangular samples from the bladder wall in the longitudinal (apex - to - base) direction. Stress - relaxation tests were split into two separate experiments (i.e., to identify location - specific behaviors an d the effect of osmolarity separately). Three bladders were used for each experiment. For the location experiment, one sample was taken from each of the five anatomical locations, as shown in Figure 3. 1b . For the osmolarity experiment, four samples were taken from the lateral location, as shown in Figure 3. 1c , to eliminate the effect of location. Punched samples were placed in air - tight bags and refrigerated at 2 °C until undergoing a swelling procedure. For the swelling procedure, samples were subm erged in 10 mL of modified Krebs - Henseleit buffer solution for 18 hours at 2 °C . For the location - specific experiment, all samples were soaked in solution with an osmolarity of 300 mOsm/L. For the variable - osmolarity experiment, samples were soaked in solut ions of either 100, 300, 600, or 900 mOsm/L. The swelling procedure was started 2 - 36 hours after slaughter and the start times of the procedure were randomized for each bladder. Directly after the swelling procedure, uniaxial stress - relaxation tests were performed on a custom uniaxial tensile testing machine with samples fully submerged in room temperature modified Krebs - Henseleit buffer solution with the specific testing osmolarity. Samples were mounted to the uniaxial testing machine using clamps with sa nd - paper grips. Force was measured with a 10lb capacity load cell (Honeywell, Model 31 Mid Range Precision Miniature Load Cell) at a sampling frequency of 200 Hz. A 0.05 N preload was added to the samples by incrementally distending the samples to a load o f 0.05 N for 10 - 15 minutes until a steady state 0.05 N load was 64 reached. Stress - relaxation steps were performed with a displacement rate of 50 mm/s. While large deformations in tissue mechanics are generally defined in terms of stretch, deformations in t his study are defined in terms of engineering strain (i.e., ) to remain consistent with common structural viscoelastic model nomenclature [11,56,59 61,64,66 68,14 1] lengths were defined during testing as distance between clamps after preloading ( ) and after each loading step ( ). Multi - step stress - relaxation was performed for loadings corresponding to strains . R elaxation times were 30 minutes for the first step, and 45 minutes for all subsequent steps, leading to step - loading timings of minutes. Figure 3. 3 shows strain and force history for a representative test. Immediately after pre loading and each loading step, top and side - view images of the samples were taken (Dual Pixel 12MP OIS, F1.7) to estimate sample cross - sectional area. No evidence of sample slipping was found in any test. Figure 3 . 3 Stress - relaxation protocol for a representative sample. Applied strain (top) and recorded force (bottom) data, as a function of test time. This protocol was employed in all stress - relaxation experiments (i.e., anatomical location and variable solu tion osmolarity). 65 3.2.3. Data analysis 3.2.3.1. Tissue swelling Two metrics were used to quantify tissue swelling: relative change in sample mass and relative change in sample volume. These metrics are defined as follows, , ( 3. 1a) , ( 3. 1b) where and are relative mass and volume, and are mass and volume measured when removed from the first solution (300 mOsm/L for all samples), and and are the final mass and volume measured when removed from the testing solutio n (100 - 900 mOsm/L). The values for mass are taken directly from the scale measurements, while volume must be calculated using top and side - view images of samples. Manual thresholding was used to convert images to binary (see Figure 3. 2a - b ). To estimate the volume, , of the samples, the following equations were implemented, , ( 3. 2a) , ( 3. 2b) where - view image, is the total number of - view image for each sample , the side - view image scale in pixels/mm, is the sample diameter (white pixels) for the - th row in the side - view binary image, is the horizontal distance between the right - most and left - most white pixels in the side - view image, and is the effective sample diameter calculated u sing the total sample area from the top - view image . See Figure 3. 2a - b for a schematic of the parameters used in Equations ( 3. 1) and ( 3. 2). 66 3.2.3.2. Stress - relaxation Note that here, and moving forward, every variable represented with a hat and a subsc ript ( i.e., ) is a variable that assumes a constant value, different for each - th loading step, while every variable represented without a hat is considered to be varying with time (i.e., its value is a function of time and could change within t he duration of each - th loading step), except material parameters which are characteristic of the tissue independent of time and of loading step (i.e., , , and ). For the stress - relaxation experiments, the stress as a function of time is calculated as follows, , ( 3. 3a) , ( 3. 3b) where is the force (function of time ) and is the cross - sectional area of the sample at the - th loading step, calculated using the top and side - view images. Figure 3. 2c - d and side - view images before and after converting to binary via manual thresholding, where is define d as the minimum sample width and is defined as the thickness of the sample at the location of . The number of data points for considered for modeling for each loading step was reduced to 200 using a custom logarithmic - like spacing. Two metrics were used to characterize the stress - relaxation behavior, namely, peak stress ( ) and relaxed stress ( ). Peak stress was defined as the maximum stress achieved after each loading step (i.e., the first point of the stress - relaxation curve ). To find the relaxed stresses, we averaged the value of stress from the last two time points for each step. Due to the optimized spacing, the final two time points spanned 103.8 seconds for all loading steps, except the first for which the spanned 63 sec onds. 67 3.2.4 Modeling 3.2.4.1 Modified Maxwell - Wiechert model Previous studies have used hyperelastic [9,13,75,76,14,15,69 74] and viscoelastic [11,12,64 68,142,21,56,57,59 63] models to describe the mechanical behavior of the bladder in various species. For this study we employed a modified Maxwell - Wi echert model with three Maxwell elements (see the schematic in Figure 3. 4 ). Several studies have used variations of the Maxwell - Wiechert model for describing the viscoelastic behavior of the bladder [11,56,60,63,64,66 68] . Nonlinear spring elements were included in the model to capture the nonlinear mechanical behavior of the bladder, similar to Mastrigt & Nagtegaal [60] . Specifically, the standal one spring has a stiffness, , that increases exponentially with strain, , ( 3. 4) where and are the spring material parameters with units of stress and dimensionless, respectively. The stress response, , of the standalone spring is, . ( 3. 5) Additionally, the Maxwell element springs have stiffness that increases linearly with strain of the spring, , , ( 3. 6) where is material parameter with units of stress for the - th spring. To decrease the number of parameters estimated in this study, is constrained to be equal for all three modified Maxwell elements. All dashpots in this model are standard dampers for which the stress is proportional to rate of strain. Th e stress response, , for the - th modified Maxwell element at the - th loading step (identified by the strain level applied at time ) can be evaluated as 68 ( 3. 7a) ( 3. 7b) ( 3. 7c) where represents the dashpot constants with units of [stress·time]. Initial conditions (for ) are needed to specify the relaxation function defined in Equations ( 3. 7), and are defined as and . The stress - time response of the whole syste m is ( 3. 8) For a standard Maxwell element, the time constant for relaxation after step - loading can be found by extending a tangent line from the relaxation function at to the intercepting point on the time - axis for the given Maxwell element. Following this method, pseudo time - constants for the modified Maxwell elements in this model are defined as ( 3. 9) Because of the strain dependent stiffness of the spring in the modified Maxwell elements, the pseudo time - constants are strain dependent, unlike standard Maxwell elements . For purposes of parameter comparison, was set as a constant with a value of 0.5, rationalized by the fact that the most common jump in strain betwe en steps is 0.5. This assumption simplifies the time - constants to . This decision only affects the calculated time - constants used for statistical analysis, and is not associated with the mathematical description of the model or the param eter estimation process. 69 Figure 3 . 4 Schematic of the modified Maxwell - stiffness increases exponentially with strain ( ), while the springs in the three Maxwell el ements have stiffnesses that increase linearly with strain ( ). The dashpots are standard linear dampers ( ). 3.2.4.2 Parameter estimation The purely elastic behavior of the tissue can be approximately identified by considering vs . This was assumed to correspond to the model undergoing deformation at a strain - rate sufficiently low that viscous effects from the dashpots were neglig ible. In this scenario, only the standalone exponential spring dictates the stress - strain response. The exponential spring parameters ( and ) were estimated by minimizing the sum of squared error (SSE) between the relaxed model response and the rel axed stress - strain behavior of the data. Then, the remaining parameters ( and ) were estimated by minimizing SSE between the total multi - step model output and the stress - relaxation data. Loading steps were considered instantaneous during parameter es timation. This method separates the parameter estimation into multiple steps, thus lowering uncertainty by decreasing the number of parameters estimated simultaneously. All parameter estimation was performed using fminsearch in MATLAB. 3.2.5 Statistical an alysis All statistical testing consisted of 2 - way or 3 - way ANOVAs (depending on the number of sources of variation), followed by Tukey - Kramer multiple comparisons tests for all pairwise multiple 70 comparison procedures . For swelling experimental data, the tw o metrics of tissue swelling, and , were the dependent variables. Sources of variation included animal, anatomical location, and solution osmolarity. For stress - relaxation experimental data, the two metrics for stress - relaxation and were the dependent variables. For the location - specific stress - relaxation experiment, sources of variation included animal, anatomical location, and strain level. For the variable - osmolarity stress - relaxation experiment, sources of variation included animal, s olution osmolarity, and strain level. For the modeling, the estimated model parameters were the dependent variable. Sources of variation included animal and location for the location - specific parameters, and animal and solution osmolarity for the variable - osmolarity parameters. 3.3. Results 3.3.1. Tissue swelling Figure 3. 5 shows the swelling of bladder tissue at different anatomical location for different osmolarity values, presented as mean and standard deviation of relative mass and relative volume. First, both relative mass and volume decrease with increasing osmolarity (p < 0.01 for both parameters). Pairwise comparisons showed differences between all groups (p<1E - 6 for , p<0.006 for ) except between 600 and 900 mOsm/L. When looking at trends in locations, it appears that swelling at lower osmolarities (100 and 300 mOsm/L) is similar between locations, but at higher osmolarities (600 and 900 mOsm/L) swelling in locations close to the ne ck of the bladder (lower - body and trigone) appears to not be affected as much as the other locations, particularly when looking at . Statistical analysis shows that dorsal samples have significantly lower relative mass than lower body (p=0.003) and trigo ne (p=0.001) samples. Some differences 71 are seen between relative mass values for different bladders (p<0.05, 2 of 10 comparisons), but no differences in relative volume. Figure 3 . 5 Relative mass ( , top) a nd relative volume ( , bottom) for the different solution osmolarities and anatomical locations, namely dorsal (D), ventral (V), lateral (L), lower body (LB), and trigone (T). Each bar represents the mean and standard deviation from 5 bladders. For 100 mO sm/L, all samples have a and almost all samples (24 of 25, 96%) have . For 300 mOsm/L, all samples have , D and V samples all have , but some L (1 of 5), LB (2 of 5), and T (1 of 5) samples have . For 600 mOsm/L some D (2 of 5) and L (1 of 5) samples have and about half of all samples show (13 of 25, 52%). For 900 mOsm/L some D (2 of 5), V (2 of 5), and L (1 of 5) sample s have and over half of all samples show (16 of 25, 64%). 3.3.2. Stress relaxation experimental data Figure 3. 3 shows plots of applied strain and recorded force history for a representative stress - relaxation experiment. Figure 3. 6 shows stress - relaxation data (reduced to 200 points per step) 72 from a representative sample with time represented relative to the start of each step. Both linear and logarithmic timescales are shown for the same data. In Figure 3. 6 it can be appreciated that stresses are greater at higher values of strain, as expected. Figure 3. 7 (top) shows peak and relaxed stresses for all anatomical locations at each loading step. It is evident that both peak and relaxed stresses increase with level of applied strain, as expected. Additionally, lower body and trigone regions appear to have higher peak and relaxed stresses than dorsal, ventral, and lateral regions. Statistical analysis shows both peak stress (p<0.0002) and relaxed stress (p=0.0002) differs with location. Pairwise dif ferences based on location are the same for peak and relaxed stresses, i.e. trigone stresses are significantly higher than dorsal (p<0.0003), ventral (p<0.05), and lateral (p<0.02), and lower body stresses are significantly higher than dorsal (p<0.02). No differences are found with respect to different bladders. Figure 3. 7 (bottom) shows peak and relaxed stresses for different solution osmolarities at each loading step. Qualitatively, stresses appear to increase with increasing osmolarity, except when com paring 100 vs 300 mOsm/L. Statistical analysis shows both peak stress (p<1E - 6) and relaxed stress (p=2E - 7) differ with osmolarity. Pairwise comparisons show 900 mOsm/L samples have significantly higher peak and relaxed stresses than 100 (p<0.001), 300 (p<7 E - 6), and 600 (p<0.008) mOsm/L samples. Unlike the location - based experiment, differences are seen between bladders (p<1E - 6 for , p<0.0002 for ) for the variable - osmolarity experiment. 73 Figure 3 . 6 Stress - relaxation curves as a function of time relative to the start of each loading step for a representative sample. The same data is shown for a linear timescale (top) and logarithmic timescale (bottom). The number of dat a points in each curve is 200 and have been identified by using a customized logarithmic - like spacing. A grey - scale color gradient has been employed to represent the different values of applied strain, from the lightest representing the smallest strain in the protocol ( ) to the darkest representing the largest strain in the protocol ( ). 74 Figure 3 . 7 S tress - relaxation results for all samples showing peak stresses ( , left) and relaxed stresse s ( , right) for different anatomical locations (top) and osmolarities (bottom). Open symbols are used to identify the anatomical location experiments and closed symbols to identify the varying solution osmolarity experiments. A grey - scale color gradi ent has been employed to represent the different values of applied strain, from the lightest representing the smallest strain in the protocol ( ) to the darkest representing the largest strain in the protocol ( ). An asterisk represents a statistically significant difference (p<0.05) and the relevant comparison is represented by an arrow. 3.3. 3 . Modeling results Figure 3. 8 shows comparisons for all material parameters and groups from the location - specific experiment. When look ing at the elastic parameters (i.e., exponential spring), is significantly higher in lateral samples when compared to trigone (p<0.05), and is significantly higher in trigone compared to all other locations (p<0.05). The only significant differen ces found in the 75 viscoelastic parameters (i.e., parameters associated with the modified Maxwell elements), are that is higher in the trigone region when compared to both the dorsal and lower body regions (p<0.05). No differences are seen between bladde rs for any model parameters in the location experiment. Figure 3. 9 shows plots of parameter estimates for all parameters and groups from the variable - osmolarity experiment. The exponential spring material parameter is significantly higher for samples tested in 900 mOsm/L solution compared to all other osmolarities (p<0.05). When considering the viscoelastic parameters, both and have significantly higher values for 900 mOsm/L compared to all other osmolarities (p<0.01). Additionally, and are significantly higher in samples tested in a 900 compared to 300 mOsm/L. No differences are seen between bladders for any model parameters in the osmolarity experiment. 76 Figure 3 . 8 Estimated values of the parameters for the modified Maxwell - Wiechert model when considering the anatomic location experiment. Open symbols are used to identify the different anatomical locations (as specified in the legend). An asterisk represents a stati stically significant difference (p<0.05) and the relevant comparison is represented by an arrow. 77 Figure 3 . 9 Estimated values of the parameters for the modified Maxwell - Wiechert model when considering the v ariable solution osmolarity experiment. Closed symbols are used to identify the different solution osmolarities (as specified in the legend). An asterisk represents a statistically significant difference (p<0.05) and the relevant comparison is represented by an arrow. 3.4. Discussion 3.4.1. Tissue swelling The results shown in Figure 3. 5 suggest that subjecting the bladder to changing levels of urine and/or serum osmolarity could result in altered bladder wall thickness and geometry. It is generally accepted that the urothelium protects the bladder wall from the osmotic challenge of urine [134,135] . However, several diseases and disfunctions of the bladder are associated with changes in urothelium permeability [134 137] . This study suggests that, in cases of compromised urothelium, urine osmolarity could lead to varying levels of tissue hydration and, consequently, changes in bladder wall thickness and ge ometry. Differences in location - based swelling suggest 78 that the regions close to the neck of the bladder (lower body and trigone) are less affected by the presence of increased osmolarity, when compared to the regions located close to the dome (particularl y the dorsal region). 3.4.2. Stress - relaxation A prior study reported on the uniaxial (apex - to - base direction) stress - relaxation behavior of porcine bladder strips taken from the lateral location [16] . The results presented in [16] show comparable values of relaxed stresses, but significantly lower values of peak stresses, when compared to our study. The discrepancy betwe en peak stresses is likely due to differences in experimental protocol. Jokandan and colleagues in [16] used a protocol significantly different than the one employed here, specifically in the loading conditions (strain levels, displacement rate, relaxation times, time submerged in isosmotic solution prior to testi ng, preconditioning), as well as in the sample geometry definition (cross - sectional area measurement, sample lengths). Furthermore, while the samples in our study were tested submerged in solution, in [16] the authors employed intermittent misting to ensure hydration of the samples. The possible effect of these p rotocol discrepancies on the values of peak stress for this tissue highlights the need for more consistent tissue testing protocols between different studies. This would minimize the amount of variability in recorded tissue behavior and increase the capabi lity of comparison across studies. Further illustrating this point, Mastrigt & Nagtegaal performed stress - relaxation tests on pig bladder strips at different strain rates and found that viscoelastic parameters depend on rate of step - wise loading [60] . When comparing peak and relaxed stresses ( Figure 3. 7 ), we found that the lower body and trigone regions showed significantly higher values than all other anatomical regions, particularly at high levels of strain. This finding suggests that the porcine bladder is stiffer closer to the neck 79 of the bladder. This supports previous work that has shown little location - based difference in porcine bladder stiffness at low levels of strain, but stiffer behavior in the lower body and trigone regions at high levels of strain [7,8] . Some significant differences are also seen for peak and relaxed stresses between solution osmolarities. Stresses generally increase with increasing osmolarity. Spe cifically, samples tested in a 900 mOsm/L solution showed significantly higher stresses than all other conditions. Knowing that urothelium permeability can increase in pathological conditions [134 137] and that 900mOsm/L is within the range of physiologic urine osmolarity [133] , these results suggest that high urine osmolarity in some pathological conditions may contribute to increased stresses felt by cells in the bladder wall, and consequently act as a contributing factor in driving remodeling. 3.4. 3. Modeling The model presented in this study provi ded a better description of the experimental data when compared to a conventional Maxwell - Wiechert model (preliminary study, model predictions not shown). First, the introduction of an exponential standalone spring allows an adequate description of the tis - like [12] . Second, a preliminary analysis showed that a prohibitively large number of Maxwell elements were necessary to achieve a reas a single Maxwell element results in a exponential relaxation, and if a single element is used to describe the behavior of this tissue only a small portion of the curve is represented adequately. Increasing the number of Maxwell elements would improve the description, but also result in an increase in the number of model parameters, resulting in higher uncertainty and lower confidence in the estimation. The model presented here aims to improve the description of the observed behavior by modifying the shape of the model relaxation curve, rather than increase the number of 80 elements. By making the spring stiffness strain - dependent, we enable the model to capture both the increased stiffnes s at high strains, which leads to faster relaxation in the short - term response, as well as decreased stiffness at low strains, which leads to slower relaxation in the long - term response. This modification of the standard Maxwell description led to an accur ate description of tissue behavior without increasing the number of elements and parameter estimate uncertainty. A measure of accuracy of the description is the normalized root mean squared error (NRMSE), for the modeled presented here the NRMSE averaged b etween all samples is 0.0222 for the exponential spring estimation step and 0.0377 for the entire stress - relaxation curve ( Figure 3.10 , in the APPENDIX , shows experimental data and model description for a representative sample). Our analysis revealed diff erences in for the trigone region compared to all other regions of the bladder , suggesting that the trigone region sees rapid increase in stress at high levels of strain ( Figure 3. 8 ). These results, once again, support what has been previously shown in the porcine bladder [7,8] . Few differences are seen in the viscoelastic parameters for the l ocation - specific experiment, suggesting that most regions of the bladder show similar time - dependent behaviors. Differences in the largest time constant ( ) are observed, however, when comparing the trigone region to dorsal and lower body regions. This w ould imply a difference in the long - time viscoelastic response of the trigone region. This difference could be a significant factor when attempting to evaluate elastic behavior with conventional repeated, low - strain rate tensile tests, and should be acknow ledged and considered when developing a testing protocol. No differences are seen between the material parameters estimated for samples tested in solutions of osmolarity 100, 300, and 600 mOsm/L. Knowing that tissue swelling is significantly dependent on solution osmolarity (as shown in Figure 3. 5 ), the absence of differences between these parameters suggests that the bladder wall mechanics is somewhat independent of the changes 81 in swelling within this range of osmolarities. However, samples tested in a 90 0 mOsm/L solution show significantly greater values of , , and when compared to all other testing solutions ( Figure 3. 9 ). This is especially significant because the long - time response of the tissue, which is the most physiologically relevant in the bladder because of the timescale of normal micturition, depends heavily on and . The increase in stress associated with higher long - time parameter values suggests, in agreement with the conclusions from the experimental data, that pathologically high urine osmolarity together with decreased efficacy of urothelial barrier may contribute to increased stresses felt by cells in the bladder wall, and consequently act as a contributing factor in driving remodeling. 3.4.4. Limitations The swelling and m echanical test protocols employed here have some limitations. Relative masses and volumes for the 300 mOsm/L samples are greater than 1, as shown in Figure 3. 5 . This could suggest that the time considered for acclimation for the swelling test (18 hours) is not long enough for the samples to reach swelling equilibrium. Additionally, swelling was performed at 2 °C , as opposed to room temperature or in vivo body te mperature. This was a necessary limitation, in the effort to minimize the effect of tissue degradation and to limit the amount of time needed to complete all swelling and stress - relaxation testing for a single bladder. Furthermore, a somewhat large amount of uncertainty can be seen in the volume estimation for the swelling experiment when compared to the mass data (see Figure 3. 5 ). This is because the volume estimation was made using only a top and side - view image for every sample. To improve the accuracy o f the volume estimation, images from more angles are needed. Moreover, the stress - relaxation tests in this study were performed without preconditioning. Hardware limitations prevented preconditioning from being performed at a displacement rate lower than t he rate used for step - straining (50 mm/s). 82 Therefore, it was deemed more reasonable to not precondition the tissue. Furthermore, a prior study has shown that muscle and fiber reorganization and reorientation occurs during bladder filling that is revolved b ack to a reference state during contraction [86] . Thus, it is unclear whether the in vivo passive mechanical response is more closely correlated with preconditioned or non - preconditioned in vitro tissue response. Finally, the variable - osmolarity stress - relaxation experiment showed some inter - animal variability when analyzing the experimentally measured peak and relaxed stresses, this difference however was not observed in t he modeling parameters. The stress relaxation model generally provided a good description of the mechanical data, but falls short in some regards. The multi - step parameter estimation process restricts the relaxed stress of the model to be represented by t he final stress values of the data in each straining step. This assumes that the final stress values in the data represent the fully relaxed stress of the tissue, which may not be the case for some samples. This could introduce error into parameter estimat es. However, preliminary analysis showed that an unrestricted parameter estimation procedure (single step) resulted in higher uncertainty in parameter estimates. Similarly, the choice of being equal for all modified Maxwell elements is a limiting assump tion that was necessary to obtain parameter estimates that converged to unique values. Additionally, the model was unable to accurately capture the strain dependence of the stresses near the peaks. It is unclear whether this is a limitation of the model or of the data collection near the peaks. It has been shown that short - time response data directly after rapid straining is subject to elevated measurement error [21,143] . 3.5 Conclusions In this study we found that the uniaxial viscoelastic behavior of the urinary bladder significantly depends on both anatomical location and solution osmolarity. This information is crucial to inform the development of both new therapeutics as well as aid i n the future design of tissue engineered 83 biomaterials. Moreover, these results will be useful in aiding the design of testing protocols for future studies. Yet, there are still unanswered questions that should be explored in the future. For example, it has been shown before that the quasi - static mechanical characteristics of the bladder are anisotropic. Therefore, performing biaxial stress - relaxation tests will increase our understanding of how viscoelastic behavior change with tissue directionality in the bladder wall. Moreover, the difference in mechanical behavior due to osmotic loading may be related to a change in collagen fibers network organization associated with hydration, which has not been explored in this work. A study that correlates microscopy with stress - relaxation could shed light on this correlation. 84 APPENDIX 85 Figure 3 . 10 Mod el description for a representative dataset. All plots show the same experimental data (solid circles) and model description (solid line), each with a different timescale representation. The top represented the consecutive loading steps as a function of testing time. The bottom figures represent the loading steps as a funct ion of time relative to the start of each loading step shown for a linear timescale (left) and logarithmic timescale (right). The normalized root mean squared error (NRMSE) averaged between all samples is 0.0222 for the exponential spring parameter estimat ion step and 0.0377 for the entire stress - relaxation curve. 86 CHAPTER 4 - CHANGES IN MORPHOLOGY AND COMPLIANCE IN THE LONG - TERM SPINAL CORD INJURED RAT BLADDER EXTRACELLULAR MATRIX 4.1. Overview SCI has been shown to alter muscle stiffness [144] and overall thigh tissue stiffness [145] in humans. Bla dder wall morphology and mechanical properties have been shown to change in as a result of a SCI . This has been shown in the past in a rat bladder model of SCI [14,21,30,31] . In the healthy rat bladder, smooth muscle cells have been shown to be oriented predominantly in the longitudinal direction, in contrast to the SCI rat bladder which shows SMCs oriented both longitudinally and circumferentially [22] . SCI rat bladders have also shown decreased collagen content and increased elastin content compared to controls [21] . In addition, c ompliance of the rat bladder wall has been shown to increase 10 and 14 days post - injury [30] , increase 3 and 6 weeks post - injury, but return close to normal levels of complianc e 10 weeks post - injury [31] . Finally , viscoelastic response of SCI rat bladders have been shown to differ from controls [21,62] . There is evidence of de no vo elastin fibers in the SCI rat bladder, which are posited to play a role in crimping the collagen fiber network, thus changing the recruitment of collagen fibers during tissue deformation, and increasing compliance [14] . The objectives of this study are to quantify the enduring changes in morphology and mechanical properties of the rat bladder after SCI. To date, the longest evaluation of mechanical properties in the SCI rat bladder post - injury previously published is 10 weeks [31] . In this study, we evaluate mechanical properties of the SCI rat bladder extracellular matrix (ECM) 1 6 weeks post - injury. Through imaging, histological analysis, tensile testing, and constitutive modeling, we are able to see increase in bladder circumference, elastin content, and distensibility. These results suggest increased bladder capacity and compliance in long - term spinal cord injury. Constitutive 87 modeling suggests that increased distensibility is facilitated by an increase in fiber waviness that alters the distribution of fiber recruitment during loading. This is supporte d by the highly coiled structure of collagen fibers in the remodeled extracellular matrix of short - term spinal cord injured rat bladders. These study in an important step in understanding the remodeling of the spinal cord injured bladder, which has implica tions for future treatment and care in long - term spinal cord injury . 4.2. Methods 4.2.1. Animal groups and tissue preparation In this study, g roups included SCI paraplegic (P, n=8), healthy age - matched controls (C, n=6), and sham surgery controls (S, n=7) , all male Sprague - Dawley rats. 8 - week old rats underwent SCI surgery to induce paraplegia (n=8) , as described in [146] . Rats were anesthetized and the spinal cord was transected between T2 3 using a microknife (10316 - 14, Fine Science Tools) and Vannas spring scissors (15000 - 08, Fine Science Tools). After surgery, animal bladders were voided manually every four hours for 7 - 10 days , at which point partial ability to void independently was gained and bladders were voided four times per day to empty residual urine volume to prevent risk of infection . Animals were sacrificed 1 6 weeks post - injury. Healthy controls were age match ed. Sham surgery controls underwent the same surgical procedure, but the spinal cord was left intact. After sacrifice, the bladders were excised and 2 circumferential rings were cut from each bladder. Samples fixed for ring histology (See section 2.3.1. Ri ng histology ) were fixed fresh, while all others were frozen in tissue embedding medium at - 80°C. Since the objective of this study is to identify differences due to SCI in bladder ECM, we performed a decellularization protocol on the tissue to eliminate the mechanical contribution of 88 the SMCs. Prior to all testing procedures (excluding ring histology), bladder rings were thawed for 1 hour at room temperature, then decellularized following a protocol similar to what has previously been used for whole hear t s [147] and bladders [14,62] from rats, which showed no adverse effects on ECM integrity . Briefly, r ings were submerged in 5 mL of heparinized saline solution for 15 minutes, 5 mL of 1% sodium - dodecyl su lfate solution for 48 hours, 5 mL of deionized water for 15 minutes, and finally 5 mL of 1% Triton X - 100 solution for 30 minutes. 4.2.2. Geometry estimation Top - view images of rings were taken (Dual Pixel 12MP OIS F1.7) before and after decellularization. NeuronJ [148] , a plugin for ImageJ, was us ed to trace the inner and outer edges of the rings. Then, i nner and outer tracing lengths were averaged to estimate effective ring circumference for each sample. 4.2.3. Histology B ladder rings from 1 6 - week paraplegic and control animals were processed for histological analysis. Samples were submerged in 10% formalin solution for 96 hours, and stored in 30% ethanol. Samples were embedded in paraffin, sectioned and stained by the Michigan State University Investigative Histopathology Lab. Samples were stained with picrosirius red (PSR) and Verhoeff - Van Gieson (VVG). Samples were imaged with an Olympus BX41 microscope using Nikon DXM1200 software. In addition, samples from a subset of rats , which underwent the same SCI procedure but died unexpectedly 1 week a fter the procedure (n=2), were used for planar histology. After isolating bladder rings as described above, the tissue w as decellularized, cut, laid flat, pinned to wax blocks, submerged in 10% formalin solution for 96 hours, then stored in 30% ethanol. Sa mples were embedded in paraffin, sectioned and stained by the Michigan State University Investigative 89 Histopathology Lab. Sectioning was performed normal to the radial direction. Two sections were taken from each sample, one as close to the inner surface a s possible (lamina propria region), and one from the center of the wall thickness (detrusor region ). Samples were stained with VVG. Imaging was performed with a Nikon Eclipse TI2 - E. Automated axis movement and stitching was used produce whole - sample images for the lamina propria and detrusor layers for each sample. Control rats ages 16 weeks (n=3) and 12 weeks (n=1) were also analyzed in the same fashion for comparison . OrientationJ (ImageJ plugin) was used to analyze fiber orientation in the planar histol ogical images. To remove artifacts from pinning and sample edges, two cropped sections were chosen from each image, which represented the largest regions devoid of samples edges or pinning. OrientationJ calculates local orientation and isotropic properties (coherency and energy) for every pixel in an image [84] . By default, OrientationJ creates a weighted histogram using coherency values to weight the orientation at each pixel. Coherency weighting gives high weight to areas of absent muscle cells (removed during decellularization) as well as highly collagenous areas , whereas weighting based on energy or pixel intensity only gives high weight to highly c ollagenous areas . For each group, local directions were weighted both with coherency, and the product of energy and pixel intensity. This allows orientation distributions to represent a combination of muscle and collagen fiber directions (coherency weighti ng), as well as only collagen fiber directions (energy×intensity weighting). 4.2.4. Mechanical testing Uniaxial ring testing was performed on decellularized bladder rings. Samples were mounted to a custom uniaxial tensile testing machine via polyester thre ad loops. Force was measure d with a 250 - gram capacity load cell (Futek, LSB 200, 250 g, JR S - Beam Load Cell). Stretch was 90 continuously recorded throughout the tests with a charge - coupled device (CCD) camera (Basler, piA1000 - 60gm). Samples were submerged in modified Krebs - Henseleit buffer solution (Sigma - Aldrich, without calcium chloride) throughout testing. Prior to preconditioning, a 2 - gram preload was applied and maintained for 10 minutes. Prior to each subsequent loading - unloading protocol , a 2 - gram pre load was reapplied and maintained for 1 minute. After each preload, front - view images (Basler, piA1000 - 60gm) and side view images (Dual Pixel 12MP OIS F1.7) were taken. Samples were , first, preconditioned for 10 cycles of loading - unloading to a maximum s tretch of 1.1 , then we performed three cyclical testing protocols, each consisting of 5 cycles of loading - unloading to maximum stretches of 1.2, 1.3, and 1.4 , respectively. Both preconditioning and testing cycles were performed at a rate of 0.01 s - 1 . Refe rence configuration for stretch was sample length following applied preload. Mechanical tests were stopped if samples ruptured. All data analysis related to the mechanical testing, including model parameter estimation, was performed on the final loading cy cle from the first loading set to surpass 120 kPa. Stress, , as a function of stretch, , was defined as follows, , ( 4. 1) where is the measured force, and is the cross - sectional area calculated for the relevant loading step , given by, , ( 4. 2) where is the initial cross - sectional area, calculated from front and side - view images taken prior to the relevant loading protocol . Images were converted to binary images using manual thresholding. Sample width and thickness were defined as the median sample wi dth and thickness from the binary front and side - view images. Initial cross - sectional area, , was calculated as the product of median width and thickness. 91 Opening angle experiments were also performed on decellularized bladder rings. Rings were plac ed in petri dishes and submerged in modified Krebs - Henseleit buffer solution. The bladder wall was cut, and images were taken at 0, 3, 6, 9, 12, 15, 30, 45, 60, 75, and 90 minutes post - cutting. After converting images to binary via manual thresholding, an ellipse was fit to every image. Opening angle was defined as the minimum angle formed by the two points at the opening, and a third point along the fitted ellipse. 4.2.4. Constitutive modeling Two constitutive models were used to describe the uniaxial mech anical data. First, a structural fiber recruitment model was used to gain insight into potential microstructural differences responsible for changes in mechanical behavior. Second, an exponential model was used to provide a classical continuum mechanics de scription of the mechanical properties. 4.2.5.1. Fiber recruitment model In this study, a structural unidirectional fiber recruitment model was used to describe the mechanical response of the bladder tissue. Figure 4. 1 shows a conceptual depiction of the fiber recruitment model, where springs in the model are linear, and representative of collagen fibers in the bladder tissue. As the tissue is stretched, springs engage and increase the stiffness of the response. When th e number of springs is large, it is assumed that the percentage of engaged springs follows a scaled cumulative beta distribution, similar to [149] . The stress - stretch response of the model is defined by the following differential equation, ( 4. 3a) ( 4. 3b) 92 where and are the initial and final slope of the stress - stretch curve, respectively, and is the beta distribution, which is a function of shape parameters and , and the normalized stretch is defined as a function of , the maximum stretch achieved during the test. The mean and variance of the beta distribution, and are defined as ( 4. 4) ( 4. 5) where and are the mean and standard deviation of recruitment stretch , as seen in [101,149] . Parameter estimation was performed in several steps (see Figure 4. 2 ). We estimated the initial slope , , as the slope of the line with the highest value when fitting a line to the first points of the stress - stretch curve, where was varied from 5 points to the total number of points on the curve, similar to [9] . was estimated in the same way, but using the final points of the stress - stretch curve. Next, w e defined as the stretch at the intersection of the initial and final slope lines. Using E quation ( 4. 4 ) , was defined as a function of and . Using the entire stress - stretch curve, we estimated ( nlinfit , MATLAB) by minimizing the sum of squared error (SSE) between the data and the stress - stretch relationship from E quation ( 4. 3a ), which was solved numerically using the ode45 function in MATLAB. 93 Figure 4 . 1 Visual representation of the fiber recruitment model. As deformation is applied, springs engage, increasing the stiffness of the response. Figure 4 . 2 Representative stress - stretch data with model fit from the fiber - recruitment model (top) and exponential continuum model (bottom). For the fiber - recruitment model, is initial slope, is final slope, and is the mean recruitment stretch defined by the intersection of the initial and final slope lines. 94 4.2.5.2. Exponential model In this study, we employ a constitutive model similar to what has been previously published [150 152] . Uniaxial deformation is described by the deformation gradient tensor, , where , , and are the principal stretch directions, defined as , and . The strain energy function for this model is defined as ( 4. 6) where is the right Cauchy - Greene deformation tensor, and and are scale and shape parameters, respectively, with units of stress and dimensionless. Cauchy stress, , is calculated as ( 4. 7) where is a Lagrange multiplier to enforce incompressibility. We performed p arameter estimation in a single step ( using the function nlinfit in MATLAB) by minimizing the SSE between the stress - stretch experimental data and the Cauchy stress defined in Equation ( 4. 7) . 4.2.6. Statistical analysis We performed s tatistical analysis to asses significance between groups for ring circumference, stretch values at various levels of stress, stretch at 100kPa stress (comparable to axial stretch in [31] ), parameter values for both models, and opening angle. The source of variation for all ANOVAs performed was injury ( control, sham, paraplegic). For the mechanical data, each curve was reduced to 12 points, corresponding to the level of stretch for given values of stress, . Repeated measure ANOVAs were performe d for ring circumferences, stretch values at , and opening angles, where the within - subject variables were thawed vs decellularized, stress level ( ), and time, respectively. 1 - way ANOVAs were performed for stretch at 100kPa stress, and parameter va lues for both models. Post - hoc analysis consisted of Tukey - Kramer multiple 95 comparisons tests for all pairwise multiple comparison procedures. Due to lack of significance between control and sham groups for mechanical data and model parameters, control and sham groups were combined, and additional repeated measure ANOVAs and 1 - way ANOVAs were performed for stretch at , stretch at 100kPa stress, and parameter values for both models. 4.3. Results 4.3.1. Ring circumference Figure 4. 3 shows mean ± standard deviation of effective ring circumference of each group before and after decellularization. R ing circumference increase d statistically through the decellularization process (p<0.05). Both sham and paraplegic groups appear to have larger ring ci rcumference than control samples, also confirmed by statistical analysis (p<0.05). Figure 4 . 3 (a) Ring images before and after decellularization and traced edges, and (b) m ean ± standard deviation for ring circumference before and after decellularization for control, sham, and paraplegic groups. 4.3.2. Histology Figure 4. 4 show s PSR and VVG stained images of different layers from control and paraplegic bladders (plane normal to the longitudinal axis). Qual itatively, paraplegic bladders tended to have 96 more visible elastin fibers than controls. Figure 4. 5 shows some particular regions of interest from paraplegic histological samples, where high collagen density and abnormal amounts of elastin can be seen. Figure 4. 6 shows planar images (normal to the radial direction) from decellularized control and 1 - we ek paraplegic bladders. T he morphology of the collagen fibers varies from lamina propria to detrusor in controls, and varies from controls to paraplegic bladders. Figure 4. 7 shows mean orientation distributions from control and 1 - week paraplegic bladders i n different layers, with local orientations weighted by either coherency or the product of energy and pixel intensity. Coherency weighting gives similar weight to collagenous areas and muscular areas with lower amounts of collagen. Weighting by energy and pixel intensity decreased the weight of muscular areas and are referring to regions that contained smooth muscle cells prior to decellularization, which can be seen in the detrusor region images of Figure 4. 6 . 97 Figure 4 . 4 PSR (left two columns) and VVG (right two columns) stained bladders in the plane normal to the longitudinal direction from control (left) and pa raplegic (right) rats in the lamina propria (top), detrusor (middle), and adventitia (bottom) Figure 4 . 5 Regions of interest from a 1 6 - week paraplegic rat bladder showing an area of high collagen density (PSR, left) and high amounts of elastin (VVG, right) 98 Figure 4 . 6 Planar images from control (left) and 1 - week paraplegic (right) rat bladders in the lamina propria (top) and detrusor (bottom) Figure 4 . 7 Mean fiber orientation distributions for control and 1 - week paraplegic rat bladders in the lamina propria (top) and detrusor (bottom) with different local fiber angle weighting. Coherency weighting (left) give high weight to formerly muscular regions as well as collagenous regions. Weighting by the product of energy and intensity (right) gives lower weighting to previously muscular areas, while keeping high weighting in collagenous regions. 99 4.3.3. Mechanical testing Figure 4. 8 shows stress - stretch curves for each group averaged by stretch at different levels of stress. It can be appreciated that control and sham bladders have nearly identical average stress - stretch curves, confirmed by statistical analysis (p=0.95). Paraplegic mechanical data is significantly rightward shifted compared to sham (p<0.05) and compared to control and sham grouped together (p<0.01). Figure 4. 9 shows mean ± standard deviation of stretch values at a stress of 100 kPa. This metric is similar to previous measures of compliance in the SCI rat bladder [31] . At 100 kPa, paraplegic bladders show significantly higher stretch than sham samples (p<0.05) and sham combined with control (p<0.01). Finally, Figure 4. 10 shows mean ± standard deviation of opening angle at different time points post - cut for control and paraplegic groups . N o statistically significant difference s between groups were observed (p=0.34), yet the opening angle assumed values larger than zero in decellularized rat bladder rings. Figure 4 . 8 Str ess - stretch curves (mean ± standard deviation) from control, sham, and paraplegic groups. Stretch values at different levels of stress are significantly higher in the paraplegic group when compared to the sham group (arrow) and the sham and control groups combined (bracket). 100 Figure 4 . 9 Mean ± standard deviation of stretch values at 100 kPa stress for control, sham, and paraplegic groups. The paraplegic group shows significantly higher stretch than the sham group (arrow) and the sham and control groups combined (bracket). Figure 4 . 10 Opening angle images at (a) 0 minutes and (b) 90 minutes post - cut, and (c) m ean ± standard deviation of opening angle vs time from control and paraplegic groups 4.3.4. Constitutive modeling Figure 4. 2 shows a representative set of mechanical data with the model fit from both the fiber recruitment mode l and the exponential continuum model. The normalized root mean squared error (NRMSE) averaged between all samples is 0.014 for the fiber recruitment mode l, and 0.017 for the exponential continuum model. 101 Figure 4. 11 shows mean ± standard deviation of parameter values for both models. No differences were seen between control and sham groups for any parameters. When comparing all groups, paraplegic samples show significantly higher mean recruitment stretch, , than the sham group (p<0.05). When combining the control and sham groups, paraplegic samples show higher mean and standard deviation of recruitment stretch, and lower initial slope when compared to the control+sham group. For the exponential continuum model, no differences are seen when comparing all groups, but is significantly lower in paraplegic compared the control+sham group. Figure 4 . 11 Mean ± standard deviation parameter values for the fiber - recruitment model ( , , , , , ), and exponential continuum model ( , ) 102 4.4. Discussion This study focuses on understanding the changes in ECM microstructure and mechanical characteristics in the bladder of an animal model of SCI, 1 6 weeks post - injury. We found that the paraplegic animals is more di stensible when compared to both control and sham animals. We have quantified this using two different metrics. First, when looking at the stress - stretch curves ( Figure 4. 8 ) the significant rightward shift observed between the tissue from sham and control g roups and the SCI group suggests higher distensibility. Second, we calculated the stretch corresponding to a stress of 100 kPa ( Figure 4. 9 ) , a measure of compliance used in prior work [31] , which exhibited significantly higher v alues in samples from the SCI group as compared to sham and the combined sham and control group . Previous work showed that compliance is highest in bladder tissue 3 - 6 weeks post - injury in a rat model of SCI , and returns close to control levels of complianc e at 10 weeks [31] . In [31] , the authors speculate d that this trend could lead to a hypocompliant bladder at a later time point, which would recapitulate what is observed in some individuals affected by SCI [153] . Our results show, however, that this is not the case afte r 1 6 weeks. Our work suggests that rather than fully returning to healthy levels of compliance or becoming less compliant than controls, the bladder of SCI rats 1 6 weeks post - injury remains at slightly elevated levels of compliance. It is commonly accept ed that c ollagen fiber recruitment is an important phenomenon in defining the mechanics of highly dynamic tissues such as the bladder . The wavy configuration of collagen fibers that is seen in many tissues allows tissue to deform with little resistance at low stresses, behavior observed in healthy bladders during low - pressure filling [9] . When collagen fibers begin to straighten, they engage and significantly contribute to increase the stiffness of the tissue overall . This correlation between microstructure and tissue behavior has been studied in 103 various tissues including rat tail tendon [77] , rabbit achilles tendons [78,79] , human skin [80] , human vena cava [81] , pig coronary adventitia [82] , rabbit carotid arteries [83,84] , pig thoracic aortas [85] , and fetal bovine bladder [86] . In addition, changes in the microstructural organization of the collagen network, for example due to disease, could significantly impact the global mechanical behavior of t he tissue. Cheng and colleagues w ere able , in a recent work, to measure collagen fiber waviness in the rat bladder at different amounts of strain . They reported experimentally that distensibility was decreased in samples that showed premature recruitment ( i.e., earlier engagement) of fibers on the outer wall of the bladder, which seemed to be correlated with aging [9] . It is intuitive to expect that a delayed engagement in collagen fibers will result in increased distensibility of the bladder ECM network as a whole. When direct measurement of fiber engagement during stretching is not available, several studies in the past have employed structural constitutive modeling to indirectly estimate the characteristics of the fibers network. Fiber recruitment models, first described by Viidik [78] , specifically correlate fiber waviness and engagement and the mechanical behavior of tissue. Lanir developed the structural theory for fiber recruitment and orientation distributions for fibrous tissues [87,88] and later incorporated fiber recruitment in a growth and remodeling model [89] . F iber recruitment models have been used in the past to describe rat carotid arteries [90] and right ventricular myocardium [149] , rabbit skin [92] , rabbit carotid arteries [83,91] , sheep digital tendon [93,94] , and SCI rat bladder [14] . Continuum models with exponential strain energy functions are also commonly used to describe the mechanical behavior of highly deformable tissues (i.e., bladders in pigs [69] , dogs [71] , and rats [9] ). In this study we have employed two constitutive models, one structural and one continuum, to quantify the changes in the ECM mechanical behavior in the bladder wall that are associated 104 with a SCI. Both the exponential continuum model and the structural fib er - recruitment model provided good descriptions of the bladder mechanical response ( Figure 4. 2 ). W hen comparing paraplegic to grouped control and sham , we observed a significant difference in the exponential continuu m model parameter ( Figure 4. 11 , bot - - stretch curve in paraplegic samples. This behavior seems to be also supported by a d ecrease in initial slope in samples from paraplegic animals, suggest ing a lower amount of initially recr uited fibers . A possible explanation for this observed behavior was first proposed in [14] . Briefly, the authors suggested that t he intertwin ing of collagen and de novo deposited elastin could lead to crimping of the collagen fibers, thus increasing compliance of the tissue [14] . In our study we observed an i ncrease in recruitment distribution parameters and in paraplegic bladders , while final slope was unchanged. T hese findings support the hypothesis that the increase in distensibility observed in bladder ECM from SCI animals as compared to controls and shams is not necessarily a result of changing fiber stiffness or quantity, but rather a change in configuration of the remodeled fiber network. The lack of differences in the distribution shape parameters and further suggest that the recruitment distribution does not change shape, but scales rightward, thus increasing and without affecting the shape of the distribution. To further investigate this hypothesis, we performed several imaging analyses on the bladder tissue collected from paraplegic and control animals. On the one hand, we observed no significant fibrosis, nor significant morphological di fferences in the collagen network between control or paraplegic bladders overall ( Figure 4. 4 ) . Additionally, preliminary image analysis showed no difference s in collagen or cellular area fractions between groups (data not shown) . On the other hand, Figure 4. 4 highlights some qualitative differences between groups: bladders from p araplegic animals seemed to have higher amounts of visible elastin fibers throughout the tissue . 105 Furthermore, we have obs erved qualitative examples of highly localized remodeling. For example, Figure 4. 5 on the left shows an area of significant localized collagen remodeling in the detrusor of a SCI animal, and on the right shows a highly localized increase in elastin content in the tissue of a paraplegic animal . This finding is also in agreement with previous work showing that SCI leads to creation of de novo elastin fibers in rat bladders 3 - 4 weeks post - injury [14] , and an increase in elastin/collagen ratio at 1.5, 3, 6, and 10 weeks post injury compared to controls [31] . Our analysis of planar histological sections ( Figure 4. 6 ) shows that in controls, collagen fibers in the lamina propria region appear thicker and more randomly oriented, whereas fibers between smooth muscle bundles appear thinner and wavier with orientations generally aligned with the direction of the muscle. It should be reiterated that these images are from decellularized samples, and areas referred to as muscle are regions where muscles were present prior to decellularization. In the 1 - week paraplegic bladders, the collagen morphology appears starkly different from controls. Fibers generally appeared the sa me between the lamina propria and detrusor regions in the 1 - week paraplegic samples. When comparing the detrusor region of controls and 1 - week paraplegic, paraplegic fibers appear highly coiled, but with overall lower density of fibers than controls. Orien tation analysis ( Figure 4. 7 ) reveals addition al information in terms of remodeling of the ECM. When weighting by coherency, which is heavily impacted by orientations of previously muscular regions, the lamina propria shows mostly isotropic orientation in c ontrols, but pronounced longitudinal orientation in 1 - week paraplegic. When weighting by the product of energy and pixel intensity, which highlights collagenous regions and lessens the impact of previously muscular regions, the lamina propria shows even mo re isotropic distribution in controls, and a less pronounced but still preferential direction in the longitudinal direction for 1 - week paraplegic. When looking in the detrusor region, controls show preferential orientation in 106 the longitudinal direction for both weightings. However, 1 - week paraplegic samples show a high degree of bi - directional orientation with coherency weighting, but similar longitudinal preferential orientation to controls when weighting by the product of energy and pixel intensity. These results suggest that healthy rat bladders have randomly oriented collagen fibers in the lamina propria, a longitudinal preferential orientation of smooth muscle bundles in the detrusor, as well as intramuscular collagen fibers oriented similarly. Addition ally, these results suggest that SCI in the short - term causes remodeling that leads to longitudinal preferential orientation of collagen fibers, and a bimodal distribution of smooth muscle bundles in the longitudinal and circumferential directions. These r esults are largely in agreement with previously published smooth muscle orientation distributions in healthy and SCI rat bladders [22] . We also observed some changes in the gross geometry of the bladder, both associated with su rgery as well as with tissue treatment (i.e., decellularization). Figure 4. 3 suggest s that long - term SCI leads to significant remodeling that results in an increase in bladder capacity compared to controls. We also observed an unexpected significant increa se in bladder diameter between sham and control animals . A possible explanation for this is that the sham surgery may induce high levels of stress or anxiety in the animals , leading to bladder dysfunction. It has been shown previously that social stress ca n lead to altered micturition patterns and bladder capacity in mice which could lead to bladder remodeling [154] . The bladder circumference also increases significantly after the decellularization process. As smooth muscle is intertwined with collagen fibers [86] , it is expected that removing smooth muscle cells w ould alter the zero - load reference state of the bladder ECM. Moreover, choice of reference configuration can significantly affect evaluated mechanical properties of soft t issues [14] . This highlights the importance of considering the impact of reference configuration on reported mechanical properties. This is especially vital in 107 the field of tissue engineering, where it is desired for tissue en gineering scaffolds to replicate mechanical functions of the native tissue ECM [155] . When designing scaffolds, it is important to consider whether to match mechanical properties based on pre or post decellularization reference configuration. Finally, we report for the first time the existence of a residual stress distribution with the bla dder wall. The o pening angle tests we performed ( Figure 4. 10 ) show that both control and paraplegic bladder ECM have a positive value of opening angle 90 minutes after the cut. These results also show that the opening angle increases with time after the cut, but is significantly different than 0 even at the time of cut for all sample . At the same time, p reliminary tests of control intact tissue showed no opening angle (data not shown) . This suggests that the rat bladder ECM may have a residual stress distribution which can be appreciated after decellularization . 4.5 Limitations A potential limitation of the compari sons between this study and previously published studies on SCI rat bladders is that differences in surgical protocol (i.e., location of transection) and post - operative care protocol (i.e., frequency of manual bladder voiding) between studies could be conf ounding factors. Bladder samples for mechanical testing were frozen prior to decellularization and testing. Testing tissue fresh is preferred, but not always logistically possible. Several studies have evaluated the effect of freezing tissue using similar protocols to this study and found little impact on mechanical response [156] . Similarly , we found no evidence of compromised extracellular matrix components after decellularization, supported by previous studies that have used similar decellularization methods [14,62,147] . Because we are using our parameter estimates comparatively within the 108 study on samples subjected to identical protocols, any small alterations in ECM integrity would be universal, likely mitigating the effect on the significant differences observed. U niaxial testing was performed in this study, whereas biaxial testing would have allowed closer comparison of mechanical data from previously published studies on the SCI rat bladder [30,31] , and allow for anisotropic behavior to be evaluated. Because of the drastic differences observed in fiber morphology and orientation in short - term SCI in this study, it is necessary to perform similar e valuations on long - term SCI tissue in the future, along with biaxial mechanical characterization. Additionally, some of the residual stress measured through opening angles could be due to swelling of the ECM during decellularization, as osmotic swelling ha s been shown to increase opening angles in other tissues [157] . While we were able to see a qualitative increase in elastin content with long - term SCI, it would be beneficial to quantify this in future studies to compare to previously reported increases in elastin/collagen ratio in the SCI rat bladde r [30,31] . The 1 - week paraplegic bladder samples used for planar histology were from rats that died unexpectedly. Because the cause of death is unknown, it is not clear whether the bladders represent normal 1 - week SCI rat bladders. Independently of this fact, the results shown highlight the extreme remodeling capabilities of the bladder in pathological c onditions. 4.6 Conclusions In this study we found that SCI rat bladder ECM 1 6 weeks post - injury is more compliant than healthy bladder ECM. This represents the longest time post - injury the mechanical behavior of the SCI rat bladder has been evaluated, to date. We have shown the extreme remodeling capabilities of the bladder in these pathological conditions. Constitutive modeling suggests that the increase in 109 compliance could be related to a change in recruitment distribution of collagen fibers during loadi ng, potentially facilitated by crimping of the ECM resulting from increased elastin fiber content , as previously postulated [14] . These findi ngs are important in terms of understanding the remodeling of the SCI bladder, which has implications for future treatment and care in long - term SCI. 110 APPENDIX 111 Table 4 . 1 Parameter estimates for the fiber recruitment and exponential continuum models for all samples [kPa] [kPa] [kPa] Control 149.4 6785.3 1.121 0.021 7.24 2.31 0.99 39.8 66.1 2381.9 1.123 0.023 6.88 2.62 0.75 30.7 111.1 2513.9 1.117 0.021 7.57 2.75 0.80 33.3 126.7 4176.0 1.127 0.021 9.57 3.51 0.99 31.9 87.0 2751.7 1.135 0.023 7.48 2.36 0.69 29.5 122.3 6954.0 1.196 0.037 6.53 2.31 3.27 14.5 Sham 111.9 2911.5 1.122 0.026 4.88 1.74 1.39 27.3 33.5 3982.9 1.135 0.029 4.47 1.39 0.90 29.8 55.1 2078.6 1.134 0.022 9.93 4.11 0.68 26.7 179.5 5192.8 1.108 0.025 3.72 1.19 1.72 36.3 79.0 9973.8 1.167 0.033 6.22 2.28 3.12 20.0 106.3 3611.1 1.130 0.019 10.66 3.47 0.62 34.5 78.5 3675.6 1.113 0.023 5.98 2.31 1.02 35.1 Paraplegic 19.8 4113.5 1.224 0.035 7.02 1.66 0.53 17.3 21.7 9030.0 1.228 0.035 5.60 1.01 0.63 19.6 46.8 4477.2 1.187 0.034 5.84 1.64 0.98 19.5 58.4 4337.4 1.130 0.026 5.86 2.05 1.01 31.0 51.9 8640.9 1.185 0.033 7.37 2.52 2.17 18.6 73.9 3010.8 1.130 0.024 6.48 2.21 0.77 30.5 115.9 13752.4 1.186 0.029 7.48 1.89 1.50 23.5 93.1 3251.2 1.140 0.026 5.46 1.52 0.90 27.3 112 CHAPTER 5 - CONCLUSIONS AND FUTURE WORK 5.1 Conclusions The work presented in this dissertation highlights some key aspects of bladder mechanics. We first compared the mechanical characteristics of human and pig bladders and found the differences appear to stem more from amorphous matrix and low - stress SMC behavior, wit h little difference between high - stress orthotropic behavior. This supports the use of the pig bladder ECM in tissue engineering of the human bladder, and more generally the use of the pig bladder as a model of the human bladder in the field of tissue mech anics . Thus, we decided to use porcine bladder tissue to investigate how swelling due to inflammatory response or urothelial disfunction can affect bladder mechanics. This is important considering it is commonly accepted that a ltered stress states in biolo gical tissue generally lead to remodeling. We have shown that osmotic swelling is a factor that can alter the stress state of the bladder , and may be a contributi ng factor in driving remodeling . This highlights the importance of maintaining healthy and fu nctioning urothelium. Finally , while our results support the use of porcine tissue as a model for the human bladder, this may not be possible for every study. For example , when studying enduring effect s of spinal cord injury (SCI) on bladder functionality , the use of a large animal model may be not feasible due to the expense and the time requirements. For this reason, we have employed a small animal (rat) model of SCI to show that long - term SCI leads to significant remodeling of the bladder wall that lead s to increased capacity and compliance. We have shown that the bladder remodels not only the amount of collagen, but also the morphology of the individual fibers and the direction of collagen fibers and SMC bundles. 113 5.2 Future work There is still much to l earn about the mechanics of the bladder. An important step in relating in vitro mechanical data to in vivo cytometric data is a better understanding of the effect of muscle contractions on the configuration of the ECM. Knowing that fiber realignment occurs during bladder filling [158] , and that contraction occurs after every filling cycle in a healthy bladder, it is possible that contraction plays a role in resetting the ECM configuration to its original state. In vitro mechanical testing of bladder tissue is generally performed with multiple loading and unloading cycle without contraction. Future work should address this question to determine whether preconditioned passive properties are comparable to post - contraction loading. W hile several studies have addressed the effect of SCI on the mechanics of the rat bladder, there are still gaps in this area of research. First, the viscoelastic behavior of the SCI rat bladder has been assessed in the short - term, but changes in viscoelast ic behavior in long - term SCI has yet to be determined. Additionally, voiding via manual compression is generally used in post - operative care for SCI rats . Clinically, different voiding techniques (i.e., manual compression, indwelling catheter, clean interm ittent catheterization) lead to different outcomes in terms of bladder health and function [159] . It would be beneficial to investigate the effect of different voiding techniques in SCI rats and evaluate how the bladder remodels in response to these different techniques. This would have clinical relevance as it could hig hlight reasons for differences in outcomes based on voiding technique. Finally , no study has investigated the role of location - specific behavior or swelling on bladder biomechanics in a pathological condition, such as SCI. A study that investigates locat ion - specific and swelling effect s in SCI using a large animal model of SCI is needed. 114 BIBLIOGRAPHY 115 BIBLIOGRAPHY [1] R. Cortivo, F. Pagano, G. Passerini, G. Abatangelo, I. Castellani, Elastin and Collagen in the Normal and Obstructed Urinary Bladder, Br. J. 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