Date 0-7639 '70“ 4! gm. Eur-M —" - :1?" 3': :3“ _-.., SE! 1 Ramses, .51 enime This is to certify that the thesis entitled THE STIFFNESS RESPONSE OF SEVERAL EXTERNAL FRACTURE FIXATION DEVICES presented by Mary Clare Verstraete has been accepted towards fulfillment of the requirements for M.S. degree in Mechanics W Major professor MaL 15 . 1984 MSU is an Affirmative Action/Equal Opportunity Institution I I 02‘in l .“., "— ‘fl‘vr 1V1£SI_J RETURNING MATERIALS: Place in book drop to LIBRARIES remove this checkout from n. your record. FINES will be charged if book is returned after the date stamped below. THE STIFFNESS RESPONSE OF SEVERAL EXTERNAL FRACTURE FIXATION DEVICES By Mary Clare Verstraete A THESIS Suhnitted to Michigan State University in partial fulfillment of the requjranents for the degree of MASTER.OF SCIENCE anr’anent of Metallurgy, Mechanics, and Laterial Science 1984 'IHESTIFFNESSRESPQBEOFSEVERAL mm FRACTIRE FIXATION IEVICES by Mary Clare Verstraete The purpose of this research was to study the stiffness response of several external fixateurs of varying geanetric designs. The fixateurs were applied to excised canine tibias and the systan subjected to an axial deflection. 'Ihe maximum stiffness of the systen was obtained fran the linear portion of the load/deflection curve. The results of these arperimental tests indicated that variations in geanetry greatly effect the stiffness response of the fixateur. The axial stiffness could be effectively increased by increasing the nunber of connecting bars, angling the f ixateur pins or using a bilateral configuration. An analytical analysis was initiated in an attanpt to provide a predictive n'odel for the various fixateurs. 'Ihe linear response of this undel did not imitate the nonlinear response of the experimental device. Hmrever, the results fran the analytical model accurately duplicated the trends in stiffness response associated with the various gecmetries. The author wishes to etptress' her deepest appreciation to the following people for making this phase of her graduate work possible: To Dr. Robert m. Soutas-Little, her major advisor, for his constant guidance and eucouraganent, and, must of all, for his invaluable friendship. To Dr. Wade 0. Brinker, for initiating interest in this project and for his valuable assistance. It: Sdiweizerische Arbeitsganeinschaft fur Osteosynthesefragen Fomdation, for their generous funding of this project. To Jane Walsh, for her support and priceless friaidship. To Robert E. Schaeffer, for his design and development of test equipment , and for his endless patience and harm friendship. To her family, especially her parents, for their understanding, encouragenent and support in her graduate work. ii ACKNOWLEDGMENTS . . . . . . LIST w mm C O O O O O LISTOFm .00... Section I. II. III. IV. INTRODUCTTON . . . . . SURVEY OF'LITERHTURE . EXPERIMENTAL METHODS . EXPERIMENTAL RESULTS . TABEE OF CONTENTS V3 ANALYTICAL METHODS AND.RESUDTS . . . . VI. CORRELATION OF RESUETS WI 0 mmION O O O O O O O O O O O O O O BIHOIW O O O O O O 0 iii Page ii iv vi 10 24 42 53 63 66 Figure 1. 2. 12. l3. 14. 15. 16. Original Kirschner Bone Potting Form. acne Pinning Form. LIST OF FIGIRES Sfl- ints O O O O O O O I NormalTestingArrangenent........ Perpendicular Testing Arranganent. . . . . Unilateral Configurations. . . . . . . . . Bilateral Omfigurations . . . . . . . . . Typical Load-Deflection Curve. . . . . . . Stiffness Response 4.0 m Pins. . . . Stiffness Response 2.5 nm Pins. . . . Stiffness Response and Pin Size . . . Stiffness Reaponse 1/8 inch Pins. . . Stiffness Response 4.0m Pins. . . . Stiffness Response 2.5 nm Pins. . . . Stiffness Response and Pin Size . . . Stiffness Response with Varying Br Nuuber with Varying Bar Nunber with Varying Bar Nunber with Varying Bar Nunber with Varying Pin Nunber with Varying Pin Nunber with Varying Pin Nunber with Varying Bilateral Cmfiguration -4.0tunPins. . . . . . . . iv Page ll 14 16 17 B 25 26 27 28 30 31 32 36 Figure Page 17 . Stiffness Response with Varying Bilateral Cmfiguratim-2.5nmPins............... 37 18. Suunary of Stiffness with Varying Cmfigurations . . . . 41 19 . Node and Elenent Nunbering for Unilateral Configurations..................... 44 20 . Node and Element Nunber ing for Bilateral Cmfigurations..................... 46 21. LinearResponseofAmlyticalModel........... 55 22. Amlyticalvs.ExperimentalResponse-meBar. . . . . 59 23. Analytical vs. Experimental Response - Tm Bars. . . . . 60 24. Aralytioal vs. Experimental Response - 'IWo Pins. . . . . 61 25. Analytical vs. Experimental Response - Three Pins. . . . 62' LIST OF MES Table 1. milateralmtaforthe4.0mPins........ 2. Unilateral mta for the 2.5mPins. . . . . . . . 3. Unilateral Data for the 1/8 inch (3.175 nm) Pins . 4. Bilateral Data for the «1.0um ............ 5. BilateralDataforthe2.5nmPins........ 6. Bilateral mta for the 1/8 inch (3.175 nm) Pins. . 7.BmePlatelhta.................. 8. Parameters Used in Ton-Dimensional Finite Element 9. Parameters Used in Wee-Dimensional Finite Elanent 10. Unilateral rats from the Analytical Model. . . . . ll. BilateralmtafrcmtheAnalyticalModel..... 12. unilateral Stiffness Data - Amlytiml vs. Dcperm‘ental... l3. Bilateral Stiffness mta - Analytical vs. Emerinental................... vi Page 33 35 39 39 39. 4o 45 4'7 49 51 56 57 I . INTRODLEI‘ION For years, the treatment of long bone fractures has utilized numerous methods and devices , but the develcpnent of any new device requires an attensive understanding of the mechanical behavior of the corpcnents of the instrument. 'nne present acceptance of bianechanical engineering principles in the field of crthopaedics, and the increased knowledge of fracture healing have nade this understanding an easier task to accarplish. 'Ihe conbined knowledge of surgeons and engineers has led to the developnnent of a greater number of orthopaedic appliances for use in fracture reduction and trams nanagenent. One such application is the external bone fixation Mice. First invented by Clayton Parkhill, 31.0., in 1897 (14), the external fixateur has undergone nutterous inprovenents and nodif ications over the years. Useful for both hnmans and animals, the ecternal fixateur allows for soft tissue nanagenent as well as rigid skeletal fixation. The fixateur applied etternally also permits freehn of joint notion above and below the fracture site which encourages circulation and minimizes muscle and bone atrophy. This type of chvice has been used in a variety of anatonical locations including the fenur, tibia, humercus, ulna, radius, and pelvis. The etternal fixateur my be euplcyed for the treatment of open fractures, infected nonunions , stabilization of bone fragments, csteotcmies, and even for limb lengthening. Smh versatility results front the nmerous geanetrical configurations available for these devices. 'Ihe form of fixation applied depends largely on the location of the fracture, the nature of the disunion, and the amount of soft tissue involvement. 'Ihe design of any erternal fracture fixation mice must satisfy several criteria. 'lhe application of the fixateur should be easily nanaged and allow for later adjustment should it becane necessary. The naterials used in the frame must be bioccmpatible with the biological enviromnent they are subjected to, and nanagenent of soft tissue injuries should be sinple and unobstructed. Dn'ability and variability are important properties of the fixateur, required to handle nunercus types of fractures in nany different locations. If possible, early patient nobility is also desired. The trust n'nportant criterion though is high rigidity, or stiffness, of the overall fixateur systen. During rehabilitation of the patient, the external fixateur is subjected to various loading conditions and these mat be taken into consideration in fixateur @ign and pin placenent. 'lhe fixateur should be able to prevent excessive tensile forces at the fracture site causing disunion, and yet allow the transmission of canpressive forces across the fracture thereby pratnoting healing. 'lhis an only be accanplished by varying fixatuer geonnetry for different types of fractures. For trams nanagenent in long bone fractures , fixateur configurations can be catagorized into five geanetric groups - unilateral, bilateral, qmdralateral, triangular, and circular. 'nnese five groups are based upon the number of connecting bars and the shape of the resultant frame structure. The mechanical behavior of these @vices varies widely. therefore, ectensive erperimental work is needed to cbtermine the nechaniml properties of each fixateur design. Although such experimental testing is important and highly effective in evaluating the nechanical performance of each device studied, it suffers fron many disadvantages. The testing procedure itself is ettrenely time consuming since the number of geonetrical variables is large. These include the number and location of the transfixing pins , their diameter and the direction of orientation. The diameter of the connecting bars can also be varied, as well as their number, arrangenent, and the distance located fron the axis of the bone. Several non-geonetric paranneters an also be altered, including pin and frame naterial and the method of loading. Simple erperimental methods provide no information an the internal stresses in each connponent in the systen or at the canplex pin-bone interface. . 'Iherefore, based on known mechanical parameters and basic structural analysis, theoretical undels have been developed to predict the behavior of such external fracture fixation @vices. 'lhese nodels allow rapid study of the effects of variation of the nunerous prameters. Finite elenent mflnods and canputer simulation have been utilized to provide overall stiffness data as well as &ta on the internal stresses developed in the systen. II. SURVEY OF LI‘ERATERE Since its first application in 1894, the erternal fixateur has been modified and utilized in numerous ways and nany published reports have discussed its behavior. In 1897, Parkhill, himself, reported on its use in 14 hunan cases (15). Shortly after, in 1902, Dr. Albin Lambotte of Antwerp, Belgian independantly (heigned and successfully installed an external fixateur. In cbcnmnenting his use of the eternal fixation device, Lambotte states: "In nunerous cases, I could avoid, thanks to the fixateur, anputations that seened inevitable." (13) A half-frame fixateur was brought into clinical use in 1937 by a Pennsylvania veternarian, Otto Stader (l7). 'lhe unilateral fixateur design has been in constant use in veternary medicine since that time. The enternal fixateur was further developed by Roger Anderson, M.D., however, his tbsign lacked the ability to adapt to different types of fractures or to provide a variety of configurations (1). In veternary practice, in the mid 1940's, the Kirsdnners redesigned the clanps utilized by Anderson and the Kirschner splint became the most canmmly used fixateur for aninals. 'Ihis popular splint used two pins clanped securely to a single connecting bar. For those ases where additional stiffness was needed, a second bar was added (Figure 1), but this configuration tended to be extremely bulky and ecpensive. In hutan medicine, nany surgeons altered the ecisting designs to suit their needs. During the second World var, a Swiss surgeon, Raoul Hoffmann, nodified and used Lambotte's fixateur. 'lhe hardaare for this Original Kirschner Splints FIGIRE 1. new fixateur became knowm as the Hoffirann device. Frequent pin track infections and fracture disunions during the war, resulting fron most types of etternal fixation, discouraged the use of the fixateur for treatment of fractures. The trial of the Haynes and Anderson fixateurs, during the same period, exposed the need for an increased study of the nechanical basis for erternal fixation. Initial investigations into the engineering concepts of eternal fixation renewed interest in this form of treatment. Preliminary bionechanical analysis of several fixateurs led to the realization that the behavior of each device (hpended greatly on the design and method of application. The Hoffmann half-frame was subjected to much experimentation in the early 1970's. J. Vidal was one of the first to study and modify this fixateur. With his addition of a qnadralateral frame and conpressicn screws , the device became known as the Boffmann-Vidal apparatus and is now widely used in nunerous orthopaedic applications. F. whey, R. murgois, and M. Donkerwinkle studied the prqnerties of the Hoffnann half-frame using a mathenatical mdel developed on the basis of clinical observation (6). Upon etamination of the numbers of pins used and their placeoent, they concluded that at least two pins must be used in each bone clanp, the clamps should be tightened as close to the bone as clinically possible and that two bars more than doubled the rigidity of the systen. Further, their etperimental analysis showed conplete agreenent with these statenents. 'Ihe Hoffmann-Vidal quadralateral fixateur was analyzed by E.Y. Chao, Ph.D., B.T. Briggs, M.D., and M.'I‘. McCoy, no. ming both ecperimental and theoretical methods in an attenpt to qnantitate the basic mechanical properties of the fixateur (8). ‘Ihe etperimental analysis was performed with 21 varying configurations and utilized five static loading conditions . In studying the fixateur stiffness at the fracture site, in the various loading nodes , they found anterior-posterior bending to have the lowest value. The overall stiffness of the fixateur could be increased by increasing the nunber of pins or the pin diameter. Decreasing the pin length, moving the connecting bar closer to the bone, or decreasing the pin separation in each sequent also helped to increase the fixateur rigidity. ‘Ihe same group performed theoretical analyses ming a two-dimensional finite elenent nodel of the device. Significant disagreement was seen between the theoretical and erperimental results. 'Ihis was claimed to be due to the fact that a two-dimensional nodal was being med to eramine a three-dimensional systen. Ghana and Briggs (4), and Chao and K. An (7), also analyzed the Hoffman-Vidal apparatm. Besides altering the geonetrical parameters of the systen, which resulted in the same conclmions as before, they varied the naterials med for the fixatenr conponents. Of the two naterials tested, stainless steel and titaniun, it was reported that me of titaniun pins and titaniun frames decreased the overall stiffness 41%. 'Ihis would be ecpected since titaniun (E = 6 16.5 x 10 psi) has an elastic modulus 41% lower than stainless steel (E = 28.0 x 106 psi). However, if stainless steel pins are med with a titaniun frame, reduction in rigidity is miniml and the overall weight of the fixateur is decreased considerably. In the mid 1970's G. Bierholzer and A. Chernovitz attenpted to specify by fracture type the tubular systen of the ASIF (Association for the Study of Internal Fixation) (12). Type I (unilateral) was prcposed for me in an cpen fracture or closed couninuted fracture of the thigh. A Type II fixateur (bilateral) was suggested for fractures with bony support at the fracture site. To bridge a large distance or to fix a snail netaphyseal fragment, they recounended the Type III (triangular) design. F. Behrens and K. Searls also analyzed the ASIF frame (Type II), reporting on the mechanical and clinical shortconings of the bilateral design for tibial fractures (3). Despite its popularity, they found that full pins, also called through and through, can often cause conpartnnent syndrones and injuries to the anterior tibial artery. mpalenent of mmcle is inevitable in this case and, nany times, this leads to a permanant decrease in ankle motion. Behrens and Searls also noted that the two connecting bars often interfere with trauma managenent and that full weight hearing was rarely allowed until conplete healing had occurred. 'Ihey concluded that nost of these shortconing could be overcone with the proper unilateral msign . The Oxford fixateur utilizes a unilateral configuration in an attenpt to overcone the disadvantages of the bilateral designs. In 1979, M. Evans, J. Kenwright, and K. Tanner examined the factors that contribute to the deflection of Cldford systen (11). They fournd that the bending of the pins could contribute to over 1/2 the total deflection. Deformation of the bone at the site of pin insertion also added to the total axial deflection. Many authors have analyzed this highly couple-r pin-bone interface region. Since little ecperimental data has been aquired concerning this area, theoretical nodels have been developed to analyze the stress distribution at the pin insertion site. mac and An mveloped such a nodel utilizing finite element methods and conputer simulation (7). Based on this three-dimensional nodal, the highest conpressive stresses were found to be lomted at the outer portion of the bone cortex directly above the pin. Ciao and An also applied cyclic bending loads to fixater pins of various diameters to deternnine their fatigue properties. The larger pins were found to have both higher yield strengths and higher fatigue strengths under similar loading nodes. The larger diameter pins were shown to increase the systen's rigidity, however, Chao and An suggested that they may also increase the stress concentration in the bone near the pin insertion site. Most of the previously mentioned fixateur designs are med solely for harm applications. In veternary practice, the most commly med configuration is the unilateral msign. Wade Brinker, D.V.M., and Gretchen Flo, D.V.M., reported on its clinical use in 1975 (5). 'lhey established a nnodified procedure utilizing two pins in each bone sequent connected by a single bar. 'lhey also found this fixateur design to be ettrenely meful in conjunction with other methods of fixation including intramedulary pins, lag screws, and orthopaedic wire. In 1982, Erick Egger, D.V.M., investigated the static strength of six different configurations utilizing the Kirschner equipnent (10). He found the cbuble clamp configuration (original Kirschner design) to be the weakest of all those tested. The triangular configuration was found to be the strongest design, yet its clinical use is limited by its obstruction of soft tissue injuries . III. EXPERIMENTAL ME'H-IODS In order to study the conpressive strength of the fixateur, in vitro studies were carried out on fresh canine tibial bones. The bones were frozen innnediately after renoval fron the animal and stored until testing could be performed. Before testing, each tibia was placed in a bath of warm water until conpletely thawed. If the bone was not conpletely thawed before potting, a pocket of moisture would fornn aronnd the bone ends and allow unwanted notion during testing. All soft tissues were rennoved fron the proximal and distal ends and small nails were inserted radially around these ends to aid in gripping. The articulating surfaces were allowed to dry slightly, since the potting naterial would nnot adnere to moist surfaces. the potting substance, Devcon Plastic Stee1* (SF), was formed by mixing 3 parts epoxy with two mrts hardener until a soft putty resulted. 'lhis putty was placed into a plastic form and the proxinal end of the tibia enbedded into it. 'lhe axis of the bone could then be linedipperpendiculartothebaseand the distal end clanped to hold its position (Figure 2). After approrinately fifteen minutes, the putty had harnhned sufficiently enough that the potting form could be inverted and the distal end of the bone set in the same nanner. men ompletely hardened, the putty provided excellent gripping of the bone ends. *Devcon Corp., Denver, bass. 01923 10 11 FIGLRE 2. Bone Potting Form 12 ‘Ihm potted, the bone was clanped into a specially designed pinning form with the proxinnal end to the left and tubercsity pointing up. The fixateur pins could then be inserted into the shaft of the tibia. The pins tested were the 2.5 nm and the 4.0 nm Sythes Eternal Fixateur No. 395* and the 1/8 inch Kirschner Splint**. Pin guides were drilled so that all pins could be placed in the sane plane and at a constant angle to the axis of the bone. Pins were inserted into the bone at either 72.5° or 90° to nnidline. When the connecting bar is attached, any pins not in the sane plane tend to prestress both the bar itself and the other pins in the systen. ‘Ihm lined up, the guide was clanped to the pinning fornn to create a rigid systen. Four separate guides were drilled; two for the unilateral configurations and two for the bilateral configurations. The 2.5 nm pins required one guide while the 4.0 nm and 1/8 inch pins utilized another pin guide. The length of each bone sanple determined the pin size med. Bones neasuring 7.5 inches to 8.0 inches med the 2.5 nm pins and any bones longer than 8.0 inches med either the 4.0 nnnn pins or the 1/8 indn pin. 'Bne pins were inserted through the guide and into the shaft of the tibia ming a conbination low speed power drill/hand dnmk. 'Ihe drill was med to make the initial perforation and the hand chuck was med to conplete the pinning and to duplicate actual sugical procedure. Pins inserted solely by the power drill tended to loosen rapidly during testing. To minimize the drilling during the testing procedure, the naximun number of pins were inserted while the sannple was clanped to the *Synthes Ltd. (U.S.A.), P.O. Box 529, Wayne, PA “Kirschner, P.O. Box 459, Aberdeen, Maryland 21001 13 pinning guide. ‘Ihe connecting bar/tars were also attached while the bone was held fixed and the clanps were tightened securely. (Figure 3) 'Ihis rigid fornn reduces the geonnetric variables of the fixateur by keeping both the placenent of the pins and the distance fron the bone to the first connecting bar a constant between specimens. After all clannps were secured, the systen was renoved fron the pinning device and a 1/2 inch section of bone was cut away at a midpoint between the two center pins. 'Ihis was time to ensure that no contact occurred at the fracture, since fracture site compression tends to increase fixateur stiffness. Also, this amount approximates a condition of a narkedly connninuted fracture, one of the prinary mes for external fixation. To simulate actual joint motion, special grips were designed to allow the fixateur to bend in the direction of least resistance. 'Ihe ends of the grips med ball and socket joints to approximate in vivo nation. The testing nachine med was an Instron* servohydraulic naterials testing nachine. The actuator was nounted in the mper crosshead to reduce nechanical noise and vibration. Load and stroke data were monitored and stored on a Nicolet digital oscilloscope, coupled to a mini floppy disk drive that allowed for permanent data storage. For consistency in protocol, each fixateur configuration was con- pressed the sane distance at a constant displacennent rate, 0.01 inch/ sec. 'Ihe displacenent was then reversed to return the systen to its initial unloaded condition. A deflection of 0.2 inch (5.08 nnn) was chosen after ten consecutive tests were connpleted on the known weakest configuration. Maximun deflections tests started at 0.1 inch and *Model 1331, Instron Corp., Canton, Mass. 14 Enos ocscfim moon .m gun—H 15 were increased until the slightest plastic defornnation could be seen in any of the fixateur members after unloading. 'Ihe 0.2 inch was well below the point of plastic response. The test protooal began by filing any loose edges fron the potted ends of the bone and then inserting the sanple tightly into the grips. 'Ihe entire systen was then placed between the mper crosshead and the load cell mounted in the lower crosshead. Nent, the actuator was lowered until contact was nade between the grips and the test nachine. (Figure 4) A 'no-load' condition was established by nnonitoring the load trace on the oscilloscope. After this initial state was attained, a 35 mn mnera was placed perpendicular to the plane of the fixateur, at amrminately four feet fron the nachine. A series of three photographs were taken for each test run; one before the test was started, another when the actuator reached 0.2 inch and a third at the end of the unloading step. For the unilateral fixateurs, two tests were run for each configuration to ensure reproducibility. 'Ihe bilateral designs required four test runs for each configuration. No were run with the systen oriented in the test nachine as stated before and two were run with the plane of the fixateur oriented perpendicular to the franne of the nachine (Figure 5). These extra tests were performed to observe the motion of the fixateur perpendicular to the plane of the device. It was observed throughout the testing procedures that bending occurred only in the plane of the fixateur for the unilateral configurations. an the other hand, bending could be seen in planes both parallel and perpendicular to the plane of the fixteur for bilateral configurations. Testing of the l6 : E. ‘\ 1. Ill. ills; ii. «11.: Ills. tilt! Normal Tmting Arrangement FIGIRE 4. «safari . , 17 Perpendicular Testing Arrangenent FIGURE 5. 18 unilateral fixateur utilized ten separate configurations; three with a single connecting bar, six with two parallel connecting bars and one with two connecting bars oriented perpendicular to each other (Figure 6). The bilateral testing was performed on five separate configurations (Figure 7). For the sake of conparison, a small nunber of tests were run utilizing bone plates. These plates were attached to the bone after potting and then rennoved again so that a section of bone could be renoved at the midpoint of the shaft. The plate, either a 3.5 nnnnn ooad (112*) or a 4.5 nm nnarrow (mm, was then reattached and testing proceeded as before. After each series of runs, the specinen was rennoved fron'the nachine and the connfiguration was dnanged by carefully rennoving pins or by increasing or decreasing the nunber of bars. 'Ihe new systen was then replaced into the testing nachine and the conpression process repeated. Renoved pins and bars were checked for any signs of plastic defornnation, butnonewasseeninanyofthetestsrun. Aneffortwasnnadeto utilize new pins and connecting bars in each test series to avoid the effect of any fatigue properties. Due to expense and availability, though, a few tests were run ming previomly tested pins, but no variations in results occurred. Load and deflection data were collected as raw voltages on the Nicolet digital oscilloscope and stored on flqznpy disks for each test run. At the conpletion of each test series, the mta was recalled and the peak load on the sanple, corresponding to a conpression of 5.08 nun, was calculated and recorded. The data fronn the disk was then transferred to a conputer file and stored on a PDP 11/23 conputer for *Synthes Ltd. (U.S.A.), P.O. Box 529, Wayne, PA l9 FIGIRE 6. Unilateral Configurations '20 FIGLRE 6. (mt'd) 21 Bilateral Configurations FIGIRE 7. 22 later analysis. A conputer program was written to convert the data fron voltages to equivalent nechanical values, expressing tine-load-stroke as seconds-Newtons-millineters. This sane program was med to analyze the data and (htermine the naximun axial stiffness for the fixateur systen during conpression. The naximun stiffness was founnd by calculating the slope of the force/displacennent curve generated by the loading mta. The curve was analyzed by windowing a set of data, calculating the stiffness and then moving the window to the next data set and repeating the process. Each stiffness value was then conpared to the previom one calculated to obtain the naximun value. As shown in Figure 8, a typical loading curve is nonlinear, and naximun stiffness occurs in the initial portion of the curve. 258 838G868.“ Aden? . a go: 9.5 2053.9 I 5.00? (M) 3030: mm nsaa IV. ECPERIMENI'AL RESULTS Presentation and conparison of the results is difficult as fifteen different configurations were tested for each of three seperate pin sizes. These configurations will be grouped into unilateral (and bilateral categories for easier enamination. Within the unilateral category, pin size and nunber were varied, as well as the nunber of tars and bar-pin attachments. Figures 9 and 10 compare the variation of connecting bar nunber and manner of attachment for the unilateral configurations utilizing two pins in each bone segnent, for pin diameters of 4.0 mm and 2.5 nun, respectively. It can be seen fron these figures that an increase fron one to two bars does not greatly increase the stiffness if only the mid-pin is clamped. This procedure does not seen to have beneficial value. However, if all pins are clamped to the additional bar, the axial stiffness of the structure is increased by 195% for the 4.0 nun pin size and 100% for the 2.5 mm pin size. Figure 11 summarizes this trend and includes the 1/8 inch (3.175 mm) pin size mta. To assist in comparison with previom works, a single set of tests were performed on the two original Kirschner designs. (See Figure l) The naximun axial stiffnesses of these splints are shown on Figure 12, along with the other configurations utilizing two 1/8 indn (3.175 mm) Kirschner pins. Both original splints showed a lower stiffness than any of the modified msigns. 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HN.mm H5.hmH mo.mv m¢.m~H mam ¢ 25>: macmmflm sz_cmoq NH\m 25$: mgmmflm .2. cmog muxm umumpa mums 36 mfim .E. cé I 833.6350 Huh—3% 9.3.85 :33 mucommwm umocmmfim .3 95on 29:50:53 m e n N w . o 8 8. E s. \z r r. l L 3N m . m m M? r. H L n. in w [ w w L 8... 32:. E... a... M 8* 20.h<¢30_u200 ..< V. ANALYTICRL ME'IHOIB AND IESUL‘IS Tnough eXperiuental testing smplies necessary information on both the behavior of the fixateur and the reaction of the bone during axial camression, it suffers frcm a ntmtber of disadvantages. 'Ihe actual testing procedure is quite time consuming (he to the number of variables, both gearetric and nongeanetric, that can be altered in nmlerous canbinations. Also, this aperinentation mly provides stiffness and deflection data for analyzing the fixateur performance. 'Ihe procedure yields no data on the internal stresses each ccmponent is subjected to. For this reason, theoretical nodels are developed, often utilizing canputer simulation and finite elanent methods. Theoretical analysis for the previome described fixateur configurations was performed by utilizing the finite elelent program ANSYS (2). ‘Ihis canputer program allows for stamination of several classes of engineering problens with static, dynamic, elastic, plastic or creep analysis. The ANSYS program uses the rave-front direct solution approach for the systen of linear eqmticns developed by the netrix displacetent nethod. Results are adiieved with both high accuracy and a minimun of conputer time. For the problem at hand, a static analysis was utilized to solve for the displacalents and forces attained in the fixateur during axial conpression. All joints were considered rigid since the pins were clamped tightly to the connecting bar and firmly inserted into the bone by means of the hand chuck, the bone was calented into the potting 42 43 naterial and the pot set securely into the grips. For the unilateral configurations, a two-dinensional frame structure vas developed, as shown in Figure 19, since all elenents renain in the x—y plane throughout the testing procedure. A total of 30 nodes and 42 elenents nede up the configuration utilizing four pins and two connecting bars, each pin cbubly clanped. To ecamine the other geanetric designs, elenents were sinply dropped fran the nodel. 'l‘wc-dinensioml elastic beam elenents were used for each component of the systen. 'Ihis element allows for tension, conpression, and bending loadings. It has three degrees of freedan at each node: translations in the x and y direction and rotation about the z-axis. ‘Ihe carponent properties for the unilateral configurations are listed in no. 8 along with the element numbers associated with each. A three-dinensional frame structure vas Melcped for the bilateral configurations, since notion ‘38 observed in all three planes during testing. The mdel created is shown in Figure 20. The initial bilateral model consisted of a total of 24 nodes and 32 elenents representing three full transfixing pins (configuration #1). Again, elelents were simply renoved to analyze the various other gearetric chsigns. 'Ihree-dinensional elastic beam elements were used to model the structural canpcnents. 'Ihis type of elenent allows for six degrees of freedan: translations in the x, y, and 2 directions, as well as rotations about all three axes. The cmponent prcperties for the bilateral configurations and the elatent nunbers associated with each are given in Table 9. For both the two dinensional and three dinensional analyses, each elenent is (hfined by the location of its two endpoints, or nodes. 44 ‘14 32 30 13 22 16 42 3 . 12 23 so 41 ll 7 W29 40 10 22 29 39 2° 9 28 33 5 28 13 27 a 20 27 7 12 25 37 4 26 5 25 36 17 5 1a 25 35 . 2 Ll—G—m—eu 34 17 24 3 33 1 2 15 9 23 31 FIGIRE 19. Node and Elenent Nunbering for Unilateral Configurations Component 4mmLPins 2.5 Pins 1/8 inch Pins 4mm Bar 3/ 16 inch Bone Grip 45 IABLE 8. Parameters UBed in Two-Dunensional Finite Element Model Area 122 mm ter E [INS Elenent (m2) (um‘) (um) (xlosN/mnz) me clamped to two connecting bars. This graph denonstrates that the load varies linearly with the applied displacenent, regardless of whether the systen is in tension or conpression. As nentioned previously, this linear response permits the naximun stiffness to be calculated by dividing the naximun load by the peak deflection. Tables 12 and 13 canpare the stiffness values calculated frann the theoretical nodel with the naximun stiffnesses obtained from identical enperinental tests for several unilateral and bilateral configurations, respectively. 'Ihis representative group of values demonstrates the variability between the two nethods of analyses. For the unilateral configurations , the error between the theoretical and eiperinental stiffness values range fronn 0.4% to 41.2%. A greater range of error can be seen in the bilateral data. The minimun difference observed between the theoretical and experinental values ves 14.5%, while the naximun error shown was 265.7%. It should be noted here that the analytical nodels developed for analysis of the external fixateurs are only first apprau‘nations. 'Ihe decision to attennpt an analytical analysis vas node long after the etperinental testing had begun. 'Ihe theoretical nodels assune the bone segnents to be circular solid beams. Yet, in vivo, the bone segnent is actually a tube of cortical bone surrounding the nedullary cavity. ‘Ihe pins are inserted through a layer of contract bone, through the narrow cavity, essentially hollow, and then pierce the other layer of canpact bone. Since the effective pin length used in the analytial nodel, frcnn 55 06 38: 13.3% no 8:88,. 85a .N anom— 35 20.5ch A .1 k; I AAA A A AAAA [TUTT'IIrIIIIIIIITTT 3? QOOQI q i 3 3, 3 (n4) 333m imlnnsaa Bar'Number 1/8 inch Tho (all pins) M (nudhrfin) N e U" 5 5‘ (all pins) (mid-pin n fi 0 O One IAEEE 12. Pin‘Number MUG-b new» Much towns. wuss MOO-h NW9 56 Analytical Stiffness (N/nm) 237.01 181.26 115.79 66.77 59.39 47.79 46.44 42.22 35.12 194.27 148.35 95.73 48.11 43.43 34.59 35.92 33.14 28.03 42.87 39.84 37.74 unilateral Stiffness Data .Analytical vs. Experimental EXperimental Stiffness (Nthn 258.60 174.50 105.61 63.29 59.62 49.90 55.21 50.02 45.90 142.75 106.00 67.81 39.04 33.04 35.79 42.98 40.25 35.19 44.33 43.04 41.08 57 TABLE 13. Bilateral Stiffness Data .Analytical vs. Experimental configuration Analytical Experimental Stiffness Stiffness (Nflmm) (Nfimm) 2.51am 1 300.59 177.37 2 167.89 129.57 3 119.39 95.29 4 135.53 118.40 1 286.61 125.02 2 154.27 90.34 3 120.43 64.40 4 138.43 83.59 4.01nn 1 1244.29 340.27 2 715.35 253.97 3 607.09 179.20 4 644.49 262.27 1 1138.98 358.90 2 739.17 282.88 3 607.48 211.30 4 644.69 276.48 58 the connecting bar to the midpoint of the shaft of the bone, is not an exact representation of this actual condition, the axial and bending forces acting at the pin-bone interface are only apprecimations. Further investigations into a three-dinensional, solid elenent model of the bone is anticipated, but is beyond the scope of the current study. It has discovered during the testing that as the geanetry of the systen becane nore canplex, i.e., the number of pins or the number of bars is increased, the load-deformation curves becane nore nonlinear. 'Ihis is denonstrated in Figure 22 and 23 for the unilateral configurations. Figure 22 shows the load-(hfonnnation curves, fron both experinental and theoretical analyses, for the frame design utilizing four 2.5 nnn pins clanped to a single connecting bar. Figure 23 shows similar curves for a configuration utilizing the sane number of pins, but dnubly clamped to two connecting bars. It can easily be seen that the second curve deviates fronn the theoretical line to a greater entent than the first curve. ‘Ihe sane type of deviation an be seen in the bilateral configurations. Figure 24 shows the load-deformation reaponse of configuration #4, utilizing two 2.5 nm through and through pins, for both ecperinental and theoretical analyses. Figure 25 demonstrates a similar response for configuration #1, utilizing three 2.5 nun through and through pins. Agin it can be seen that as the geoletry of the systen becanes nore couplex, the experinental curve deviates frcm the linear response to a greater extent. 59 ".3 58 So u 888m Began .9 ”Guiana ..- $5lo 9.: 20:85 >1 us 2. 2953.13 oi ad ad. . . + . q a i 3 I..- ah ll :62. (N) 3030.1 mm nsaa s-s mumm 95. n $833 33% .o> Hungag .9 mg: 95 zofidro .7 we. 2. 2953.3 0.... ad ad - . - w :6 u a ! (n) 303m mm new 61 mesh 02. n 8888 Hughes .9 H83»? .3 @5on 9.5. 20:85 T we. 2. 20.85.18 0.... o." . ad - n - u g J a - (n) 3030: mm r1333 62 9.3 one»? n $833 385% .n> .303»? .3 an 95 20:85 >1 we. 2. 2953.9 3 as .3. — . u u u ad (u) 30qu mm nee VII. MGION As stated frequently in the literature, variation in the geonetric paraneters of the enternal fixation device has a great effect on the frame's stiffness response to any applied loading. ‘Ihe changes in axial stiffness caused by varying the configuration of the fixateurs enamined in this study closely follow the trends reported on by all previous authors. 'Ihe increase in pin size showed a definite effect on the rigidity of the fixation device, for both the unilateral and bilateral frames. An increase of as mmh as 187% was observed when the pin diameter was increased from 2.5 nun to 4.0 nm. For the unilateral designs, the relation between the pin nunber and the stiffness of the systen is highly dependent on the number of connecting bars utilized. If only a single connecting bar is to be used, increasing the nunber of pins perforating the bone does little to affect the rigidity of the frame. A higher stiffness response can be obtained, in the unilateral designs, without any increased soft tissue involvenent, by the addition of a second connecting bar, attached parallel to the first. ‘men this additional connecting bar is clanped solely to the mid-pin, the increase in stiffness is again mininel and therefore not profitable. However, if this second bar is securely clanped to every pin transfixing the bone, the stiffness of the fixateur increases greatly. 'Ihis arrangennent was shown to increase the rigidity of the systen by as mmh as 195% for the two pin arrangement. If an 63 64 even higher axial stiffness is required for fracture healing and a unilateral device is to be used, increasing the nunber of pins (bubly clanped to both connecting bars effectively increases the rigidity of the systen. Three pins raise the stiffness 44% and four pins increase the stiffness approximtely 102%. This advantage of increased rigidity must be weighed against the clinical shortconings created by the additional invasion of soft tissues, to arrive at the best fixateur frane configuration to suit the needs of the specific fracture type. The bilateral configurations showed a consistantly higher axial stiffness than the unilateral configurations tested. A naximun increase of 325% could be seen in the stiffness response of the bilateral designs when conpared to unilateral frames utilizing the sane number of pins. Within the bilateral category, it ves shown that by increasing the total number of full, or through and though pins, the axial stiffness of the fixateur can also be effectively increased. If two full transfixing pins are to be solely utilized in the bilateral frane, the axial stiffness of the systen can be increased apprecinetely 33% by inserting the mid-pin at an angle of 72.50 to the axis of the bone. Agin the increased stiffness factors not be conpared to the possible danage created by inserting the full fixation pins through the tissues and vessels not previously invaded by the unilateral chsigns. The ulitization of an analytical nodal can effectively decrease the tine and expense necessary for an experinental analysis. The finite elenent nodel used in this analysis accurately duplicated the trends observed fron the experinental testing. Varying the geonnetric paraneters in the connputer nodel produced similar variations in 65 stiffness as developed dlring experinentation. For both analyses, axial stiffness could be increased by increasing bar nunber or by increasing pin nunber, if two bars are used and all pins are doubly clamped, in the unilateral configurations, or by using one of the bilateral configurations. The ANSYS static analysis utilized in this study was shown to produce a linear response approxineting the linear portion of the load/deformation curve observed during the experinental testing. The stiffness response cbveloped by the static analysis nore closely represented the response of the elennentary fixateur designs. This was due to the fact that the erperinental load/deformation response becane nonlinear as the systen's geonetry bee-me nore connplex, i.e., the nunber of pins and/or bars are increased. In conclusion, it was (htemined that the analytical nodel developed in this study predicts the change in stiffness associated with a specific nodificntion of a fixateur's geon'etry. Therefore, any alteration in the configuration of an external fixation évice an be analyzed, quickly and with confidence, without the drawtncks of an ecperinental analysis. Although the nonlinearity of the fixateurs' stiffness responses have yet to analyzed, it is the subject of future studies to develop a predictive nodel to incorporate these prqnerties. 1. 10. BIBLICXZRAPHY Anderson, R., 'An Ambulatory Method of Treating Fractures of the Shaft of the Fenur," Surg. Gynecol. 0b., Vol. 62, pp. 865-873, 1936. ANSYS-Engineering Analysis Systen User's Manual, Swanson Analysis Systens, Inc., Houston, PA, 1979. Behrens, F., and K. Searls, "Unilateral Eternal Fixation Eperience with the ASIF 'Tubular' Frane," Current Concgjé of Eternal Fixation of Fractures, Ed. by H. tl'nthoff, pp. 177-183, 1982. Briggs, B.T., and E.Y. Chao, "The Mechanical Performance of the Standard Hoffmann-Vidal External Fixation Apparatus” , Journal Of Bone and Joint Surgery, Vol. 64-A, No. 4, pp. 566-573, 1982. Brinker, W.0., and G.L. Flo, “Principles and Application of External Skeletal Fixation," Yeternary Clinics of North America, Vol. 5, No. 2, pp. 197-207, 1975. Burny, F., R. Bourgois, and M. Donkerwolkcke, “Elastic Eternal Fixation: A Bionechanical Study of the Half-Frane," Congts in Eternal Fixation, Ed. by D. Seligson and M. Pcpe, pp. 67-78, 1982. Chao, E.Y., and K.N. An, 'Bionnechanicol Analysis of Eternal Fixation Devices for the Treatment of Open Bone Fractures,” Finite Elenents in Bionneghanics, Ed. by R.H. allagher, B.R. Sinon, and J.F. Gross, pp. 195-222, 1982. Chao, E.Y, B.T. Briggs, and M.T. McCoy, “'nneoretical and Eperimental Analysis of the Hoffman-Vidal Eternal Fixation System" Eternal Fixation - ‘Ihe Caring Statefi of the Art, Ed. by A.F. Brooker and C.C. Edwards, pp. 345-370, 1979. Chao, E.Y., and M.H. Pros, "The Mechanical Basis of Eternal Fixation," Concepts in Eternal Fixation, Ed. by D. Seligson and M.H. Pqne, pp. 13-39, 1981. Egger, E.L., "Static Strength Evaluation of Six Eternal Skeletal Fixation Configurations," Veternary Surg , Vol. 12, No. 3, pp. 130-136, 1983. 66 11. 12. 13. 14. 15. 16. 17. 67 Evans, M., J. Kenwright, and K. Tanner, "Analysis of Single-Sided Eternal Fracture Fixation,” Engineerng in Medicine, Vol. 8, No. 3, pp. 133-137, 1979. Hierholzer, G., and A. Chernowitz, "Eternal Fixation, Tubular ASIF Set," Current Cmggts of Eternal Fixation of Fractures, Ed. by He [hthOff’ We 75-82, 19820 Lambotte, A., "Chirurgie Operatoire des Fractures,” Paris, Masson et Cie, 1913. Parkhill, C., "A New Apparatus for the Fixation of Bones After Resection and in Fractures with a Tendency to Displacennent, " Transactions 0L the Anerican Surgical Association, Vol. 15, pp. 251-256, 1897. Parkhill, C., ”Further Observations Regarding the Use of the Bone Clanp in Ununited Fractures, Fractures with Malunion, and Recent Fractures with a Tendency to Displacement," Ann. Surg., Vol. 27, pp. 553-570, 1898. Pope, M.H., and M. Evans, "Design Considerations in Eternal Fixation," Concepts in Eternal Fixation, Ed. by D. Seligson and M. Pope, pp. 109-135, 1982. Stader, 0., "A Preliminary Announcenent of a New Method of Treating Fractures," North American Veternarian, Vol. 18, pp. 37-38, 1937. s In . 'llllall -‘II ill.l‘n‘ll’ LI"!