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Ir" ad?" _u .. no" 1" f. .w _ ‘. _. , ,.v.--' ‘ , v .ul 'V . _,-.~ .4! 0“ . . .. -, . . . .'fl . m- _ V ".1 .A—V‘ -: —,.ty,r’:Aw-_ L 3..- NO I ‘ ' llllllmlllllm 2* ?“ LIBRARY Michigan State ;_ University w This is to certify that the thesis entitled A METHOD FOR ANALYZING THREE-DIMENSIONAL HUMAN WRIST MOTION USING A JOINT COORDINATE SYSTEM presented by John Timothy Zipple has been accepted towards fulfillment of the requirements for MASTER'S degree in BIOb/IBCI‘IANICS Major professor Date //"?"g7 0-7639 MS U is an Affirmative Action/Equal Opportunity Institution PLACE IN RETURN BOX to remove this checkout trom your record. TO AVOID FINES return on or before date due. I DATE DUE DATE DUE DATE DUE 'I l 02 1% II MSU Is An Affirmative ActiorVEqual Opportunity Institution cWMa-D. ' A METHOD FOR ANALYZING THREE-DIMENSIONAL HUMAN WRIST MOTION USING A JOINT COORDINATE SYSTEM BY John Timothy Zipple A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Biomechanics College of Osteopathic Medicine 1989 LO 6% o in ABSTRACT The purpose of this study was to provide a methodology for the analysis of three dimensional motion of the human wrist using a three degrees-of—freedom model. A multiple camera video system was synchronized with a dynamic image video processor. Filmed at 60 hertz, the data were digitized automatically by a computer software program which calculated target centroids from pixel-perfect video images. The technique for analyzing motion involved a non-invasive, surface-targeting scheme on the wrist and forearm, using retro-reflective tape. Local segment coordinate systems were formed and wrist motion about a non-orthogonal coordinate system was calculated using Euler angles. Knowledge of wrist kinematics will be an important tool in the studies of human upper extremity function in activities of daily living (ADL’s). This study was supported in part by the National Foundation for Food and Pharmacological Packaging Research to model wrist action when opening child- resistant medicine caps. DED I CAT I ON I wish to dedicate this work to the three most important women in my life; to my wife Nancy, who tolerated my crazy schedules and obsessive-compulsive behavior, to my daughter Monica, who was born during the writing of this thesis and provided disruptions in my circadian rhythms and a reason to work hard to finish, and to my mother Joan K. Zipple who died in September of 1989, she gave me love and encouragement for 28 years and I miss her deeply. ii ACKNOWLEDGEMENT I wish to thank the following individuals for their generous support and sharing of knowledge that made this work possible. First, to my teachers and advisors: Robert Soutas-Little PhD., Roger Haut PhD., Herbert (Mac) Reynolds PhD., Robert Hubbard PhD., James Rechtien D.O., PhD, and Dianne Ulibarri PhD., thanks for giving me a piece of your minds. Secondly, to the secretaries: Sharon Husch, LeAnn Slicer, and Brenda Robinson, thanks for keeping me on schedule and for "showing me the ropes". Finally, thanks to Cliff Beckett, my technical advisor , and to the biomechanics students too numerous to mention, I learned as much from your wealth of ideas as I did from my courses. iii TABLE OF CONTENTS LIST OF TABLES LIST OF FIGURES INTRODUCTION REVIEW OF LITERATURE METHODOLOGY: DEVELOPMENT OF THE CALIBRATION STRUCTURE TARGETING SCHEME DEFINITION OF JOINT COORDINATE SYSTEM EXPERIMENTAL PROTOCOL ANALYTICAL METHODS RESULTS DISCUSSION CONCLUSIONS APPENDIX BIBLIOGRAPHY GENERAL REFERENCES iv Page 11. 15. 15. 17. 22. 32. 50. 55. 59. 62. 65. Table 1: Table 2: Table 3: LIST OF TABLES Three-dimensional Position Data Active Range of Motion of Three Degree-of—Freedom Wrist Model Previously Reported Ranges of Motion Page 23. 51. 53. Figure Figure Figure Figure Figure Figure Figure Figure 8 Figure Figure Figure Figure Figure Figure Figure Figure Figure \ImU'l 10: 11: 12: 13: 14: 15: 16: 17: TABLE OF FIGURES Motions About the Two Wrist Axes Target Fabrication Materials The Calibration Structure Targeting Scheme Camera Positioning Wrist Triads Non-orthogonal Coordinate System Supination and Pronation Superimposed Tracings of all Frames of Circumduction (Trial 1) Superimposed Tracings of Every Tenth Frame of Circumduction (Trial 2) Circumduction Position Data By Percentage of Time Interval Flexion/Extension Position Data By Percentage of Time Interval Radial/Ulnar Deviation Position Data By Percentage of Time Interval Accesory Hand Triad (4-7-8) Angle Displacement Plots for Circumduction (Trial 1) Angle Displacement Plots for Circumduction (Trial 2) Angle Displacement Plots for Flexion/Entension (Trial 1) vi Page 5. 12. 13. 16. 20. 25. 29. 30. 33. 34. 35. 36. 37. 38. 40. 41. 42. Figure Figure Figure Figure Figure Figure Figure 18: 19: 20: 21: 22: 23: 24: Angle Displacement Plots for Flexion/Extension (Trial 2) Angle Displacement Plots for Radial/Ulnar Deviation (Trial 1) Angle Displacement Plots for Radial/Ulnar Deviation (Trial 2) Neutral Joint Angle Curves Flexion-extension Displacement Angle Plot for Circumduction (Trial 1) Radial-ulnar Deviation Displacement Angle Plot for Circumduction (Trial 1) Supination-pronation Displacement Angle Plot for Circumduction (Trial 2) vii 43. 44. 45. 46. 47. 48. 49. INTRODUCTION The wrist, or carpus, is a deformable anatomic entity composed of eight small carpal bones (scaphoid, lunate, triquetrum, pisiform, hamate, capitate, trapezium, and trapezoid) and the surrounding supportive structures. These soft tissue structures include the tendons that cross and/or attach within the carpus, and those ligamentous structures that connect the carpal bones to each other and to the bony elements of the hand and forearm. The wrist functions both kinetically by transmitting forces from the hand to the forearm and from the forearm to the hand, and kinematically by allowing changes in the location and orientation of the hand relative to the forearm (Taleisnik, 1985). In order to understand this complex joint, the wrist was modeled as an unknown mechanism connected between two rigid bodies: the hand and the forearm. In the joint kinematic analysis of three- dimensional motion between rigid bodies, it is necessary to obtain the position history of a minimum of three non- colinear points. Therefore, a reliable experimental apparatus is required to continuously monitor the positions of these non-colinear points in the rigid bodies. By setting up local coordinate systems on the hand and forearm 2 and by using Euler angles (Goldstein, 1960) to analyze the motions between the two rigid body segments, this study provided a reliable way of capturing human wrist kinematics. The relative position and attitude of body segments connected by an anatomical joint may be measured by a variety of methods. Various investigators have used stereoscopic and plain roentgenograms (Brumbaugh, Crowninshield, Blair, & Andrews, 1982; Bryce, 1896), plaster molds and dissections, still and high speed cine photography (Carr, 1989; Chao & Morrey, 1978; Grood & Suntay, 1983; Soutas-Little, Beavis, Verstraete, & Markus, 1987), and sonic digitizers, using a range of two to six degrees-of- freedom modeling systems. Since the complex motions of the human wrist occur in three—dimensions, the data in this study were collected on the Sun-4 Motion Analysis System, using a three-camera, video-synchronized set-up. This system has an automated digitization software program, which decreased the incidence of human error and sped up data analysis. REVIEW OF L I TERATURE A complete understanding of wrist joint kinetics and kinematics is necessary for: an objective analysis of human wrist function during activities of daily living (ADL’s), for comparison of endoprosthetic joint replacements, and for diagnosis of traumatic or pathologic joint disorders. In defining two-dimensional range of motion of the wrist, various authors (DeBrunner, 1982; Heck, Hendryson, & Rowe, 1965; Hoppenfeld, 1976; Polley & Hunter, 1978) have reported different values. These normal (average) ranges of motion were based on clinical measurements of wrist motion using a standard goniometer (a protractor with two extended arms). Although triaxial electrogoniometers provide three dimensional rotation measurements, the accuracy of these techniques needed to be verified (Chao & Morrey, 1978). There was a possibility of human error introduced in these two techniques of motion measurement, depending on placement and/or fixation of the goniometer to the body (Chao, 1980). The movements included in Circumduction of the wrist, which were analyzed for this work, were defined by Kapandji (1985) as the combination of the movements of flexion, extension, adduction, and abduction. The motions take place simultaneously about the two axes of the wrist in anatomical 4 position. The transverse axis (AA’) and the antero- posterior axis (BB’) of the wrist are shown in Figure 1 and the definitions of the individual motions of the wrist are as follows; 1. Flexion (arrow 1): the ventral (palmar) surface of the hand moves towards the ventral aspect of the forearm. 2. Extension (arrow 2): the dorsal (back) surface of the hand moves towards the dorsal aspect of the forearm. 3. Ulnar deviation or adduction (arrow 3): the hand moves towards the axis of the body and its medial (ulnar) border forms an obtuse angle with the ulnar bone of the forearm. 4. Radial deviation or abduction (arrow 4): the hand moves away from the axis of the body and its lateral (radial) border forms and obtuse angle with the radial bone of the forearm. 5. Circumduction: the hand moves in a conical path with apex at the wrist as all four of the previous motions are combined. Early functional analysis of carpal bone complex modeling resulted in several conceptual types. In a model by Fick (1910), the proximal and distal row of carpal bones, each as a fixed group were thought to rotate around a fixed axis in both flexion and deviation of the hand. In a study by Gilford, Bolton, and Lambrinudi (1943), they proposed A EXTENSION FLEXION ' . . . |u\ \“ “"~ / 2 1 Al I B RADIAL DEVIATION Figure 1: Motions About the Two Wrist Axes 6 that the wrist joint performed as a system of three longitudinal chains of which the capitate-lunate-radius chain formed the central part. Contrary to the fixed row concept, the longitudinal chain concept stimulated synchronous movement of the carpal bones during flexion, explained through the actions of the scaphoid, which bridges the proximal and distal bones in the central chain (Gilford et al., 1943). In a study by DeLange, VanLeeuwen, Kauer, and Huiskes (1984), the authors attempted to obtain kinematic information about the individual carpal bones during flexion of the hand of one human specimen. Using a roentgen stereophotogrammetric system, DeLange et al. proposed to clear up the discrepancies between the fixed row and the longitudinal chain models. DeLange et al. (1984) stated that the distal carpal row performed nearly the same flexion excursions during flexion and extension and therefore can be approximated as a fixed row concept. The proximal carpal bones however showed different flexion angles which was contrary to the fixed row concept. Secondly, they found that both carpal rows moved synchronously and uniformly, supporting the longitudinal chain concept of Fick (1910). The contributions of the intercarpal and radiocarpal joints to the total are of flexion differ in the three longitudinal chains: radius-scaphoid-trapezoid (R-S-T), radius-lunate-capitate (R-L-C), and ulna-triquetrum-hamate 7 (U-T-H) (DeLange et al., 1984). It was concluded by DeLange et al. that for the medial (U-T—H) as well as for the lateral (R-S-T) chain, the radiocarpal joint contributed most to the total are of flexion. In the central chain, this was also true for the intercarpal joint. Hence, treatments of the proximal and distal carpal rows as fixed units appeared incorrect. Investigations by Volz, Lieb and Benjamin (1980) and Youm and Flatt (1980) found different results from DeLange et al. (1984) when comparing carpal movement. While both studies found that both the radiocarpal and intercarpal joints contributed to all phases of flexion-extension motion of the wrist, the contributions of the proximal and distal carpal rows to radial and ulnar deviations were found to be different. Volz et al. (1980) stated that with radial and ulnar deviation, the proximal and distal rows moved in opposite directions with the distal row being displaced toward the direction of the hand deviation. Youm and McMurty (1978) found no proximal carpal row movement with radial deviation, while ulnar deviation resulted in motion of both the intercarpal and the radiocarpal joints. In another anatomical joint model proposed by Sommer and Miller (1980), the authors used the optimization technique to estimate the separation of, and the angle between the two axes of a universal joint with skew-oblique revolutes as a biomechanical wrist model. 8 In wrist analysis, there was confusion surrounding the location of the center of rotation for radial and ulnar deviation of the hand relative to the forearm in subjects with non-pathologic wrists. Kapandji (1985) stated that this center of rotation lies between the lunate and the capitate, where Volz et al. (1980) contended that it remained in the head of the capitate. Wright (1935) stated that the center is in the head of the capitate for radial deviation and in the waist or neck of the capitate during ulnar deviation. The center of rotation for flexion and extension motion of the wrist is also controversial. Kapandji (1985) believed that there were two parallel and closely spaced axes of rotation located in the radiocarpal and midcarpal joints. Volz et al. (1980) and MacConaill (1941) each stated that there was a single axis of rotation that remained in the head of the capitate. Wright (1935) also believed that the center of the rotation was located in the head of the capitate during flexion, but stated that for extension, the center lies at the intercarpal joint. With the advancements in the field of knowledge of the biomechanics of the wrist, several authors have attempted to use certain hand-wrist parameters to diagnose internal disease or derangement. Youm and Flatt (1980) believed that the carpal height (the distance from the base of the third metacarpal to distal articular surface of the radius) was 9 constant throughout radial—ulnar deviation of the normal wrist and could be used as a measure of carpal collapse. Wrist joint replacement, limited and total wrist arthrodesis, and proximal row carpectomy are common operative procedures for disorders involving the wrist. In an effort to evaluate the effects of these common operative procedures, several in-vivo and in-vitro investigations have been performed by Mann, Werner, and Palmer (1989) to examine the motion of the wrist during various functional activities. Using a frequency spectral analyzer, they found that the average predominant frequency component of these activities of daily living (ADL’s) was approximately 1 Hz, with 75% of the spectral energy less than 5 Hz. The authors felt that spectral analysis would be of value in the development of a wrist motion simulator, which required sufficient frequency response to track desired wrist motion. In the developing field of biomedical engineering, prosthetic wrist replacements are becoming more common as a means to decrease pain, maintain range of motion, and restore functional ability. The purpose of a study by Tolbert, Blair, Andrews, and Crowninshield (1985) was to describe normal wrist kinetics and investigate the in-vitro kinetics of four currently available wrist prostheses named the Swanson, the Meuli, the V012, and the Hamas. The authors found that the total wrist prostheses examined were unable to reproduce normal wrist kinetics. Perhaps human wrist motion is impossible to imitate by mechanical means. 10 The purpose of this research was to provide a method for accurately analyzing human wrist rotations in three dimensions using a joint coordinate system. This method has been used in previous studies (Grood & Suntay, 1983; Chao & Morrey, 1978; Soutas-Little, et al., 1987; Carr, 1989) for analysis of the three-dimensional joint motions of the knee, elbow, ankle, and temporo-mandibular joints respectively. DeLange, VanLeeuwen, Kauer, Huiskes and Huson (1983) used stereoradiography to record the movements of each of the carpal bones. Three non-colinear tantalum pellets in each bone were used to set up local coordinate systems to calculate the rotations (Euler angles) and translations of the carpal complex in three dimensions. METHODOLOGY The methodology developed and utilized in this study provided a routine for the analysis of wrist motion. The methodology was designed around the use of the Sun-4 Motion Analysis System which was operational in May, 1989. I) DEVELOPMENT OF THE CALIBRATION STRUCTURE The pre-existing calibration structures in the laboratory were designed for the calibration of a space for lower body or total body motion analysis. The motion of the relatively smaller hand and forearm body segments occurred in a controlled area of approximately one cubic foot, and therefore, construction of a new calibration structure was necessary. Design and materials specifications for the calibration structure were suggested by Walton (1989). The calibration structure frame was fabricated from half inch plexiglass plates and one inch plexiglass rods. Ultra-flat black paint was used to cover the frame in order to decrease the reflectivity of the surfaces of the plexiglass. The targets used as control points were 0.75 inch brass ball bearings covered with 3M Scotchlite Brand High Gain 7610 Sheeting (retro-reflective tape)(see Figure 2). Retro- reflective tape has a reflectivity 1600 times the 11 12 Figure 2: Target Fabrication Materials reflectivity of a piece of white paper and provided clear pixel-imaging for digitization. The target spacers were brass tubes, machined and painted with ultra-flat black enamel. To prevent variation in the lengths of the target—hanging system, surveying thread was used. The calibration structure was leveled, utilizing three leveling bolts on the undersurface of the frame and a circle-level on the top plate. The level top plate of the frame provided an accurate X-Y plane for motion analysis. For an illustration of the structure, refer to Figure 3. 13 Figure 3: The Calibration Structure 14 Calibration of the structure was accomplished using a vernier caliper and an anthropometer to measure the target diameters, the target spacer lengths and the distances between the holes on the undersurface of the top plate of the frame. Measurements of the calibration space were accurate to within 1.0 millimeter because the anthropometer allowed measurements in millimeter increments. The computer software has an environmental operator which gave values to the targets (environmental variables) during calibration of the space where motion took place. A measure of the accuracy of the values of the three-dimensional coordinates of the targets given to the computer was reported as the parameter: "norm of residuals". The residual value of less than 0.3 calculated for all cameras fell below the system requirements for residual values of less than 2.0 indicating an accurate calibration space. 15 II) TARGETING SCHEME The targeting of the human wrist for analysis of motion may be variable, depending on the intricacies of the motion that is being examined. For the purposes of this study, a relatively simple scheme was chosen to target the two "rigid" body segments of the wrist and hand. For an illustration of the targeting scheme, refer to Figure 4. Plastic beads covered with 3M Scotchlite Brand High Gain 7610 Sheeting (retro-reflective tape) and glued to a nuagahyde backing were attached to the hand using double— sided, non-allergetic tape. The targets weighed an average of 0.85 grams each and did not interfere with wrist motion. In an attempt to minimize the soft tissue movement error of the hand and forearm, the majority of the targets were placed over bony prominences. The spherical retro-reflective targets were attached to the following skin surfaces of the right forearm and hand: 1) mid-forearm, midway between the ulna and radius, 2) dorsal surface of radial styloid, 3) head of the capitate, 4) dorsal surface of ulnar styloid, 5) second metacarpal head, and 6) third metacarpal head. The photographic representation of this targeting scheme is illustrated in Figure 4. III) DEFINITION OF JOINT COORDINATE SYSTEM An experimental protocol developed by Grood and Suntay 16 Figure 4: Targeting Scheme 17 analyze foot motion during gait, used a method of measuring three-dimensional rotation of one rigid body relative to another through use of two coordinate systems. This system of Euler angles used one coordinate system attached to the object and one attached to the laboratory to measure rotations about one axis on each system and the third rotation about a floating axis. The floating axis was calculated by a cross product of the axes from the two coordinate systems. By modeling the hand and forearm as two rigid bodies and by applying the local segment coordinate system to the three-dimensional target data, relative joint angle motion was determined. Specifically, wrist flexion and extension, and radial deviation and ulnar deviation about the two axes of motion were analyzed. Supination and pronation, which are defined in the analytical methods section, were also analyzed. IV) EXPERIMENTAL PROTOCOL An experimental protocol was established to measure three dimensional motion of the hand about the joint coordinate reference axes. Video data collection involved the use of three solid-state, shuttered, video cameras. Data were collected at 60 frames per second at one millisecond per frame. The data from the three cameras were synchronized by an advanced VP-320 model dynamic image processor. 18 The filming of the motion of the human hand was performed at the Biomechanical Evaluation Laboratory of Michigan State University at Saint Lawrence Hospital in Lansing, Michigan on August 2nd, 1989. The subject was a 28 year old, white male with no previous associated medical history and no history of traumatic injury to his right upper extremity. The subject reported that he was right handed and the targeting was performed on the right hand and forearm in accordance with the targeting scheme previously defined. The small plastic beads were chosen as targets because of their size compared to the relatively small surface area of the human hand and to prevent target cross-over with the software tracking program. Cross-over of the reflective targets becomes a problem while tracking the hand with this automated digitizing program because as the targets overlap each other on the two-dimensional video image, the targets merge and the centroid is calculated for the merged spheres as if they were a single target. Target size was also of major concern since the automated digitizing system of target tracking is quite different from the high speed cine—photogrammetric techniques previously used for motion analysis. The Expertvision three-dimensional (EV3D) software digitizing program sweeps across a grid of pixels on the video image (240 height x 256 width pixels) and averages the centroid of each sweep to find the centroid of the target. Therefore, 19 larger targets provide a greater pixel surface area from which to average. Traditionally, the high speed cine- photogrammetric techniques have benefited from a smaller target size to minimize human error in digitizing. Since digitization is automatic with the system used, the concern for target size was that they had to be small enough to decrease the incidence of target cross-over and large enough to give an accurate video image for an automated centroid calculation. The three recording video cameras were brought in close to the subject’s targeted extremity to provide the tracking system an adequate pixel number to find a centroid. The three cameras were spaced approximately 91.44 cm. from the center of the calibrated space and at 45 degree angles from the surface of the subject's arm. This set-up was adequate for capturing the movement patterns selected for analysis. The cameras are shown in their respective positions in Figure 5. Note that the height of the three cameras was equal (156.2 cm.). Illumination for the retro-reflective targets was provided by flood lights attached approximately two inches from the center of the camera lens. The proximity of the flood light to the lens enabled the tape to reflect light at maximum intensity since the reflected light is sensitive to observation angle. The observation angle is the angle between the incidence light ray, the reflective target, and the reflective ray reaching the camera lens. Each increase 20 Figure 5: Camera Positioning of one degree of observation angle, reduces the intensity of the reflected light by a factor of 16 (3M Products Bulletin, 1989). Therefore, the light source needs to be close enough to the lens to create the smallest observation angle, yet far enough away to prevent thermal distortion or damage to the lens and camera. The sequence for data acquisition began with the filming of the calibration structure. A lab coordinate system with origin at the corner of a horizontal plane connecting the four bottom targets was established and the exact three-dimensional locations of the calibration targets were calculated by the EV3D software program. Video taping of the static structure allowed the EV3D program to calibrate the necessary transformation coefficients for a 21 direct linear transformation, enabling the three-dimensional positions of the targets to be calculated during the motion sequence (Walton, 1981). The subject was instructed to stand next to the table on which the calibration structure was previously positioned, with his right hand and forearm in the calibrated space. The right upper extremity was positioned in 90 degrees of elbow flexion with the forearm in a neutral position (midway between supination and pronation with thumb facing superiorly). Data were collected for five seconds at 60 hertz as the subject performed Circumduction of the targeted wrist. The sequence of individual motions of the wrist was: extension, ulnar deviation, flexion, and radial deviation. This sequence was performed for two trials at the subject’s natural rhythm of approximately one to two hertz. Two trials each of simple flexion-extension and radial-ulnar deviation motions were collected with the subject attempting to follow a single plane of motion for each trial. The three-dimensional position data for each target were computed by the software program developed by Walton (1981). The necessary direct linear transformations were performed using the calibration coefficients determined in the environment operator program. The environment program functions to set the internal system environment by giving values to the environment variables, thus providing a calibrated space in which the wrist motion can be analyzed. The three-dimensional coordinates recorded in centimeters 22 are shown in Table 1. Frame number and time in milliseconds were included with the position data. V) ANALYTICAL METHODS Analysis of the three-dimensional position data involved the use of several EV3D software subprograms and a joint coordinate system program to adequately represent the wrist motion of the subject. For an animated stick—figure modeling of the wrist, the position data were tracked using the three-dimensional tracking program. The tracking program functions to track objects moving in three-dimensional object space by computing 3-D paths from two or more time-matched video files (Motion Analysis Corporation, 1987). By intializing the data points, a set of targets were identified in a single frame of data to check the correspondence among the cameras’ images. This automated digitizing program computed the three-dimensional paths of the targets, allowing the three non-colinear targets of the hand to be linked together, and the three targets of the forearm to be linked together. Target linkages were necessary to perform the stick figure plots which will be discussed in the results section. To edit the digitized tracking files, the three- dimensional track editor was used. This automatic program performed four automatic editing functions and provided 3-D paths to be edited in an interactive mode. The data editing Table l: PAT" NUMBER 23 Three-dimensional Position Data FRAME NUMBER Object Name : rtforearm 1 pope—eh.p—ee—eu—su—euuflg—eg—eu—e—e—ee—b—n—e—u—oflmmu—H—bI—o—o—o—c—e—eup‘u—SH—op‘ mmqamaumr— TIME seconds 0. 0.1678-01 .3338-01 5008-01 .6678-01 .8338-01 100 .117 .133 .150 .167 183 .200 .217 .233 .250 .267 .283 .300 .317 .333 .350 .367 .383 .400 .417 .133 .150 .467 .483 .500 .517 .533 .550 .567 .583 .600 617 .633 .650 .667 .683 .700 COCOOOCOOOCOOOOCOOGGOOCOOOOOOOCOCOOOOCOCO X 10.7625 10.7625 10.7408 10.7543 10.6885 10.7066 10.7542 10.7542 10.7885 10.8127 10.8294 10.8247 10.8294 10.8294 10.8294 10.8294 10.8322 10.8322 10.8125 10.8533 10.8456 10.8577 10.8687 10.9108 10.9108 10.9918 10.9918 10.9918 10.9467 10.9611 10.9658 10.9658 10.9685 10.9497 10.9685 10.9428 10.9707 10.9500 10.9500 10.9500 10.9397 10.9397 10.9397 Y 15.5523 15.5523 15.5936 15.5968 15.6029 15.6334 15.6218 15.6218 15.5859 15.5888 15.5525 15.5612 15.5525 15.5525 15.5525 15.5525 15.5351 15.5351 15.4944 15.5417 15.4887 15.4715 15.5076 15.4758 15.4758 15.4719 15.4719 15.4719 15.4230 15.3746 15.3629 15.3629 15.3155 15.3381 15.3455 15.3051 15.2981 15.2757 15.2757 15.2757 15.2645 15.2645 15.2645 2 centimetercentimetercentimeter 110.0684 110.0684 110.0694 110.0850 110.1471 110.1502 110.1657 110.1657 110.1594 110.1622 110.1592 110.1591 110.1592 110.1592 110.1592 110.1592 110.1436 110.1436 110.1238 110.0965 110.1002 110.1201 110.1004 110.1296 110.1296 110.1031 110.1031 110.1031 110.1269 110.1129 110.1130 110.1130 110.0973 110.0779 110.0973 110.0638 110.0376 110.0486 110.0486 110.0486 110.0540 110.0540 110.0540 24 functions automatically performed were: elimination of all trajectories not associated with a named target, removal of all one-point paths (a one-point path has no slope and cannot be joined to other portions of the same path using cubic splines), interpolation over all gaps in each path using cubic splines, and removal of all beginning and end frames that did not contain a complete set a data (Motion Analysis Corporation, 1987). In the interactive editing mode, the tracked files were selectively cut and joined over specific time intervals where data were unavailable due to target cross-over or where system noise interferred with path curves. A computer software program written to calculate Euler angles using the track-edited files will be found in Appendix I. The individual target path data from the track editor files were separated and the target paths were then split into x-axis, y-axis, and z-axis coordinate components in order to utilize the data to form two local coordinate systems. Unit vectors were formed from the separated three- dimensional position data. The targets on the head of the third metatarsal and over the head of the capitate represented a proximal-distal axis which is commonly used by physical and occupational therapists to measure the range of motion of the wrist. The target on the head of the second metacarpal completed the triad of non-colinear points which formed the basis for the development of the local coordinate system of the hand 25 Figure 6: Wrist Triads 26 (see Figure 6). The forearm axis, usually determined to be a proximal-distal axis lying between the radius and ulna (bisecting the forearm) was not selected for the local coordinate system. Instead, an axis was formed between the radial and ulnar styloids (see Figure 6) because of the prominence of the bony styloids and the minimal skin motion which occurs over these landmarks. Soft-tissue motion causes distortion of data as skin motion will be falsely calculated as rigid body motion. A target on the dorsum of the forearm completed the triad of the forearm. The axes through the styloids and through the third metacarpal were approximately perpendicular. The two local right-handed coordinate systems were formed with the origin of the hand segment coordinate system at the target over the head of the capitate and the forearm segment coordinate system over the ulnar styloid. The following vector formulas were used in the calculations of these coordinate systems: -D —. _, -9 -—D -P 36 = P6 - P3 42 = P2 - P4 (1) -e -e -e _. -> -o 35 = P5 - P3 41 ; Pl - P4 A . A Hy= 373713731 Fz = 4'5 / [4'2] (2) A -o -v -e -O A -v -o -o —o Hx = 36x35 / [35x36] Fx = 42x41 / [42x41] (3) A A A A A A Hz = Hx x Hy Fy = Fz x Fx (4) 27 —. where: Pn is the position data for target n. A A A Hx, Hy, Hz are the unit vectors for the hand coordinate system. -9 —e A X B is the cross product of A cross B A A A Fx, Fy, F2 are the unit vectors for the forearm coordinate system. j -9 [AB] =/(Bx - Ax)2 + (By - Ay)2 + (82 - Az)2 The above formulas defined the formation of unit vectors perpendicular to the dorsal body segments from the cross- products of the vectors created on the segment surface. The third orthogonal coordinate vectors of the two local segment coordinate systems were formed by the cross products of the third metacarpal axis with the perpendicular dorsal vector and by the cross product of the styloid axis with the perpendicular vector formed there. A joint coordinate system having unit base vectors denoted 31, $2, and 33 suggested by Grood and Suntay (1983) was formed. An illustration of unit vectors is found in Figure 7. The unit coordinate vector 21 was selected to coincide with the HE-axis of the hand (H = hand). The :8 unit coordinate vector was chosen to coincide with the EE-axis of the forearm (F = forearm). A third non-orthogonal unit coordinate vector (also called the "floating axis") 28 which is mutually perpendicular to and formed from the cross product of the other two unit coordinate vectors (see Figure 7) was calculated as follows: A A el = HX (5) A .A e3 = F2 (6) g - 2 e / [3 x g ] (7) 2 a x 1 3 1 where: [QB X £1] = V//(§3ye1z-gazg1y) .+ (33281x-géx2‘z) + (23xg1y-23yg1x) A Rotations about the floating axis e2 were reported as supination and pronation although this definition is a misnomer. Traditionally, pronation and supination are defined as movements of the forearm about its longitudinal axis. This rotatory movement of the forearm involves the mechanically linked superior and inferior radio-ulnar joints and not the radiocarpal or midcarpal joints of the wrist. For simplicity, the designations of supination and pronation were used because they are familiar to all clinicians. With the elbow flexed at 90 degrees and the thumb pointing superiorly, a supinating rotation was defined as rotating the palm to face superiorly and the thumb to point laterally (Kapandji, 1985) (see Figure 8a). A pronating rotation caused the palm to face inferiorly and the thumb to point medially (see Figure 8b). 29 . 255% 936.600 Ecomoctoucoz K mSmE PW. XI< 30 a. supi nation b. pronation Figure 8: Supination and Pronation Construction of the non-orthogonal joint coordinate system allowed three independent Euler angles to be calculated from the dot products (projections) between the two local segment and the joint coordinate system. Since the joint coordinate system remains on the body segments during motion, the joint angles could be calculated independent of the order of rotation. The following equations were used for angle calculations: . . _ . -1 A A Ulnar(+) and radial(-) dev1ation = Sln (Hz * e2) (8) — A A Extension(+) and flexion(-) = sin 1(Fx * e2) (9) 31 Pronation(+) and supination(-) = sin '(e *_ (10) where: * is the dot product sign For an illustration of the vectors used in these dot product equations, refer to Figure 7. The Expertvision software provided a smoothing operator which took a weighted average of thirteen points for computation of the centroid thus forming a thirteen point window. This program removed angle path spikes by averaging the data over a group of data. Hence, the greater the window value, the smoother the path. This smoothing program acted as a low-pass filter that supressed localized deviations without substantially changing the overall form of path and time series data. A thirteen point window was chosen because, according to Mann et al.(l989), 75% of the spectral energy of the wrist occured at less than five hertz. Since the data were collected at 60 frames per second, normal wrist motion will occur every twelveth frame. The computer software accepted only odd numbers for window width and thus a thirteen point window was chosen. RESULTS To adequately evaluate the motions of the human wrist, two computer software programs were utilized. The first utilized the motion analysis software package which provided a three-dimensional stick-figure software graphics operator. The stick command produced six different orthogonal views of the stick figure data where the images were projected onto the view plane using an orthographic projection (Motion Analysis Corporation, 1987). The superimposed stick figure tracings and the target path trajectories of a particular wrist motion provided a graphical model for analysis. An example of superimposing the full 300 frames of the file containing wrist Circumduction motion is illustrated in Figure 9, while the model in Figure 10 has every tenth frame superimposed. Superimposed tracings may also be divided into different time increments throughout the motion cycle to improve visualization of motion irregularities. The stick figure program also allowed the baseline to be labeled in frames, in percentage of the time interval, or in time units. Stick figure graphics from the position data of Circumduction, flexion/extension, and radial/ulnar deviation motions illustrated in Figures 11, 12, and 13 respectively, were plotted by percentage of time. Note that the second 32 33 "or 11011111 P91 1 Hon (can! hunter) Figure 9: Superimposed Tracings of all Frames of Circumduction (Trial 1) 34 Figure 10: Superimposed Tracings of Every Tenth Frame of Circumduction (Trial 1) 35 cow-on coo-om OON OOOH-omH can oom-om Awnmav mmpzsm w wmgqom coo-m¢ om¢-om omH ooua 0mm 0mm Amwmav Hnnz«m¢u com com OON coma 005 com fichmfiv ngmmzmmmom cow com OON coma com com flmcmav mumm cah-mm oo¢-om oom-mN oomfl-mw coo-mm coo-om flNmeV mmzzammma onH«H>ma 7,53% zofigma 7.89ng bmxmd 8:85. qgwoe m¢zga 4