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Biomechanical analysis of wrist motion in highly repetitive, hand-intensive industrial jobs
Schoenmarklin, Richard William, Ph.D.
The Ohio State University, 1991
UMI 300 N. Zeeb Rd. Ann Arbor, MI 48106
BIOMECHANICAL ANALYSIS OF WRIST MOTION IN HIGHLY REPETITIVE, HAND-INTENSIVE INDUSTRIAL JOBS
DISSERTATION
Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University
by
Richard William Schoenmarklin, B.F.A, M.S.
*****
The Ohio State University 1991
Dissertation Committee: Approved by W.S. Marras C.H. Reilly Adviser S.E. Leurgans Department of Industrial and Systems Engineering ACKNOWLEDGMENTS
I would like to thank my mentor, Dr. William Marras, for his guidance and insight throughout my doctoral program. I would also like to thank the other members of my committee, Drs. Charles Reilly and Sue Leurgans, for their comments and constructive criticism on my dissertation. I am also thankful to the graduate and undergraduate students in the Biodynamics Laboratory for their support, encouragement, and sense of humor. The technical assistance of Robert Miller is also appreciated. I would also like to thank the National Institute for Occupational Safety and Health for supporting part of this research (Grant Nos. 1 R01 OH02621-01 and 02). To my wife, Susan, I am grateful to you for your support, both emotionally and fiscally, patience, and flexibility in life's plans. VITA
October 28, 1956...... Born - St. Louis, MO, USA 1981...... B.F.A., Industrial Design, University of Kansas, Lawrence, KS 1981-1985 ...... Senior Associate Industrial Designer, IBM Corporation, Rochester, MN 1988...... M.S., Industrial and Systems Engineering, The Ohio State University, Columbus, OH
PUBLICATIONS Schoenmarklin, R.W. and Marras, W.S. (1987). Measurement of hand and wrist position by a wrist monitor. In Proceedings of the IXth International Conference on Production Research. Cincinnati, OH, 410-416. Schoenmarklin, R.W. (1988b). The effect of angled hammers on wrist motion. In Proceedings of the 32nd Meeting of the Human Factors Society. Anaheim, CA, 651-655. Schoenmarklin, R.W. and Marras, W.S. (1989a). Validation of a hand/wrist electromechanical goniometer. In Proceedings of the 33rd meeting of the Human Factors Society. Denver, CO, 718-722. Schoenmarklin, R.W. and Marras, W.S. (1989b). Effects of handle angle and work orientation on hammering: Part I. Wrist motion and hammering performance. Human Factors. 31(4), 397-411. Schoenmarklin, R.W. and Marras, W.S. (1989c). Effects of handle angle and work orientation on hammering: Part II. Muscle fatigue and subjective ratings of body discomfort. Human Factors. 31(4), 397-411. Schoenmarklin, R.W. and Marras, W.S. (1990). A dynamic biomechanical model of the wrist joint. In Proceedings of the 34th meeting of the Human Factors Society. Orlando, FL., 805-809. Marras, W.S. and Schoenmarklin, R.W. (1991). Quantification of wrist motion in highly repetitive, hand-intensive industrial jobs. National Institute for Occupational Safety and Health, Grant Nos. 1 R01 OH02621-01 and 02. Marras, W.S., Greenspan, G.J., and Schoenmarklin, R.W. (1991). Quantification of wrist motions during scanning. Report for NCR Corporation, Dayton, OH.
FIELD OF STUDY Major Field: Industrial and Systems Engineering TABLE OF CONTENTS
ACKNOWLEDGEMENTS...... ii VITA...... iii LIST OF TABLES...... X LIST OF FIGURES ...... xiii EXECUTIVE SUMMARY ...... xviii CHAPTER PAGE I. RESEARCH GOALS Introduction . . , ...... 1 Research Voids ...... 1 Research Goals ...... 1
II. LITERATURE REVIEW Magnitude of CTDs...... 3 Carpal Tunnel Syndrome ...... 6 Literature Review of CTD Risk Factors...... 8 Wrist Posture ...... 9 Repetition...... 11 Tendon Force...... 14 Literature Review of Biomechanical Modeling of Wrist Joint...... 15 Armstrong's and Chaffin's(1979) Model. . 15 Schoenmarklin's and Marras' (1991) Model. 22 Literature Review of Measurement of Wrist Motion ...... 30 Cinematographic Methods ...... 30 Electromechanical Devices...... 32 Review of Research Voids and Objectives. . . . 34 v III. INDUSTRIAL QUANTIFICATION OF WRIST MOTION A p p r o a c h ...... 38 Methods Subjects...... 39 Experimental Design ...... 39 Apparatus Wrist Monitor...... 42 Pronation/Supination Device...... 45 Selection of Sampling Frequency. . .47 Advantages of Wrist Monitor and Pronation/Supination Device . . . 50 Data Conditioning F i l t e r ...... 51 Concept of Filter...... 51 Implementation of Filter ...... 55 Validation of Filter ...... 56 Integrated Data Collection System .... 61 Selection of Participating Companies. . . 64 Factory Floor Protocol...... 68 Results — Subject Characteristics Age and Work Experience ...... 70 Handedness...... 70 Job Satisfaction...... 72 Anthropometric Dimensions ...... 72 Maximal Wrist Movement Performance. . . .72 Results — Job Characteristics Number of Wrist Movements ...... 73 Incidence Rate...... 73 Lost and Restricted Days...... 73 Turnover Rate ...... 75 Physical Attributes of Workplace...... 75 Handgrip Types and Forces ...... 75 Structure of Statistical Analysis...... 76 Results — Descriptive Analysis of Wrist Motion Scatter Plots ...... 78 Partitioning of Variance...... 81 Means of High vs. Low Risk Values .... 81 Results — MANOVA and ANOVAs of Wrist Motion . 90 Results — Principal Components Analysis . . . 92
vi Results — Discriminant Function Analysis (DFA) Stepwise DFA on All Variables ...... 104 Stepwise DFA on Structured Sets of Variables...... 105 Results — Multiple Logistic Regression (MLR) Stepwise MLR on All Variables ...... 110 Stepwise MLR on Structured Sets of Variables...... 110 Discussion — Job Characteristics CTD Risk Levels ...... 115 Number of Wrist Movements ...... 115 Force Levels...... 115 Partitioning of Variance...... 117 Discussion — Subject Characteristics...... 119 Discussion — Wrist Motion as Function of CTD Risk Analysis of Variance...... 119 Predictive Models ...... 121 Dose-Response Relationship...... 125 Causality — Need for a Biomechanical Model...... 129
BIOMECHANICAL MODEL OF THE WRIST JOINT: MODEL STRUCTURE Introduction ...... 132 Goals...... 133 Model Overview ...... 134 Anatomical Assumptions Anatomical Structure of Wrist Joint . . . 138 Anatomical Structure of Tendons and Sheaths ...... 139 Specific Model Structure Flow Diagram...... 139 Transverse Plane of Wrist Joint ...... Anatomical Characteristics — Tendon Moment Arms...... 142 Anatomical Characteristics — Geometric Orientation of Tendons. . . .144 Model Input ...... 145 Determining Force from EMG Signal . . . .146 Mechanical Aspects of Muscle Contraction. 148 vii EMG-Force Relationship...... 148 Physiologic Cross-Sectional Area...... 149 Force-Velocity Relationship ...... 150 Gain...... 150 Partitioning of Tendon Force...... 155 Calculation of Predicted Torque ...... 156 Computation of Compression and Shear Forces...... 160 Computation of Frictional Work...... 162 Model Output...... 166
V. BIOMECHANICAL MODEL OF THE WRIST JOINT: VALIDATION AND EMPIRICAL RESULTS Introduction ...... 167 A p p r o a c h ...... 168 S u b j e c t s ...... 169 Experimental Design...... 169 Apparatus...... 171 Procedure...... 174 Data Conditioning...... 177 Validation of Model Length-Strength Parameters...... 177 Selection of Angular Intervals...... 179 Squared Correlation Statistics...... 179 Results Maximum Force and Torque...... 181 Kinetics...... 181 Gain...... 198 Compression ...... 198 Flexion/Extension Shear ...... 199 Radial/Ulnar Shear...... 199 Normalized Frictional Work ...... 199 Discussion Maximum Pinch and Power Grip Force. . . . 201 Maximum Flexion Torque...... 202 Angular Interval of Interest...... 203 Match Between Predicted and Measured Torque ...... 205 Gain...... 206 Compression on Wrist Joint...... 208 Flexion/Extension Shear on Wrist Joint. . 210 Radial/Ulnar Shear on Wrist Joint . . . .211 Frictional W o r k ...... 212 Minimal Cocontraction of Antagonists. . .217 viii VI. IMPACT OF THIS RESEARCH: PRESENT AND FUTURE CTDs: Workplace Injuries of the 1990s...... 225 A Research Approach to Preventing CTDs . . . .228 Applications of this Research Industrial Surveillance ...... 230 Biomechanical Modeling of Wrist ...... 231 Future Research Industrial Surveillance ...... 234 Modeling...... 236
LIST OF REFERENCES ...... 239 APPENDICES A. Subject Information Forms ...... 251 B. Tabulation of data in Figure 26 ...... 259 C. Compute Code of Biomechanical Model of Wrist Joint...... 261
ix LIST OF TABLES TABLES PAGE 1. Values of minimum and maximum flexor tendon force as a function of angular acceleration and wrist angle...... 27 2. Values of resultant reaction force as a function of angular acceleration and wrist angle...... 27 3. Type of manufacturing operation and number of jobs and subjects...... 65 4. Number of fundamental wrist movements in each monitored job...... 66 5. Summary statistics of subject characteristics and anthropometric dimensions...... 71 6. Summary statistics of job characteristics. . 74 7. Summary statistics of kinematic wrist motion data from low and high risk CTD groups . . . 84 8. Increase of high risk kinematic values as a percentage of low risk values...... 86 9. Results of analysis of variance of motion variables...... 91 10. Key to coding of wrist motion variables. . . 95 11. Results of principal components analysis of average, minimum, and maximum variables in radial/ulnar, flexion/extension, and pronation/supination planes...... 96
x TABLES PAGE 12. Results of principal components analysis of average, minimum, and maximum acceleration variables...... 100
13. Results of principal components analysis of position, velocity, and acceleration variables in the flexion/extension planes...... 102 14. Results of stepwise discriminant analysis on structured sets of average velocity data . . 106 15. Results of stepwise discriminant analysis on structured sets of average acceleration data 107 16. Results of stepwise logistic regression on average and maximum difference variables . . Ill 17. Results of stepwise logistic regression on structured sets of range of position variables...... 112 18. Results of stepwise logistic regression on structured sets of average velocity variables...... 113 19. Results of stepwise logistic regression on structured sets of average acceleration variables...... 114 20. Average moment arms of tendons passing through Wrist joint...... 143 21. Average physiological cross-sectional area of extrinsic muscles in forearm ...... 149 22. Tendon force per unit of external flexor force for the flexor digitorum superficialis profundus...... 156 23. Anthropometric dimensions of subjects. . . . 170 24. Parameters of extreme value distribution for s u b j e c t s ...... 178 25. Squared correlation values of each subject's pinch and power grip trials...... 180
xi TABLES PAGE 26. Kinetic results of constant torque trials of 4 N-m exerted with a pinch grip...... 184 27. External and frictional work calculated for constant torque trials of 4 N-m exerted with a pinch g r i p ...... 185 28. Kinetic results of constant torque trials of 8 N-m exerted with a pinch grip...... 186 29. External and frictional work calculated for constant torque trials of 8 N-m exerted with pinch g r i p ...... 187 30. Kinetic results of constant torque trials of 4 N-m exerted with a power grip...... 188 31. External and frictional work calculated for constant torque trials of 4 N-m exerted with power g r i p ...... 189 32. Kinetic results of constant torque trials of 8 N-m exerted with a power grip...... 190 33. External and frictional work calculated for constant torque trials of 8 N-m exerted with power g r i p ...... 191
xii LIST OF FIGURES FIGURES PAGE 1. Percentage of occupational illness due to repeated trauma in U.s...... 4 2. Cross-section of the wrist illustrating the carpal tunnel...... 7 3. Three planes of movement of the hand .... 10 4. Landsmeer's (1962) model I of a tendon wrapping around a joint...... 16 5. Armstrong's and Chaffin's (1979) biomechanical model of a flexor tendon wrapping around the flexor retinaculum ...... 17 6. The resultant reaction force, as modeled by Armstrong and Chaffin (1979), that is exerted against the flexor tendons as a function of wrist angle and tendon force . .20 7. The free body diagram and mass*acceleration diagram of Schoenmarklin's and Marras' (1991) model of a flexor tendon accelerating the h a n d ...... 23 8. Relationship between the maximum and minimum forces of a tendon and the resultant reaction force...... 26 9. The resultant reaction force exerted by the carpal bones or flexor retinaculum against a flexor tendon as a function of wrist angle and acceleration ...... 29 10. Old wrist monitor and calibration equipment. 33 11. Experimental design of the industrial quantification phase ...... 41
xiii FIGURES PAGE 12. Bony landmarks on the elbow, wrist, and hand that were used to align the wrist in a neutral position ...... 44 13. Displacement of a maximal wrist movement from full extension to flexion...... 48 14. Three first order low pass filters cascaded t o g e t h e r ...... 53 15. Product of the three low pass filters shown in figure 1 4 ...... 53 16. Expansion of the filtershown in Figure 15 . 54 17. Matrix form of the filter shown in Figure 16...... 57 18. Displacement of the raw and filtered* position of a fast radial/ulnar movement . . 59 19. Displacement of the raw and filtered position of a slow flexion/extension m o v e m e n t ...... 60 20. Integrated data collection system consisting of hardware and software ...... 62 21. Trace of wrist velocity data during a ten second trial ...... 63 22. Conditioning of data collapsed over intervals and trials ...... 77 23. Statistical analysis of data collapsed over h a n d e d n e s s ...... 77 24. Structure of independent variable (CTD risk) and kinematic dependent variables...... 79 25. Scatter plot of flexion/extension mean acceleration as a function of CTD risk level ...... 80 26. Partitioning of mean acceleration variance into two components, job and subject .... 82
xiv FIGURES PAGE 27. Mean values of wrist position in the radial/ulnar and flexion/extension planes as a function of CTD risk level...... 87 28. Mean values of wrist velocity inthe radial/ulnar and flexion/extension planes as a function of CTD risk level...... 88 29. Mean values of wrist accelerationin the radial/ulnar and flexion/extension planes as a function of CTD risk level...... 89 30. First component's coefficients from principal components analysis (PCA) on all mean, minimum, and maximum position, velocity, and acceleration variables ...... 98 31. Second component's coefficients from principal components analysis (PCA) on all mean, minimum, and maximum position, velocity, and acceleration variables...... 99 32. Results from principal components analysis (PCA) on all acceleration variables...... 101 33. Results from principal components analysis (PCA) on all variables in the flexion/extension plane...... 103 34. Mean acceleration benchmarks and their distributions in the flexion/extension plane as a function of CTD risk level...... 127 35. Maximum difference of acceleration benchmarks and their distributions in the flexion/extension plane as a function of CTD risk level ...... 128 36. Overview of model macro-structure and principal inputs and their function...... 135 37. Flow chart of model's micro-structure and logic...... 140 38. Transverse plane of the wrist...... 141
xv FIGURES PAGE 39. Geometric orientation of tendons passing through the wrist...... 147 40. Relationship among contractile force, sarcomere length, and filament overlap within a muscle fiber ...... 152 41. Family of extreme value distributions. . . . 154 42. Measured wrist flexor torque vs. torque predicted by the biomechanical model .... 159 43. Decomposition of forces within a tendon that transmits force from the a forearm muscle to the h a n d ...... 163 44. Schematic of how frictional work between a tendon and its sheath is computed for an extension to flexion movement...... 165 45. Apparatus for the modeling experiment. . . . 172 46. Flow of data in the modeling experiment. . .175 47. Maximal pinch and power grip force as a function of wrist angle...... 182 48. Maximal pinch and power flexion torque as a function of wrist angle...... 183 49. Mean fina^ gain of all pinch and power grip c o n d i t i o n s ...... 192 50. Mean normalized compression on the wrist joint in pinch and power grip conditions . .193 51. Mean normalized flexion/extension shear on the wrist joint in pinch and power grip c o n d i t i o n s ...... 194 52. Mean normalized radial/ulnar shear on the wrist joint in pinch and power grip c o n d i t i o n s ...... 195 53. Mean normalized frictional work between wrist tendons and their sheaths in pinch grip exertions...... 196 xvi FIGURES PAGE 54. Mean normalized frictional work between wrist tendons and their sheaths in power grip exertions...... 197 55. Contents of the carpal tunnel...... 213 56. Trace of wrist angle during a rapid succession of ballistic oscillations .... 218 57. Ergonomic research approach used by Dr. William Marras in Biodynamics L a b o r a t o r y ...... 229
xvii EXECUTIVE SUMMARY
Cumulative trauma disorders (CTDs) are disorders of the body's tendons, muscles, and nerves due to repeated exertions and excessive movements. Workers in industrial tasks who have to move their hands and wrists repeatedly and forcefully are susceptible to CTDs. The most widely- publicized CTD is carpal tunnel syndrome (CTS). One of the major research voids in the study of occupational wrist CTDs is the quantification of the relationship between the known kinematic risk factors, such as wrist angle and repetition, and CTD risk. The first objective of this research was to determine quantitatively the association between specific wrist motion parameters and the incidence of CTDs as a group. In order to quantify the link between wrist motion parameters and CTD risk, a quantitative surveillance study was performed in industry in which workers' wrist motion was monitored on the factory floor. A total of forty subjects from eight industrial plants participated in this study (twenty workers in each of two risk groups, low and high). CTD risk level was determined by OSHA 200 logs and medical xviii records. The wrist motion parameters that were monitored on each subject were static (position) and dynamic (velocity and acceleration) measures in each plane of movement (radial/ulnar, flexion/extension, and pronation/supination). Of all the kinematic parameters measured, statistical analysis of the motion data revealed that mean acceleration in the flexion/extension plane discriminated the best between low and high risk groups (824 vs. 494 deg/secA2 for high and low risk groups, respectively). Mean flexion/extension velocity was the second best discriminator between risk groups (45 vs. 30 deg/sec for high and low risk groups, respectively). Static position variables predicted risk level poorly. The epidemiological association between flexion/extension acceleration and CTD risk is compatible with results from empirical studies and theoretical models in the physiologic and biomechanical literature. The significant prediction of CTD risk from flexion/extension acceleration only applies to jobs that are highly repetitive and dynamic in nature. The lack of a significant correlation between wrist position and CTD risk does not mean wrist posture is not a risk factor of CTDs. Wrist position would still be considered a risk factor in many industrial jobs, such as gripping a tool or manipulating parts or tools with a deviated wrist posture. xix The mean acceleration values of high and low CTD risk groups can serve as preliminary, albeit crude, benchmarks to establish injurious and safe levels of wrist motion in industry. Industrial practitioners can use these data as a basis to prevent CTDs in the workplace. These kinematic data can be used to enhance present methods of ergonomic assessments of jobs in that now ergonomic practitioners have a methodology and benchmarks to quantitatively evaluate risk level of jobs and test alternative workplace designs. The second objective of this research was to develop a biomechanical model of the wrist joint that incorporated dynamic components of wrist motion. The biomechanical model had two purposes. The first purpose of this model was to explain biomechanically why those high risk motion parameters found in the industrial surveillance were associated with CTDs. This model attempted to provide a mechanism for estimating the physical stress on the anatomical structures in the wrist under dynamic exertions simulating those found in industry. Second, this model attempted to enhance our general understanding of the kinematic and kinetic aspects of the wrist joint. This information would be helpful not only to researchers in biomechanics but also clinicians. The biomechanical structure of this 3-D wrist model consisted of a transverse plane cutting through the wrist xx and force vectors representing the seven major tendons passing through the wrist. These tendons transmit the force exerted by the extrinsic muscles in the forearm to the hand and fingers for grip or pinch force and torque generation about the wrist. The seven muscles consisted of the following four flexor and three extensor groups:
Flexor carpi radialis FCR Flexor digitorum superficialis FDS Flexor digitorum profundus FDP Flexor carpi ulnaris FCU Extensor carpi radialis ECR Extensor digitorum communist EDC Extensor carpi ulnaris ECU
This model was data-driven by electromyographic (EMG) signals from the seven muscles listed above. EMG data were used to estimate muscle forces, which in turn, were assumed to be tendon forces passing through the wrist. The key outputs of the model were loading on the wrist (compression and shear) and frictional work between tendons and their sheaths or between tendons and carpal bones and ligaments. The main inputs to the model consisted of kinematics (wrist angle and velocity), kinetics (pinch or grip force and torque about the wrist joint), EMG data from seven forearm muscles, and each subject's anthropometric dimensions. The flow of data and analysis within the model proceeded as follows. First, EMG signals from seven major extrinsic muscles were normalized with respect to maximum xxi EMG values, and then they were modulated for velocity artifacts and the length-strength relationship and physiological cross-sectional area (PCSA) for each muscle. Each muscle's force was calculated by multiplying normalized EMG by a factor called gain. Muscle force for FDS and FDP was partitioned into components that produced pinch or power grip force and generated wrist flexor torque. The gain for all muscles, which was the force relative to PCSA, was set at a minimum threshold and incremented upward until external work predicted by the model exceeded measured external work. Once predicted work surpassed measured work, then compression and shear forces on the wrist joint and frictional work between the tendons and their supporting structures were calculated. In addition, a squared correlation was computed to assess how well predicted torque matched measured external torque. The hypothesis of the laboratory experiment was that frictional work between the tendons and their sheaths or between tendons and carpal bones and ligaments would be greater when the wrist is moving at velocities found in high risk CTD jobs than low risk velocities. A controlled laboratory experiment was setup to validate the model and test the hypothesis. In this experiment, subjects exerted constant wrist torque in the flexion/extension plane under isokinetic (constant velocity) velocities. Constant xxii velocity movements were monitored because the relationship between electromyography (EMG) and muscle force is stable and reliable when muscle fibers are shortening at a constant rate. EMG, which measures the electrical activity of muscular contraction, was the method of estimating muscle force in this experiment. Accelerative movements were not monitored in this study because the relationship between EMG and acceleration is not known at this point. An isokinetic Cybex dynamometer was used to control angular velocity of the wrist and also to measure external torque and wrist position. A custom-built handle outfitted with a loadcell measured pinch or power grip force. EMG signals from all seven extrinsic forearm muscles were monitored with fine wire electrodes. The experimental design consisted of two angular velocities (30 and 45 deg/sec), two torque levels (four and eight N-m), and two grip orientations fpinch and power grip). 30 and 45 deg/sec were the mean flexion/extension velocities that were measured in the low and high risk CTD jobs, respectively, in the industrial surveillance phase of this research. The results from this laboratory experiment include the following: 1. Final gains ranged from 20 to 60 N/cmA2 of muscle area. These values are consistent with reported gains in the literature. xxiii 2. Torque predicted under pinch grip conditions matched measured external torque better than power grip trials. Low squared correlation values for power grip trials might have been due to less than optimal partitioning of FDS and FDP force into grip force and torque generating components. 3. Absolute compression on the wrist joint reached a peak of 500 N, which appears to be anatomically feasible. The wrist is capable of withstanding substantial compressive forces because of its tightly-fitting multifaceted bones and taut ligaments. Compression normalized to external torque did not reveal a velocity or torque effect. Normalized compression was approximately 50 to 60 N per N-m of external torque. 4. Similar to compression, normalized shear in the radial/ulnar and flexion/extension planes did not reveal a velocity or torque effect. Normalized shear in the radial/ulnar and flexion/extension planes averaged about ten and five N per N-m of torque, respectively. 5. Frictional work between tendons and their sheaths and between tendons and carpal bones and ligaments was calculated for three sets of tendons: three tendons passing through the carpal tunnel (FCR, FDS, and FDP), four flexor tendons (FCR, FDS, FDP, and FCU), and all flexor and extensor tendons (includes ECR, EDC, and ECU). In addition, frictional work was normalized with respect to external xx iv work. The values of normalized frictional work averaged about 0.0004, 0.0008, and 0.0009 N-m of frictional work per each N-m of external work for the three sets of tendons, respectively. Overall, results of frictional work were mixed. In four N-m pinch grips, frictional work at 45 deg/sec trials were about 10 to 20% greater than at 30 deg/sec. There was no difference at the eight N-m pinch grip level. In contrast, frictional work during power grips was greater at 30 deg/sec for one subject at each torque level. These results may indicate an interaction between velocity and muscle force. The mixed results of frictional work could possibly be traced to statistical or biomechanical roots. Statistically, the small sample size (two subjects and two to three repetitions) might not have been enough to elicit steady state trends. Biomechanically, there might not have been any true difference in frictional work and wrist loadings between velocity levels because of minimal, and often nonexistent, cocontraction of the extensor (antagonist) muscles. In studies involving the trunk, cocontraction of agonist and antagonistic muscles during constant velocity exertions increased as a function of velocity, thereby generating higher compressive and shear loads on the spine. It appears that the trunk requires intense cocontraction of agonists and antagonists in order
XXV to maintain postural stability. However, considering the wrist's light weight and moment of inertia, lack of cocontraction of the wrist muscles due to reciprocal inhibition of the antagonistic muscles enables the wrist to move swiftly. Contrary to results from constant velocity exertions, there may be differences in frictional work between flexion/extension movements that vary in acceleration. In the industrial surveillance phase of this dissertation, flexion/extension acceleration was the strongest discriminator between CTD risk levels. Biomechanical theory and modeling support flexion/extension acceleration as a risk factor of CTDs. Acceleration of the wrist would require greater tendon forces, which in turn would increase frictional work between the tendons and their supporting structures. Furthermore, the resultant reaction force on the tendons from their supporting structures would increase, which could possibly contribute to tendinitis, tenosynovitis, or CTS. In the future, decomposition of EMG signals into their spectral components may provide a mechanism for measuring muscle force under constant acceleration movements.
xxvi CHAPTER I RESEARCH GOALS
Introduction Cumulative trauma disorders (CTDs) are disorders of the soft tissues (most frequently the tendons, muscles, and nerves) due to repeated exertions and excessive movements of the body (Armstrong, 1986a). In this document, the term CTDs will refer to only the CTDs of the wrist. Workers in industrial tasks who have to move their hands and wrists repeatedly and/or forcefully are susceptible to CTDs. Some specific CTDs of the hand and wrist are carpal tunnel syndrome (CTS), tenosynovitis, tendinitis, and De Quervain's disease.
Research Voids Deviated wrist postures and high repetitions of the hand in industrial tasks are known to be important risk factors associated with CTDs (Armstrong, 1986a). One of the major research voids in the study of occupational wrist CTDs is the quantification of the link between the known kinematic risk factors, such as wrist angle and repetition, and CTD risk. One objective of this research was to determine quantitatively the association between specific wrist motion parameters and the incidence of CTDs as a group. Accurate, reliable data on wrist motions of workers in industrial jobs of low and high CTD risk were guantified and related to incidence rate. Quantification of the relationship between wrist motion parameters and CTDs can be used to redesign industrial tools and tasks in order to reduce the incidence of CTDs in the workplace. Another research void in the area of CTDs is the lack of models of the wrist joint that explain biomechanically why the high risk motion parameters might expose a worker to CTDs. Biomechanical modeling provides theoretical knowledge that can help explain statistical findings from the industrial surveillance phase of this study.
Research Goals The goals of this research were: 1) Estimate the extent to which specific wrist motion parameters were associated with high incidence rates of CTDs in industry. 2) Develop a biomechanical model that incorporates dynamic components of wrist motion and explain through laboratory experimentation and modeling why those high risk motion parameters are associated with CTDs. CHAPTER II LITERATURE REVIEW
Magnitude of CTDs CTDs can be generally defined by investigating the meaning of each word in the term CTD (Putz-Anderson, 1988). Unlike instantaneous trauma, "cumulative" means that the injury developed gradually over a period of time as a result of repeated stress. "Trauma" means bodily injury from mechanical stress, and "disorder" indicates physical ailments or abnormal conditions. CTDs appear to be work-related in that they occur more often in working people than the general population (Putz- Anderson, 1988). The overall incidence of CTDs in the industrialized world is unknown, but epidemiological data reveal that CTDs are a growing problem. According to the Bureau of Labor Statistics (1990), industrial injuries due to repeated trauma increased from approximately 20% of all recorded injuries in 1981 to almost 50%, or 115,000 cases, in 1988. Figure l illustrates this precipitous trend. Overall, CTDs are the second most frequently reported category of occupational illness after skin disease (Tanaka, Seligman, Halperin, Thun, Timbrook, and Wasil, 1988). 4 1988
1987
1986
1985
1984 YEAR
1983
1982
1981 DUE DUE TO REPEATED TRAUMA 10 20 50 40 SOURCE: U.S. DEPARTMENT OF LABOR, BUREAU OF LABOR STATISTICS PERCENT OF OCCUPATIONAL ILLNESS Q.UJCCOUJZI- repeated trauma in U.S. as reportedLabor from to U.S. to Department1981 1988 (Bureauof of Labor Statistics, 1990). Figure 1. Percentage of occupational illness due to 5
Because of the frequency and impact of CTDs on worker health, the National Institute of Occupational Safety and Health (NIOSH) has designated musculoskeletal injuries (including CTDs) as one of the ten leading work-related diseases and injuries (Tanaka et al., 1988). During the five year period from 1980 through 1984, data from the Ohio Industrial Commission showed that the wrist was affected in almost half of all CTD claims, and 75% of the wrist CTDs cases were "tenosynovitis due to continuous motion" (Tanaka et al., 1988). During the same period, the number of overall CTD cases increased dramatically. This increase was partially due to growing awareness of CTDs among workers, employers, and health professionals (Tanaka et al, 1988). The incidence rate of CTDs varies according to individual work sites, but reports from some sites suggest that the incidence rate "approaches epidemic proportions and are a major cause of lost work in some settings" (Armstrong, 1986a, p. 553). From three years of data collected in an electronics firm, Hymovich and Lindolm (1966) reported an incidence rate of 6.6 cases per 200,000 work hours. In a poultry processing plant, Armstrong et al. (1982) found an incidence rate of 12.8 cases per 200,000 work hours. In a study of 574 active workers from six different industrial plants, Silverstein, Fine, and Armstrong (1986) found CTD prevalence rates of 4.2% and 13.6% in male and female workers, respectively. (If 100 employees worked 50 weeks * 40-hour weeks = 200,000 hours, then the incidence rate per 200,000 work hours would equal the prevalence.) Based on available data from reported cases, CTDs appear to be a major health problem in some industries (Armstrong, 1986a). However, the incidence rates of CTDs are generally underreported, so the total costs to these industries would be even greater. CTDs are underreported for several reasons (Armstrong, 1986a). First, CTDs develop gradually and are difficult to trace to a specific event. Some of the symptoms of CTDs, such as pain, stiffness, and numbness, occur at night and are difficult to trace to occupational causes. Workers may be treated by personal physicians rather than by company physicians. Also, CTDs may be miscategorized and may be omitted from CTD data banks.
Carpal Tunnel Syndrome A specific CTD that has been receiving much attention in the research community and the general population is carpal tunnel syndrome (CTS). CTS is a disorder that affects the median nerve as it passes through the carpal tunnel at the wrist joint. As illustrated in Figure 2, the carpal tunnel is a tunnel formed by the wrist bones on the 7
SECTION
FLEXOR DIGSTORUM TENDON EXON RETINACULUM
TENDON SYNOVIUM LOAO IN 0RIP MEDIAN NERVE
FLEXOR OIG1TORUM MUSCLES
LEXON TENOONS
CARPAL WRIST BONES
^-EXTENSOR RETINACULUM EXTENSOR TENOONS ( SYNOVIA
EXPANOED SECTION AT CARPAL TUNNEL
Figure 2. Cross-section of the wrist illustrating the carpal tunnel. The carpal tunnel is formed by the carpal bones on the dorsal side and the flexor retinaculum on the palmar side. Ten tendons (eight flexor digitorum superficialis and profundus, flexor pollicus longus, and flexor carpi radialis) and the median nerve pass through the carpal tunnel. This figure is from Chaffin and Andersson (1984). dorsal side of the wrist and the carpal ligament, a strong transverse ligament, on the palmar side. Ten tendons transmitting mechanical forces from the extrinsic muscles in the forearm to the hand and digits pass through the carpal tunnel. As the hand and digits are repeatedly moved, the tendons rub against the carpal tunnel structures and each other. Excessive repetition and force could cause excessive lubrication between tendons and their sheaths or supporting structures, which could increase the pressure on the median nerve. Excessive repetition and force could also decrease the natural lubrication and cause tendinous inflammation. The inflamed tendons will occupy more volume in the carpal tunnel and will impinge upon the median nerve. The inflamed tendons and compressed median nerve could cause motor and sensory decrements, including (Armstrong, 1983):
1) reduced muscle control in the thumb and ultimately thenar muscle atrophy. 2) diminished grip strength and hand clumsiness. 3) numbness, tingling, and pain, particularly during the night. 4) loss of sensory feedback (e.g. many CTS patients cannot distinguish hot from cold). 5) loss of sweat function in areas of hand innervated by median nerve, resulting in reduced ability to grasp and manipulate objects with the hand.
Literature Review of CTD Risk Factors The epidemiological and biomechanical literature is replete with references to wrist posture, repetition, and 9 force as risk factors for CTS and CTDs overall. Before these risk factors are discussed, the kinematic movement in the wrist and forearm will be briefly described (refer to figure 3). There are two degrees of freedom in the wrist joint, radial/ulnar (R/U) and flexion/extension (F/E). The third degree of freedom, pronation/supination (P/S), is generated in the forearm by the radial bone crossing over the ulna bone. Wrist Posture. Wrist posture has been cited often as a risk factor for CTS and CTDs overall (Alexander and Pulat, 1985; Armstrong, 1983, 1986a, 1986b; Armstrong and Chaffin, 1979a, 1979b; Armstrong, Foulke, Joseph, Goldstein, 1982; Armstrong, Radwin, Hansen, and Kennedy, 1986; Browne, Nolan, and Faithful, 1984; Charasch, 1989; Eastman Kodak Co., 1986; Fraser, 1989; Greenberg and Chaffin, 1975; Konz, 1983; McCormick and Sanders, 1982; Phalen, 1966; Tichauer, 1966, 1978). Wrist flexion and extension are associated with CTS and tenosynovitis of the flexor tendons (Phalen, 1966), and wrist radial and ulnar deviation are associated with tenosynovitis and De Quervain's disease (Armstrong, 1983). Even though wrist posture has been cited often as a risk factor for CTDs overall, few researchers have mentioned the issue of "how much" wrist deviation exposes a worker to CTDs. The suggested association between wrist posture and CTDs has been explained biomechanically. When the wrist is 10
Ulnar
Flexion Extension
Pronation Supination
Right Hand
Figure 3. Three planes of movement of the hand. Radial/ulnar deviation and flexion/extension occur in the wrist joint, and pronation/supination is a function of the radius rotating around the ulna in the forearm. maintained in a neutral position, the tendons of the flexor and extensor finger muscles that pass through the wrist, are "well separated, run straight, and can operate efficiently" (Tichauer, 1978, p. 67). When the wrist is in extreme deviated postures, the high shear forces and friction exerted by the sheaths, carpal bones, and ligaments on the tendons could irritate and inflame the tendon sheaths, causing a common CTD, tenosynovitis (Tichauer, 1978). The inflamed flexor tendon sheaths also occupy more space in the carpal tunnel, thus compressing the median nerve and contributing to CTS (Cunningham and Johnston, 1985). Armstrong and Chaffin (1979a) developed a static biomechanical model of the wrist that demonstrated theoretically why deviated wrist angles could expose workers to CTS and CTDs overall. In their model, as wrist angle deviated from the neutral position, the resultant reaction forces on the median nerve and flexor tendons increased, which would make the wrist vulnerable to CTS and CTDs. (Armstrong's and Chaffin's (1979a) model will be discussed in detail in the review of biomechanical models.) Repetition. Silverstein, Fine, and Armstrong (1986, 1987) and Silverstein, Fine, Armstrong, Joseph, Buchholz, and Robertson (1985) conducted two epidemiological studies that provided evidence for a crude dose-response relationship between jobs that required highly repetitive wrist movements and incidence of CTS and CTDs overall. After controlling for potential confounders, Silverstein et al. (1987) reported that the odds ratios for high force-high repetition industrial jobs compared to low force-low repetition jobs were more than 14 and 30 for CTS and CTDs, respectively. High repetition-low force jobs had odds ratio of 1.9 and 3.6 for CTS and CTDs, respectively, compared to low repetition-low force jobs. Unlike static wrist posture, repetition involves the dynamic components of angular velocity and acceleration, which could contribute to CTS and CTDs risk. Technically, repetition can be defined in biomechanical terms as cyclic angular acceleration, peak velocity, and deceleration about the wrist joint. In order to accelerate the hand or digits, the extrinsic muscles in the forearm have to generate force based on Newton's second law of motion, F = M*A. Based on this law, the force that these extrinsic muscles in the forearm have to exert is proportional to the acceleration of the hand. Schoenmarklin and Marras (1991a) developed a dynamic biomechanical model of the wrist joint that explained how angular acceleration of the wrist theoretically increased the resultant reaction force on the flexor tendons and median nerve, thereby increasing the risk of CTS and CTDs overall. (Schoenmarklin's and Marras' 13
(1991a) model will be discussed in detail in the review of biomechanical modeling.) Due to the friction between the tendons and their adjacent surfaces, part of the tendon force generated by the extrinsic muscles will be lost to friction. As the tendon is moved over the adjacent surfaces, frictional energy is generated. This frictional energy, which is absorbed by the tendons and/or their surrounding tissues, could deteriorate and inflame the tendons, thereby contributing to CTS and CTDs. Tanaka and McGlothlin (1989), Moore and Wells (1989), and Moore (1988) hypothesized frictional work as a major cause of CTDs. Another biomechanical way in which repetition could cause CTS and CTDs overall is based on the force-velocity relationship of muscle As the velocity of shortening of a muscle increases, the maximal force that the muscle can generate decreases (Winter, 1979). Compared to a static posture, the extrinsic muscles in the forearm have to expend more energy to exert the same external force in a dynamic movement. The greater expenditure of energy will lead to earlier muscle fatigue. Premature muscle fatigue could bring about substitution patterns in muscle activation, and muscles which are not normally recruited may be activated in fatigued states. This abnormal usage may change the nature of forces within the wrist and put these seldom recruited 14 muscles' tendons at risk of inflammation in the carpal tunnel, which could lead to CTS. Tendon Force. Similar to repetition, Silverstein et al. (1986, 1987) found a crude dose-response relationship between a job's force requirements and the incidence rate of CTS and CTDs overall. The odds ratios for CTS and CTDs overall for jobs with high force-low repetition requirements and low force-low repetition jobs were 1.8 and 4.9, respectively. With respect to resultant reaction forces, the association between tendon force and incidence of CTDs can be explained by Armstrong and Chaffin's (1979a) static model of the wrist. The resultant reaction force on flexor tendons and median nerve increased linearly as tendon force increased. The resultant reaction force contributes theoretically to the deterioration and inflammation of tendons and their sheaths. With respect to friction between tendons and their adjacent structures, an increase in total tendon force also increases the frictional force component within the tendon (except when the wrist is in a neutral posture). The friction between the tendons and their sheaths or between tendons and the bones and ligaments was hypothesized as a major contributor to CTDs (Tanaka and McGlothlin, 1989; Moore and Wells, 1989? Moore, 1988). 15
Literature Review of Biomechanical Modeling of Wrist Joint
Armstrong's and Chaffin's (1979a) Static Model. Armstrong's and Chaffin's (1979a) model of the wrist is a static model that is based on based on Landsmeer's (1962) model I. Figure 4 shows Landsmeer's model of a tendon bent around a fixed pulley. Figure 5 illustrates Armstrong and Chaffin's model as a reasonable representation of Landsmeer's model. When the wrist is flexed, the flexor tendons bend around the flexor retinaculum that is assumed to have a constant radius. When the wrist is extended, the flexor tendons are supported on the dorsal side by the carpal bones that are assumed to have a constant radius. Armstrong and Chaffin (1978) found that the radius in a flexed posture is larger than in an extended posture. The arc length of the tendon wrapping around the pulley is defined in equation (1).
X = R * © (1) where: X = tendon arc length around pulley R = radius of curvature around supporting tissues © = angle of deviation of wrist from neutral (in radians)
The reaction forces acting normal to the tendon are shown in figure 5 and defined in equation (2). 16
[MODEL I]
Figure 4. Landsmeer's (1962) model I of a tendon wrapping around a joint. This illustration is from Chao, Cooney, and Linscheid (1982) . 17
F,
Fr ■ 2 * Ft * sin(angle/2)
Figure 5. Armstrong's and Chaffin's (1979a) biomechanical model of a flexor tendon wrapping around the flexor retinaculum. Ft is the tendon force, and Fr is the resultant reaction force exerted against the tendon. This illustration from Chaffin and Andersson (1984). 18
Pn = (Ft * eA(u*©)) / R (2) where: Pn = normal supporting force per unit of arc length (N/mm) Ft = average tendon force in tension (N) u = coefficient of friction between tendon and supporting synovia 0 = wrist deviation angle (in radians)
Since u is considered small (on the order of 0.015 (LeVeau, 1977)), it can be approximated by zero. This changes equation (2) to equation (3).
Fn = Ft / R (3)
Equation (3) reveals Fn is a function of the tendon force and radius of curvature. As the radius of curvature decreases, the normal supporting force per unit of arc •v-. length increases. The normal supporting force for women would be greater than for men because women have smaller wrists. Also, as the tendon force increases, the normal supporting force increases. The total supporting force Fr in figure 5 is the force of the ligaments, bones, and median nerve in the carpal tunnel acting on the flexor tendons. Fr is defined in equation (4). 19 Fr = 2 * Ft * sin(©/2) (4) where: Fr = resultant force exerted by adjacent wrist structures on the flexor tendons Ft = tendon force © = wrist deviation angle (in radians)
Equation (4) indicates that Fr is a function of the tendon force and wrist deviation angle, but is independent of radius of curvature. Figure 6 illustrates this relationship. As the tendon force and wrist angle increase, the resultant force Fr increases linearly. The significance of Fn and Fr is based on the theory that the increased normal forces place greater stress on the synovial fluid surrounding the tendons passing through the carpal tunnel. This greater normal force could cause the tendons to inflame, which would compress the median nerve, and thereby contribute to CTS and other CTDs, such as tenosynovitis. If the tendons inflame, then the coefficient of friction would increase, which would increase Fn even more (see equation (2)). Dynamic movements that accelerate and decelerate the tendons around the pulley could exacerbate the trauma imposed on the tendons. The advantage of Armstrong's and Chaffin's (1979a) model is that it provides a relatively simple mechanism for calculating normal forces which are thought to be 20
EXTENSION FLEXION
400
F. = 200 N F, * 200N
300
u ZOO F. s IOON F, > IOON
b.
100 F. = SON F =50N
- 100 * -50* 0* SO* 100 * « WRIST ANGLE (DEGREES FROM STRAIGHT)
Figure 6. The resultant reaction force (Fr), as modeled by Armstrong and Chaffin (1979a), that is exerted against the flexor tendons as a function of wrist angle and tendon force. This figure is from Chaffin and Andersson (1984). 21 contributing factors in CTS and CTDs. The model is deterministic and produces point values as output. In addition, the assumptions of this model have an anatomical basis. The limitations of Armstrong's and Chaffin's (1979a) model are the following: 1) This model does not include the dynamic components of repetition (velocity and acceleration), which have been shown in the epidemiological literature to be associated with CTDs (Silverstein et al., 1986, 1987). Estimates of the resultant reaction forces on the flexor tendons are underestimated in this model because angular acceleration is not incorporated. 2) The 2-D nature of this model limits its applications to monoplanar movements. Analysis of the biomechanical impact of a normal oblique motion of the wrist, such as a dart thrower's motion (radial/extension to ulnar/flexion) (Caillet, 1984; Capenar, 1956), would be limited by this model. 3) Coactivation of the antagonistic extensor muscles are not included in this model. For a given external flexor torque, coactivation of the extensor muscles would increase the required flexor tendon force, thereby exacerbating the risk of CTS and CTDs. 22
Schoenmarklin1s and Marras1 (1991a) Dynamic Model. The objective of this dynamic model was to explain how the component of angular acceleration could increase a worker's risk of developing CTDs. This dynamic model uses the assumption of the rope:fixed pulley analogy in Armstrong's and Chaffin's (1979a) model. The dynamic model is two- dimensional in that only the forces in the flexion/extension plane were analyzed. This model analyzes the effects of peak angular acceleration on the resultant reaction force that the wrist bones and ligaments exert on tendons and their sheaths. In order to maintain determinacy in the two-dimensional example, all the flexor tendons are grouped together as one tendon force vector. As illustrated in figure 7, an extended male hand with 50th% length was selected as the hand configuration'to demonstrate this model. The quantitative effects of the wrist's peak angular acceleration on resultant reaction forces were based on the free body diagram (FBD) and mass*acceleration diagram (MAD) approach in engineering dynamics (Meriam and Kraige, 1986). Figure 7 illustrates a wrist and hand in midposition (neither pronated or supinated). There is no externally applied load in the hand. The hand is rotated in the horizontal plane around a vertical z axis, so the effects of gravity do not play a role in this example. 23
FREE BODY DIAGRAM MASS*ACCELERATION DIAGRAM
(0.00085 kg-m**2)*(e)
CM CM
M*At - M*(r* ©) = Wy (0.57kg)*(0.0553ra)*(©) (0.03152)*(©)
r * 0.01045 m
flexor tendons
Mw - (0.00085)*(§) •k. (0.03152)*(g)*(0.0553m) Mw *= (0. 002593) * ( g ) but Mv « (Ft)*(0.01045) SO (0 .002593)*(©) = (Ft)*(0.01045) 0.01045 m Ft = (0.2481)*(©)
Figure 7. The free body diagram (FBD) and mass*acceleration diagram (MAD) of Schoenmarklin's and Marras' (1991a) model of a flexor tendon (Ft) accelerating the hand. 24
The FBD in figure 7 shows the reaction forces on the center of the wrist (Wx and Wy) and the moment (Mw = tendon force * radius of curvature) that is required to flex the wrist. The MAD in figure 7 illustrates the inertial forces and moment about the wrist. The inertial forces are composed of the tangential force (mass * tangential acceleration (At)) and centripetal force (mass * centripetal acceleration (Ac)). The inertial moment is the moment of •• inertia (I) * angular acceleration (©), acting around the hand's CM. In this example, the hand is assumed to accelerate from a stationary posture, so the angular velocity is theoretically zero, resulting in zero centripetal force (Ac = (V**2)/r = 0 because V = 0) . The peak acceleration is calculated just before the hand reaches a level of angular velocity. The forces and,moments in figure 7 represent a statically determinate system in that the number of unknowns (Wx, Wy, and Mw) equals the number of equations (3). In the three equations, the sum of x and y forces in the FBD equals the inertial forces in the MAD, and the magnitude of moment around the wrist (Mw) in the FBD equals the inertial moment in the MAD. Since the only unknown of interest is (Mw) in the FBD and the couple in the MAD is dependent only on known quantities (mass, r, I, and 0), then it is only necessary to 25 look at the summation of moments equation to solve for (Mw). In the lower left hand corner of figure 7, the summation of • • moments equation results in Mw = (0.002593)*(©), but since Mw = Ft*(0.01045m), then the tendon force Ft = (O.2481)*(0). Ft is the maximum force in the flexor tendon vector. Table 1 lists the max tendon force (Ftmax) as a • • function of five peak angular accelerations (0 = 3000, 6000, 9000, 12000, and 15000 deg/sec**2). Based on empirical data from normal subjects, 15000 deg/sec**2 was found to be about 50% of the peak wrist acceleration in the flexion/extension plane. Table 1 also lists the Ftmax forces as a function of the wrist extension angle. The Ftmax force is illustrated in figure 8 and is derived from equation (5) (LeVeau, 1977).
Ftmax = Ftmin * (eA(u*©)) (5) where: Ftmax maximum force in flexor tendons Ftmin minimum force in flexor tendons u coefficient of friction between tendons and carpal bones and ligaments wrist deviation angle in radians
Since the coefficient of friction for human synovial joints bones is estimated to be very low (0.0032 according to Fung, 1981) then the calculation of Ftmax force is very close to Ftmin force (see table 1 and equation (1)). In 26
Fr
Ftmax
Ftmax = Ftmin * (e**(u*angle))
Figure 8. Relationship between the maximum (Ftmax) and minimum (Ftmin) forces of a tendon and the resultant reaction force (Fr). The flexor tendon is wrapped around the wrist's carpal bones or flexor retinaculum. Ftmax and Ftmin are used in Schoenmarklin's and Marras' (1991a) dynamic model of a flexor tendon passing through the wrist joint. The equation for Ftmax and Ftmin is from LeVeau (1977). 27 table 2, Fr was calculated as the resultant force necessary to resist Ftmax and Ftmin.
Table 1. Values of minimum and maximum flexor tendon force (Ftmin and Ftmax) as a function of angular acceleration (0) and wrist extension angle (©) •
• • •• © © Ftmin Value of Ftmax as fct of an< (deg/ (rad/ secA2 secA2 0 deg 30 60 90 0 0 0 N 0 N 0 N 0 N 0 N 3000 52.4 13 13 13.10 13.21 13.31 6000 104.7 26 26 26.20 26.41 26.62 9000 157.1 39 39 39.31 39.62 39.93 12000 209.4 52 52 52.41 52.82 53.24 15000 261.8 65 65 65.51 66.03 66.55
Table 2. Values of resultant reaction force (Fr) as a function of angular acceleration (©) and wrist extension angle (©).
© Values of Fr as fct of extension angle (deg/secA2) 0 deg 30 60 90
0 0 N 0 N 0 N 0 N 3000 0 6.7 13.0 18.4 6000 0 13.5 26.0 36.8 9000 0 20.2 39.0 55.1 12000 0 26.9 52.0 73.5 15000 0 33.6 65.0 91.9 Note: since Ftmin £ Ftmax for u = 0.0032 (Fung, 1981), then Fr = 2*Ftmin*sin(©/2) 28 As shown in figure 9, Pr increases approximately linearly as wrist angle or angular acceleration increases, resulting in a curved plane that signifies an interactive effect between wrist angle and angular acceleration. The graph in figure 9 is significant in three ways. First, figure 9 provides theoretical support to why repetition, which can be partially considered cyclic acceleration and deceleration of the wrist, is considered a risk factor of CTDs. This statement assumes that increases in Fr would increase the supporting force that the carpal bones exert on the flexor tendons, thereby increasing the chance of inflammation and risk of CTS (Armstrong and Chaffin, 1979a) and CTDs. In addition, the flexor tendons would exert a supporting force directly on the median nerve, which would also increase the risk of CTS. Second, figure 9 shows how the coupling of repetition and deviated wrist posture, which is another risk factor for CTS and CTDs (Armstrong, 1983), results in an interactive effect on Fr. This interactive effect indicates that the highest peak reaction forces occur when the wrist is accelerated in deviated wrist postures. The coupling of high angular acceleration in deviated wrist postures exacerbates the risk of CTS exposure to workers. Third, figure 9 illustrates the high peak reaction forces exerted on the flexor tendons and median nerve are 29
Fr (N)
15000
12000
9000 90
Angular 6000 Acceleration (deg/sec**2) 3000 Wrist Extension Angle (deg)
Figure 9. The resultant reaction force (Fr) exerted by the carpal bones or flexor retinaculum against a flexor tendon as a function of wrist angle and acceleration. This figure is from Schoenmarklin and Marras (1991a). 30 due solely to wrist motion without any externally applied load in the hand. If loads were applied in the hand ( e.g. power grip, pinch grip, etc.) while the hand was accelerated in deviated postures, then Fr would increase even more, resulting in even more stress on the flexor tendons and median nerve. The advantage of Schoenmarklin's and Marras' (1991a) model is that it incorporates the dynamic component of acceleration into assessment of normal forces on the flexor tendons. However, the model is limited because it is 2-D and it does not take into account coactivation of antagonistic extensor muscles.
Literature Review of Measurement of Wrist Motion Cinematographic Methods. Heretofore, the state of the art technique in quantifying wrist movement in the workplace was cinematography. Cinematography produced gross angular results and required much effort to analyze. Armstrong et al. (1979) described a method for documenting hand position by filming a task with a super 8 mm motion picture camera and, subsequently, recording manually the type of hand position for each frame on a sheet of paper. This method required much time and effort because each individual frame had to be analyzed manually, and this method was also subject to human errors in angle measurement. In addition, 31 two cameras were required to record the wrist angles in the R/U and F/E planes, and synchronization of the wrist angles from these two cameras was difficult. The cinematographic method was used in an investigation of hand and arm movement in a poultry processing plant (Armstrong et al., 1982) and in a task where a typewriter housing's flashings were filed (Burnett and Bhattacharya, 1986). In the poultry plant case, wrist positions were catalogued into a few discrete angles in increments of 25 to 45 degrees. The gross documentation of wrist angles in the poultry plant case is a product of the insensitivity of the cinematographic method. Fine adjustments in wrist angle, velocity, and acceleration and quick wrist movements, such as jerking the wrist, would be difficult to measure and calculate using the cinematographic method. Knowlton and Gilbert (1983) used high speed photography to record the ulnar deviation of a carpenter striking nails. Like Armstrong's et al. (1979) method, Knowlton and Gilbert's method appeared to require excessive time to measure the ulnar angle on each frame, as evinced by the fact that they measured the ulnar deviation of only one subject instead of all their subjects. Cinematography is an impractical technique to assess the biomechanical impact of highly repetitive wrist motion found in industry. Electromechanical Devices. A few electromechanical devices have been developed to measure wrist angle, but their use appears to have been limited to measuring wrist motion in ordinary tasks of daily living. Brumfield and Champoux (1984) developed a uniaxial electrogoniometer that measured wrist flexion and extension. An, Askew, and Chao (1986) and Palmer, Werner, Murphy, and Glisson (1985) developed electrogoniometers that measured wrist motion in both planes of movement, and they recorded empirical data on the range and nature of wrist movement in daily tasks ranging from turning a steering wheel to combing hair. Tobey, Woolley, and Armstrong (1985) developed a photogoniometer that measured wrist motion data from two lines that were attached to the back of the hand and are connected to two sliding wires. As the sliding wires were linearly displaced by the two lines, an optical encoder mechanism converted the linear displacement into analog voltages. The wrist angle data were synchronized with two video camera images for evaluation. Schoenmarklin and Marras (1987) developed an electromechanical device that accurately measured wrist motion in two planes, and this device was used to measure wrist motion in simulated industrial tasks. This device was called a wrist monitor, and is shown in figure 4. The wrist monitor was a small plastic box that was strapped to the 33
Potentiometer # I Potentiometer # 0
Aluminum Frame
Velcro/Elastic Band Orthoplast Cuff
B
Handle used in Calibration .Table
Figure 10. Wrist monitor and calibration equipment described in Schoenmarklin and Marras (1987) and used in Schoenmarklin (1988a). A) shows the wrist monitor strapped to a subject's wrist. B) shows the the Orthoplast cuff that is custom-molded to a subject's wrist. C) illustrates handle and pointer used to calibrate the monitor. D) shows a subject sitting nest to the calibration table with his hand aligned on top of the table. The two semi-circular arcs have tic marks to record the angles in the radial/ulnar and flexion/extension planes. wrist and collected voltages from two potentiometers. Two lines were connected to the index and ring fingers, and as the hand moved, the two lines pulled at different distances from the box. As the wrist was ulnarly or radially deviated, one line increased its distance from the monitor while the other shortened its distance. This resulted in one voltage increasing and one voltage decreasing. As the wrist was flexed or extended, the voltages increased or decreased in tandem. The wrist monitor produced accurate and repeatable results, even during a hammering task in which the arm and hand were vigorously shaken and the wrist was repeatedly snapped (Schoenmarklin, 1988a, 1988b). The disadvantages of this wrist monitor were that R/U and F/E angles were not measured independently and extensive calibration was required for each subject.
Review of Research Voids and Objectives The relationship between the three most cited occupational factors, wrist posture, repetition, and force, and specific wrist CTDs has been cited often in the literature. Except for a few notable studies (Armstrong et al., 1982; Silverstein et al., 1986, 1987), the context of this relationship has been qualitative and unsubstantiated by epidemiological data. With respect to wrist posture, the discussion has not even considered the full range of 35 anatomical issues. Much of the discussion in the literature on wrist posture has centered on F/E and R/U deviation, neglecting the third degree of movement, P/S. In Silverstein's et al. (1986, 1987) studies, a gross dose-response relationship was established between dichotomous levels of repetition and incidence of CTS and CTDs overall. These investigators found that the odds ratios for risk of CTS and CTDs were 1.9 and 3.6, respectively, in high repetition jobs compared to jobs that required a low number of repetitions. Silverstein et al. (1986, 1987) demonstrated that workers in jobs that required highly repetitious, hand-intensive work were at a significantly greater risk of developing CTS and CTDs than their counterparts in low repetition jobs. However, these researchers did not investigate the dynamic components that comprise repetitious wrist motions, angular velocity and acceleration. The work of Silverstein et al. (1986, 1987) provided the basis for the followup question: "What type" and "how much" wrist motion in highly repetitious jobs exposes a worker to CTDs? Heretofore, there was a lack of data on the kinematic aspects of wrist motion in industrial jobs, and no one had been able to quantify precisely wrist angle, velocity, and acceleration in high risk repetitive industrial tasks. Thus, we were not able to understand 36 which specific wrist motion parameters were associated with wrist CTDs as a group. In order to effectively prevent CTD injuries in the workplace, industry needs quantitative guidelines on the specific wrist motion parameters that expose workers to CTDs. Qualitative guidelines, such as "Keep your wrist in a neutral position", are impractical for industry to use as a preventive tool. Quantitative guidelines are needed to evaluate the CTD risk level of jobs and test alternative workplace layouts. The first major objective of this doctoral research was to determine quantitatively what kind (R/U, F/E, and P/S) and how much wrist motion (e.g. angle, velocity, and acceleration) were associated with high risk of CTDs. The association between wrist motion parameters and CTD risk is important to know since most jobs require some wrist motion, yet heretofore the quantity of wrist motion that was injurious to workers was not known. Since most of the symptoms of CTDs in industry are recorded generically on OSHA 200 logs as wrist strains, sprains, or tendinitis and also since the symptoms of many CTDs overlap, then a study associating wrist motion with a specific CTD, such as CTS, is impractical. Practically speaking, in order to determine the association between wrist motion and CTDs, CTDs were considered a group. The 37 intent of this research study was to determine the association between wrist motion and wrist CTDs as a group. The second major objective of this doctoral research, development of a biomechanical model of the wrist joint, complements the first objective in that modeling could explain why those motions found in the epidemiological study expose workers to risk of CTDs. Modeling could possibly provide a biomechanical mechanism for the deleterious effects of repetition and wrist angle on anatomical structures in the wrist, and it also could provide a structure for teasing out spurious statistical correlations between specific wrist motion parameters and CTDs. The model developed in this research improves upon previous models (Armstrong and Chaffin, 1979a; Schoenmarklin and Marras, 1991a) in that it is 3-D and includes coactivation of antagonistic muscles. Research in biomechanical modeling also benefits the engineering, medical, and clinical communities by expanding our general knowledge of the wrist joint. CHAPTER III INDUSTRIAL QUANTIFICATION OF WRIST MOTION
Approach The incidence of CTDs is growing in the workplace, yet up until now we did not have any quantitative guidelines on two often cited occupational risk factors, wrist posture and repetition, for industry to utilize. One of the major research voids in the study of occupational CTDs was the lack of quantification of the link between static (wrist angle) and dynamic (velocity and acceleration) kinematic parameters of wrist motion and incidence of CTDs. The objective of the industrial quantification phase was to determine quantitativelv the association between specific wrist motion parameters and incidence of CTDs as a group. Industry can use these quantitative guidelines to evaluate CTD risk levels of jobs and establish effective ergonomic programs to prevent CTDs. The approach in the industrial quantification phase was a study in which wrist motion data were collected from industrial workers at the factory floor level. Industrial plants in the Midwest that required highly repetitious,
38 hand-intensive work were selected as sites for data collection. Dichotomous CTD risk levels (low and high) of repetitive jobs in the participating plants were determined by OSHA and medical records, and wrist motion of workers in high and low risk jobs was monitored on the factory floor while they were performing their tasks in a normal manner. Wrist motion data were analyzed as a function of CTD risk level in order to establish quantitative guidelines or
"benchmarks" for industry to utilize.
Methods Subjects. A total of 40 subjects volunteered to participate in this study. The gender distribution of subjects within each risk group was identical in that there were 11 men and nine women in each of the low and high risk groups. Although a few of the subjects did have previous CTD injuries, all of the subjects were healthy at the time their wrist motion was monitored. Experimental Design. In epidemiological terms, the experimental design was a cross-sectional cohort study in which the only independent variable was exposure to CTDs in selected jobs at participating companies. Exposure had two nomimal levels, jobs that had low and high risk of CTDs. Risk of CTDs was determined from evaluation of Occupational 40 Safety and Health Administration (OSHA) 200 logs and medical records in participating companies. The experimental design was a fully nested design, as illustrated in figure 11. Subjects, which were nested under jobs, and jobs, which were nested under risk levels, were random variables. Risk was a fixed variable. Within each risk level, ten repetitious, hand-intensive jobs were randomly selected from the set of participating companies. Within each job, two subjects were randomly selected. The dependent variables comprised three categories: subject characteristics, job characteristics, and wrist motion metrics. The subject characteristics were age, gender, handedness, work experience, job satisfaction, and anthropometric dimensions, whereas the job characteristics included number of wrist motions per eight hour shift, weight of loads, handgrip types and forces, work heights, and motion descriptions. The wrist motion measures consisted of the following statistics in the radial/ulnar, flexion/extension, and pronation/supination planes:
1. mean, minimum, maximum, and range* of wrist angle 2. mean, minimum, maximum, and maximum difference* of angular velocity 3. mean, minimum, maximum, and maximum difference* of angular acceleration * range = maximum - minimum * maximum difference = maximum - minimum 41
NESTED EXPERIMENTAL DESIGN
N = 40.
Fixed: Risk (2) Low (20) High (20)
Random: Job (10) hi
Random: Subject (2)
Figure 11. Experimental design of the industrial quantification phase. The experimental design was a fully nested design in which CTD risk level was fixed at two levels. Jobs were nested under risk level, and subjects were nested under jobs. Jobs and subjects were randomly selected. 42 Apparatus. Goniometric instrumentation was used to collect wrist motion data in the R/U, F/E, and P/S planes. These devices are described in the following sections. Apparatus — Wrist Monitor. A wrist monitor was developed in the Biodynamics Laboratory to collect on-line data on wrist angle in R/U and F/E planes simultaneously, and further analysis of wrist angle data yielded velocity and acceleration in both planes of motion. This wrist monitor was composed of two segments of thin metal feeler stock that were joined by a rotary potentiometer. The potentiometer measured the angle between the two segments of feeler stock. The potentiometers were placed on the center of the wrist in the R/U and F/E planes. Compared to the monitor discussed in Chapter 2 and reported in Schoenmarklin and Marras (1989a, 1989b), this wrist monitor was smaller, lighter (approximately 0.05 kg.), less intrusive, recorded R/U and F/E angles independently, and did not have to be calibrated extensively for each subj ect. The monitor was calibrated to each subject by recording the voltages of the R/U and F/E potentiometers while the subject's wrist was in neutral position on a calibration table. The bony landmarks shown in figure 12 were used as reference points to align the wrist in the R/U and F/E planes. In both the R/U and F/E planes, the wrist is in a neutral position when the longitudinal axis of the radius is parallel to the third metacarpal bone (Taleisnik, 1985; Palmer et al., 1985). Neutral position in the R/U plane was accomplished by aligning marks placed on the third metacarpophalangeal joint (middle finger knuckle), the center of the wrist, and lateral epicondyle of the elbow (Taylor and Blaschke, 1951; Knowlton and Gilbert, 1983). The center of the wrist on the dorsal side is the "palpable groove between the lunate and capitate bones, on a line with the third metacarpal bone" (Webb Associates, 1978, p. IV- 61). The wrist was aligned in a neutral position in the F/E plane when the center of the second metacarpal head, radial styloid, and lateral epicondyle were collinear (Brumfield and Champoux, 1984) . The angular deviation of the wrist in the R/U and F/E planes was calculated according to equation (6).
© = (Vij - Vnj) * (65 deg/volt) (6) where: © = angular deviation in deg. from neutral angle in plane j (plane j corresponds to potentiometer j) Vij = voltage recorded at time i from potentiometerj Vnj = voltage recorded at neutral angle from pot. j 65 = ratio between angular deviation and change in voltage 44
Flexion
RadialLateral Second Extension A) Epicondyle Styloid Metacarpophalangeal Joint
Radiol
Ulnar
Lateral Palpable Groove Third B) Epicondyle between Metacarpophalangeal Lunate and Capitate Joint
Figure 12. Bony landmarks on the elbow, wrist, and hand that were used to align the wrist in a neutral position in the radial/ulnar and flexion/extension planes. This figure is from Schoenmarklin and Marras (1989a). 45 The constant ratio of 65 degrees per volt obviated exhaustive calibration of each subject. Only the neutral voltages in the R/U and F/E planes were needed to provide reference voltages in each plane. Once the reference voltages were known, then all wrist angles during the trials were calculated according to equation (6). The sign convention for angles in the R/U and F/E planes was as follows: R/U: Pos = radial deviation Neg = ulnar deviation F/E: Pos = flexion Neg = extension
Apparatus — Pronation/Supination Device. The pronation/supination device.recorded the P/S angle of the forearm. The P/S device consists of a rod that remained parallel to the forearm during rotation. The rod was attached to a bracket affixed to the proximal end of the forearm with a velcro cuff. The rod did not rotate with respect to the proximal cuff. On the distal end of the forearm, the rod was connected to a potentiometer that was attached to a bracket. As the forearm rotated, the potentiometer rotated with respect to the fixed rod, and voltages from the potentiometer record the angular displacement of the forearm. The ratio between angular excursion and change in voltages was not constant for subjects in the P/S plane, so this ratio had to be calculated for each subject. The P/S device was calibrated by the use of a P/S dial. While a subject held his elbow at 90 degrees next to his side and his forearm parallel to the ground, the experimenter adjusted the height of the calibration dial. The subject grasped the handle on the dial. When the handle was aligned vertically, this position was defined as the neutral P/S angle. Voltages were collected from the P/S potentiometers in both arms when the forearms were aligned in a neutral position. Then, the subject was asked to maximally pronate his forearms within comfortable limits. Voltages were recorded while his forearms were maximally pronated. Maximal supination was recorded in a manner similar to pronation. Based on the three pairs of angular and voltage data, a best-fitting regression line was calculated for each subject's forearm. The relationship between P/S and voltage was linear, as evinced by squared coefficients of determination that averaged about 0.98. The P/S angle was calculated according to regression equation (7). 47 0 (7) where: 0 = pronation/supination angle at time i Bo = regression intercept B1 = regression slope Vi = voltage at time i
The sign convention for angles in the P/S plane was as follows: P/S: Pos = pronation Neg = supination
Apparatus — Selection of Sampling Frequency. The R/U, F/E, and P/S voltages were monitored at 300 Hz. This frequency was selected based on computations of the minimum frequency needed to capture a reasonable amount of information in maximal extension/flexion (E/F) movements. Based on empirical data, a person can move from a maximal extension angle to flexion angle within approximately 0.1 seconds. Figure 13 represents the angular displacement of a maximal E/F movement. The angular displacement of a maximal E/F movement as a function of time was approximated by an exponential decay function. The exponential model that is illustrated in figure 13 is defined in equations (8) and (9) . Displacement in Flex/Ext plane (deg) x(tO) x(tl) x(tl) oeet smdlda eaieepnnil function. exponential negative a as modeled is movement this task in approximately 0.1 seconds. The path of wrist wrist of path The seconds. 0.1 approximately in task this iue 3 Dslcmn famxmlwitmvmn from movement wrist maximal a of Displacement 13. Figure full extension to flexion. Normal subjects can accomplish accomplish can subjects Normal flexion. to extension full to \ > ------ie (sec) Time .0 sec 0.100 t1 ah f maximal of Path movement (1 - e( (1t Mxt )) x(tO )M *(t1-tO (e*(B - x(t1) xoeta function: Exponential xeso t flexion to extension
00 ■tt 49
x(tl) = (eA(b*(tl - to)) )*(x(tO)) (8) x(tl)/x(to) = eA(b*(tl - to)) (9) where: to = start of maximal extension to flexion movement tl = end of " " " " " " " x(tO) = wrist angle at time to x(tl) = wrist angle at time tl b = coefficient of exponential model tl-tO = time interval of maximal movement, approximately 0.1 seconds
Solving for b in equation (9) with natural logarithms results in equation (10). For (tl - tO) = 0.1 seconds and an maximum allowable value of x(tl)/x(t0) = 5% or 0.05, b = -30.
b s ln( x (tl)/ x (to) ) / (tl - to) (10)
The estimation of b is sensitive to the time interval (tl - to), but more importantly, the exponential model is only a crude estimate because the displacement curve in figure 13 is clearly not a pure exponential function. However, this model does provide a rough estimate of the angular displacement path of the wrist. The change in angle between two consecutive sampling points should be less than 10%, which can also be expressed as a 90% ratio of angles between two consecutive sampling points. The maximum time interval between consecutive sampling points is A . The two consecutive sampling points 50 are at tiroes ((n+l)*A) and (n*ti). Equation (11) is a transformation of equation (9) using sampling rate variables.
x((n+l)*A) / x(n*A) = eA (b*A) (11) where: A = maximum time interval x((n+l)*A) = wrist angle at data point n+1 x(n*A) = wrist angle at data point n b = coefficient of exponential model
Solving for A in equation (11) results in equation
(12).
6 = ln( x((n+l)*A) / x(n*A) ) / b (12)
For b = -30 (from equation (10)) and x((n+1)*A)/x(n*A) = 0.90, D = 0.003512 seconds. The inverse of 0 is 285 Hz, which is the minimum sampling rate. Asampling frequency of 300 Hz was selected to ensure an upper limit of 10% change in displacement between consecutive data points during maximal wrist movements. Advantages of Wrist Monitor and P/S Device. The wrist monitor and P/S device were used as a means to quantify wrist motion in high and low risk industrial jobs. These monitors provided data that addressed the research void of the association between specific wrist motions and CTD risk. 51
Strapped to workers' wrists and forearms in industry, the monitors collected three-dimensional wrist motion and repetition data at high frequencies (3 00 Hz) for long sampling periods.
Data Conditioning — Filter. The filter utilized in this project is structurally different from the conventional finite difference method used to compute velocity and acceleration. With the finite difference method, the position of each point in time is computed, and then the velocity is calculated as the derivative of position. Subsequently, acceleration is computed as the derivative of velocity. However, the filter in this study calculated position, velocity, and acceleration simultaneously. In addition to the computation of three kinematic measures, the filter conditioned the data by sifting out a certain amount of noise. Data Conditioning — Concept of Filter. The filter is a sequence of three simple first order low pass filters cascaded together. The parameters, a, B, and r, determine the cutoff frequency in radians/sec. Figure 14 illustrates the three cascaded filters in which the Laplace transforms of raw data, d(s), and filtered data, y(s), are the inputs and outputs of the model, respectively. The three cascaded filters in figure 14 can also be represented as the flow 52 chart in figure 15. By expansion, the flow chart in figure 16 is identical to figure 15. The form in figure 15 communicates the intuitive nature of how the low-pass filter works. For steady state operations with sinusoidal inputs, s a j*w, where j = (-1) A (. 5) and w is a frequency. Therefore, each block of the form, r/(j*w + r), is a complex number. For w < k, where k is the cutoff frequency/ the magnitude of the complex number approaches 1. For w > k, the magnitude approaches 0. The filter passes frequencies below k unattenuated and greatly attenuates higher frequency signals. The form of the filter in figure 16 is equivalent to the first form (figure 15), but it is better suited for the task of estimating velocity and acceleration. The transfer function in figure' 16 provides the basic structure and mathematical properties of the filter, but it does not specify its implementation. By writing the differential equation of the filter and inverting the transform, the filter becomes equation (13) . d(s) y(s)
d(s) = Laplace transform of raw data y(s) * Laplace transform of filtered data
Figure 14. Three first order low pass filters cascaded together. The Laplace transforms of the raw data and filtered data (d(s) and y(s)) are the input and output.
d(s) y(s)
Figure 15. Product of the three low pass filters shown in figure 14. This filter is identical to the one in figure 14. O? U> s 3 + ( . * +(2>+ r ) 5 x + + <*r)s
d(s) = Laplace transform of raw data y(s) = Laplace transform of filtered data
Figure 16. Expansion of the filter shown in figure 15. This filter is identical to the one in figure 15.
ui d(t) = y (t) + (a + B + D*y(t) + (an + nr + ar)*y(t) + (aflr)*y(t) (13) where: d(t) = continuous data signal (not available due to sampling) v(t) = filtered position signal y(t) = filtered velocity signal y(t) = filtered acceleration signal y(t) = filtered derivative of acceleration
Data Conditioning — Implementation of Filter. The filter must be expressed in a form suitable for use with sampled data. The following is one way to achieve that end.
Define:
xi(t) = y(t) (14) X2(t) = y(t) X3(t) = ytt)
The x variables on the left of (14) are state variables correponding to data of interest, namely, position, velocity, and acceleration.
Xl(t) = X2(t) (15) X2(t) = X3(t) X3(t) = - (aer) *xi (t) - (aB + Br + an*x2(t) -(a + 13 + n*X3(t) + (afiD *d(t)
The first two equations in (15) are definitions of the variables, and the third equation is derived from equation (13). The equations in (15) can be expressed in matrix 56 form, as Indicated in Figure 17. Based on linear systems theory, the matrix equation in Figure 17 was modified for computation and transformed into a software program. Values of 105, 107, and 109, were selected for a, fl, and r, respectively. These values correspond to cutoff frequencies of approximately 17 Hz. In order to filter out noise, the data were passed through the filtering system twice. In the first pass, the raw position data entered the filter and the position, velocity, and acceleration were calculated. In the second pass, the estimated position data from the first pass entered the filter and the position, velocity, and acceleration were calculated in a similar manner. The effect of the two passes on the kinematic measures was a time delay of approximately 0.06 sec (18 data points sampled at 300 Hz) between the raw and calculated position data, as illustrated in figures 18 and 19. pata Conditioning — Validation of Filter. When compared to a video-based Motion Analysis system, the position data from the wrist monitor and P/S device were within 4% of the Motion Analysis angular data. Since Motion Analysis collects data at a slow rate of 60 Hz, data from the wrist monitor and P/S device, which are collected at 300 Hz, are probably more believable, particularly in dynamic movements. The filter was validated by comparing the traces x1(t) 0 1 0 x1(t) 0 x2(t) 0 0 1 x2(t) + 0 d(t) x3(t) - oft - r + ” ^ +r) x3(t)
X(t) A _x(t) + B d(t)
X(t) A*x(t) + B*d(t)
Figure 17. Matrix form of the filter shown in figure 16. Refer to text for definitions of variables.
Ul 58 of the raw and calculated position data. Figures 18 and 19 show the traces of the position data from maximal ballistic R/U and slow F/E movements, respectively. The calculated position followed the the path of the raw position quite well in both plots. The filter was further validated by integrating the calculated acceleration twice, which resulted in position estimates, during maximal ballistic movements in the R/U, F/E, and P/S planes. The range of motion (ROM) of estimated position data from integration was compared to the raw ROM. In the R/U and F/E planes, the estimated ROMs were within 3%, while the estimated ROMs were within 7.5% in the P/S plane. The integration method confirms the extremely large peak accelerations and velocities that were measured in maximal ballistic motions. Based on empirical data, peak accelerations in the R/U, F/E, and P/S planes were approximately 15,000, 30,000, and 90,000 deg/secA2, respectively. Peak velocities in the three planes were within upper limits of 1000, 2000, and 3000 deg/sec. The high compatibility between the raw ROM and ROM from integration confirms the extremely high accelerations and velocities that were calculated during ballistic trials. In order to physically move from one extreme angle to another 59
RAW VS. CALC P O S FAST R /U MOVEMENT 300 HZ. *-105.107,109. 2 PASSES. LEFT 50
30 -
20 -
10 -
- 1 0 -
- 2 0 -
- 3 0 -
- 4 0 0 0.4 0.6 0.8 1 1.2 1.6 1.8 2 TIME (SEC) RAW LEFT R/U — ™ CALC R/U POS
Figure 18. Displacement of the raw and filtered position of a fast radial/ulnar movement. Figure 19. Displacement of the raw and filtered position position filtered movement. and raw ofthe flexion/extension slow Displacement a 19. Figure POS (DEC) 0 5 - - 0 4 - -10 - 0 3 - 0 2 - A LF F/ O i « « i POS /E F LEFT RAW 0 2 - 30 50 - - 60 70 10 - - - - A V. AC O — SO F/ MOVEMENT /E F SLOW — POS CALC VS. RAW 2 2.2 2.4 300 HZ. *-105.107.109. 2 PASSES. LEFT PASSES. 2 *-105.107.109. HZ. 300 2.6 2.8 IE SEC) C E (S TIME 3 CALC LEFT F /E CALC LEFT /E F POS .3 44 3.63.4 61 within a brief time interval (approximately 0.1 seconds), the wrist has to accelerate at an immense rate. Integrated Data Collection System. The goniometers were combined with customized data collection software into a portable, self-contained system. Figure 20 shows a schematic of the flow of data. Six channels of wrist motion were monitored directly on the factory floor, and these voltages were transmitted to a 12 bit analog-to-digital (A/D) converter board (Labmaster). The six channels comprised R/U, F/E, and P/S motion of both upper extremities. In addition to the six channels of wrist motion, two time marker channels were transmitted to the A/D board. These time markers signaled the start and end of selected intervals of interest, as illustrated in figure 21. Each interval represented a motion component during the repetitive cycle; the idle time between motion components during a cycle was not of interest. Each interval was recorded by the experimenter pressing hand-held switches at the start and end of each interval. The switches generated electronic pulses that were transmitted to the A/D board. The data from all eight channels were stored on a portable 386 micro-computer and analyzed later in the laboratory. In the laboratory, the wrist motion voltages were converted into R/U, F/E, and P/S angles by equations Calibration Software Time Equation (calculates Markers (converts pos, vel, volts to and accel) degrees) --
A /D Board Portable Position 8 channels Micro Velocity (volts) computer Accel
Figure 20. Integrated data collection system consisting of hardware and software that monitor wrist motion on the factory floor and process the data in the laboratory.
o> fo SAMPLE DATA Demonstration of Time Markers 900 800 - 700 - 600 - 500 - 400 - 300 -
200 -
100 -
-100 -
-200 - -300 - -400 - -500 - -600 - -700 - -800 0 Z 4 6 8 10
Time (s e c )
Figure 21. Trace of wrist velocity data during a ten second trial. Within the ten second period, there were two time intervals of interest. Each interval represented a motion component. (6) and (7), and the position, velocity, and acceleration were calculated according to the filter described earlier. The summary statistics (mean, maximum, minimum, and range/maximum difference) of the position, velocity, and acceleration were computed for each interval within all the data trials. These summary statistics were transmitted to an IBM mainframe computer and were analyzed by SAS Institute software. Selection of Participating Companies and Jobs. Eight manufacturers in the Midwest volunteered to participate in this study. All of these companies' manufacturing operations required repetitive, hand-intensive work, and most of these companies manufactured products for the transportation industry. As part of the agreement between Ohio State University and the participating companies, the identity and location of these manufacturing plants will remain confidential. The type of manufacturing operation and the number of jobs and subjects who were monitored at the plants are listed in table 3. Table 3. Type of manufacturing operation and number of jobs and subjects whose wrist motion was monitored.
Type of mfg operation # of Jobs # of Subj in participating companies Automotive suspension parts and assembly* Automotive engine parts and assembly Automotive brake parts and assembly Automobile final assembly Truck parts assembly Plastic injection molding Commerical building products** Vehicle seating and upholstery assembly Total: 8 plants 20 jobs 40 subjects * only one subject was monitored in one job ** three subjects were monitored in one job 66
Table 4. Number of fundamental wrist movements per eight hour shift in each monitored job.
High Risk Jobs # of wrist movements Vehicle strut assembly 20,250 Shock absorber rod loader 25,200 Brake liner loader 30,926 Steering column assembly 16,400 Oil filter string tie 51,428 Oil filter welder 25,920 Rubber hose molder 17,590 Pipe insulation jacketer 22,793 Vehicle weatherstrip assembly 16,400 Vehicle seat assembly 19,200
mean = 24,738 S . d . = 10,432
Low Risk Jobs # of wrist : Shock absorber bracket installer 19, 000 Shock absorber cap installer 37, 500 Shock absorber rod installer 37, 500 Brake liner cutter 13, 130 Oil filter bracket inspector 20, 160 Large oil filter assembly 63, 000 Rubber parts inspector 24, 000 Pipe insulation socker 17, 500 Air hose terminator 14, 000 Air hose assembly 15, 530 mean = 26,132 s.d.= 15,259 67 The jobs within the eight plants were selected based on number of wrist movements, personnel policies, and risk of CTDs. The minimum acceptable number of wrist movements was 13,000 fundamental wrist movements (Barnes, 1981) during an eight hour shift, which represents one wrist movement approximately every two seconds (refer to table 4). In addition, potential jobs were scrutinized according to whether there was job rotation among workers. The presence of job rotation could artificially lower the actual incidence rate of CTDs. Only jobs that met the minimum number of wrist movements and did not involve rotation among workers were candidates for inclusion in this study. The risk of CTDs was computed according to equation
(1 .6 ) from 1988 or 1989 OSHA 200 log data. Based on a survey of over ten companies, reports of CTDs were not generally recorded on OSHA logs until 1988 or 1989. incid = ( (#inc)/( (workers) *(hrs/wk)*(wks/yr) ) (16) rate *(200,000 worker-hrs) where: incid number of incidents recorded on OSHA 200 rate logs per 200,000 worker-hours of exposure for a particular job line number of incidents recorded on OSHA 200 logs during a one year period workers number of workers in a particular job hrs/wk average number of hours each worker on a particular job worked during the week wks/yr average number of weeks that each worker in a particular job worked during the year 200,000 the aggregate number of worker-hrs of 100 worker- full-time workers who work 50 40-hour weeks hours a year 68
A low risk job was defined as having a zero incidence rate, whereas a high risk job was defined as having an incidence rate of eight or more. Factory Floor Protocol. Subjects who met the prerequisites in the Subjects section filled out a consent form and a background survey form shown in the Appendix. The background survey form included age, health status, history of CTDs, work experience, number of years worked on current job, job satisfaction, etc. In addition, anthropometric recordings of each subject's gross and upper extremity dimensions were measured. The wrist monitor and P/S device were strapped on the subject's right and left forearms and hands, and neutral calibration voltages were recorded, as described in this Chapter. The calibration data were recorded on forms that are shown in the Appendix. With his arms at his sides and elbows bent at 90 degrees, the subject moved his hands from one extreme angle to another as quickly as he could in the R/U, F/E, and P/S planes. The data from these dynamic trials were later analyzed in the laboratory to compute the maximum range of motion, velocity, and acceleration in each plane. After the setup, calibration, and dynamic trials were completed, a brief task analysis of the subject's job was performed. In consultation with the subject, specific phases of the subject's job were selected to monitor. Wrist motion during the idle time between cycles or within a cycle was not monitored. Next, the subject was asked to perform his job while we collected wrist motion data during ten second sampling periods. A minimum of ten trials was collected from each subject. As described in the Apparatus section, time markers were used to mark the time that intervals of interest started and ended throughout the ten second trials. Through the use of time markers, the wrist motion of motion components and specific phases of each subject's job was monitored. The number and distribution of intervals and ten second trials were time-weighted in order to represent the percentage of time that each subject spent in each phase of his job. During data collection, the subject performed his job with real parts or tools in a normal manner. Every attempt was made to minimize any possible interference with the job. Video documentation was used to document finger position, hand configuration, and work ambience. After data collection, the wrist monitor was taken off the subject, and anthropometric dimensions of the full body and upper extremities were measured. The subject was asked to simulate the amount of force that he exerts on the job on a Smedley grip strength dynamometer. The distance between the Smedley's gripping surfaces were adjusted to reflect the grip span of the worker's hand configuration on the job. 70 The subject was then thanked for his time and efforts and was given a. Biodynamics Lab T-shirt in return for his participation.
Results — Subject Characteristics Age and Work Experience. As indicated in table 5, the subjects in the low risk group were significantly older than their counterparts in the high risk group (46.9 vs. 36.6 years old). The low risk employees also worked about twice as many years for their respective companies than the workers in the high risk group (20.0 vs. 10.9 years). The fact that the workers in the low risk group were older and had a longer tenure with the company is probably partially due to the seniority system. In most of the eight participating companies, the management and union worked out a structured job selection system in which workers could select their jobs based on seniority. Since most of the low risk workers had more seniority than their high risk counterparts, they had the opportunity to bid for the less strenuous jobs. Handedness. All the workers in the high risk group were right-handed, and nineteen of the twenty subjects in the low risk group were right-handed. 71 Table 5. Mean values, standard deviations, and probability of type I error of subject characteristics and anthropometric dimensions. The effect tested was risk of CTDs (DF = 1) , and the error term was job nested within risk level (DF = 18). High Risk Low Risk P-value Dependent Var. Mean St. Dev. Mean St.Dev. SUBJECT CHARACTERISTICS Age (years) 36.6 (10.2) 46.9 (8.12) 0.0025* Years on job 3.90 (3.40) 7 . 00 (6.13) 0.1751 Years with company 10.9 (8 . 10) 20.0 (5.45) 0.0024* Job satisfaction** 6.45 (2.11) 7 .40 (1.93) 0.1527 ANTHROPOMETRIC DIMENSIONS Gross Dimensions (kg and cm) Weight 77.5 (15.7) 84.6 (15.2) 0.2084 Stature 173.4 (9.68) 171.3 (10.8) 0.5999 Shoulder height 143.3 (9.17) 142.8 (9.20) 0.8677 Arm length 76.2 (4 . 80) 75.9 (5.97) 0.8728 Trunk depth 23.7 (4.42) 28.0 (5.72) 0.0202* Shoulder-elbow length 36.5 (2.44) 3 6.6 (3.03) 0.9210 Elbow-wrist length 28.4 (2.07) 28.7 (2.36) 0.7094 Elbow-hand length 46.3 (2.49) 46.7 (3.68) 0.7769 Dominant Hand Dimensions (cm) Hand length 18.3 (1.06) 18.4 (1.46) 0.7034 Thumb length 5.84 (0.40) 5.85 (0.83) 0.9759 Middle finger length 7.75 (0.43) 7.96 (1.05) 0.5085 Hand breadth 8.03 (1.35) 8 .33 (0.76) 0.4967 Hand thickness 3.08 (1.16) 2 .92 (0.33) 0.5728 Wrist breadth 5.79 (0.87) 6.04 (0.64) 0.3928 Wrist thickness 4.03 (0.49) 4 • 13 (0.46) 0.5222 Wrist circum. 16.6 (1.62) 17. 6 (1.74) 0.1082 Forearm circum. 26.70 (3.11) 26.73 (4.79) 0.9852 Maximum grip strength (kgf) 39.4 (14.9) 36.8 (15.1) 0.6539 * statistically significant at the 0.05 level ** job satisfaction data were analyzed by the Kruskal-Wallis one-way nonparametric test, which employs a chi-square reference distribution. 72 Job Satisfaction. The mean subjective ratings of job satisfaction between the low and high risk groups were not significantly different, as indicated in table 5. Since the subjective rating scales were not continuous but ordinal in nature, a nonparametric Kruskal-Wallis one-way procedure was used to test for significant differences in ratings. Anthropometric Dimensions. Except for trunk depth, the gross and upper extremity dimensions were not significantly different between subjects in both risk groups (refer to table 5). The greater trunk depth of the low risk subjects is probably attributable to the positive correlation between weight and age (Webb Associates, 1978). The anthropometric data in table 5 were measured according to established guidelines in NASA 1024 (Webb Associates, 1978; Garrett, 1970a and 1970b) for gross and upper extremity dimensions, respectively. Maximal Wrist Movement Performance. The summary statistics of the maximal dynamic movements in the R/U, F/E, and P/S planes generally did not reveal any pattern of significant differences between subjects from both risk groups. Results — Job Characteristics Number of Wrist Movements. The mean number of fundamental wrist motions in both risk levels did not significantly differ, as shown in table 6. The mean number of wrist motions per eight hour shift was approximately
25,000. Incidence Rate. As indicated in table 6, the median incidence rate of the high risk jobs was 18.4 reported claims per 200,000 hours of exposure. By definition, all the low risk jobs had an incidence rate of zero. Lost and Restricted Days. The median number of lost and restricted days in high risk jobs were 111.5 and 42.9, respectively. These values were normalized to 100 full-time workers per year (200,000 hours of exposure), which is the statistical convention that the Bureau of Labor (1990) employs. The median value of 111.5 lost days from the high risk jobs in this study is approximately the same as the 107.4 lost work days that the Bureau of Labor Statistics (1990) reported for the national manufacturing industry as a whole (based on 1988 data). By definition, there were no lost or restricted days in the low risk jobs in this study. 74 Table 6. Mean values, standard deviations, and probability of type I error of job characteristics. The effect tested was risk of CTDs (DF = 1), and the error term was job nested within risk level (DF = 18). High Risk Low Risk P-value Dependent Var. Mean St.Dev. Mean St.Dev. JOB CHARACTERISTICS Number of wrist movement** 24738 10432 26132 15259 0.8178 Number of workers 16.9 (15.6) 6.50 (2.56) 0.0581 Number of incidents 3.90 (3.14) 0 -- Incidence rate*** 39.30 (56.0) 0 - - Lost days**** 111.50 (419) 0 -- Restricted days**** 42.90 (131) 0 - - Turnover rate (%) 33.00 (85.7) 0.500 (6.06) 0.0569 Wt. of object (kg) 1.38 (1.51) 0.87 (1.31) 0.4320 Work height (m) 0.87 (0.15) 1.01 (0.13) 0.0328* Moment arm (m) 0.70 (0.25) 0.60 (0.13) 0.2609 Left hand grip force (kgf) 12.8 (8.65) 4.80 (3.73) 0.0198* Right hand grip force (kgf) 12.0 (8.26) 4.58 (3.96) 0.0194* 0 median value * statistically significant at the 0.05 level ** per eight hour shift *** normalized to 200,000 hours of exposure **** normalized to 100 full-time workers per year 75 Turnover rate. The turnover rate of workers in each job was calculated according to equation (17). (Note: the turnover rate can be greater than 100%.)
turnover rate = (wleft / positions) * 100 (17) where: wleft = number of workers who left job during time period that OSHA logs were monitored #positions = number of positions (workers) within job
The median turnover rate in the high risk jobs was approximately 66 times as great as in low risk jobs (33% vs. 0.5%) . Physical Attributes of Workplace. Except for the work height, the weights of parts and moment arm from the work area to the lower spine were not significantly different (refer to table 6). The work height in the low risk jobs was higher than in high risk jobs. Handgrip Types and Forces. The type of hand configurations that workers utilized to perform their tasks were classified into two general groups, power and pinch grips. The power and pinch grasps were split about evenly among the subjects within each risk group. As estimated by the Smedley grip strength dynamometer, the grip forces required in the high risk jobs were about three times as great as the low risk grip forces (left hand: 76 12.8 kgf vs. 4.8; right hand; 12.0 vs. 4.58) (see table 6). These values are similar to the grip forces that Silverstein et al. (1986, 1987) measured in jobs that were classified as high and low force jobs. In Silverstein's et al. (1986) epidemiolical study investigating CTDs, the mean adjusted grip forces in the high and low force jobs were 12.7 and 3.0 kgf, respectively. In Silverstein's et al. (1986, 1987) studies, the mean adjusted grip force was defined according to equation (18).
Mean adjusted force (kgf) = (var/mean) + mean (18) where: var = variance of grip force within a subject during a task mean = mean grip force within a subject during a task
Structure of Statistical Analysis The statistical analyses of wrist motion data were structured according to figures 22 and 23. In figure 22, there were three sets of data, with each of the latter two sets encompassing the collapsed means of the previous set. For example, the first data set, Dl, contained all the data from all intervals within trials. Dl had 1528 intervals of wrist motion. The summary statistics of the intervals were then averaged and collapsed over all trials to obtain set D2, which contained 528 trials. Likewise, all the summary D1 D2 D3
Risk Risk Rlak Data Right Hand Job Job Job Files Subl Sub] Subj Trial Trial Lalt Hand (N ! # of N • 1628 628 40 Observations)
Figure 22. Conditioning of data collapsed over intervals and trials.
D3 D3B Data Right Hand Risk Risk One Hand Files Job Job Left Hand Subj Subj (N - # of N - 40 N - 40 observations)
Analyala Statistical of Variance Analysis % Variance Partitioning: Job, Subj
Principal Componenta Analyala
Dlacrimlnant Function Analyala
M ultiple Loglatlc Regreaalon
Figure 23. Statistical analysis of data collapsed over hands. 78 statistics from the trials were averaged and collapsed over all subjects to produce the 40 observations in set D3. Each observation in D3 referred to a subject. In order to remove handedness from the dataset, the kinematic data from both hands were then collapsed into one hand, as indicated in figure 23. This was accomplished by considering the wrist motion from only the injured hand in high risk jobs, which was determined from OSHA logs and medical records, and only the hand of dominant motion in low risk jobs. Figure 24 represents the structure of data from set D3B.
Results — Descriptive Analysis of Wrist Motion Scatter Plots. With respect to each kinematic variable, the means were plotted against the standard deviation of each subject. Figure 25 illustrates the scatter plot for F/E acceleration, which was typical for most Kinematic variables. Figure 25 clearly shows the separation between the low and high risk values. The high standard deviation of the point in the upper right hand corner of figure 25 was due to abnormally high variance between subtasks for a particular job. MOTION DEP. VARIABLES
RAD/ULN FLEX/EXT PRON/SUP
POSVEL ACCEL
A M M R A M M D A M M D 11 II II II V i a g V i a i V i a i 9 n X e n X I 9 n X 1 Subj 1 Job 1 Subj 2
Subj 3 Job 2 HIGH Subj 4 RISK II ii II II
Subj 19 Job 10 Subj 20
Subj 21 Job 11 Subj 22
Subj 23 Job 12 LOW Subj 24 RISK ■I n ii n
Subj 39 Job 20 Subj 40
Figure 24. Structure of independent variable (CTD risk) and kinematic dependent variables. Each horizontal line represents one subject's data, and each vertical line represents mean values of the respective parameter for each subj ect. Std. Oev. Within Subject (dog/see*2) MEAN FLEXION/EXTENSION ACCELERATION 1000 ceeaina a ucino T iklvl Ec symbol Each level. risk CTD of function a as acceleration 1500 represents one subject's respective data. mean respective subject's one flexion/extension of represents plot Scatter 25. Figure 500 0 0 enAclrto dgsc 2) (deg/sec‘ Acceleration Meen 500 1000 1500 A gh sk Subject t c e j b u S k is R h ig H □ Ri t c e j b u S k is R w o L o 00 81 Partitioning of Variance — Job and Subject. Since the experimental design in this study was a fully nested design (refer to figure 11), the percentage of variance attributable to individual sources was partitioned from data in set D3B (refer to figure 23). Figure 26 illustrates the percentage of variance of acceleration variables attributable to two components, jobs nested within risk and subjects nested within jobs. (Tabulation of data in Figure 26 is shown in Appendix B.) The pattern in figure 26 was similar to the overall patterns for position and velocity in that the variance between subjects within jobs accounted for a substantial, and often majority, amount of variance. Wrist Motion — Means of High vs. Low Risk Values. The average values of the wrist motion summary statistics are listed in table 7 and illustrated in bar chart form in figures 27 through 29. These values are the collapsed results from both hands of data (set D3B, figure 23) . Within each bar chart, the mean, minimum, maximum, and maximum difference were plotted as a function of risk level. The maximum difference was calculated according to equation
(19). 82
% Variance - Acceleration
AVG MIN MAX
R/U
F/E
P/S
Job Subj(Job)
Figure 26. Partitioning of mean acceleration variance into two components, job and subject nested under job. 83
Maximum Difference = Max - Min (19) where: Max = maximum value minus minumum value within an Diff. interval, trial, subject, or risk level Max = maximum value within an interval, trial, subject, or risk level Min = minimum value within an interval, trial, subject, or risk level
The pictorial trend across all the position, velocity, and acceleration values in figures 27 through 29 is that the mean high risk values were generally greater in absolute magnitude than the mean low risk values. Moreover, the velocity and acceleration measures appeared to separate CTD risk levels more distinctly than position measures. According to table 8, the percentage increase of the high risk position values were about 20% to 30% greater than low risk with a mean of 28.1%. As groups, the velocity and acceleration variables showed increases in high risk levels of 46.2% and 67.1%, respectively, over the low risk values. 84
Table 7. Summary statistics of the kinematic wrist motion data from low and high CTD risk groups.
Motion Low Risk High Risk Variables Mean Std. Dev. Mean Std. Dev. Position (deg) R/U Pos Avg -7.62 4.42 -6.73 4.66 R/U Pos Min -16.51 5.57 -18.96 5.78 R/U Pos Max 1.12 6.17 4.69 4.76 R/U Pos Diff. 17.64 7 .53 23.65 6.71 F/E Pos Avg -10.09 11.88 -12.02 7.16 F/E Pos Min -23.58 13 .12 -29.08 7.32 F/E Pos Max 4.35 12 .36 6.56 11.11 F/E Pos Diff. 27.95 9 .92 35.63 11.53 P/S Pos Avg 2.47 38 .63 8.30 20.50 P/S Pos Min -31.84 38 .76 -38.93 23.40 P/S Pos Max 37.36 38 .69 47.70 19.48 P/S Pos Diff. 69.91 29 .55 86.63 25.47 Velocity (deg/sec) R/U Vel Avg 17.0 6.7 25.9 6.7 R/U Vel Min -79.3 34.9 -115.1 36.5 R/U Vel Max 77.3 31.1 115.7 39.5 R/U Vel Diff. 156.6 63.4 230.8 71.9 F/E Vel Avg 28.7 7.6 42.2 11.7 F/E Vel Min -121.2 42.8 -183.7 76.8 F/E Vel Max 120.3 38.1 174.2 58.4 F/E Vel Diff. 241.5 78.2 358.0 128.5 P/S Vel Avg 67.7 19.5 91.3 23.3 P/S Vel Min -289 .9 112.0 -403.2 149.1 P/S Vel Max 300.2 129. 0 449.2 256.2 P/S Vel Diff. 590.5 211.2 852.0 394.6 Table 7 (continued). Summary statistics of the kinematic wrist motion data from low and high risk groups of CTD risk.
Motion Low Risk High Risk Variables Mean Std. Dev. Mean Std. Acceleration (deg/secA2) R/U Acc Avg 301 125 494 142 R/U Acc Min -1755 818 -2776 913 R/U Acc Max 1759 834 3077 1313 R/U Acc Diff. 3518 1641 5853 2176 F/E Acc Avg 494 156 824 268 F/E Acc Min -2788 862 -4927 1913 F/E Acc Max 2588 802 4471 1527 F/E Acc Diff. 5377 1630 9398 3388 P/S Acc Avg 1222 384 1824 533 P/S Acc Min -6811 2571 -11987 6330 P/S Acc Max 7169 2980 11291 4954 P/S Acc Diff. 14000 5545 23490 11483 86 Table 8. Increase of high risk kinematic values as a percentage of low risk values.
Kinematic Plane of Motion Variable R/U F/E P/S Pos Avg NA NA NA Pos Min 14.8% 23.3% 22. 3% Pos Max 318.0%* 50.8% 27.7% Pos Diff. 34 .1% 27.5% 23.9% Vel Avg 52.4% 47.0% 34.9% Vel Min 45.1% 51.6% 39.1% Vel Max 49.7% 44.8% 49. 6% Vel Diff. 47.4% 48.2% 44.3%
Acc Avg 64.1% 66.8% 49. 3% Acc Min 58.2% 76.7% 76.0% Acc Max 74.9% 72.8% 57.5% Acc Diff. 66.4% 74.8% 67.8% * this appears to be an outlier because of the small value in the denominator (1.12 deg) WRIST POSITION
1 High Risk I Low Risk
(Deg)
R a 1 ' d / F I e x
U I n / E X t
“I----- 1----- 1----- 1 Q — i---- 1------1-----1— — i---- T------1----- r -6 M ean Mln Max R an g eM ea n Min Max Range M ean Min Max Range aig. 0 06 level Radial/Ulnar Flex/Ext Pron/Supin
Figure 27. Mean values of wrist position in the radial/ulnar and flexion/extension planes as a function of CTD risk level. WRIST VELOCITY
High Risk I Low Risk
( D e g /S e c ) (D e g /S e c ) 1400 R 1200 a 5 0 0- d 1000 / 4 0 0 - F I 3 0 0- e x 200 -
1 0 0 -
U I n / -200 E x -400 t -400 1 4a 1 a 1 a 1 a 1 4a 1 a 1 a 1 a" 1 4a 1 a ' a ' a M ean Min Max Diff. M ean Min Max Diff. Mean Min Max Diff.
• • 8lg 0.06 level Radial/Ulnar Flex/Ext Pron/Supin A Mean ABS(Vei)
Figure 28. Mean values of wrist velocity in the radial/ulnar and flexion/extension planes as a function of CTD risk level. WRIST ACCELERATION
I High Risk I Low Risk (D e g /S e c (D e g /S e c 2)
T h o llr u s a n d s
9 '9 '*9 9 1 9 r 9 ' +9 , 1 9 r « Meaif^Min Max Diff. M ean Min Max Diff. M ean MinMax Diff.
# • slg 0 06 level Radial/Ulnar Flex/Ext Pron/Supin £ Mean ABS(Accel)
Figure 29. Mean values of wrist acceleration in the radial/ulnar and flexion/extension planes as a function of CTD risk level. 90 Results — MANOVA and ANOVAs of Wrist Motion A multivariate analysis of variance (MANOVA) was performed on all the mean, minimum, and maximum wrist motion data from set D3B (refer to figure 23). The CTD risk effect was significant at the 0.007 level. As a followup, individual analyses of variance (ANOVAs) were performed on the effect of CTD risk on each dependent variable. Since the experimental design was a nested design, the error term for risk level was job nested within risk level (Montgomery, 1984). The statistical results of the ANOVAs are shown in table 9. For each significant t-test, the high risk value was greater than the low risk value. The overall pattern of table 9 shows that the mean, minimum, maximum, and difference values of velocity and acceleration significantly discriminated between low and high risk groups, whereas only one position variable significantly discriminated between risk levels. The results from the MANOVA and ANOVAs provide statistical evidence for the gestaltic conclusion made from the bar charts in figures 27 through 29 — velocity and acceleration measures distinguished between the CTD risk levels more distinctly than position variables. 91 Table 9. Probability of type I error from analysis of variance of motion variables from one hand. The effect tested was risk of CTDs (DF = 1), and the error term was job nested within risk level (DF = 18).
AVG MIN MAX DIFF
R/U POS .5995 .2781 .0920 .0429* F/E Pos .5644 .1821 .5560 .0666 P/S Pos .6279 .5761 .3658 .1267 R/U Vel .0016* .0148* .0074* .0081* F/E Vel .0014* . 0099* .0104* . 0085* P/S Vel .0079* .0223* .0357* .0210* R/U Accel .0005* .0040* .0018* .0024* F/E Accel .0008* .0006* .0003* .0004* P/S Accel .0018* .0073* .0112* .0080* * = significant at the 0.05 level R/U = radial/ulnar F/E = flexion/extension P/S = pronation/supination 92
Results — Principal Components Analysis Principal components analysis (PCA) is a method of analyzing the variance-covariance structure of a dataset with a few linear combinations of the original variables (Johnson and Wichern, 1988). One of the goals of PCA is to reduce a large number of variables to a few subsets. Since the dependent variable (risk of CTDs) is not a part of PCA/ Tabachnick and Fidell (1989) warn that one of the main problems with PCA is that "there is no criterion beyond interpretability against which to test the solution" (p. 598) . PCA was performed on the following sets of wrist motion variables from dataset D3B, which contained wrist motion from the affected hand (refer to figure 23): 1) all mean, min, and max variables 2) all position variables 3) all velocity variables 4) all acceleration variables 5) all R/U variables 6) all F/E variables 7) all P/S variables PCAs were also performed on the above sets of variables as a function of CTD risk. As stated earler, the risk of CTDs was not involved in these six PCAs. The covariance matrix was used in the PCAs of position, velocity, and acceleration variables because the units of measure were homogenous within each PCA. However, the correlational matrix was used in the PCAs of 93 all variables and in each plane because the units were heterogeneous (deg, deg/sec, and deg/secA2). Typically in PCA of covariance matrices, the variables that have the highest coefficients within the components are those variables with the highest standard deviations. The results of the PCAs are as follows: 1) As shown in table 11 and figures 30 and 31, the results of PCA on all mean, minimum, and maximum variables indicated that the velocity and acceleration variables dominated the first principal component. Within the first component, the mean and maximum differences (maximum - minimum) in velocity and acceleration accounted for a majority of variance. The second principal component was dominated by the differences between F/E and P/S position variables (refer to figure 31). 2) Separate PCA of blocks of position, velocity, and acceleration resulted in similar patterns. Table 12 and figure 32 reveal that the maximum difference of P/S acceleration was most highly correlated with the first component, and the P/S variables along with maximum difference of R/U dominated the second component. Differences in patterns of variables within the second component did occur over position, velocity, and acceleration PCAs, but these differences were 94 inconsequential considering the second component comprised only a small percentage of variance (usually less than 10%). 3) PCA of kinematic variables within planes resulted in similar patterns. The dynamic (velocity and acceleration) and static (position) variables were most highly correlated with the first and second components, respectively. As indicated in table 13 and figure 33, the mean and maximum difference of velocity and acceleration dominated the first component, while position variables accounted for the second component. 4) The results from PCA within each risk group were overall similar. 95
Table 10. Key to coding of wrist motion variables. First character: R = radial/ulnar F = flexion/extension P = pronation/supination Second character: P = position V = velocity A = acceleration Third through fifth characters: AVG average MIN minimum MAX maximum RGE range (range = max - min) Note: range applies to position only DIF = difference (difference = max - min) Examples: RPAVG = radial/ulnar average position FVDIF = flexion/extension difference of velocity PAMAX = pronation/supination maximum acceleration PPMIN = pronation/supination minimum position 96 Table 11. Results of principal components analysis (PCA) of all average, minimum, and maximum variables in the R/U, F/E, and P/S planes. This PCA was performed on a combined set of high and low risk data. The sign preceding each variable represents whether the variable is positively or negatively correlated with the component. Refer to table 10 for key to coding of variables.
Component Variable Coefficient Proportion Cum. of Variance Variance First RPAVG . 00 0. 54 0.54 Component RPMIN -.16 RPMAX .14 FPAVG -.07 FPMIN -.15 FPMAX .05 PPAVG .06 PPMIN -.07 PPMAX .12 RVAVG .21 RVMIN -.23 RVMAX .23 FVAVG .22 FVMIN -.21 FVMAX .23 PVAVG .20 PVMIN -.21 PVMAX .22 RAAVG .22 RAMIN -.23 RAMAX .22 FAAVG .22 FAMIN -.24 FAMAX .24 PAAVG .22 PAMIN -.23 PAMAX .24 (continued) Table 11 (continued). Results of principal components analysis (PCA) of all average, minimum, and maximum variables in the R/U, F/E, and P/S planes.
Component Variable Coefficient Proportion cum. of variance Variance
Second RPAVG .04 0.66 Component RPMIN .10 RPMAX .06 FPAVG -.42 FPMIN -.31 FPMAX -.44 PPAVG .41 PPM IN .42 PPMAX .35 RVAVG .06 RVMIN .00 RVMAX .00 FVAVG -.01 FVMIN . 11 FVMAX -.11 PVAVG .02 PVMIN .06 PVMAX -.03 RAAVG .05 RAMIN -.04 RAMAX .02 FAAVG -.02 FAMIN .05 FAMAX -.10 PAAVG .02 PAMIN .07 PAMAX -.02 PCA OF ALL VARIABLES Coefficients — 1st Component
Coefficient 0 .5
0 .4
0 .3
0.2 0.1 i 0 i .*j 0.1 l i 0.2
0.3
0 .4
0 .5 Av Mn Mx Av Mr Mx Av Mn MxAv Mn Mx Av Mn MxAv Mr MxAv Mn Mx Av Mn Mx Av Mn Mx R/U F/E P/3 R/U F/E P/S R/U F/E P/3 POSITION VELOCITY ACCELERATION
Figure 30. First component's coefficients from principal components analysis (PCA) on all mean, minimum, and maximum position, velocity, and acceleration variables. Av = average; Mn = minimum; Mx = maximum. PCA OF ALL VARIABLES Coefficients ~ 2nd Component
Cotfflolvnt 0 .5
0 .4
0 .3
0.2
0.1 0 fLli fiJLg fir®
0.1
0.2
0 .3
0.4
0 .5 Av Mn Mx Av Mn Mx Av Mn MxAv Mn Mx Av Mn Mx Av Mn MxAv Mn Mx Av Mn Mx Av Mn Mx R/U F/E P/3 R/U F/E P/3 R/U F/E P/3 POSITION VELOCITY ACCELERATION
Figure 31. Second component's coefficients from principal components analysis (PCA) on all mean, minimum, and maximum position, velocity, and acceleration variables. Av - average; Mn = minimum; Mx = maximum. 100
Table 12. Results of principal components analysis (PCA) of the all average, minimum, and maximum acceleration variables. This PCA was performed on a combined set of high and low risk data. The sign preceding each variable represents whether the variable is positively or negatively correlated with the component. Refer to table 10 for key to coding of variables.
Component Variable Coefficient Proportion Cum. of Variance Variance
First RAAVG -.02 0.93 0 .93 Component RAMIN . 10 RAMAX -.14 FAAVG -.03 FAMIN .22 FAMAX -.18 PAAVG -.06 PAMIN .73 PAMAX -.60
Second RAAVG .05 0.03 0.96 Component RAMIN -.40 RAMAX . 38 FAAVG .00 FAMIN .11 FAMAX .00 PAAVG .08 PAMIN .58 PAMAX .58 PCA OF ACCELERATION VARIABLES Coefficients of Variables
Coefficient 0.8 0.7 0.6 0.5 0.4 0.3 0.2 O.t W I 1 m - 11 0 W - 0.1 I 1 - 0.2 -0.3 -0.4 -0.5
- 0.6 -0.7 I I I I I I I I 1— I + * I I— I I I H / - 0.8 Avg Min Max Avg Min Max Avg Min Max Avg Min Max Avg Min Max Avg Min Max R/U F/E P/S R/U F/E P/S lat Component 2nd Component
Figure 32. Results from principal components analysis (PCA) on all acceleration variables. 102 Table 13. Results of principal components analysis (PCA) of the all position, velocity, and acceleration variables in the F/E plane. This PCA was performed on a combined set of high and low risk data. The sign preceding each variable represents whether the variable is positively or negatively correlated with the component. Refer to table 10 for key to coding of variables.
Component Variable coefficient Proportion Cum. of Variance Variance First FPAVG -.05 0. 64 0.64 Component FPMIN -.20 FPMAX . 16 FVAVG .40 FVMIN -.39 FVMAX .39 FAAVG .39 FAMIN -.40 FAMAX .40 Second FPAVG .63 0.27 0.91 Component FPMIN .53 FPMAX .57 FVAVG .00 FVMIN -.07 FVMAX .05 FAAVG -.01 FAMIN .00 FAMAX .02 PCA OF FLEX/EXT VARIABLES Coefficients of Variables
Co#f flcUnt 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
- 0.1
- 0.2 i -0.3 -0.4 -0.5
- 0.6 -0.7
- 0.8 Avg Min Max Avg Min Max Avg Min Max Avg Min Max Avg Min Max Avg Min Max Poa Val Aceal Poa Val Accal lat Component 2nd Component
Figure 33. Results from principal components analysis (PCA) on all variables in the flexion/extension plane. EOT 104 Discriminant Function Analysis (DFA^. Discriminant function analysis is a statistical technique whose purpose is to predict group membership from a set of predictors (Tabachnik and Fidell, 1989). In this study, group membership was risk of CTDs (low vs. high), and the set of predictors were wrist motion variables. DFA assumes that the covariance matrices within risk groups are homogenous. The test statistic in DFA is the percentage of subjects correctly classified into CTD risk groups. The normal DFA will produce biased, overclassified results, so a jackknifed DFA is recommended to reduce the bias in classification. A jackknifed DFA from BMDP software (procedure 7M) was used in this analysis to estimate the percentage of correctly classified subjects. Jackknifed stepwise DFA were performed on the data sets that contained wrist motion from only the affected hand (refer to set D3B in figure 23). Stepwise DFA on All Variables. A stepwise DFA was performed on all the average and maximum difference wrist motion variables collectively. The maximum difference variables were chosen over the maximum and minimum variables for the sake of parsimony and also to avoid the problem of singularity in DFA. (Since the maximum difference is a linear combination of minimum and maximum, it is perfectly correlated to the minimum and maximum.) The significant 105 predictor variables in this stepwise DFA were R/U range of position, average R/U velocity, and maximum difference of R/U acceleration, which resulted in an overall 78.4% correct classification. Stepwise DFA on Structured Sets of Variables. Stepwise DFA were performed on permutations (combinations of one, two, and three variables) of five structured sets of predictor variables: range of position, average velocity, velocity difference, average acceleration, acceleration difference. Tables 14 and 15 reveal the results of DFA on average velocity and acceleration variables. DFA results suggest the following: 1) velocity and acceleration variables classified risk level better than range of position variables. 2) the sets of average velocity, average acceleration, and acceleration difference predicted group membership about equally well, with an average percentage of correctly classified subjects of approximately 73%. Table 14 and 15 show the results of average velocity and acceleration analyses. 3) based on F test statistics, the F/E plane tended to predict CTD risk the best. 4) based on conclusions 2) and 3) from DFA, the wrist motion variables that appeared to discriminate most 106 effectively between CTD risk levels were average velocity and average and difference of acceleration in the F/E plane.
Table 14. Results of stepwise discriminant analysis on structured sets of average velocity data from dataset D3B (refer to figure 23). The classification variable was risk with two levels, low and high. The percentages of correct classification were results from jackknifed stepwise discriminant analysis (BMDP, procedure 7M) . Refer to table 10 for key to coding of variables.
Signif. F Value % correct % Correct % Correct Variables* Low Risk High Risk Total RVAVG* 17.7 70 75 72.5 FVAVG* 18.9 85 60 72.5 PVAVG* 11.1 77.8 73.7 75.7
RVAVG* 3.7 75 70 72.5 FVAVG* 18.9 RVAVG* 17.8 77.8 73.7 75.7 PVAVG FVAVG* 20.2 83.3 63.2 73.0 PVAVG* 2.0
RVAVG* 3.4 77.8 73.7 75.7 FVAVG* 20.2 PVAVG
* F to enter = 1.05 F to remove = 1.00 107 Table 15. Results of stepwise discriminant analysis on structured sets of average acceleration data from set D3B (refer to figure 23). The classification variable was risk with two levels, low and high. The percentages of correct classification were results from jackknifed stepwise discriminant analysis (BMDP, procedure 7M). Refer to table 24 for key to coding of variables.
Signif. F Value % Correct % Correct % Correct Variables* Low Risk High Risk Total RAAVG* 20.7 80 65 72.5 FAAVG* 22.8 85 60 72.5 PAAVG* 15.4 72.2 84.2 78.4
RAAVG* 2.9 75 70 72.5 FAAVG* 22.8 RAAVG* 19.4 72.2 63.2 67.6 PAAVG* 1.9 FAAVG* 24.4 77.8 57.9 67.6 PAAVG* 1.1
RAAVG* 2.2 77.8 68.4 73.0 FAAVG* 24.4 PAAVG
* F to enter = 1.05 F to remove = 1.00 108 Multiple Logistic Regression (MLR). Multiple logistic regression is a technique in which two or more continuous variables predict discrete levels of a dependent variable. MLR has less stringent assumptions than DFA in that no parametric assumptions are made on the underlying distributions of the dependent variable. Data from set D3B were analyzed with MLR (refer to figure 23). A commonly used statistic in MLR is the odds ratio. The odds of an event is the ratio of the probability of an event divided by its complementary probability, as defined in equation (15).
Odds = p / q (20) where: p = probability of an event occurring q = 1 - p = probability of an event not occurring
For this study, the odds ratio was defined as the odds of a high risk of CTDs given a predictor variable at the midpoint of the low and high risk values (one half the distance between the low and high risk values) divided by the odds of a high risk of CTDs given a predictor variable at the mean low risk value. The odds ratio for only one predictor variable assumes all the other predictor variables are held constant. An odds ratio for a group of predictor variables is defined in equations (21), (22) , (23). 109
O.R. = (eA (Bl*Dl) )*(eA (B2*D2) )* ... (21) *(eA (Bn*Dn) )
O.R. = e A ( B1*D1 + B2*D2 + .... + Bn*Dn ) (22) log(O.R.) = B1*D1 + B2*D2 + .... + Bn*Dn (23) where: O.R. = ratio of the odds of a high risk of CTDs given i = l..n predictor variables at the midpoints of the low and high risk values (gand means) divided by the odds of a high risk of CTDs given i = l..n predictor variables at the low risk values Bi = coefficient of the ith predictor variable (i = l..n) Di = one-half of the difference between the mean high and low risk values of predictor variable i
95% confidence intervals were computed for the odds ratio according to equations (24) through (27). The confidence intervals in (24) through (27) are applicable for only one predictor variable.
log(0.R.lower) = log(O.R.) - (1.96)*(Dl)* (S.E.) (24) log(O.R.upper) = log(0.R.) + (l.96)*(Dl)* (S.E.) (25) O.R.lower eA (log(O.R.) - (1.96)*(D1)*(S.E.)) (26) O.R.upper eA(log(0.R.) + (1.96)*(D1)*(S.E.)) (27) where: O.R. lower lower bound of 95% confidence interval O.R. upper upper bound of " " " " S.E. standard error of first predictor variable's coefficient (Bl) Dl one-half of difference between mean high and low risk values of first predictor variable 110 Stepwise MLR on All Variables. Similar to DFA, a stepwise MLR was performed on all the average and maximum differences of wrist motion variables collectively. Similar to DFA, the maximum difference variables werechosen over minimum and maximum for parsimony and to avoid problems of multicollinearity. As indicated in table 16, the sole significant variable was F/E acceleration, with an odds ratio of 6.05. Stepwise MLR on Structured Sets of Variables. Stepwise MLR was performed on permutations of the following five structured sets of predictor variables: 1) range of position (table 17) 2) average velocity (table 18) 3) difference of velocity 4) average acceleration (table 19) 5) difference of acceleration The statistical results in tables 17 through 19 suggest the following: 1) F/E average acceleration appeared to predict CTD risk better than any other variable, with odds ratios ranging from approximately 5 to 6. 2) The second best predictor appeared to be F/E average velocity, with an odds ratio of approximately 3.8. 3) Position variables predicted CTD risk poorly. Ill Table 16. Results of stepwise multiple logistic regression on all average and maximum difference variables from data set D3B (refer to figure 23). The dependent variable is CTD risk with twolevels, low and high. Refer to table 10 for key to coding of variables.
Variable* Regression Model Odds Odds Ratio Coefficient Chi- Ratio 95% Confidence Square Interval FAAVG* 0.01091 21.92 6.05 1.66 - 22-02 * significant at the 0.05 level 112 Table 17. Results of stepwise multiple logistic regression on structured sets of range of position variables from data set D3B (refer to figure 23). The dependent variable is CTD risk with two levels, low and high. Refer to table 10 for key to coding of variables.
Variable* Regression Model Odds Odds Ratio Coefficient Chi- Ratio 95% Confidence Square Interval RPRGE* 0.1203 6.74 1.443 1.062 - 1.961 FPRGE* 0.06907 5.01 1.305 1.013 - 1.680 PPRGE 0.02439 3.51 1.226 0.9693 - 1.550 RPRGE* 0.1203 6.74 1.443 1.062 - 1.961 FPRGE RPRGE* 0.1363 7.48 1.515 1.080 - 2.127 PPRGE FPRGE* 0.07075 5.14 1.312 1.015 - 1.698 PPRGE RPRGE* 0.1203 6.74 1.443 1.062 - 1.961 FPRGE PPRGE * significant at the 0.05 level 113 Table 18. Results of stepwise multiple logistic regression on structured sets of average velocity variables from data set D3B (refer to figure 23). The dependent variable is CTD risk with two levels, low and high. Refer to table 10 for key to coding of variables.
Variable* Regression Model Odds Odds Ratio Coefficient Chi-* Ratio 95% confidence Square interval RVAVG* 0.2000 14.83 2.435 1.369 - 4.330 FVAVG* 0.1841 17.72 3.465 1.477 - 8.132 PVAVG* 0.0564 10.41 1.952 1.179 - 3.232
RVAVG 17.72 3.465 1.477 - 8.132 FVAVG* 0.1841 RVAVG* 0.1985 14.58 2.419 1.359 - 4.308 PVAVG FVAVG* 0.1977 18.46 3.798 1.499 - 9.632 PVAVG
RVAVG 18.46 3.798 1.499 - 9.632 FVAVG* 0.1977 PVAVG
* significant at the 0.05 level 114 Table 19. Results of stepwise multiple logistic regression on structured sets of average acceleration variables from data set D3B (refer to figure 23). The dependent variable is CTD risk with two levels, low and high. Refer to table 10 for key to coding of variables.
Variable* Regression Model Odds Odds Ratio Coefficient Chi- Ratio 95% Confidence Square Interval RAAVG* 0.01030 16.53 2.690 1.460 - 4.930 FAAVG* 0.009302 20.59 4.640 1.642 - 12.99 PAAVG* 0.003608 14 .80 2.962 1.368 - 6.416
RAAVG 20.59 4.640 1.642 - 12.99 FAAVG* 0.009302 RAAVG* 0.009908 15.38 2.589 1.422 - 4.711 PAAVG FAAVG* 0.01091 21.92 6.050 1.660 - 22.02 PAAVG
RAAVG 21.92 6.050 1.660 - 22.02 FAAVG* 0.01091 PAAVG
* significant at the 0.05 level 115 Discussion — Job Characteristics CTD Risk Levels. According to epidemiological criteria, the high risk jobs that were monitored in this study definitely exposed workers to elevated risk of CTDs. The median incidence rate of 18.4 and average lost days count of 111.5 per 200,000 hours of exposure corroborate the high risk level of the monitored jobs (refer to table 6). If each worker worked 2000 hours per year (50 weeks * 40 hrs/week = 2000 hours; 200,000 hours for 100 workers) in these high risk jobs, then an alarming 18.4% of all the workers in these jobs reported CTDs. Based on Wehrle's (1976) epidemiological reports of 25.6 CTS cases per 200,000 hours in some high risk jobs in industry, an incidence rate of 18.4 would probably be considered high risk. Number of Wrist Movements. The jobs that were monitored in both the high and low risk groups were highly repetitious jobs, as demonstrated by the approximately 25,000 wrist movements that were recorded per shift. 25,000 wrist movements translates into a worker completing a fundamental wrist movement almost every second. The number of wrist motions were not significantly different between high and low risk groups. Force Levels. While the mix of hand grip types was approximately the same in both high and low risk jobs, there were major differences in grip force. As indicated in table 116 6, the mean grip force in high risk jobs was about 2.5 times as great as in low risk jobs (left hand: 12.8 vs. 4.8 kgf; right hand: 12.0 vs. 4.58 kgf). The greater force values are similar to the grip forces that Silverstein et al. (1986, 1987) measured in jobs that were classified as high force. In Silverstein1s et al. (1986) epidemiological study investigating CTDs, the mean adjusted grip force in the high force group was 12.7 kgf. Although the difference in grip force between high and low risk jobs in the present study may appear to be a potentially confounding factor, its confounding is mitigated by the grip force protocol. After the task, each subject was asked to squeeze a Smedley grip strength dynamometer in either a pulp pinch or power grip with approximately the same force that he/she exerts on the job. The type of grip was determined by the predominant hand configuration in each worker's job. This grip strength protocol had two potential problems that may have caused the difference in grip force between high and low risk jobs. First, each subject might have simulated the peak force required in the job, which would have resulted in an overestimate of the average force. Second, the position of the fingers and thumb on the Smedley might not have been identical to hand configurations on the job. 117 Partitioning of Variance. The fact that variance between subjects within jobs accounted for a substantial percentage of total variance in wrist motion warranted monitoring two subjects per job in this study (refer to figure 26). If subject variance had been consistently dominated by job variance, then one subject per job would have sufficed. The large percentage of variance due to subjects could have been due to the following reasons: 1) In this study, the variance between subjects within a job was not purely due to differences between people but included variance due to performing the job in a slightly different orientation or with slightly dissimilar equipment or materials. Differences in orientation and equipment occurred in a minority of the twenty jobs we monitored. For example, the only feasible way to monitor the job that required application of weatherstripping around automobile windows was to measure the wrist motion of two workers. Each subject worked on only one side of the vehicle. The two workers were executing essentially the same motions but with different hands. 2) For some jobs in this study, the workstations were not precisely designed to dictate physically the motion patterns of the workers. The subjects were free to perform the task in a variety of ways — hence, a large variance due 118 to subjects in these jobs was not surprising. A well- designed ergonomic workstation should have engineering controls built into them in order to physically guide the worker's motion patterns. 3) Lacquaniti and Soechting (1982) found that wrist motion in simple arm movements tended to vary greatly, even though final target performance was accurate and repeatable. The wrist tended to vary its motion pattern across trials of whole arm movements, yet the hand consistently reached its destination with a high degree of accuracy. The large inter-subject variance could have been attributable to differences in motion strategies among workers. Some variation in wrist motion between subjects is expected, even in well-designed ergonomic workstations. Based on the substantial percentage of variance due to subjects within a 'job, the protocol of monitoring two subjects per job should be continued in future studies of this kind. 119 Discussion — Subject Characteristics The physical characteristics of subjects between risk levels were comparable in several respects, thereby limiting the number of potential confounding factors. The subjects had identical gender distribution, similar distribution of handedness, similar gross and upper extremity anthropometric measures (except for trunk depth, which should not affect wrist motion), and overall a lack of significant differences in the wrist's biomechanical capabilities. However, the subjects in the low risk group were on the average ten years older and had about ten more years of seniority than their counterparts in the high risk group. The potential confounding due to differences in age between the two risk groups is minimal considering the the wrist's biomechanical capabilities (maximum and minimum position, velocity, and acceleration) of both groups were similar overall. niscussion — Wrist Motion as a Function of CTD Risk Analysis of Variance. As indicated in Table 9, the velocity and acceleration measures were overall significantly different between high and low risk jobs while the position measures were not. These results demonstrate the importance of dynamic components in assessing CTD risk. Wrist posture has been cited often as a risk factor of CTS and CTDs overall in the literature (Alexander and Pulat, 1985; Armstrong, 1983, 1986a, 1986b; Armstrong and Chaffin, 1979a, 1979b; Armstrong et al., 1982; Armstrong et al., 1986; Browne et al., 1984; Eastman Kodak Co., 1986; Fraser, 1989; Greenberg and Chaffin, 1975; Konz, 1983; McCormick and Sanders, 1982; Tichauer, 1966, 1978). Deviated wrist postures appear to have a theoretical base for causing CTDs, as demonstrated by Armstrong's and Chaffin's (1979a) model. In their model, as the wrist was deviated from a neutral position, the resultant reaction force on the tendons increased (refer to figure 6). This increase in resultant reaction force could irritate and inflame the tendons, thereby contributing to tenosynovitis and CTS. Based on the results from this study, the lack of significant differences in wrist position in all three planes between low and high risk groups suggests that orthogonal wrist posture alone may not be as powerful predictor of CTD risk as the dynamic components of motion. However, wrist posture may play a discriminating role that would otherwise not be revealed by the orthogonal analysis performed in this study. All the kinematic data in this study were analyzed orthogonally, independent of coupled posture. Coupled wrist posture in two or more planes or wrist posture coupled with dynamic components may actually be significant predictors of CTD risk. 121 Biomechanically, the association between coupled static and dynamic components and CTDs have a theoretical basis, as demonstrated by Schoenmarklin's and Marras' (1990 and 1991a) model. In their model, the greatest resultant reaction force on the tendons occurred when the hand was deviated and accelerated quickly (refer to figure 9). This resultant reaction force, which resisted the tendon force from deviated posture and hand acceleration, was much greater than the reaction force from a static, deviated posture. A fecund future research project would be analyzing the kinematic data from this study as coupled sets of static and dynamic measures. Predictive Models. The results from multiple logistic regression (MLR) demonstrated the parsimony and strength of the predictive models. As indicated in the analysis of structured data sets, F/E acceleration was consistently the best discriminator between risk levels. The odds ratio between high and low risk groups for F/E acceleration was 6.05 (refer to tables 16 and 19). The results from discriminant function analysis (DFA) corroborate the predictive power of F/E acceleration (refer to table 15). F/E acceleration was able to correctly classify approximately 70% of all into their respective risk groups. In both DFA and MLR, all the position variables were poor discriminators of CTD risk levels. 122
The association between the F/E plane and CTD risk is supported by anatomical and physiological literature. According to Robbins (1963), extreme flexion and extension of the wrist reduced the volume of the carpal tunnel, thereby augmenting compression on the median nerve. Phalen (1966) states that wrist flexion and extension increase pressure within proximal half of the carpal tunnel, whereas only extensor deviations generate higher pressures in the distal half. Phalen (1966) developed a diagnostic test for CTS in which patients push their forearms together in an axial direction while flexing their wrists maximally. In an anatomical study on cadavers, Smith, Sonstegard, and Anderson (1977) replaced the median nerve with a water- filled cylindrical balloon and found that pressure on the median nerve increased when the wrist was flexed to an extreme angle and also when the flexor tendons were tensed at various wrist flexion angles. During a flexed posture, the median nerve is squeezed between the flexor retinaculum and the overlying flexor tendons, thereby exposing a worker
to CTS. Armstrong, Castelli, Evans, and Diaz-Perez (1984) investigated the histological changes in the flexor tendons as they pass through the carpal tunnel, and they found hyperplasia and increased density in the synovial tissue in the carpal tunnel area. These authors suggested that 123 biomechanical factors, such as repeated exertions with a flexed or extended wrist posture, could partially cause these degenerative changes in tendon tissue. In an investigation of the viscoelastic properties of tendons and their sheaths, Goldstein, Armstrong, Chaffin, and Matthews (1987) found that F/E wrist angle increased the shear traction forces between tendons, their sheaths, and bones and ligaments that form the anatomical pulley. These authors concluded that stresses at the tendon-sheath interface are significant and dependent on F/E wrist angle. The literature on biomechanical modeling of the wrist also supports the association between F/E acceleration and CTD risk. Armstrong and Chaffin (1979a) modeled the wrist's tendons statically in the F/E plane, and they showed that angular deviations from the neutral position generate large resultant reaction'forces on the flexor tendons. Schoenmarklin and Marras (1990) used the basic structure of Armstrong's and Chaffin's (1979a) model and added the dynamic component of acceleration. When the tendons are accelerated, the resultant reaction force increases dramatically over those forces in static loading (refer to figure 9) . The resultant reaction force on the tendons from F/E acceleration could degenerate and inflame the tendons, thereby causing tenosynovitis, or compress the median nerve between the carpal ligament and tendons, which could caxise 124
CTS. Quick decelerations in the F/E plane could likewise generate high loads on the wrist joint. Compared to static loading on the elbow joint, Amis, Dowson, and Wright (1980) predicted a 25-30% increase in elbow joint forces during the deceleration phase of fast elbow flexions. The association between F/E acceleration and CTD risk can also be explained biomechanically by the concepts of Newtonian mechanics and friction. In order to accelerate the wrist, the extrinsic muscles in the forearm have to exert force which is transmitted to the tendons. Some of the force transmitted through the tendon is lost to friction against the ligaments and bones that form the carpal tunnel. This frictional force could irritate the tendons' synovial membranes and cause "synovitis", the thickening of the synovial membrane (Armstrong, 1983). Irritation could precipitate tendon inflammation, which could result in tenosynovitis and/or CTS through compression of the median nerve. In a histological investigation of tendon sheaths, Armstrong et al. (1984) found sizeable increases in synovial hyperplasia and synovium density in the carpal tunnel area, which they attributed to repeated flexion/extension
exertions. Tanaka and McGlothlin (1989) hypothesized that the friction between tendons and adjacent structures is a major cause of CTDs, and Moore and Wells (1989) and Moore (1988) 125 showed that the frictional work generated in the carpal tunnel supported Silverstein1 s et al. (1986, 1987) dose- response relationship between repetition and CTD risk. The deleterious effects of frictional work generated between the tendons and their sheaths or supporting structures is exacerbated by coactivation of the extensor muscles during movements. Varying amounts of extensor muscle force during any static or dynamic movement are required to guide the hand and stabilize the hand so it can generate power or pinch force. In order for the wrist and hand to maintain the same flexor torque or power/pinch force, the flexor muscles have to exert more force to overcome the extensor force. Greater forces in the flexor muscles will generate increased frictional work between the flexor tendons and their adjacent structures, thereby exposing workers to increased risk of CTDs. Dose-Responso Relationship. The relationship between CTD incidence rate and occupational factors, such as repetition and wrist posture, has been qualitatively established by extensive discussions in the literature
(Armstrong, 1983, 1 9 8 6 ? Armstrong et al., 1982? Armstrong and Chaffin, 1979a? Birkbeck and Beer, 1975? Jensen, Klein, and Sanderson, 1983? Tichauer, 1966, 1978? Welch, 1972) and epidemiological studies (Armstrong and Chaffin, 1979b? Hymovich and Lindhoin, 1966? silverstein et al., 1985, 1986, 126 1987; Tanaka et al., 1988). Qualitative links are ineffective tools for industry to use to prevent CTD injuries because they do not relate the magnitude of specific wrist motions to CTD risk. The objectives of the industrial surveillance phase were to quantify the dose-response relationship between wrist motion and CTD risk and develop preliminary quantitative guidelines on the type and amount of wrist motion that exposes workers to CTDs. As stated earlier, the variable that appears to best discriminate between low and high levels of CTD risk is F/E acceleration. Figures 34 and 3 5 illustrate the mean and maximum difference values of F/E acceleration, respectively, for both risk levels. The values for each risk group in figures 34 and 35 should not be taken as discrete cutoffs between risk because of the probabilistic distributions underlying each mean value. However, these benchmarks do provide some insight into approximate levels of injurious and safe levels of F/E acceleration, and they also provide ergonomic practitioners in industry with preliminary quantitative guidelines for risk evaluation of jobs. In the present study, the dose consisted of continuous measures of wrist motion but the response was partitioned into two discrete extremes of CTD risk. The prediction of CTD risk from dosage was limited because of the discrete MEAN FLEXION/EXTENSION ACCELERATION BENCHMARKS
Low Risk Mean 494 High Risk Mean 824
0 100 300 500 700 900 1100 1300 1500 5% Low 5% High 95% Low 95% High 174 492 776 1366
Accel (deg/sec''2)
Figure 34. Mean acceleration benchmarks and their distributions in the flexion/extension plane as a function of CTD risk level. MAXIMUM DIFFERENCE FLEX/EXT ACCELERATION BENCHMARKS
Low Risk Mean 5377 / \ High Risk Mean \ 9400
0 1000 3000 5000 7000 9000 11000 13000 15000 17000 19000 5% Low 5% High 95% Low 95% High 1935 4326 7680 16593
Accel (deg/sec~2)
Figure 35. Maximum difference of acceleration benchmarks and their distributions in the flexion/extension plane as function of CTD risk level. 129 nature of the response. Ultimately, industry needs a continuous dose-response relationship in order to effectively evaluate jobs and prevent injuries. In order to predict specific CTD risk as a continuous variable of
incidents per 200,000 hours, more subjects will have to be monitored in jobs that vary from low to high incidence rates. In addition, more data are needed in order to verify the wrist motion benchmarks and make the benchmarks more generalizable to industry. The established and proven setup of hardware, software, and experimental protocol makes a continuation of the present study quite feasible. Causality — Need for a Biomechanical Model. An epidemioligical study such as the present study has inherent limitations, chiefly the difficulty of inferring cause and effect from statistical associations. In order to infer cause and effect from epidemiological associations, several factors have to be considered (Armstrong and Silverstein, 1987). These factors include:
1 . exposure or cause occurred prior to disease (temporal relationship). 2 . strength of association between dose and response is high. 3. association cannot be fully explained by confounding factors. 4. association is biologically plausible. 5. association is consistent with literature. 130 One of the most important factors in inferring causal associations is the formation of a biological mechanism. If there were no plausible biological mechanism, then it would be difficult to determine whether significant statistical correlations derived from epidemilogical studies are valid or spurious. With respect to the wrist joint, a biomechanical model provides a theoretical basis for why certain motions found in the industrial surveillance phase are injurious to workers. A biomechanical model of the wrist is also needed to overcome the limitations of current wrist models. The limitations that are common to Armstrong's and Chaffin's (1979) and Schoenmarklin's and Marras' (1991) models are that these models are only 2-D and do not take into account coactivation of antagonist muscles. A 3-D model is needed to represent with more accuracy the anatomical structure of the wrist and investigate the oblique orientation and force components of tendons. Coactivation of the antagonist muscles, which is a natural phenomenon in static and dynamic exertions, must also be considered because of its impact on the agonist muscles. Coactivation aids in guiding the hand throughout its path and stabilizing the hand and wrist joint in pinch and power grips. Models that ignore coactivation will underestimate the forces and stresses on tendons passing through the wrist. 131 The biomechanical model described in the next two chapters addresses the modeling voids discussed above and focuses on the alleged linchpin that relates the major occupational factors as an aggregate with CTD risk. The variable that ties occupational factors, such as repetition (acceleration and velocity), grip force, and v/rist posture, with CTD risk is hypothesized to be frictional work between tendons and their supporting structures. Details of the model, laboratory experiment, and logic behind calculation of frictional work will be provided in the next two chapters. CHAPTER IV BIOMECHANICAL MODEL OF THE WRIST JOINT: MODEL STRUCTURE
Introduction The main reported occupational risk factors associated with CTDs are repetition (cyclic acceleration and velocity), grip force, and posture. The industrial surveillance phase of this dissertation focused on the kinematic aspects of the repetition risk factor. F/E acceleration and velocity were found statistically to be the kinematic parameters that discriminated the most between CTD risk groups. In order to corroborate these statistical correlations, a biological mechanism is needed to explain theoretically why F/E motions above certain thresholds are injurious to workers. The 3-D biomechanical model described in the following chapters is the mechanism that attempts to provide a theoretical basis for determining whether the statistical correlations between motions and CTD risk found in the surveillance phase are valid or spurious. The biomechanical vehicle that this 3-D model uses to ascertain validity is frictional work. Frictional work between the tendons and
132 133 their supporting structures is the metric that relates all three major reported risk factors (repetition, grip force, and wrist angle) biomechanically. Theoretically, frictional work could be used to ascertain why F/E acceleration and velocity at the high risk CTD level expose workers to CTDs. This biomechanical model also calculates the 3-D loading on the wrist joint. This model takes into account the time dependency of loading from synergism of agonist muscles (flexors) and coactivation of antagonist muscles (extensors) during dynamic flexion exertions. Peak and mean loadings are computed throughout the course of exertions.
Goals The goals for this biomechanical model of the wrist are to calculate the frictional work and loadings within the wrist joint during flexion movements and quantify the effect of velocity on wrist friction and loading. Quantification of the loadings and frictional work within the wrist joint might provide a biomechanical explanation for why the high risk wrist motions found in the industrial surveillance phase expose workers to CTDs. An additional benefit of this model would be to increase our general understanding of the biomechanics of the wrist joint. 134 Model Overview This wrist model is based on the 3-D lumbar model by Marras and Sommerich (1991a, 1991b), which is the latest enhancement to the early work in 3-D dynamic modeling by Marras and Reilly (1989) and Reilly and Marras (1989). Figure 36 shows the logic behind this wrist model. The output of this model are calculated wrist loading and frictional work between the tendons and their sheaths or supporting structures. These outputs are time-dependent in that they are calculated at each sample point throughout the exertion. The key inputs to this model consist of three categories: external kinematics and kinetics, electromyographic (EMG) signals (which are used to estimate internal muscle forces), and subject characteristics. First, the external measures consist of kinematic data (F/E angle and angular velocity), torque about the wrist's lateral axis, and grip force (either pinch or power). These external measures are put into equilibrium equations, which are used to calculate internal forces within the wrist joint. The grip force is required to partition the force components of the muscles that exert grip force and generate torque. Second, in order to estimate internal loadings and frictional work, it is necessary to estimate the internal tendon forces. Since the tendons are at a mechanical Subj Char EMG Wrist Kinematics Kinetics
Anthrop Amplitude Temporal Angle Velocity Torque G.Force
PCSA L-S Mod Vel Mod t
Processed EMG
Gain
Estimate Muscle Force Partition Muscle Force Estimate Wrist Torque Compare Predicted vs. Measured Torque Compute Compression & Shear
Compute Frictional Work
Figure 36. Overview of model macro-structure and principal inputs and their function. 135 136 disadvantage for exerting torque (i.e. very small moment arms about the wrist axes), they contribute much more to compression and shear on the wrist than external forces and torques. Muscle force can be used to estimate tendon force, since a tendon's sole function is to transmit force from a muscle to a joint. In estimating muscle force, the physiologic aspects of muscle force must be considered. These aspects are the EMG signal, physiologic cross- sectional area (PCSA), length-strength relationship, and force attenuation due to velocity. The EMG signal monitors the electrical activity of the muscle's action potentials. Two aspects of the integrated EMG signal are considered: EMG amplitude, which is an indirect measure of muscle force, and EMG1s temporal relationships with respect to external torque and wrist angle. Temporal EMG information is necessary to track the EMG signal during dynamic movements and also to estimate the effects of peak muscle exertions and coactivation on wrist loading. Third, subject characteristics include forearm, wrist, and hand dimensions. These dimensions are used to estimate tendon moment arms and geometric orientation of tendons. The angle of tendons with respect to the forearm axis is required to calculate the shear components of tendon forces within the wrist joint. 137 The basic movement that was modeled was an isokinetic wrist flexion performed at two angular velocities, 30 and 45 deg/sec, on a Cybex isokinetic dynamometer. As measured in the industrial surveillance phase, these velocities were the mean F/E velocities in the low and high risk CTD groups. Constant F/E velocity movements were monitored instead of constant F/E acceleration, which was the best predictor of CTD risk from industrial surveillance, because the relationship between electromyographic signals (EMG) and muscle force is known and stable when muscle fibers are shortening at a constant rate. In this study, EMG was the method used to estimate muscle force. The relationship between EMG signals and muscle force is not known under accelerative movements of muscle fibers, so monitoring constant accelerative exertions is infeasible at this time. Subjects exerted constant torque with two types of grips, power and pinph. EMG data from seven muscles in the forearm were collected during each isokinetic trial, and these data were used to estimate internal tendon force after being modulated by physiologic factors. Flexion torque was predicted from the internal tendon force and was increased in small increments until the external work as predicted by tendon forces surpassed the external work as measured by the Cybex. The predicted and measured torque were compared and checked for goodness-of-fit. Finally, the loadings on the 138 wrist joint and frictional work between the tendons and their sheaths or supporting structures were computed.
Anatomical Assumptions Anatomical Structure of Wrist Joint. The axis of the wrist joint was assumed to be a point in the F/E plane around which the wrist rotated. Anatomically, the wrist is not a single pivot joint. The wrist is composed cf eight multi-faceted carpal bones that fit together with great precision (Volz, Lieb, and Benjamin, 1980). These bones form two rows, a proximal row and a distal row. Rotation in the F/E plane occurs at both the radiocarpal and midcarpal joints. 40% and 60% of F/E rotation are due to rotation of the radiocarpal and midcarpal joints, respectively (Sarrafian, Melamed, and Goshgarian, 1977). Even though the wrist anatomically is not a single pivot point, its instantaneous center of rotation moves within a closely clustered set of loci (Volz et al., 1980). In a study investigating wrist kinematics, Youm and Flatt (1980) inserted metal pins into six cadaver hands and measured the center of rotation in the F/E plane. These researchers found that the path of F/E rotation described almost perfect circular arcs. Youm and Flatt's (1980) work provides empirical support for assuming a single point in the F/E plane around which the wrist rotated. 139 Anatomical Structure of Tendons and Sheaths. This model assumes the tendons passing through the wrist bend inside their sheaths much like a rope bends around a fixed pulley (LeVeau, 1977). At the contact points between the tendon and its sheath or supporting structures, the shape of the tendon is assumed to be a circular arc with a radius that is based on the tendons's physical location inside the wrist joint and also whether the wrist is flexed or extended. Using this mechanical analogy (Marks, 1978; LeVeau, 1977) , the frictional force between the tendons and their their adjacent structures can be computed. The frictional force is required to calculate frictional work between tendons and their supporting structures.
Specific Model Structure Flow Diagram. Figure 37 illustrates the inner workings of the model. It may be useful to refer to figure 37 throughout discussion of the model structure. Transverse Plane of Wrist Joint. This model calculates the loads on the wrist in a transverse plane that cuts through the wrist joint, as illustrated in figure 38. The transverse plane concept has been used in models of the lumbar spine (Marras and Sommerich, 1991a,1991b; Schultz and Andersson, 1981). Seven groups of tendon forces were 140
Input data into i torque, grip force, angle, velocity, 4 EMG during dynamic exertion and tub) anthropometry
Oeflne angular intarval of intaraat -ik- Raad in typa of grip (pinen or povar)
Read in aax EMC for aaaaurad anglaa
Pradiet aax BIG for eaeh aaapla point with ragraaaion aquationa
Noraalisa DIG aaplituda at aaen aaapla point with raapaet to aax EMG
A. Hodulata EMG for valoeity Oeteralne aaaaurad I torgua and grip forea at each aaapla point Hodulata EMG for langth-atrangtA vlthin intarval of I intaraat Hodulata EMG for croee-aectional araa (PCSA) \|/ Calculata total aaaaurad •xtamal work during interval Aaaign g a m • l N/ca*2 for eaeh auaela of inttreat
iI------calculata auaela foreea1------at aach aaapla point i------u:------i Partition FDS, POP, and EDC auaela forca i into grip forea and torqua ganarating coapenanta
calculata flaxion torqua at aach aaapla point gain ■ gain • l 3Z Calculata total external work froa pradletad torqua data during intarval of intaraat
pradletad torqua graatar
torqua?
Calculata r-equare between pradletad and aaaaurad torqua
Caleulata absolute and noi vriat loadings
Caleulata abaoluta and normallsad frictional work batvaan tandons and carpal bonaa and ligaaant
PCS,POS,POP, PCR.ECR.EDC
Nrita ealeulatad valuaa to .SUM fila
Start nav fila? Zf yaa, return to beginning.
Figure 37. Flow chart of model's micro-structure and logic. 141
Carpal Tunnel
Figure 38. Transverse plane of the wrist. The vectors for FCR, FDP, FDS, FCU, ECR, EDC, and ECU represent tendons passing through the wrist. Wx, Wy, and Wz are the net reaction forces on the wrist. The shaded area is the carpal tunnel, a passageway created by carpal bones and ligament through which the FCR, FDS, and FDP tendons pass. 142 estimated in this model; these groups and number of tendons within each group are listed below:
Flexor tendons: Abbreviation # of t Flexor carpi radialis* FCR (1 ) Flexor digitorum superficialis* FDS (4) Flexor digitorum profundus* FDP (4) Flexor carpi ulnaris FCU (1 ) Extensor tendons: Extensor carpi radialis ECR (2 ) Extensor digitorum communist EDC (4) Extensor carpi ulnaris ECU (1 ) *pass through carpal tunnel (Johnson, 1988)
FCR, FCU, ECR, and ECU's primary function is to move the wrist, while FDS, FDP, and EDC are secondary wrist movers. FDS, FDP, and EDC's primary function is to flex and extend the fingers, respectively (Basmajian, 1982; Soderberg, 1986; Youm, Ireland, Sprague, and Flatt, 1976), and secondarily to rotate the wrist. Anatomical Characteristics— Tendon Moment Arms. The moment arms of each subject's tendons, which were assumed constant throughout each extension to flexion exertion, were based on Brand's work (1985) and each subject's individual anthropometry. An anthropometric coefficient was calculated for each subject according to equation (28). This coefficient was used to adjust Brand's (1985) tendon moment arms to each subject. 143 anthrop. coef. (i) = ( wrist thickness(i) ) / (PL-EDC distance) (28) where: anthrop. = anthropometric coefficient for subject i coef. wrist = wrist thickness of subject i thickness PL-EDC = distance between palmaris longus (PL) distance and extensor digitorum communist (EDC) from Brand (1985).
The distance between the PL and EDC is assumed to represent the average of all subjects' wrist thicknesses among Brand's (1985) cadaver specimens. In order to calculate moment arms for each subject, all of Brand's (1985) average tendon moment arms were multiplied by each subject's anthropometric coefficient. Brand's (1985) average tendon moment arms are listed in table 2 0 .
Table 2 0 . Average moment arms of tendons passing through the wrist (Brand, 1985). Positive moment arms are in the radial and flexion directions.
Moment Arms (cm) Tendon Rad/Uln Plane Flex/Ext Plane
FCR 1.00 1.75 FDS -0.25 1.50 FDP -0.30 1.25 FCU -1.625 1.90 ECR 1.75 -1.20 EDC -0.35 -1.50 ECU -2.50 -0.85 144 Anatomical Characteristics — Geometric Orientation of Tendons. The tendons that transmit force from the forearm musculature to the hand and fingers are not exactly parallel to the axis of the forearm. The acute angles between the tendons and forearm axis in the R/U and F/E planes, which are illustrated in figure 39, were computed according to equations (29) through (32).
BETA(i,j) = arctan( (elb_width(i) / 2) + momarm_rad(i,j) ) / med_epic (29) where: BETA(i;j ) = acute angle between subject's i flexor tendon j and forearm axis in the rad/uln plane elb_width(i) = elbow width of subject i momarm_rad(i,j) = rad/uln moment arm of tendon j of subject i med_epic = subject's i distance between wrist and medial epicondyle
BETA(i,j) = arctan( (elb_width(i) / 2) + momarm_rad(i,j) ) / lat_epic (30) where: BETA(i,j) = acute angle between subject's extensor tendon j and forearm axis in the rad/uln plane elb_width(i) = elbow width of subject i momarm_rad(i,j) = rad/uln moment arm of tendon j of subject i lat_epic = subject's i distance between wrist and lateral epicondyle 145 GAMMA(i/j) = arctan( momarm_flex(i,j) / med_epic) (31) where: GAMMA(i,j) = acute angle between subject's i flexor tendon j and forearm axis in the flex/ext plane •lb_yidth(i) = elbow width of subject i momarm_flex(i,j) = flex/ext moment arm of tendon j of subject i med_epic = subject's i distance between wrist and medial epicondyle
GAMMA(i/j) = arctan( momarm_flex(i/j) / lat_epic) (32) where: GAMMA(i/j) = acute angle between subject's i extensor tendon j and forearm axis in the flex/ext plane elb_width(i) = elbow width of subject i momarm_flex(i/j) = flex/ext moment arm of tendon j of subject i lat_epic = subject's i distance between wrist and lateral epicondyle
Model Input. The model uses as input data from isokinetic wrist flexions at constant velocities performed on an isokinetic dynamometer. Subjects attempted to exert constant torque throughout a wide range of F/E motion. This task simulates wrist flexion movements found in highly repetitive, hand-intensive industrial jobs.
The inputs to the model are subject anthropometry, EMG signals from the seven forearm muscles, wrist kinematics, exernal torque, and grip force (pinch or power). Subject anthropometry were used to calculate tendon moment arms and geometric orientation of tendons with respect to the 146 forearm. Integrated EMG signals were monitored from the seven muscles via fine wire electrodes (Basmajian and DeLuca, 1985). Maximum integrated EMG were recorded for each muscle at regular intervals throughout the range of motion. Maximum integrated EMG is equated with a maximum level of force generation capability. A regression equation was computed for each muscle in order to predict maximum EMG as a function of wrist angle. Actual EMG values at each wrist angle were divided by their respective maximum values to determine the activity level at which the muscles were operating. Wrist kinematics and torque were recorded from the isokinetic dynamometer throughout the entire flexion movement. Wrist angle was recorded from the isokinetic dynamometer and angular velocity was subsequently calculated as the derivative of angle with respect to time. External torque was also recorded from the isokinetic dynamometer. Grip force was recorded from a load cell in the handle. Determining Force from EMG Signal. Equation (33) sums up all the modifications made to the EMG signal in order to derive a tension level for each muscle at each sample point. The components in equation (33) change as a function of time or wrist position (wrist position is directly correlated with time in isokinetic exertions). 147
FCU FDR FDS FCR ECU EDC ECR -m mm— -to- a.---
■ a
Medial Elbow Lateral Medial & Epicondyle Eplcondyle Lateral Eplcondyles
Figure 39. Geometric orientation of tendons passing through the wrist. Beta ( 0) angles are in the radial/ulnar plane, and gamma ($ ) angles are in the flexion/ extension plane. 148 Force = Gain * EMG * Vel mod * L-S mod * PCSA (33) EMGmax where: Force = muscle tension (N) associated with EMG Gain = factor which includes muscle force per unit of muscle area (N/cmA2) (PCSA) EMG = integrated EMG signal (volts) EMGmax = maximum EMG value (volts) for a particular muscle Vel mod = velocity modulation factor (0 to 1) L-S mod = length-strength modulation factor (0 to 1) PCSA = physiologic cross-sectional area of muscle (cmA2 )
The workings of the gain factor, velocity and length- strength modulation factors, and PCSA will be described in detail in the following sections. Mechanical Aspects of Muscle Contraction. The force of the muscle is indirectly measured by the EMG signal. However, the EMG signal can be perturbed by several factors. One of the major features of Marras and Sommerich's model (1991a, 1991b) was^ the addition of several devices to compensate for various factors which are known to affect the EMG signal. These factors include PCSA, velocity of contraction, and muscle length. EMG-Force Relationship. The number of recruited muscle fibers and frequency of excitation determine the electrical activity of a muscle (Bigland-Ritchie, 1981). The relationship between external force and integrated EMG was assumed linear. This assumption of linearity holds well for low to medium force levels (Perry and Bekey, 1981) . 149 Assuming this linear relationship between EMG and force, the EMG signal is normalized by dividing the EMG signal by the maximum EMG for a specific muscle at a particular angle {refer to EMG/EMGmax in equation (33)). The quotient is the percentage of maximum force that the muscle is exerting. Physiologic Cross-Sectional Area (PCSA). A muscle's PCSA is an indicator of the amount of force that it can exert — the greater the PCSA, the more force the muscle can exert. PCSA of the seven extrinsic muscles in this model were based on Chao's et al. (1982) work. The PCSA of each muscle is reported in table 21. The EMG signal was multipled by the PCSA of each muscle in equation (33).
Table 21. Average physiologic cross-sectional area (PCSA) of the seven extrinsic muscles utilized in this model. These values represent the aggregate PCSA of all tendons within each group (e.g. the PCSA of all four FDP muscles is 14.4 cmA2). These PCSA values are from Chao et al. (1982)
Muscle # of Tendons PCSA (cmA2)
FCR 1 5.2 FDS 4 12.3 FDP 4 14.4 FCU 1 1 0 . 0 ECR 2 8.9 EDC 4 4.5 ECU 1 3.5 150 Force-Velocitv Relationship. The amount of force that a muscle can exert is partially determined by the velocity of contraction. Based on a series of experiments, Hill (1938) found that the maximal power that a muscle can exert is constant. Since power is equal to force times velocity, then it follows that force and velocity have a reciprocal relationship for maximal exertions. During generation of a constant concentric force, higher rates of muscle shortening resulted in increased levels of integrated EMG (Bigland and Lippold, 1954). In this model, EMG signals were reduced to account for the velocity artifact. Based on substantial work investigating the relationship between force and velocity in trunk muscles, Marras and Mirka (1991) documented the velocity artifact in EMG. Marras and Mirka's (1991) quantification of EMG-velocity relationship was used in this wrist model to compensate for the velocity artifact. EMG signals in the 30 and 45 deg/sec trials were reduced by four and six percent, respectively. The Vel Mod factor in equation (33) was 0.96 and 0.94 for the 30 and 45 deg/sec trials, respectively. Lenath-Strenath Relationship. A muscle cannot exert the same maximal external force throughout its range of contraction. Each muscle has an optimal length at which it can produce maximal external force. Shortening or lengthening the muscle beyond its optimal length will reduce 151 its force capability. The exertion of force is accompanied by the sliding of actin (thin) and myosin (thick) elements within the muscle fibers. The cross-bridge theory is the most popular theory that explains the length-strength relationship within muscle fibers (Enoka, 1988). As illustrated in figure 40, cross-bridges are formed on the thick elements and attach to the thin elements. Tensile force is generated when the cross-bridges attach to the thin elements. The greatest force that a muscle can exert occurs at the optimal length, where there is maximum overlap between thick and thin elements (refer to figure 40) . The graph in figure 40 represents the active contractile process of muscle. Muscle can also exert force through passive means, due to the thick connective tissue which acts like a stiff elastic band (Enoka, 1988). Since the EMG signal records only the active contractile process of force exertion, the length-strength curve in this model was tailored similar to figure 40. The length-strength graph in figure 40 is obviously skewed. An extreme value distribution, which mimicks the skewed length-strength curve in figure 40, was selected as the length-strength curve to modulate EMG. The extreme value distribution is defined in equation (34) (King, 1971) and illustrated in figure 41. 152
5 4 3 2
2 1 0 0 r
2.25 1.27 1.67:2.0 3.65 2.0 2.5 3.0 3.5 4.0 c Striation Spacing (jim)
O*m)h-0.99-i— 1.67— h-0 .9 9 -h | IWHUHM ~~~~| 1
C I 3 tWMIIWtW 4 |*wmmin i'J— 5
B m U n t n W l O
Figure 40. Relationship among contractile force, sarcomere length, and filament overlap within a muscle fiber. This curve represents the active component of the length-strength characteristics of muscle fibers. From Enoka (1988). 153
f(x) = alpha * exp( -y - exp(-y) ) (34) subject to: y = alpha * ( x - mode ) -infinity < y < +infinity where: f(x) = weighting at angle x x = wrist angle (deg) y = normalized unit variable alpha = measure of dispersion mode = angle of central tendency (deg)
The L-S Mod factor in equation (33) is defined in equation (35).
L-S Mod = f(x) / f(mode) (35) where: L-S Mod = length-strength factor that modulates EMG signals f(x) = weighting at wrist angle x f(mode) = weighting at wrist angle mode
As illustrated in figure 41 and defined in equation (34), the maximum weighting occurs at the mode. As defined in equation (35) , the L-S Mod factor is less than or equal to one. EMG signals that occur at non-optimal wrist angles (angles not at the mode) are reduced by the L-S Mod factor. Gain. Gain is a factor which accounts for the force per unit area in the muscles (N/cmA2). Values of maximal force per unit area range from 30 to 100 N/cmA2 in the literature (Alexander and Vernon, 1975; Farfan, 1973; Haxton, 1944; Ikai and Fukunaga, 1968; Maughan, 1983; a Probability Density 0.001 0.002 0.003 0.004 0.006 0.005 0.005 0.007 0.008 0.009 0.009 0.011 0.012 a—0.015 a—0.015 0.01 0.01 0
2 4 60 40 20 O 0 2 - 0 4 - 0 6 - mode fixed at 15 degrees and alpha values varying from 0.015 0.015 from varying values alpha and degrees 15 at fixed mode to 0.030. This type of distribution was used to model the the model to used was distribution of type This 0.030. to length-strength characteristics of contracting muscles. contracting of characteristics length-strength Figure 41. Family of extreme value distributions with the the with distributions value extreme of Family 41. Figure EXTREME VALUE DISTRIBUTION ■ 0. 0 2 .0 -0 a +■ eghSrnt Rl; oe deg 5 1 = Mode Rel.; Length—Strength rs Age (deg) Angle Wrfst 4 a«0.025 a«0.025 A.
0. 0 3 .0 -0 a 4 5 1 155
Morris, Lucas, and Bresler, 1961; Schultz and Andersson, 1982; Weis-Fogh and Alexander, 1977). The gain factor also compensates for deficiencies in other modulation devices. Partitioning of Tendon Force. Since torque generation at the wrist is only a secondary function of the FDS, FDP, and EDC muscles, the estimated muscle force of the FDS, FDP, and EDC muscles (as calculated by equation (33)) was partitioned into two components: production of grip force (pinch or power) and generation of wrist torque. The amount of FDS, FDP, and EDC force needed to exert the measured external grip force was calculated first, and the remainder of the FDS, FDP, and EDC force was designated for torque generation. The force required to exert grip force was estimated according to a 3-D model of the fingers developed by Chao, Opgrande, and Axmear (1976). In their model, Chao et al. (197 6) determined the tendon force required to exert one unit of external flexor force in the distal phalanx of the index, middle, and little fingers. The ratios of each finger's tendon force to external force were weighted according to the contribution each finger makes to pinch and power grips. Hazelton, Smidt, Flatt, and Stephans (1975) found that the index, middle, ring, and little fingers contribute 25%, 33.5%, 25%, and 16.5% to total pinch and 156 power force. Table 22 lists the weighted tendon force per unit of external flexor force for pinch and power grips.
Table 22. Tendon force per unit of external flexor force for the flexor digitorum superficialis (FDS) and profundus (FDP) and extensor digitorum communist (EDC) . The external flexor force is applied perpendicular to the distal phalanx. The EDC force is an antagonistic force. Each tendon force ratio is weighted according to the contribution that each finger makes towards the aggregate pinch or power grip force.
Ratio of Tendon Force to Unit of External Flexor Force Tendon Pinch Grip Power Grip FDP 3.786 3.073 FDS 1.756 3.564 EDC 0.816 0.0
At each wrist angle throughout the exertion, the tendon force required to exert the measured grip force was calculated according to the ratios in Table 22. For the FDS, FDP, and EDC, the partitioned force was subtracted from its respective total force, as computed by equation (33), and the remainder of the force was used for torque generation. Calculation of Predicted Torque. The predicted flexor torque was calculated according to equation (36). The four flexor tendons (FCR,FDS, FDP,FCU) act as agonists (positive 157 torque) and contribute to flexor torque while the three extensors (ECR,EDC,ECU) act as antagonists (neg. torque). The partitioned force of the FDS, FDP, and EDC are calculated according to equations (37), (38), and (39). The first component in each of these equations is tne total tendon force, and the latter component is the force required to generate measured grip force. The predicted torque is calculated at each stage of an iterative process in which the gain is incremented by one N/cmA2. This process continues until the total external work as predicted by the model surpasses the total external work as measured by instrumentation. As illustrated in figure 42, the total external work is the area under the predicted torque curve within the interval of interest. Once this iterative process terminates, the squared correlation is computed between the measured and predicted torque. The squared correlation is a guage of how well the predicted torque matches the measured torque. 158 Pred_Torq(t) = (36) ( COS(BETA(FCR)) * COS(GAMMA(FCR)) * gain * EMG(FCR,t) * momarm_flex(FCR) ) + ( force_FDS_z(t) * momarm_flex(FDS) ) + ( force_FDP_z(t) * momarm_flex(FDP) ) + ( COS(BETA(FCU)) * COS(GAMMA(FCU)) * gain * EMG(FCU,t) * momarm_flex(FCU) ) + ( COS(BETA(ECR)) * COS(GAMMA(ECR)) * gain * EMG(ECR,t) * momarm_flex(ECR) ) + ( force_EDC_z(t) * momarm_flex(EDC) ) + ( cos(BETA(ECU)) * COS(GAMMA(ECU) ) * gain * EMG(ECU,t) * momarm_flex(ECU) )
PARTITIONING OF FDS, FDP, AND EDC FORCE: force_FDS_z(t) = (37) ( COS(BETA(FDS)) * COS(GAMMA(FDS)) * gain * EMG(FDS,t)) - ( ext_force(t) * fds_ratio ) force_FDP_z(t) = (38) ( COS(BETA(FDP)) * COS(GAMMA(FDP)) * gain * EMG(FDP,t)) - ( ext_force(t) * fdp_ratio ) force_EDC_z(t) = (39) ( cos(BETA(EDC)) * COS(GAMMA(EDC)) * gain * EMG(EDC,t)) - ( ext force(t) * edc ratio ) where: Pred_torq(t) predicted flexor torque (N-m) at time t BETA(i) acute angle between tendon i and forearm axis in the rad/uln plane GAMMA(i) acute angle between tendon i and forearm axis in the flex/ext plane gain force per unit area of muscle (N/cmA2) EMG(i,t) modulated, normalized integrated EMG signal from muscle i at time t momarm_flex(i) moment arm (m) of tendon i in flex/ext plane force_XXX_z(t) partitioned force (N) of tendon XXX that generates flexor torque at time t ext_force(t) external grip force (N) exerted at time t (either pinch or power) xxx ratio ratio of tendon force per unit of external grip force (either pinch or power) for tendon xxx PREDICTED VS. MEASURED TORQUE
_ r
-50 -30 -1 0 10 Wrist Angle (deg) □ Measured torque + Predicted torque
Figure 42. Measured wrist flexor torque vs. torque predicted by the biomechanical model within an interval of -45 deg extension to 15 deg flexion . The plotted torques are from a 30 deg/sec wrist flexion movement (GF71). Computation of Compression and Shear Forces. The compression and shear forces on the wrist joint were calculated according to equations (40), (41), and (42). Compression is the net reaction force exerted along the forearm axis that counteracts primarily the tendon forces. Positive radial shear is the net reaction force in the radial direction. Positive flexion shear is the net reaction force in the flexion direction. (Refer to figure 38 for directions of compression and shear forces). 161 Compression(t) = (40) COS (BETA(FCR)) * COS (GAMMA(FCR)) * EMG(FCR/t) * gain) + force_FDS_z(t) ) + force_FDP_z(t) ) + COS (BETA(FCU)) * COS (GAMMA(FCU)) * EMG(FCU,t) * gain) + COS (BETA(ECR)) * COS (GAMMA(ECR)) * EMG(ECR,t) * gain) + force_EDC_z(t) ) + COS (BETA(ECU)) * cos(GAMMA(ECU)) * EMG(ECU,t) * gain)
Flex_shear(t) = (41) (COS(BETA(FCR)) * sin(GAMMA(FCR)) EMG(FCR,t) * gain) + (COS(BETA(FDS)) * sin(GAMMA(FDS)) force_FDS(t)* gain) + (COS(BETA(FDP)) * sin(GAMMA(FDP)) force_FDP(t)* gain) + (COS(BETA(FCU)) * sin(GAMMA(FCU)) EMG(FCU,t) * gain) + (COS(BETA(ECR)) * sin(GAMMA(ECR)) EMG(ECR,t) * gain) + (COS(BETA(EDC)) * sin(GAMMA(EDC)) force_EDC(t)* gain) + (COS(BETA(ECU)) * sin(GAMMA(ECU)) EMG(ECU,t) * gain)
Rad_shear(t) = (42) (Sin(BETA(FCR)) * COS(GAMMA(FCR)) * EMG(FCR,t) * gain) + (Sin(BETA(FDS)) * COS(GAMMA(FDS)) * force_FDS(t)* gain) + (sin(BETA(FDP)) * COS(GAMMA(FDP)) * force_FDP(t)* gain) + (sin(BETA(FCU)) * COS(GAMMA(FCU)) * EMG(FCU,t) * gain) -I- (sin (BETA(ECR) ) * COS(GAMMA(ECR)) * EMG(ECR,t) * gain) + (sin(BETA(EDC)) * cos(GAMMA(EDC)) * force_EDC(t)* gain) -I- (Sin (BETA (ECU) ) * cos(GAMMA(ECU)) * EMG(ECU,t) * gain) where: force_FDS(t) = force_FDS_Z(t) / (COS(BETA(FDS)*COS(GAMMA(FDS)) force_FDP(t) = force_FDP_Z(t) / (COS(BETA(FDP)*COS(GAMMA(FDP)) force_EDC(t) = force_EDC_Z(t) / (COS(BETA(EDC)*COS(GAMMA(EDC)) BETA(i) = acute angle between tendon i and forearm axis in the rad/uln plane GAMMA(i) = acute angle between tendon i and forearm axis in the flex/ext plane gain = force per unit area of muscle (N/cmA2) EMG(i,t) = modulated, normalized integrated EMG signal from muscle i at time t force_XXX_z(t) = compression component of partitioned force (N) of tendon XXX that generates flexor torque at time t force XXX(t) = partitioned force (N) of tendon XXX that generates flexor torque at time t 162
Computation of Frictional Work. The calculation of frictional work between the tendons that pass through the wrist joint and their sheaths was based on a rope:fixed pulley mechanical analogy (Marks, 1978; LeVeau, 1977). Figure 43 illustrates a side view of one tendon as it rubs against its sheath or bones and ligaments. The sheath is supported by the carpal bones and ligament. Since there is friction between the tendon and its adjacent structure, the force that the muscle has to generate (Fmax) is equal to the sum of the force required to move and exert torque in the hand (Fmin) and frictional force (Ffriction). Equation (43) defines the components of Fmax tendon force. If the system were frictionless, then Fmax would be equal to Fmin.
Fmax = Ffriction + Fmin (43)
According to the rope:fixed pulley analogy, the relationship between. Fmax and Fmin is expressed in equation (44). The frictional force is defined in equation (45).
Fmax = Fmin * eA(u*0) (44) Ffriction = ( Fmin * eA(u*0) ) - Fmin (45) where: Fmax = force (N) that the muscle generates and is transmitted proximal to the carpal tunnel Ffriction = tendon force (N) that is lost due to friction with its adjacent structures Fmin = tendon force distal to the carpal tunnel that moves and exerts torque in the hand u = coefficient of friction between tendon and its adjacent anatomical structure © = flexion/extension angle of wrist (radians) 163
Hand extended at & degrees
Fmax
(" —> + 1 ) Fmax Ffriction Fmin
Fmax
Hand flexed at 9 degrees
Figure 43. Decomposition of forces within a tendon that transmits force from the a forearm muscle to the hand. Fmax is the force that the muscle generates and Fmin is the force transmitted to the hand. Ffriction is the force lost to friction with adjacent anatomical structures. 164 In this model, the coefficient of friction between the tendons and their adjacent anatomical structures was assumed to be 0.0032. 0.0032 is an approximate coefficient of friction for human synovial joints (Fung, 1981). This value agrees well with experimental data from animal studies. In a study investigating a dog's ankle joint, Linn (1968) reported 0.0044 as a coefficient of friction for synovia. Friction work is the product of the frictional force and the distance that the tendon travels. Figure 44 shows a schematic of how frictional work between a tendon and its adjacent anatomical structures is computed for a single extension to flexion movement. For each small angular interval, @, the frictional work was calculated. Equation (45) defines the total frictional work of one extension to flexion movement.
»AA Vl Frictional Work (Ffriction * (r * @i)) (45) where: Ffriction = tendon force that is lost due to friction against sheath r = radius of curvature of tendon bending around carpal bones or ligament @l+@2 +@n= total angular excursion within the interval of interest m = number of tendons passing through either carpal tunnel or entire wrist joint 165
V ' * ' - F. W ork = Ffric * (r*@>1)
t
f— * @2 F. W ork * Ffric * (r*@ 2)
@3 F. W ork = Ffric * (r*@ 3) - 4
. @4 /*^y- F. Work ■ Ffric * (r*@4)
Figure 44. Schematic of how frictional work between a tendon and its adjacent structures is computed for an extension to flexion movement. Ffric is the same as the Ffriction force in figure 43. 166 The radius of curvature (r) for each of the tendons was based on Armstrong and Chaffin's (1978) investigations into displacement of wrist tendons. Model Output. The output of this model were stored in a summary file. This summary file includes the following: 1. Squared correlation between predicted and measured torque. 2. Final gain (N/cm*2) of muscle output. 3. Average torque (N-m) exerted within the interval. 4. Peak and average compression and radial and flexion shear on the wrist joint. These values were in absolute units (N) and also normalized to the average external torque (N force / N-m of measured torque). 5. Total external work (N-m) generated throughout the interval of interest. 6. Frictional work generated by the tendons rubbing against its supporting structures within the interval of interest. These values were in absolute units (N-m work) and also normalized to the external work generated within the interval of interest ( N-m frictional work / N-m external work) . Frictional work was calculated for three sets of tendons: a. FCR,FDS,FDP: tendons passing through carpal tunnel b. FCR,FDS,FDP,FCU: all four flexor tendons c. FCR,FDS,FDP,FCU,ECR,EDC,ECU: all seven tendons (four flexors, three extensors) CHAPTER V BIOMECHANICAL MODEL OF THE WRIST JOINT: VALIDATION AND EMPIRICAL RESULTS
Introduction In the industrial surveillance phase of this project (Chapters 1,11, and III), wrist motion components of workers who performed highly repetitive, hand-intensive industrial jobs of low and high CTD risk were monitored. F/E components of wrist motion (acceleration and velocity) discriminated the best between workers who performed highly repetitive, hand-intensive work in industrial jobs of low and high risk of CTDs. A 3-D biomechanical model of the wrist joint, which was described in detail in Chapter IV, was developed to evaluate the impact of repetitive movements and wrist torques on the anatomical structures within the wrist. With regard to this research project, the specific objective of the biomechanical model was to evaluate the mechanical effect of F/E velocity on the tendons that pass through the wrist and possibly explain why F/E velocity at the high risk velocity exposes workers to CTDs.
167 168 Since this investigation was exploratory, the intent of this modeling phase was to conduct preliminary research and enhance our general understanding of the complex relationship among repetitive movements, external forces, and internal stresses on the anatomical structures in the wrist. This chapter discusses the validation of the biomechanical model and results of an experiment that simulated the repetitive wrist motions found in industry.
Approach In order to achieve the objective of this modeling research, it was necessary to preserve the relationship between muscle force and EMG. A highly controlled experiment was designed in which subjects exerted wrist flexion movements at constant torque and constant velocity. The velocities were the mean F/E velocities found in jobs of low and high risk of CTDs. The velocity was controlled because the relationship between EMG and muscle force is relatively linear and stable when muscle fibers are shortening at a constant rate (Bigland and Lippold, 1954). Even though F/E acceleration predicted CTD risk most distinctly in the industrial surveillanc phase, wrist motions that controlled acceleration were not incorporated into this experiment. Currently, the relationship between EMG and muscle force under constant acceleration is unstable 169 and unknown, so an experiment focusing on F/E acceleration is infeasible at this time.
Subjects Two male subjects (mean age 24) volunteered for this experiment. It should be emphasized that this was an exploratory study. Both subjects were healthy and had no history of upper extremity injuries or disorders. Table 23 lists the anthropometric dimensions of these two subjects.
Experimental Design The experimental design was a repeated measures, full factorial design. The independent variables were grip orientation (pinch and power), angular velocity (30 and 45 deg/sec wrist flexions), and constant torque (four and eight N-m). Angular velocities of 30 and 45 deg/sec were the mean F/E velocities of the low and high risk CTD groups, respectively, as measured in the industrial surveillance phase of this project. Eight N-m of torque was selected as the upper bound for torque in this experiment because eight N-m was approximately the maximum torque that normal subjects could exert with a pinch grip at a wrist angle of 60 deg flexion. The first subject repeated the four and eight N-m constant torque exertions twice, and the second subject repeated them thrice. 170 Table 23. Anthropometric dimensions of subjects. The gross dimensions were measured according to Webb Associates (1978), and the hand dimensions were measured according to protocol established by Garrett (1970a and 1970b).
Subj#l Subj #2 Age (years) 25 23 Gross Dimensions (kg and cm) Weight 84.1 79.6 Stature 198.1 175.4 Shoulder height 166.7 143 .4 Arm length 88.1 72.7 Trunk depth 21.5 23.7 Shoulder-elbow length 43.1 35.0 Elbow-wrist length 33.9 29.2 Elbow-hand length 55.0 45.7 Dominant Hand Dimensions (cm) Hand length 21.3 17.3 Thumb length 5.8 5.65 Middle finger length 9.4 7.9 Hand breadth 9.3 8.6 Hand thickness 3.0 2.8 Wrist breadth 6.3 6.1 Wrist thickness 4.4 4.3 Wrist circum. 18.0 17.0 Forearm circum. 27.8 29.0 Elbow width 7.7 7.0 Wrist to med. epic. 32.3 27.3 Wrist to lat. epic. 31.2 26.9
Grip Strength (kgf) Maximum grip strength (kgf) 34 44 The dependent variables were integrated EMG signals from seven extrinsic muscles in the forearm. Lippold (1952) and Bigland and Lippold (1954) have shown that the integrated EMG activities of a muscle operating under isometric or constant velocity conditions are linearly related to the amount of force the muscle is producing. The muscles monitored in this study, which are listed below, are the predominant wrist and finger flexors and extensors.
Flexor carpi radialis FCR Flexor digitorum superficialis FDS Flexor dititorum profundus FDP Flexor carpi ulnaris FCU Extensor carpi radialis ECR Extensor digitorum communist EDC Extensor carpi ulnaris ECU
Apparatus Wrist flexion velocity was controlled by a Cybex isokinetic dynamometer, illustrated in figure 45. The Cybex shaft was aligned with the center of the wrist in the F/E plane. The subject placed his arm in a fixture that supported his arm during the trials. The subject grasped a handle that measured pinch and power grip force. The handle had two thin metal surfaces that served as the grasping medium for a pinch grip. Two hemispherical shells were added to the thin metal surfaces to make the handle oval- Cybex isokinetic Counterbalance dynamometer weight
Isokinetic Armrest fixture conditions connected to controlled Cybex bench by Cybex
Fine wire electrodes Power/pinch force measured Torque & wrist angle by ioadcell in vertical plane measured by Cybex
Figure 45. Apparatus for the modeling experiment. 172 173 shaped for power gripping. The load cell in the handle measured both pinch and power grip force. The subject controlled the wrist torque throughout each trial. The torque signal from the Cybex was fed into an oscilloscope. The subject was told to keep the torque within a desired window on the oscilloscope, which was +/- 0.7 N-m and +/- 1.0 N-m of the targeted four and eight N-m torque levels, respectively. EMG signals from the seven forearm muscles were monitored with fine wire electrodes. The fine wire was 0.003 inch diameter stainless steel wire with a Teflon coating (California Fine Wire, Grove City, CA). The total diameter of the fine wire was 0.0038 inches. The wires were threaded through a 25 gage, 1.5 inch long injection needle, and bent over the needle to form barbs. The purpose of the barbs was to hook the wire into the muscle fiber so it would not dislodge while the muscles moves. The Teflon coating around the barbed ends of the wire was scraped off with an X-acto knife.
The EMG signal from the pair of fine wire electrodes was amplified 1000X with a lightweight preamplifier, which rested on the subject's thigh during the experiment. The signal then travelled through a shielded cable to the EMG processor, where it was amplified another lOx (approximately). Total amplification was approximately 174 10,OOOx. The integration window was set at 20 msec, and the EMG signal was filtered with a 60 Hz notch filter and a 1000 Hz low pass filter. As shown in figure 46, all the data were processed by a 12 bit analog to digital converter, which sampled the data at 100 Hz. The data consisted of two channels from the Cybex (wrist angle and torque), one channel from the load cell in the handle, and seven channels from the EMG system. The digitized data were then fed into a portable microcomputer for storage and analysis.
Procedure Before the day of data collection, each subject practiced the constant torque exertions at the two velocities until he gained a facility for maintaining the desired torque. During the setup before data collection, seven pairs of fine wire electrodes were inserted into the subject's forearm by a licensed physician. The skin was cleaned with alcohol prior to insertion. The physician injected the 25 gage needle into the muscle belly, and the needle was removed while the barbed wires remained lodged in their respective muscle belly. The fine wires were taped to the skin near the point at which they exited the skin. There was a small amount of slack in the wire between the point of Pinch Srip Force Power
Wrist Angle — Cybex Torque *
Electrodes EMG Preamps System *
Ch. 1
Ch. 2 Wrist: Ch. 3 Computer Biom. Board Model Forces Ch. 4 Work
Ch. 5 Ch. 6 Ch. 7
Oscilloscope
Figure 46. Flow of data in the modeling experiment. The sampling rate of the A/D board was 100 Hz. 176 egress from the skin and where it was taped in order to allow the fine wire to move with the muscle belly during dynamic exertions. Each EMG signal was tested for muscle selectivity and strength via an oscilloscope. The handle was set up for one of the two grip orientations. EMG signals, torque, and pinch and grip force were recorded while the subject exerted maximum torque and grip force contractions at seven wrist angles: -60 (ext), -40, -20, 0, 20, 40, and 60 deg (flex). The subject rested two minutes between maximal contractions. After all the static exertions were complete, the experiment proceeded to the dynamic trials. The Cybex was set to one of the two prescribed constant velocities (30 or 45 deg/sec). The subject started each exertion at approximately -70 deg extension and terminated at approximately 70 deg flexion. Even though data wdre analyzed only between -60 and 60 deg, the subject moved an extra 10 deg at the beginning and end of each exertion in order to build up and maintain torque at the desired level and reach a steady state velocity. During the entire range of motion, the subject monitored the torque on an oscilloscope and attempted to maintain torque within the targeted window. Two torque levels (four and eight N-m) were tested within each constant velocity. Before moving on to the next grip orientation, the subject and experimenters took a 45 minute break to minimize fatigue. 177 After all the experimental conditions were completed, the fine wires were pulled slowly from their respective muscle bellies. The subject was thanked for his participation and given a T-shirt for his efforts.
Data Conditioning The data were processed and conditioned according to the procedures described in Chapter IV. As listed in Chapter IV, the model output were r-square (statistical measure of match between predicted and mesured torque), external work, absolute and normalized compression and shear, and absolute and normalized frictional work.
Validation of Model Lenath-Strenath Parameters. The mode and alpha, measures of central tendency and dispersion for the extreme value distribution, were adjusted until the predicted torque matched the measured torque relatively well. The extreme value distribution mimicks the pattern of force production
as a function of muscle length (length-strength relationship) (refer to figures 40 and 41). Throughout this iterative process, values of the mode and alpha were set within estimated physiologic bounds. Table 24 shows the final mode and alpha values for both subjects. For the flexors, the mode was set at either a neutral or flexed 178 angle because the mode, which represents the peak force of a muscle's active contractile process, occurs when the muscle is shortened (refer to figure 40). In a similar fashion, the mode was set at a neutral or extended angle for the extensor muscles.
Table 24. Parameters of the extreme value distribution for subjects ML and GF. The extreme value distribution mimicked the length-strength curve for the forearm musculature. The mode is a measure of central tendency, and alpha is a measure of dispersion. Positive angles are wrist flexion, and negative angles are extension.
Subject Muscle ML GF Pinch Grip FDS,FDP mode = 0 deg mode = 7 . 5 deg alpha 0 . 0 1 7 5 alpha — 0 . 0 1 7 5
EDC mode = 0 mode = - 7 . 5 alpha = 0 . 0 1 7 5 alpha — 0 . 0 1 7 5
F C R , F C U mode ss 0 mode - 7 . 5 alpha ss 0 . 0 2 0 0 alpha 0 . 0 2 0 0
E C R , EC U mode ss 0 mode = - 7 . 5 alpha = 0 . 0 2 0 0 alpha = 0 . 0 2 0 0
Power Grip FDS,FDP mode = 0 deg mode = 1 5 . 0 deg alpha = 0 . 0 1 7 5 alpha = 0 . 0 2 2 5
EDC mode ss 0 mode s - 1 5 . 0 alpha ss 0 . 0 1 7 5 alpha ss 0 . 0 2 2 5
F C R , F C U mode — 0 mode “ 1 5 . 0 alpha = 0 . 0 2 0 0 alpha = 0 . 0 2 0 0
E C R , EC U mode s 0 mode — - 1 5 . 0 alpha = 0 . 0 2 0 0 alpha = 0 . 0 2 0 0 179 Selection of Angular Intervals. The model predicted torque well within an angular interval of -45 to 15 deg. The model underestimated torque at extreme extension (-60 to -45 deg) and overestimated torque at moderate to extreme flexion angles (15 to 60 deg). The interval between -45 and 15 deg was selected as the region in which all the kinetic measures were analyzed for two reasons. First, -45 to 15 deg liberally encloses the F/E range of motion found in the industrial surveillance phase (refer to table 7). Second, the model predicted torque relatively well within this angular interval. Squared Correlation Statistics. Table 25 lists the squared correlation between measured and predicted torque for both subjects. The squared correlation, which ranges from 0 to 1.0, measures how well the torque predicted by the model matches the torque measured by the Cybex. The squared correlation statistics are reported for all trials and also for only those trials that resulted in values greater than 0.250. All of the pinch trials generated values greater than 0.250; however, five of subject ML trials and one of subject GF trials did not meet the 0.250 threshold. The pinch conditions matched the measured torque well, as evinced by median squared correlation values of 0.648 and 0.750 for both subjects. In addition to lower standard deviations, the mean and median squared correlation values 180 for pinch conditions were approximately 0.200 greater for both subjects than power grip conditions.
Table 25. Squared correlation between predicted and measured torque for each subject's pinch and power grip trials. All squared correlation values were calculated within an angular interval between -45 deg (extension) to 15 deg (flexion). The summary statistics of r-square values were computed for all trials within grip orientation and only those trials with r-squares greater than 0.250.
Subject ML GF
Pinch Grip Trials w/ squared corr. greater than 0.250 All trials All trials n = 12 n = 8 med = 0.648 med = 0.750 avg = 0.654 avg = 0.715 sd = 0.157 sd = 0.117
Power Grip All trials All trials n = 12 n = 8 med = 0.471 med = 0.566 avg = 0.413 avg = 0.525 sd = 0.342 sd 0.216 Trials w/ squared corr. greater n = 7 n = 7 med = 0.750 med = 0.613 avg = 0.667 avg — 0.584 sd = 0.169 sd = 0.147 n = number of observations med = median avg = mean sd = standarddeviation 181 Results Maximum Force and Torque. Each subject exerted maximum pinch and grip force and flexor torque at seven wrist angles (-60, -40, -20, 0, 20, 40, and 60 deg) in order to generate maximum values of internal output (maximum EMG for normalization) and also maximum external output (force and torque). The absolute maximum grip force and flexor torque were measured with a load cell in the handle and the Cybex isokinetic dynamometer, respectively, and these values are illustrated in figures 47 and 48. The overall trend of the maximum force exertions indicate the peak values occurred at a neutral angle or slightly extended angle and also a marked force decrement due to wrist flexion (refer to figure 47). Maximum pinch forces were about 50% of the maximum power grip forces. As shown in figure 48, the trend of the maximum torques with respect to wrist angle agree with maximum force. However, contrary to force results, there was no decrement in pinch flexor torque with respect to power grip flexor torque. The pinch and power grip torques were about equal within each subject. Kinetics. The kinetic results of both subjects' constant torque trials are reported in tables 26 through 33. These kinetic parameters include final muscle gain, wrist loading (compression and shear), external work, and frictional work. The data in tables 26 through 33 are M—OE + G-OE O LPNH GF-PINCH A ML-PINCH O GF-POWER + ML—POWER□ Fore* (N) 300 450 200 250 350 of wrist angle. ofwrist 150 iue4. aia ic n oe rp oc sa function a as force grip power and pinch Maximal 47. Figure 100 50 60- 0 -4 0 -6 MAXIMAL PINCH AND POWER GRIP FORCE -20 ujcs L GF & ML Subjects rs Age (deg) AngleWrist 0 20 40
60 182 LPWR FPWR M-IC A GF-PINCH A ML-PINCH O GF-POWER + ML-POWER □ Torqua (N —i 20 8 - 18 6 - 16 - 17 - 19 3 - 13 14 10 12 5 - 15 8 - 5 - 4 - - - - 60 -6 ~2
iue 8 Mxmlpnhadpwr lxo oqea a as torque flexion power and pinch Maximal 48. Figure function of wrist angle. wrist of function MAXIMAL PINCH AND POWER FLEX TORQUE 40 -4 -20 ujcs L GF & ML Subjects rs Age (deg) Angle Wrist 0 20 40
60 183 184 Table 26. Kinetic results of both subjects' constant torque trials of four N-m (nominal) exerted with a pinch grip. All values are calculated within the interval -45 deg (extension) to 15 deg (flexion). Loading on the wrist (compression, F/E shear, and R/U shear) were normalized to N of loading / N-m of torque. Each value represents one trial; only those trials that resulted in a r-square greater than 0.250 are listed.
Subject ML Subject GF 30 d/S 45 d/S 30 d/S 45 d/S Average Measured Torque (N-m) 3.09 2.94 3.58 3.34 3.09 2.82 3.12 3.54 3.11 3.37 Gain of all Muscles (N/cmA2) 28 21 26 22 24 22 25 25 25 24 Compression on Wrist (Absolute) 182 169 193 179 (N) 177 166 166 196 177 198 (Norm.) 58.9 57.5 53.8 53.6 57.2 58.8 53.1 55.4 56.9 58.7 F/E Shear on Wrist (Absolute) 34.3 32.6 33.6 31.3 (N) 34.1 31.2 29.4 33.5 34.3 37.3 (Norm.) 11.1 11.1 9.38 9.37 11.0 11.1 9.43 9.47 11.0 11.1 R/U Shear on Wrist (Absolute) 16.4 17.1 15.4 15.0 (N) 17.4 16.6 12.7 16.3 17.1 19.5 (Norm.) 5.30 5.80 4.30 4.49 5.62 5.88 4.07 4.60 5.49 5.79 185 Table 27. External and frictional work calculated for both subject's constant torque trials of four N-m (nominal) exerted with a pinch grip. All values are calculated within the interval -45 deg (extension) to 15 deg (flexion). Each value represents one trial; only those trials that resulted in a r-square greater than 0.250 are listed. Differences of less than 10% frictional work between 30 and 45 deg/sec trials were labelled no difference.
Subject ML Subject GF 30 d/S 45 d/s 30 d/s 45 d/S
Measured External Work (N-m) 3.09 2.91 3.62 3.39 3.07 2.78 3.17 3.61 3.09 3.34
Normalized Frictional Work Tendons (N-m of FW / N-m of External Work) FCR,FDS .000394 .000455 .000350 .000389 6 FDP .000451 .000486 .000281 .000373 .000436 .000470 mean= means mean= mean= .000427 .000500 .000316 .000381 >by 10.1% >by 20.6
FCR/FDS .000590 .000818 .000818 .000780 FDP/FCU .000852 .000846 .000821 .000784 .000862 .000837 mean= mean= mean= mean= .000768 .000834 .000820 .000782 No diff. No diff.
FCR/FDS .000924 .000879 .000858 .000816 FDP,FCU .000911 .000916 .000861 .000823 ECR,EDC .000919 .000912 ECU mean= mean= mean== mean= .000918 .000902 .000860 .000820 No diff. NO diff. 186 Table 28. Kinetic results of both subjects' constant torque trials of eight N-m (nominal) exerted with a pinch grip. All values are calculated within the interval -45 deg (extension) to 15 deg (flexion). Loading on the wrist (compression, F/E shear, and R/U shear) were normalized to N of loading / N-m of torque. Each value represents one trial; only those trials that resulted in a r-square greater than 0.250 are listed. Subject ML Subject GF 30 d/S 45 d/S 30 d/S 45 d/S Average Measured Torque (N-m) 6.81 7.08 6.50 7.02 7.12 6.77 6.67 6.86 6.88 7.22 Gain of all Muscles (N/cmA2) 29 28 38 34 30 34 37 34 30 32 Compression on Wrist (Absolute) 390 416 343 375 (N) 421 389 344 356 386 406 (Norm.) 57.2 58.8 52.8 53.5 59.1 57.5 51.5 51.9 56.0 56.2 F/E Shear on Wrist (Absolute) 75.9 78.6 61.5 66.8 (N) 78.9 75.0 62.8 65.0 76.2 79.5 (Norm.) 11.2 11.1 9.45 9.52 11.1 11.1 9.42 9.46 11.1 11.0 R/U Shear on Wrist (Absolute) 35.2 38.3 29.0 33.2 (N) 36.0 35.0 29.2 30.7 34.6 33.2 (Norm.) 5.17 5.41 4.46 4.73 5.05 5.17 4.38 4.48 5.03 4.60 187
Table 29. External and frictional work calculated for both subject's constant torque trials of eight N-m (nomimal) exerted with a pinch grip. All values are calculated within the interval -45 deg (extension) to 15 deg (flexion). Each value represents one trial; only those trials that resulted in a r-square greater than 0.250 are listed. Differences of less than 10% frictional work between 30 and 45 deg/sec trials were labelled no difference. Subject ML Subject GF 30 d/S 45 d/S 30 d/S 45 d/s
Measured External Work (N-m) 6.78 7.00 6.61 7.17 7.09 6.64 6.77 6.95 6.89 7.15
Normalized Frictional Work Tendons (N-m of FW / N-m of External Work) FCR,FDS .000356 .000414 .000360 .000386 6 FDP .000388 .000354 .000339 .000341 .000341 .000291 mean= mean= mean= xnean= .000362 .000353 .000350 .000364 No. diff. No diff.
FCR,FDS .000836 .000798 .000807 .000783 FDP,FCU .000850 .000774 .000800 .000762 .000791 .000788 mean= mean= mean= mean= .000826 .000787 .000804 .000773 No diff. No diff.
FCR,FDS .000885 .000854 .000837 .000808 FDP,FCU .000919 .000834 .000826 .000787 ECR,EDC .000844 .000345 ECU mean= mean= mean= mean= .000883 .000844 .000831 .000798 No diff. No diff. 188 Table 30. Kinetic results of both subjects' constant torque trials of four N-m (nominal) exerted with a power grip. All values are calculated within the interval -45 deg (extension) to 15 deg (flexion). Loading on the wrist (compression, F/E shear, and R/U shear) were normalized to N of loading / N-m of torque. Each value represents one trial; only those trials that resulted in a r-square greater than 0.250 are listed. Subject ML Subject GF 30 d/S 45 d/S 30 d/S 45 d/s Average Measured Torque (N-m) 3.25 3.02 3.36 4.82 3.53 3.17 3.55
Gain of all Muscles (N/cmA2) 40 32 31 36 42 36 30
Compression on Wrist (Absolute) 230 202 194 264 (N) 236 210 197
(Norm.) 70.6 67.0 57.6 54.8 67.0 66.1 55.4
F/E Shear on wrist (Absolute) 55.3 51.0 47.0 66.9 (N) 59.6 53.6 49.2
(Norm.) 17.0 16.9 14.0 13.9 16.9 16.9 13.9
R/U Shear on Wrist (Absolute) 26.9 20.8 13.2 18.3 (N) 26.9 23.0 13.3
(Norm.) 8.28 6.89 3.93 3.81 7.63 7.27 3.73 189 Table 31. External and frictional work calculated for both subject's constant torque trials of four N-m (nomimal) exerted with a power grip. All values are calculated within the interval -45 deg (extension) to 15 deg (flexion). Each value represents one trial; only those trials that resulted in a r-square greater than 0.250 are listed. Differences of less than 10% frictional work between 30 and 45 deg/sec trials were labelled no difference. Subject ML Subject GF 30 d/S 45 d/S 30 d/S 45 d/S Measured External Work (N-m) 3.25 2.99 3.42 4.96 3.51 3.14 3.61
Normalized Frictional Work Tendons (N-m of FW / N-m of External work) FCR,FDS .000782 .000652 .000257 .000248 & FDP .000741 .000716 .000216 mean= mean= mean= .000761 .000684 .000237 >by 11.3% No diff.
FCR,FDS .000874x .000890 .000832 .000798 FDP,FCU .000880' .000894 .000794 mean= mean= mean= .000877 .000892 .000813 NO diff. No diff.
FCR,FDS .001008 .001009 .000885 .000853 FDP,FCU .000988 .001013 .000839 ECR,EDC ECU mean= mean= mean= .000998 .001011 .000862 No diff. No diff. 190 Table 32. Kinetic results of both subjects' constant torque trials of eiqht N-m (nominal) exerted with a power grip. All values are calculated within the interval -45 deg (extension) to 15 deg (flexion). Loading on the wrist (compression, F/E shear, and R/U shear) were normalized to N of loading / N-m of torque. Each value represents one trial; only those trials that resulted in a r-square greater than 0.250 are listed.
Subject ML Subject GF 30 d/S 45 d/s 30 d/s 45 d/S Average Measured Torque (N-m) 7.27 6.59 7.06 7.37 6.69 6.88 7.59 Gain of all Muscles (N/cmA2) 48 54 58 48 45 57 53
Compression on Wrist (Absolute) 451 355 371 (N) 460 365 380 520 (Norm.) 62.0 53.8 52.5 62.4 54.5 55.2 68.5 F/E Shear on Wrist (Absolute) 123 92.1 98.8 (N) 125 93.1 96.1 128
(Norm.) 16.9 14.0 14.0 16.9 13.9 14.0 16.9 R/U Shear on Wrist (Absolute) 42.5 24.8 26.3 (N) 44.2 25.5 28.6 49.1 (Norm.) 5.85 3.76 3.72 5.99 3.81 3.43 6.46 191 Table 33. External and frictional work calculated for both subject's constant torque trials of eight N-m (nomimal) exerted with a power grip. All values are calculated within the interval -45 deg (extension) to 15 deg (flexion). Each value represents one trial; only those trials that resulted in a r-square greater than 0.250 are listed. Differences of less than 10% frictional work between 30 and 45 deg/sec trials were labelled no difference. Subject ML Subject 6F 30 d / s 45 d / S 30 d / s 45 d /S Measured External Work (N-m) 7.24 6.66 7.21 7.33 6.80 7.08 7.59
Normalized Frictional Work Tendons (N-m of FW / N-m of External Work) FCR,FDS .000476 .000210 .000213 & FDP .000487 .000259 .000187 .000560 mean= mean= mean= .000508 .000235 .000200 >by 17.5%
FCR,FDS .000857 .000813 .000834 FDP,FCU .000870 .000820 .000857 .000907 mean= mean= mean= .000878 .000817 .000845 No diff.
FCR,FDS .000941 .000857 .000879 FDP,FCU .000959 .000862 .000926 ECR,EDC .001019 ECU mean= mean= mean= .000973 .000860 .000902 No diff. 192 MEAN G AIN PINCH GRIP CONDITIONS Subjacta UL * OF
BO -
10 -I A)
Nominal Tarauo (N -m ) □ ML—30 + ML—48 O OF-JO A OF—46
MEAN GAIN — POWER GRIP CONDITIONS Subjacta ML * OF --
60 - i
40 -■
£
20 -1
10 -j
B) —I------1------r - 6 7 Nominal Torqua (N -m ) □ ML—30 UL—46 O O F -30 A OF—46
Figure 49. Mean final gain of all pinch (a) and power grip (b) conditions. 30 and 45 refer to isokinetic velocity (deg/sec) . 193
NORMALIZED COMPRESSION — PINCH GRIP Subject* ML * OF 80 -
70 -
! 80 - £f % so -1 f j 40 - j w1 i i t so -! S I 20 -1 z i 1° -1 1 A) 0 4 ------1------,------p - 3 6 7 Nominal Terqua (N -m ) ML—30 + ML-48 * OF—30 OF—40
NORMALIZED COMPRESSION — POWER GRIP 80 Subject* UL * OF
7° -J
80 - j
50 - i E1 ! 40 -
30 - |
JO -
B)
Nominal Torque (N -m ) □ ML—30 + ML-48 ♦ OF—30 A OF—48
Figure 50. Mean normalized compression on the wrist joint in pinch (a) and power grip (b) conditions. Compression (N) is normalized to average flexion torque (N-m) between -45 (extension) and 15 deg (flexion) wrist angle. 194 NORMALIZED FLEX/EXT SHEAR PINCH GRIP Subjacta UL ft OF 20 19 - ia - 17 19 5 19 f 5 14 J E 12 - I 11 - 10 - I 9 “ i L i £ «1 m 7 H 6 i 61 *i 3i 2 ”
A) o4- ! ]------6 Nominal Torque (N -m ) U L-30 UL—45 O OF—30 OF—45
NORMALIZED FLEX/EXT SHEAR POWER GRIP Subjacta UL ft OF
EI I
B)
Nominal Tarquo (N -m ) UL—30 UL—45 « O F -30 OF—45
Figure 51. Mean normalized flexion/extension shear on the wrist joint in pinch (a) and power grip (b) conditions. Shear (N) is normalized to average flexion torque (N-m) between -45 (extension) and 15 deg (flexion) wrist angle. 195
NORMALIZED RAD/ULN SHEAR — PINCH GRIP Subject* ML ft OF 10 > - a -
7 - i % •i Ei I 5 - j 4 L 3 - 2 -I 1 -
A) 0 - t - 1------1------T- 3 5 7 Nominal Torque (N -m ) ML—30 ML—48 0 OF—30 A OF—48
NORMALIZED RAD/ULN SHEAR — POWER GRIP Subjacta ML * OF
? I • EI I
B)
Nominal Torque (N -m ) D ML—30 ML-48 0 OF—30 OF—48
Figure 52. Mean normalized radial/ulnar shear on the wrist joint in pinch (a) and power grip (b) conditions. Shear (N) is normalized to average flexion torque (N-m) between -45 (extension) and 15 deg (flexion) wrist angle. 196 NORMALIZED FRICTIONAL WORK - PINCH GRIP Nominal Torque ■■ 4 N -m 0.001 - r -
0.0 008 -
0.0 008 -
0.0007 -r E I I 0.0 000 - 10.1% EI 0.0 009 - L_ wz 0.0 004 - 1 04)003 - r * 0.0002 - 20.1%
0.0001 - A)
Numbor of Tendone U L -30 ML—40 O 0 F -3 0 OF—40
NORMALIZED FRICTIONAL WORK - PINCH GRIP Nominal Torque - 8 N -m 0.001
? > 0.0008
E 0.0007 I I 0.0008 - EI 0.0 000 - Z w 1 0.0003 - i c 04)002 -|
0.0001 - B) 2 4 6 Numbor of Tandem ML—30 ML—40 O OF—30 OF—40
Figure 53. Mean normalized frictional work between wrist tendons and their sheaths in 4 N-m (a) and 8 N-m (b) pinch grip exertions. Three tendons are FCR, FDS, and FDP; the fourth tendon is FCU; the remaining tendons are ECR, EDC, and ECU. 197
NORMALIZED FRICTIONAL WORK POWER GRIP Nominal Torque - 4 N-m 0.0011
0.001 -
0.0000 - 11.3% 0.0000 - E I 0.0007 -
! 0.0000 - I Ei ! h 0.0005 -II I I 0.0004 - j 0.0003 H i 0.0002 -I I 0.0001 A) 0
Number of Tendone ML—30 ML—46 0 OF—30 OF—46
NORMALIZED FRICTIONAL WORK - POWER GRIP Nominal Torque - 6 N-m 0.0011
f 0.0000 J
0.0000 1
0.0000
I 0.0004 J 17.6% 0.0003
0.0002 H B)
Number of ML—30 OF—30 OF—46
Figure 54. Mean normalized frictional work between wrist tendons and their sheaths in 4 N-m (a) and 8 N-m (b) power grip exertions. Three tendons are FCR, FDS, and FDP; the fourth tendon is FCU; the remaining tendons are ECR, EDC, and ECU. 198
condensed into graphic form in figures 49 through 54 in order to convey the information more readily and display patterns. In figures 49, 50, 51, 52, and 54, the respective values for subject ML's eight N-m power grip conditions are not shown because the r-square for these trials did not exceed the threshold of 0.250. Gain. The final muscle gains are shown in figure 49.
The gain is the relative amount of force generated by a muscle that is necessary to exert a desired external torque. A muscle's gain is relative to its cross-sectional area (PCSA). As indicated in figure 37, the gain was increased in one N/cmA2 increments until the the predicted external work exceeded the measured external work. At each level throughout the iterative process, the gains for all muscles were equal. All the mean gains in figure 49 ranged from 20 to 60 N/cmA2. The muscular gains required to exert eight N-m of external torque were greater than their four N-m counterparts. With respect to pinch grip conditions, the power grip gains were about 10 to 20 N/cm*2 greater. Compression. Compression on the wrist joint is the resultant reaction force (Wz) required to resist tendon and
external forces, as illustrated in figure 38. Figure 50 displays normalized compression on the wrist in pinch and power grip conditions. Compression was normalized to N of 199 compression per N-m of external torque in order to account for subjects over and undershooting the targeted nominal torque. Normalized compression, which ranged from 50 to 70 N/N-m of torque, was greater in the power grip conditions by about five to ten N/N-m of torque. Normalized compression was approximately equal for four and eight N-m exertions. Flexion/Extension Shear. F/E shear is the resultant reaction force (Wy) required to counteract vertical components of tendon forces and external loads, as illustrated in figure 38. As indicated in figure 51, normalized F/E shear forces ranged from nine to 17 N of shear per N-m of external torque. Similar to compression, F/E shear forces in the power grip conditions were about five N per N-m torque greater than in pinch trials. Radial/Ulnar Shear. R/U shear is the resultant reaction force (wx) required to resist those horizontal components of tendon forces and external loads that are perpendicular to the forearm axis (refer to figure 38). Figure 52 shows normalized R/U shear forces ranging from four to eight N/N-m torque. R/U shear in the power grip was greater than pinch grip for one subject. Normalized Frictional Work. The frictional work between the tendons and their supporting structures was normalized to external work generated between -45 and 15 deg of wrist angle. Frictional work was normalized in order to 200 account for subjects over and undershooting the targeted nominal torque. Frictional work was computed for three sets of tendons: 1. Three tendons: FCR,FDS,FDP — these are the tendons that pass through the carpal tunnel. 2. Four tendons: FCR,FDS,FDP,FCU — these are the major flexors of the wrist and fingers. 3. Seven tendons: FCR,FDS,FDP,FCU,ECR,EDC,ECU — these are the major flexors and extensors of the wrist and fingers. Frictional work for pinch and power trials are displayed in figures 53 and 54, respectively. Normalized frictional work ranged from 0.0002 to 0.0005 N-m of FW per N-m of external work for the tendons passing through the carpal tunnel. For the group of flexor tendons, normalized frictional work ranged from approximately 0.0008 to 0.0009. The additional frictional work from the extensor tendons was minimal, if not neglible, as illustrated by the slight increase in frictional work between four and seven tendons. Of primary interest in figures 53 and 54 is whether frictional work in the 45 deg/sec trials is greater than their 30 deg/sec counterparts. Considering the limited number of trials and small sample size of subjects in this pilot study, only those differences greater than 10% were reported. For groups of four and seven tendons, there were no differences in frictional work greater than 10% between the 30 and 45 deg/sec. However, there were differences in frictional work for the carpal tunnel tendons. In the four 201 N-m pinch grip conditions, there were 10.1% and 20.1% greater frictional work in the 45 deg/sec trials than their 30 deg/sec counterparts (refer to figure 53). However, in power grip exertions, the frictional work was greater in the 30 deg/sec trials than the 45 deg/sec conditions (11.3% and 17.5%) (refer to figures 54a and 54b).
Discussion Maximum Pinch and Power Grip Force. The maximum pinch and power grip forces that are displayed in figures 47 and 48 are consistent with reported values in the literature. Maximum power grip forces in the range of 300 to 400 N at a neutral wrist angle agree with the maximum grip strength of males measured by Bechtol (1954) and Garrett (1968) (refer to figure 47) . Maximum pinch forces in the range of 100 to 200 N at a neutral wrist angle are similar to pinch strength of males recorded by Kellor, Frost, Silberberg, Iversen, and Cummings (1971) (refer to figure 47). As illustrated in figure 47, the general shape of the pinch and power grip forces as a function of wrist angle reflect the length-strength relationship of muscles based on active (contractile) and passive (elastic) components. The maximum force was achieved at either -20 deg extension or a neutral angle, with force decrements occuring at extended and flexed angles beyond this range of peak strength. Both 202
« subjects showed more force decrement with a power grip at extreme flexion wrist angles than extreme extension angles, which is compatible with the literature. Volz et al. (1980) found that maximum power grip force was attained at -20 deg extension, and maximal strength at -60 deg extension was only slightly less than at -20 deg extension. However, there was a marked reduction in force at 40 deg flexion. Volz et al. (1980) attributed this pattern of force decrements to active and passive forces of the extrinsic extensor muscles. These researchers found coactivation of the extensors when the wrist was exerting a power grip in a flexed posture of 40 deg. The increased active force of the extensor muscles from coactivation along with the extensors' elastic passive force (due to the flexing of the fingers in a power grip) produced a significant extensor force that counteracted the flexor muscles' capability to exert a strong power grip. Maximal Flexion Torcrue. Maximal flexion torque for both subjects agree well with reported torques in the literature (refer to figure 48). Based on a small sample of six males, Van Swearingen (1981) reported an average maximal flexion torque of 22.3 N-m. As displayed in figure 48, the shape of maximal flexion torques as a function of wrist angle is similar to maximal pinch and power grip force. Generally, maximal flexion torque was generated at a neutral wrist angle, and the torque decrement at flexed wrist angles was more severe than at extended wrist angles. However, what is noteworthy about figure 48 is that maximal pinch and power grip torques were about equal within each subject. Unlike maximal pinch and power grip forces, there was no decrement in flexor torque with a pinch posture as compared with a power grip. The reason for the parity in torque with a pinch and power grip is that the muscles that are the primary wrist flexors are the FCR and FCU, which attach to the base of metacarpals II and III and the pisiform bone, respectively (Basmajian, 1982). The FCR's and FCU's length-strength relationship and force capability are not dependent on type of grip; therefore, they would be expected to exert approximately the same flexor torque, regardless of grip posture. Angular Interval of Interest. A -45 to 15 deg interval was selected for analysis because it enclosed F/E range of motion found in industrial jobs on the factory floor and also the model predicted torque relatively well within this range. Outside of this range, the model consistently either underestimated or overestimated torque. The mechanism for bias of torque prediction is probably passive forces in the forearm musculature. A muscle can exert force either by contraction (active) or by stretch (passive), much like a 204 spring. EMG can monitor active force production in a muscle, but not passive force. Underestimation of torque at extreme extension angles was probably due to the flexor muscles exerting a flexor torque by being stretched. This passive contribution to torque was not measured by EMG. Therefore, EMG data, which drive this model, would underestimate the total flexor torque. The model consistently overestimated torque beyond 15 deg flexion. This overestimation was probably due to passive forces, from the stretching of the extensor musculature, exerting an antagonistic torque. The flexor muscles would have to exert more active force to offset antagonistic passive torque from the stretching of the extensors. This additional flexor force, which was monitored by EMG, was input into the model; the passive force from the extensors, which was not monitored, did not enter the model. Consequently, the model overestimated torque beyond 15 deg flexion. The reason prediction of torque went awry closer to neutral from the flexor side (15 deg) and farther from neutral from the extensor side (-45 deg) is probably because of finger geometry. The finger phalanges were partially or fully flexed in pinch and power grip orientations, respectively. Flexing the finger phalanges independently of 205 wrist angle will lengthen the the EDC muscle and increase its passive force. Orienting the fingers in a pinch or power grip at 15 deg wrist flexion angle would increase the antagonistic passive torque, thereby contributing to overestimation of torque. Finger flexion also explains why torque bias did not occur until -45 deg extension. Finger flexion shortens the length of the flexor muscles when the wrist is extended, thereby reducing the flexor muscles' passive force. Match Between Predicted and Measured Torque. As indicated in table 25, predicted torque matched measured torque in pinch grip trials much better than power grip conditions. In fact, five out of ML's 12 power grip trials did not meet the 0.250 threshold for acceptance. The low squared correlation statistics from the power grip trials may have been due to less than optimal partitioning of power grip force. EMG data from the FDS and FDP were partitioned into two components, those producing grip force and torque generation. Grip force was estimated first and the remainder of the EMG signal was designated for torque generation. Grip force was estimated from a ratio of tendon force to external force based on work from Chao et al. (1976). Based on a biomechanical model of the fingers, these researchers estimated tendon forces in the fingers in different configurations, including a pinch grip and a 206 medial grasp, which was used to resemble the power grip in this study. (Chao et al. (1976) did not model a classic power grip.) The pinch configuration in this study matched Chao's et al. (1976) pinch geometry well, but the medial grasp and power grip were not as closely matched. The difference in force ratios between a medial grasp and a classic power grip may have been enough to cause the power grip's lower squared correlation values. Another reason for the power grip's lower squared correlation values could be due to complexity of grip geometry. In a power grip, the FDS and FDP wrap around the handle, and contraction of the FDS and FDP will generate high grip force but will produce minimal, if not any, flexor torque, in a pinch grip, the FDS and FDP can produce substantial flexor torque because the fingers serve as a direct mechanical linkage from the hand to the surface where torque is measured. The partially flexed geometry of the fingers in a pinch grip allow for the distal phalanges to exert pinch force and flexor torque. Using external torque as a criterion to guage this biomechanical model, the pinch grip appears to be mechanically more straightforward and an easier grip to model than the power grip. Gain. As indicated in figures 49a and b, the final gains ranged from 20 to 60 N/cmA2 of muscle area. These values are consistent with the literature in that reported 207 values of maximal force per unit area range from 30 to 100 N/cmA2 (Alexander and Vernon, 1975; Farfan, 1973; Haxton, 1944; Ikai and Fukunaga, 1968; Maughan, 1983; Morris, Lucas, and Bresler, 1961; Schultz, Andersson, Ortengren, Haderspeck, and Nachemson, 1982; Weis-Fogh and Alexander, 1977). Although the reported force capacities in the literature were derived from maximal exertions and the force capacities in this pilot study were calculated for constant torque conditions, there is relevance between the two sets of values. In this pilot study, the higher gains approaching 60 N/cmA2 were generated in the eight N-m conditions. Exertions of eight N-m for both subjects were strenuous, and for subject ML, eight N-m of torque was maximal or close to maximal within the interval analyzed (-45 to 15 deg) (refer to figure 48). Therefore, comparison of force capacities from this study and the literature are germaine, and the values reported in the literature and calculated in this study appear to agree well. As expected, the gains required to exert eight N-m of torque were greater than four N-m of torque. In order to exert eight N-m of external torque, the extrinsic flexor muscles in the forearm have to exert more force per unit area than in the four N-m torque conditions. The gains in the power grip conditions were greater than in pinch grip trials. This difference can be explained by functional anatomy and mechanical linkage. The primary function of the FDS and FDP is to flex the proximal and distal interphalangeal joints, respectively (Basmajian, 1982) . In a pinch posture, application of a flexion force from the finger phalanges will produce a flexion torque because of the direct mechanical linkage from hand to pinch surface. However, in a power grip posture, forces from the finger phalanges primarily squeeze the handle and secondarily exert a flexion torque. Therefore, in order to exert the same external flexion torque, a person with a power grip has to rely almost solely on the FCR and FCU (primary wrist flexors) , whereas in a pinch grip, he can generate flexor torque with the finger flexors (FDS, FDP) along with the FCR and FCU. Compression on Wrist Joint. The absolute compression forces on the wrist joint for the eight N-m efforts reached a peak of approximately 500 N (refer to tables 28 and 32). 500 N appears to be a feasible force that the wrist structure can resist considering the joint forces on the elbow, which is a much larger joint than the wrist, peaked at approximately 2500 N during maximal isometric flexion exertions (Amis, Dowson, and Wright, 1980). Even though the wrist is composed of several small bones, it is capable of withstanding substantial compressive forces because of its sculpted bone surfaces and ligamental structures. The 209 opposing surfaces of the multi-faceted carpal bones are precisely contoured to match their neighbors and several intra- and inter-capsular ligaments hold the bones taut (Volz et al., 1980). Compression normalized to external torque did not reveal a velocity or torque level effect, as shown in figure 50. The relatively constant normalized compression of 50 to 60 N per N-m of external torque indicates that the effect of dynamic loading on the wrist joint was about the same for both the 30 and 45 deg/sec velocity conditions and proportional for the two nominal torque levels. However, there appears to be a grip orientation effect in that normalized compression during power grip exertions is greater than their pinch grip counterparts. This difference in normalized compression due to grip orientations is probably due to the relationship between finger geometry and functional anatomy. As stated earlier, the function of the FDS and FDP is to flex the proximal and interphalangeal joints, respectively (Basmajian, 1982). in power grips, the FDS and FDP can contribute minimally, at best, to flexor torque, because contraction of the FDS and FDP primarily squeezes the handle, generating grip force and minimal flexion torque. Due to finger extension in pinch grips, contraction of the FDS and FDP can theoretically contribute to pinch force and a significant amount of flexor 210 torque. The main component of compression on the wrist is due to internal forces (i.e. tendon forces) because the tendons have small moment arms compared to the location of the external load (i.e. handle). Therefore, in power grips, the wrist joint is compressed with essentially non-torque producing forces from the FDS and FDP. However, in pinch grips the FDS and FDP would contribute more to torque production than in power grips, thereby lessening the compressive loads on the wrist and reducing the overall gain (N/cm^2) of all the flexor muscles. Flexion/Extension Shear on Wrist Joint. Similar to compressive loading, normalized F/E shear revealed no velocity or torque level effects. As illustrated in figure 51, normalized F/E shear for pinch grip trials was approximately 10 N / N-m of torque. In contrast, normalized F/E shear in power grip trials was approximately 50% greater than pinch exertions. Again, this differential is probably due to functional anatomy of the wrist flexors. In power grips, the main contributors to torque production are FCR and FCU. Of all the flexor muscles, FCR and FCU have the longest moment arms (1.75 and 1.90 cm — refer to table 20), which increase the gamma angles between tendons and forearm axis (refer to figure 39). The gamma angle directly affects the magnitude of the F/E component of the force vector, as shown in equation (41). An increase in gamma increases the 211 F/E shear component. Since power grip exertions rely predominantly on the two muscles (FCR and FCU) with the greatest moment arms and pinch grip conditions share torque production with the FDS and FDP (1.50 and 1.25 cm moment arms), then it follows that F/E shear in power grips would be greater than in pinch grips. The F/E shear force on the joint could possibly have been absorbed by three mechanisms in this experiment: 1) tightly-webbed network of intra- and inter-capsular ligaments in the wrist 2) antagonistic extensor forces 3) velcro strap in the fixture that held the forearm in place. Point 2) is not supported by review of graphical plots of raw EMG data that displayed little cocontraction of the extensors. Load cells on the velcro strap would be required to investigate point 3). Point 1) is infeasible to measure invivo now because of its invasive nature. Further research is needed to tease out how which mechanisms counteract the shear forces caused by the flexor forces. Radial/Ulnar Shear on Wrist Joint. Similar to compression and F/E shear, there were no velocity or torque level effects for R/U shear. Subject ML's R/U shear in the power grip was greater than in pinch grip, but subject GF showed no grip orientation effect. Subject ML's greater R/U shear in power grip conditions could have been due to greater reliance on the FCR muscle, which has the longest 212 moment arm and greatest beta angle with respect to the medial epicondyle (refer to figure 39). Frictional Work. Frictional work between the tendons and their sheaths or tendons and the carpal bones and ligaments was partitioned into three sets of tendons: the tendons passing through the carpal tunnel (FCR, FDS, and FDP) , the flexor tendons (FCR, FDS, FDP, and FCU), and all the flexor and extensor tendons. The tendons passing through the carpal tunnel are illustrated in a cross- sectional view of the wrist in figure 55. These are the tendons that if inflamed could compress the median nerve and cause CTS. Inflammation of the FDS or FDP's sheaths could result in tenosynovitis, and inflammation of the FCR, FCU, or extensors could result in tendinitis. The experimental hypothesis in the modeling phase of this research was that frictional work in the 45 deg/sec trials would be greater than in the 30 deg/sec trials. Frictional work between the tendons and their sheaths or between tendons and carpal bones and ligaments has been hypothesized as a major risk factor of CTDs (Tanaka and McGlothlin, 1989). Of several mechanical parameters, Moore (1988) and Moore and Wells (1989) concluded that frictional work discriminated the best between low and high levels of grip force and repetition. The basis for this hypothesis resides in the three reported occupational risk factors of 213
MEDIAN A. a N. FLEXOR OKJITORUM SUPERFICIAUS . FLEXOR RETINACULUM
PISIFORM ...... FLEXOR CARPI RADIALIS
-FLEXOR POLLICIS LONGUS
FLEXOR OIGITORUM SCAPHOID PROFUNDUS
CAPITATE TRIQUETRAL ’ LUNATE
Figure 55. Contents of the carpal tunnel. Adapted from Johnson (1980). 214 CTDs: repetition, grip force, and wrist angle. These three risk factors are all required to compute frictional work between the tendons and their supporting anatomical structures. The advantage of frictional work is that it reduces a capacious multivariate vector into a succinct univariate measure. Overall, the frictional work results supported the experimental hypothesis in pinch conditions but not power grip trials. As illustrated in figures 53 and 54, frictional work in the 45 deg/sec trials was greater than their 30 deg/sec counterparts in four N-m torque pinch conditions, but the results were opposite in power grip conditions. In pinch grip trials, the difference in frictional work in four N-m torque levels and the absence of any difference in eight N-m torque trials could have been due to rate and recruitment coding of muscle fibers from the central nervous system (CNS). The four N-m torque level is more representative of the flexion torques estimated for actual industrial jobs. These torque values, which range from approximately 1.5 to 3 N-m, were estimated based on hand and object weight. Since exertions of four N-m of torque are easily generated and not maximal exertions, the CNS might have selectively recruited only those muscles necessary for the exertion and rate coded them as needed. If this CNS 215 strategy actually occured, then the frictional work results for pinch grips suggest that the flexor and extensor muscles were exerting slightly more force in the 45 deg/sec exertions than 30 deg/sec trials. In contrast to four N-m torque trials, eight N-m torque exertions were strenuous, if not maximal at some wrist angles, and the CNS might have sent out a preprogrammed showering of neuronal signals to recruit all muscles and fire them at maximal frequency (Mustard and Lee, 1987). Preprogrammed motor control messages are examples of open- loop strategies within the CNS (Stark, 1968). If this CNS strategy actually occurred, then no difference in flexor and extensor tendon force would be expected between the two velocities because all muscle fibers would be working at maximal capacity. The unexpected greater frictional work in the 30 deg/sec trials with power grips might have been due to the poor match between predicted and measured torque, chance due to small sample size, measuring the wrong part of the muscle with fine wire electrodes, or not monitoring the muscles that might have generated more frictional work at 45 deg/sec. First, since computation of frictional force is very sensitive to wrist angle (refer to equations (44) and
(45) and figure 43) , then any overestiraation of tendon force at deviated wrist angles could exaggerate the calculation of 216 frictional work. Within the -45 to 15 deg interval, if the predicted torque were overestimated at deviated angles but underestimated at near neutral angles, then the frictional work would be inflated. This scenario might have been the the cause of greater frictional work in the 30 deg/sec conditions. Second, the unexpected frictional results might have been due to chance, and collection of more data may show a steady state reversal of results. Third, the fine wire electrodes might have been inserted in a part of the muscle that was not sensitive to changes in contractile force. For example, if the electrodes were inserted into fibers near the ends of the contractile range of muscle fibers (i.e. near the tendons), then the EMG signal might not have recorded the electrical activity of the more active fibers contracting near the muscle belly. The fourth explanation for the power grip's frictional work results is that the muscles monitored in this study were not the muscles that might have generated more frictional work at 45/sec than 30 deg/sec. The palmaris longus (PL), flexor pollicis longus (FPL), and abductur pollicis longus (APL), which were not monitored in this study, pass through the wrist joint and are secondary wrist flexors (Basmajian, 1982; Soderberg, 1986). The FPL and 217 APL, whose primary functions are to flex and abduct the thumb, are instrumental in exerting and stabilizing a power grip. Since a power grip depends on the major thumb (pollicis) muscles and these muscles also exert some flexor torque, then these muscles might be the muscles of interest with regards to frictional work. Minimal Cocontraction of Antagonists. Under constant submaximal torque exertions at varying constant velocities, the primary mechanism that increases tendon forces, and in turn increases frictional work, is cocontraction of antagonistic muscles. In order to maintain the targeted external torque, the agonist muscles have to exert additional force to overcome antagonistic force. These greater force levels increase loading on the joint and friction between the tendons and their adjacent structures. With respect to the trunk, Marras and Sommerich (1991b) found substantial cocontraction of the anterior muscles during trunk extensions as velocity increased. This cocontraction of the anterior muscles, which increased compression and shear on the spine, stabilized the trunk as it extended from almost full flexion to an upright position. Cocontraction of the trunk muscles is critical for a person to maintain his balance. In this study, there was minimal, and often no cocontraction of the antagonistic extensor muscles during Flex/Ext Wrist Angle (dag) -40 of ballistic oscillations. ballistic of Figure 56. Trace of wrist angle during a rapid succession succession rapid a during angle wrist of Trace 56. Figure AIU FE/X OSCILLATIONS FLEX/EXT MAXIMUM TSOI06 Loft Hand ie (sec) Time " T 2 A
r ~ 3 218 wrist flexions. The lack of cocontraction is probably due to the fact that the wrist is light in weight, is intended to move swiftly, and does not jeopardize the postural stability of the body, as does the trunk. The light weight and low moment of inertia of the hand (approximately 5 N and 0.0012 kgA2-m for subjects in this study) allow the hand to oscillate ballistically in rapid successions. Figure 56 illustrates the wrist angle of a subject oscillating his hand as quickly as possible. A person can oscillate his hand with large and small angular excursions up to frequencies of approximately six and 12 Hz, respectively. Unlike the trunk, swift hand movements during brief bouts are not injurious. Furthermore, rapid hand movements will not destabilize a person's balance. The literature corroborates the observed lack of cocontraction found in this study. The body appears to have a built-in mechanism, reciprocal inhibition, to promote swift hand movements with minimal cocontraction. In a study of the distribution of muscle activity about the wrist, Backdahl and Carlsoo (1961) found reciprocal inhibition operating in both wrist flexion and extension movements. In wrist extensions, only a few potentials could be elicited from the flexor muscles. These researchers said the limitation of extension and stabilization of the wrist are performed by bones and ligaments. In wrist flexions, ECR 220 and EDC were silent but the ECU did show some activity. Backdahl and Carlsoo (1961) concluded the ECU serves to stabilize the ulnar side of the wrist since it has a less developed ligamentous and skeletal structure than the radial side. In a study of rapid sinusoidal wrist movements, Stark (1968) found that the stretch reflex of the antagonistic muscles was inhibited. This phenomenon appears to aid swift oscillations of the hand. As cited in this study, all of the cocontraction references with respect to the wrist joint discussed rapid movements with low or no application of external force or torque. However, cocontraction will probably occur in wrist flexion exertions greater than eight N-m. Eight N-m of torque is close, if not greater, than the maximum torque that can be generated at extreme flexion (60 deg), and qualitative review of EMG traces showed much cocontraction near and at a wrist angle of 60 deg. Although eight N-ra is close to the maximum torque at extreme flexion angles, it is submaximal near neutral wrist angles (refer to figure 48) . At wrist angles near neutral, torque exertions greater than eight N-m may produce cocontraction of the antagonistic muscles. Moreover, for strong male subjects, it may require torque exertions substantially greater than eight N-m to elicit coactivity patterns because eight N-m may be a small percentage of maximum torque for some male subjects. 221 The lack of cocontraction of antagonistic muscles shows promise for modeling the wrist joint as a statically determinate model or with optimization. One of the primary advantages of a data-driven model, as exemplified by the model in this study, is that it can account for numerous variables and produce actual force values for all muscles of interest. In modeling a joint, cocontraction of antagonistic muscles adds variables that produces or exacerbates static indeterminacy (static indeterminacy occurs when the total number of unknown forces exceeds the number of equations — six equations for equilibrium). Without cocontraction, the number of unknown forces is reduced substantially, resulting in either a statically determinate model or an optimization model. In this study, the paucity of empirical cocontraction in wrist flexion provides an opportunity to transform the model from a data- driven model to one that can estimate tendon forces with static determinacy or with an optimization model with only one degree of freedom. The advantage of this transformation in modeling is that it obviates measuring muscle activity with fine wire EMG, which is time-consuming and cumbersome. The overall observed lack of cocontraction in the constant velocity conditions suggest that any differences, if they exist, in frictional work between low and high risk velocity levels will be slight. However, there may be substantial differences in frictional work between low and high risk F/E acceleration levels. In the industrial quantification study, F/E acceleration was the strongest discriminator between CTD risk levels, and the mean high risk F/E acceleration was substantially greater than the mean low risk F/E acceleration (824 vs. 494 deg/secA2; refer to table 7)• Actual wrist movements in industry are not controlled constant velocity exertions, but are staccatic movements in which the hand is accelerating and decelerating. Accelerative movements were not monitored in this study because the relationship between EMG signals and muscle force under constant acceleration is not known at this time. Therefore, estimating force of muscle fibers shortening at constant rates of acceleration is currently
infeasible. Biomechanical theory supports F/E acceleration as a risk factor. As shown in figure 7, tendon force is required to accelerate the center of gravity of the hand, and additional tendon force is necessary to rotate the dispersion of mass particles in the hand (moment of inertia). As indicated in figure 7, the required tendon force is linearly related to angular acceleration. Acceleration of the wrist at the mean high risk level (824 deg/secA2) would require greater tendon forces than at the 223 low risk level (494 deg/secA2), and in turn, would generate greater frictional work at the high risk level between the tendons and their supporting structures. In addition to greater frictional work, the resultant reaction force (Pr in figure 8) on the tendons from the wrist's supporting structures (sheaths, bones, and ligaments) increases as a function of acceleration (refer to figure 9). This increased resultant reaction could cause microtrauma to the tendon or its sheath, thereby contributing to tendinitis, tenosynovitis, or CTS. In order to test whether there is increased frictional work at high risk F/E accelerations, the force of the flexor and extensor muscles would have to be measured. Presently, it is not feasible to estimate muscle force from EMG signals during controlled acceleration exertions. The relationship between controlled acceleration of muscle fibers and the resulting EMG signal is not stable or reliable enough to predict muscle force. However, spectral characteristics of the EMG signal has potential for estimating muscle force during acceleration. In a study of spectral EMG during plantar flexion of the ankle, Rajulu (1990) successfully decomposed the EMG signal into components of torque, velocity, and position during constant velocity trials. Decomposition of the EMG signal from a muscle shortening 224 under constant acceleration might enable quantification of muscle force in the future. CHAPTER VI IMPACT OF THIS RESEARCH: PRESENT AND FUTURE
CTDs: Workplace Injuries of the 1990s CTDs are disorders which primarily affect the soft tissues of the musculoskeletal system, such as muscles, tendons, and nerves, and these disorders are associated with "repeated or sustained exertions in awkward or static postures" (Putz-Anderson, 1988, p. 113). The incidence of CTDs of the hand/wrist grew at an alarming rate in the 1980s, to the point where it reached almost epidemic proportions in some industries (Armstrong, 1983). As shown in figure 1, the percentage of occupational illness due to repeated trauma increased from approximately less than 20% in 1981 to over 50% today. In a recently published article, Franklin, Haug, Heyer, Checkoway, and Peck (1991) evaluated 1984-1988 workers' compensation claims of CTS from the state of Washington and found an industry-wide incidence rate of 1.74 claims of CTS per 1000 full-time employees (FTEs). The incidence rate was dependent on occupation, as exemplified by incidence rates
225 226 of 23.9 and 18.2 claims per 1000 FTEs for workers in meat/poultry and fish canning industries, respectively. The link between occupation and CTS is further supported by reports of female/male gender ratio. The ratio of females to males developing CTS from occupational causes was 1.2:1, whereas the non-occupational ratio was 3:1. These ratios appear to "support the concept that workplace exposures may be responsible for a substantial proportion of physician- reported CTS cases" (Franklin et al., 1991, p. 744). The general transformation of our manufacturing economy from the post World War II era that involved heavy manual materials handling (MMH) to MMH of lighter goods and parts in the 1970s and 1980s brought about more repetitious assembly operations and lower task diversity. Often, these repetitious assembly operations involved primarily the upper extremities. Lower task diversity in hand-intensive jobs is likely to increase the risk factors of CTDs by increasing repetition ana static loading (Bammer, 1987). According to Bammer (1989), blue collar workers in light assembly industries are severely affected with CTDs. In many cases, the diminution of task diversity was driven by new technology. For example, the transformation from electric typewriters to computerized word processors eliminated the physical manipulation of the carriage. Despite the improvements in productivity, the diversity of 227 the typing task was diminished and led to more repetitious activity of the fingers and static postures of the arm and forearm. In this case, savings through increased productivity may be offset by increased costs of CTD injuries. Bammer (1987) reported that two Austrialian Public Service departments threw out their word processors and reintroduced electric typewriters. According to newspaper reports, CTDs dropped in one of these offices
(Bammer, 1987) . It appears that highly repetitious, hand-intensive industrial jobs will continue into the 1990s. If this trend continues without any ergonomic intervention, then rates of CTDs will probably rise, given the abundance of repetitious jobs and growing public awareness of CTDs. In addition, costs of occupational injuries will rise if the present trend goes unchecked. One of the missions of the ergonomics profession in the 1990s is to redesign the workplace to lower the risk of CTD injuries without retarding new technology or progress. Ergonomists can accomplish this mission in part by taking a proactive approach to new technology, rather than reactive. This proactive approach would require involvement in the research and development of new technology at its incipient stage. 228 A Research Approach to Prevent:ina CTDs The research approach utilized in this dissertation is and has been the rubric of ergonomic research employed by Dr. William Marras in the Biodynamics Laboratory. As illustrated in Figure 57, ergonomic research starts and terminates in the workplace, the raison d'etre for ergonomics. The first phase of research is industrial surveillance, as exemplified by the monitoring of wrist motion on the factory floor in the present study. At the end of this first phase, applications of quantitative surveillance data bifurcate. Empirical surveillance data can apply directly to the workplace in the form of wrist motion benchmarks, for example, but they also are essential input data to the laboratory experimentation and modeling phases. In these two phases, the biomechanical impact of industrial work motions and practices are evaluated by simulation in the laboratory and theoretical models. The biomechanical model of the wrist developed in the present study and the model's validation and laboratory implementation are examples of the latter two phases of this research rubric. Then, the modeling results are fed back into the workplace, where work motions and practices are modified in order to reduce biomechanical stress on anatomical structures and reduce the incidence of occupational injuries. The process illustrated Workplace
Benchm arks
Surveillance Lab Study Model (Risk - Motion) (Joint loading)
Figure 57. Ergonomic research approach used by Dr. William Marras in the Biodynamics Laboratory at The Ohio State University. 230 in Figure 57 is cyclical in that it may take a few or several full iterations to achieve the ultimate objective of ergonomics — prevention of occupational injuries.
Applications of This Research Industrial Surveillance. The relationship between CTD incidence rate and occupational factors, such as repetition and wrist posture, has been qualitatitively established by extensive discussions in the literature. Qualitative associations between incidence and risk factors are ineffectual tools for industry to use to prevent CTDs because they do not relate the magnitude of risk factors to CTD risk. In other words, qualitative guidelines do not answer the following questions that are often asked by industrial practitioners: "How much wrist deviation is bad?" or "How much repetition is injurious to workers?". The objective of the surveillance phase of this research was to quantify the dose-response relationship between wrist motion parameters and CTD risk and develop quantitative guidelines on the nature and amount of wrist motion that expose workers to CTDs. The orthogonal variable that appears to best discern between low and high levels of CTD risk is flexion/extension (F/E) acceleration. The mean and maximum difference values of F/E acceleration for both the low and high risk levels are illustrated in Figures 34 231 and 35. The mean acceleration values of high and low CTD risk groups can serve as preliminary, albeit crude, benchmarks to establish injurious and safe levels of wrist motion in industry. Industrial practitioners can use these data as quantitative guidelines to prevent CTDs in the workplace by evaluating existing work stations and testing alternative designs. With respect to wrist posture monitored in this study, the poor correlation between wrist angle and CTD risk does not mean wrist angle is not a risk factor of CTDs. The wrist motion results from this study only pertain to highly repetitious, hand-intensive dynamic jobs. In contrast, there are many repetitive jobs in industry that require static wrist postures, such as gripping a power tool, or manipulating parts with a deviated wrist posture. In these jobs, deviated wrist angle appears to be a risk factor of CTDs, as the literature suggests. Biomechanical Modeling of the Wrist. Like most epidemiological studies, the surveillance phase of this research had the inherent limitation of inferring cause and effect from statistical associations. One of the most important factors in inferring causal associations in epidemiological studies is the formation of a biological mechanism that explains the logic behind statistical associations (Armstrong and Silverstein, 1987). The model 232 of the wrist joint presented in this study attempted to explain bioxnechanically why wrist motions found in the industrial surveillance phase are injurious to workers. The second purpose of this biomechanical model was to enhance
our general understanding of the kinematics and kinetics of the wrist joint. This biomechanical model attempted to explain the association between F/E dynamic motion and CTD risk through calculation of frictional work between tendons and their sheaths or between tendons and carpal bones and ligaments. The experimental hypothesis was that frictional work between tendons and their supporting structures was greater at the m e a n high r i s k F/E velocity (45 deg/sec) than the mean low risk velocity (30 deg/sec). The results from this model were mixed. The data from pinch grip trials supported the hypothesis frictional work was greater in the 45 deg/sec trials than their 30 deg/sec counterparts in four N-m torque trials. However, in the power grip conditions, frictional work was greater in the 30 deg/sec trials for one subject at
each torque level, in addition to frictional work, there were no differences in compression and shear forces on the wrist joint between the low and high risk F/E velocities. The mixed results of frictional work could possibly be traced to statistical or biomechanical origins. Statistically^ the small sample size might not have been large enough to evoke steady state trends. Biomechanically, there may not be an actual difference in frictional work between the two constant velocities because of the lack of cocontraction of the antagonistic muscles during constant velocity exertions. However, there may be differences in frictional work between F/E movements that vary in acceleration. Industrial surveillance results elicited F/E acceleration as the strongest discriminator between low and high CTD risk levels. Biomechanical theory shows that frictional work from high risk F/E acceleration movements should be greater than movements at low risk F/E acceleration. Schoenmarklin and Marras (1990) showed through theoretical calculations based on fundamentals of dynamics that tendon forces increase linearly with respect to angular wrist acceleration. Increases in tendon force would generate more friction between the tendons and their adjacent structures, particularly at deviated wrist angles. If this frictional work surpasses an individual's threshold, then microtrauma to the tendons and sheaths could develop and expose the worker to CTDs. Despite the mixed results in supporting the experimental hypothesis of this study, this biomechanical model of the wrist does advance our knowledge of the wrist joint and our capability of quantifying mechanical loading. 234 This model represents the wrist in a more realistic manner than previous models in that it is 3-D and takes into account antagonistic forces. Because it is data-driven by EMG, this model can estimate the loading on the wrist joint as a function of time without resorting to optimization. In addition, many of all the components required for calculation of mechanical measures, such as frictional work, are either inputs to this model or computed by this model. In summary, this model would be of use to biomechanicians and clinicians in estimating the mechanical loads on the wrist joint during static and dynamic movements.
Future Research Industrial Surveillance. The research from this dissertation could be used as a springboard for the following future projects: 1. Monitor risk of CTDs as a continuous variable. In the present study, the dose consisted of continous measures of wrist motion but the response was partitioned into two discrete extremes of CTD risk. Prediction of CTD risk from dosage was limited because of the discrete nature of the response. Ultimately, industry needs CTD risk defined on a continuous scale (incidents per 200,000 hours of exposure) in order to precisely predict risk of CTDs and evaluate 235 jobs. The present study could easily be expanded to include jobs of varying risk levels of CTDs. 2. Monitor more subjects and more jobs. Since only eight manufacturing plants were monitored in the present study, the quantitative wrist motion benchmarks are not generalizable to all industries. In order to make the quantitative prediction of CTD risk more powerful and generalizable, more subjects in more industries will have to be monitored in jobs that vary from low to high incidence rates, inclusive. More subjects are needed to increase predictive power. In addition, more jobs and industries are needed to verify whether the wrist motion benchmarks found in the present study are generalizable to other industries. Considering the established and proven setup of hardware, software, and experimental protocol, the present study could easily be expanded to include more subjects and jobs in industries that were not already monitored. 3. Analyze motion, data as coupled data. The wrist motion data from the present and future studies need to be analyzed as coupled data. All the motion data in the present study were analyzed orthogonally, and orthogonal analysis suggests F/E acceleration is the best predictor of CTD risk. Orthogonal analysis does partially fill the vacuum of quantitative motion data by providing a basis for establishing preliminary motion benchmarks for industry. 236 However, F/E acceleration coupled with a specific loci of oblique or monoplanar wrist posture may actually be a more powerful predictor of CTD risk than F/E acceleration alone. Enlarging the analysis to include coupled sets of static and dynamic parameters would be quite feasible in a continuation of the present study. 4. Monitor grip force. In the present study, pinch or grip force that workers exerted in their jobs was estimated with a Smedley dynamometer. This protocol produced only a rough estimate of actual grip force exerted on the job. Occupational pinch or grip forces need to be measured more precisely in order to hone the quantification of mechanical stress on anatomical structures within the wrist. Measurement of occupational pinch or grip force is a prerequisite for calculating frictional work between the FDS and FDP tendons andT their adjacent structures. The FDS and FDP tendons, which are the primary force generators of pinch and power grips, travel through the carpal tunnel and are in proximity to the median nerve. Inflammation of these tendons or their common sheath due to friction with adjacent structures could easily compress the median nerve and contribute to CTS. Modeling. The biomechanical modeling phase of this dissertation highlighted the need for the following research projects: 237 1. Establish a stable and reliable relationship between EMG and muscle force under constant acceleration. The constant velocity trials in the present study elicited minimal, if any, difference in frictional work from the tendons and their supporting structures between low and high risk velocities. Results from this study's industrial surveillance and biomechanical theory and modeling suggest F/E acceleration may account for the hypothesized difference in frictional work between low and high risk jobs. However, monitoring muscle force from EMG under constant acceleration is infeasible currently. Research is needed into establishing a stable and reliable relationship between EMG and muscle force in accelerative movements in order to better evaluate the full magnitude of biomechanical stress on anatomical tissues. Decomposing EMG signals into their spectral components offers potential in estimating muscle force during dynamic movements (Rajulu, 1990). 2. Develop a technique that measures a muscle's passive force. In the present model of the wrist, analysis of wrist loading and frictional work was limited to a subinterval of wrist movement because the model underpredicted torque at extreme extension angles and overpredicted torque at moderate to extreme flexion angles. This bias in predicted torque was probably caused by passive forces generated by the stretching of agonist and antagonistic muscles. A 238 method or instrument that measures passive force of stretched muscles would broaden the span of wrist angles in which predicted and measured torque match well, sharpen the model's predictive power of torque, and hone the calculation of wrist loading and frictional work. 3. Monitor directly the frictional work between tendons and their supporting structures. The method of calculating frictional work in this study was indirect because it relied on EMG, which is not a measure of actual output (force) of muscular contractions (EMG measures the electrical input to muscular contractions). A method of monitoring frictional work directly would enable keen calculations of the effect of dynamic wrist movements on tendons and their surrounding structures. 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Silverstein, B.A., Fine, L.J., and Armstrong, T.J. (1987). Occupational factors and carpal tunnel syndrome. American Journal of Industrial Medicine. 11, 343-358. Smith, E.M., Sonstegard, D.A., and Anderson, W.H. (1977). Contribution of flexor tendons to the carpal tennel syndrome. Archives of Physical Medicine and Medical Rehabilitation. 58, 379-385. Soderberg, G.L. (1986). Kinesiology: Application to Pathological Motion. Williams and Wilkins. Stark, L. (1968). Neurological Control Systems: Studies in Bioengineering. Plenum Press. Tabachnick, B.G. and Fidell, L.S. (1989). Using Multivariate Statistics. Second Edition. Harper & Row, Publishers. Taleisnik, J. (1985). The Wrist. New York: Churchill Livingstone. Tanaka, S. and McGlothlin, J.D. (1989). A conceptual model to assess musculoskeletal stress of manual work for establishment of quantitative guidelines to prevent hand and wrist cumulative trauma disorders (CTDs). In Advances in Industrial Ergonomics and Safety I. A. Mital, editor, Taylor and Francis, 419-425. Tanaka, S., Seligman, P., Halperin, W., Thun, M., Timbrook, C.L., and Wasil, J. (1988). Use of workers' compensation claims data for surveillance of cumulative trauma disorders. Journal of Occupational Medicine. 30(6), 488-492. 249 Taylor, C.L. and Blaschke, A.C. (1951). A method for kinematic analysis of motions of the shoulder, arm, and hand complex. Annals of New York Academy of Sciences. 51, 1251-1265. Tichauer, E.R. (1966). Some aspects of stresses on the forearm and hand in industry. Journal of Occupational Medicine. 8, 67-71. Tichauer, E.R. (1978). The biomechanical basis of ergonomics: anatomy applied to the design of work stations. John Wiley and Sons. Tobey, S.W., Woolley, C.B., and Armstrong, T.J. (1985). Postural analysis system for the industrial environment. In Proceeding of IXth Annual Meeting of the American Society of Biomechanics (pp. 89-90). Ann Arbor, MI. Van Swearingen, J.M. (1981). Clinical objective measurement of static and dynamic wrist muscle strength. Master's thesis, The Ohio State University. Volz, R.G., Lieb, M., and Benjamin, J. (1980). Biomechanics of the wrist. Clinical Orthopaedics and Related Research. No. 149, 112-117. Webb Associates, (1978). Anthropometric Source Book: Volume I: Anthropometry for Designers. (NASA Reference Publication 1024). Wehrle, J. (1976). Chronic wrist injuries associated with repetitive hand motions in industry. Occupational Health and Safety Technical Report, Dept, of Industrial and Operations Engineering. University of Michigan, Ann Arbor, MI. Weis-Fogh, T. and Alexander, R.M. (1977). The sustained power output from striated muscle. _In Scale Effects in Animal Locomotion (edited by Pawley, T.J.). London: Academic Press, 511-525. Welch, R. (1972). The causes of tenosynovitis in industry. Industrial Medicine. 41. No. 10, 16-19. Winter, D.A. (1979). Biomechanics of Human Movement. Second Edition. John Wiley and Sons. 250 Youm, Y. , Ireland, D.C.R., Sprague, B.L., and Flatt, A.E. (1976). Moment arm analysis of the prime wrist movers. In Biomechanics V-A. P. Komi, editor. Youm, Y. and Flatt, A. (1980). Kinematics of the wrist. Clinical Orthopaedics and Related Research. No. 149, 21-32.
v*. APPENDIX A
251 THE OHIO STATE UNIVERSITY Protocol No. 89HO999 CONSENT TO INVESTIGATIONAL TREATMENT OR PROCEDURE I. . hereby authorize or direct W.S. Marras aaaoclatas or aaalstaats of har choosing, to parfora tba following craacaant or procadura (daacrlba In ganaral Caras) , strap wrist sonitor to each forearm and hand with either a plastic cuff or hypoallergenic tape, measure maximum wrist motion in all directions, measure wrist motion while subject is performing an occupational task, take body measurements, videotaping of experimental session.
upon . (ayaclf or naae of subject)
The experimental (research) portion of the treatment or procedure Is: measurinr’: wrist motion with wrist monitor
This la dona aa part of an Investigation entitled: Quantitative Measures of Hand/Wrist Motions Quantitative Measures of Wrist Motions Investigation of wrist motions contributing to carpal tunnel syndrome risk in 1. Purpose of the procedure or treatment: the design of retail scanners 1) to build a database of wrist motion measures 2) to correlate specific wrist motion parameters with risk level of cumulative trauma disorders, such as carnal tunnel svndrome. 3) to determine how the design of retail scanners and checkout stands affect wrist motion 2. Possible appropriate alternative procedures or treatment (not to participate In the study Is alwaya an option): Not to participate in study. 3. Discomforts and risks reaaonablv to be expected: I will be asked to move my wrist to the limits of comfort; therefore, I may experience minimal discomfort. Extremely small chance of skin irritation from tape. Only hypoallergenic tape will be used. Skin burn due to application of hot orthoplast. A. Possible benefits for subjects/society: 1) Establishment of a set of work practices guidelines for the prevention of cumulative trauma disorders in the workplace. 2) Diagnosis of wrist disorders and monitoring of rehabilitation. 3. Anticipated duration of subjects participation (including nuaber of visits): Maximum of three hours during each visit. Maximum of three visits per iU D j C C t * I hereby acknowledge chat W.S. Marras has provided information about the procedure described above, about my rlghta as a subject, and he/she answered all auestlons to my satisfaction. I understand that I may contact him/her at Phone No(614)292-6670 should I have additional questions. He/She has explained the rlska described above and I understand them; he/ahe has also offered to explain all possible risks or complications. Page 1 of 2 I understand that, where appropriate, the U.S. Food and Drug Administration may inspect records pertaining to this study. I understand further that records obtained during ay participation In this study chat may contain my name or other personal Identifiers may be made available to the sponsor of this study. Beyond this, I understand that my participation will remain confidential.
I understand that I am free to withdraw my consent and participation In this project at any time after notifying the project director without prejudicing future care. No guarantee has been given to me concerning this treatment or procedure.
In the unlikely event of injury resulting from participation In this study, I understand that lamediate medical treatment Is available at University Hospital of The Ohio State University. I also understand that the costs of such treatment will be at my expense and that financial compensation is not available. Questions about this should be directed to the Human Subjects Review Office at 292-9046.
I have read and fully understand the consent form. I sign It freely and voluntarily. A copy has been given to me.
AM Date: Time PM Signed (Subject^
Witness (es) If " (Person Authorized to Consent for Subject, Required If Required)
I certify that I have personally completed all blanks In this form and explained them to the subject or his/her representative before requesting the subject or his/her representative to sign It.
Signed (Signature of Project Director or his/her Authorized Representative)
Page 2 of 2
HS-028A (Rev. 4/89) SUBJECT INFORMATION SHEET
Name of company:______Industry:_____ [ Risk #: Location:______
Contact person:______Phone #:
Date: ______Subject ID: Subject Name:______Gender (M) / (F) Age:______Job Title:______Occupation:______Job Description:______
Experience a) present job b) in the company c) previous experience in repetitious work or manual material handling
Job Satisfaction: SUBJECT INFORMATION SHEET (cont) SUBJ ID
History of upper extremities injuries: ____
History of low back pain:
Any other symptoms of bodily injuries:
JOB CHARACTERISTICS Repetition rate(s):______
Weight(s) of lifts: ______
Force(s) of pinch/grasp: ______
Height of lifts: __ Motion descriptions: NAME OF COMPANY:______SUBJECT NAME:______SUBJECT ID NUMBER______DATE:______CHANNEL # 1 LEFT R/U CHANNEL # 2 LEFT F/E CHANNEL # 3 LEFT P/S CHANNEL # 4 RIGHT R/U CHANNEL # 5 RIGHT F/E CHANNEL # B RIGHT P/S ANGLE OF NEUTRAL CALIBRATION TABLE ______W.M. NEUTRAL CALIBRATION FILES before EXPERIMENT (1 SEC) FILENAME LEFT VOLTAGES RIGHT VOLTAGES R/U F/E P/S R/U F/E P/S
P/S CALIBRATION FILES before EXPERIMENT NEUTRAL LEFT HAND RIGHT HAND FILENAME P/S VOLT MAX OK? P/S VOLT MAX OK? ANGLE ANGLE
PRONATION FILENAME
SUPINATION FILENAME SUBJECT ID
FILENAME # MOMENT WORK DESCRIPTION OF TASK SEC ARM HEIGHT (INCLUDES WT OF OBJECTS & BEG/END BEG/END FORCE OF PINCH/GRASP) SUBJECT #: DATE:
GROSS DIMENSIONS (NA8A 1024 DIM. #'S)
STANDING POSITION WITH ARMS BANGING AT SIDES #957 WEIGHT...... #805 STATURE...... # 2 3 ACROMIAL (SHOULDER) HT...... # 32 ACROMION TO DACTYLION LENGTH...... (ACROMION TO TIP OF MIDDLE FINGER) #896 TRUNK DEPTH (BELOW BUST)......
ARM BENT AT 90 DEGREES #751 SHOULDER-ELBOW LENGTH...... (ACROMION TO OLECRANON) #3 24 ELBOW-WRIST LENGTH...... (OLECRANON TO LUNATE-CAPITATE GROOVE) #381 FOREARM-HAND LENGTH...... (OLECRANON TO TIP OF MIDDLE FINGER)
HAND DIMENSIONS (DIM. i'S FROM GARRETT, 1970) DOMINANT HAND (L) (R) (CIRCLE ONE) LEFT HAND RIGHT HAND # 1 HAND LENGTH...... #47 DIGIT 1 LENGTH...... (THUMBTIP TO CROTCH LEVEL) #49 DIGIT 3 LENGTH...... (MIDDLE FINGER) # 2 HAND BREADTH-METACARPAL LEVEL...... # 8 HAND THICKNESS-METACARPAL 3...... (MIDDLE FINGER) #37 WRIST BREADTH...... # WRIST THICKNESS...... # 7 WRIST CIRCUMFRENCE...... (FOREARM IN MIDPOSITION) # FOREARM CIRCUMFRENCE...... _
GRIP STRENGTH TRIAL #1 TRIAL #2 TRIAL #3 APPENDIX B
259 260 Tabulation of data in Figure 26 — partitioning of acceleration variance into two components, job and subject nested under job.
Percentage of Acceleration Variance Avg Accel Min Accel Max Accel Job Subj (Job) Job Subj (Job) Job Subj (Job)
Rad/Uln 43.1% 56.9% 44.1% 55.9% 31.0% 69.0% Flex/Ext 59.2% 40.8% 47.3% 52.7% 48.0% 52.0% Pron/Sup 40.9% 59.1% 32.6% 67.4% 33.2% 66.8% APPENDIX C 262 JENPUT.C file #include
/********************************************************/ /* HERE IS THE MAIN PROGRAM */ /********************************************************/ void main(void) { char replyl; do { clrscr(); printf("\n main program starting ... \n"); w_anthro() ; w_inkey(); /* w_max_file() ; */ w_emg_file(); w_prep_dat(); w_compute_torq(); w_compute_load() ; w_compute_fric () ; } while ( toupper( (replyl = w_end_loop() ) ) != 'Y' ); } y**********************************************************/ /* END OF MAIN PROGRAM */ 263
/ft*********************************************************/
/******************************** ** ******** •** ********** ****/ /* ASSIGN VALUES THAT ARE SPECIFIC TO SUBJECT */ /A*********************************************************/ float coef ,med_epic, lat_epic,elb_width, cutoff, step, Pi ,mu; float flex_rad, ext_rad, fdp_pn, fdp__pw, fds_pn, f ds_pw, edc_jpn, edc_pw; float LLIM_PW, ULIM_PW, LLIM_PN, ULIM_PN, LLIM_ANG, ULIM__ANG float vel_30,vel_45,gain_min; ~ float inean[2] [8 ] ,sigma[2 ] [8],mode[2 ] [8],alpha [2 ] [8]; float MOMARM_PINCH,MOMARM_POWER; int plot, muscles, ls_norm; w_anthro() { int ch,p; /* INDIVIDUAL SUBJECT'S ANTHROPOMETRIC DATA THESE MEASURES ARE USED IN ALMOST ALL FILES IN . PRJ */ coef = 1.21; med_epic = 0.317; lat_epic = 0.313; elb_width = 0.071; plot =1; cutoff = 0.80; PI = 3.14159; mu = 0.003 2 ; MOMARM_PINCH = 0.12 5; MOMARM_POWER = 0.070; vel_30~= 0.96; vel_45 = 0.94 ; LLIM_ANG = -60; ULIM_ANG = 60; LLIM_PW = -45.0; ULIM_PW = 15.0; LLIM_PN = -45.0; ULIM_PN = 15.0 ; muscles = 7; gain_min *= 0.005; step = 0.001; flex_rad = 0.0205; ext_rad = 0.0140; fdp_pn - 3.786; fdp_pw = 3.073 fds_pn = 1.756; fds_pw = 3.564 edc__pn = 0.816; edc_pw = o.o 264 /* LENGTH-STRENGTH PARAMETERS FOR MUSCLE */ /* mean and sigma for symmetric normal distribution */ /* mode and alpha for skewed extreme value distribution */ ls_norm =1; /* ls_norm = 1: use ext. value dist */ for (p=0; p<=l; p++) for (ch=l; c h < - 7 ; ch++) { if (p==0) { if ((ch==l) jj (ch==4)) { mean[p] [ch] = 15.0; /* FCR and FCU — PINCH */ sigma[p][ch] = 50.0; mode[p][ch] = 0.0; alpha[p][ch] = 0.0200; } if ((ch==5) jj (ch==7)) { mean[p][ch] - -15.0; /* ECR and ECU — PINCH */ sigma[p][ch] = 50.0; mode[p][ch] = 0.0; alpha[p][ch] = 0.0200; } } /* end of p==0 PINCH */ else { if ((ch—=1) j| (ch==4)) { mean[p] [ch] = 15.0; /* FCR and FCU — POWER */ sigma[p][ch] = 50.0; mode[p][ch] = 15.0; alpha[p][ch] = 0.0200; } if ((ch==5) Jj (ch==7)) { mean[p][chj = -15.0; /* ECR and ECU — POWER */ sigma[p][ch] = 50.0; mode[p][ch] = -15.0; alpha[p][ch] = 0.0200; } } /* end of p==l POWER */ if (p==0) { if ((ch=—2) jj (ch==3)) { mean[p] [ch] = 0.0; /* FDS and FDP — PINCH */ sigma[p][ch] = 60.0; mode[p][ch] = 0.0; alpha[p][ch] = 0.0150; ) 265 if (ch==6) { mean[p][ch] = 0.0; /* EDC “ PINCH */ sigma[p][ch] = 60.0; mode[p][ch] = 0.0; alpha[p][ch] = 0.0150; } } /* end of p==0 PINCH */ else { if ((ch==2) jj (ch==3)) { mean[p][ch] = 15.0; /* FDS and FDP — POWER */ sigma[p][ch] = 60.0; mode[p][ch] = 15.0; alpha[p][ch] = 0.0150; } if (ch==6) { mean[p][ch] -15.0; /* EDC — POWER */ sigma[p][ch] 60.0; mode[p][ch] -15.0; alpha[p][ch] 0.0150; } } /* end of p==l POWER */ > /* end of ch for loop */ /***** PRINT L-S PARAMETERS TO SCREEN ******/ /*** for (p=0; p<=l; p++) { for (ch-1; ch<=7; ch++) printf(" %0.Of %0.Of ",xnean[p] [ch] ,sigxna[p] [ch]) ; printf("\n"); } hold_screen(); * * * j return(0); }
/A*********************************************************/ /* INPUT INFILE INFORMATION FROM KEYBOARD (w_inkey) */ int grip, electrodes, control; int vel, torq, force; char input_fn[5], min_fn[7]; /* input_fn[4] means it reserves 5 memory spaces (0,1,2,3,4) for filename; space #4 is for NULL; min_fn[6] means it reserves 7 mem spaces (0,1,2,3,4,5,6) for *.min file; space #6 is for NULL; */ 266 w_inkey() { typedef enuxn { FALSE=0, TRUE=1 } OOPSJTYPE; OOPS_TYPE oops_flag; int response; clrscr(); printf("\n w_inkey starting ... \n") ; printf(" [1] File name [e.g. GF40 maximum of 4 char] = = > " ) ; scanf("%4s",input_fn) ;
/***** printf(" [2] .MIN name [e.g. GF.MIN maximum of 6 char] ==>"); scanf("%6s",min_fn); * * * * * j
oops_flag = TRUE; while(oops_flag == TRUE) { printf("\n [2] Type of grip [1 = pinch, 2 = power] = = > " ) ; scanf("%i",&response); if (response == 1) { grip = 0; oops_flag = FALSE; ) if (response ==2) { grip = 1; oops_flag = FALSE; ) if ( (response != l) && (response != 2) ) { printf("\n\tChoose 1 or 2, you bozo! try again..,\n"); oops_flag = TRUE; } ) oops_flag = TRUE; while(oops_flag == TRUE) { printf("\n [3] Velocity [1= 30 D/S, 2= 45 D/S ] ==>") ; scanf("%i",&response); if (response ==1) { 267 vel = 30; oops_flag = FALSE; } if (response ==2) { vel = 45; oops_flag = FALSE; } if ( (response != 1) && (response != 2) ) { printf("\n\tChoose 1 or 2, you bozo! try again...\n"); oops_flag = TRUE; } } oops_flag = TRUE; while(oops_flag == TRUE) { printf("\n [4] Control [1 = TORQ, 2 = FORCE] = = > " ) ; scanf C^ i " , &response) ; if (response ==1) { control = 0; oops_flag = FALSE; } if (response ==2) { control = 1; oops_flag = FALSE; ) if ( (response != 1) && (response != 2) ) ( printf(M\n\tChoose 1 or 2, you bozo! try again...\n"); oops_flag = TRUE; > } if (control ==0) { oops_flag = TRUE; while(oops_flag == TRUE) { printf("\n [5] Torque [1=2 N-m, 2 = 4 N-m, 3 = 8 N-m] ==>"); scanf("%i",&response); if (response ==1) { torq = 2; oops_flag = FALSE; ) if (response ==2) { torq = 4; oops_flag = FALSE; } if (response ==3) { torq = 8; 268 oops_flag = FALSE; } if ( (response != 1) && (response != 2) && (response != 3) ) < printf("\n\tChoose 1 or 2, you bozo! try again. ..\n"); oops_flag = TRUE; } } } else { oops_flag = TRUE; while(oops_flag == TRUE) { printf("\n [5] Force [1=7 LBS, 2 = 14 LBS] ==>'•) ; scanf("%i",&response); if (response ==1) { force = 7 ; oops_flag = FALSE; } if (response ==2) { force = 14; oops_flag = FALSE; } if ( (response != 1) && (response != 2) ) { printf("\n\tChoose 1 or 2, you bozo! try again. ..\n"); oops_flag = TRUE; ) ) /* end of while */ } /* end of else */ oops_flag = TRUE; while(oops_flag == TRUE) { printf("\n [6] Electrodes [ 1 = surface , 2 = fine wires] ==>"); scanf("%i",&response); if (response ==1) { electrodes = 0; oops_flag = FALSE; } if (response ==2) { electrodes = 1; oops_flag = FALSE; } if ( (response != 1) && (response != 2) ) { printf ("\n\tChoose 1 or 2, you bozo! try again. ..\n"); oops_f lag = TRUE; ) 269
} printf("\n\n w_inkey complete ... \n"); return(0); }
/**********************************************************/ /* INPUT EMG MAX AND MIN VALUES (w_max_file) */ /**********************************************************/ FILE *maxfile,*minfile; int EMG_MAX[8][8],EMG_MIN[8][8]; w__max_f ile () { int ch,ang,ANGLE; float input; printf("\n w_max_file starting ... \n")? if ( (minfile = fopen(min_fn,"r")) == NULL) printf("Unable to open file %s\n",minfile); for (ang=l; ang<=7; ang++) { fscanf(minfile,"%i", &ANGLE); for (ch=l; ch<=7; ch++) { fscanf(minfile,"%f",Sinput); EMG_MIN[ang][ch] = 1000*input; } ) fclose(minfile); printf("\n w_max_file complete ... \n"); return(0); }
/* INPUT EMG VALUES (w_emg_file) */ FILE *inputfile, *outfile; int TIME, HZ, LEN, EMG[8][700]; float ANG[700],TORQ[700],FORCE[700]; w_emg_file() { int ch,t; int CHN,MO,DAY,YR,DATCOUNT; float input,junk; 270 printf("\n w__emg_file starting ... \n") ; /* THE STRUCTURE OF THE DATA FILE IS AS FOLLOWS: FIRST LINE: EXPERIMENT -- THROW AWAY SECOND LINE: SUBJECT -- THROW AWAY THIRD LINE: TECHNICAL DESCRIPTORS OF DATAFILE CH 0: TIME — THROW AWAY CH 1,2,3: ANGLE,TORQUE,GRIP FORCE CH 4 - 11: FINE WIRE EMG CH 12: DUMMY */ inputfile = fopen(input_fn,"r"); fscanf(inputfile,"%*s %*s %i %i %i %i %i %i",&CHN,&HZ,&LEN,&MO,&DAY,&YR); TIME = (HZ * LEN) - 1; for (t = 0; t <= TIME; t++) { fscanf(inputfile,"%*f %f%f%f ",&(ANG[t]), &(TORQ[t]), & (FORCE[t]) ); ANG[t] = 71.61 + (-36.046 * ANG(t]); /* if you used Gary's A/D board on EMG rack, reduce torque by 0.070 V */ TORQ(t] = TORQ[t] - 0.070; if (T0RQ[t] < .275) TORQ[t] = -1.709 + (24.396 * TORQ[t]); else TORQtt] = -4.650 + (35.912 * TORQ[t]); FORCE[t] = -6.482 + (50.580 * FORCE[t)); for(ch = 1; ch <= 7; ch++) ( fscanf(inputfile,"%f",&input); EMG[ch][t] = (int)(input * 1000.0); } fscanf(inputfile,"%*f"); } /* end of TIME loop */ fclose(inputfile); /* ****** The following code can be used to check ANG, TORQ, and FORCE: ****** */ /* PUT QUOTATION MARKS AROUND "chck.ang" BECAUSE IT'S A STRING VAR */ outfile = fopen("chck.ang","w"); fprintf(outfile,"\n check on angle(v)(deg), torq(v)(ft-lb),") ; fprintf(outfile," and force(v)(lbs): \n") ; for (t=0; t<=TIME; t++) { fprintf(outfile," %0.4f %0.3f", ANG[t],(float)( (ANG[t] + 71.61) / 36.046) ); fprintf(outfile," %0.4f %0.3f", TORQ[t],(float)( (TORQ[t] + 1.709) / 24.396) ); fprintf(outfile," %0.4f %0.3f", FORCE[t] , (float) ( (FORCE[t] + 6.482) / 50.580) ),* fprintf(outfile,"\n"); } fclose(outfile);
/ * * * * * * * The following code can be used to check the EMG array: * * * * * * */ /* outfile = fopen("chck.emg","w") ; fprintf(outfile,"\n check on emgs(volts): \n"); for (t=0; t<=TIME; t++) { for (ch = 1? ch <=7 ; ch++) fprintf(outfile," %0.3f ",(float)( (float)EMG[ch][t] / 1000.0) ); fprintf(outfile,"\n"); } fclose(outfile); */ / * * * * * * * END OF DEBUGGING CODE ****** */ printf("\n w_emg_file complete ... \n"); return(0); } 272 y*********************************************************** ** / /* w_end_loop fct: ASK IF YOU WANT TO ANALYZE ANOTHER FILE */ y*********************************************************** ** y char w_end_loop() { char reply[15]; clrscr(); printf("\n\n\n main program complete ... \n"); printf("\n\n\n END OF LOOP? [Y OR N] ==>"); scanf("%s",reply); return (reply[0]); } y**************** END OF w input.c FILE *******************y APPENDIX D
273 274 _PREP.C file #include
/**********************************************************/ /* w prep dat FUNCTION; w_prep_dat CALLS OTHER FUNCTIONS IN THIS FILE */ /**********************************************************/ void w prep dat () { int t,ch,CH,CHH; float T E M P [700] ; /**** PLOT ANGLE, TORQ, AND FORCE ****/ plot_xy (1,0,4, "ANGLE", ANG) ; plot_xy (2,0,2, "E X T . TORQUE" , TORQ) ; plot_xy (3,0,14, "GRIP FORCE" , FORCE) ? printf(" %s", input_fn) ; hold_screen () ; /* printf ("\n ORIGINAL DATA VALUES \n") ; print_debug() ; */ norm_emg () ; /* printf ("\n EMG NORMALIZED BY MAX EMG VALUES \n") ; print_debug() ; */ emg_length(); /* printf ("\n EMG MODIFIED BY LENGTH-STRENGTH \n") ; print_debug () ? */ 275 emg_vel() ; /* printf ("\n EMG MODIFIED BY VELOCITY \n") ; print_debug () ; */ smooth_emg() ; /* printf ("\n EMG SMOOTHED BY HANNING FILTER; \n") ; printf (" IX FOR FINE WIRE; 3X FOR SURFACE ELECTRODES \n ") ; print_debug(); */ erng_pcsa () ; /* THIS IS RWS' WAY TO TAKE INTO ACCOUNT MUSCLE PCSA; THE GAIN IS NEWTONS/SQ CM ! I YOU HAVE TO MULTIPLE FINAL GAIN BY 1000X TO GET N/CM^2 BECAUSE EMG IS INTEGER (1000 =1.0 NORM). */ /* printf ("\n EMG MODIFIED BY MUSCLE PCSA (AFTER SMOOTHING) \n"); print_debug () ; */ /**** PLOT EMG DATA (3 EMG TRACES PER SCREEN; 3 SCREENS) ****/ for (ch=0 ; ch<=6 ; ch+=3) { for (CH=1 ; CH<=3 ; CH++) { CHH = ch + CH; if ( (CHH != 8) && (CHH != 9) ) { for (t=0 ; t<=TIME ; t++) TEMP[t] = (float) (EMG[CHH] [t']) ; plot_xy (CH ,0,4 , "EMG", TEMP) ; } /* end of if */ } /* end of 3 traces on screen */ printf(" %s", input_fn); hold_screen(); ) /* end of 3 screens */ ) /****************** END OF main FUNCTION *****************/ 276
/****************************************************/ /* NORMALIZE EMG[] VALUES RELATIVE TO EMGMAX[] */ /****************************************************/
/* THESE EQUATIONS ARE FOR AN INDIVIDUAL SUBJECT ONLY! */ norm_emg() { int t,ch,p=2; float MAXEMG,MINEMG; printf ("\n NORMALIZE EMG DATA \n") ; for (ch=l ; ch<=7 ; ch++) for (t=0 ; t<=TIME ; t++) { /* ONLY NORMALIZE EMG VALUES FOR ANGLES BETWEEN -75 AND 75 DEGREES */ if ( (ANG[t] >= -75.0) && (ANG[t] <= 75.0) ) { if (grip == 0) { if (ch==l) MAXEMG = 1.699 + (-.008275*ANG[t]); if (Ch==2) MAXEMG = 1.311 + (.005955*ANG[t]); if (ch==3) MAXEMG = 1.261 + (.006907*ANG[t]); if (Ch==4) MAXEMG = 0.7637 + (-0.009264*ANG[t ]); if (ch==5) MAXEMG = 3.517 + (-0.003238*ANG[t ]) + (-.0002578)*(float) (pow((double)ANG[t],(double)p))y if (ch==6) MAXEMG = 1.547 + (-0.0161*ANG[t]); if (ch==7) MAXEMG = 1.578 + (-0.007066*ANG[t]); ) /* end of grip == 0 (pinch) */ else { if (ch==l) MAXEMG = 0.7436 + (-.006584*ANG[t]); if (ch==2) MAXEMG = 1.080 + (.003025*ANG[t]); if (ch==3) MAXEMG = 2.865 + (-.003504*ANG[t]); if (ch==4) MAXEMG = 1.471 + (-.001659*ANG[t]); if (ch==5) 277 MAXEMG = 3.745 + (-.0006768*ANG[t]) + (-.0002830)*(float) (pow((double)ANG[t],(double)p)); if (ch— 6) MAXEMG = 2.006 + (-.0009054*ANG[t)) + (-.0001287)*(float) (pow((double)ANG[t],(double)p)); if (ch==7) MAXEMG = 2.430 + (.0007911*ANG(t]) + (-.0001890)*(float) (pow((double)ANG[t],(double)p)); } /* end of grip = l (power) */
/**** NOW NORMALIZE EMG; NORMALIZED EMG IS AN INTEGER (1000 =1.0 NORM EMG) ****/ /* EMG[ch][t] = (int)( ( (float)(EMG[ch][t]) / (MAXEMG*1000.0) )*1000.0);*/ EMG[ch][t] = (int)( (float)(EMG[ch][t]) / MAXEMG );
if (EMG[ch][t] < 0) EMG[ch][t] = 0; if (EMG[ch][t] > 1000 ) EMG[ch][t] = 1000; } /* end of if (angle between -75 and 75 degrees) */ else EMG[ch][t] = 0; if (t > (int)(cutoff* TIME) ) EMG[ch][t] = 0; } /* end of t for loop */ return(0); }
/* MODIFY EMG[] FOR LENGTH-STRENGTH RELATIONSHIP */ /A***************************************************/ emg_length() ( float y ,WT,MAXWT[2)[8],WT_FACTOR; int ch,t,p; /** LENGTH-STRENGTH WEIGHTED ACCORDING TO EITHER SYMMETRIC NORMAL DISTRIBUTION OR SKEWED EXTREME VALUE DISTRIBUTION; SEE w_input.c FOR VALUES OF mean,sigma,mode, & alpha; 278 L-S WEIGHTING AT EACH ANGLE NORMALIZED TO MAXWT **/
/** CALCULATE MAX WEIGHT AT ANGLE THAT IS MEAN OR MODE OF DISTRIBUTION; THE EXP PART OF NORMAL DIST. EQ. IS 1 AT MEAN OF NORMAL DIST ; THE EXP PART OF EXT. VALUE DIST. EQ. IS EXP TO NEG ONE POWER **/ for (p=0; p<=l; p++) { for (ch=l; ch <=7; ch++) { if (ls_norm ==0) /* sym. normal dist. */ MAXWT[p][ch] = (float)( 1.0 / (float)( sqrt(2 * PI * sigma[p][ch])) ); if (ls_norm ==1) /* skewed ext. value dist. */ /* maxwt at mode; at mode, y = 0 */ MAXWT[p][ch] = alpha[p][ch] * (float)( exp(-l.O) ); } /* end of ch for loop */ } /* end of p for loop */
/** CALCULATE WT OF EACH CHANNEL AT EACH ANGLE; WT OF F D S,FDP, AND EDC DEPEND ON GRIP ORIENTATION **/ if (grip ==0) p = 0; if (grip == 1) p = 1; /* print_weight(l,ANG[0],0.0,0); */ for (t=0; t<=TIME; ,t++) { for (ch=l; ch<=7; ch++) ( if (ls_norm == 0) WT = (float)(.1.0 / (float)( sqrt(2 * PI * sigma[p][ch])) ) * (float)(exp(-0.5 * pow(((ANG[t] - mean[p][ch])/sigma[p][ch]),2.0))); else ( if ( (ch>=l) && (ch<=4) ) y = alpha[p][ch] * (mode[p][ch] - ANG[t]); else y = alpha[p][ch] * (ANG[t] - mode[p][ch]); WT = alpha[p][ch] * (float)( exp( -(y) - (exp(-(y))) ) ); } /* end of ls_norm = 1 */ WT_FACTOR = WT / MAXWT[p][ch]; /* if (ch==7) print_weight(2,A N G [t ],W T ,1); 279 else print_weight(2,ANG[t],WT,0); */ EMG[ch][t] = (int)( (float)(EMG[ch][t ]) * WT_FACTOR ); } /* end of channel for loop */ } /* end of time for loop */ /* print_weight(3,0.0,0.0,0); */ return(0); }
/*********************************************************/ /* MODIFY EMG[ ] FOR VELOCITY-STRENGTH RELATIONSHIP */ /*********************************************************/ emg_vel() { int t,ch; float factor; /* TAKEOUT VELOCITY ARTIFACT FROM EMG; */ /* THESE % REDUCTIONS FROM MIRKA'S EMPIRCAL TRUNK DATA */ if (vel == 30) factor = vel_30; if (vel == 45) factor = vel_45; for (t=0; t<=TIME; t++) for (ch-1; ch <=7; ch++) EMG[ch] [t] = (.int) ( (float) (EMG[ch] [t]) * factor); return (0); )
/*********************************************************/ /* SMOOTH EMG[] DATA */ /* */ /* NOTE; SMOOTH EMG DATA BETWEEN -75 AND 75 DEG BECAUSE HANNING WINDOW SMOOTHS BASED ON PAST AND FUTURE DATA, THEN CONVERT EMG DATA < -60 AND > 60 DEGREES TO ZERO. */ /*********************************************************/ smooth_emg() { int ch,t; printf ("\n SMOOTH EMG DATA \n CHN #"); 280 for (ch=l ; ch<=7 ; ch++) { printf ("%d ",ch);
if (electrodes ==0) filter_int(17,3,EMG[ch]); /* electrodes = 0 (surface) */ else filter int(17,l,EMG[ch]); /* electrodes = 1 (fine wire) */ /* CONVERT EMG DATA < -60 AND > 60 DEG TO ZERO */ for (t=i; t<=TIME; t++) if ( (ANG[t] < LLIM_ANG) j J (ANG[t] > ULIM_ANG) !j (t > (int) (cutoff * TIME)) ) EMG[ch] [t] = 0;
} return(0) ; }
/*********************************************************/ /* HANNING WINDOW TIME DOMAIN FILTER */ /*********************************************************/ filter_int(int BW, int cycles, int *A) { int t,T,i; int FILTER[700]; float PI=3.1415,NORM; for (i=l ; i<=cycles ; i++) { for (t=o ; t<=TlME ; t++) { FILTER[t] = 0; NORM = 0; for (T»0 ; T<=(BW-1)/2 ; T++) { if ((t+T) < TIME) { FILTER[t] += A[t+T] * cos(PI*T/BW) ; NORM += cos(PI*T/BW) ; } if ((t-T) > 0) { FILTER[t] += A[t-T] * cos(PI*T/BW) ; NORM += 2*cos(PI*T/BW); )}) for (t=0 ,* t<=TIME ; t++) A[t] = FILTER[t ]/NORM; > return (0) ; 281
}
/********************************************************/ /* CORRECT FOR MUSCLE PCSA (SQ CM) */ emg_pcsa() { int t; /* THESE PCSA UNITS ARE FROM CHAO'S BOOK"BIOM OF THE HAND", P. 44 (1989); PCSA UNITS ARE IN SQ CM */ for (t=0 ; t<=TlME ; t++) { EMG[1][t] = (int)( (float)(EMG[1][t ) * 5.2 ) ; /*FCR */ EMG[2][t] — (int)( (float)(EMG[2][t ) * 12.3 ); /*FDS (all 4)*/ EMG[3][t] (int)( (float)(EM G [3][t ) * 14.4 ) ; /*FDP (all 4)*/ EMG[4][t] = (int)( (float)(EMG[4][t ) * 10.0 ) ; /*FCU */ EMG[5][t] 2 (int)( (float)(EMG[5][t ) * 8.9 ) ; /*ECRL & ECRB*/ EMG[6][t] 2 (int)( (float)(EMG[6)[t ) * 4.5 ) ; /*EDC (all 4)*/ EMG[7][t] = (int)( (float)(EMG[7][t ) * 3.5 ) ; /*ECU */ } return(0); ) y**********************************************************/ /* PRINT TIME, EMG[], ANG[] , TORQ[], FORCE[], AND EMG[] FOR DEBUG */ /**********************************************************/ print_debug() { int t,ch,count»0; printf("\n "); printf ("TIME ANG TORQ GFORCE #1 #2 #3 #4 #5 #6 #7"); for (t=0 ; t<=TIME ; t+=4) { 282 count++; if (count > 20) { hold_screen(); count = 0; } printf ("\n%3d ",t) ; printf("%0.2f %0.2f %0.2f ",ANG[t],T0RQ[t],F0RCE[t])» for (ch=l ; ch<=7 ; ch++) printf("%4i ", EMG[ch][t]); > printf ("\n\n") ; hold_screen () ; return (0) ; )
/**********************************************************/ /* PRINT L-S WEIGHTS OF ALL 7 CHANNELS */ /**********************************************************/ print_weight (key, angle, weight, end_line) int key,end_line; float angle,weight; { FILE *fileout; char output_fn[9]; if (key ==1) { strcpy (output_fn, input_fn); strcat (output_fn, ". LSW") ; fileout = fopen(output_fn,"w"); fprintf(fileout," %0.2f ", angle); } if (key == 2) { if (end_line == l) { fprintf(fileout," %0.5f \n",weight); fprintf(fileout," %0.2f ", angle); } else fprintf(fileout," %0.5f ",weight); ) if (key == 3) f close(fileout); 283 return(0); } /******* END OF w prep.c FILE ***************************/ APPENDIX E
284 285 _TORQ.C file #include
/**********************************************************/ /* COMPUTE MEASURED-TORQ AND PREDICTED-TORQ; */ /* ITERATE TO ADJUST GAIN TO MATCH MEAS & PRED TORQ; */ /**********************************************************/ void w_compute_torq() { external_torq(); internal_torq(); /* print_momarms_angles(); */ /* print_torq(); */ } /**********************************************************/ /* EXTERNAL TORQUE */ external_torq() { int t; /* ALL EXTERNAL TORQUES ARE FLEXION AND WERE MEASURED BY CYBEX. EXT TORQUES RESIDE IN TORQ[] ARRAY. */ /* CONVERT EXT. TORQ FROM FT-LBS TO NEWTON-METERS; */ /* CONVERT EXTERNAL GRIP FORCE FROM LBS TO NEWTONS; */ 286 /* CONVERT ONLY VALUES WITHIN ANGLE OF INTEREST? */ for (t=0; t<=TIME; t++) { if ( (ANG[t] >= LLIM_ANG) && (ANG[t] <= ULIM_ANG) && (t <= (int)(cutoff * TIME)) ) { TORQ[t ] = TORQ[t ] * 1.3558; FORCE[t] = FORCE[t] * 4.4482? } else { TORQtt] = 0.0; FORCE[t] = 0.0; } } /* end of t for loop */ /* OTHER CONVERSION FACTORS THAT YOU MAY NEED IN FUTURE Force; 1 lb 4.4482 N Length: 1 ft 0.3048 m Work: 1 lb-ft 1.3558 N-m Energy: 1 ft-lb 1.3558 Joule Energy (heat): 1 calorie 4.1868 joules •i it 1000 calories = 1 kilocalorie = 1 Calorie Temperature: deg C = ( deg F - 32 ) * (5/9) Water: 1 g / cmA3; specific heat = 1; */ return(0); }
/*********************************************************/ /* PREDICT TORQ FROM EMG VALUES; */ /* ITERATE TO'ADJUST GAIN TO MATCH MEAS & PRED TORQ */ /*********************************************************/ /* EMG[1][t] = FCR EMG[2][t] = FDS */ /* EMG[3][t] = FDP EMG[4][t] = FCU */ /* EMG[5][t] = ECRL EMG[6][t] = EDC */ /* EMG[7][t] = ECU */ /*********************************************************/ float INTJTORQX[700], G A I N [8], MOMARMX[8], MOMARMY[8]; float EMGFORCE_FDS[700],EMGFORCE_FDP[700],EMGFORCE_EDC[700]; float force_fds_grip, force_fdp_grip, force_edc_grip; double BETA[8], GAMMA[8]; /* NOTES ON VARIABLE NAMES AND SIGN CONVENTION; Sign convention for TORQUE follows RIGHT HAND RULE; Forearm is supinated; POS X axis points towards RADIAL direction from center of wrist; 287 POS Y axis points towards FLEXOR direction from center of wrist; POS Z axis points towards HAND from center of wrist; MOM_ARM[] is moment arm of [i]th tendon. BETA[] is angular deviation of tendons in RAD/ULN plane; GAMMA[ ] is angular deviation of tendons in FLEX/EXT plant; */ internal_torq() { int ch, t,MAX_T; float LLIM,ULIM; /* DEFINE LIMITS FOR INTEGRATION -- DEPENDS ON GRIP — SEE w_input.c */ if (grip == 0) { LLIM = LLIM_PN; ULIM = ULIM_PN; } else { LLIM = LLIM_PW; ULIM = ULIM_PW; } /* grip = 1 */ /* DEFINE MOMENT ARMS IN X (RAD/ULN) AND Y (FLEX/EXT) PLANES */ MOMARMX[1] = .01 * c o e f ; MOMARMY[1] = .0175 * c o e f ; MOMARMX[2] = - .0025 * c o e f ; MOMARMY[2] = .0150 * c o e f ; MOMARMX[3] = -.003 * coef; MOMARMY[3] .0125 * coef; MOMARMX[4] = -.01625 * c o e f ; MOMARMY[4] = .0190 * c o e f ; MOMARMX[5] = . 0175 * coef; MOMARMY[5] -.0120 * coef; MOMARMX[6] -.0035 * coef; MOMARMY[6] SS -.0150 * c o e f ; = MOMARMX[7] -.025 * coef; MOMARMY[7] =s -.0085 * c o e f ; = /* CALCULATE BETA (RAD/ULN) AND GAMMA (FLEX/EXT) ANGLES OF TENDONS */ /* BETA AND GAMMA ANGLES ARE IN RADIANS */ for (ch=l; ch<=4; ch++) BETA[ch] = atan( ( ((double) (elb_width)/2.0) + 288 (double) (MOMARMX[ch]) ) / (double) (xned_epic) ); for (ch=5; ch<=7; ch++) BETA[ch] = atan( -( ((double)(elb_width)/2.0) - (double)(MOMARMX[ch]) ) / (double)(lat_epic) ); for (ch=l; ch<=4; ch++) GAMMA[ch] = atan( (double)(MOMARMY[ch]) / (double)(med_epic) ) ; for (ch=5; ch<=7; ch++) GAMMA[ch] = atan( (double)(MOMARMY[ch]) / (double)(lat_epic) ) ;
/* SET GAINS IN ALL 7 CHANNELS EQUAL TO MINIMUM VALUE */ for (ch=l; ch<=7; ch++) GAIN[ch] = gain_min; /* PLOT EXTERNAL TORQUE (N-m) */ MAX_T = plot_xy(1,0,4,"TORQ (N-m)",TORQ); /* PRINT FILE NAME AT TOP OF SCREEN THAT ITERATES TORQUE */ printf(" %s",input_fn); /* NOW START ITERATIONS OF GAIN WITH DO LOOP */ do { /* FOR FIRST PASS, STEP UP GAINS IN ALL 7 CHANNELS */ for (ch=l; ch<=7; ch++) GAIN[ch] += step; for (t=0; t<=TIME; t++) { /* PARTITION MUSCULAR FORCE OF FDP,FDS,AND EDC INTO GRIP FORCE COMPONENT AND TORQUE GENERATING COMPONENT */ if (grip == 0) { force_fds_grip = FORCE[t] * fds_pn; force_fdp_grip = FORCE[t] * fdp_pn; force_edc_grip = FORCE[t] * edc_pn; ) /* if grip is pinch */ else { force_fds_grip = FORCE[t] * fds__pw; force_fdp_grip = FORCE[t] * fdp_pw; force__edc_grip = FORCE[t] * edc_pw; } /* else grip is power */
/* if ( (GAIN[1] > .050) && (t > 100) && (t<500) ) printf("t = %i fds_pn = %0.3f fdp__pn = %0.3f edc_pn = 289
%0.3f\n", t ,fds_pn,fdp_pn,edc_pn); if ( (GAIN[1] > .050) && (t > 100) && (t<500) ) printf("t = %i fds_pw = %0.3f fdp_pw = %o.3f edc__pw = %0.3f\n", t,fds_pw,fdp_pw,edc_pw); if ( (GAIN[1] > .050) && (t > 100) && (t<500) ) printf("t = %i force_fds_grip = %0.3f force_fdp_grip = %0.3f force_edc_grip = %0.3f\n", t,force_fds_grip,force_fdp_grip,force_edc_grip); */ EMGFORCE_FDS[t] = ( (float)(fabs( (CO S (BETA[2]))*(COS(GAMMA[2]))) ) * ( GAIN[2] * (float)(EMG[2][t]) ) ) - force_fds_grip; if (EMGFORCE_FDS[t] < 0.0) EMGFORCE_FDS[t] = 0.0;
/* if ( (GAIN[1] > .050) && (t > 100) && (t<500) ) printf("BETA[2] = %0.4f GAMMA[2] = %0.4f GAIN[2] = %0.3f EMG[2][t ) = %i FDS = %0.3f \n", BETA[ 2 ] ,GAMMA[ 2 ] , GAIN[ 2 ] ,EMG[2][t],EMGFORCE_FDS[t ]); */ EMGFORCE_FDP[t) = ( (float)(fabs( (co s (BETA[3]))*(c o s (GAMMA[3]))) ) * ( GAIN[3] * (float)(EMG[3][t]) ) ) - force_fdp_grip; if (EMGFORCE_FDP[t] < 0.0) EMGFORCE_FDP[t] = 0.0;
/* if ( (GAIN[1] > .050) && (t > 100) && (t<500) ) printf("BETA[3] = %0.4f GAMMA[3] = %0.4f GAIN[3] - %0.3f EMG[3][t] = %i FDP = %0.3f \n", BETA[3],GAMMA[3],GAIN[3],EMG[3][t],EMGFORCE_FDP[t]); */ EMGFORCE_EDC[t] = ( (float)(fabs( (CO S (BETA[6]))*(C O S (GAMMA[6]))) ) * ( GAIN[6] * (float)(EMG[6][t]) ) ) - force_edc_grip; if (EMGFORCE_EDC[t] < 0.0) EMGFORCE_EDC[t] = 0.0;
/* if ( (GAIN[1] > .050) && (t > 100) && (t<500) ) printf("BETA[6] - %0.4f GAMMA[6] = %0.4f GAIN[6] - %0.3f EMG[6][t ] - %i EDC = %0.3f \n", BETA[6],GAMMA[6],GAIN[6],EMG[6][t],EMGF0RCE_EDC[t]); 290
*/ /* CALCULATE INTERNAL FLEXION TORQUE (TORQUE ABOUT X AXIS) */ if (muscles == 7) INT_TORQX[t] = ( (float)(fabs( (cos(BETA[1]))*(cos(GAMMA[1]))) ) * ( GAIN[1] * (float)(EMG[1][t]) * MOMARMY[1] ) ) + ( EMGFORCE_FDS[t] * MOMARMY[2] ) + ( EMGFORCE_FDP[t] * MOMARMY[3] ) + ( (float)(fabs( (COS(BETA[4]))*(COS(GAMMA[4]))) ) * ( GAIN[4] * (float)(EMG[4][t]) * MOMARMY[4] ) ) + ( (float)(fabs( (COS(BETA[5]))*(COS(GAMMA[5]))) ) * ( GAIN[5] * (float)(EMG[5](t]) * MOMARMY(5] ) ) + ( EMGFORCE_EDC[t] * MOMARMY[6] ) + ( (float)(fabs( (cos(BETA[7]))*(cos(GAMMA[7]))) ) * ( GAIN[7] * (float)(EMG[7][t]) * MOMARMY[7] ) ) ? /* if ( (GAIN[1] > .050) && (t > 100) && (t<500) ) printf("INT_TORQX(t] = %0.4f \n\n",INT_TORQX[t]); */ /**** count += 1; if (count ==50) { printf(" %4d %0.2f %0.3f \n",t ,GAIN[1),INTJTORQX[ t ]) ; count = 0; } * * * * j
) /* end of TIME (t) for loop */ plot_xy (1,MAX_T, 14, " " , INT_TORQX) ; ) while (integral(TORQ,LLIM,ULIM) > integral (INTJTORQX, LLIM,ULIM)) ;
printf("\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n"); printf("\n NUMBER OF MUSCLES THAT GENERATE TORQUE = %i \n",muscles) ; printf("\n INTEGRAL OF EXT TORQUE BET %0.0f AND %0.0f = 291 %0.1f \n", LLIM,ULIM, integral (TORQ, LLIM,ULIM)) ; printf (" INTEGRAL OF INT TORQUE BET %0.0f AND %0.0f = %0.1f \n", LLIM,ULIM, integral (INTJTORQX, LLIM,ULIM)) ; printf ("\n INTERNAL TORQUE IS NOW GREATER THAN EXTERNAL TORQUE \n ") ; printf ("\n FINAL GAIN = %0.1f N/cmA2 \n", (GAIN[1]*1000.0) ); hold_screen(); return(0); >
/*********************************************************** */ /* PRINT MOMENT ARMS AND ANGLES TO ".mom" FILE */ y*********************************************************** */ print_momarms_angles() { FILE *fileout; char output_fn(9]; int t,ch; printf ("\n WRITING .mom FILE \n") ; strcpy(output_fn, input_fn) ; strcat (output_fn,". MOM"); fileout = fopen(output_fn,"w"); fprintf (fileout," MOMENT ARMS (m) IN X (R/U) PLANE \n") ; for (ch=l; ch<=7; ch++) fprintf(fileout," %0.5f ", MOMARMX [ch]); fprintf(fileout,"\n\n"); fprintf (fileout," MOMENT ARMS (m) IN Y (F/E) PLANE \n") ; for (ch*=l; ch<=7; ch++) fprintf(fileout," %0.5f ",MOMARMY [ch]); fprintf(fileout,"\n\n") ; fprintf (fileout," BETA ANGLES (DEG) IN X (R/U) PLANE \n") ; for (ch=l; ch<=7; ch++) fprintf(fileout," %0.2f ",(BETA[ch] * (180.0/PI)) ); fprintf(fileout,"\n\n"); 292 fprintf(fileout," GAMMA ANGLES (DEG) IN Y (F/E) PLANE \n"); for (ch=l; ch<=7; ch++) fprintf(fileout," %0.2f ",(GAMMA[ch] * (180.0/PI)) ); fprintf(fileout,"\n\n"); fclose(fileout) ; return(0) ; )
/******************************************************/ /* WRITE MEASURED AND PREDICTED TORQUE TO ".trq" FILE*/ /******************************************************/ print_torq() { FILE *fileout; char output_fn[9]; int t,ch; printf("\n WRITING .trq FILE \n"); strcpy (output_fn, input_fn); strcat(output_fn,".TRQ"); fileout = fopen(output_fn,"w"); fprintf(fileout," GAIN = %0.1f \n\n", (GAIN[1] * 1000.0) ) ; fprintf(fileout," TIME ANGLE(deg) G.FORCE(N) EXT.TRQ(N-m) INT.TRQ(N-m)\n"); for (t=0; t<=TIMI2; t++) { if ( (ANG[t] >= LLIM_ANG) && (ANG[t] <= ULIM_ANG) && (t <= (int)(cutoff * TIME)) ) fprintf(fileout," %i %0.2f %0.3f %0.3f %0.3f \n", t, ANG[t] ,FORCE[t ] ,TORQ[t ] , INTJTORQX[t ] ) J ) fprintf(fileout,"\n"); fclose(fileout) ; return(0) ; )
/******* END OF w torq.c FILE **************************/ APPENDIX E 294 _LOAD.C file #include
/**********************************************************/ /* COMPUTE LOADS ON WRIST; */ y**********************************************************/ void w_compute_load() { wrist_load() ; /* print_load(); */ }
/**********************************************************/ /* WRIST COMPRESSION, RU_SHEAR, FE_SHEAR */ /**********************************************************/ int NETRF_X[700],NETRF_Y[700],NETRF_Z[700]; wrist_load() { int t,ch; float EXTF_Y,EXTF_Z,M0MARM_T0RQ,temp[700]; 295 /* CONVERT ALL ANG[t] FROM DEGREES TO RADIANS (RAD REQUIRED BY C++) */ for (t=0; t<=TIME; t++) ANG[t] = ANG[t] * (PI / 180.0); if (grip == 0) MOMARM_TORQ = MOMARM_PINCH; if (grip == 1) MOMARM_TORQ = MOMARM_POWER; for (t=0; t<=TIME; t++) { /* CALCULATE COMPRESSION (Z AXIS) */ EXTF_Z = (float)(sin( (double)(ANG[t]) )) * (TORQ[t] / MOMARM_TORQ) ; NETRF_Z[t] = (int)( -(EXTF_Z) + ( (float)( COS(BETA[1]) * COS(GAMMA[1]) )*(float)(EMG[1][t])*GAIN[1] ) + EMGFORCE_FDS[t] + EMGFORCE_FDP[t] + ( (float)( COS(BETA[4]) * COS(GAMMA[4]) )*(float)(EMG[4][t])*GAIN[4] ) + ( (float)( COS(BETA[5]) * COS(GAMMA[5]) )*(float)(EMG[5][t])*GAIN[5] ) + EMGFORCE_EDC[t] + ( (float)( cos(BETA[7]) * cos(GAMMA[7]) )*(float)(EMG[7][t])*GAIN[7] ));
/* CALCULATE FLEX/EXT SHEAR (Y AXIS) */ EXTF_Y = (float)(cos( (double)(ANG[t]) )) * (TORQ[t] / MOMARM_TORQ); NETRF_Y[t] = (int)( +(EXTF_Y) + ( (float)( COS(BETA[1]) * sin(GAMMA[1]) )*(float)(EMG[1][t])*GAIN[l] ) + ( (float)( COS(BETA[2]) * sin(GAMMA[2]) )*EMGFORCE_FDS[t ] ) + ( (float)( COS(BETA[3]) * sin(GAMMA[3]) )*EMGFORCE_FDP[t] ) + ( (float)( COS(BETA[4]) * sin(GAMMA[4]) )*(float)(EMG[4][t])*GAIN[4] ) + ( (float)( COS(BETA[5]) * sin(GAMMA[5]) )*(float)(EMG[5][t])*GAIN[5] ) + ( (float)( cos(BETA[6]) * sin(GAMMA[6]) )*EMGFORCE_EDC[t) ) + ( (float)( COS(BETA[7]) * sin(GAMMA[7]) )*(float)(EMG[7][t])*GAIN[7] )); 296
/* CALCULATE RAD/ULN SHEAR (X AXIS) */ /* no EXTF_X because torque was measured in flex/ext plane only */ NETRF_X[t] = (int)( + ( (float)( sin(BETA[l]) * cos(GAMMA[1]) )*(float)(EMG[1][t])*GAIN[l] ) + ( (float)( sin(BETA[2]) * cos(GAMMA[2]) )*EMGFORCE_FDS[t] ) + ( (float) ( sin(BETA[3]) * COS(GAMMA[3]) )*EMGFORCE_FDP[t] ) + ( (float)( sin(BETA[4]) * COS(GAMMA[4]) )*(float)(EMG[4][t])*GAIN[4] ) + ( (float)( sin(BETA[5]) * COS(GAMMA[5]) )*(float)(EMG[5][t])*GAIN[5] ) + ( (float) ( sin(BETA[6]) * COS(GAMMA[6]) ) *EMGFORCE__EDC [ t ] ) + ( (float)( sin(BETA[7]) * COS(GAMMA[7]) ) *(float) (EMG[7][t ])*GAIN[7] )); } /* end of time for loop */ for (t=0; t<=TIME; t++) temp[t] = NETRF_X[t]; plot_xy(1,0,4,"R/U SHR(N)",temp); for (t=0; t<=TIME; t++) temp[t] = NETRF_Y[t]; plot_xy(2,0,2,"F/E SHR(N)", temp); for (t=0; t<=TIME; t++) temp[t] = NETRF_Z[t]; plot_xy(3,0,14,"COMPRESS (N)",temp); printf(" %s",input_fn); hold_screen(); return(0); ) /A********************************************************/ /* WRITE WRIST LOADS TO FILE ".lod" */ /***************'**'****************************************/ print_load() { FILE *fileout; char output_fn[9]; float ru_max,ru_avg,fe_max, fe_avg,comp_max,comp_avg ? int t,ch; 297 printf("\n WRITING .lod FILE \n") ; strcpy (output_fn, input__fn) ; strcat(output_fn,".LOD"); fileout = fopen(output_fn,"w"); fprintf(fileout," TIME ANG(rad) ANGLE(deg)")? fprintf(fileout," NETRF_X(N) NETRF_Y(N) NETRF_Z(N) \n"); for (t=0; t<=TIME; t++) { if ( ((ANG[t]*(180/PI)) >= LLIM_ANG) && ((ANG[t]*(180/PI)) <= ULIM_ANG) && (t <= (int)(cutoff * TIME)) ) fprintf(fileout," %i %0.3f %0.2f %i %i %i \ n", t,ANG[t],( ANG[t]*(180/PI) ),NETRF_X[t],NETRF_Y[t],NETRF_Z[t]); } fclose(fileout); return(0); }
/*********** END OF w load.c FILE ***********************/ APPENDIX F
298 299 FRIC.C file
#include
/**********************************************************/ /* COMPUTE FRICTIONAL WORK */ void w_compute_fric() { wrist_fric () ; norm_wrist_fric(); /* print_extwork() ; */ print_sumstats(); /* test_case(); */ /* print_test_case() ; */ }
/* FRICTIONAL WORK */ /*********************************************************/ float FRIC_3_WORK[700] ,FRIC_4_WORK[700] ,FRIC_7_WORK[700] ; wrist_f ric () 300
{ int t,ch,p,q,MAX_W; float FWORK,FMIN,FFRIC,INTERVAL_ANG,EXCURSION,ratio[2][8],radius[2 ] [8] ? /* ratio = RATIO OF MOMENT ARM (Y) TO MOMENT ARM OF FDS; MOMENT ARMS NORMALIZED TO FDS BECAUSE RADII OF CURVATURE ARE REPORTED FOR FDS IN ARMSTRONG AND CHAFFIN (1978) ; USE THIS RATIO TO ADJUST RADIUS OF CURVATURE FOR EACH TENDON; NORMALIZED TO MOMENT ARM OF FDS FROM BRAND */ /* 0 = extension; 1 = flexion */ ratio[0 [1] = 0.0175 / 0.0150 ; ratio[0 [2] = 0.0150 / 0.0150 ; ratio[0 [3] = 0.0125 / 0.0150 ; ratio[0 [4] SB 0.0190 / 0.0150 ; • ratio[0 [5] = (0.0150 + (0.0150 - 0.0120)) / 0.0150 9 = • ratio[0 [6] (0.0150 + (0.0150 - 0.0150)) / 0.0150 9 • ratio[0 [7] = (0.0150 + (0.0150 - 0.0085)) / 0.0150 9
= • ratio[1 [1] (0.0150 + (0.0150 - 0.0175)) / 0.0150 9 • ratio[1 [2] = (0.0150 + (0.0150 - 0.0150)) / 0.0150 9 SB • ratio[1 [3] (0.0150 + (0.0150 - 0.0125)) / 0.0150 9 • ratio[1 [4] = (0.0150 + (0.0150 - 0.0190)) / 0.0150 9 ratio[i; [5] = 0.0120 / 0.0150 ; ratio [i; [6] S= 0.0150 / 0.0150 ; ratio[1 (7] = 0.0035 / 0.0150 ;
/* radius = RADIUS OF CURVATURE (m) OF TENDONS AS FCT OF FLEX AND EXT; THESE VALUES ARE FROM ARMSTRONG AND CHAFFIN (1978) AND OCCUPATIONAL BIOMECHANICS (2ND ED) (1991) P. 244; THESE VALUES ARE FOR 95% MALE ONLY — THEY APPLY TO GIOVANNI; 0 = extension; 1 = flexion */ /* FOR 95% MALE WRIST THICKNESS: ext_rad = 0.0144; flex_rad =0.0205 */ radius[0][1] = ratio[0][1]*ext_rad; radius[1][1] = ratiofl][l]*flex_rad; radius[0][2] = ratio[0][2]*ext_rad; radius[1][2] = 301 ratio[1][2]*flex_rad; radius[0][3] = ratio[0][3]*ext_rad; radius[l][3] = ratio[1][3]*flex_rad; radius[0][4] = ratio[0][4]*ext_rad; radius[1][4] = ratio[1][4]*flex_rad; radius[0][5] = ratio[0][5]*ext_rad? radius[1][5] = ratio[1][5]*flex_rad; radius[0][6] = ratio[0][6]*ext_rad; radius[1][6] = ratio[1][6]*flex_rad; radius[0][7] = ratio[0][7]*ext_rad; radius[1][7] = ratio[l][7]*flex_rad; /* printf("\n HZ = %i vel = %i \n",HZ,vel); printf("\n ext_rad = %0.4f flex_rad = %0.4f \n\n",ext_rad,flex_rad);
printf(" ratio [][] \n"); for (p=0; p<=l; p++) { for (q=l; q<=7; q++) { printf(" %0.3f ",ratio[p][q]); } printf("\n"); } printf(" radius [][] \n"); for (p=0; p<=l; p++) { for (q=l; q<=7; q++) { printf(" %0.3f ", radius[p][q]); } printf("\n"); } hold_screen(); */ for (t=0; t<=TIME; t++) {
FRIC_3_W0RK[t] = 0.0; FRIC_4_W0RK[t] = 0.0; FRIC_7_WORK[t] = 0.0;
for (ch=l; ch<=7; ch++) {
/* FMIN IS THE TENDON FORCE DISTAL TO WRIST JOINT THAT GENERATES WRIST TORQUE AND FINGER FORCE; FMAX IS THE PROXIMAL FORCE THAT THE MUSCLE GENERATES AND TRANSMITS THROUGH THE TENDONS TO THE WRIST AND HAND 302
*/
/* if (t > 495) { printf(" t = %i: ch = %i: BETA = %0.4f: GAMMA = %0.4f: EMG = %i: GAIN « %0.4f\n", t,ch,BETA[ch],GAMMA[ch],EMG[ch][t],GAIN[ch] ); ) */ FMIN = (float)( cos(BETA[ch]) * cos(GAMMA[ch]) ) * (float)(EMG[ch][t]) * GAIN[ch] ;
if (Ch == 2) FMIN = EMGFORCE_FDS[t]; if (Ch == 3) FMIN = EMGFORCE_FDP[t]; if (Ch == 6) FMIN = EMGFORCE_EDC[t];
/* FRIC_FORCE IS THE COMPONENT OF FMAX THAT IS LOST TO FRICTION BETWEEN TENDONS AND ADJACENT STRUCTURES; FMAX = FMIN + FFRIC */
/* if (t > 495) ( printf(" t = %i: ch = %i: FMIN = %0.7f: mu = %0.4f: fabs(ANG) = %0.4f\n", t,ch,FMIN,mu,fabs((double)(ANG[t])) ); > */ FFRIC = FMIN * (float)( exp( (double)(mu) * fabs(ANG[t]) ) - 1.0 );
/* if (t > 495) { printf ('• FFRIC = %0.9f\n",FFRIC) ; } */ /* INTERVAL_ANG IS THE ANGLE (RAD) EXCURDED BETWEEN SAMPLE POINTS */ if (vel == 30) INTERVAL_ANG * (30.0 * (PI/180.0)) * (1.0 / (float) (HZ)) ; if (vel == 45) INTERVAL_ANG = (45.0 * (PI/180.0)) * (1.0 / (float)(HZ)) ;
/* if (t > 495) { printf(" t = %i: ch = %i: radius[0][ch] = %o.7f: 303
INTERVAL_ANG = %0.7f:\n", t, ch ,radius[0][ch],INTERVAL_ANG); } */ /* EXCURSION IS DISTANCE (m) TENDON TRAVELS BETWEEN SAMPLE POINTS */ if (ANG[t] <= 0.0) EXCURSION = radius[0][ch] * INTERVAL_ANG; if (ANG[t] > 0.0) EXCURSION = radius[1][ch] * INTERVAL_ANG; /* if (t > 495) { printf(" EXCURSION = %0.7f\n",EXCURSION); } */ /* FRICTIONAL WORK IS PRODUCT OF FRICTIONAL FORCE AND TENDON EXCURSION */
FWORK = FFRIC * EXCURSION; if ( (ch >= 1) && (ch <= 3) ) FRIC_3 WORK[t] = FRIC_3_WORK[t] + FWORK; if ( (Ch >= 1) && (ch <= 4) ) FRIC_4 WORK[t] = FRIC_4_WORK[t] + FWORK; FRI C_7_WORK [ t ] = FRI C_7_WORK [ t ] + FWORK;
/* if (t > 495) { printf (•' FRIC 7_WORK [ t] = %0. 9f\n" , FRIC_7_WORK[t] ); printf(" FRICJJ_WORK[t] = %0.9f\n\n",FRIC_3_WORK[t] ); ) */ ) /* end of ch for loop */ ) /* end of t for loop */
/* MULTIPLY FRICTIONAL WORK BY 1000X SO YOU CAN PLOT IT */ for (t=0; t<=TIME; t++) { FRIC_3 WORK(t] = 1000.0 * FRIC_3_WORK[t]; FRI C_4 ”~WORK [ t ] = 1000.0 * FRIC_4_WORK[t]; FRIC_7^WORK[t] = 1000.0 * FRIC_7_WORK[t]; > /* PLOT FRICTIONAL WORK */ MAX_W = plot_xy (1,0, 2, "F. WORK (J) " ,FRIC_3_WORK ); plot__xy(1,MAX_W,4,"",FRIC_4_WORK ) ; plot_xy(1,MAX_W,14,'"',FRIC_7_WORK ) ; 304
printf(" %s",input_fn); hold_screen();
/* NOW DIVIDE FRICTIONAL WORK BY 1000X TO GET BACK TO TRUE VALUES */ for (t=0; t<=TIME; t++) { FRIC_3_WORK[t] = FRIC 3_WORK[t] / 1000.0; FRIC_4_WORK[t] = FRIC~4_WORK[t] / 1000.0; FRIC_7_WORK[t] = FRIC_7_WORK[t] / 1000.0; ) return(0); }
/*********************************************************/ /* NORMALIZE FRICTIONAL WORK TO EXTERNAL WORK */ /*********************************************************/ f 1 oat ext_work [700], EXT_TOT_WORK [16]; float F_TOT3_WORK [ 16 ] , F_TOT4_WORK [ 16 ] , F__TOT7_WORK [ 16 ] ; f 1 oat F_TOT3_NORM [16], F_TOT4_NORM [16], F_TOT7_NORM [16]; norm_wrist_fric() { int t,ch,n,count; float MOMARM_TORQ, handle_force, handle_excursion, INTERV_ANG; if (grip == 0) MOMARM_TORQ = MOMARM_PINCH; if (grip == 1) MOMARM_TORQ = MOMARM_POWER;
/* INTERV_ANG IS THE ANGLE (RAD) EXCURDED BETWEEN SAMPLE POINTS */ if (vel == 30) INTERV_ANG = (30.0 * (PI/180.0)) * (1.0 / (float) (HZ)) ; if (vel == 45) INTERV_ANG = (45.0 * (PI/180.0)) * (1.0 / (float)(HZ)) ; for (t=0; t<=TIME; t++) {
/* handle_force IS THE FORCE EXERTED ON HANDLE TO GENERATE EXT TORQUE */ hand 1 e_force = TORQ [ t ] / MOMARM_TORQ;
/* handle_excursion IS THE DISTANCE THE HANDLE MOVES BET. SAMPLE POINTS */ handle_excursion = MOMARM_TORQ * INTERV_ANG;
/* ext_work IS THE WORK EXERTED ON HANDLE BET. SAMPLE POINTS */ ext_work[t] = handle_force * handle_excursion; 305
/**** printf ("TIME = %i TORQ = %0.4f MOMARM = %0.4f HANDLE FORCE = %0.4f\n", t,TORQ[t],MOMARM_TORQ,handle_force); printf(" INTERV_ANG = %0.4f HANDLE EXCURSION = %0.4f EXTWORK = %0.6f\n", INTERV_ANG,handle_excurs ion,ext_work[t]); ****/
} /* end of t for loop */ /* CALCULATE TOTAL EXTERNAL WORK DURING DIFFERENT ANGULAR INTERVALS */ EXT_TOT_WORK [ 1 ] = sum( ext_work, (-30.0*PI/180.0) , (60.0*PI/180.0) ) ; EXT_TOT_WORK [ 2 ] = sum ( ext_work, (-30.0*PI/180.0),(45.0*PI/180.0) ) ; EXT_TOT_WORK [ 3 ] = sum ( ext_work,(-30.0*PI/180.0),(30.0*PI/180.0) ); EXT_TOT_WORK [ 4 ] = sum ( ext_work,(-30.0*PI/180.0),(15.0*PI/180.0) ); EXT_TOT_WORK[5] = sum( ext_WOrk, (-30. 0*PI/180. 0) , (0. 0) )? EXT_TOT_WORK [ 6 ] = sum ( ext_work,(-45.0*PI/180.0),(60.0*PI/180.0) ); EXT_TOT_WORK [ 7 ] = sum ( ext_work, (-45.0*PI/180.0),(45.0*PI/180.0) ); EXT_TOT_WORK [ 8 ] = sum ( ext_work,(-45.0*PI/180.0),(30.0*PI/180.0) ); EXT_TOT_WORK [ 9 ] = sum ( ext_work, (-45.0*PI/180.0)#(15.0*PI/180. 0) ) ; EXT_TOT_WORK[10] = sum( ext_work,(-45.0*PI/180.0),(0.0) ) ? EXT_TOT_WORK [11] = sum( ext_work,(-60.0*PI/180.0),(60.0*PI/180.0) ); EXT_TOT_WORK [ 12 ] = sum( ext_work, (-60.0*PI/180.0) , (45.0*PI/180.0) ); EXT_TOT_WORK [ 13 ] = sum( ext_work,(-60.0*PI/180.0),(30.0*PI/180.0) ); EXT_TOT_WORK [ 14 ] = sum( ext_work, (-60.0*PI/180.0) , (15.0*PI/180.0) ); EXT_TOT_WORK[15] = sum( ext_Work, (-60.0*PI/180.0),(0.0) ); /* CALCULATE TOTAL FRICTIONAL WORK OF THREE CARPAL TUNNEL TENDONS */ F TOT3_WORK [ 1 ] = sum( 306
FRIC_3_WORK,(-30.0*PI/180.0),(60.0*PI/180.0) ); F_TOT3_WORK[2] = sum( FRIC 3_WORK,(-30.0*PI/180.0),(45.0*PI/180.0) ); F~TOT3_WORK[3] = sum( FRIC_3 WORK,(-30.0*PI/180.0),(30.0*PI/180.0) ); F_TOT3_WORK[4] = sum( FRIC_3_WORK,(-30.0*PI/180.0),(15.0*PI/180.0) )? F T0T3_W0RK[5] « sum( FRIC_3_WORK,(-30.0*PI/180.0),(0.0) ); F_TOT3_WORK[6] = sum( FRIC 3_WORK, (-45.0*PI/180.0) , (60.0*PI/180.0) ) ,* F~TOT3_WORK[ 7 ] = sum( FRIC_3_WORK,(-45.0*PI/180.0),(45.0*PI/180.0) ); F_TOT3_WORK[8] = sum( FRIC_3_WORK,(-45.0*PI/180.0),(30.0*PI/180.0) ); F__TOT3_WORK [ 9 ] = sum( FRIC_3_WORK,(-45.0*PI/180.0),(15.0*PI/180.0) ); F TOT3_WORK[10] ■ sum( FRIC_3_WORK,(-45.0*PI/180.0),(0.0) ) ; F_TOT3_WORK[11] = sum( FRIC 3_WORK,(-60.0*PI/180.0),(60.0*PI/180.0) ); F~TOT3_WORK[12] = sum( FRIC_3_WORK,(—60.0*PI/180.0),(45.0*Pl/180.0) ); F_TOT3_WORK[13] = sum( FRIC_3_WORK,(-60.0*PI/180.0),(30.0*PI/180.0) ); F_TOT3_WORK[14] = sum( FRIC_3_WORK,(-60.0*PI/180.0),(15.0*PI/180.0) ); F_TOT3_WORK[15] = sum( FRIC_3_WORK,(-60.0*PI/180.0),(0.0) ) ; /* CALCULATE TOTAL FRICTIONAL WORK OF FOUR FLEXOR TENDONS */ F_TOT4_WORK[1] = sum( FRIC_4_WORK,(-30.0*PI/180.0),(60.0*PI/180.0) ); F_TOT4_WORK(2] = sum( FRIC_4_WORK,(-30.0*PI/180.0),(45.0*PI/180.0) ); F_TOT4_WORK[3] = sum( FRIC_4_WORK,(-30.0*PI/180.0),(30.0*PI/180.0) ); F_TOT4_WORK(4] = sum( FRIC_4_WORK,(—30.0*PI/180.0),(15.0*PI/180.0) ); F_TOT4_WORK[5] = sum( FRIC_4_WORK,(-30.0*PI/180.0),(0.0) ) ? F_TOT4_WORK[6) = sum( FRIC_4_WORK,(—45.0*PI/180.0),(60.0*PI/180.0) ) ; F_TOT4_WORK[7] = sum( FRIC_4_WORK,(—45.0*PI/180.0),(45.0*PI/180.0) ); F_TOT4_WORK[8] = sum( 307
FRIC_4_WORK,(-45.0*PI/180.0),(30.0*PI/180.0) )I F_TOT4_WORK[9] = sum( FRIC_4_WORK, (-45. 0*PI/180. 0) , (15. 0*PI/180. 0) ) ,* F_TOT4_WORK[10] = sum( FRIC_4_WORK,(-45.0*PI/180.0),(0.0) ); F_TOT4_WORK[ll] = sum( FRIC_4_WORK,(—60.0*PI/180.0),(60.0*PI/180.0) ); F_TOT4_WORK[12] = sum( FRIC_4_WORK,(-60.0*PI/180.0),(45.0*PI/180.0) ),* F_TOT4_WORK[13] = sum( FRI C_4_WORK, (-60.0*PI/180.0), (30.0*PI/180.0) ) ; F_TOT4_WORK[14] = SUItl( FRIC_4_WORK,(-60.0*PI/180.0),(15.0*PI/180.0) ); F_TOT4_WORK[ 15 ] * sum( FRIC_4_WORK,(-60.0*PI/180.0),(0.0) )? /* CALCULATE TOTAL FRICTIONAL WORK OF ALL SEVEN TENDONS */ F__TOT7_WORK [ 1 ] = sum( FRIC_7_WORK, (-30.0*PI/180.0),(60.0*PI/180.0) ); F__TOT7_WORK [ 2 ] = sum( FRIC_7_WORK,(-30.0*PI/180.0),(45.0*PI/180.0) ); F_TOT7_WORK [ 3 ] = sum( FRIC_7_WORK,(-30.0*PI/180.0),(30.0*PI/180.0) ); F_TOT7_WORK [ 4 ] = sum ( FRIC_7_WORK,(—30.0*PI/180.0),(15.0*PI/180.0) ); F_TOT7_WORK[5] = sum( FRIC_7_WORK,(-30.0*PI/180.0),(0.0) ); F_TOT7_WORK [ 6 ] = sum( FRIC_7_WORK/ (—45. 0*PI/180. 0) , (60. 0*PI/180. 0) ) F_TOT7_WORK [ 7 ] = sum( FRIC_7_WORK,(-45.0*PI/180.0),(45.0*PI/180.0) ); F_TOT7_WORK[8] = sum( FRIC_7_WORK,(-45.0*PI/180.0),(30.0*PI/180.0) ); F_TOT7_WORK [ 9 ] * sum ( FRIC_7_WORK,(—45.0*PI/180.0),(15.0*PI/180.0) ); F_TOT7_WORK[10] = sum( FRIC_7_WORK,(-45.0*PI/180.0),(0.0) ); F__TOT7_WORK [11] = sum( FRIC_7_WORK,(-60.0*PI/180.0),(60*PI/180.0) ); F_TOT7_WORK[12] = sum( FRIC_7_WORK/(-60.0*PI/180.0),(45*PI/180.0) ); F_TOT7_WORK[13] = sum( FRIC_7_WORK/ (—60.0*PI/180.0),(30*PI/180.0) ) ; F_TOT7_WORK[14] = sum( FRIC_7_WORK/ (—60. 0*PI/180. 0) , (15*PI/180. 0) ) F_TOT7_WORK[15] = sum( FRIC_7_WORK,(-60.0*PI/180.0),(0.0) 308
) ; /* NORMALIZE FRICTIONAL WORK TO TOTAL EXTERNAL WORK */ for (n=l; n<=15; n++) F_TOT3_NORM[n] = F_TOT3_WORK[n] / EXTJTOT WORK[n] ; for (n=l; n<=15; n++) F_TOT4_NORM[n] = F_TOT4_WORK[n] / EXT_TOT_WORK[n] ; for (n=l; n<=15; n++) F_TOT7_NORM[n] = F_TOT7_WORK[n] / EXT_TOT__WORK[n] ; return(0)? } /******************************************************/ /* PRINT ".ext" FILE */ /* ARRAY OF ACTUAL EXTERNAL WORK PRODUCED BY WRIST */ /******************************************************/ print_extwork () { FILE *fileout; char output_fn[9]; int t , ch ; printf(»\n WRITING .ext FILE \n") ; strcpy (output_fn, input_fn) ; strcat(output_fn,".EXT"); fileout = fopen(output_fn,"w"); fprintf(fileout," TIME ANG(rad) ANG(deg) ACTUAL EXTERNAL WORK (N-m) \n") ; for (t=0; t<=TIME; t++) fprintf(fileout," %i %0.5f %0.2f %0.7f \n", t ,ANG[t],(ANG[t]*180.0/PI),ext_work[t3); fclose(fileout); return(0) ; )
/******************************************************/ /* PRINT ".sum" FILE */ /* COMPUTE R-SQUARE OF MEASURED AND PREDICTED TORQUE;*/ /* WRITE AVERAGE AND MAXIMUM COMPRESSION; */ /* WRITE FRICTIONAL WORK RESULTS; */ /******************************************************/ print_sumstats() { 309
FILE *fileout; char output_fn[9] , textl [6] ,text2[6] ,text3 [10]; int t , p, ch, numl, n, LLIMIT, ULIMIT, count; float R_SQ, LLIM, ULIM, avgtorq; f 1 oat ru_max, ru_avg, fe_max, fe_avg, comp_max, comp_avg; f 1 oat ru_max_norm, ru_avg_norm, fe_max_norm; float fe_avg_norm, comp_max_norm, comp_avg_norxn; float temp[700];
/* DEFINE INTEGRATION WINDOW AND LIMITS FOR CALCULATING AVERAGE COMPRESS */ if (grip == 0) { LLIM = LLIM_PN; ULIM = ULIM_PN; } else { LLIM = LLIM_PW; ULIM = ULIM_PW; } /* grip = 1 */ printf("\n WRITING .sum FILE \n"); strcpy (output_fn,input_fn); strcat (output_fn,11. SUM") ; fileout = fopen(output_fn, "w") ;
if (grip == 0) strcpy (textl, "PINCH") ; else strcpy (textl, "POWER") ; if (control == 0) strcpy(text2,"TORQ") ; else strcpy (text2, "FORCE") ; if (control == 0) { if (torq == 2) numl = 2; if (torq == 4) numl = 4y if (torq == 8) numl = 8; } else { if (force == 7) numl = 7; else numl =14; ) if (electrodes == 0) strcpy(text3;"SURFACE") ; else strcpy (text3 , "FINE WIRE");
fprintf (fileout," FILE = %s \n" ,output_fn); fprintf (fileout," %s; %i DEG/SEC; CONSTANT %s; %i N-m; %S ELECTRODES ; \n", textl, ve l , text2, numl, text3) ;
fprintf (fileout," USED GARY'S COMPUTER; REDUCED TORQUE BY 0.70 V \n\n") ;
fprintf (fileout," mu = %0.4f \n\n",mu) ;
fprintf (fileout," PARAMETERS CALCULATED WITHIN %0.0f AND 310
%0.0f DEG \n\n", LLIM_ANG,ULIM_ANG)7
fprintf(fileout," INTEGRATION WINDOW BETWEEN %0.0f AND %0.0f DEG \n\n", LLIM,ULIM);
fprintf(fileout, " # OF MUSCLES IN TORQ EQUATION = %i \n\n",muscles)7
fprintf(fileout," FINAL GAIN IN ALL SEVEN CHANNELS (N/cmA2) \n"); for (ch=l; ch<=7; ch++) fprintf(fileout," %0.lf ", (GAIN[ch] * 1000.0) ); fprintf(fileout,"\n\n"); fprintf(fileout," PINCH RATIOS: FDS = %0.2f FDP = %0.2f EDC = %0.2f \n", fds_pn,fdp_pn,edc_pn);
fprintf(fileout," POWER RATIOS: FDS = %0.2f FDP = %0.2f EDC = %0.2f \n", fds_pw,fdp_pw,edc_pw);
fprintf(fileout,"\n\n DIST. OF LENGTH-STRENGTH MODULATION = %i\n",ls_norm); fprintf(fileout," 0 = SYM. NORMAL DIST; 1 = SKEWED EXT. VALUE DIST;\n");
if (ls_norm ===0) {
fprintf(fileout, "\n LENGTH-STRENGTH PARAMETERS FOR PINCH (MEAN & S.D.)\n"); for (ch=l; ch<=7; ch++) { fprintf(fileout," %0.1f %0.0f " ,mean[0][ch],sigma[0][ch]); if (ch == 4) fprintf(fileout,"\n"); ) fprintf(fileout,"\n"); fprintf(fileout,
"\n LENGTH-STRENGTH PARAMETERS FOR POWER (MEAN & S.D.)\n")7 for (ch=l7 ch<=7; ch++) { fprintf(fileout," %0.1f %0.0f ",mean[l][ch],sigma[l][ch]); if (ch == 4) fprintf(fileout,"\n"); } 311
fprintf(fileout,"\n\n");
} /* if ls_norm == 0 */
else {
fprintf(fileout, 11 \n LENGTH-STRENGTH PARAMETERS FOR PINCH (mode & alpha)\n"); for (ch=l; ch<=7; ch++) { fprintf(fileout," %0.1f %0.4f ",mode[0][ch],alpha[0][ch]) ; if (ch == 4) fprintf(fileout,"\n"); } fprintf(fileout,"\n");
fprintf(fileout, "\n LENGTH-STRENGTH PARAMETERS FOR POWER (mode & alpha)\n"); for (ch=l; ch<=7? ch++) { fprintf(fileout," %0.1f %0.4f ",mode[l][ch],alpha[l][ch]); if (ch == 4) fprintf (fileout, "\n11) ; } fprintf(fileout,"\n\n");
} /* if ls_norm == 1 */ /****** PRINT R-SQUARE RESULTS ****************************/ /* PASS ANGLE IN RADIANS TO correlation FCT BEC. ANG[t] IS NOW IN RAD */
fprintf(fileout,"\n R-SQUARE RESULTS: \n") ;
R_SQ = correlation(TORQ,INT_TORQX,(-30.0*PI/180.0),(ULIM_ANG*PI/180 . 0)) ; fprintf(fileout," R_SQ BETWEEN -30 AND %0.0f DEGREES = %0.3f \n", ULIM_ANG,R_SQ);
R_SQ = correlation(TORQ,INT_TORQX,(-30.0*PI/180.0),(45.0*PI/180.0))
fprintf(fileout," R_SQ BETWEEN -30 AND 45 DEGREES ■ %0.3f \n",R_SQ); R_SQ = correlation(TORQ,INT_TORQX,(-30.0*PI/180.0) , (30.0*PI/180.0)) 312
fprintf(fileout," R_SQ BETWEEN -30 AND 30 DEGREES = %0.3f \n",R_SQ);
R_SQ = correlation(TORQ,INT_TORQX,(-30.0*PI/180.0),(15.0*PI/180.0) ) fprintf(fileout," R_SQ BETWEEN -30 AND 15 DEGREES = %0.3f \n",R_SQ);
R_SQ = correlation(TORQ,INTJTORQX, (-30.0*PI/180.0),0.0); fprintf(fileout," R_SQ BETWEEN -30 AND 0 DEGREES = %0.3f \n\n",R_SQ);
R_SQ = correlation(TORQ,INT_TORQX,(-45.0*PI/180.0),(ULIM_ANG*PI/180 - 0 )) ; fprintf(fileout," R_SQ BETWEEN -45 AND %0.0f DEGREES = %0.3f \n", ULIM_ANG,R_SQ);
R_SQ = correlation(TORQ,INTJTORQX,(-45.0*PI/180.0),(45.0*PI/180.0))
fprintf(fileout," R_SQ BETWEEN -45 AND 45 DEGREES - %0.3f \n",R_SQ);
R_SQ = correlation(TORQ,INT_TORQX,(-45.0*PI/180.0),(30.0*PI/180.0))
fprintf(fileout," R_SQ BETWEEN -45 AND 30 DEGREES = %0.3f \n",R_SQ);
R_SQ = correlation(TORQ,INT_TORQX,(-45.0*PI/180.0) , (15.0*PI/180.0) )
fprintf(fileout," R_SQ BETWEEN -45 AND 15 DEGREES = %0.3f \n",R_SQ);
R_SQ = correlation(TORQ,INT_TORQX, (-45.0*PI/180.0),0.0); fprintf (fileout," R_SQ BETWEEN -45 AND 0 DEGREES = %0.3f \n\n",R_SQ);
R_SQ = correlation(TORQ,INT_TORQX,(-60.0*PI/180.0),(ULIM_ANG*PI/180 .0)); fprintf(fileout," R_SQ BETWEEN -60 AND %0.0f DEGREES = 313 %0.3f \n", ULIM_ANG,R_SQ) ;
R_SQ = correlation(TORQ,INTJTORQX,(-60.0*PI/180.0),(45.0*PI/180.0))
fprintf (fileout," R_SQ BETWEEN -60 AND 45 DEGREES = %0.3f \n",R_SQ); R_SQ = correlation(TORQ,INTJTORQX,(-60.0*PI/180.0),(30.0*PI/180.0))
fprintf (fileout," R_SQ BETWEEN -60 AND 30 DEGREES = %0.3f \n",R_SQ);
R_SQ = correlation(TORQ,INT_TORQX,(-60.0*PI/180.0),(15.0*PI/180.0))
fprintf (fileout," R_SQ BETWEEN -60 AND 15 DEGREES = %0.3f \n",R_SQ); R_SQ = correlation(TORQ,INTJTORQX,(-60.0*PI/180.0),0.0); fprintf (fileout," R_SQ BETWEEN -60 AND 0 DEGREES = %0.3f \n\n",R_SQ); /* PRINT WRIST LOAD RESULTS *****************************/ /* PASS ANGLE IN RADIANS TO average FCT BECAUSE ANG[t] IS NOW IN RADIANS */
for (t=0; t<=TIME; t++) temp[t] = NETRF_X[t] ; rujmax == max (temp) ; ru_avg = average(temp, (LLIM*PI/180.0), (ULIM*PI/180.0) ) ; for (t=0; t<=TIME; t++) temp[t] = NETRF_Y[t]; fe_max = max(temp); fe_avg = average(temp, (LLIM*PI/180.0), (ULIM*PI/180.0) ) ? for (t=0; t<=TIME; t++) temp[t] = NETRF_Z[t]? comp_max = max(temp); comp_avg * average(temp, (LLIM*PI/180.0), (ULIM*PI/180.0) ) ; fprintf (fileout, "\n ABSOLUTE WRIST LOADS COMPUTED"); fprintf(fileout," BETWEEN %0.0f AND %0.0f DEG: \n",LLIM,ULIM) ; fprintf (fileout," MAX RU_SHR = %0.2f N; AVERAGE RU_SHR = %0.2f N \n", 314
ru_max,ru_avg); fprintf(fileout," MAX FE_SHR = %0.2f N; AVERAGE FE_SHR = %0.2f N \n", fe_max,fe_avg); fprintf(fileout," MAX COMPRS = %0.2f N; AVERAGE COMPRS = %0.2f N \n", comp_max,coxnp_avg) ;
avgtorq = average(TORQ, (LLIM*PI/180.0), (ULIM*PI/180.0) ); ru_max_norm = rujmax / avgtorq; ru_avg_norm = ru_avg / avgtorq; . fe_xnax_norm = fe__max / avgtorq; fe_avg_norm = fe_avg / avgtorq; coinp_max_nonn = comp_max / avgtorq; comp_avg_norm = comp_avg / avgtorq;
fprintf(fileout,"\n AVERAGE TORQUE (N-m) BET."); fprintf(fileout," %0.0f AND %0.0f DEG: %0.2f \n",LLIM,ULIM,avgtorq);
fprintf(fileout,"\n NORMALIZED WRIST LOADS (N load/N-m torque) COMPUTED"); fprintf(fileout," BETWEEN %0.0f AND %0.0f DEG: \n",LLIM,ULIM) ; fprintf(fileout," MAX RU_SHR = %0.2f N; AVERAGE RU_SHR = %0.2f N \n", ru_max_norm,ru_avg_norm); fprintf(fileout," MAX FE_SHR = %0.2f N; AVERAGE FE_SHR = %0.2f N \n", fe_max_norm,fe_avg_norm); fprintf(fileout," MAX COMPRS = %0.2f N; AVERAGE COMPRS = %0.2f N \n\n", comp_max_nonn, comp_avg_norm) ; /** PRINT EXTERNAL WORK RESULTS *************************/
fprintf(fileout,"\n CHECK ON EXTERNAL WORK: \n"); fprintf(fileout," EXTERNAL WORK BETWEEN -60 AND 30 DEG « %0.3f N-m\n", EXT_TOT_WORK(13]); fprintf(fileout," EXTERNAL WORK BETWEEN -45 AND 30 DEG - %0.3f N-m\n", EXT_TOT_WORK[8]); fprintf(fileout," EXTERNAL WORK BETWEEN -45 AND 15 DEG = %0.3f N-m\n", EXT_TOT_WORK[9]);
/* PRINT FRICTIONAL WORK RESULTS ***********************/ 315 fprintf (fileout, "\n\n TOTAL NORM. FRIC. WORK FOR FCR, FDS, &FDP TENDONS: \n") ; LLIMIT = -30? ULIMIT = 60; count = 0; for (n=l; n<=15; n++) { if (count >= 5) { LLIMIT « LLIMIT - 15; ULIMIT = 60; count = 0; fprintf (fileout, "\n") ; } fprintf (fileout," %i TO %i d EG: %0.8f N-m\n", LLIMIT, ULIMIT, F TOT3_N0RM [ n ] ) ? ULIMIT = ULIMIT - 15; ' count = count + 1 ; } /* end of n for loop */ fprintf (fileout, "\n TOTAL NORM. FRIC. WORK FOR FCR, FDS, FDP , &FCU TENDONS: \n") ; LLIMIT = -30? ULIMIT = 60; count = 0; for (n=l; n<=15; n++) { if (count >= 5) { LLIMIT = LLIMIT - 15; ULIMIT = 60; count = 0? fprintf (fileout, "\n") ; } fprintf (fileout," %i TO %i d EG: %0.8f N-m\n", LLIMIT, ULIMIT, F TOT4_N0RM [ n ] ) ? ULIMIT = ULIMIT - 15; ' count = count + 1 ; } /* end of n for loop */ fprintf (fileout, "\n TOTAL NORM. FRIC. WORK FOR ALL SEVEN TENDONS :\n") ; LLIMIT = -30? ULIMIT = 60; count = 0; for (n=l; n<=15; n++) { if (count >=5) { LLIMIT = LLIMIT - 15; ULIMIT = 60; count = 0? fprintf (fileout, "\n"); } fprintf (fileout," %i TO %i d EG: %0.8f N-m\n", LLIMIT,ULIMIT,F TOT7_NORM(n] ) ; ULIMIT * ULIMIT - 15; " count « count + 1 ? } /* end of n for loop */
/**** fprintf (fileout," TIME ANG(r a d ) ANGLE(DEG) ") ; fprintf (fileout," FRIC_3_W0RK FRIC 4_WORK FRI C_7_W0RK\n ") ; for (t=0; t<=TIME; t++) { if ( ((ANG[t] * 180/PI) >= LLIM_ANG) && ( (ANG[t] * 180/PI) 316
<= ULIM_ANG) && (t <= (int)(cutoff * TIME)) ) fprintf(fileout," %i %0.4f %0.3f %0.8f %0.8f %0.8f\n", t , ANG[t] , (ANG[ t] *18O/PI) , FRIC_3_WORK[t] , FRIC_4_WORK[t] , FRIC_ 7_W0RK[t]); } ****/ fclose(fileout); return(0); }
/********************************************************/ /* TEST CASE: */ /* THIS TEST CASE COMPUTES THE FRICTIONAL WORK (ACTUAL AND NORMALIZED) */ /* COMPUTED FROM A SIMPLE ONE TENDON MODEL (WITHOUT COACTIVATION)? */ /* COMPARE THESE RESULTS WITH RESULTS FROM THE EXPANDED 7 TENDON MODEL */ /* (WITH COACTIVATION) */ /******************************************************/ float t_tot_fric,t_totb_fric,t_norm_fric,t_nonnb_fric; test_case() { int t , ch; float T_INTERV_ANG, moment_arm, t_f orce, t_excursion, t_f ric_f orce, t_f ric_work;
/* INTERV_ANG IS THE ANGLE (RAD) EXCURDED BETWEEN SAMPLE POINTS */ if (vel == 30) T_INTERV_ANG = (30.0 * (PI/180.0)) * (1.0 / (float)(HZ)) ; if (vel — 45) T_INTERV_ANG = (45.0 * (PI/180.0)) * (1.0 / (float)(HZ)) ; /* moxnent_arxn IS THE AVERAGE MOMENT ARM OF THE 4 FLEXOR MUSCLES */ moment_arm - 0.016; moment arm = moment arm * coef; 317
t_tot_fric = 0.0; t_totb_fric = 0.0; for (t=0; t<=TIME; t++) { t_force = T0RQ[t] / moment_arm; if ( ANG[t] <= 0.0) t_excursion = ext_rad * T_INTERV_ANG; else t_excursion = flex_rad * T_INTERV_ANG;
t_fric_force = t_force*(float)( exp( (double)(mu)*fabs(ANG[t]) ) - 1.0 ); t_fric_work = t_fric_force * t_excursion;
if ( ((ANG[t]*(180/PI)) > -60.0) && ((ANG[t]*(180/PI)) < 30.0) ) t_tot_fric = t_tot_fric + t_fric_work; if ( ((ANG[t]*(180/PI)) > -30.0) && ((ANG[t]*(180/PI)) < 30.0) ) t_totb_fric = t_totb_fric + t_fric_work;
} /* end of t for loop */
/* NORMALIZE TOTAL TENDON FRICTIONAL WORK TO EXTERNAL WORK */ t_norm_fric = t_tot_fric / EXT_TOT_WORK[13]; t_normb_fric = t_totb_fric / EXT_TOT_WORK[3J; return(0); }
/I*********************************************************/ /* WRITE TEST CASE RESULTS TO FILE ".tst" */ /*********************************************************/ print_test_case() { FILE *fileout; char output_fn[9]; printf("\n WRITING .tst FILE \n") ; strcpy(output_fn,input_fn) ; strcat(output_fn,".TST”) ; fileout = fopen(output_fn, "w") ; fprintf(fileout," ONE TENDON: TOTAL FRIC. WORK COMPUTED BET. -60 AND 30* DEG\n") ; 318
fprintf(fileout," t_tot_fric = %0.81f \n\n",t_tot_fric);
fprintf(fileout," ONE TENDON: TOTAL FRIC. WORK COMPUTED BET. -30 AND 30 DEG\n"); fprintf(fileout," t_totb_fric = %0.8lf \n\n",t_totb_fric);
fprintf(fileout," ACTUAL TOTAL EXT. WORK COMPUTED BET. -60 AND 30 DEG\n"); fprintf(fileout," EXT_TOT_WORK = %0.3f N-m \n\n",EXT_TOT_WORK[13]);
fprintf(fileout," ACTUAL TOTAL EXT. WORK COMPUTED BET. -30 AND 30 DEG\n"); fprintf(fileout," EXT_TOT_WORK = %0.3f N-m \n\n",EXT_TOT_WORK[ 3 ]) ;
fprintf(fileout," ONE TENDON: NORMALIZED FRIC. WORK BET. -60 AND 30 DEG\n"); fprintf(fileout," t_norm_fric = %0.8lf \n\n",t_norm_fric);
fprintf(fileout," ONE TENDON: NORMALIZED FRIC. WORK BET. -30 AND 30 DEG\n"); fprintf(fileout," t_normb_fric = %0.81f \n\n",t_normb_fric);
fclose(fileout); return (0); )
/************** e n d OF w fric.C FILE *********************/ APPENDIX G
319 320
STAT.C file
#include
/* printf("\n CORR FCT: LOWER = %0.1f UPPER ■ %0.1f \n",LOWER,UPPER);*/ AVG_X = average(X,LOWER,UPPER); AVG_Y = average(Y,LOWER,UPPER);
/* printf("\n CORR FCT: AVG_X = %0.2f AVG_Y = %0.2f \n",AVG_X,AVG_Y);*/
for (t=0 ; t<=TIME'; t++) {
if ( (ANG[t] >= LOWER) && (ANG[t] <= UPPER) && (t <= (int)(cutoff * TIME)) ) { Sxx = SXX + (X[t) - AVG_X) * (X[t] - AVG_X); Syy = Syy + (Y[t] - AVG_Y) * (Y[t] - AVG_Y); Sxy = Sxy + (X[t] - AVG_X) * (Y[t] - AVG_Y); ) ) /* end of t for loop */ if ( (Sxx * Syy) > 0.0 ) R_2 = (Sxy * Sxy) / (Sxx * Syy); if ( fabs(R_2) > 1.0 ) R_2 = -1.0;
/* printf("\n CORR FCT: R-SQUARE « %0.2f \n",R_2); */ return(R_2); } 321 /************************************* ************** *******/ /* COMPUTE AVERAGE VALUE OF IMPORTED VARIABLE */ /**********************************************************/ float average(A, LOWER, UPPER) float A[ ] , LOWER, UPPER; { int t,count=0; float SUM=0.0,AVG;
/* printf("\n AVG FCT; LOWER = %0.lf UPPER = %0.1f \n", LOWER, UPPER) ; */
for (t— 0 ; t
return(AVG); )
/A*********************************************************/ /* COMPUTE INTEGRAL VALUE OF IMPORTED VARIABLE */ /**********************************************************/ float integral(A, LOWER, UPPER) float A [ ], LOWER, UPPER; ( int t; float INTEGRAL=0.0;
for (t=0 ; t