- Email: [email protected]
Sensitivity of muscle force estimates in human gait to variations in muscle-tendon properties
Track 2. Musculoskeletal Mechanics-Joint ISB Track 45.7±22.5 °, ant./sup, translation -0.6±2.0/0.5±2.3 mm) a significant difference (p <0.05) was found in the maximum abduction and external rotation angles and in anterior/superior humeral translation at maximum abduction. Tendontransfer-2 restored glenohumeral kinematics closer to the intact condition. Performing a pectoralis major tendon transfer in subscapularis deficient shoulders partially restores intact glenohumeral kinematics. One reason for the greater effect of tendon-transfer-2 could be that a pectoralis major tendon transfer underneath the conjoined tendon more closely resembles the line of action of the subscapularis. From a biomechanical standpoint this surgical technique is preferable when performing a pectoralis major tendon transfer in subscapularis deficient shoulders. References [1] Resch. JBJS 2000; 82: 372-382. [2] Wirth. JBJS 1997; 79: 722-731. 6342 We, 12:00-12:15 (P30) Shape memory alloy staple for correction in adolescent idiopathic scoliosis K. Saidane 1, C.-E. Aubin 1,2. 1Department of Mechanical Engineering, Ecole
Polytechnique, Montreal, Canada, 2Biomechanical Modeling and Computer Assisted Surgery Lab, Research Center, Sainte-Justine Hospital, Montreal, Canada. In order to develop a smart and minimal invasive system for vertebral correction based on the control of growth of the vertebrae for children with progressive scoliosis and whose osseous growth is not completed. This therapeutic tool for the correction of the immature vertebrae will exploit the unique properties of SMA staple. Our hypothesis is that the forces generated by this system will induce a modulation and a progressive correction of the bone, according to the direction of the loads. For SMA device the optimal design has been difficult due to lack of appropriate design tool. In this study we developed a SMA staple model using unified thermodynamic constitutive law. An elastic predictor-transformation corrector return mapping algorithm has been adopted. This algorithm is divided into: 1. A thermo elastic predictor step to preview the direction of a strain and a stress variation. 2. A transformation corrector step to compute transformation strain, correcting stress value and deduce tangent stiffness tensor for each load and temperature increment. The model was implemented and tested successfully in UMAT in the commercial FEA software. 7131 We, 12:15-12:30 (P30) Evaluation of carpal tunnel mechanics using a three-dimensional computerized model J.P.M. Mogk, P.J. Keir. School of Kinesiology & Health Science, York
University, Toronto, Canada A three-dimensional model of the wrist and carpal tunnel (CT) is being developed to predict posture-related changes in CT dimensions and evaluate CT dynamics as a mechanism in median nerve trauma. Magnetic resonance (MR) images of a neutral wrist were used to reconstruct the carpal tunnel as a modified cylinder consisting of two surfaces; one for the carpal arch and one for the transverse carpal ligament (TCL). Three-dimensional carpal bone positions were also determined from the MR images with the wrist at 300 flexion and 300 extension, and the changes between the two positions were used to predict CT dimension changes. While individual carpal bone motions effectively predicted posture-related changes in size and shape of the carpal arch surface, the motion of the TCL was not adequate, indicating the need to incorporate material properties of the ligament to improve estimates of tunnel volume. A series of springs was used to mimic the elastic properties of the TCL surface with the stiffness and resting length of each spring being adjustable. While incorporation of the spring surface resulted in the TCL tightening as the tunnel widened, its response to narrowing was dependent on the posture in which the spring surface was generated. Results indicate that the initial spring parameters are of the utmost importance to ligament performance, particularly the resting or start length of the springs. Also, current spring alignment accounts only for transverse stretching of the TCL surface, and thus may require additional springs arranged longitudinally and/or obliquely to capture changes in ligament length resulting from movement between the proximal and distal carpal rows. A cadaveric study has been initiated to determine the physiological properties of the TCL and flexor retinaculum, specifically to determine spring stiffness and resting length parameters, as well as spatial configuration of the spring surface. The addition of empirical ligament property data will also assist in modeling the effects of normal forces applied to the TCL by the finger flexor tendons as they pass through the carpal tunnel. Funded by NSERC.
2.7. Musculoskeletal Modelling Meets Muscle Physiology
$51
5282 We, 14:00-14:15 (P33) A musculoskeletal model for the determination of muscle forces and joint reactions in human legs during jumps W. Blajer, K. Dziewiecki, Z. Mazur. Institute efApplied Mechanics, Technical
University of Radom, Poland A musculoskeletal human model is presented, build as a planar kinematic structure consisting of ten rigid segments branching from the pelvis in open chain linkages. It is aimed at analyzing human movements such as standing long jumps, vertical jumps and jumps down from a height. Since the attention is focused on lower limb motion control and Ioadings, only the motions in the hip, knee and ankle joints are modeled as enforced by muscle forces applied to the tendon attachment points, and the other (upper body part) joint motions are actuated by means of torques representing the muscle action. The details relating the assumptions for the physical model and its identification will be reported. Then, a projection method for the derivation of dynamic equations in independent coordinates of the musculoskeletal model will be described, involving a novel effective scheme for the determination of reaction forces in the leg joints. The reaction forces from the ground during the support phases of the jumps can also be obtained after subjecting the dynamic equations of the flying body model to the ground constraints. Using the developed mathematical model, based on measured motion characteristics during analyzed jumps, the inverse dynamics solution will result in predicted time-variations of the joint torques, and in the hip, knee and ankle joints the respective torques can be shared on particular muscle forces following an optimization procedure. The latter problem is associated with control redundancy, some of the muscles contribute to torques in more then one joint and appropriate muscle force descriptions need to be applied. Apart from understanding of how the muscle excitations are coordinated during the jumps, the internal loads in the leg joints can be evaluated, which may be especially high in the upward propulsion and landing phases. Some results of numerical simulations will be reported. 5294 We, 14:15-14:30 (P33) Sensitivity of muscle force estimates in human gait to variations in muscle-tendon properties C. Redl 1, M. Gfoehler1, M.G. Pandy2. 1Institute for Engineering Design and
Logistics Engineering, Vienna University of Technology, Vienna, Austria, 2Department of Mechanical and Manufacturing Engineering, University of Melbourne, Victoria, Australia The objective of this study was to determine the sensitivity of muscle force estimates to changes in some of the parameters that are commonly used to describe models of muscle-tendon actuation. The body was modeled as a 10-segment, 23 degree-of-freedom skeleton, actuated by 54 musculotendinous units [1]. Static optimization theory was used to calculate the time histories of leg-muscle forces for one cycle of normal walking [1]. The sensitivity analysis was performed on three musculotendon parameters: optimal muscle-fiber length, muscle physiological cross-sectional area (PCSA), and tendon rest length. The muscles selected for the analysis were posterior gluteus medius/minimus, vasti, soleus, and sartorius. Each parameter was perturbed from its nominal value [2], and the optimization problem was solved to determine the relative influence of each parameter on the calculated values of muscle force. The sensitivity of muscle force to changes in muscle properties was quantified by computing an integrated sensitivity ratio, which was found by integrating values of an instantaneous sensitivity ratio over the simulated gait cycle. The instantaneous sensitivity ratio was defined as the ratio of the difference between the nominal and perturbed values of muscle force to the difference between the nominal and perturbed values of a selected parameter (e.g., muscle-fiber length). The results showed that muscle force estimates for walking are most sensitive to changes in tendon rest length and least sensitive to changes in muscle PCSA. For soleus, the integrated sensitivity ratios for tendon rest length were an order of magnitude greater than those for muscle-fiber length and PCSA. For vasti, the integrated sensitivity ratios for tendon rest length were twice as large as those for muscle-fiber length and nearly an order of magnitude greater than those for PCSA. The results emphasize the importance of obtaining accurate estimates of tendon rest length and muscle-fiber length in musculoskeletal modeling. References [1] Anderson FC, Pandy MG. J Biomech Eng 2001; 123: 381-390. [2] Anderson FC, Pandy MG. J Biomech 2001; 34: 153-161.
Polytechnique, Montreal, Canada, 2Biomechanical Modeling and Computer Assisted Surgery Lab, Research Center, Sainte-Justine Hospital, Montreal, Canada. In order to develop a smart and minimal invasive system for vertebral correction based on the control of growth of the vertebrae for children with progressive scoliosis and whose osseous growth is not completed. This therapeutic tool for the correction of the immature vertebrae will exploit the unique properties of SMA staple. Our hypothesis is that the forces generated by this system will induce a modulation and a progressive correction of the bone, according to the direction of the loads. For SMA device the optimal design has been difficult due to lack of appropriate design tool. In this study we developed a SMA staple model using unified thermodynamic constitutive law. An elastic predictor-transformation corrector return mapping algorithm has been adopted. This algorithm is divided into: 1. A thermo elastic predictor step to preview the direction of a strain and a stress variation. 2. A transformation corrector step to compute transformation strain, correcting stress value and deduce tangent stiffness tensor for each load and temperature increment. The model was implemented and tested successfully in UMAT in the commercial FEA software. 7131 We, 12:15-12:30 (P30) Evaluation of carpal tunnel mechanics using a three-dimensional computerized model J.P.M. Mogk, P.J. Keir. School of Kinesiology & Health Science, York
University, Toronto, Canada A three-dimensional model of the wrist and carpal tunnel (CT) is being developed to predict posture-related changes in CT dimensions and evaluate CT dynamics as a mechanism in median nerve trauma. Magnetic resonance (MR) images of a neutral wrist were used to reconstruct the carpal tunnel as a modified cylinder consisting of two surfaces; one for the carpal arch and one for the transverse carpal ligament (TCL). Three-dimensional carpal bone positions were also determined from the MR images with the wrist at 300 flexion and 300 extension, and the changes between the two positions were used to predict CT dimension changes. While individual carpal bone motions effectively predicted posture-related changes in size and shape of the carpal arch surface, the motion of the TCL was not adequate, indicating the need to incorporate material properties of the ligament to improve estimates of tunnel volume. A series of springs was used to mimic the elastic properties of the TCL surface with the stiffness and resting length of each spring being adjustable. While incorporation of the spring surface resulted in the TCL tightening as the tunnel widened, its response to narrowing was dependent on the posture in which the spring surface was generated. Results indicate that the initial spring parameters are of the utmost importance to ligament performance, particularly the resting or start length of the springs. Also, current spring alignment accounts only for transverse stretching of the TCL surface, and thus may require additional springs arranged longitudinally and/or obliquely to capture changes in ligament length resulting from movement between the proximal and distal carpal rows. A cadaveric study has been initiated to determine the physiological properties of the TCL and flexor retinaculum, specifically to determine spring stiffness and resting length parameters, as well as spatial configuration of the spring surface. The addition of empirical ligament property data will also assist in modeling the effects of normal forces applied to the TCL by the finger flexor tendons as they pass through the carpal tunnel. Funded by NSERC.
2.7. Musculoskeletal Modelling Meets Muscle Physiology
$51
5282 We, 14:00-14:15 (P33) A musculoskeletal model for the determination of muscle forces and joint reactions in human legs during jumps W. Blajer, K. Dziewiecki, Z. Mazur. Institute efApplied Mechanics, Technical
University of Radom, Poland A musculoskeletal human model is presented, build as a planar kinematic structure consisting of ten rigid segments branching from the pelvis in open chain linkages. It is aimed at analyzing human movements such as standing long jumps, vertical jumps and jumps down from a height. Since the attention is focused on lower limb motion control and Ioadings, only the motions in the hip, knee and ankle joints are modeled as enforced by muscle forces applied to the tendon attachment points, and the other (upper body part) joint motions are actuated by means of torques representing the muscle action. The details relating the assumptions for the physical model and its identification will be reported. Then, a projection method for the derivation of dynamic equations in independent coordinates of the musculoskeletal model will be described, involving a novel effective scheme for the determination of reaction forces in the leg joints. The reaction forces from the ground during the support phases of the jumps can also be obtained after subjecting the dynamic equations of the flying body model to the ground constraints. Using the developed mathematical model, based on measured motion characteristics during analyzed jumps, the inverse dynamics solution will result in predicted time-variations of the joint torques, and in the hip, knee and ankle joints the respective torques can be shared on particular muscle forces following an optimization procedure. The latter problem is associated with control redundancy, some of the muscles contribute to torques in more then one joint and appropriate muscle force descriptions need to be applied. Apart from understanding of how the muscle excitations are coordinated during the jumps, the internal loads in the leg joints can be evaluated, which may be especially high in the upward propulsion and landing phases. Some results of numerical simulations will be reported. 5294 We, 14:15-14:30 (P33) Sensitivity of muscle force estimates in human gait to variations in muscle-tendon properties C. Redl 1, M. Gfoehler1, M.G. Pandy2. 1Institute for Engineering Design and
Logistics Engineering, Vienna University of Technology, Vienna, Austria, 2Department of Mechanical and Manufacturing Engineering, University of Melbourne, Victoria, Australia The objective of this study was to determine the sensitivity of muscle force estimates to changes in some of the parameters that are commonly used to describe models of muscle-tendon actuation. The body was modeled as a 10-segment, 23 degree-of-freedom skeleton, actuated by 54 musculotendinous units [1]. Static optimization theory was used to calculate the time histories of leg-muscle forces for one cycle of normal walking [1]. The sensitivity analysis was performed on three musculotendon parameters: optimal muscle-fiber length, muscle physiological cross-sectional area (PCSA), and tendon rest length. The muscles selected for the analysis were posterior gluteus medius/minimus, vasti, soleus, and sartorius. Each parameter was perturbed from its nominal value [2], and the optimization problem was solved to determine the relative influence of each parameter on the calculated values of muscle force. The sensitivity of muscle force to changes in muscle properties was quantified by computing an integrated sensitivity ratio, which was found by integrating values of an instantaneous sensitivity ratio over the simulated gait cycle. The instantaneous sensitivity ratio was defined as the ratio of the difference between the nominal and perturbed values of muscle force to the difference between the nominal and perturbed values of a selected parameter (e.g., muscle-fiber length). The results showed that muscle force estimates for walking are most sensitive to changes in tendon rest length and least sensitive to changes in muscle PCSA. For soleus, the integrated sensitivity ratios for tendon rest length were an order of magnitude greater than those for muscle-fiber length and PCSA. For vasti, the integrated sensitivity ratios for tendon rest length were twice as large as those for muscle-fiber length and nearly an order of magnitude greater than those for PCSA. The results emphasize the importance of obtaining accurate estimates of tendon rest length and muscle-fiber length in musculoskeletal modeling. References [1] Anderson FC, Pandy MG. J Biomech Eng 2001; 123: 381-390. [2] Anderson FC, Pandy MG. J Biomech 2001; 34: 153-161.