A weighted cost function to deal with the muscle force sharing problem in injured subjects: A single case study

The human body is an over-actuated multi-body system, as each joint degree of freedom can be controlled by more than one muscle. Solving the force-sharing problem (i.e. finding out how the resultant joint torque is shared among the muscles actuating that joint) calls for an optimization process where a cost function, representing the strategy followed by the central nervous system to activate muscles, is minimized. The main contribution of the present study has been the particular formulation of that cost function for the case of the pathological gait of a single subject suffering from anterior cruciate ligament rupture. Our hypothesis was that the central nervous system does not weight equally the muscles when trying to compensate for a lower limb injury during gait (in contrast to what is the usual practice for healthy gait where all muscles are weighted equally). This hypothesis is supported by the fact that muscle activity in injured individuals differs from that of healthy subjects. Different functions were tested until we finally came out with a cost function that was consistent with experimental electromyography measurements and inverse dynamics results for a subject suffering this particular pathology.

[1]  Ayman Habib,et al.  OpenSim: Open-Source Software to Create and Analyze Dynamic Simulations of Movement , 2007, IEEE Transactions on Biomedical Engineering.

[2]  Kurt Manal,et al.  Gait and neuromuscular asymmetries after acute anterior cruciate ligament rupture. , 2012, Medicine and science in sports and exercise.

[3]  F.E. Zajac,et al.  An interactive graphics-based model of the lower extremity to study orthopaedic surgical procedures , 1990, IEEE Transactions on Biomedical Engineering.

[4]  T. Andriacchi,et al.  Gait Adaptations by Patients Who Have a Deficient Anterior Cruciate Ligament , 1990 .

[5]  Daniel Vélez Día,et al.  Biomechanics and Motor Control of Human Movement , 2013 .

[6]  Javier Cuadrado,et al.  Solution methods for the double-support indeterminacy in human gait , 2013 .

[7]  L. Snyder-Mackler,et al.  Knee instability after acute ACL rupture affects movement patterns during the mid‐stance phase of gait , 2007, Journal of orthopaedic research : official publication of the Orthopaedic Research Society.

[8]  R. Crowninshield,et al.  A physiologically based criterion of muscle force prediction in locomotion. , 1981, Journal of biomechanics.

[9]  David E. Hardt,et al.  Determining Muscle Forces in the Leg During Normal Human Walking—An Application and Evaluation of Optimization Methods , 1978 .

[10]  Marko Ackermann,et al.  Dynamics and Energetics of Walking with Prostheses , 2007 .

[11]  Vladimir Medved,et al.  Standards for Reporting EMG Data , 2000, Journal of Electromyography and Kinesiology.

[12]  Antonie J. van den Bogert,et al.  Exotendons for assistance of human locomotion , 2003 .

[13]  B. Freriks,et al.  Development of recommendations for SEMG sensors and sensor placement procedures. , 2000, Journal of electromyography and kinesiology : official journal of the International Society of Electrophysiological Kinesiology.

[14]  M. Axe,et al.  1998 Basmajian Student Award Paper: Movement patterns after anterior cruciate ligament injury: a comparison of patients who compensate well for the injury and those who require operative stabilization. , 1998, Journal of electromyography and kinesiology : official journal of the International Society of Electrophysiological Kinesiology.

[15]  Petros Koumoutsakos,et al.  Reducing the Time Complexity of the Derandomized Evolution Strategy with Covariance Matrix Adaptation (CMA-ES) , 2003, Evolutionary Computation.

[16]  J. O'Connor,et al.  Gait and electromyographic analysis of anterior cruciate ligament deficient subjects , 1996 .

[17]  Walter Herzog,et al.  Model-based estimation of muscle forces exerted during movements. , 2007, Clinical biomechanics.

[18]  F. Zajac.  Muscle and tendon: properties, models, scaling, and application to biomechanics and motor control. , 1989, Critical reviews in biomedical engineering.

[19]  Urbano Lugrís,et al.  Simulation and design of an active orthosis for an incomplete spinal cord injured subject , 2011 .

[20]  Yasin Y Dhaher,et al.  The effect of vastus medialis forces on patello-femoral contact: a model-based study. , 2002, Journal of biomechanical engineering.

[21]  L. Menegaldo,et al.  Biomechanical modeling and optimal control of human posture. , 2003, Journal of biomechanics.

[22]  Scott M Lephart,et al.  The Sensorimotor System, Part II: The Role of Proprioception in Motor Control and Functional Joint Stability. , 2002, Journal of athletic training.

[23]  Scott L Delp,et al.  Knee muscle forces during walking and running in patellofemoral pain patients and pain-free controls. , 2009, Journal of biomechanics.

[24]  Sofia Heintz,et al.  Static optimization of muscle forces during gait in comparison to EMG-to-force processing approach. , 2007, Gait & posture.

[25]  G. Ferrigno,et al.  Derivation of Centers and Axes of Rotation for Wrist and Fingers in a Hand Kinematic Model: Methods and Reliability Results , 2005, Annals of Biomedical Engineering.

[26]  W Baumann,et al.  The three-dimensional determination of internal loads in the lower extremity. , 1997, Journal of biomechanics.

[27]  Maarten F. Bobbert,et al.  The contribution of muscle properties in the control of explosive movements , 1993, Biological Cybernetics.

[28]  Paul DeVita,et al.  Functional Knee Brace Alters Predicted Knee Muscle and Joint Forces in People With ACL Reconstruction During Walking , 2001 .

[29]  Wendy J Hurd,et al.  Perturbation training improves knee kinematics and reduces muscle co-contraction after complete unilateral anterior cruciate ligament rupture. , 2005, Physical therapy.