Modeling and Simulation


The purpose of the course is to familiarize with issues related to the development, modeling and simulation of human neuromusculoskeletal dynamic systems for the analysis of different motor activities. Within these lectures the student will understand what is a dynamic system, how to model, how the simulation is conducted and how these techniques can be used to solve biomedical related problems in the study of human movement.

There will be an introduction to basic concepts of physics, dynamical systems, state space representation, control, numerical integration and transformations. Basic robotics concepts will be used to model and derive the equation of motion of the skeletal system, which will be the basis for understanding and modeling the motion of the human neuromusculoskeletal system. Finally, different simulation algorithms will be studied (forward and inverse), that are constantly used and applied by the biomechanical community.

As part of the lectures there will be an extensive discussion on classical work in the area and the student will be entrusted with the study of selected publications. The laboratories are consistent with the understanding of the material, while solving practical applications. Intermediate assignments will be presented at the end of the courses to help in understanding the material.

Teaching Material

  1. Francisco J. Valero-Cuevas, Fundamentals of Neuromechanics, Springer, 2014
  2. David A. Winter, Biomechanics and Motor Control of Human Movement, Forth Edition, Wiley, 2009
  3. Roy Featherstone, Rigid Body Dynamics Algorithms, Springer, 2007
  4. John J. Craig, Introduction to Robotics Mechanics and Control, Third Edition, Prentice Hall, 2005
  5. John Enderle, Susan Blanchard, Joseph Bronzino, Introduction to Biomedical engineering, Academic Press Series in Biomedical Engineering, 2005
  6. Suresh R. Devasahayam, Signals and Systems in Biomedical Engineering, Second Edition, Springer, 2013
  7. Erwin Kreyszig, Herbert Kreyszig, Edward J. Norminton, Advanced Engineering Mathematics, Tenth Edition, Wiley, 2011

During the course additional material will be provided to facilitate and understanding the concepts.


OpenSim: tools and algorithms for modeling and simulation of the human body for the study of motion

Simbody: physics engine which is the basis of OpenSim

pydy: a python library to study the analytical expression of multi-body dynamics


This course is partially based on materials developed by members of the Neuromuscular Biomechanics Lab in the Department of Bioengineering at Stanford University, including Scott Delp, Ajay Seth, Jennifer Hicks, Ayman Habib, Jeff Reinbolt, Sam Hamner, Matt DeMers, Katherine Steele, Edith Arnold, Chand John, Joy Ku and others. Moreover, we would like to acknowledge, Prof. Stephen Robinovitch (KIN 840 Department of Biomedical Physiology and Kinesiology School of Engineering Science Simon Fraser University) and Prof. Francisco J. Valero-Cuevas (BME/BKN 504 University of Southern California).


Anderson, F. C., & Pandy, M. G. (2001). Static and dynamic optimization solutions for gait are practically equivalent. Journal of Biomechanics, 34(2), 153–161.

Buchanan, T. S., Lloyd, D. G., Manal, K., & Besier, T. F. (2006). Neuromusculoskeletal Modeling: Estimation of Muscle Forces and Joint Moments and Movements From Measurements of :Neural Command. Journal of Applied Biomechanics, 20(4), 367–395.

Erdemir, A., McLean, S., Herzog, W., & van den Bogert, A. J. (2007). Model-based estimation of muscle forces exerted during movements. Clinical Biomechanics, 22(2), 131–154.

Hicks, J. L., Uchida, T. K., Seth, A., Rajagopal, A., & Delp, S. (2014). Is my model good enough? Best practices for verification and validation of musculoskeletal models and simulations of human movement. Journal of Biomechanical Engineering, 137(February), 1–14.

Millard, M., Uchida, T., Seth, A., & Delp, S. L. (2013). Flexing computational muscle: modeling and simulation of musculotendon dynamics. Journal of Bomechanical Engineering, 135(2), 1–12.

Pandy, M. G. (2001). Computer Modeling and Simulation of Human Movement. Annals of Biomedical Engineering, 3, 245–73.

Seth, A., Sherman, M., Reinbolt, J. a., & Delp, S. L. (2011). OpenSim: a musculoskeletal modeling and simulation framework for in silico investigations and exchange. IUTAM Symposium on Human Body Dynamics, 2, 212–232.

Sherman, M. A., Seth, A., & Delp, S. L. (2013). What is a moment arm? Calculating muscle effectiveness in biomechanical models using generalized coordinates. Proceeding of the ASME, 1–9.

Thelen, D. G., & Anderson, F. C. (2006). Using computed muscle control to generate forward dynamic simulations of human walking from experimental data. Journal of Biomechanics, 39(6), 1107–15.

Zajac, F. E. (1989). Muscle and Tendon: Properties, Models, Scaling and Application to Biomechanics and Motor Control. Critical Reviews in Biomedical Engineering, 17(4), 359–411.