Bioengineering and Public Health: Biomedical Materials and Devices for Bridging the Biotic-Abiotic Interface
Mathematical Modeling and Control of Mechanical and Biological Systems
Luciano Menegaldo, Biomedical Engineering Department, Institute for Graduate Studies and Research in Engineering (COPPE), Federal University of Rio de Janeiro, Brazil
This presentation addresses some topics regarding the mathematical modeling of musculoskeletal systems, with examples taken mainly from our current research. The modeling problem will be initially addressed from the point of view of the possible kinds of mathematical representations for these systems, usually partial or ordinary differential equations. A critical problem for the modeling of biological systems is obtaining the values for the equations’ parameters, requiring experimental and numerical techniques. The main methodological steps for deriving a musculoskeletal model will be discussed: kinematics, muscle dynamics, geometric modeling of anatomy and multi-body dynamics.
Examples of musculoskeletal models applications will be shown. Inverse dynamics analysis can be used for data pre-processing, before applying classification algorithms for subtle gait impairments detection. Direct dynamics can be used to estimate muscle forces using EMG-driven models , with examples of applications in force training and aging. Other interesting application for direct dynamics is orthopedic surgery simulation, which is being studied for hand surgery tendon transfers. The use of musculoskeletal models in control problems will be illustrated by two examples: suppression of whole-body vibration pointing error in military tanks and real-time estimation of muscle state using Kalman filters.
 Menegaldo, LL., Oliveira, LF., The influence of modeling hypothesis and experimental methodologies in the accuracy of muscle force estimation using EMG-driven models, Multibody System Dynamics, 28: 21-36, 2012