Physiology and Muscle Modeling

Muscle Modeling

Mathematical muscle modeling has a long history, dating back to Hill’s original force velocity equation and there are a wide variety of muscle models available in the literature today.  We are focusing on developing and incorporating mathematical representations of muscle force, muscle activation strategies, musculotendinous stress, and fatigue into our digital human modeling.  In addition, we are interested in mathematical representations of human performance and capability measures including energy expenditure and aerobic capacity, muscle torque-velocity maxima, core body temperature, etc.

Torque Velocity (T-V) Curves

Isolated muscle has been repeated demonstrated to exhibit a curvilinear force-velocity relationship, where force declines with increasing contraction velocity [2].  Similarly, in humans, we can measure joint torque velocity relationships, which generally mirror the force – velocity curve.  This information can be useful to represent human torque capabilities during dynamic movements. 

The T-V curves may be used iteratively to determine feasible solutions during dynamic motion prediction, may be used as a means to represent fatigue or decreasing force generating capabilities by lowering the T-V curve over time, or as a post-processing check point to assess the relative difficulty of a simulated task by plotting the modeled T-V data points relative to maximum experimental T-V curves.

 Muscle Activation and Loading Prediction:

 This research is aimed at creating advanced real-time simulation methods for predicting muscle loading and activation.  A novel method has been developed that is based on optimization, and that allows a user to interact with the 3D model of the musculoskeletal system (Fig. 1).   By specifying the load, the system then calculates the various torques generated by the muscles in 3D and they move.  Muscles attachments are accurately represented and are allowed to "wrap" around the various anatomical structures.  This wrapping motion is very important and provides for a very accurate modeling and simulation system.  It is believed that this is the first and only system of its nature in the world.  

Oxygen Consumption: 

The metabolic energy expended by the human body at rest or with movement cannot be measured directly, but indirectly through the oxygen consumed (basically inhaled versus exhaled oxygen).  Using energy expenditure estimates (link to this section?), we are able to estimate oxygen consumption during simulated dynamic motion.  This is a valuable physiologic estimate as it provides an indication of the relative difficulty of a simulated task, considering cardiovascular function.  The simulated oxygen consumption can be normalized by known standards for aerobic capacity based on gender, age and fitness (maximum oxygen uptake).  Typically activities that require low percentages of maximum oxygen uptake (< 30%) can be maintained for very long periods of time (hours), whereas high percentages of max oxygen uptake (> 90%) can typically be maintained on the order of minutes.  This provides a means to estimate how long and how well a digital human can maintain a simulated task.

Muscle Fatigue

This is an aggressive area of research with significant long term potential.  It allows users of the Santos environment to predict when the digital human will be fatigued, how much load should he/she carry, and how many repetetions are allowable under certain loading conditions (Figs 2 &3).

Fig. 1: This is a real-time simulation musculoskeletal model
using optimization to determine activation/loading

Fig. 2: Muscle Fatigue modeling allows Santos to
predict when he cannot carry a load

Fig. 3:  Muscle recruitment