Strength and Fatigue: Experiments and Modeling - Human Motion Simulation: Predictive Dynamics - page 141

Active
(M A )

Resting
(M R )

Fatigued
(M A )

FIGURE 6.12
Schematic representation of the three-compartment fatigue model.
Reprinted with permission from Frey-Law et al., 2012a

data points) and generated new intensity-ET curves for a “general” model as well as
six joint-specific models ( Figure 6.11 ): hand/grip, elbow, shoulder, trunk, knee, and
ankle ( Frey-Law and Avin, 2010 ). These statistical models provide a simplified means
to estimate the development of fatigue (e.g., by estimating maximum endurance time)
for digital human applications.
These intensity-ET relationships are particularly relevant for static, sustained
tasks with no rest intervals; however, most activities involve some component of
dynamic movement and/or relative rests. Thus analytical, heuristic models which
can represent the actual changes in peak force-production are needed to represent
the decay and recovery of muscle fatigue at the joint-level for DHM applications.
Several models have been proposed to model fatigue, but relatively few are
specifically for DH applications. Ding and colleagues developed a muscle fatigue
model that was aimed at clinical applications for electrical stimulation of para-
lyzed muscle ( Ding et al., 2000, 2002a,b, 2003 ). This modeling approach is an
adaptation to a muscle model by adding a decay component and requires esti-
mates of stimulation frequency input to the motor neurons. We developed a dif-
ferent approach to model fatigue which is capable of addressing the effects of
work intensity, joint position, contraction velocity, and rest intervals ( Xia and
Frey-Law, 2008a,b ).
Our model ( Figure 6.12 ) was adapted from a previous model first proposed
for modeling only maximal contractions ( Liu et al., 2002 ), employing a three-
compartmental approach. Muscle tissues are considered to be in one of three
states (i.e., three compartments) at any time: resting (

M R ), activated ( M A ), or

fatigued ( M F ). We added a feedback control loop to the model, allowing for sub-

maximal contractions to be modeled. Muscle activation-deactivation (

M R 2M A )
is simulated using a bounded proportional controller to regulate (i.e., match)
required work intensity (as predicted by a DHM). The fatigue ( M A -M F ) and

recovery ( M F -M R ) processes are regulated by two transfer rate coefficients,