Strength and Fatigue: Experiments and Modeling - Human Motion Simulation: Predictive Dynamics - page 142

F and R, representing the fatigue and recovery properties, respectively. The sys-
tem can maintain a steady torque output by increasing muscle activation until fail-
ure, i.e. maximum holding time (MHT), occurs. Additionally, the model can
calculate the level of fatigue at any given time during a task as the proportion of
the muscle in the “fatigued” state (i.e., in

M F ).
The model consists of several differential equations defining the flow rates
between compartments, where the rate is proportional to the concentration (vol-
ume) of each compartment (see Equations 6.5

6.7 ) and an equation for the con-
troller depending on the situation ( Equations 6.8 6.10 ). The input required is the

relative task intensity, which may simply be known (i.e., for a simple task) or can
be modeled using DHM to estimate required net joint torques standardized by the
3D strength surfaces (as a function of joint angle and velocity). Thus, in this way,
even a complex dynamic task can be represented as a time-vector of task intensity
values (i.e., ranging in value from 1 100% intensity) as previously depicted sche-

matically in Figure 6.10 . We can represent joint-specific fatigue behavior through
variations in the model parameters, F and R:

R M F

dM R =

t 52 CðtÞ 1

d (6.5)

t 5 CðtÞ 2 F M A dM A = d (6.6)

dM F = d t 5 F M A 2 R M F

(6.7)

L ð

CðtÞ 5 TL M A Þ (6.8)

2

i.e., activation of muscle, if there is sufficient “muscle” available in the active
and/or resting compartment to meet the target level requirements

L M R CðtÞ 5 (6.9)

i.e., activation of muscle, if there is insufficient “muscle” available in the active
and/or resting compartment to meet the target level requirements

L ð CðtÞ 5 TL M A Þ (6.10)

2

i.e., deactivation of muscle, if the active compartment is exceeding the target
level
where

C( t ) 5 the controller denoting the muscle activation-deactivation drive;

F 5 fatigue parameter defining the rate of change between the active and

fatigued compartments;
R recovery parameter defining the rate of change between the fatigued and

resting compartments;
L

5

an arbitrary constant tracking factor to ensure good system behavior ( Xia
and Frey-Law, 2008a ). We found a value of 10 is reasonable based on a
sensitivity analysis ( Xia and Frey-Law, 2008c ); and

5