Table 1.

Definition of variables used in the equations for calculating contact forces across the knee joint.

Variable	Definition	Method of Obtaining
${\mathrm{M}}_{\mathrm{external}}^{\mathrm{x}}$, ${\mathrm{M}}_{\mathrm{external}}^{\mathrm{y}}$, ${\mathrm{M}}_{\mathrm{external}}^{\mathrm{z}}$	external moment about the x, y, and z-axis of the knee joint	gait analysis
${\mathrm{F}}_{\mathrm{external}}^{\mathrm{x}}$, ${\mathrm{F}}_{\mathrm{external}}^{\mathrm{y}}$, ${\mathrm{F}}_{\mathrm{external}}^{\mathrm{z}}$	external force about the x, y, and z-axis of ihe knee joint	gait analysis
${\mathrm{M}}_{\mathrm{i}}^{\mathrm{x}}$, ${\mathrm{M}}_{\mathrm{i}}^{\mathrm{y}}$, ${\mathrm{M}}_{\mathrm{i}}^{\mathrm{z}}$	maximum x, y, and z-direction moment for the ith muscle or passive structure in each group	SIMM output and Matlab software
${\mathrm{F}}_{\mathrm{i}}^{\mathrm{x}}$, ${\mathrm{F}}_{\mathrm{i}}^{\mathrm{y}}$, ${\mathrm{F}}_{\mathrm{i}}^{\mathrm{z}}$	maximum x, y, and z-direction force for the ith muscle or passive structures in each group	SIMM output and Matlab software
${\mathrm{ma}}_{\mathrm{lateral}}^{\mathrm{x}}$, ${\mathrm{ma}}_{\mathrm{medial}}^{\mathrm{x}}$	x-direction distance from the origin of the coordinate system to the contact point (x-direction moment arm for z-direction contact forces).	coordinate of contact point
${\mathrm{ma}}_{\mathrm{lateral}}^{\mathrm{y}}$, ${\mathrm{ma}}_{\mathrm{medial}}^{\mathrm{y}}$	y-direction distance from the origin of the coordinate system to the contact point (y-direction moment arm for z-direction contact forces).	coordinate of contact point
ml_ratio	ratio defining the percent load transferred through the medial versus lateral side of the tibial plateau	set by the user
ai, bi, ci	relative activation level for the ith muscle in each agonist group	parametrically varied
A, B, C	group activation levels for each muscle agonist group	unknown, solve using equations
D	activation level for passive structures	0 (on) or 1 (off)
E	activation level for antagonist muscles	set by the user
${\mathrm{F}}_{\mathrm{lateral}}^{\mathrm{x}}$, ${\mathrm{F}}_{\mathrm{medial}}^{\mathrm{x}}$	x-direction contact forces	unknown, solve using equations
${\mathrm{F}}_{\mathrm{lateral}}^{\mathrm{y}}$, ${\mathrm{F}}_{\mathrm{medial}}^{\mathrm{y}}$	y-direction contact forces	unknown, solve using equations
${\mathrm{F}}_{\mathrm{lateral}}^{\mathrm{z}}$, ${\mathrm{F}}_{\mathrm{medial}}^{\mathrm{z}}$	z-direction contact forces	unknown, solve using equations

¹lateral and medial indicate the lateral or medial side of the tibial plateau, respectively