Table 1.

Model variables.

Symbol	Description
t	time
X	position of a material point in the reference configuration
χ(X, t)	placement function
x(X, t)	position of the material point in the actual configuration
F(X, t)	material deformation gradient tensor
C(X, t)	right Cauchy-Green deformation tensor
E(X, t)	Green's strain tensor
T(x, a0, fs)	Cauchy stress tensor
S(C, a0, fs)	second Piola-Kirchhoff stress tensor
a0(X)	referential unit vector in fiber direction
I1(C)	first principal invariant of C
I4(C, a0)	fourth (mixed) invariant of C
λf(C, a0)	fiber stretch
ℓS(λf)	sarcomere length
${\dot{\ell }}_S$(${\dot{\lambda }}_f$)	sarcomere contraction velocity
B(fs, ${\dot{\ell }}_S$)	sarcomere-based active stress
γ(fs, ℓS, ${\dot{\ell }}_S$)	normalized sarcomere-based active stress
Ξ(ℓS)	active force-length relation
x1(fs, ${\dot{\ell }}_S$, t)	average distortion of XBs in the A1 state
x2(fs, ${\dot{\ell }}_S$, t)	average distortion of XBs in the A2 state
[D2](fs, t)	concentration of XBs in the detached state
[A1](fs, t)	concentration of XBs in the attached pre-power stroke state
[A2](fs, t)	concentration of XBs in the attached post-power stroke state
f0([A1], [A2], x1, x2)	XB-attachment rate
g0(x2)	XB-detachment rate (from A2)
Vm(fs, t)	membrane voltage
y(fs, t)	state variables of the biophysical half-sarcomere model
Iion(t, Vm, y)	ionic currents crossing the cell membrane