Table 2.

Summary of structural constitutive models for passive behavior of myocardium^a

General form for structurally informed models W = W^g(I₁ ) + W ^f (E, N, R, D)	Reference
ψ^g = 0, ψ ^f = ψ^m + ψ^c $Ψ^{m} = \int_{- π / 24}^{π / 24} R_{1} w_{1}^{*} d α$ , $Ψ^{c} = \int_{- π / 24}^{- π / 24} \int_{0}^{2 π} \int_{0}^{π} R_{2} w_{2} J d ϕ d θ d α$ $w_{k} = A_{k} ϵ_{k}^{2}, D_{k} (x) = 1 / (\sqrt{2 π} σ_{k}) e^{- (m_{k} - x) / 2 σ_{k}^{2}}$ , k = 1, 2, ‹ is the fiber true strain	Horowitz et al. (87)
$Ψ^{g} = A [e^{B (I_{1} - 3)} - 1]$ , $Ψ^{f} = \int_{R_{i}}^{R_{o}} w d R$ $w = C [ϵ^{D {(\sqrt{I^{f}} - 1)}^{2}} - 1]$	Humphrey & Yin (80)
ψ^g = 0, $Ψ^{f} = \int_{- π / 2}^{π / 2} R_{1} w_{1} d θ + \int_{0}^{π} R_{2} w_{2} d θ + \int_{0}^{π} \int_{0}^{π / 2} R_{3} w_{3} d θ d ϕ$ $w_{k} = A_{k} ϵ^{2} / {(B - ϵ)}^{C}$ , $k = 1, 2, 3$ , $ϵ = (I^{f} - 1) / 2$	Hunter et al. (74)
ψ^g = ϕ^g k^g/2 (I₁ − 3), $Ψ^{m} = \frac{ϕ^{m}}{H} \int_{0}^{H} \int_{- π / 2}^{π / 2} R^{m} (θ, z) w^{m} (I^{m}) d θ d z$ , $Ψ^{c} = \frac{ϕ^{c}}{H} \int_{0}^{H} \int_{- π / 2}^{π / 2} R^{c} (θ, z) w^{* c} (I^{c}) d θ d z$ , $Ψ^{i} = \frac{ϕ^{c}}{H} \int_{0}^{H} \int_{- π / 2}^{π / 2} \int_{- π / 2}^{π / 2} R^{m} (θ^{m}, z) R^{c} (θ^{c}, z) w^{* i} (I^{m}, I^{c}) d θ^{m} d θ^{c} d z$ , $w^{m} = \frac{k_{1}^{m}}{2 k_{m}^{2}} [e^{k_{2}^{m} {(\sqrt{I^{m}} - 1)}^{2}} - 1]$ , $w^{* c} = \frac{k^{c}}{2} {(\sqrt{I^{c}} / λ_{c} - 1)}^{2}$ , $w^{* i} = \frac{k_{1}^{i}}{2 k_{i}^{2}} {e^{k_{2}^{i} (I^{m} + I^{c} - 2)} - [k_{2}^{i} (I^{c} / λ_{c}^{2} - 1) + 1] e^{k_{2}^{i} (I^{m} - 1)}}$	Avazmohammadi et al. (88)

The reader is referred to the respective references for additional details on the constants and variables.