Electrophysiological Muscle ODE System

Available identifiers

MaRDI QIDQ6674244

three-dimensional electrophysiological model for a muscle

Description

One continuum mechanics three-dimensional model for each participant. The equations originate from conservation of mass and momentum for each participant.

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Defining Formula: $\begin{array}{cccc}{\rho }_{\text{M}1}{\ddot{𝐱}}_{\text{M}1}& =\mathrm{\nabla }\cdot ({𝐏}_{\text{passive}}({𝐅}_{\text{M}1})+{𝐏}_{\text{active}}({𝐅}_{\text{M}1},{\gamma }_{\text{M}1})-p_{\text{M}1}{𝐅}_{\text{M}1}^{-T}),& \mathrm{\nabla }\cdot {\dot{𝐱}}_{\text{M}1}=0& \text{in}{\Omega }_{\text{M}1}\times [0,T_{\text{end}})\\ {\rho }_{\text{M}2}{\ddot{𝐱}}_{\text{M}2}& =\mathrm{\nabla }\cdot ({𝐏}_{\text{passive}}({𝐅}_{\text{M}2})+{𝐏}_{\text{active}}({𝐅}_{\text{M}2},{\gamma }_{\text{M}2})-p_{\text{M}2}{𝐅}_{\text{M}2}^{-T}),& \mathrm{\nabla }\cdot {\dot{𝐱}}_{\text{M}2}=0& \text{in}{\Omega }_{\text{M}2}\times [0,T_{\text{end}})\\ {\rho }_{\text{T}}{\ddot{𝐱}}_{\text{T}}& =\mathrm{\nabla }\cdot ({𝐏}_{\text{passive}}({𝐅}_{\text{T}})-p_{\text{T}}{𝐅}_{\text{T}}^{-T}),& \mathrm{\nabla }\cdot {\dot{𝐱}}_{\text{T}}=0& \text{in}{\Omega }_{\text{T}}\times [0,T_{\text{end}})\end{array}$

$\ddot{𝐱}$ symbol represents Material Point Acceleration

$\dot{𝐱}$ symbol represents Material Point Velocity

$\gamma$ symbol represents Lumped Activation Parameter

$𝐏$ symbol represents Stress Tensor (Piola-Kirchhoff)

$𝐱$ symbol represents Displacement Muscle Tendon

$\rho$ symbol represents Material Density

$p$ symbol represents Pressure

$t$ symbol represents Time

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