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Model Mathematics

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Component: environment

Component: Crossbridges_attached

\frac{d}{d t} (n) = f (A_c - n) - (g n)

Component: f

f = \{\begin{matrix} 0 if x < 0 \\ \frac{f_1 x}{h} if x \geq 0 \land x < h \\ 0 otherwise \end{matrix}

Component: g

g = \{\begin{matrix} g_2 if x < 0 \\ \frac{g_1 x}{h} if x \geq 0 \land x < h \\ \frac{g_1 x}{h} otherwise \end{matrix}

Component: Ca_sarcoplasm

Ca_f = Ca_0 | 1 - (ⅇ^{(- a_1) t^{2}}) | ⅇ^{(- b_1) {(t - t_d)}^{2}}

Component: Actin_free

c_2 = c_2_0 ⅇ^{k_i {(\frac{s_h}{1})}^{q}} \frac{d}{d t} (A_c) = c_1 {(\frac{Ca_f}{1})}^{2} (AT_0 - A_c) - (c_2 A_c)

Component: Series_Elastic_Element

F_SE = alpha_s (ⅇ^{\frac{beta_s x_s}{1 1}} - 1)

Component: SE_constants

x_s = x_so + s_h + x_m - L_max

Component: Parallel_Elastic_Element

F_PE = alpha_p (ⅇ^{\frac{beta_p x_p}{1 1}} - 1)

Component: PE_constants

x_p = x_po - s_h

Component: Contractile_Element

F_CE = F_SE - F_PE

Component: s_h

s_h = x_po - (\frac{1 1 \log_{10} (1 + \frac{F_PL}{alpha_p})}{beta_p})

Component: X_0

X_S_0 = \frac{1 1 \log_{10} (1 + \frac{F_PL}{alpha_s})}{beta_s} X_M_0 = X_S_0 + L_max - s_h - x_so

Source: Derived from workspace Panerai, 1980 at changeset 421685629652.

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A Model of Cardiac Muscle Mechanics and Energetics