Model Mathematics

Component based math viewer is available

Component: Vm

V = p1 (time - t0 - tss) + p2 p1 = \{\begin{matrix} 0 if time - tss < 0.4742 \\ 0.2508 if time - tss \geq 0.4742 \land time - tss < 9.7684 \\ - 4.2966 if time - tss \geq 9.7684 \land time - tss < 10.8076 \\ 3.6283 if time - tss \geq 10.8076 \land time - tss < 12.0313 \\ 6.7127 if time - tss \geq 12.0313 \land time - tss < 18.3268 \\ 3.6151 if time - tss \geq 18.3268 \land time - tss < 19.7879 \\ - 6.8481 if time - tss \geq 19.7879 \land time - tss < 21.9031 \\ - 0.0369 if time - tss \geq 21.9031 \land time - tss < 55.9040 \\ - 66.1632 if time - tss \geq 55.9040 \land time - tss < 56.2152 \\ - 1.4456 if time - tss \geq 56.2152 \land time - tss < 62.2548 \\ - 0.1557 if time - tss \geq 62.2548 \land time - tss < 82.4301 \\ - 0.0623 if time - tss \geq 82.4301 \land time - tss < 113.9610 \\ 0 otherwise \end{matrix} p2 = \{\begin{matrix} - 63.0930 if time - tss < 0.4742 \\ - 63.0930 if time - tss \geq 0.4742 \land time - tss < 9.7684 \\ - 60.7620 if time - tss \geq 9.7684 \land time - tss < 10.8076 \\ - 65.2270 if time - tss \geq 10.8076 \land time - tss < 12.0313 \\ - 60.7870 if time - tss \geq 12.0313 \land time - tss < 18.3268 \\ - 18.5270 if time - tss \geq 18.3268 \land time - tss < 19.7879 \\ - 13.2450 if time - tss \geq 19.7879 \land time - tss < 21.9031 \\ - 27.7300 if time - tss \geq 21.9031 \land time - tss < 55.9040 \\ - 28.9850 if time - tss \geq 55.9040 \land time - tss < 56.2152 \\ - 49.5750 if time - tss \geq 56.2152 \land time - tss < 62.2548 \\ - 58.3060 if time - tss \geq 62.2548 \land time - tss < 82.4301 \\ - 61.4480 if time - tss \geq 82.4301 \land time - tss < 113.9610 \\ - 63.411 otherwise \end{matrix} t0 = \{\begin{matrix} 0 if time - tss < 0.4742 \\ 0.4742 if time - tss \geq 0.4742 \land time - tss < 9.7684 \\ 9.7684 if time - tss \geq 9.7684 \land time - tss < 10.8076 \\ 10.8076 if time - tss \geq 10.8076 \land time - tss < 12.0313 \\ 12.0313 if time - tss \geq 12.0313 \land time - tss < 18.3268 \\ 18.3268 if time - tss \geq 18.3268 \land time - tss < 19.7879 \\ 19.7879 if time - tss \geq 19.7879 \land time - tss < 21.9031 \\ 21.9031 if time - tss \geq 21.9031 \land time - tss < 55.9040 \\ 55.9040 if time - tss \geq 55.9040 \land time - tss < 56.2151 \\ 56.2151 if time - tss \geq 56.2151 \land time - tss < 62.2548 \\ 62.2548 if time - tss \geq 62.2548 \land time - tss < 82.4301 \\ 82.4299 if time - tss \geq 82.4301 \land time - tss < 113.9610 \\ 0 otherwise \end{matrix}

Component: control_para

Component: outputs

Component: EC_uSMC

Component: K_1

K_1 = \frac{{Cai}^{n_M}}{{Ca_halfMLCK}^{n_M} + {Cai}^{n_M}} 1

Component: E_Na

Component: E_Ca

Component: E_K

Component: Nernst_potential

E = \frac{R T}{z F} \ln (\frac{X_o}{X_i})

Component: Nernst_potential

E = \frac{R T}{z F} \ln (\frac{X_o}{X_i})

Component: Nernst_potential

E = \frac{R T}{z F} \ln (\frac{X_o}{X_i})

Component: CB4HM

norm = M + Mp + AM + AMp \frac{d}{d time} (M) = \frac{(- K_1) M}{norm} + \frac{K_2 Mp}{norm} + \frac{K_7 AM}{norm} \frac{d}{d time} (Mp) = \frac{K_4 AMp}{norm} + \frac{K_1 M}{norm} - (\frac{(K_2 + K_3) Mp}{norm}) \frac{d}{d time} (AM) = \frac{K_5 AMp}{norm} - (\frac{(K_6 + K_7) AM}{norm}) \frac{d}{d time} (AMp) = \frac{K_3 Mp}{norm} + \frac{K_6 AM}{norm} - (\frac{(K_4 + K_5) AMp}{norm}) stress = AMp + AM phosphorylation = AMp + Mp

Component: J_VOCC

rho_vCa = \frac{1}{1 + ⅇ^{\frac{V_Cahalf - V}{K_Cahalf}}} J_VOCC = \frac{- I_VOCC}{2 V_cell F}

Component: J_CaPump

J_CaPump = \frac{(- V_pmax) {Cai}^{n}}{{K_ph}^{n} + {Cai}^{n}}

Component: J_NaCa

V_mNaCa = 3 E_Na - (2 E_Ca) J_NaCa = \frac{G_NaCa Cai}{Cai + K_NaCa} (V - V_mNaCa)

Component: Cai

\frac{d}{d time} (Cai) = J_VOCC + inhPump J_CaPump + J_NaCa

Component: Ionic_currents

I = g_max PO (V - E)

Model Mathematics

Component: Vm

Component: control_para

Component: outputs

Component: EC_uSMC

Component: K_1

Component: E_Na

Component: E_Ca

Component: E_K

Component: Nernst_potential

Component: Nernst_potential

Component: Nernst_potential

Component: CB4HM

Component: J_VOCC

Component: J_CaPump

Component: J_NaCa

Component: Cai

Component: Ionic_currents

Component: time_ms

Component: time_s

Component: constants

Component: model_para

Component: initials