Model Mathematics

\frac{d}{d time} (cp) = alpha ((I_rel - I_d) + i_Ca)

\frac{d}{d time} (cf_jsr) = I_tr - I_rel

I_rel = gs a (cf_jsr - cp) \frac{d}{d time} (a) = \frac{a_infinity - a}{tau_a} a_infinity = \frac{{cp}^{2.0}}{{cp}^{2.0} + {cp_}^{2.0}} tau_a = \frac{1.0}{kd ({cp}^{2.0} + {cp_}^{2.0})}

I_d = \frac{cp - cs}{tau_p}

I_tr = \frac{cf_nsr - cf_jsr}{tau_tr}

I_Ca = M Po i_Ca Po = d_infinity f q q_infinity = \frac{1.0}{1.0 + {(\frac{cs}{cs_})}^{gamma}} tau_q = \frac{q_infinity}{ko} alpha_q = \frac{q_infinity}{tau_q} beta_q = \frac{1.0 - q_infinity}{tau_q} \frac{d}{d time} (q) = alpha_q (1.0 - q) - (beta_q q) i_Ca = \frac{i_Ca_P_Ca \frac{4.0 V F^{2.0}}{R T} \frac{cs ⅇ^{\frac{2.0 V F^{2.0}}{R T}} - (0.341 Cao)}{ⅇ^{\frac{2.0 V F^{2.0}}{R T}} - 1.0}}{M}

alpha_d = \frac{d_infinity}{tau_d} d_infinity = \frac{1.0}{1.0 + ⅇ^{\frac{- (V - 5.0)}{6.24}}} beta_d = \frac{1.0 - d_infinity}{tau_d} \frac{d}{d time} (d) = alpha_d (1.0 - d) - (beta_d d)

alpha_f = \frac{f_infinity}{tau_f} f_infinity = \frac{1.0}{1.0 + ⅇ^{\frac{V + 35.0}{8.6}}} beta_f = \frac{1.0 - f_infinity}{tau_f} \frac{d}{d time} (f) = alpha_f (1.0 - f) - (beta_f f)

I_NaCa = K_NaCa \frac{1.0}{{K_mNa}^{3.0} + {Nao}^{3.0}} \frac{1.0}{K_mCa + Cao} \frac{1.0}{1.0 + K_sat ⅇ^{(eta - 1.0) V \frac{F}{R T}}} (ⅇ^{eta V \frac{F}{R T}} {Nai}^{3.0} Cao - (ⅇ^{(eta - 1.0) V \frac{F}{R T}} {Nao}^{3.0} cs))

I_up = \frac{vup {ci}^{2.0}}{{ci}^{2.0} + {cup}^{2.0}}

\frac{d}{d time} (CaTi) = I_trpn_i I_trpn_i = kT_on ci (BT - CaTi) - (kT_off CaTi) beta_ci = {(1.0 + \frac{BSR KSR}{{(ci + KSR)}^{2.0}} + \frac{BCd KCd}{{(ci + KCd)}^{2.0}})}^{-1.0} \frac{d}{d time} (CaTs) = I_trpn_s I_trpn_s = kT_on cs (BT - CaTs) - (kT_off CaTs) beta_cs = {(1.0 + \frac{BSR KSR}{{(cs + KSR)}^{2.0}} + \frac{BCd KCd}{{(cs + KCd)}^{2.0}})}^{-1.0}

\frac{d}{d time} (cs) = beta_cs (\frac{vi}{vs} ((I_r - (\frac{cs - ci}{taus} + I_Ca)) + I_NaCa) - I_trpn_s)

\frac{d}{d time} (ci) = beta_ci (\frac{cs - ci}{taus} - (I_up + I_trpn_i))

\frac{d}{d time} (cj) = I_up - I_r

\frac{d}{d time} (cj_) = \frac{cj - cj_}{taua}

I_r = - (g I_Ca Q \frac{I_r}{taur}) N = - (g I_Ca A) Q = \{\begin{matrix} 0.0 if cj_< 50.0 \land cj_> 0.0 \\ cj_- 50.0 if cj_< 115.0 \land cj_\geq 50.0 \\ u cj_+ s if cj_\geq 115.0 \end{matrix}

V = \{\begin{matrix} Vmin + (Vmax - Vmin) {(1.0 - ({(\frac{time - (m T)}{m T})}^{2.0}))}^{0.5} if time ≦ m T + x T \land time \geq m T \\ Vmin if time < (m + 1.0) T \land time > m T + x T \end{matrix} x = \frac{a}{a + T}

Nai = \frac{a}{1.0 + b T^{0.5}}