Model Mathematics

\frac{d}{d time} (R) = (phi_2_O - (phi_2 p R + phi_1 R)) + (l_2_+ k_1_) I_1

\frac{d}{d time} (O) = (phi_2 p R - ((phi_2_+ phi_4 + phi_3) O)) + phi_4_A + k_3_S

\frac{d}{d time} (A) = (phi_4 O - (phi_4_A + phi_5 A)) + (k_1_+ l_2_) I_2

\frac{d}{d time} (I_1) = phi_1 R - ((k_1_+ l_2_) I_1)

\frac{d}{d time} (I_2) = phi_5 A - ((k_1_+ l_2_) I_2)

\frac{d}{d time} (S) = phi_3 O - (k_3_S)

P_IPR = {(0.1 O + 0.9 A)}^{4.0}

phi_1 = \frac{(k_1 L_1 + l_2) c}{L_1 + c (1.0 + \frac{L_1}{L_3})} phi_2 = \frac{k_2 L_3 + l_4 c}{L_3 + c (1.0 + \frac{L_3}{L_1})} phi_2_= \frac{k_2_+ l_4_c}{1.0 + \frac{c}{L_5}} phi_3 = \frac{k_3 L_5}{c + L_5} phi_4 = \frac{(k_4 L_5 + l_6) c}{c + L_5} phi_4_= \frac{(k_1 L_1 + l_2) c}{c + L_1} phi_5 = \frac{L_1 (k_4_+ l_6_) c}{c + L_1}

P_RyR = \frac{w (1.0 + {(\frac{c}{Kb})}^{3.0})}{1.0 + {(\frac{Ka}{c})}^{4.0} + {(\frac{c}{Kb})}^{3.0}} w_infinity_c = \frac{1.0 + {(\frac{Ka}{c})}^{4.0} + {(\frac{c}{Kb})}^{3.0}}{1.0 + \frac{1.0}{Kc} + {(\frac{Ka}{c})}^{4.0} + {(\frac{c}{Kb})}^{3.0}} Ka = \frac{ka_minus}{ka_plus} Kb = \frac{kb_minus}{kb_plus} Kc = \frac{kc_minus}{kc_plus} \frac{d}{d time} (w) = \frac{kc_minus (w_infinity_c - w)}{w_infinity_c}

\frac{\partial}{\partial time} (c) = Dc c_x2 + (k_f P_IPR + v_1 P_RyR + J_er) (c_e - c) + delta (J_in p - J_pm) - (J_serca + J_mito) \frac{\partial^{2.0}}{\partial x^{2.0}} (c) = c_x2 \frac{d}{d time} (c_e) = gamma (J_serca - ((k_f P_IPR + v_1 P_RyR + J_er) (c_e - c)))

J_pm = \frac{V_pm c^{2.0}}{{K_pm}^{2.0} + c^{2.0}}

J_serca = \frac{V_serca c}{K_serca + c} \frac{1.0}{c_e}

J_mito = \frac{V_mito c}{1.0 + {(\frac{1.0}{c})}^{2.0}}

J_in = 0.2 + 0.05 p

p = p0 ⅇ^{(-0.8) time}