Model Mathematics

q_TRPN = q_TRPN_mcrossbridge_TRPN + q_TRPN_init q_Cai = q_Cai_mcrossbridge_TRPN + q_Cai_init q_Ca_TRPN = q_Ca_TRPN_mcrossbridge_TRPN + q_Ca_TRPN_init q_B = q_B_mcrossbridge_TRPN + q_B_init q_U = q_U_mcrossbridge_TRPN + q_U_init q_W = q_W_mcrossbridge_TRPN + q_W_init q_S = q_S_mcrossbridge_TRPN + q_S_init

mu_TRPN = R T \ln (K_TRPN q_TRPN_global) mu_Cai = R T \ln (K_Cai q_Cai_global) mu_Ca_TRPN = R T \ln (K_Ca_TRPN q_Ca_TRPN_global) mu_B = R T \ln (K_B q_B_global) mu_U = R T \ln (K_U q_U_global) mu_W = R T \ln (K_W q_W_global) mu_S = R T \ln (K_S q_S_global) v_R_TRPNCa = kappa_R_TRPNCa (ⅇ^{\frac{mu_Cai + mu_TRPN}{R T}} - (ⅇ^{\frac{mu_Ca_TRPN + mu_tension}{R T}})) v_R_BU = kappa_R_BU (ⅇ^{\frac{mu_B + n_Tm mu_Ca_TRPN}{R T}} - (ⅇ^{\frac{mu_U + n_Tm mu_Ca_TRPN}{R T}})) v_R_UW = kappa_R_UW (ⅇ^{\frac{mu_U}{R T}} - (ⅇ^{\frac{mu_W}{R T}})) v_R_WS = kappa_R_WS (ⅇ^{\frac{mu_W}{R T}} - (ⅇ^{\frac{mu_S}{R T}})) v_R_SU = kappa_R_SU (ⅇ^{\frac{mu_S}{R T}} - (ⅇ^{\frac{mu_U}{R T}})) \frac{d}{d time} (q_Cai) = - v_R_TRPNCa \frac{d}{d time} (q_TRPN) = - v_R_TRPNCa \frac{d}{d time} (q_Ca_TRPN) = v_R_TRPNCa \frac{d}{d time} (q_B) = - v_R_BU \frac{d}{d time} (q_U) = (v_R_BU - v_R_UW) + v_R_SU \frac{d}{d time} (q_W) = v_R_UW - v_R_WS \frac{d}{d time} (q_S) = v_R_WS - v_R_SU

tension = T_total 1 e 3 n = kf_coeff R T mu_tension = hh n tension

A_w = \frac{A_eff r_s}{(1 - r_s) r_w + r_s} A_s = A_w c_w = \frac{phi k_uw (1 - r_w)}{r_w} c_s = \frac{phi k_ws (1 - r_s) r_w}{r_s} v_1 = \frac{mu_1}{v_to_mu} mu_2 = (- A_w) v_2 v_to_mu mu_3 = c_w G_w v_to_mu v_4 = \frac{mu_4}{v_to_mu} mu_5 = (- A_s) v_2 v_to_mu mu_6 = c_s G_s v_to_mu \frac{d}{d time} (G_w) = v_1 \frac{d}{d time} (SL) = v_2 \frac{d}{d time} (G_s) = v_4 mu_1 = - mu_2 - mu_3 mu_4 = - mu_5 - mu_6

T_active = mu_T_a mu_T_S = \frac{T_ref}{SL_0 q_MS r_s} q_S (G_s + SL_0) mu_T_W = \frac{T_ref}{SL_0 q_MS r_s} q_W G_w mu_T_a = mu_T_S + mu_T_W

eta = \{\begin{matrix} eta_l if mu_d > 0 \\ eta_s otherwise \end{matrix} \frac{d}{d time} (Cdd) = v_Cdd v_Cdd = \frac{mu_d}{v_to_mu} mu_k = \frac{k}{eta} Cdd v_to_mu mu_f = \frac{k}{eta} (SL - SL_0) v_to_mu mu_d = (- mu_k) + mu_f mu_T_passive = \frac{alpha eta}{SL_0} v_Cdd T_passive = mu_T_passive

T_total = T_active + T_passive