# Model Mathematics

### Component: membrane_potential

$i_Stim=stim_amplitudeiftime≥stim_start∧time≦stim_end∧time-stim_start-⌊time-stim_startstim_period⌋⁢stim_period≦stim_duration0otherwiseddtimeV=-1Cm⁢i_Na+i_b_Na+i_K1+i_K+i_to+i_b_K+i_Ca_L+i_b_Ca+i_NaCa+i_NaK+i_Stim$

### Component: reversal_potentials

$E_Na=R⁢TF⁢ln⁡Na_oNa_iE_K=R⁢TF⁢ln⁡K_oK_iE_Ca=0.5⁢R⁢TF⁢ln⁡Ca_oCa_iE_mh=R⁢TF⁢ln⁡Na_o+0.12⁢K_oNa_i+0.12⁢K_i$

### Component: fast_sodium_current

$i_Na=g_Na⁢m3⁢h⁢V-E_mh$

### Component: fast_sodium_current_m_gate

$E0_m=V+41alpha_m=2000if|E0_m|

### Component: fast_sodium_current_h_gate

$alpha_h=20⁢ⅇ-0.125⁢V+75-shift_hbeta_h=20001+320⁢ⅇ-0.1⁢V+75-shift_hddtimeh=alpha_h⁢1-h-beta_h⁢h$

### Component: time_dependent_rectifier_potassium_current

$i_K=i_Kmax⁢x⁢K_i-K_o⁢ⅇ-V⁢FR⁢T140$

### Component: time_dependent_rectifier_potassium_current_x_gate

$alpha_x=0.5⁢ⅇ0.0826⁢V+501+ⅇ0.057⁢V+50beta_x=1.3⁢ⅇ-0.06⁢V+201+ⅇ-0.04⁢V+20ddtimex=alpha_x⁢1-x-beta_x⁢x$

### Component: time_independent_potassium_current

$i_K1=g_K1⁢K_oK_o+K_mk1⁢V-E_K1+ⅇ2⁢F⁢V-E_K-10R⁢T$

### Component: transient_outward_current

$i_to=g_to⁢s⁢r⁢V-E_K$

### Component: transient_outward_current_s_gate

$alpha_s=0.033⁢ⅇ-V17beta_s=331+ⅇ-0.125⁢V+10ddtimes=alpha_s⁢1-s-beta_s⁢s$

### Component: transient_outward_current_r_gate

$ddtimer=333⁢11+ⅇ-V+45-r$

### Component: L_type_Ca_channel

$i_Ca_L_Ca=4⁢d⁢f⁢P_Ca_L_Ca⁢V-50⁢FR⁢T⁢1-ⅇ-2⁢V-50⁢FR⁢T⁢Ca_i⁢ⅇ100⁢FR⁢T-Ca_o⁢ⅇ-2⁢V-50⁢FR⁢Ti_Ca_L_K=0.002⁢d⁢f⁢P_Ca_L_Ca⁢V-50⁢FR⁢T⁢1-ⅇ-V-50⁢FR⁢T⁢K_i⁢ⅇ50⁢FR⁢T-K_o⁢ⅇ-V-50⁢FR⁢Ti_Ca_L_Na=0.01⁢d⁢f⁢P_Ca_L_Ca⁢V-50⁢FR⁢T⁢1-ⅇ-V-50⁢FR⁢T⁢Na_i⁢ⅇ50⁢FR⁢T-Na_o⁢ⅇ-V-50⁢FR⁢Ti_Ca_L=i_Ca_L_Ca+i_Ca_L_K+i_Ca_L_Na$

### Component: L_type_Ca_channel_d_gate

$E0_d=V+24-5alpha_d=speed_d⁢120if|E0_d|<0.00001speed_d⁢30⁢E0_d1-ⅇ-E0_d4otherwisebeta_d=speed_d⁢120if|E0_d|<0.00001speed_d⁢-12⁢E0_d1-ⅇE0_d10otherwiseddtimed=alpha_d⁢1-d-beta_d⁢d$

### Component: L_type_Ca_channel_f_gate

$E0_f=V+34alpha_f=speed_f⁢25if|E0_f|<0.00001speed_f⁢6.25⁢E0_f-1+ⅇE0_f4otherwisebeta_f=speed_f⁢501+ⅇ-E0_f4ddtimef=alpha_f⁢1-f-beta_f⁢f$

### Component: sodium_calcium_exchanger

$i_NaCa=i_NaCa_max⁢ⅇgamma⁢V⁢FR⁢T⁢Na_i3⁢Ca_o-ⅇgamma-1⁢V⁢FR⁢T⁢Na_o3⁢Ca_i1+Ca_i0.0069$

### Component: sodium_potassium_pump

$i_NaK=i_NaK_max⁢K_oK_mK+K_o⁢Na_iK_mNa+Na_i⁢11+0.1245⁢ⅇ-0.1⁢V⁢FR⁢T+0.0353⁢ⅇ-V⁢FR⁢T$

### Component: calcium_background_current

$i_b_Ca=g_b_Ca⁢V-E_Ca$

### Component: potassium_background_current

$i_b_K=g_b_K⁢V-E_K$

### Component: sodium_background_current

$i_b_Na=g_b_Na⁢V-E_Na$

### Component: CaMKII_factor

$Inf_CaMK=Cmdn_Ca0.00005ddtimeF_CaMK=Inf_CaMK-F_CaMKTau_CaMK$

### Component: RyR

$N_CaMK=F_CaMK0.72k_1=gain_k1⁢30625000⁢Ca_i2-245⁢i_Ca_Lk_2=gain_k2⁢4501+0.36Ca_SRk_3=gain_k3⁢1.885⁢F_SRCa_RyR0.22N_CaMKk_4=gain_k4⁢1.8ddtimeF_1=k_3⁢F_3-k_4⁢F_1-k_1⁢F_1ddtimeF_2=k_1⁢F_1-k_2⁢F_2F_3=1-F_1+F_2F_rel=F_2F_2+0.252ddtimeF_SRCa_RyR=Ca_SR-F_SRCa_RyRTau_SRCa_RyRK_rel=K_rel_max⁢F_SRCa_RyRF_SRCa_RyR+0.2j_rel=K_rel⁢F_rel+K_leak_rate⁢Ca_SR-Ca_i$

### Component: SERCA

$f_b=Ca_i0.000242r_b=Ca_SR1.642j_up=F_CaMK⁢V_max_f⁢f_b-V_max_r⁢r_b1+f_b+r_b$

### Component: calmodulin

$dCmdn_Ca_dtime=alpha_cmdn⁢Cmdn_tot-Cmdn_Ca⁢Ca_i-beta_cmdn⁢Cmdn_CaddtimeCmdn_Ca=alpha_cmdn⁢Cmdn_tot-Cmdn_Ca⁢Ca_i-beta_cmdn⁢Cmdn_Ca$

### Component: troponin

$dTrpn_Ca_dtime=alpha_trpn⁢Trpn_tot-Trpn_Ca⁢Ca_i-beta_trpn⁢1+2⁢1-Force_norm3⁢Trpn_CaddtimeTrpn_Ca=alpha_trpn⁢Trpn_tot-Trpn_Ca⁢Ca_i-beta_trpn⁢1+2⁢1-Force_norm3⁢Trpn_Ca$

### Component: intracellular_calcium_concentration

$ddtimeCa_i=-i_Ca_L_Ca+i_b_Ca-2⁢i_NaCa2⁢v_i⁢F-j_up+j_rel⁢v_SRv_i-dCmdn_Ca_dtime-dTrpn_Ca_dtime$

### Component: SR_calcium_concentration

$ddtimeCa_SR=j_up⁢v_iv_SR-j_rel$

### Component: intracellular_sodium_concentration

$ddtimeNa_i=-i_Na+i_b_Na+i_Ca_L_Na+3⁢i_NaCa+3⁢i_NaKv_i⁢F$

### Component: intracellular_potassium_concentration

$ddtimeK_i=-i_K1+i_K+i_to+i_b_K+i_Ca_L_K-2⁢i_NaKv_i⁢F$

### Component: Force

$f_01=3⁢f_XBf_12=10⁢f_XBf_23=7⁢f_XBg_01=g_XB⁢2-SL_normg_12=2⁢g_XB⁢2-SL_normg_23=3⁢g_XB⁢2-SL_normSL_norm=SL-1.70.7N_tm=3.5+2.5⁢SL_normK_tm=11+beta_trpnalpha_trpn0.0017-0.0009⁢SL_normalpha_tm=beta_tm⁢Trpn_CaTrpn_tot⁢K_tmN_tmddtimeN_0=beta_tm⁢P_0-alpha_tm⁢N_0+g_01⁢N_1ddtimeP_0=-beta_tm+f_01⁢P_0+alpha_tm⁢N_0+g_01⁢P_1ddtimeP_1=-beta_tm+f_12+g_01⁢P_1+alpha_tm⁢N_1+f_01⁢P_0+g_12⁢P_2ddtimeP_2=-f_23+g_12⁢P_2+f_12⁢P_1+g_23⁢P_3ddtimeP_3=-g_23⁢P_3+f_23⁢P_2N_1=1-N_0+P_0+P_1+P_2+P_3sigma_paths=1⁢g_XB⁢2⁢g_XB⁢3⁢g_XB+1⁢f_01⁢2⁢g_XB⁢3⁢g_XB+1⁢f_01⁢1⁢f_12⁢3⁢g_XB+1⁢f_01⁢1⁢f_12⁢1⁢f_23P_1_max=1⁢f_01⁢2⁢g_XB⁢3⁢g_XBsigma_pathsP_2_max=1⁢f_01⁢1⁢f_12⁢3⁢g_XBsigma_pathsP_3_max=1⁢f_01⁢1⁢f_12⁢1⁢f_23sigma_pathsForce_max=P_1_max+2⁢P_2_max+3⁢P_3_maxphi_SL=SL-0.61.4ifSL≥1.7∧SL≦21ifSL>2∧SL≦2.23.6-SL1.4ifSL>2.2∧SL≦2.3Force_norm=phi_SL⁢P_1+N_1+2⁢P_2+3⁢P_3Force_maxForce=zeta⁢Force_norm$
Source
Derived from workspace Iribe, Kohl, Noble, 2006 at changeset 78cd0f4ae9b3.
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