# Model Mathematics

### Component: cell

$FonRT=FR⁢Tpast=⌊timestim_period⌋⁢stim_periodi_Stim=stim_amplitudeiftime-past≥stim_offset∧time-past≦stim_offset+stim_duration0otherwiseI_tot=i_Na+i_Ca+i_to+i_Kr+i_Ks+i_K1+i_NaCa+i_NaK+i_b_Na+i_b_Ca+i_StimddtimeV=dVdtdVdt=V_hold-V1ifV_clamp=1∧time≦500∨time>800V_step-V1ifV_clamp=1∧time>500∧time≦800-1⁢I_tototherwise$

### Component: INa

$i_Na=g_Na⁢m3⁢h⁢j⁢V-E_NaE_Na=ln⁡NaoNaiFonRT$

### Component: INa_m_gate

$alpha_m=0.32⁢V+47.131-ⅇ-0.1⁢V+47.13if|V+47.13|>0.0013.2otherwisebeta_m=0.08⁢ⅇ-V11ddtimem=alpha_m⁢1-m-beta_m⁢m$

### Component: INa_h_gate

$alpha_h=0.135⁢ⅇ80+V-6.8ifV<-400otherwisebeta_h=3.56⁢ⅇ0.079⁢V+3.1e5⁢ⅇ0.35⁢VifV<-4010.13⁢1+ⅇ-V+10.6611.1otherwiseddtimeh=alpha_h⁢1-h-beta_h⁢h$

### Component: INa_j_gate

$alpha_j=-127140⁢ⅇ0.244⁢V-3.474e-5⁢ⅇ-0.04391⁢V⁢V+37.781+ⅇ0.311⁢V+79.23ifV<-400otherwisebeta_j=0.1212⁢ⅇ-0.01052⁢V1+ⅇ-0.1378⁢V+40.14ifV<-400.3⁢ⅇ-2.535e-7⁢V1+ⅇ-0.1⁢V+32otherwiseddtimej=alpha_j⁢1-j-beta_j⁢j$

### Component: ICa

$i_Ca=g_Ca_max⁢d⁢f⁢f_Ca⁢V-E_CaE_Ca=ln⁡CaoCai2⁢FonRT$

### Component: ICa_d_gate

$alpha_d=14.985916.6813⁢2⁢π⁢ⅇ-V-22.3616.681322beta_d=0.1471-5.314.93⁢2⁢π⁢ⅇ-V-6.274414.9322ddtimed=alpha_d⁢1-d-beta_d⁢d$

### Component: ICa_f_gate

$alpha_f=6.872e-31+ⅇV-6.15466.1223beta_f=0.0687⁢ⅇ-0.1081⁢V+9.8255+0.01121+ⅇ-0.2779⁢V+9.8255+5.474e-4ddtimef=alpha_f⁢1-f-beta_f⁢f$

### Component: ICa_f_Ca_gate

$f_Ca=Km_CaKm_Ca+Cai$

### Component: Ito

$g_to_max=0.3iffailing=00.191otherwisei_to=g_to_max⁢r⁢t⁢V-E_toE_to=ln⁡0.043⁢Nao+Ko0.043⁢Nai+KiFonRT$

### Component: Ito_r_gate

$ddtimer=alpha_r⁢1-r-beta_r⁢ralpha_r=0.5266⁢ⅇ-0.0166⁢V-42.29121+ⅇ-0.0943⁢V-42.2912beta_r=5.186e-5⁢V+0.5149⁢ⅇ-0.1344⁢V-5.00271+ⅇ-0.1348⁢V-5.186e-5$

### Component: Ito_t_gate

$ddtimet=alpha_t⁢1-t-beta_t⁢talpha_t=5.612e-5⁢V+0.0721⁢ⅇ-0.173⁢V+34.25311+ⅇ-0.1732⁢V+34.2531beta_t=1.215e-4⁢V+0.0767⁢ⅇ-1.66e-9⁢V+34.02351+ⅇ-0.1604⁢V+34.0235$

### Component: IKs

$i_Ks=g_Ks_max⁢Xs2⁢V-E_KsE_Ks=ln⁡0.01833⁢Nao+Ko0.01833⁢Nai+KiFonRT$

### Component: IKs_Xs_gate

$ddtimeXs=alpha_Xs⁢1-Xs-beta_Xs⁢Xsalpha_Xs=3.013e-31+ⅇ7.4454-V+1014.3171beta_Xs=5.87e-31+ⅇ5.95+V+1015.82$

### Component: IKr

$i_Kr=g_Kr_max⁢Xr⁢rik⁢V-E_KE_K=ln⁡KoKiFonRTrik=11+ⅇV+2623$

### Component: IKr_Xr_gate

$ddtimeXr=alpha_Xr⁢1-Xr-beta_Xr⁢Xralpha_Xr=0.005⁢ⅇ5.266e-4⁢V+4.0671+ⅇ-0.1262⁢V+4.067beta_Xr=0.016⁢ⅇ1.6e-3⁢V+65.661+ⅇ0.0783⁢V+65.66$

### Component: IK1

$g_K1_max=2.5iffailing=02otherwisei_K1=g_K1_max⁢K1_infinity⁢V-E_K1E_K1=ln⁡KoKiFonRT$

### Component: IK1_K1_gate

$K1_infinity=alpha_K1alpha_K1+beta_K1alpha_K1=0.11+ⅇ0.06⁢V-E_K1+200beta_K1=3⁢ⅇ2e-4⁢V+100+-E_K1+1⁢ⅇ0.1⁢V-10+E_K11+ⅇ-0.5⁢V-E_K1$

### Component: ICab

$g_b_Ca_max=0.00085iffailing=00.0013otherwisei_b_Ca=g_b_Ca_max⁢V-E_Ca$

### Component: INab

$g_b_Na_max=0.001iffailing=00otherwisei_b_Na=g_b_Na_max⁢V-E_Na$

### Component: INaK

$I_NaK_max=1.3iffailing=00.75otherwisef_NaK=11+0.1245⁢ⅇ-0.1⁢V⁢FonRT+0.0365⁢sigma⁢ⅇ-V⁢FonRTsigma=17⁢ⅇNao67.3-1i_NaK=I_NaK_max⁢f_NaK⁢11+K_mNaiNai1.5⁢KoKo+K_mKo$

### Component: INaCa

$K_NaCa=1000iffailing=01650otherwisei_NaCa=K_NaCa⁢1K_mNa3+Nao3⁢1K_mCa+Cao⁢11+K_sat⁢ⅇeta-1⁢V⁢FonRT⁢ⅇeta⁢V⁢FonRT⁢Nai3⁢Cao-ⅇeta-1⁢V⁢FonRT⁢Nao3⁢Cai$

### Component: Irel

$ddtimeAPtrack=100⁢1-APtrack-0.5⁢APtrackifdVdt>150-0.5⁢APtrackotherwiseddtimeAPtrack2=100⁢1-APtrack2-0.5⁢APtrack2ifAPtrack<0.2∧APtrack>0.18-0.5⁢APtrack2otherwiseddtimeAPtrack3=100⁢1-APtrack3-0.5⁢APtrack3ifAPtrack<0.2∧APtrack>0.18-0.01⁢APtrack3otherwiseddtimeCainfluxtrack=-Cm⁢i_Ca-i_NaCa+i_b_Ca2⁢V_myo⁢FifAPtrack>0.20ifAPtrack2>0.01∧APtrack≦0.2-0.5⁢CainfluxtrackotherwiseddtimeOVRLDtrack=0⁢50⁢1-OVRLDtrackif11+K_mCSQNCa_JSR>CSQNthresh∧OVRLDtrack3<0.37∧APtrack3<0.37-0⁢0.5⁢OVRLDtrackotherwiseddtimeOVRLDtrack2=0⁢50⁢1-OVRLDtrack2ifOVRLDtrack>Logicthresh∧OVRLDtrack2Logicthresh∧OVRLDtrack3delta_Ca_ith0⁢G_rel_overload⁢1-OVRLDtrack2⁢OVRLDtrack2ifCainfluxtrack≦delta_Ca_ith∧OVRLDtrack2>00otherwisei_rel=G_rel⁢Ca_JSR-Cai$

### Component: Iup

$I_up_max=0.0045iffailing=00.0015otherwisei_up=I_up_max⁢CaiCai+K_mup$

### Component: Ileak

$K_leak=0.00026iffailing=00.00017otherwisei_leak=K_leak⁢Ca_NSR$

### Component: Itr

$i_tr=1⁢Ca_NSR-Ca_JSRtau_tr$

### Component: calcium_buffers_in_the_myoplasm

$Cai_bufc=11+buffon⁢CMDN_max⁢K_mCMDNK_mCMDN+Cai2+Tn_max⁢K_mTnK_mTn+Cai2$

### Component: calcium_buffers_in_the_JSR

$Ca_JSR_bufc=11+CSQN_max⁢K_mCSQNK_mCSQN+Ca_JSR2$

### Component: Ionic_concentrations

$volume=π⁢preplength⁢radius2V_myo=0.68⁢volumeV_NSR=0.0552⁢volumeV_JSR=0.0048⁢volumeddtimeNai=-1⁢Cm⁢i_Na+i_b_Na+i_NaCa⁢3+i_NaK⁢3V_myo⁢FddtimeKi=-1⁢Cm⁢i_to+i_Kr+i_K1+i_Stim+i_Ks-2⁢i_NaKV_myo⁢FddtimeCai=Cai_bufc⁢-Cm⁢i_Ca-2⁢i_NaCa+i_b_Ca2⁢V_myo⁢F+i_rel⁢V_JSRV_myo+i_leak-i_up⁢V_NSRV_myoddtimeCa_JSR=Ca_JSR_bufc⁢i_tr-i_relddtimeCa_NSR=-1⁢i_leak+V_JSRV_NSR⁢i_tr-i_up$

### Component: Ions_n_reversal_potentials

Source
Derived from workspace Priebe, Beuckelmann, 1998 at changeset 02ebb36177b7.
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