# Model Mathematics

### Component: cell

$i_Stim=-12iftime-⌊timestim_Period⌋⁢stim_Period≥100∧time-⌊timestim_Period⌋⁢stim_Period≦1030otherwisei_tot=i_K1+i_to+i_Kr+i_Ks+i_CaL+i_NaK+i_Na+i_b_Na+i_NaCa+i_b_Ca+i_p_K+i_p_Ca+i_StimddtimeV=-i_tot$

### Component: reversal_potentials

$E_Na=R⁢TF⁢ln⁡Na_oNa_iE_K=R⁢TF⁢ln⁡K_oK_iE_Ks=R⁢TF⁢ln⁡K_o+P_kna⁢Na_oK_i+P_kna⁢Na_iE_Ca=0.5⁢R⁢TF⁢ln⁡Ca_oCa_i$

### Component: IK1

$i_K1=g_K1_0⁢T35-557⁢K_o5.4⁢xK1_inf⁢V-E_K$

### Component: iK1_rectification

$KiMg=2.8⁢ⅇ-V-fac⁢E_K180KbMg=0.45⁢ⅇ-V-fac⁢E_K20Kd1SPM=0.7 e -3⁢ⅇ-V-fac⁢E_K+8⁢Mg_Buf4.8Kd2SPM=40 e -3⁢ⅇ-V-fac⁢E_K9.1temp=1+Mg_BufKbMgrec1=temp⁢tempSPMKd1SPM+Mg_BufKiMg+temp⁢temp⁢temprec2=11+SPMKd2SPMxK1_inf=phi⁢rec1+1-phi⁢rec2$

### Component: IKr

$i_Kr=g_Kr_0⁢T35-557⁢K_o5.4⁢Or4⁢V-E_K$

### Component: iKr_Markov

$alpha_xr1=1⁢TT_Base⁢ⅇ24.335+T_BaseT⁢0.0112⁢V-25.914beta_xr1=1⁢TT_Base⁢ⅇ13.688+T_BaseT⁢-0.0603⁢V-15.707alpha_xr2=1⁢TT_Base⁢ⅇ22.746+T_BaseT⁢0⁢V-25.914beta_xr2=1⁢TT_Base⁢ⅇ13.193+T_BaseT⁢0⁢V-15.707alpha_xr3=1⁢TT_Base⁢ⅇ22.098+T_BaseT⁢0.0365⁢V-25.914beta_xr3=1⁢TT_Base⁢ⅇ7.313+T_BaseT⁢-0.0399⁢V-15.707alpha_xr4=1⁢TT_Base⁢ⅇ30.016+T_BaseT⁢0.0223⁢V-30.888⁢5.4K_o0.4beta_xr4=1⁢TT_Base⁢ⅇ30.061+T_BaseT⁢-0.0312⁢V-33.243ddtimeCr1=beta_xr1⁢Cr2-alpha_xr1⁢Cr1ddtimeCr2=alpha_xr1⁢Cr1+beta_xr2⁢Cr3-alpha_xr2+beta_xr1⁢Cr2ddtimeCr3=alpha_xr2⁢Cr2+beta_xr3⁢Or4-alpha_xr3+beta_xr2⁢Cr3ddtimeOr4=alpha_xr3⁢Cr3+beta_xr4⁢Ir5-alpha_xr4+beta_xr3⁢Or4-OtoB+BtoOddtimeIr5=alpha_xr4⁢Or4-beta_xr4⁢Ir5$

### Component: iKr_Markov_Sotalol_block

$OtoB=O⁢Sotalol_mM⁢kBindingBtoO=BOr4⁢kDissddtimeBCr1=beta_xr1⁢BCr2-alpha_xr1⁢BCr1ddtimeBCr2=alpha_xr1⁢BCr1+beta_xr2⁢BCr3-alpha_xr2+beta_xr1⁢BCr2ddtimeBCr3=alpha_xr2⁢BCr2+beta_xr3⁢BOr4-alpha_xr3+beta_xr2⁢BCr3ddtimeBOr4=alpha_xr3⁢BCr3+beta_xr4⁢BIr5-alpha_xr4+beta_xr3⁢BOr4+OtoB-BtoOddtimeBIr5=alpha_xr4⁢BOr4-beta_xr4⁢BIr5$

### Component: IKs

$i_Ks=g_Ks⁢Xs2⁢V-E_Ks$

### Component: iKs_Xs_gate

$xs_inf=11+ⅇ-5-V14alpha_xs=14001+ⅇ5-V6beta_xs=11+ⅇV-3515tau_xs=1⁢alpha_xs⁢beta_xs+80ddtimeXs=xs_inf-Xstau_xs$

### Component: Ito

$i_to=g_to⁢r⁢s⁢V-E_K$

### Component: ito_s_gate

$s_inf=11+ⅇV+205tau_s=85⁢ⅇ-V+452320+51+ⅇV-205+3ddtimes=s_inf-stau_s$

### Component: ito_r_gate

$r_inf=11+ⅇ20-V6tau_r=9.5⁢ⅇ-V+4021800+0.8ddtimer=r_inf-rtau_r$

### Component: INa

$i_Na=g_Na⁢m3⁢h⁢j⁢V-E_Na$

### Component: iNa_m_gate

$m_inf=11+ⅇ-56.86-V9.032alpha_m=11+ⅇ-60-V5beta_m=0.11+ⅇV+355+0.11+ⅇV-50200tau_m=1⁢alpha_m⁢beta_mddtimem=m_inf-mtau_m$

### Component: iNa_h_gate

$h_inf=11+ⅇV+71.55-shift_INa_inact7.432alpha_h=0.057⁢ⅇ-V+80-shift_INa_inact6.8ifV<-40+shift_INa_inact0otherwisebeta_h=2.7⁢ⅇ0.079⁢V-shift_INa_inact+310000⁢ⅇ0.3485⁢V-shift_INa_inactifV<-40+shift_INa_inact0.770.13⁢1+ⅇV+10.66-shift_INa_inact-11.1otherwisetau_h=1alpha_h+beta_hddtimeh=h_inf-htau_h$

### Component: iNa_j_gate

$j_inf=11+ⅇV+71.55-shift_INa_inact7.432alpha_j=-25428⁢ⅇ0.2444⁢V-shift_INa_inact-6.948 e -6⁢ⅇ-0.04391⁢V-shift_INa_inact⁢V+37.7811+ⅇ0.311⁢V+79.23-shift_INa_inactifV<-40+shift_INa_inact0otherwisebeta_j=0.02424⁢ⅇ-0.01052⁢V-shift_INa_inact1+ⅇ-0.1378⁢V+40.14-shift_INa_inactifV<-40+shift_INa_inact0.6⁢ⅇ0.057⁢V-shift_INa_inact1+ⅇ-0.1⁢V+32-shift_INa_inactotherwisetau_j=1alpha_j+beta_jddtimej=j_inf-jtau_j$

### Component: INab

$i_b_Na=g_bna⁢V-E_Na$

### Component: ICaL

$i_CaL=g_CaL⁢d⁢f⁢f2⁢fCass⁢z2⁢V-15⁢F2R⁢T⁢0.25⁢Ca_ss⁢ⅇ2⁢V-15⁢FR⁢T-Ca_oⅇ2⁢V-15⁢FR⁢T-1$

### Component: iCaL_d_gate

$d_inf=11+ⅇd_inf_shift-V7.5alpha_d=1.41+ⅇ-35-V13+0.25beta_d=1.41+ⅇV+55gamma_d=11+ⅇ50-V20tau_d=1⁢alpha_d⁢beta_d+gamma_dddtimed=d_inf-dtau_d$

### Component: iCaL_f_gate

$f_inf=11+ⅇV+207tau_f=1102.5⁢ⅇ-V+272225+2001+ⅇ13-V10+1801+ⅇV+3010+204ddtimef=f_inf-ftau_f$

### Component: iCaL_f2_gate

$f2_inf=0.751+ⅇV+357+0.25tau_f2=562⁢ⅇ-V+272240+311+ⅇ25-V10+801+ⅇV+30102ddtimef2=f2_inf-f2tau_f2$

### Component: iCaL_fCass_gate

$fCass_inf=0.41+Ca_ss0.052+0.6tau_fCass=801+Ca_ss0.052+2ddtimefCass=fCass_inf-fCasstau_fCass$

### Component: ICab

$i_b_Ca=g_bca⁢V-E_Ca$

### Component: IpCa

$i_p_Ca=g_pCa⁢Ca_iCa_i+K_pCa$

### Component: IpK

$i_p_K=g_pK⁢V-E_K1+ⅇ25-V5.98$

### Component: INaK

$i_NaK=P_NaK⁢K_oK_o+K_mk⁢Na_iNa_i+K_mNa1+0.1245⁢ⅇ-0.1⁢V⁢FR⁢T+0.0353⁢ⅇ-V⁢FR⁢T$

### Component: INaCa

$i_NaCa=K_NaCa⁢ⅇgamma⁢V⁢FR⁢T⁢Na_i3⁢Ca_o-ⅇgamma-1⁢V⁢FR⁢T⁢Na_o3⁢Ca_i⁢alphaKm_Nai3+Na_o3⁢Km_Ca+Ca_o⁢1+K_sat⁢ⅇgamma-1⁢V⁢FR⁢T$

### Component: Ca

$ddtimeCa_i=Ca_i_bufc⁢i_leak-i_up⁢V_srVol_c+i_xfer-i_b_Ca+i_p_Ca-2⁢i_NaCa⁢Cm2⁢Vol_c⁢FddtimeCa_SR=Ca_sr_bufsr⁢i_up-i_rel+i_leakddtimeCa_ss=Ca_ss_bufss⁢-i_CaL⁢Cm2⁢V_ss⁢F+i_rel⁢V_srV_ss-i_xfer⁢Vol_cV_ss$

### Component: Ileak_Iup_Ixfer

$i_up=Vmax_up1+K_up2Ca_i2i_leak=Vol_leak⁢Ca_SR-Ca_ii_xfer=Vol_xfer⁢Ca_ss-Ca_i$

### Component: Irel

$kcasr=max_sr-max_sr-min_sr1+ECCa_SR2k1=k1_primekcasrk2=k2_prime⁢kcasrO=k1⁢Ca_ss2⁢R_primek3+k1⁢Ca_ss2i_rel=Vol_rel⁢O⁢Ca_SR-Ca_ssddtimeR_prime=-k2⁢Ca_ss⁢R_prime+k4⁢1-R_prime$

### Component: Ca_buffer

$Ca_i_bufc=11+Buf_c⁢K_buf_cCa_i+K_buf_c2Ca_sr_bufsr=11+Buf_sr⁢K_buf_srCa_SR+K_buf_sr2Ca_ss_bufss=11+Buf_ss⁢K_buf_ssCa_ss+K_buf_ss2$

### Component: Na

$ddtimeNa_i=-i_Na+i_b_Na+3⁢i_NaK+3⁢i_NaCa⁢CmVol_c⁢F$

### Component: K

$ddtimeK_i=-i_K1+i_to+i_Kr+i_Ks+i_p_K+i_Stim-2⁢i_NaKVol_c⁢F⁢Cm$

### Component: Ions_n_reversal_potentials

Source
Derived from workspace Fink, Noble, Virag, Varro, Giles, 2008 at changeset 0628c5ca2f03.
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