# Model Mathematics

### Component: membrane

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

### 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: time_independent_potassium_current

$i_K1=g_K1⁢K_oK_o+K_mk1⁢V-E_K1+ⅇV-E_K-10⁢F⁢2R⁢T$

### Component: time_dependent_potassium_current

$I_K=i_K_max⁢K_i-K_o⁢ⅇ-V⁢FR⁢T140i_K=x⁢I_K$

### Component: time_dependent_potassium_current_x_gate

$E0xa=V+50alpha_x=0.5⁢ⅇ0.0826⁢E0xa1+ⅇ0.057⁢E0xaE0xb=V+20beta_x=1.3⁢ⅇ-0.06⁢E0xb1+ⅇ-0.04⁢E0xbddtimex=alpha_x⁢1-x-beta_x⁢x$

### Component: potassium_background_current

$i_b_K=g_bk⁢V-E_K$

### 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: sodium_background_current

$i_b_Na=g_bna⁢V-E_Na$

### Component: L_type_Ca_channel

$i_Ca_L_Ca=4⁢P_Ca_L⁢d⁢f⁢V-50⁢FR⁢T1-ⅇ-V-50⁢F⁢2R⁢T⁢Ca_i⁢ⅇ100⁢FR⁢T-Ca_o⁢ⅇ-V-50⁢F⁢2R⁢Ti_Ca_L_K=P_CaK⁢P_Ca_L⁢d⁢f⁢V-50⁢FR⁢T1-ⅇ-V-50⁢FR⁢T⁢K_i⁢ⅇ50⁢FR⁢T-K_o⁢ⅇ-V-50⁢FR⁢Ti_Ca_L_Na=P_CaNa⁢P_Ca_L⁢d⁢f⁢V-50⁢FR⁢T1-ⅇ-V-50⁢FR⁢T⁢Na_i⁢ⅇ50⁢FR⁢T-Na_o⁢ⅇ-V-50⁢FR⁢Ti_Ca_L=i_Ca_L_Ca+i_Ca_L_K+i_Ca_L_Na$

### Component: L_type_Ca_channel_d_gate

$E0_d=V+24-5alpha_d=120if|E0_d|<0.000130⁢E0_d1-ⅇ-E0_d4otherwisebeta_d=120if|E0_d|<0.000112⁢E0_dⅇE0_d10-1otherwiseddtimed=speed_d⁢alpha_d⁢1-d-beta_d⁢d$

### Component: L_type_Ca_channel_f_gate

$E0_f=V+34alpha_f=25if|E0_f|

### Component: calcium_background_current

$i_b_Ca=g_bca⁢V-E_Ca$

### Component: transient_outward_current

$i_to=g_to⁢g_tos+s⁢1-g_tos⁢r⁢V-E_K$

### 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: sodium_potassium_pump

$i_NaK=i_NaK_max⁢K_oK_mK+K_o⁢Na_iK_mNa+Na_i$

### Component: sodium_calcium_exchanger

$i_NaCa=k_NaCa⁢ⅇgamma⁢n_NaCa-2⁢V⁢FR⁢T⁢Na_in_NaCa⁢Ca_o-ⅇgamma-1⁢n_NaCa-2⁢V⁢FR⁢T⁢Na_on_NaCa⁢Ca_i1+d_NaCa⁢Ca_i⁢Na_on_NaCa+Ca_o⁢Na_in_NaCa⁢1+Ca_i0.0069$

### Component: sarcoplasmic_reticulum_calcium_pump

$K_1=K_cyca⁢K_xcsK_srcaK_2=Ca_i+Ca_up⁢K_1+K_cyca⁢K_xcs+K_cycai_up=Ca_iK_2⁢alpha_up-Ca_up⁢K_1K_2⁢beta_up$

### Component: calcium_translocation

$i_trans=50⁢Ca_up-Ca_rel$

### Component: calcium_release

$VoltDep=ⅇ0.08⁢V-40RegBindSite=Ca_iCa_i+K_m_Ca2ActRate=500⁢RegBindSiteInactRate=60+500⁢RegBindSitePrecFrac=1-ActFrac-ProdFracddtimeActFrac=PrecFrac⁢ActRate-ActFrac⁢InactRateddtimeProdFrac=ActFrac⁢InactRate-1⁢ProdFraci_rel=ActFracActFrac+0.252⁢K_m_rel+K_leak_rate⁢Ca_rel$

### Component: intracellular_sodium_concentration

$ddtimeNa_i=-11⁢V_i⁢F⁢i_Na+i_b_Na+3⁢i_NaK+3⁢i_NaCa+i_Ca_L_Na$

### Component: intracellular_potassium_concentration

$ddtimeK_i=-11⁢V_i⁢F⁢i_K1+i_K+i_Ca_L_K+i_to+i_b_K-2⁢i_NaK$

### Component: intracellular_calcium_concentration

$V_Cell=3.141592654⁢radius2⁢lengthV_i_ratio=1-V_e_ratio-V_up_ratio-V_rel_ratioV_i=V_Cell⁢V_i_ratioddtimeCa_i=-12⁢1⁢V_i⁢F⁢i_Ca_L_Ca+i_b_Ca-2⁢i_NaCa+i_rel⁢V_rel_ratioV_i_ratio-ddtimeCa_Calmod-ddtimeCa_Trop-i_upddtimeCa_up=V_i_ratioV_up_ratio⁢i_up-i_transddtimeCa_rel=V_up_ratioV_rel_ratio⁢i_trans-i_relddtimeCa_Calmod=alpha_Calmod⁢Ca_i⁢Calmod-Ca_Calmod-beta_Calmod⁢Ca_CalmodddtimeCa_Trop=alpha_Trop⁢Ca_i⁢Trop-Ca_Trop-beta_Trop⁢Ca_Trop$
Source
Derived from workspace Noble, Noble, Bett, Earm, Ho, So, 1991 at changeset ac23e1a2b164.
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