/* * Contributions of HERG K+ current to repolarization of the human * ventricular action potential * * Model Status * * This model is known to run in OpenCell and COR to reproduce * the published results. Units have been checked. COR reports * they are balanced and consistent while OpenCell is reporting * some inconsistencies. OpenCell is currently having unit "issues" * and we believe the units are correct in this CellML model. * * Model Structure * * ABSTRACT: Action potential repolarization in the mammalian heart * is governed by interactions of a number of time- and voltage-dependent * channel-mediated currents, as well as contributions from the * Na+/Ca2+ exchanger and the Na+/K+ pump. Recent work has shown * that one of the K+ currents (HERG) which contributes to repolarization * in mammalian ventricle is a locus at which a number of point * mutations can have significant functional consequences. In addition, * the remarkable sensitivity of this K+ channel isoform to inhibition * by a variety of pharmacological agents and clinical drugs has * resulted in HERG being a major focus for Safety Pharmacology * requirements. For these reasons we and others have attempted * to define the functional role for HERG-mediated K+ currents * in repolarization of the action potential in the human ventricle. * Here, we describe and evaluate changes in the formulations for * two K+ currents, IK1 and HERG (or IK,r), within the framework * of ten Tusscher model of the human ventricular action potential. * In this computational study, new mathematical formulations for * the two nonlinear K+ conductances, IK1 and HERG, have been developed * based upon experimental data obtained from electrophysiological * studies of excised human ventricular tissue and/or myocytes. * The resulting mathematical model provides much improved simulations * of the relative sizes and time courses of the K+ currents which * modulate repolarization. Our new formulation represents an important * first step in defining the mechanism(s) of repolarization of * the membrane action potential in the human ventricle. Our overall * goal is to understand the genesis of the T-wave of the human * electrocardiogram. * * The complete original paper reference is cited below: * * Contributions of HERG K+ current to repolarization of the human * ventricular action potential, Martin Fink, Denis Noble, Laszlo * Virag, Andras Varro, and Wayne R. Giles, 2008, Progress in Biophysics * and Molecular Biology 96, (1-3), 357-376. PubMed ID: 17919688 * * cell diagram * * [[Image file: tentusscher_2006.png]] * * A schematic diagram describing the ion movement across the cell * surface membrane and the sarcoplasmic reticulum, which are described * by the Fink et al. 2008 mathematical model of the human ventricular * myocyte. */ import nsrunit; unit conversion on; // unit nanolitre predefined // unit millisecond predefined unit per_millisecond=1E3 second^(-1); // unit millivolt predefined unit millivolt2=1E-6 kilogram^2*meter^4*second^(-6)*ampere^(-2); unit per_millivolt=1E3 kilogram^(-1)*meter^(-2)*second^3*ampere^1; unit milliS=.001 kilogram^(-1)*meter^(-2)*second^3*ampere^2; unit microS=1E-6 kilogram^(-1)*meter^(-2)*second^3*ampere^2; unit nanoF=1E-9 kilogram^(-1)*meter^(-2)*second^4*ampere^2; unit nanoA=1E-9 ampere^1; unit microS_per_nanoF=1E3 second^(-1); unit nanoA_per_nanoF=1 kilogram^1*meter^2*second^(-4)*ampere^(-1); // unit molar predefined // unit millimolar predefined unit millivolt_per_millimolar=.001 kilogram^1*meter^5*second^(-3)*ampere^(-1)*mole^(-1); unit millimolar_per_millisecond=1E3 meter^(-3)*second^(-1)*mole^1; unit per_millimolar_per_millisecond=1E3 meter^3*second^(-1)*mole^(-1); unit per_millimolar2_per_millisecond=1E3 meter^6*second^(-1)*mole^(-2); unit millijoule_per_mole_kelvin=.001 kilogram^1*meter^2*second^(-2)*kelvin^(-1)*mole^(-1); unit coulomb_per_mole=1 second^1*ampere^1*mole^(-1); unit litre_per_farad_millisecond=1 kilogram^1*meter^5*second^(-5)*ampere^(-2); math main { realDomain time millisecond; time.min=0; extern time.max; extern time.delta; real R millijoule_per_mole_kelvin; R=8314.472; real T kelvin; T=310; real F coulomb_per_mole; F=96485.3415; real K_o millimolar; K_o=5.4; real Ca_o millimolar; Ca_o=2; real Na_o millimolar; Na_o=140; real V(time) millivolt; when(time=time.min) V=-86.45; real Cm nanoF; Cm=0.115; real Vol_c nanolitre; Vol_c=0.016404; real i_K1(time) nanoA_per_nanoF; real i_to(time) nanoA_per_nanoF; real i_Kr(time) nanoA_per_nanoF; real i_Ks(time) nanoA_per_nanoF; real i_CaL(time) nanoA_per_nanoF; real i_NaK(time) nanoA_per_nanoF; real i_Na(time) nanoA_per_nanoF; real i_b_Na(time) nanoA_per_nanoF; real i_NaCa(time) nanoA_per_nanoF; real i_b_Ca(time) nanoA_per_nanoF; real i_p_K(time) nanoA_per_nanoF; real i_p_Ca(time) nanoA_per_nanoF; real i_Stim(time) nanoA_per_nanoF; real i_tot(time) nanoA_per_nanoF; real stim_Period millisecond; stim_Period=1000; real E_Na(time) millivolt; real E_K(time) millivolt; real E_Ks(time) millivolt; real E_Ca(time) millivolt; real P_kna dimensionless; P_kna=0.03; real K_i(time) millimolar; when(time=time.min) K_i=141.0167; real Na_i(time) millimolar; when(time=time.min) Na_i=7.940167; real Ca_i(time) millimolar; when(time=time.min) Ca_i=1.092e-4; real g_K1_0 microS_per_nanoF; g_K1_0=0.6821; real xK1_inf(time) dimensionless; real Mg_Buf millimolar; Mg_Buf=0.0356; real SPM millimolar; SPM=1.4613e-3; real fac dimensionless; fac=1.0648; real phi dimensionless; phi=0.8838; real temp(time) dimensionless; real rec1(time) dimensionless; real rec2(time) dimensionless; real KiMg(time) millimolar; real KbMg(time) millimolar; real Kd1SPM(time) millimolar; real Kd2SPM(time) millimolar; real g_Kr_0 microS_per_nanoF; g_Kr_0=0.024; real Or4(time) dimensionless; when(time=time.min) Or4=0.014; real Cr1(time) dimensionless; when(time=time.min) Cr1=0.9786; real Cr2(time) dimensionless; when(time=time.min) Cr2=0.0031; real Cr3(time) dimensionless; when(time=time.min) Cr3=0.0029; real Ir5(time) dimensionless; when(time=time.min) Ir5=0.0014; real T_Base kelvin; T_Base=310; real alpha_xr1(time) per_millisecond; real beta_xr1(time) per_millisecond; real alpha_xr2(time) per_millisecond; real beta_xr2(time) per_millisecond; real alpha_xr3(time) per_millisecond; real beta_xr3(time) per_millisecond; real alpha_xr4(time) per_millisecond; real beta_xr4(time) per_millisecond; real OtoB(time) per_millisecond; real BtoO(time) per_millisecond; real Sotalol_mM millimolar; Sotalol_mM=0; real BCr1(time) dimensionless; when(time=time.min) BCr1=0; real BCr2(time) dimensionless; when(time=time.min) BCr2=0; real BCr3(time) dimensionless; when(time=time.min) BCr3=0; real BOr4(time) dimensionless; when(time=time.min) BOr4=0; real BIr5(time) dimensionless; when(time=time.min) BIr5=0; real kBinding per_millimolar_per_millisecond; kBinding=5e-3; real kDiss per_millisecond; kDiss=0.00125; real g_Ks microS_per_nanoF; g_Ks=0.0392; real Xs(time) dimensionless; when(time=time.min) Xs=0.00303; real xs_inf(time) dimensionless; real alpha_xs(time) dimensionless; real beta_xs(time) dimensionless; real tau_xs(time) millisecond; real g_to microS_per_nanoF; g_to=0.2; real s(time) dimensionless; when(time=time.min) s=1; real r(time) dimensionless; when(time=time.min) r=2.11e-8; real s_inf(time) dimensionless; real tau_s(time) millisecond; real r_inf(time) dimensionless; real tau_r(time) millisecond; real g_Na microS_per_nanoF; g_Na=11; real shift_INa_inact millivolt; shift_INa_inact=0; real m(time) dimensionless; when(time=time.min) m=0.00132; real h(time) dimensionless; when(time=time.min) h=0.7768; real j(time) dimensionless; when(time=time.min) j=0.7766; real m_inf(time) dimensionless; real alpha_m(time) dimensionless; real beta_m(time) dimensionless; real tau_m(time) millisecond; real h_inf(time) dimensionless; real alpha_h(time) per_millisecond; real beta_h(time) per_millisecond; real tau_h(time) millisecond; real j_inf(time) dimensionless; real alpha_j(time) per_millisecond; real beta_j(time) per_millisecond; real tau_j(time) millisecond; real g_bna microS_per_nanoF; g_bna=0.00029; real g_CaL litre_per_farad_millisecond; g_CaL=2e-5; real Ca_ss(time) millimolar; when(time=time.min) Ca_ss=1.893e-4; real d(time) dimensionless; when(time=time.min) d=5.06e-6; real f(time) dimensionless; when(time=time.min) f=0.9999; real f2(time) dimensionless; when(time=time.min) f2=0.9995; real fCass(time) dimensionless; when(time=time.min) fCass=1; real z dimensionless; z=2; real d_inf(time) dimensionless; real alpha_d(time) dimensionless; real beta_d(time) dimensionless; real gamma_d(time) millisecond; real tau_d(time) millisecond; real d_inf_shift millivolt; d_inf_shift=5; real f_inf(time) dimensionless; real tau_f(time) millisecond; real f2_inf(time) dimensionless; real tau_f2(time) millisecond; real fCass_inf(time) dimensionless; real tau_fCass(time) millisecond; real g_bca microS_per_nanoF; g_bca=0.0004736; real g_pCa nanoA_per_nanoF; g_pCa=0.0619; real K_pCa millimolar; K_pCa=0.0005; real g_pK microS_per_nanoF; g_pK=0.00973; real P_NaK nanoA_per_nanoF; P_NaK=1.297; real K_mk millimolar; K_mk=1; real K_mNa millimolar; K_mNa=40; real K_NaCa nanoA_per_nanoF; K_NaCa=200; real K_sat dimensionless; K_sat=0.1; real alpha dimensionless; alpha=2.5; real gamma dimensionless; gamma=0.35; real Km_Ca millimolar; Km_Ca=1.38; real Km_Nai millimolar; Km_Nai=87.5; real Ca_SR(time) millimolar; when(time=time.min) Ca_SR=2.7656; real Ca_i_bufc(time) dimensionless; real Ca_sr_bufsr(time) dimensionless; real Ca_ss_bufss(time) dimensionless; real V_sr nanolitre; V_sr=0.001094; real V_ss nanolitre; V_ss=0.00005468; real i_rel(time) millimolar_per_millisecond; real i_up(time) millimolar_per_millisecond; real i_leak(time) millimolar_per_millisecond; real i_xfer(time) millimolar_per_millisecond; real Vol_xfer per_millisecond; Vol_xfer=0.0038; real K_up millimolar; K_up=0.00025; real Vol_leak per_millisecond; Vol_leak=0.00036; real Vmax_up millimolar_per_millisecond; Vmax_up=0.006375; real R_prime(time) dimensionless; when(time=time.min) R_prime=0.9864; real k1_prime per_millimolar2_per_millisecond; k1_prime=0.15; real k2_prime per_millimolar_per_millisecond; k2_prime=0.045; real EC millimolar; EC=1.5; real max_sr dimensionless; max_sr=2.5; real min_sr dimensionless; min_sr=1; real k3 per_millisecond; k3=0.06; real k4 per_millisecond; k4=0.005; real Vol_rel per_millisecond; Vol_rel=0.306; real Irel.O(time) dimensionless; real kcasr(time) dimensionless; real k1(time) per_millimolar2_per_millisecond; real k2(time) per_millimolar_per_millisecond; real Buf_c millimolar; Buf_c=0.2; real K_buf_c millimolar; K_buf_c=0.001; real Buf_sr millimolar; Buf_sr=10; real K_buf_sr millimolar; K_buf_sr=0.3; real Buf_ss millimolar; Buf_ss=0.4; real K_buf_ss millimolar; K_buf_ss=0.00025; // // i_Stim=(if (((time-floor(time/stim_Period)*stim_Period)>=(100 millisecond)) and ((time-floor(time/stim_Period)*stim_Period)<=(103 millisecond))) (-1)*(12 nanoA_per_nanoF) else (0 nanoA_per_nanoF)); i_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_Stim); V:time=((-1)*i_tot); // E_Na=(R*T/F*ln(Na_o/Na_i)); E_K=(R*T/F*ln(K_o/K_i)); E_Ks=(R*T/F*ln((K_o+P_kna*Na_o)/(K_i+P_kna*Na_i))); E_Ca=(.5*R*T/F*ln(Ca_o/Ca_i)); // i_K1=(g_K1_0*(T/(35 kelvin)-(55 kelvin)/(7 kelvin))*sqrt(K_o/(5.4 millimolar))*xK1_inf*(V-E_K)); // KiMg=((2.8 millimolar)*exp((-1)*(V-fac*E_K)/(180 millivolt))); KbMg=((.45 millimolar)*exp((-1)*(V-fac*E_K)/(20 millivolt))); Kd1SPM=((7E-4 millimolar)*exp((-1)*(V-fac*E_K+(8 millivolt_per_millimolar)*Mg_Buf)/(4.8 millivolt))); Kd2SPM=((.04 millimolar)*exp((-1)*(V-fac*E_K)/(9.1 millivolt))); temp=(1+Mg_Buf/KbMg); rec1=(temp*temp/(SPM/Kd1SPM+Mg_Buf/KiMg+temp*temp*temp)); rec2=(1/(1+SPM/Kd2SPM)); xK1_inf=(phi*rec1+(1-phi)*rec2); // i_Kr=(g_Kr_0*(T/(35 kelvin)-55/7)*sqrt(K_o/(5.4 millimolar))*Or4*(V-E_K)); // alpha_xr1=((1 per_millisecond)*T/T_Base*exp(24.335+T_Base/T*((.0112 per_millivolt)*V-25.914))); beta_xr1=((1 per_millisecond)*T/T_Base*exp(13.688+T_Base/T*((-1)*(.0603 per_millivolt)*V-15.707))); alpha_xr2=((1 per_millisecond)*T/T_Base*exp(22.746+T_Base/T*((0 per_millivolt)*V-25.914))); beta_xr2=((1 per_millisecond)*T/T_Base*exp(13.193+T_Base/T*((0 per_millivolt)*V-15.707))); alpha_xr3=((1 per_millisecond)*T/T_Base*exp(22.098+T_Base/T*((.0365 per_millivolt)*V-25.914))); beta_xr3=((1 per_millisecond)*T/T_Base*exp(7.313+T_Base/T*((-1)*(.0399 per_millivolt)*V-15.707))); alpha_xr4=((1 per_millisecond)*T/T_Base*exp(30.016+T_Base/T*((.0223 per_millivolt)*V-30.888))*((5.4 millimolar)/K_o)^.4); beta_xr4=((1 per_millisecond)*T/T_Base*exp(30.061+T_Base/T*((-1)*(.0312 per_millivolt)*V-33.243))); Cr1:time=(beta_xr1*Cr2-alpha_xr1*Cr1); Cr2:time=(alpha_xr1*Cr1+beta_xr2*Cr3-(alpha_xr2+beta_xr1)*Cr2); Cr3:time=(alpha_xr2*Cr2+beta_xr3*Or4-(alpha_xr3+beta_xr2)*Cr3); Or4:time=(alpha_xr3*Cr3+beta_xr4*Ir5-(alpha_xr4+beta_xr3)*Or4-OtoB+BtoO); Ir5:time=(alpha_xr4*Or4-beta_xr4*Ir5); // OtoB=(Or4*Sotalol_mM*kBinding); BtoO=(BOr4*kDiss); BCr1:time=(beta_xr1*BCr2-alpha_xr1*BCr1); BCr2:time=(alpha_xr1*BCr1+beta_xr2*BCr3-(alpha_xr2+beta_xr1)*BCr2); BCr3:time=(alpha_xr2*BCr2+beta_xr3*BOr4-(alpha_xr3+beta_xr2)*BCr3); BOr4:time=(alpha_xr3*BCr3+beta_xr4*BIr5-(alpha_xr4+beta_xr3)*BOr4+OtoB-BtoO); BIr5:time=(alpha_xr4*BOr4-beta_xr4*BIr5); // i_Ks=(g_Ks*Xs^2*(V-E_Ks)); // xs_inf=(1/(1+exp(((-1)*(5 millivolt)-V)/(14 millivolt)))); alpha_xs=(1400/sqrt(1+exp(((5 millivolt)-V)/(6 millivolt)))); beta_xs=(1/(1+exp((V-(35 millivolt))/(15 millivolt)))); tau_xs=((1 millisecond)*alpha_xs*beta_xs+(80 millisecond)); Xs:time=((xs_inf-Xs)/tau_xs); // i_to=(g_to*r*s*(V-E_K)); // s_inf=(1/(1+exp((V+(20 millivolt))/(5 millivolt)))); tau_s=((85 millisecond)*exp((-1)*(V+(45 millivolt))^2/(320 millivolt2))+(5 millisecond)/(1+exp((V-(20 millivolt))/(5 millivolt)))+(3 millisecond)); s:time=((s_inf-s)/tau_s); // r_inf=(1/(1+exp(((20 millivolt)-V)/(6 millivolt)))); tau_r=((9.5 millisecond)*exp((-1)*(V+(40 millivolt))^2/(1800 millivolt2))+(.8 millisecond)); r:time=((r_inf-r)/tau_r); // i_Na=(g_Na*m^3*h*j*(V-E_Na)); // m_inf=(1/(1+exp(((-1)*(56.86 millivolt)-V)/(9.03 millivolt)))^2); alpha_m=(1/(1+exp(((-1)*(60 millivolt)-V)/(5 millivolt)))); beta_m=(.1/(1+exp((V+(35 millivolt))/(5 millivolt)))+.1/(1+exp((V-(50 millivolt))/(200 millivolt)))); tau_m=((1 millisecond)*alpha_m*beta_m); m:time=((m_inf-m)/tau_m); // h_inf=(1/(1+exp((V+(71.55 millivolt)-shift_INa_inact)/(7.43 millivolt)))^2); alpha_h=(if (V<((-1)*(40 millivolt)+shift_INa_inact)) (.057 per_millisecond)*exp((-1)*(V+(80 millivolt)-shift_INa_inact)/(6.8 millivolt)) else (0 per_millisecond)); beta_h=(if (V<((-1)*(40 millivolt)+shift_INa_inact)) (2.7 per_millisecond)*exp((.079 per_millivolt)*(V-shift_INa_inact))+(3.1E5 per_millisecond)*exp((.3485 per_millivolt)*(V-shift_INa_inact)) else (.77 per_millisecond)/(.13*(1+exp((V+(10.66 millivolt)-shift_INa_inact)/((-1)*(11.1 millivolt)))))); tau_h=(1/(alpha_h+beta_h)); h:time=((h_inf-h)/tau_h); // j_inf=(1/(1+exp((V+(71.55 millivolt)-shift_INa_inact)/(7.43 millivolt)))^2); alpha_j=(if (V<((-1)*(40 millivolt)+shift_INa_inact)) ((-1)*(25428 per_millisecond)*exp((.2444 per_millivolt)*(V-shift_INa_inact))-(6.948E-6 per_millisecond)*exp((-1)*(.04391 per_millivolt)*(V-shift_INa_inact)))*(V+(37.78 millivolt))/(1 millivolt)/(1+exp((.311 per_millivolt)*(V+(79.23 millivolt)-shift_INa_inact))) else (0 per_millisecond)); beta_j=(if (V<((-1)*(40 millivolt)+shift_INa_inact)) (.02424 per_millisecond)*exp((-1)*(.01052 per_millivolt)*(V-shift_INa_inact))/(1+exp((-1)*(.1378 per_millivolt)*(V+(40.14 millivolt)-shift_INa_inact))) else (.6 per_millisecond)*exp((.057 per_millivolt)*(V-shift_INa_inact))/(1+exp((-1)*(.1 per_millivolt)*(V+(32 millivolt)-shift_INa_inact)))); tau_j=(1/(alpha_j+beta_j)); j:time=((j_inf-j)/tau_j); // i_b_Na=(g_bna*(V-E_Na)); // i_CaL=(g_CaL*d*f*f2*fCass*z^2*(V-(15 millivolt))*F^2/(R*T)*(.25*Ca_ss*exp(2*(V-(15 millivolt))*F/(R*T))-Ca_o)/(exp(2*(V-(15 millivolt))*F/(R*T))-1)); // d_inf=(1/(1+exp((d_inf_shift-V)/(7.5 millivolt)))); alpha_d=(1.4/(1+exp(((-1)*(35 millivolt)-V)/(13 millivolt)))+.25); beta_d=(1.4/(1+exp((V+(5 millivolt))/(5 millivolt)))); gamma_d=((1 millisecond)/(1+exp(((50 millivolt)-V)/(20 millivolt)))); tau_d=((1 millisecond)*alpha_d*beta_d+gamma_d); d:time=((d_inf-d)/tau_d); // f_inf=(1/(1+exp((V+(20 millivolt))/(7 millivolt)))); tau_f=(((1102.5 millisecond)*exp((-1)*(V+(27 millivolt))^2/(225 millivolt2))+(200 millisecond)/(1+exp(((13 millivolt)-V)/(10 millivolt)))+(180 millisecond)/(1+exp((V+(30 millivolt))/(10 millivolt)))+(20 millisecond))/4); f:time=((f_inf-f)/tau_f); // f2_inf=(.75/(1+exp((V+(35 millivolt))/(7 millivolt)))+.25); tau_f2=(((562 millisecond)*exp((-1)*(V+(27 millivolt))^2/(240 millivolt2))+(31 millisecond)/(1+exp(((25 millivolt)-V)/(10 millivolt)))+(80 millisecond)/(1+exp((V+(30 millivolt))/(10 millivolt))))/2); f2:time=((f2_inf-f2)/tau_f2); // fCass_inf=(.4/(1+(Ca_ss/(.05 millimolar))^2)+.6); tau_fCass=((80 millisecond)/(1+(Ca_ss/(.05 millimolar))^2)+(2 millisecond)); fCass:time=((fCass_inf-fCass)/tau_fCass); // i_b_Ca=(g_bca*(V-E_Ca)); // i_p_Ca=(g_pCa*Ca_i/(Ca_i+K_pCa)); // i_p_K=(g_pK*(V-E_K)/(1+exp(((25 millivolt)-V)/(5.98 millivolt)))); // i_NaK=(P_NaK*K_o/(K_o+K_mk)*Na_i/(Na_i+K_mNa)/(1+.1245*exp((-1)*.1*V*F/(R*T))+.0353*exp((-1)*V*F/(R*T)))); // i_NaCa=(K_NaCa*(exp(gamma*V*F/(R*T))*Na_i^3*Ca_o-exp((gamma-1)*V*F/(R*T))*Na_o^3*Ca_i*alpha)/((Km_Nai^3+Na_o^3)*(Km_Ca+Ca_o)*(1+K_sat*exp((gamma-1)*V*F/(R*T))))); // Ca_i:time=(Ca_i_bufc*((i_leak-i_up)*V_sr/Vol_c+i_xfer-(i_b_Ca+i_p_Ca-2*i_NaCa)*Cm/(2*Vol_c*F))); Ca_SR:time=(Ca_sr_bufsr*(i_up-(i_rel+i_leak))); Ca_ss:time=(Ca_ss_bufss*((-1)*i_CaL*Cm/(2*V_ss*F)+i_rel*V_sr/V_ss-i_xfer*Vol_c/V_ss)); // i_up=(Vmax_up/(1+K_up^2/Ca_i^2)); i_leak=(Vol_leak*(Ca_SR-Ca_i)); i_xfer=(Vol_xfer*(Ca_ss-Ca_i)); // kcasr=(max_sr-(max_sr-min_sr)/(1+(EC/Ca_SR)^2)); k1=(k1_prime/kcasr); k2=(k2_prime*kcasr); Irel.O=(k1*Ca_ss^2*R_prime/(k3+k1*Ca_ss^2)); i_rel=(Vol_rel*Irel.O*(Ca_SR-Ca_ss)); R_prime:time=((-1)*k2*Ca_ss*R_prime+k4*(1-R_prime)); // Ca_i_bufc=(1/(1+Buf_c*K_buf_c/(Ca_i+K_buf_c)^2)); Ca_sr_bufsr=(1/(1+Buf_sr*K_buf_sr/(Ca_SR+K_buf_sr)^2)); Ca_ss_bufss=(1/(1+Buf_ss*K_buf_ss/(Ca_ss+K_buf_ss)^2)); // Na_i:time=((-1)*(i_Na+i_b_Na+3*i_NaK+3*i_NaCa)*Cm/(Vol_c*F)); // K_i:time=((-1)*(i_K1+i_to+i_Kr+i_Ks+i_p_K+i_Stim-2*i_NaK)/(Vol_c*F)*Cm); // // // }