Model Mathematics

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Component: time

Component: stimulus_current

Istim = \{\begin{matrix} stimCurrent if time mod stimPeriod < stimDuration \\ 0.0 otherwise \end{matrix}

Component: model

Component: parameters

Component: initial_values

Component: model_1

Component: computed_constants

Vtotal = \frac{Vmyo + VJSR + VNSR + VSS}{0.64}

Vmito = Vtotal 0.36

f_01 = 3.0 f_xb

f_12 = 10.0 f_xb

f_23 = 7.0 f_xb

g0_01 = 1.0 gmin_xb

g0_12 = 2.0 gmin_xb

g0_23 = 3.0 gmin_xb

paths = g0_01 g0_12 g0_23 + f_01 g0_12 g0_23 + f_01 f_12 g0_23 + f_01 f_12 f_23

P1max = \frac{f_01 2.0 gmin_xb 3.0 gmin_xb}{paths}

P2max = \frac{f_01 f_12 3.0 gmin_xb}{paths}

P3max = \frac{f_01 f_12 f_23}{paths}

Fmax = P1max + 2.0 P2max + 3.0 P3max

fnormmax = \frac{Fmax}{3.0}

SLnorm = \frac{SL - 1.7}{0.6}

Ktrop_Ca = \frac{kltrpn_minus}{kltrpn_plus}

Ktrop_half = \frac{1.0}{1.0 + \frac{Ktrop_Ca}{\frac{1.7}{1000.0} + \frac{\frac{0.9}{1000.0} - (\frac{1.7}{1000.0})}{2.3 - 1.7} (SL - 1.7)}}

Ntrop = 3.5 SL - 2.0

fnormmax2 = P1max + P2max + P3max

La = 1.0

Lm_prime = 1.5

Lz = 0.1

Lb = 0.1

Lm = Lm_prime - Lb

mod_factor = 1.0 + \frac{2.3 - SL}{{(\frac{2.3 - 1.7}{1.0})}^{1.6}}

alpha_SL = \{\begin{matrix} min {1.0, \frac{(SL - (2.0 La)) + (Lm_prime - Lz)}{Lm}} if SL < 2.2 \\ 1.0 - (\frac{SL - 2.2}{Lm}) otherwise \end{matrix}

g_01_mod = g0_01 mod_factor

g_12_mod = g0_12 mod_factor

g_23_mod = g0_23 mod_factor

g_01_off = \frac{30.0}{1000.0}

g_01_off_mod = g_01_off mod_factor

RT_over_F = \frac{R T}{Faraday}

G_Ks = 0.282 \sqrt{\frac{Ko}{5.4}}

G_K1 = 0.75 \sqrt{\frac{Ko}{5.4}}

inv_5p98 = \frac{1.0}{5.98}

FaradayE3 = 1000.0 Faraday

Cao_341 = Cao 341.0

ICamax_LHospital = 2.0 PCa 1000.0 Faraday (1.0 - (341.0 Cao))

Pca_4En3 = 4.0 (1.0e-3) PCa

F_over_RT = \frac{1.0}{RT_over_F}

inv_ICahalf = \frac{1.0}{ICahalf}

PKFe3 = FaradayE3 PK

sigma = 0.0365 \frac{ⅇ^{\frac{Nao}{67.3}} - 1.0}{7.0}

inv_KmNai = \frac{1.0}{KmNai}

INaKmax_Ko_Ko_KmKo = INaKmax \frac{Ko}{Ko + KmKo}

inv_Ki1AD_NaK = \frac{1.0}{Ki1AD_NaK}

eta_1 = eta - 1.0

Nao_p3 = \frac{{Nao}^{3.0}}{Cao}

KmCa_Cao = (KmCa + Cao) \frac{{KmNa}^{3.0} + {Nao}^{3.0}}{kNaCa Cao}

KmCa_Cao_ksat = KmCa_Cao ksat

inv_KiADP_CaP = \frac{1.0}{KiADP_CaP}

KmnsCa_p3 = {KmnsCa}^{3.0}

V_AM_scaler_max_1_f_01_12_23 = V_AM_scaler \frac{V_AM_max}{f_01 + f_12 + f_23}

KmATP_AM_Ki_AM = \frac{KmATP_AM}{Ki_AM}

DmuH_Constant = (-2.303) RT_over_F DpH

VCS_C1 = \frac{KCS EtCS AcCoA}{KmAcCoA + AcCoA}

one_inv_KACOeq = 1.0 + \frac{1.0}{KACOeq}

VIDH_Constant = 1.0 + \frac{H}{kh_1} + \frac{kh_2}{H}

kIDH_EtID = kIDH EtID

inv_KADP = \frac{1.0}{KADP}

inv_KaCa = \frac{1.0}{KaCa}

inv_KidhNADH = \frac{1.0}{KidhNADH}

KmKGNAD_KmIDNAD = \frac{KmKGNAD}{KmIDNAD}

Mg_Kmg_1 = \frac{Mg}{Kmg} + 1.0

Mg_Kmg_1_Kca = \frac{Mg_Kmg_1}{Kca}

kKGDH_EtKG = kKGDH EtKG

CoA_KSLeq = \frac{CoA}{KSLeq}

kSDH_EtSDH = kSDH EtSDH

KmSucc_KiFUM = \frac{KmSucc}{KiFUM}

inv_KiOxaa = \frac{1.0}{KiOxaa}

kfFH_KFHeq = \frac{kfFH}{KFHeq}

kMDH_Fh_EtMD = {(\frac{1.0}{1.0 + \frac{Kh3}{H} + Kh3 \frac{Kh4}{H^{2.0}}})}^{2.0} (\frac{1.0}{1.0 + \frac{H}{Kh1} + \frac{H^{2.0}}{Kh1 Kh2}} + Koff) kMDH EtMD

Kmal_Kioaa = \frac{Kmal}{Kioaa}

VAAT_Constant = kfAAT GLU kcnsASP \frac{KAATeq}{kfAAT}

kcnsASP_KAATeq_kfAAT = kcnsASP \frac{KAATeq}{kfAAT}

KfAAT_GLU = kfAAT GLU

KfAAT_KAATeq = \frac{kfAAT}{KAATeq}

kres_sq_KmIDNAD = kres \frac{kres}{KmIDNAD}

exp_6_FRT_Dpsio = ⅇ^{6.0 Dpsio F_over_RT}

FRT_6_g = 6.0 g F_over_RT

ra_rc1_exp_6_FRT_Dpsio = ra + rc1 exp_6_FRT_Dpsio

r1_exp_6_FRT_Dpsio = r1 exp_6_FRT_Dpsio

rhoREN_ra_rc1_exp_6_FRT_Dpsio = 0.5 rhoREN ra_rc1_exp_6_FRT_Dpsio

rhoREN_rc2 = 0.5 rhoREN rc2

rhoREN_ra = 0.5 rhoREN ra

rhoRen_6_ra = 6.0 rhoREN ra

rhoRen_6_ra_rb = 6.0 rhoREN (ra + rb)

AREF = RT_over_F \log_{10} (kresf \sqrt{\frac{FADH2}{FAD}})

exp_AREF_FRT = ⅇ^{AREF F_over_RT}

ra_rc2_exp_AREF_FRT = 0.5 (ra + rc2 exp_AREF_FRT)

VFO_C1 = (ra + rc1 exp_6_FRT_Dpsio) exp_AREF_FRT 0.5

ra_exp_AREF_FRT = 4.0 ra exp_AREF_FRT

ra_rb = 4.0 (ra + rb)

VFO_VHFe_C1 = (1.0 + r1 exp_AREF_FRT) exp_6_FRT_Dpsio

r2_r3_exp_AREF_FRT = r2 + r3 exp_AREF_FRT

exp_3_FRT_Dpsio = ⅇ^{3.0 Dpsio F_over_RT}

FRT_3 = 3.0 F_over_RT

kf1_Pi = \frac{kf1}{Pi}

VATPase_C1 = 100.0 pa + pc1 exp_3_FRT_Dpsio

pa_pb_3 = 3.0 (pa + pb)

pa_300 = 300.0 pa

p1_exp_3_FRT_Dpsio = p1 exp_3_FRT_Dpsio

hm_F_over_RT = hm F_over_RT

VmDT_75 = 0.75 VmDT

VmDT_20 = 20.0 VmDT

inv_Kfb = \frac{1.0}{Kfb}

inv_Krb = \frac{1.0}{Krb}

inv_tautr = \frac{1.0}{tautr}

inv_tauxfer = \frac{1.0}{tauxfer}

KmATP_SR_Ki_SR = \frac{KmATP_SR}{Ki_SR}

inv_Ki_prime_SR = \frac{1.0}{Ki_prime_SR}

alpha_SL_fnormmax2 = \frac{alpha_SL}{fnormmax2}

alpha_SL_fnormmax = \frac{alpha_SL}{fnormmax 3.0}

inv_LTRPNtot_Ktrop_half = \frac{1.0}{LTRPNtot Ktrop_half}

kTrop_pn_f_01 = - kTrop_pn - f_01

kTrop_pn_f_12_g_01_mod = - (kTrop_pn + f_12 + g_01_mod)

f_23_g_12_mod = - (f_23 + g_12_mod)

CMDNtot_KmCMDN = CMDNtot KmCMDN

CSQNtot_KmCSQN = CSQNtot KmCSQN

inv_ktrans = \frac{1.0}{ktrans}

inv_kact = \frac{1.0}{kact}

Vmuni_ktrans = \frac{Vmuni}{ktrans}

FRT2 = 2.0 F_over_RT

b_05 = b 0.5

Acap_Vmyo_F = \frac{Acap}{Vmyo Faraday 1000.0}

Acap_VSS_F = \frac{Acap}{2.0 VSS Faraday 1000.0}

VJSR_VSS = \frac{VJSR}{VSS}

Vmyo_VSS = \frac{Vmyo}{VSS}

Vmyo_VNSR = \frac{Vmyo}{VNSR}

VJSR_VNSR = \frac{VJSR}{VNSR}

inv_C_m = \frac{1.0}{C_m}

inv_bL = \frac{1.0}{bL}

inv_Cmito = \frac{1.0}{Cmito}

two_b = 2.0 b

inv_keq = \frac{1.0}{keq}

zeta_alpha_SL_fnormmax = zeta alpha_SL_fnormmax

Component: model_2

ADP = 8.0 - ATPi

inv_ATPi = \frac{1.0}{ATPi}

VF_over_RT = V F_over_RT

exp_VF_over_RT = ⅇ^{VF_over_RT}

VFsq_over_RT = FaradayE3 VF_over_RT

exp2VFRT = exp_VF_over_RT exp_VF_over_RT

O1_RyR = 1.0 - (C1_RyR + C2_RyR + O2_RyR)

V_30 = V + 30.0

V_E_K = V - E_K

INa = G_Na mNa mNa mNa hNa jNa (V - E_Na)

IKs = G_Ks xKs xKs \frac{V - E_Ks}{1.0 + ⅇ^{\frac{V - 40.0}{40.0}}}

K1Alpha = \frac{1.02}{1.0 + ⅇ^{0.2385 (V_E_K - 59.215)}}

K1Beta = \frac{0.4912 ⅇ^{0.08032 (V_E_K + 5.476)} + ⅇ^{0.06175 (V_E_K - 594.31)}}{1.0 + ⅇ^{(-0.5143) ((V - E_K) + 4.753)}}

K1_inf = \frac{K1Alpha}{K1Alpha + K1Beta}

IK1 = G_K1 K1_inf V_E_K

INab = G_Nab (V - E_Na)

IKp = G_Kp \frac{V_E_K}{1.0 + ⅇ^{(7.488 - V) inv_5p98}}

ICamax = \{\begin{matrix} Pca_4En3 (exp2VFRT - Cao_341) (0.5 - (0.02 V)) if | V | < LHospitalThreshold \\ Pca_4En3 VFsq_over_RT \frac{exp2VFRT - Cao_341}{exp2VFRT - 1.0} otherwise \end{matrix}

ICaK = \{\begin{matrix} PKFe3 (Open + OCa) yCa (Ki exp2VFRT - Ko) \frac{0.5 - (0.02 V)}{1.0 + ICamax inv_ICahalf} if | V | < LHospitalThreshold \\ PKFe3 (Open + OCa) yCa (Ki exp2VFRT - Ko) \frac{VF_over_RT}{(exp2VFRT - 1.0) (1.0 + ICamax inv_ICahalf)} otherwise \end{matrix}

ICa = 6.0 ICamax yCa Open

NaiP1p5 = \sqrt{Nai Nai Nai}

INaK = INaKmax_Ko_Ko_KmKo \frac{NaiP1p5}{(NaiP1p5 + \sqrt{KmNai KmNai KmNai}) (1.0 + 0.1245 ⅇ^{(-0.1) VF_over_RT} + \frac{sigma}{exp_VF_over_RT}) (1.0 + Km1AT_NaK inv_ATPi (1.0 + ADP inv_Ki1AD_NaK))}

exp_eta_VF_over_RT = ⅇ^{eta VF_over_RT}

exp_eta1_VF_over_RT = \frac{exp_eta_VF_over_RT}{exp_VF_over_RT}

INaCa = \frac{exp_eta_VF_over_RT Nai Nai Nai - (exp_eta1_VF_over_RT Nao_p3 Cai)}{KmCa_Cao + KmCa_Cao_ksat exp_eta1_VF_over_RT}

ICab = G_Cab (V - E_Ca)

IpCa = IpCamax \frac{Cai}{KmpCa + Cai} (\frac{1.0}{1.0 + Km1ATP_CaP inv_ATPi (1.0 + ADP inv_KiADP_CaP)} + \frac{1.0}{1.0 + Km2ATP_CaP inv_ATPi})

CaiP3 = Cai Cai Cai

common = \{\begin{matrix} 0.75 CaiP3 \frac{1.0 - (0.02 V)}{CaiP3 + KmnsCa_p3} if | V | < LHospitalThreshold \\ 0.75 CaiP3 \frac{VFsq_over_RT}{(exp_VF_over_RT - 1.0) (CaiP3 + KmnsCa_p3)} otherwise \end{matrix}

InsNa = PnsNa common (Nai exp_VF_over_RT - Nao)

InsK = PnsK common (Ki exp_VF_over_RT - Ko)

InsCa = InsNa + InsK

V_AM = V_AM_scaler_max_1_f_01_12_23 \frac{f_01 P0 + f_12 P1 + f_23 P2}{1.0 + inv_ATPi (KmATP_AM + KmATP_AM_Ki_AM ADP)}

ATPm = Cm - ADPm

DmuH = DmuH_Constant + Dpsi

NAD = CPN - NADH

KmIDNAD_NAD = \frac{KmIDNAD}{NAD}

exp_FRT_6_g_DmuH = ⅇ^{FRT_6_g DmuH}

FRT2_Dpsi = FRT2 (Dpsi - 91.0)

VCS = VCS_C1 \frac{Oaa}{Oaa + KmOaa}

VACO = kfACO (CIK - (AKG + SCoA + Succ + FUM + MAL + Oaa + ISOC one_inv_KACOeq))

Fa = \frac{1.0}{(1.0 + ADPm inv_KADP) (1.0 + Cam inv_KaCa)}

Fi = 1.0 + NADH inv_KidhNADH

VIDH = \frac{kIDH_EtID}{VIDH_Constant + KmIDNAD_NAD Fi + {(\frac{Kmiso}{ISOC})}^{nID} Fa (1.0 + KmIDNAD_NAD Fi)}

a__1 = Mg_Kmg_1 + Mg_Kmg_1_Kca Cam

VKGDH = kKGDH_EtKG \frac{a__1}{a__1 + {(\frac{KmKG}{AKG})}^{nKG} + KmKGNAD_KmIDNAD KmIDNAD_NAD}

VSL = kfSL (SCoA ADPm - (CoA_KSLeq Succ ATPm))

VSDH = kSDH_EtSDH \frac{Succ}{Succ + (KmSucc + KmSucc_KiFUM FUM) (1.0 + inv_KiOxaa Oaa)}

VFH = kfFH FUM - (kfFH_KFHeq MAL)

VMDH = kMDH_Fh_EtMD MAL \frac{NAD}{(MAL + Kmal + Oaa Kmal_Kioaa) (KmmNAD + NAD)}

VAAT = VAAT_Constant \frac{Oaa}{kcnsASP_KAATeq_kfAAT + AKG}

AREN = \sqrt{NADH kres_sq_KmIDNAD KmIDNAD_NAD}

denominator1 = \frac{1.0}{exp_6_FRT_Dpsio + r1_exp_6_FRT_Dpsio AREN + (r2 + r3 AREN) exp_FRT_6_g_DmuH}

VNO = ((rhoREN_ra_rc1_exp_6_FRT_Dpsio + rhoREN_rc2 exp_FRT_6_g_DmuH) AREN - (rhoREN_ra exp_FRT_6_g_DmuH)) denominator1

VHNe = (rhoRen_6_ra AREN - (rhoRen_6_ra_rb exp_FRT_6_g_DmuH)) denominator1

denominator2 = \frac{rhoREF}{VFO_VHFe_C1 + r2_r3_exp_AREF_FRT exp_FRT_6_g_DmuH}

VHFe = (ra_exp_AREF_FRT - (ra_rb exp_FRT_6_g_DmuH)) denominator2

exp_3FRT_DmuH = ⅇ^{FRT_3 DmuH}

AF1 = kf1_Pi \frac{ATPm}{ADPm}

denominator3 = - (\frac{rhoF1}{exp_3_FRT_Dpsio + p1_exp_3_FRT_Dpsio AF1 + (p2 + p3 AF1) exp_3FRT_DmuH})

VATPase = ((VATPase_C1 + pc2 exp_3FRT_DmuH) AF1 - (pa exp_3FRT_DmuH)) denominator3

Vhu = (pa_300 + (pa_300 AF1 - (pa_pb_3 exp_3FRT_DmuH))) denominator3

ATPi_ADP = \frac{ATPi}{ADP}

ADPm_ATPm = \frac{ADPm}{ATPm}

VANT = \frac{VmDT_75 - (VmDT_20 ATPi_ADP ADPm_ATPm ⅇ^{- (F_over_RT Dpsi)})}{(1.0 + \frac{10.0}{9.0} ATPi_ADP ⅇ^{- (hm_F_over_RT Dpsi)}) (1.0 + 18.0 ADPm_ATPm)}

Vhleak = gh DmuH

MAlpha = \{\begin{matrix} 3.2 if V = -47.13 \\ 0.32 \frac{V + 47.13}{1.0 - (ⅇ^{(-0.1) (V + 47.13)})} otherwise \end{matrix}

MBeta = 0.08 ⅇ^{- (V \frac{1.0}{11.0})}

inv_MBeta_MAlpha = \frac{1.0}{MBeta + MAlpha}

tmNa = \{\begin{matrix} MAlpha inv_MBeta_MAlpha if inv_MBeta_MAlpha < 0.03 \\ mNa otherwise \end{matrix}

HAlpha = \{\begin{matrix} 0.135 ⅇ^{\frac{-80.0}{6.8}} ⅇ^{\frac{-1.0}{6.8} V} if V < -40.0 \\ 0.0 otherwise \end{matrix}

HBeta = \{\begin{matrix} 3.56 ⅇ^{0.079 V} + 310000.0 ⅇ^{0.35 V} if V < -40.0 \\ \frac{1.0}{0.13 + 0.13 ⅇ^{- (\frac{10.66}{11.1})} ⅇ^{V \frac{-1.0}{11.1}}} otherwise \end{matrix}

JAlpha = \{\begin{matrix} ((-127140.0) ⅇ^{0.2444 V} - ((3.474e-5) ⅇ^{(-0.04391) V})) \frac{V + 37.78}{1.0 + ⅇ^{0.311 (V + 79.23)}} if V < -40.0 \\ 0.0 otherwise \end{matrix}

JBeta = \{\begin{matrix} 0.1212 \frac{ⅇ^{(-0.01052) V}}{1.0 + ⅇ^{(-0.1378) (V + 40.14)}} if V < -40.0 \\ 0.3 \frac{ⅇ^{(-2.535e-7) V}}{1.0 + ⅇ^{(-0.1) V - 3.2}} otherwise \end{matrix}

\frac{d}{d time} (mNa) = MAlpha (1.0 - tmNa) - (MBeta tmNa)

\frac{d}{d time} (hNa) = HAlpha (1.0 - hNa) - (HBeta hNa)

\frac{d}{d time} (jNa) = JAlpha (1.0 - jNa) - (JBeta jNa)

\frac{d}{d time} (xKs) = (7.19e-5) \frac{V_30}{1.0 - (ⅇ^{(-0.148) V_30})} (1.0 - xKs) - ((1.31e-4) \frac{V_30}{ⅇ^{0.0687 V_30} - 1.0} xKs)

fb = {(Cai inv_Kfb)}^{Nfb}

rb = {(CaNSR inv_Krb)}^{Nrb}

Jup = KSR \frac{vmaxf fb - (vmaxr rb)}{(1.0 + fb + rb) (inv_ATPi (KmATP_SR + ADP KmATP_SR_Ki_SR) + 1.0 + ADP inv_Ki_prime_SR)}

Jrel = v1 (O1_RyR + O2_RyR) (CaJSR - CaSS)

Jtr = (CaNSR - CaJSR) inv_tautr

Jxfer = (CaSS - Cai) inv_tauxfer

P1_N1_P2_P3 = P1 + N1 + P2 + P3

FN_Ca = alpha_SL_fnormmax2 P1_N1_P2_P3

force_norm = alpha_SL_fnormmax (P1_N1_P2_P3 + P2 + P3 + P3)

force = zeta_alpha_SL_fnormmax (P1_N1_P2_P3 + P2 + P3 + P3)

kTrop_np = kTrop_pn {(LTRPNCa inv_LTRPNtot_Ktrop_half)}^{Ntrop}

\frac{d}{d time} (P0) = P0_differential P0_differential = kTrop_pn_f_01 P0 + kTrop_np N0 + g_01_mod P1

\frac{d}{d time} (P1) = P1_differential P1_differential = kTrop_pn_f_12_g_01_mod P1 + kTrop_np N1 + f_01 P0 + g_12_mod P2

\frac{d}{d time} (P2) = P2_differential P2_differential = f_23_g_12_mod P2 + f_12 P1 + g_23_mod P3

\frac{d}{d time} (P3) = P3_differential P3_differential = (- (g_23_mod P3)) + f_23 P2

\frac{d}{d time} (N1) = N1_differential N1_differential = kTrop_pn P1 - ((kTrop_np + g_01_off_mod) N1)

\frac{d}{d time} (N0) = - P0_differential - (P1_differential + P2_differential + P3_differential + N1_differential)

\frac{d}{d time} (LTRPNCa) = LTRPNCa_differential LTRPNCa_differential = kltrpn_plus Cai (LTRPNtot - LTRPNCa) - (kltrpn_minus LTRPNCa (1.0 - (\frac{2.0}{3.0} FN_Ca)))

\frac{d}{d time} (HTRPNCa) = HTRPNCa_differential HTRPNCa_differential = khtrpn_plus Cai (HTRPNtot - HTRPNCa) - (khtrpn_minus HTRPNCa)

Jtrpn = LTRPNCa_differential + HTRPNCa_differential

beta_SS = \frac{1.0}{1.0 + \frac{CMDNtot_KmCMDN}{(CaSS + KmCMDN) (CaSS + KmCMDN)}}

beta_JSR = \frac{1.0}{1.0 + \frac{CSQNtot_KmCSQN}{(CaJSR + KmCSQN) (CaJSR + KmCSQN)}}

beta_i = \frac{1.0}{1.0 + \frac{CMDNtot_KmCMDN}{(Cai + KmCMDN) (Cai + KmCMDN)}}

Cai_ktrans_plus1 = 1.0 + Cai inv_ktrans

Cai_ktrans_plus1_p3 = Cai_ktrans_plus1 Cai_ktrans_plus1 Cai_ktrans_plus1

Vuni = Vmuni_ktrans Cai FRT2_Dpsi \frac{Cai_ktrans_plus1_p3}{(Cai_ktrans_plus1_p3 Cai_ktrans_plus1 + \frac{L}{{(1.0 + Cai inv_kact)}^{na}}) (1.0 - (ⅇ^{- FRT2_Dpsi}))}

VnaCa = VmNC ⅇ^{b_05 FRT2_Dpsi} \frac{Cam}{Cai {(1.0 + \frac{Kna}{Nai})}^{n} (1.0 + \frac{Knca}{Cam})}

\frac{d}{d time} (Nai) = - ((INa + INab + InsNa + 3.0 (INaCa + INaK)) Acap_Vmyo_F) - (VnaCa 0.615)

\frac{d}{d time} (Ki) = - ((InsK + IKs + IK1 + IKp + ICaK + (Istim - (2.0 INaK))) Acap_Vmyo_F)

\frac{d}{d time} (Cai) = beta_i ((Jxfer - (Jup + Jtrpn + 0.25 Acap_Vmyo_F ((ICab - (2.0 INaCa)) + IpCa))) + (VnaCa - Vuni) 0.615)

\frac{d}{d time} (CaSS) = beta_SS (Jrel VJSR_VSS - (Jxfer Vmyo_VSS + ICa Acap_VSS_F))

\frac{d}{d time} (CaJSR) = beta_JSR (Jtr - Jrel)

\frac{d}{d time} (CaNSR) = Jup Vmyo_VNSR - (Jtr VJSR_VNSR)

\frac{d}{d time} (V) = - (inv_C_m (INa + ICa + ICaK + IKs + IK1 + IKp + INaCa + INaK + InsCa + IpCa + ICab + INab + Istim))

\frac{d}{d time} (C1_RyR) = (- (kaplus {CaSS}^{ncoop} C1_RyR)) + kaminus O1_RyR

\frac{d}{d time} (O2_RyR) = kbplus {CaSS}^{mcoop} O1_RyR - (kbminus O2_RyR)

\frac{d}{d time} (C2_RyR) = kcplus O1_RyR - (kcminus C2_RyR)

alpha = 0.4 ⅇ^{(V + 2.0) 0.1}

beta = 0.05 ⅇ^{(V + 2.0) \frac{-1.0}{13.0}}

alpha_prime = aL alpha

beta_prime = beta inv_bL

C0_to_C1 = 4.0 alpha

C1_to_C2 = 3.0 alpha

C2_to_C3 = 2.0 alpha

C3_to_C4 = alpha

CCa0_to_CCa1 = 4.0 alpha_prime

CCa1_to_CCa2 = 3.0 alpha_prime

CCa2_to_CCa3 = 2.0 alpha_prime

CCa3_to_CCa4 = alpha_prime

C1_to_C0 = beta

C2_to_C1 = 2.0 beta

C3_to_C2 = 3.0 beta

C4_to_C3 = 4.0 beta

CCa1_to_CCa0 = beta_prime

CCa2_to_CCa1 = 2.0 beta_prime

CCa3_to_CCa2 = 3.0 beta_prime

CCa4_to_CCa3 = 4.0 beta_prime

gamma = 0.1875 CaSS

C0_to_CCa0 = gamma

C1_to_CCa1 = aL C0_to_CCa0

C2_to_CCa2 = aL C1_to_CCa1

C3_to_CCa3 = aL C2_to_CCa2

C4_to_CCa4 = aL C3_to_CCa3

CCa0_to_C0 = omega

CCa1_to_C1 = CCa0_to_C0 inv_bL

CCa2_to_C2 = CCa1_to_C1 inv_bL

CCa3_to_C3 = CCa2_to_C2 inv_bL

CCa4_to_C4 = CCa3_to_C3 inv_bL

\frac{d}{d time} (C0) = C1_to_C0 C1 + (CCa0_to_C0 CCa0 - ((C0_to_C1 + C0_to_CCa0) C0))

\frac{d}{d time} (C1) = C0_to_C1 C0 + C2_to_C1 C2 + (CCa1_to_C1 CCa1 - ((C1_to_C0 + C1_to_C2 + C1_to_CCa1) C1))

\frac{d}{d time} (C2) = C1_to_C2 C1 + C3_to_C2 C3 + (CCa2_to_C2 CCa2 - ((C2_to_C1 + C2_to_C3 + C2_to_CCa2) C2))

\frac{d}{d time} (C3) = C2_to_C3 C2 + C4_to_C3 C4 + (CCa3_to_C3 CCa3 - ((C3_to_C2 + C3_to_C4 + C3_to_CCa3) C3))

\frac{d}{d time} (C4) = C3_to_C4 C3 + gL Open + (CCa4_to_C4 CCa4 - ((C4_to_C3 + fL + C4_to_CCa4) C4))

\frac{d}{d time} (Open) = fL C4 - (gL Open)

\frac{d}{d time} (CCa0) = CCa1_to_CCa0 CCa1 + (C0_to_CCa0 C0 - ((CCa0_to_CCa1 + CCa0_to_C0) CCa0))

\frac{d}{d time} (CCa1) = CCa0_to_CCa1 CCa0 + CCa2_to_CCa1 CCa2 + (C1_to_CCa1 C1 - ((CCa1_to_CCa0 + CCa1_to_CCa2 + CCa1_to_C1) CCa1))

\frac{d}{d time} (CCa2) = CCa1_to_CCa2 CCa1 + CCa3_to_CCa2 CCa3 + (C2_to_CCa2 C2 - ((CCa2_to_CCa1 + CCa2_to_CCa3 + CCa2_to_C2) CCa2))

\frac{d}{d time} (CCa3) = CCa2_to_CCa3 CCa2 + CCa4_to_CCa3 CCa4 + (C3_to_CCa3 C3 - ((CCa3_to_CCa2 + CCa3_to_CCa4 + CCa3_to_C3) CCa3))

\frac{d}{d time} (CCa4) = CCa3_to_CCa4 CCa3 + gprime OCa + (C4_to_CCa4 C4 - ((CCa4_to_CCa3 + fprime + CCa4_to_C4) CCa4))

\frac{d}{d time} (yCa) = \frac{\frac{1.0}{1.0 + ⅇ^{(V + 55.0) \frac{1.0}{7.5}}} + (\frac{0.5}{1.0 + ⅇ^{(21.0 - V) \frac{1.0}{6.0}}} - yCa)}{20.0 + \frac{600.0}{1.0 + ⅇ^{(V + 30.0) \frac{1.0}{9.5}}}}

\frac{d}{d time} (OCa) = fprime CCa4 - (gprime OCa)

Vt_CRP2 = kt_2 (CrPi_mito - CrPi_cyto)

VCK_cyto = kf_2 ((CRT_cyto - CrPi_cyto) ATPi_cyto - (CrPi_cyto (8.0 - ATPi_cyto) inv_keq))

VCK_mito = kf_3 ((CRT_mito - CrPi_mito) ATPi - (CrPi_mito ADP inv_keq))

\frac{d}{d time} (CrPi_mito) = VCK_mito - Vt_CRP2

\frac{d}{d time} (CrPi_cyto) = Vt_CRP2 + VCK_cyto

\frac{d}{d time} (ATPi) = (1.0 - clamp_ATPi) (0.615 VANT - (V_AM + 0.5 Jup + (6.371e-5) (INaK + IpCa) + VCK_mito))

\frac{d}{d time} (ATPi_cyto) = (1.0 - clamp_ATPi_cyto) (- VCK_cyto - VATPase_cyto)

\frac{d}{d time} (Cam) = fm (Vuni - VnaCa)

\frac{d}{d time} (ADPm) = VANT - (VATPase + VSL)

\frac{d}{d time} (Dpsi) = - (((- VHNe - VHFe) + Vhu + VANT + Vhleak + two_b VnaCa + 2.0 Vuni) inv_Cmito)

\frac{d}{d time} (NADH) = (- VNO) + VIDH + VKGDH + VMDH

\frac{d}{d time} (ISOC) = VACO - VIDH

\frac{d}{d time} (AKG) = VIDH + (VAAT - VKGDH)

\frac{d}{d time} (SCoA) = VKGDH - VSL

\frac{d}{d time} (Succ) = VSL - VSDH

\frac{d}{d time} (FUM) = VSDH - VFH

\frac{d}{d time} (MAL) = VFH - VMDH

\frac{d}{d time} (Oaa) = VMDH - (VCS + VAAT)

\frac{d}{d time} (ASP) = VAAT - (kcnsASP ASP)

Component: ENa

reversal_potential = \frac{R T}{z F} \ln (\frac{extracellular_concentration}{intracellular_concentration})

Component: EK

reversal_potential = \frac{R T}{z F} \ln (\frac{extracellular_concentration}{intracellular_concentration})

Component: ECa

reversal_potential = \frac{R T}{z F} \ln (\frac{extracellular_concentration}{intracellular_concentration})

Component: EKs

reversal_potential = \frac{R T}{z F} \ln (\frac{multiplier_1 extracellular_concentration_1 + multiplier_2 extracellular_concentration_2}{multiplier_1 intracellular_concentration_1 + multiplier_2 intracellular_concentration_2})