You are here: Home / Exposures / Tomek, Jakub, et al. (2019)- A computational human ventricular electrophysiological model / Tomek, Jakub, et al. (2019)- A computational human ventricular electrophysiological model (endocardial)

Model Mathematics

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Component: environment

Component: extracellular

Component: physical_constants

Component: cell_geometry

vcell = 1000 3.14 rad rad L Ageo = 2 3.14 rad rad + 2 3.14 rad L Acap = 2 Ageo vmyo = 0.68 vcell vnsr = 0.0552 vcell vjsr = 0.0048 vcell vss = 0.02 vcell

Component: membrane

Istim = \{\begin{matrix} i_Stim_Amplitude if time \geq i_Stim_Start \land time ≦ i_Stim_End \land time - i_Stim_Start - (⌊ \frac{time - i_Stim_Start}{i_Stim_Period} ⌋ i_Stim_Period) ≦ i_Stim_PulseDuration \\ 0 otherwise \end{matrix} vffrt = \frac{v F F}{R T} vfrt = \frac{v F}{R T} \frac{d}{d time} (v) = - (INa + INaL + Ito + ICaL + ICaNa + ICaK + IKr + IKs + IK1 + INaCa_i + INaCa_ss + INaK + INab + IKb + IpCa + ICab + IClCa + IClb + I_katp + Istim)

Component: CaMK

CaMKb = \frac{CaMKo (1 - CaMKt)}{1 + \frac{KmCaM}{cass}} CaMKa = CaMKb + CaMKt \frac{d}{d time} (CaMKt) = aCaMK CaMKb (CaMKb + CaMKt) - (bCaMK CaMKt)

Component: intracellular_ions

cmdnmax = \{\begin{matrix} cmdnmax_b 1.3 if celltype = 1 \\ cmdnmax_b otherwise \end{matrix} \frac{d}{d time} (nai) = \frac{(- (INa + INaL + 3 INaCa_i + ICaNa_i + 3 INaK + INab)) Acap}{F vmyo} + \frac{JdiffNa vss}{vmyo} \frac{d}{d time} (nass) = \frac{(- (ICaNa_ss + 3 INaCa_ss)) Acap}{F vss} - JdiffNa \frac{d}{d time} (ki) = \frac{(- ((Ito + IKr + IKs + IK1 + IKb + I_katp + Istim - (2 INaK)) + ICaK_i)) Acap}{F vmyo} + \frac{JdiffK vss}{vmyo} \frac{d}{d time} (kss) = \frac{(- ICaK_ss) Acap}{F vss} - JdiffK Bcai = \frac{1}{1 + \frac{cmdnmax kmcmdn}{{(kmcmdn + cai)}^{2}} + \frac{trpnmax kmtrpn}{{(kmtrpn + cai)}^{2}}} \frac{d}{d time} (cai) = Bcai ((\frac{(- (ICaL_i + IpCa + ICab - (2 INaCa_i))) Acap}{2 F vmyo} - (\frac{Jup vnsr}{vmyo})) + \frac{Jdiff vss}{vmyo}) Bcass = \frac{1}{1 + \frac{BSRmax KmBSR}{{(KmBSR + cass)}^{2}} + \frac{BSLmax KmBSL}{{(KmBSL + cass)}^{2}}} \frac{d}{d time} (cass) = Bcass (\frac{(- (ICaL_ss - (2 INaCa_ss))) Acap}{2 F vss} + \frac{Jrel vjsr}{vss} - Jdiff) \frac{d}{d time} (cansr) = Jup - (\frac{Jtr vjsr}{vnsr}) Bcajsr = \frac{1}{1 + \frac{csqnmax kmcsqn}{{(kmcsqn + cajsr)}^{2}}} \frac{d}{d time} (cajsr) = Bcajsr (Jtr - Jrel)

Component: reversal_potentials

ENa = \frac{R T}{zna F} \ln (\frac{nao}{nai}) EK = \frac{R T}{zk F} \ln (\frac{ko}{ki}) EKs = \frac{R T}{zk F} \ln (\frac{ko + PKNa nao}{ki + PKNa nai}) ECl = \frac{R T}{zcl F} \ln (\frac{clo}{cli})

Component: I_katp

akik = {(\frac{ko}{K_o_n})}^{0.24} bkik = \frac{1}{1 + {(\frac{A_atp}{K_atp})}^{2}} I_katp = fkatp gkatp akik bkik (v - EK)

Component: INa

mss = \frac{1}{{(1 + ⅇ^{\frac{- (v + 56.86)}{9.03}})}^{2}} tm = 0.1292 ⅇ^{- ({(\frac{v + 45.79}{15.54})}^{2})} + 0.06487 ⅇ^{- ({(\frac{v - 4.823}{51.12})}^{2})} \frac{d}{d time} (m) = \frac{mss - m}{tm} hss = \frac{1}{{(1 + ⅇ^{\frac{v + 71.55}{7.43}})}^{2}} ah = \{\begin{matrix} 0 if v \geq - 40 \\ 0.057 ⅇ^{\frac{- (v + 80)}{6.8}} otherwise \end{matrix} bh = \{\begin{matrix} \frac{0.77}{0.13 (1 + ⅇ^{\frac{- (v + 10.66)}{11.1}})} if v \geq - 40 \\ 2.7 ⅇ^{0.079 v} + 3.1 e 5 ⅇ^{0.3485 v} otherwise \end{matrix} th = \frac{1}{ah + bh} \frac{d}{d time} (h) = \frac{hss - h}{th} aj = \{\begin{matrix} 0 if v \geq - 40 \\ \frac{((- 2.5428 e 4) ⅇ^{0.2444 v} - (6.948 e -6 ⅇ^{(- 0.04391) v})) (v + 37.78)}{1 + ⅇ^{0.311 (v + 79.23)}} otherwise \end{matrix} bj = \{\begin{matrix} \frac{0.6 ⅇ^{0.057 v}}{1 + ⅇ^{(- 0.1) (v + 32)}} if v \geq - 40 \\ \frac{0.02424 ⅇ^{(- 0.01052) v}}{1 + ⅇ^{(- 0.1378) (v + 40.14)}} otherwise \end{matrix} jss = hss tj = \frac{1}{aj + bj} \frac{d}{d time} (j) = \frac{jss - j}{tj} hssp = \frac{1}{{(1 + ⅇ^{\frac{v + 77.55}{7.43}})}^{2}} \frac{d}{d time} (hp) = \frac{hssp - hp}{th} tjp = 1.46 tj \frac{d}{d time} (jp) = \frac{jss - jp}{tjp} fINap = \frac{1}{1 + \frac{KmCaMK}{CaMKa}} INa = GNa (v - ENa) m^{3} ((1 - fINap) h j + fINap hp jp)

Component: INaL

mLss = \frac{1}{1 + ⅇ^{\frac{- (v + 42.85)}{5.264}}} tmL = 0.1292 ⅇ^{- ({(\frac{v + 45.79}{15.54})}^{2})} + 0.06487 ⅇ^{- ({(\frac{v - 4.823}{51.12})}^{2})} \frac{d}{d time} (mL) = \frac{mLss - mL}{tmL} hLss = \frac{1}{1 + ⅇ^{\frac{v + 87.61}{7.488}}} \frac{d}{d time} (hL) = \frac{hLss - hL}{thL} hLssp = \frac{1}{1 + ⅇ^{\frac{v + 93.81}{7.488}}} thLp = 3 thL \frac{d}{d time} (hLp) = \frac{hLssp - hLp}{thLp} GNaL = \{\begin{matrix} GNaL_b 0.6 if celltype = 1 \\ GNaL_b otherwise \end{matrix} fINaLp = \frac{1}{1 + \frac{KmCaMK}{CaMKa}} INaL = GNaL (v - ENa) mL ((1 - fINaLp) hL + fINaLp hLp)

Component: Ito

ass = \frac{1}{1 + ⅇ^{\frac{- (v + EKshift - 14.34)}{14.82}}} ta = \frac{1.0515}{\frac{1}{1.2089 (1 + ⅇ^{\frac{- (v + EKshift - 18.4099)}{29.3814}})} + \frac{3.5}{1 + ⅇ^{\frac{v + EKshift + 100}{29.3814}}}} \frac{d}{d time} (a) = \frac{ass - a}{ta} iss = \frac{1}{1 + ⅇ^{\frac{v + EKshift + 43.94}{5.711}}} delta_epi = \{\begin{matrix} 1 - (\frac{0.95}{1 + ⅇ^{\frac{v + EKshift + 70}{5}}}) if celltype = 1 \\ 1 otherwise \end{matrix} tiF_b = 4.562 + \frac{1}{0.3933 ⅇ^{\frac{- (v + EKshift + 100)}{100}} + 0.08004 ⅇ^{\frac{v + EKshift + 50}{16.59}}} tiS_b = 23.62 + \frac{1}{0.001416 ⅇ^{\frac{- (v + EKshift + 96.52)}{59.05}} + 1.78 e -8 ⅇ^{\frac{v + EKshift + 114.1}{8.079}}} tiF = tiF_b delta_epi tiS = tiS_b delta_epi AiF = \frac{1}{1 + ⅇ^{\frac{v + EKshift - 213.6}{151.2}}} AiS = 1 - AiF \frac{d}{d time} (iF) = \frac{iss - iF}{tiF} \frac{d}{d time} (iS) = \frac{iss - iS}{tiS} i = AiF iF + AiS iS assp = \frac{1}{1 + ⅇ^{\frac{- (v + EKshift - 24.34)}{14.82}}} \frac{d}{d time} (ap) = \frac{assp - ap}{ta} dti_develop = 1.354 + \frac{1 e -4}{ⅇ^{\frac{v + EKshift - 167.4}{15.89}} + ⅇ^{\frac{- (v + EKshift - 12.23)}{0.2154}}} dti_recover = 1 - (\frac{0.5}{1 + ⅇ^{\frac{v + EKshift + 70.0}{20.0}}}) tiFp = dti_develop dti_recover tiF tiSp = dti_develop dti_recover tiS \frac{d}{d time} (iFp) = \frac{iss - iFp}{tiFp} \frac{d}{d time} (iSp) = \frac{iss - iSp}{tiSp} ip = AiF iFp + AiS iSp Gto = \{\begin{matrix} Gto_b 2 if celltype = 1 \\ Gto_b 2 if celltype = 2 \\ Gto_b otherwise \end{matrix} fItop = \frac{1}{1 + \frac{KmCaMK}{CaMKa}} Ito = Gto (v - EK) ((1 - fItop) a i + fItop ap ip)

Component: ICaL

dss = \{\begin{matrix} 1 if v \geq 31.4978 \\ 1.0763 ⅇ^{(- 1.0070) ⅇ^{(- 0.0829) v}} otherwise \end{matrix} td = offset + 0.6 + \frac{1}{ⅇ^{(- 0.05) (v + vShift + 6)} + ⅇ^{0.09 (v + vShift + 14)}} \frac{d}{d time} (d) = \frac{dss - d}{td} fss = \frac{1}{1 + ⅇ^{\frac{v + 19.58}{3.696}}} tff = 7 + \frac{1}{0.0045 ⅇ^{\frac{- (v + 20)}{10}} + 0.0045 ⅇ^{\frac{v + 20}{10}}} tfs = 1000 + \frac{1}{0.000035 ⅇ^{\frac{- (v + 5)}{4}} + 0.000035 ⅇ^{\frac{v + 5}{6}}} Afs = 1 - Aff \frac{d}{d time} (ff) = \frac{fss - ff}{tff} \frac{d}{d time} (fs) = \frac{fss - fs}{tfs} f = Aff ff + Afs fs fcass = fss tfcaf = 7 + \frac{1}{0.04 ⅇ^{\frac{- (v - 4)}{7}} + 0.04 ⅇ^{\frac{v - 4}{7}}} tfcas = 100 + \frac{1}{0.00012 ⅇ^{\frac{- v}{3}} + 0.00012 ⅇ^{\frac{v}{7}}} Afcaf = 0.3 + \frac{0.6}{1 + ⅇ^{\frac{v - 10}{10}}} Afcas = 1 - Afcaf \frac{d}{d time} (fcaf) = \frac{fcass - fcaf}{tfcaf} \frac{d}{d time} (fcas) = \frac{fcass - fcas}{tfcas} fca = Afcaf fcaf + Afcas fcas jcass = \frac{1.0}{1.0 + ⅇ^{\frac{v + 18.08}{2.7916}}} \frac{d}{d time} (jca) = \frac{jcass - jca}{tjca} tffp = 2.5 tff \frac{d}{d time} (ffp) = \frac{fss - ffp}{tffp} fp = Aff ffp + Afs fs tfcafp = 2.5 tfcaf \frac{d}{d time} (fcafp) = \frac{fcass - fcafp}{tfcafp} fcap = Afcaf fcafp + Afcas fcas km2n = jca 1 anca_ss = \frac{1}{\frac{k2n}{km2n} + {(1 + \frac{Kmn}{cass})}^{4}} \frac{d}{d time} (nca_ss) = anca_ss k2n - (nca_ss km2n) Io = \frac{0.5 (nao + ko + clo + 4 cao)}{1000} Iss = \frac{0.5 (nass + kss + cli + 4 cass)}{1000} constA = 1.82 e 6 {(dielConstant T)}^{- 1.5} gamma_cass = ⅇ^{(- constA) 4 (\frac{\sqrt{Iss}}{1 + \sqrt{Iss}} - (0.3 Iss))} gamma_cao = ⅇ^{(- constA) 4 (\frac{\sqrt{Io}}{1 + \sqrt{Io}} - (0.3 Io))} gamma_nass = ⅇ^{(- constA) 1 (\frac{\sqrt{Iss}}{1 + \sqrt{Iss}} - (0.3 Iss))} gamma_nao = ⅇ^{(- constA) 1 (\frac{\sqrt{Io}}{1 + \sqrt{Io}} - (0.3 Io))} gamma_kss = ⅇ^{(- constA) 1 (\frac{\sqrt{Iss}}{1 + \sqrt{Iss}} - (0.3 Iss))} gamma_ko = ⅇ^{(- constA) 1 (\frac{\sqrt{Io}}{1 + \sqrt{Io}} - (0.3 Io))} PhiCaL_ss = \frac{4 vffrt (gamma_cass cass ⅇ^{2 vfrt} - (gamma_cao cao))}{ⅇ^{2 vfrt} - 1} PhiCaNa_ss = \frac{1 vffrt (gamma_nass nass ⅇ^{1 vfrt} - (gamma_nao nao))}{ⅇ^{1 vfrt} - 1} PhiCaK_ss = \frac{1 vffrt (gamma_kss kss ⅇ^{1 vfrt} - (gamma_ko ko))}{ⅇ^{1 vfrt} - 1} PCa = \{\begin{matrix} PCa_b 1.2 if celltype = 1 \\ PCa_b 2 if celltype = 2 \\ PCa_b otherwise \end{matrix} PCap = 1.1 PCa PCaNa = 0.00125 PCa PCaK = 3.574 e -4 PCa PCaNap = 0.00125 PCap PCaKp = 3.574 e -4 PCap fICaLp = \frac{1}{1 + \frac{KmCaMK}{CaMKa}} ICaL_ss = ICaL_fractionSS ((1 - fICaLp) PCa PhiCaL_ss d (f (1 - nca_ss) + jca fca nca_ss) + fICaLp PCap PhiCaL_ss d (fp (1 - nca_ss) + jca fcap nca_ss)) ICaNa_ss = ICaL_fractionSS ((1 - fICaLp) PCaNa PhiCaNa_ss d (f (1 - nca_ss) + jca fca nca_ss) + fICaLp PCaNap PhiCaNa_ss d (fp (1 - nca_ss) + jca fcap nca_ss)) ICaK_ss = ICaL_fractionSS ((1 - fICaLp) PCaK PhiCaK_ss d (f (1 - nca_ss) + jca fca nca_ss) + fICaLp PCaKp PhiCaK_ss d (fp (1 - nca_ss) + jca fcap nca_ss)) anca_i = \frac{1}{\frac{k2n}{km2n} + {(1 + \frac{Kmn}{cai})}^{4}} \frac{d}{d time} (nca_i) = anca_i k2n - (nca_i km2n) Ii = \frac{0.5 (nai + ki + cli + 4 cai)}{1000} gamma_cai = ⅇ^{(- constA) 4 (\frac{\sqrt{Ii}}{1 + \sqrt{Ii}} - (0.3 Ii))} gamma_nai = ⅇ^{(- constA) 1 (\frac{\sqrt{Ii}}{1 + \sqrt{Ii}} - (0.3 Ii))} gamma_ki = ⅇ^{(- constA) 1 (\frac{\sqrt{Ii}}{1 + \sqrt{Ii}} - (0.3 Ii))} PhiCaL_i = \frac{4 vffrt (gamma_cai cai ⅇ^{2 vfrt} - (gamma_cao cao))}{ⅇ^{2 vfrt} - 1} PhiCaNa_i = \frac{1 vffrt (gamma_nai nai ⅇ^{1 vfrt} - (gamma_nao nao))}{ⅇ^{1 vfrt} - 1} PhiCaK_i = \frac{1 vffrt (gamma_ki ki ⅇ^{1 vfrt} - (gamma_ko ko))}{ⅇ^{1 vfrt} - 1} ICaL_i = (1 - ICaL_fractionSS) ((1 - fICaLp) PCa PhiCaL_i d (f (1 - nca_i) + jca fca nca_i) + fICaLp PCap PhiCaL_i d (fp (1 - nca_i) + jca fcap nca_i)) ICaNa_i = (1 - ICaL_fractionSS) ((1 - fICaLp) PCaNa PhiCaNa_i d (f (1 - nca_i) + jca fca nca_i) + fICaLp PCaNap PhiCaNa_i d (fp (1 - nca_i) + jca fcap nca_i)) ICaK_i = (1 - ICaL_fractionSS) ((1 - fICaLp) PCaK PhiCaK_i d (f (1 - nca_i) + jca fca nca_i) + fICaLp PCaKp PhiCaK_i d (fp (1 - nca_i) + jca fcap nca_i)) ICaL = ICaL_ss + ICaL_i ICaNa = ICaNa_ss + ICaNa_i ICaK = ICaK_ss + ICaK_i

Component: IKr

alpha = 0.1161 ⅇ^{0.2990 vfrt} beta = 0.2442 ⅇ^{(- 1.604) vfrt} alpha_2 = 0.0578 ⅇ^{0.9710 vfrt} beta_2 = 0.349 e -3 ⅇ^{(- 1.062) vfrt} alpha_i = 0.2533 ⅇ^{0.5953 vfrt} beta_i = 0.06525 ⅇ^{(- 0.8209) vfrt} alpha_C2ToI = 0.52 e -4 ⅇ^{1.525 vfrt} beta_ItoC2 = \frac{beta_2 beta_i alpha_C2ToI}{alpha_2 alpha_i} \frac{d}{d time} (C3) = beta C2 - (alpha C3) \frac{d}{d time} (C2) = alpha C3 + beta_1 C1 - ((beta + alpha_1) C2) \frac{d}{d time} (C1) = alpha_1 C2 + beta_2 O + beta_ItoC2 I - ((beta_1 + alpha_2 + alpha_C2ToI) C1) \frac{d}{d time} (O) = alpha_2 C1 + beta_i I - ((beta_2 + alpha_i) O) \frac{d}{d time} (I) = alpha_C2ToI C1 + alpha_i O - ((beta_ItoC2 + beta_i) I) GKr = \{\begin{matrix} GKr_b 1.3 if celltype = 1 \\ GKr_b 0.8 if celltype = 2 \\ GKr_b otherwise \end{matrix} IKr = GKr \sqrt{\frac{ko}{5}} O (v - EK)

Component: IKs

xs1ss = \frac{1}{1 + ⅇ^{\frac{- (v + 11.6)}{8.932}}} txs1 = 817.3 + \frac{1}{2.326 e -4 ⅇ^{\frac{v + 48.28}{17.8}} + 0.001292 ⅇ^{\frac{- (v + 210)}{230}}} \frac{d}{d time} (xs1) = \frac{xs1ss - xs1}{txs1} xs2ss = xs1ss txs2 = \frac{1}{0.01 ⅇ^{\frac{v - 50}{20}} + 0.0193 ⅇ^{\frac{- (v + 66.54)}{31}}} \frac{d}{d time} (xs2) = \frac{xs2ss - xs2}{txs2} KsCa = 1 + \frac{0.6}{1 + {(\frac{3.8 e -5}{cai})}^{1.4}} GKs = \{\begin{matrix} GKs_b 1.4 if celltype = 1 \\ GKs_b otherwise \end{matrix} IKs = GKs KsCa xs1 xs2 (v - EKs)

Component: IK1

aK1 = \frac{4.094}{1 + ⅇ^{0.1217 (v - EK - 49.934)}} bK1 = \frac{15.72 ⅇ^{0.0674 (v - EK - 3.257)} + ⅇ^{0.0618 (v - EK - 594.31)}}{1 + ⅇ^{(- 0.1629) ((v - EK) + 14.207)}} K1ss = \frac{aK1}{aK1 + bK1} GK1 = \{\begin{matrix} GK1_b 1.2 if celltype = 1 \\ GK1_b 1.3 if celltype = 2 \\ GK1_b otherwise \end{matrix} IK1 = GK1 \sqrt{\frac{ko}{5}} K1ss (v - EK)

Component: INaCa

hca = ⅇ^{qca vfrt} hna = ⅇ^{qna vfrt} h1_i = 1 + \frac{nai}{kna3} (1 + hna) h2_i = \frac{nai hna}{kna3 h1_i} h3_i = \frac{1}{h1_i} h4_i = 1 + \frac{nai}{kna1} (1 + \frac{nai}{kna2}) h5_i = \frac{nai nai}{h4_i kna1 kna2} h6_i = \frac{1}{h4_i} h7_i = 1 + \frac{nao}{kna3} (1 + \frac{1}{hna}) h8_i = \frac{nao}{kna3 hna h7_i} h9_i = \frac{1}{h7_i} h10_i = kasymm + 1 + \frac{nao}{kna1} (1 + \frac{nao}{kna2}) h11_i = \frac{nao nao}{h10_i kna1 kna2} h12_i = \frac{1}{h10_i} k1_i = h12_i cao kcaon k2_i = kcaoff k3p_i = h9_i wca k3pp_i = h8_i wnaca k3_i = k3p_i + k3pp_i k4p_i = \frac{h3_i wca}{hca} k4pp_i = h2_i wnaca k4_i = k4p_i + k4pp_i k5_i = kcaoff k6_i = h6_i cai kcaon k7_i = h5_i h2_i wna k8_i = h8_i h11_i wna x1_i = k2_i k4_i (k7_i + k6_i) + k5_i k7_i (k2_i + k3_i) x2_i = k1_i k7_i (k4_i + k5_i) + k4_i k6_i (k1_i + k8_i) x3_i = k1_i k3_i (k7_i + k6_i) + k8_i k6_i (k2_i + k3_i) x4_i = k2_i k8_i (k4_i + k5_i) + k3_i k5_i (k1_i + k8_i) E1_i = \frac{x1_i}{x1_i + x2_i + x3_i + x4_i} E2_i = \frac{x2_i}{x1_i + x2_i + x3_i + x4_i} E3_i = \frac{x3_i}{x1_i + x2_i + x3_i + x4_i} E4_i = \frac{x4_i}{x1_i + x2_i + x3_i + x4_i} allo_i = \frac{1}{1 + {(\frac{KmCaAct}{cai})}^{2}} JncxNa_i = 3 (E4_i k7_i - (E1_i k8_i)) + E3_i k4pp_i - (E2_i k3pp_i) JncxCa_i = E2_i k2_i - (E1_i k1_i) Gncx = \{\begin{matrix} Gncx_b 1.1 if celltype = 1 \\ Gncx_b 1.4 if celltype = 2 \\ Gncx_b otherwise \end{matrix} INaCa_i = (1 - INaCa_fractionSS) Gncx allo_i (zna JncxNa_i + zca JncxCa_i) h1_ss = 1 + \frac{nass}{kna3} (1 + hna) h2_ss = \frac{nass hna}{kna3 h1_ss} h3_ss = \frac{1}{h1_ss} h4_ss = 1 + \frac{nass}{kna1} (1 + \frac{nass}{kna2}) h5_ss = \frac{nass nass}{h4_ss kna1 kna2} h6_ss = \frac{1}{h4_ss} h7_ss = 1 + \frac{nao}{kna3} (1 + \frac{1}{hna}) h8_ss = \frac{nao}{kna3 hna h7_ss} h9_ss = \frac{1}{h7_ss} h10_ss = kasymm + 1 + \frac{nao}{kna1} (1 + \frac{nao}{kna2}) h11_ss = \frac{nao nao}{h10_ss kna1 kna2} h12_ss = \frac{1}{h10_ss} k1_ss = h12_ss cao kcaon k2_ss = kcaoff k3p_ss = h9_ss wca k3pp_ss = h8_ss wnaca k3_ss = k3p_ss + k3pp_ss k4p_ss = \frac{h3_ss wca}{hca} k4pp_ss = h2_ss wnaca k4_ss = k4p_ss + k4pp_ss k5_ss = kcaoff k6_ss = h6_ss cass kcaon k7_ss = h5_ss h2_ss wna k8_ss = h8_ss h11_ss wna x1_ss = k2_ss k4_ss (k7_ss + k6_ss) + k5_ss k7_ss (k2_ss + k3_ss) x2_ss = k1_ss k7_ss (k4_ss + k5_ss) + k4_ss k6_ss (k1_ss + k8_ss) x3_ss = k1_ss k3_ss (k7_ss + k6_ss) + k8_ss k6_ss (k2_ss + k3_ss) x4_ss = k2_ss k8_ss (k4_ss + k5_ss) + k3_ss k5_ss (k1_ss + k8_ss) E1_ss = \frac{x1_ss}{x1_ss + x2_ss + x3_ss + x4_ss} E2_ss = \frac{x2_ss}{x1_ss + x2_ss + x3_ss + x4_ss} E3_ss = \frac{x3_ss}{x1_ss + x2_ss + x3_ss + x4_ss} E4_ss = \frac{x4_ss}{x1_ss + x2_ss + x3_ss + x4_ss} allo_ss = \frac{1}{1 + {(\frac{KmCaAct}{cass})}^{2}} JncxNa_ss = 3 (E4_ss k7_ss - (E1_ss k8_ss)) + E3_ss k4pp_ss - (E2_ss k3pp_ss) JncxCa_ss = E2_ss k2_ss - (E1_ss k1_ss) INaCa_ss = INaCa_fractionSS Gncx allo_ss (zna JncxNa_ss + zca JncxCa_ss)

Component: INaK

Knai = Knai0 ⅇ^{\frac{delta vfrt}{3}} Knao = Knao0 ⅇ^{\frac{(1 - delta) vfrt}{3}} P = \frac{eP}{1 + \frac{H}{Khp} + \frac{nai}{Knap} + \frac{ki}{Kxkur}} a1 = \frac{k1p {(\frac{nai}{Knai})}^{3}}{{(1 + \frac{nai}{Knai})}^{3} + {(1 + \frac{ki}{Kki})}^{2} - 1} b1 = k1m MgADP a2 = k2p b2 = \frac{k2m {(\frac{nao}{Knao})}^{3}}{{(1 + \frac{nao}{Knao})}^{3} + {(1 + \frac{ko}{Kko})}^{2} - 1} a3 = \frac{k3p {(\frac{ko}{Kko})}^{2}}{{(1 + \frac{nao}{Knao})}^{3} + {(1 + \frac{ko}{Kko})}^{2} - 1} b3 = \frac{k3m P H}{1 + \frac{MgATP}{Kmgatp}} a4 = \frac{\frac{k4p MgATP}{Kmgatp}}{1 + \frac{MgATP}{Kmgatp}} b4 = \frac{k4m {(\frac{ki}{Kki})}^{2}}{{(1 + \frac{nai}{Knai})}^{3} + {(1 + \frac{ki}{Kki})}^{2} - 1} x1 = a4 a1 a2 + b2 b4 b3 + a2 b4 b3 + b3 a1 a2 x2 = b2 b1 b4 + a1 a2 a3 + a3 b1 b4 + a2 a3 b4 x3 = a2 a3 a4 + b3 b2 b1 + b2 b1 a4 + a3 a4 b1 x4 = b4 b3 b2 + a3 a4 a1 + b2 a4 a1 + b3 b2 a1 E1 = \frac{x1}{x1 + x2 + x3 + x4} E2 = \frac{x2}{x1 + x2 + x3 + x4} E3 = \frac{x3}{x1 + x2 + x3 + x4} E4 = \frac{x4}{x1 + x2 + x3 + x4} JnakNa = 3 (E1 a3 - (E2 b3)) JnakK = 2 (E4 b1 - (E3 a1)) Pnak = \{\begin{matrix} Pnak_b 0.9 if celltype = 1 \\ Pnak_b 0.7 if celltype = 2 \\ Pnak_b otherwise \end{matrix} INaK = Pnak (zna JnakNa + zk JnakK)

Component: IKb

xkb = \frac{1}{1 + ⅇ^{\frac{- (v - 10.8968)}{23.9871}}} GKb = \{\begin{matrix} GKb_b 0.6 if celltype = 1 \\ GKb_b otherwise \end{matrix} IKb = GKb xkb (v - EK)

Component: INab

INab = \frac{PNab vffrt (nai ⅇ^{vfrt} - nao)}{ⅇ^{vfrt} - 1}

Component: ICab

ICab = \frac{PCab 4 vffrt (gamma_cai cai ⅇ^{2 vfrt} - (gamma_cao cao))}{ⅇ^{2 vfrt} - 1}

Component: IpCa

IpCa = \frac{GpCa cai}{KmCap + cai}

Component: ICl

IClCa_junc = \frac{Fjunc GClCa}{1 + \frac{KdClCa}{cass}} (v - ECl) IClCa_sl = \frac{(1 - Fjunc) GClCa}{1 + \frac{KdClCa}{cai}} (v - ECl) IClCa = IClCa_junc + IClCa_sl IClb = GClb (v - ECl)

Component: diff

JdiffNa = \frac{nass - nai}{tauNa} JdiffK = \frac{kss - ki}{tauK} Jdiff = \frac{cass - cai}{tauCa}

Component: ryr

a_rel = \frac{0.5 bt}{1} Jrel_inf_b = \frac{\frac{(- a_rel) ICaL_ss}{1}}{1 + {(\frac{cajsr_half}{cajsr})}^{8}} Jrel_inf = \{\begin{matrix} Jrel_inf_b 1.7 if celltype = 2 \\ Jrel_inf_b otherwise \end{matrix} tau_rel_b = \frac{bt}{1 + \frac{0.0123}{cajsr}} tau_rel = \{\begin{matrix} 0.001 if tau_rel_b < 0.001 \\ tau_rel_b otherwise \end{matrix} \frac{d}{d time} (Jrel_np) = \frac{Jrel_inf - Jrel_np}{tau_rel} btp = 1.25 bt a_relp = \frac{0.5 btp}{1} Jrel_infp_b = \frac{\frac{(- a_relp) ICaL_ss}{1}}{1 + {(\frac{cajsr_half}{cajsr})}^{8}} Jrel_infp = \{\begin{matrix} Jrel_infp_b 1.7 if celltype = 2 \\ Jrel_infp_b otherwise \end{matrix} tau_relp_b = \frac{btp}{1 + \frac{0.0123}{cajsr}} tau_relp = \{\begin{matrix} 0.001 if tau_relp_b < 0.001 \\ tau_relp_b otherwise \end{matrix} \frac{d}{d time} (Jrel_p) = \frac{Jrel_infp - Jrel_p}{tau_relp} fJrelp = \frac{1}{1 + \frac{KmCaMK}{CaMKa}} Jrel = Jrel_b ((1 - fJrelp) Jrel_np + fJrelp Jrel_p)

Component: SERCA

upScale = \{\begin{matrix} 1.3 if celltype = 1 \\ 1 otherwise \end{matrix} Jupnp = \frac{upScale 0.005425 cai}{cai + 0.00092} Jupp = \frac{upScale 2.75 0.005425 cai}{cai + 0.00092 - 0.00017} fJupp = \frac{1}{1 + \frac{KmCaMK}{CaMKa}} Jleak = \frac{0.0048825 cansr}{15} Jup = Jup_b ((1 - fJupp) Jupnp + fJupp Jupp - Jleak)

Component: trans_flux

Jtr = \frac{cansr - cajsr}{60}

Source: Derived from workspace A computational human ventricular electrophysiological model at changeset bfc578e28020.

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