You are here: Home / Exposures / C. Trovato, E. Passini, N. Nagy, et al. (2019),A computational human cardiac Purkinje electrophysiological model / C. Trovato, E. Passini, N. Nagy, et al. (2019),A computational human cardiac Purkinje electrophysiological model (sedml)

Model Mathematics

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Component: environment

Component: extracellular

Component: physical_constants

Component: cell_geometry

vcell = 1000 3.14159265 rad rad L Ageo = 2 greekpi rad rad + 2 greekpi rad L Acap = 2 Ageo vmyo = 0.6 vcell vnsr = 0.04 vcell vjsr = 0.002 vcell vcsr = 0.008 vcell vss = 0.02 vcell vsl = 0.15 vcell

Component: membrane

Istim = \{\begin{matrix} amp if time ≦ duration \\ 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 + Isus + ICaL + ICaT + ICaNa + ICaK + IKr + IKs + If + IK1 + INaCa_i + INaCa_ss + INaK + INab + IpCa + ICab + 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

\frac{d}{d time} (nai) = \frac{JgapNa vsl}{vmyo} \frac{d}{d time} (nasl) = \frac{(- (INa + INaL + 3 INaCa_i + 3 INaK + IfNa + INab)) Acap cm}{F vsl} + \frac{JdiffNa vss}{vsl} + (- JgapNa) \frac{d}{d time} (nass) = \frac{(- (ICaNa + 3 INaCa_ss)) cm Acap}{F vss} - JdiffNa \frac{d}{d time} (ki) = \frac{JgapK vsl}{vmyo} \frac{d}{d time} (ksl) = \frac{(- (Ito + Isus + IKr + IKs + IfK + IK1 + Istim - (2 INaK))) cm Acap}{F vsl} + \frac{JdiffK vss}{vsl} + (- JgapK) \frac{d}{d time} (kss) = \frac{(- ICaK) cm 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{Jgap vsl}{vmyo} + \frac{Jrel2 vcsr}{vmyo} - (\frac{Jup2 vnsr}{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 - (2 INaCa_ss))) cm Acap}{2 F vss} + \frac{(Jrel1 + Jip3) vjsr}{vss} - Jdiff) Bcasl = \frac{1}{1 + \frac{cmdnmaxsl kmcmdn}{{(kmcmdn + casl)}^{2}} + \frac{trpnmaxsl kmtrpn}{{(kmtrpn + casl)}^{2}}} \frac{d}{d time} (casl) = Bcasl ((\frac{(- (IpCa + ICab + ICaT - (2 INaCa_i))) cm Acap}{2 F vsl} - (\frac{Jup1 vnsr}{vsl})) + (- Jgap) + \frac{Jdiff vss}{vsl}) \frac{d}{d time} (cansr) = Jup1 + Jup2 - (\frac{Jtr1 vjsr}{vnsr} + \frac{Jtr2 vcsr}{vnsr}) Bcajsr = \frac{1}{1 + \frac{csqnmaxsl kmcsqn}{{(kmcsqn + cajsr)}^{2}}} \frac{d}{d time} (cajsr) = Bcajsr (Jtr1 - (Jrel1 + Jip3)) Bcacsr = \frac{1}{1 + \frac{csqnmax kmcsqn}{{(kmcsqn + cacsr)}^{2}}} \frac{d}{d time} (cacsr) = Bcacsr (Jtr2 - Jrel2)

Component: reversal_potentials

ENa = \frac{R T}{F} \ln (\frac{nao}{nasl}) EK = \frac{R T}{F} \ln (\frac{ko}{ksl}) ECa = \frac{R T}{2 F} \ln (\frac{cao}{casl}) EKs = \frac{R T}{F} \ln (\frac{ko + PKNa nao}{ksl + PKNa nasl})

Component: INa

mss = \frac{1}{1 + ⅇ^{\frac{- (v + mssV1)}{mssV2}}} tm = \frac{1}{mtD1 ⅇ^{\frac{v + mtV1}{mtV2}} + mtD2 ⅇ^{\frac{- (v + mtV3)}{mtV4}}} \frac{d}{d time} (m) = \frac{mss - m}{tm} hss = \frac{1}{1 + ⅇ^{\frac{v + hssV1}{hssV2}}} thf = \frac{1}{3.686 e -6 ⅇ^{\frac{- (v + 3.8875)}{7.8579}} + 16 ⅇ^{\frac{v - 0.4963}{9.1843}}} ths = \frac{1}{0.009794 ⅇ^{\frac{- (v + 17.95)}{28.05}} + 0.3343 ⅇ^{\frac{v + 5.73}{56.66}}} Ahs = 1 - Ahf \frac{d}{d time} (hf) = \frac{hss - hf}{thf} \frac{d}{d time} (hs) = \frac{hss - hs}{ths} h = Ahf hf + Ahs hs jss = hss tj = 4.859 + \frac{1}{0.8628 ⅇ^{\frac{- (v + 116.7258)}{7.6005}} + 1.1096 ⅇ^{\frac{v + 6.2719}{9.0358}}} \frac{d}{d time} (j) = \frac{jss - j}{tj} hssp = \frac{1}{1 + ⅇ^{\frac{v + 84.7}{6.22}}} thsp = 3 ths \frac{d}{d time} (hsp) = \frac{hssp - hsp}{thsp} hp = Ahf hf + Ahs hsp 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 = tm \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} 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{20 - v}{13}}} iss = \frac{1}{1 + ⅇ^{\frac{27 + v}{13}}} taua = \frac{1.0515}{\frac{1}{1.2089 (1 + ⅇ^{\frac{- (v - 18.4099)}{29.3814}})} + \frac{3.5}{1 + ⅇ^{\frac{v + 100}{29.3814}}}} tauis = 43 + \frac{1}{0.001416 ⅇ^{\frac{- (v + 96.52)}{59.05}} + 0.0000000178 ⅇ^{\frac{v + 114.1}{8.079}}} tauif = 6.162 + \frac{1}{0.3933 ⅇ^{\frac{- (v + 100)}{100}} + 0.08004 ⅇ^{\frac{v - 8}{8.59}}} \frac{d}{d time} (a) = \frac{ass - a}{taua} \frac{d}{d time} (i1) = \frac{iss - i1}{tauis} \frac{d}{d time} (i2) = \frac{iss - i2}{tauif} Ito = Gto a i1 i2 (v - EK)

Component: Isus

asus = \frac{1}{1 + ⅇ^{\frac{- (v - 12)}{16}}} Isus = Gsus asus (v - EK)

Component: ICaL

dss = \frac{1}{1 + ⅇ^{\frac{- (v + 3.94 + 3.3)}{4.23}}} td = 0.6 + \frac{1}{ⅇ^{(- 0.05) (v + 6)} + ⅇ^{0.09 (v + 14)}} \frac{d}{d time} (d) = \frac{dss - d}{td} fss = \frac{1}{1 + ⅇ^{\frac{v + 19.58 + 3.3}{3.696}}} tff = 7 + \frac{1}{0.0045 ⅇ^{\frac{- (v + 20 + 15.19)}{10}} + 0.0045 ⅇ^{\frac{v + 20 + 15.19}{10}}} tfs = 1000 + \frac{1}{0.000035 ⅇ^{\frac{- (v + 5 + 15.19)}{4}} + 0.000035 ⅇ^{\frac{v + 5 + 15.19}{6}}} Aff = 0.6 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 = 0.72 (7 + \frac{1}{0.04 ⅇ^{\frac{- (v + 15.19 - 4)}{7}} + 0.04 ⅇ^{\frac{v + 15.19 - 4}{7}}}) tfcas = 0.49 (100 + \frac{1}{0.00012 ⅇ^{\frac{- (v + 15.19)}{3}} + 0.00012 ⅇ^{\frac{v + 15.19}{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 tjca = 75 \frac{d}{d time} (jca) = \frac{fcass - 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 = \frac{1}{\frac{k2n}{km2n} + {(1 + \frac{Kmn}{cass})}^{4}} \frac{d}{d time} (nca) = anca k2n - (nca km2n) PhiCaL = \frac{4 vffrt (cass ⅇ^{2 vfrt} - (0.341 cao))}{ⅇ^{2 vfrt} - 1} PhiCaNa = \frac{1 vffrt (0.75 nass ⅇ^{1 vfrt} - (0.75 nao))}{ⅇ^{1 vfrt} - 1} PhiCaK = \frac{1 vffrt (0.75 kss ⅇ^{1 vfrt} - (0.75 ko))}{ⅇ^{1 vfrt} - 1} 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 = (1 - fICaLp) PCa PhiCaL d (f (1 - nca) + jca fca nca) + fICaLp PCap PhiCaL d (fp (1 - nca) + jca fcap nca) ICaNa = (1 - fICaLp) PCaNa PhiCaNa d (f (1 - nca) + jca fca nca) + fICaLp PCaNap PhiCaNa d (fp (1 - nca) + jca fcap nca) ICaK = (1 - fICaLp) PCaK PhiCaK d (f (1 - nca) + jca fca nca) + fICaLp PCaKp PhiCaK d (fp (1 - nca) + jca fcap nca)

Component: ICaT

bss = \frac{1}{1 + ⅇ^{\frac{- (v + 30)}{7}}} gss = \frac{1}{1 + ⅇ^{\frac{v + 61}{5}}} taub = \frac{1}{1.068 ⅇ^{\frac{v + 16.3}{30}} + 1.068 ⅇ^{\frac{- (v + 16.3)}{30}}} taug = \frac{1}{0.015 ⅇ^{\frac{v + 71.7}{15.4}} + 0.015 ⅇ^{\frac{- (v + 71.7)}{83.3}}} \frac{d}{d time} (b) = \frac{bss - b}{taub} \frac{d}{d time} (g) = \frac{gss - g}{taug} ICaT = GCaT b g (v - ECa)

Component: IKr

xrss = \frac{1}{1 + ⅇ^{\frac{- (v + 8.337)}{6.789}}} txrf = 12.98 + \frac{1}{0.3652 ⅇ^{\frac{v + 17.6 - 31.66}{3.869}} + 4.123 e -5 ⅇ^{\frac{- (v + 17.6 - 47.78)}{20.38}}} txrs = 1.865 + \frac{1}{0.06629 ⅇ^{\frac{v + 17.2 - 34.7}{7.355}} + 1.128 e -5 ⅇ^{\frac{- (v + 17.2 - 29.74)}{25.94}}} Axrf = \frac{1}{1 + ⅇ^{\frac{v + 54.81}{38.21}}} Axrs = 1 - Axrf \frac{d}{d time} (xrf) = \frac{xrss - xrf}{txrf} \frac{d}{d time} (xrs) = \frac{xrss - xrs}{txrs} xr = Axrf xrf + Axrs xrs rkr = \frac{\frac{1}{1 + ⅇ^{\frac{v + 55}{0.32 75}}} 1}{1 + ⅇ^{\frac{v - 10}{0.32 30}}} IKr = GKr \sqrt{\frac{ko}{5.4}} xr rkr (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}{casl})}^{1.4}} IKs = GKs KsCa xs1 xs2 (v - EKs)

Component: If

yss = \frac{1}{1 + ⅇ^{\frac{v + 87}{9.5}}} tauy = \frac{2000}{ⅇ^{\frac{v + 57}{60}} + ⅇ^{\frac{- (v + 132)}{10}}} \frac{d}{d time} (y) = \frac{yss - y}{tauy} IfNa = GfNa y y (v - ENa) IfK = GfK y y (v - EK) If = IfNa + IfK

Component: IK1

xk1ss = \frac{1}{1 + ⅇ^{\frac{- (v + 2.5538 ko + 144.59)}{1.5692 ko + 3.8115}}} txk1 = \frac{122.2}{ⅇ^{\frac{- (v + 127.2)}{20.36}} + ⅇ^{\frac{v + 236.8}{69.33}}} \frac{d}{d time} (xk1) = \frac{xk1ss - xk1}{txk1} rk1 = \frac{1}{1 + ⅇ^{\frac{v + 116 - (5.5 ko)}{11}}} IK1 = GK1 2.3238 \sqrt{\frac{ko}{5.4}} rk1 xk1 (v - EK)

Component: INaCa_i

hca = ⅇ^{\frac{qca v F}{R T}} hna = ⅇ^{\frac{qna v F}{R T}} h1_i = 1 + \frac{nasl}{kna3} (1 + hna) h2_i = \frac{nasl hna}{kna3 h1_i} h3_i = \frac{1}{h1_i} h4_i = 1 + \frac{nasl}{kna1} (1 + \frac{nasl}{kna2}) h5_i = \frac{nasl nasl}{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 casl 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}{casl})}^{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) INaCa_i = 0.8 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 = 0.2 Gncx allo_ss (zna JncxNa_ss + zca JncxCa_ss)

Component: INaK

Knai = Knai0 ⅇ^{\frac{delta v F}{3 R T}} Knao = Knao0 ⅇ^{\frac{(1 - delta) v F}{3 R T}} P = \frac{eP}{1 + \frac{H}{Khp} + \frac{nasl}{Knap} + \frac{ksl}{Kxkur}} a1 = \frac{k1p {(\frac{nasl}{Knai})}^{3}}{{(1 + \frac{nasl}{Knai})}^{3} + {(1 + \frac{ksl}{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{ksl}{Kki})}^{2}}{{(1 + \frac{nasl}{Knai})}^{3} + {(1 + \frac{ksl}{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)) INaK = Pnak (zna JnakNa + zk JnakK)

Component: INab

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

Component: ICab

ICab = \frac{PCab 4 vffrt (casl ⅇ^{2 vfrt} - (0.341 cao))}{ⅇ^{2 vfrt} - 1}

Component: IpCa

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

Component: diff

JdiffNa = \frac{nass - nasl}{sstau} JgapNa = \frac{nasl - nai}{gaptau} JdiffK = \frac{kss - ksl}{sstau} JgapK = \frac{ksl - ki}{gaptau} Jdiff = \frac{cass - casl}{sstau} Jgap = \frac{casl - cai}{gaptau}

Component: ryr

REL = - (\frac{ICaL Acap}{vss F 2} + \frac{(- (Jrel1 + Jip3)) vjsr}{vss} + Jdiff) ireltau = \frac{2 (1 + \frac{1 1}{1 + {(\frac{0.28}{CaMKa})}^{8}})}{1 + \frac{0.0123}{cajsr}} irelss = \{\begin{matrix} \frac{15 (1 + \frac{1 1}{1 + {(\frac{0.28}{CaMKa})}^{8}}) REL}{1 + {(\frac{1}{cajsr})}^{8}} if REL > 0 \\ 0 otherwise \end{matrix} \frac{d}{d time} (Jrel1) = \frac{irelss - Jrel1}{ireltau} REL2 = \frac{Jgap vsl}{vmyo} + \frac{(- Jup2) vnsr}{vmyo} + \frac{Jrel2 vcsr}{vmyo} ireltau2 = \frac{6 (1 + \frac{1 1}{1 + {(\frac{0.28}{CaMKa})}^{8}})}{1 + \frac{0.0123}{cacsr}} irelss2 = \{\begin{matrix} \frac{91 (1 + \frac{1 1}{1 + {(\frac{0.28}{CaMKa})}^{8}}) REL2}{1 + {(\frac{1}{cacsr})}^{8}} if REL2 > 0 \\ 0 otherwise \end{matrix} \frac{d}{d time} (Jrel2) = \frac{irelss2 - Jrel2}{ireltau2}

Component: SERCA

dkmplb = \frac{dkmplbbar CaMKa}{CaMKa + KmCaMK} dqupcamk = \frac{dqupcamkbar CaMKa}{CaMKa + KmCaMK} Jup1 = \frac{0.0002 (dqupcamk + 1)}{1 + \frac{kmup - dkmplb}{casl}} - (\frac{0.00105 cansr}{nsrbar}) Jup2 = \frac{0.0026 (dqupcamk + 1)}{1 + \frac{kmup - dkmplb}{cai}} - (\frac{0.0042 cansr}{nsrbar})

Component: IP3

\frac{d}{d time} (u) = cass k2 (1 - u) - (k2a u) POip3 = \frac{tauip3 IP3 cass (1 - u)}{(1 + \frac{IP3 k0}{k0a}) (1 + \frac{cass k1}{k1a})} Jip3 = 10.92 POip3 (cajsr - cass)

Component: trans_flux

Jtr1 = \frac{cansr - cajsr}{120} Jtr2 = \frac{cansr - cacsr}{120}

Source: Derived from workspace A computational human cardiac Purkinje electrophysiological model at changeset 13d5908f9122.

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C. Trovato, E. Passini, N. Nagy, et al. (2019),A computational human cardiac Purkinje electrophysiological model (sedml)