Model Mathematics

Ist = \{\begin{matrix} I_test if time > test_start \land time < test_end \\ I_hold otherwise \end{matrix}

I_Ca_tot = ical + icat + insca I_tot = ina + ih + inaca + inak + ical + icat + icl + ik1 + ik2 + ika + iBKa + iBKab + insna + insk + insca + ib \frac{d}{d time} (v) = - (I_tot + Ist)

J_Ca_mem = \frac{AV Cm buff}{zca frdy} I_Ca_tot

jcamem_plot = J_Ca_mem conversion jpmca_plot = jpmca conversion jnaca_plot = jnaca conversion J_tot = J_Ca_mem + jnaca + jpmca \frac{d}{d time} (cai) = - J_tot

ki = 140.0 nai = 4.0 cli = 46.0 ko = 6.0 cao = 2.5 nao = 130.0 clo = 130.0 mgo = 0.5 buff = 0.015 AV = 4.0 zca = 2.0 zna = 1.0 zk = 1.0 R = 8314.0 frdy = 96485.0 temp = 308.0 Cm = 1.0 gna = 0 gcal = 0.6 ecal = 45.0 kmca = 0.001 gcat = 0.058 ecat = 42.0 gkca = 0.8 gb = 0.004 gk1 = 0.52 gk2 = 0.032 gbka = 0.2 gbkab = 0.1 gka = 0.16 gcl = 0.1875 gh = 0.0542 gns = 0.0123 PnsK = 1.3 PnsNa = 0.9 PnsCa = 0.89 PnsCs = 1.0 gnsCa = 0.5 gnsNa = 1.0 gnsK = 1.19 gnsCs = 1.6 ginak = 1.7 nakKmko = 2.0 nakKmnai = 22.0 PK = 1.0 PNa = 0.35 Jpmca = 0.00000035 Kmpmca = 0.0005 npmca = 2 Jnaca = 0.0000035 Kmallo = 0.0003 nallo = 4 ksat = 0.27 xgamma = 0.35 Kmnai = 30.0 Kmcai = 0.007 Kmnao = 87.5 Kmcao = 1.3 Fmax = 3.0 FKm = 161.301 Fn = 3.60205

vFRT = \frac{v frdy}{R temp} ena = \frac{R temp}{frdy} \ln (\frac{nao}{nai}) ek = \frac{R temp}{frdy} \ln (\frac{ko}{ki}) eh = \frac{R temp}{frdy} \ln (\frac{ko + \frac{PNa}{PK} nao}{ki + \frac{PNa}{PK} nai}) ecl = \frac{R temp}{frdy} \ln (\frac{cli}{clo}) enscc = \frac{R temp}{frdy} \ln (\frac{PnsK ko + PnsNa nao + \frac{4 PnsCa cao}{1.0 + ⅇ^{vFRT}}}{PnsK ki + PnsNa nai + \frac{4 PnsCa cai}{1.0 + ⅇ^{vFRT}}})

wss = \frac{1.0}{1.0 + {(\frac{FKm conversion}{cai})}^{Fn}} wtc = 4000.0 (0.234845 + \frac{1.0 - 0.234845}{1.0 + {(\frac{cai}{FKm conversion})}^{Fn}}) Force = Fmax (w - 0.2345) \frac{d}{d time} (w) = \frac{wss - w}{wtc}

mss = \frac{1.0}{1.0 + ⅇ^{\frac{- (v + 35.9584)}{9.24013}}} hss = \frac{1.0}{1.0 + ⅇ^{\frac{v + 57.0}{8.0}}} mtc = 0.25 + \frac{7.0}{1.0 + ⅇ^{\frac{v + 38.0}{10.0}}} htc = 0.9 + \frac{1002.85}{1.0 + {(\frac{v + 47.5}{1.5})}^{2}} ina = gna m m m h (v - ena) \frac{d}{d time} (m) = \frac{mss - m}{mtc} \frac{d}{d time} (h) = \frac{hss - h}{htc}

fca = \frac{1.0}{1.0 + {(\frac{cai}{kmca})}^{4.0}} dss = \frac{1.0}{1.0 + ⅇ^{\frac{- (v + 22.0)}{7.0}}} fss = \frac{1.0}{1.0 + ⅇ^{\frac{v + 38.0}{7.0}}} dtc = 2.29 + \frac{5.7}{1.0 + {(\frac{v + 29.97}{9.0})}^{2}} f1tc = 12.0 f2tc = 90.9699 (1.0 - (\frac{1.0}{(1.0 + ⅇ^{\frac{v + 13.9629}{45.3782}}) (1.0 + ⅇ^{\frac{- (v + 9.49866)}{3.3945}})})) ical = gcal fca d d (0.8 f1 + 0.2 f2) (v - ecal) \frac{d}{d time} (d) = \frac{dss - d}{dtc} \frac{d}{d time} (f1) = \frac{fss - f1}{f1tc} \frac{d}{d time} (f2) = \frac{fss - f2}{f2tc}

bss = \frac{1.0}{1.0 + ⅇ^{\frac{- (v + 54.23)}{9.88}}} gss = 0.02 + \frac{0.98}{1.0 + ⅇ^{\frac{v + 72.978}{4.64}}} btc = 0.45 + \frac{3.9}{1.0 + {(\frac{v + 66.0}{26.0})}^{2}} gtc = 150.0 (1.0 - (\frac{1.0}{(1.0 + ⅇ^{\frac{v - 417.43}{203.18}}) (1.0 + ⅇ^{\frac{- (v + 61.11)}{8.07}})})) icat = gcat b b g (v - ecat) \frac{d}{d time} (b) = \frac{bss - b}{btc} \frac{d}{d time} (g) = \frac{gss - g}{gtc}

ib = gb (v - ek)

qss = \frac{0.978613}{1.0 + ⅇ^{\frac{- (v + 18.6736)}{26.6606}}} rss = \frac{1.0}{1.0 + ⅇ^{\frac{v + 63.0}{6.3}}} qtc = \frac{500.0}{1.0 + {(\frac{v + 60.71}{15.79})}^{2}} r1tc = \frac{5000.0}{1.0 + {(\frac{v + 62.7133}{35.8611})}^{2}} r2tc = 30000.0 + \frac{220000.0}{1.0 + ⅇ^{\frac{v + 22.0}{4.0}}} ik1 = gk1 q q (0.38 r1 + 0.63 r2) (v - ek) \frac{d}{d time} (q) = \frac{qss - q}{qtc} \frac{d}{d time} (r1) = \frac{rss - r1}{r1tc} \frac{d}{d time} (r2) = \frac{rss - r2}{r2tc}

pss = \frac{0.948}{1.0 + ⅇ^{\frac{- (v + 17.91)}{18.4}}} kss = \frac{1.0}{1.0 + ⅇ^{\frac{v + 21.2}{5.7}}} ptc = \frac{100.0}{1.0 + {(\frac{v + 64.1}{28.67})}^{2}} k1tc = 1000000.0 (1.0 - (\frac{1.0}{(1.0 + ⅇ^{\frac{v - 315.0}{50.0}}) (1.0 + ⅇ^{\frac{- (v + 74.9)}{8.0}})})) k2tc = 2500000.0 (1.0 - (\frac{1.0}{(1.0 + ⅇ^{\frac{v - 132.868}{25.3992}}) (1.0 + ⅇ^{\frac{- (v + 24.9203)}{2.67915}})})) ik2 = gk2 p p (0.75 k1 + 0.25 k2) (v - ek) \frac{d}{d time} (p) = \frac{pss - p}{ptc} \frac{d}{d time} (k1) = \frac{kss - k1}{k1tc} \frac{d}{d time} (k2) = \frac{kss - k2}{k2tc}

sss = \frac{1.0}{1.0 + ⅇ^{\frac{- (v + 27.79)}{7.57}}} xss = 0.02 + \frac{0.98}{1.0 + ⅇ^{\frac{v + 69.5}{6.0}}} stc = \frac{17.0}{1.0 + {(\frac{v + 20.5232}{35.0})}^{2}} xtc = 7.5 + \frac{10.0}{1.0 + {(\frac{v + 34.1765}{120.0})}^{2}} ika = gka s x (v - ek) \frac{d}{d time} (s) = \frac{sss - s}{stc} \frac{d}{d time} (x) = \frac{xss - x}{xtc}

xass_z = \frac{- 0.749234}{1.0 + {(\frac{cai conversion - 0.0630535}{0.161942})}^{2}} + \frac{8.38384}{1.0 + {(\frac{cai conversion + 1538.29}{739.057})}^{2}} xass_vh = \frac{5011.47}{1.0 + {(\frac{cai conversion + 0.237503}{0.000239278})}^{0.42291}} - 37.5137 xass = \frac{1.0}{1.0 + ⅇ^{\frac{(- xass_z) frdy (v - xass_vh)}{R temp}}} xatc = \frac{2.40914}{1.0 + {(\frac{v - 158.779}{- 52.1497})}^{2}} iBKa = gkca gbka xa (v - ek) \frac{d}{d time} (xa) = \frac{xass - xa}{xatc}

xabss_z = \frac{- 0.681249}{1.0 + {(\frac{cai conversion - 0.218988}{0.428335})}^{2}} + \frac{1.40001}{1.0 + {(\frac{cai conversion + 228.71}{684.946})}^{2}} xabss_vh = \frac{8540.23}{1.0 + {(\frac{cai conversion + 0.401189}{0.00399115})}^{0.668054}} - 109.275 xabss = \frac{1.0}{1.0 + ⅇ^{\frac{(- xabss_z) frdy (v - xabss_vh)}{R temp}}} xabtc = \frac{13.8049}{1.0 + {(\frac{v - 153.019}{66.4952})}^{2}} iBKab = gkca gbkab xab (v - ek) \frac{d}{d time} (xab) = \frac{xabss - xab}{xabtc}

yss = \frac{1.0}{1.0 + ⅇ^{\frac{v + 105.39}{8.6553}}} ya = 0.0000035 ⅇ^{(- 0.0497) v} yb = 0.04003 ⅇ^{0.05211 v} ytc = \frac{1.0}{ya + yb} ih = gh y (v - eh) \frac{d}{d time} (y) = \frac{yss - y}{ytc}

K1cl = 0.0006 ⅇ^{2.53 vFRT} K2cl = 0.1 ⅇ^{(- 5.0) vFRT} css = \frac{1.0}{1.0 + K2cl ({(\frac{K1cl}{cai})}^{2} + \frac{K1cl}{cai} + 1.0)} ctc = (- 160.0) + \frac{210.0}{1.0 + ⅇ^{\frac{v + 4.56}{11.62}}} + \frac{170.0}{1.0 + ⅇ^{\frac{- (v + 25.5)}{11.62}}} icl = gcl c (v - ecl) \frac{d}{d time} (c) = \frac{css - c}{ctc}

fmg = 0.108043 + \frac{0.903902}{1.0 + {(\frac{mgo}{0.281007})}^{1.29834}} gs_nao = \frac{\frac{1}{0.0123} 0.03}{1.0 + {(\frac{150.0}{nao + tinyamount})}^{2}} gs_ko = \frac{\frac{1}{0.0123} 0.03}{1.0 + {(\frac{150.0}{ko + tinyamount})}^{2}} gs_cao = \frac{\frac{1}{0.000525} 0.03}{1.0 + {(\frac{150.0}{cao + tinyamount})}^{2}} insca = fmg gs_cao gnsCa gns (v - enscc) insna = fmg gs_nao gnsNa gns (v - enscc) insk = fmg gs_ko gnsK gns (v - enscc)

fnak = \frac{1.0}{1.0 + 0.1245 ⅇ^{(- 0.1) vFRT} + 0.00219 ⅇ^{\frac{nao}{49.71}} ⅇ^{(- 1.9) vFRT}} knak = \frac{1.0}{1.0 + {(\frac{nakKmko}{ko})}^{1.5}} nnak = \frac{1.0}{1.0 + {(\frac{nakKmnai}{nai})}^{2}} inak = ginak knak nnak fnak

inaca = \frac{0.5 zca frdy}{AV Cm buff} inaca_sign jnaca

f1naca = ⅇ^{(xgamma - 1.0) vFRT} f2naca = ⅇ^{xgamma vFRT} fallo = \frac{1.0}{1.0 + {(\frac{Kmallo}{cai})}^{nallo}} naca_Eup = {nai}^{3} cao f2naca - ({nao}^{3} cai f1naca) naca_Ed1 = 1.0 + ksat f1naca naca_Ed2 = Kmcao {nai}^{3} + {Kmnao}^{3} cai + {Kmnai}^{3} cao (1.0 + \frac{cai}{Kmcai}) naca_Ed3 = cao {nai}^{3} + {nao}^{3} cai + {nao}^{3} Kmcai (1.0 + {(\frac{nai}{Kmnai})}^{3}) jnaca = \frac{jnaca_sign Jnaca fallo naca_Eup}{naca_Ed1 (naca_Ed2 + naca_Ed3)}

jpmca = \frac{Jpmca}{1.0 + {(\frac{Kmpmca}{cai})}^{npmca}}