"""This module contains a Tentusscher_panfilov_2006_M_cell cardiac cell model
The module was autogenerated from a gotran ode file
"""
from __future__ import division
from collections import OrderedDict
import ufl
from cbcbeat.dolfinimport import *
from cbcbeat.cellmodels import CardiacCellModel
[docs]class Tentusscher_panfilov_2006_M_cell(CardiacCellModel):
def __init__(self, params=None, init_conditions=None):
"""
Create cardiac cell model
*Arguments*
params (dict, :py:class:`dolfin.Mesh`, optional)
optional model parameters
init_conditions (dict, :py:class:`dolfin.Mesh`, optional)
optional initial conditions
"""
CardiacCellModel.__init__(self, params, init_conditions)
@staticmethod
[docs] def default_parameters():
"Set-up and return default parameters."
params = OrderedDict([("P_kna", 0.03),
("g_K1", 5.405),
("g_Kr", 0.153),
("g_Ks", 0.098),
("g_Na", 14.838),
("g_bna", 0.00029),
("g_CaL", 3.98e-05),
("g_bca", 0.000592),
("g_to", 0.294),
("K_mNa", 40),
("K_mk", 1),
("P_NaK", 2.724),
("K_NaCa", 1000),
("K_sat", 0.1),
("Km_Ca", 1.38),
("Km_Nai", 87.5),
("alpha", 2.5),
("gamma", 0.35),
("K_pCa", 0.0005),
("g_pCa", 0.1238),
("g_pK", 0.0146),
("Buf_c", 0.2),
("Buf_sr", 10),
("Buf_ss", 0.4),
("Ca_o", 2),
("EC", 1.5),
("K_buf_c", 0.001),
("K_buf_sr", 0.3),
("K_buf_ss", 0.00025),
("K_up", 0.00025),
("V_leak", 0.00036),
("V_rel", 0.102),
("V_sr", 0.001094),
("V_ss", 5.468e-05),
("V_xfer", 0.0038),
("Vmax_up", 0.006375),
("k1_prime", 0.15),
("k2_prime", 0.045),
("k3", 0.06),
("k4", 0.005),
("max_sr", 2.5),
("min_sr", 1),
("Na_o", 140),
("Cm", 0.185),
("F", 96485.3415),
("R", 8314.472),
("T", 310),
("V_c", 0.016404),
("stim_amplitude", 0),
("stim_duration", 1),
("stim_period", 1000),
("stim_start", 1),
("K_o", 5.4)])
return params
@staticmethod
[docs] def default_initial_conditions():
"Set-up and return default initial conditions."
ic = OrderedDict([("V", -85.423),
("Xr1", 0.0165),
("Xr2", 0.473),
("Xs", 0.0174),
("m", 0.00165),
("h", 0.749),
("j", 0.6788),
("d", 3.288e-05),
("f", 0.7026),
("f2", 0.9526),
("fCass", 0.9942),
("s", 0.999998),
("r", 2.347e-08),
("Ca_SR", 4.272),
("Ca_i", 0.000153),
("Ca_ss", 0.00042),
("R_prime", 0.8978),
("Na_i", 10.132),
("K_i", 138.52)])
return ic
def _I(self, v, s, time):
"""
Original gotran transmembrane current dV/dt
"""
time = time if time else Constant(0.0)
# Assign states
V = v
assert(len(s) == 18)
Xr1, Xr2, Xs, m, h, j, d, f, f2, fCass, s, r, Ca_SR, Ca_i, Ca_ss,\
R_prime, Na_i, K_i = s
# Assign parameters
P_kna = self._parameters["P_kna"]
g_K1 = self._parameters["g_K1"]
g_Kr = self._parameters["g_Kr"]
g_Ks = self._parameters["g_Ks"]
g_Na = self._parameters["g_Na"]
g_bna = self._parameters["g_bna"]
g_CaL = self._parameters["g_CaL"]
g_bca = self._parameters["g_bca"]
g_to = self._parameters["g_to"]
K_mNa = self._parameters["K_mNa"]
K_mk = self._parameters["K_mk"]
P_NaK = self._parameters["P_NaK"]
K_NaCa = self._parameters["K_NaCa"]
K_sat = self._parameters["K_sat"]
Km_Ca = self._parameters["Km_Ca"]
Km_Nai = self._parameters["Km_Nai"]
alpha = self._parameters["alpha"]
gamma = self._parameters["gamma"]
K_pCa = self._parameters["K_pCa"]
g_pCa = self._parameters["g_pCa"]
g_pK = self._parameters["g_pK"]
Ca_o = self._parameters["Ca_o"]
Na_o = self._parameters["Na_o"]
F = self._parameters["F"]
R = self._parameters["R"]
T = self._parameters["T"]
K_o = self._parameters["K_o"]
# Init return args
current = [ufl.zero()]*1
# Expressions for the Reversal potentials component
E_Na = R*T*ufl.ln(Na_o/Na_i)/F
E_K = R*T*ufl.ln(K_o/K_i)/F
E_Ks = R*T*ufl.ln((Na_o*P_kna + K_o)/(K_i + P_kna*Na_i))/F
E_Ca = 0.5*R*T*ufl.ln(Ca_o/Ca_i)/F
# Expressions for the Inward rectifier potassium current component
alpha_K1 = 0.1/(1 + 6.14421235333e-06*ufl.exp(-0.06*E_K + 0.06*V))
beta_K1 = (3.06060402008*ufl.exp(0.0002*V - 0.0002*E_K) +\
0.367879441171*ufl.exp(0.1*V - 0.1*E_K))/(1 + ufl.exp(0.5*E_K -\
0.5*V))
xK1_inf = alpha_K1/(alpha_K1 + beta_K1)
i_K1 = 0.430331482912*g_K1*ufl.sqrt(K_o)*(-E_K + V)*xK1_inf
# Expressions for the Rapid time dependent potassium current component
i_Kr = 0.430331482912*g_Kr*ufl.sqrt(K_o)*(-E_K + V)*Xr1*Xr2
# Expressions for the Slow time dependent potassium current component
i_Ks = g_Ks*(Xs*Xs)*(-E_Ks + V)
# Expressions for the Fast sodium current component
i_Na = g_Na*(m*m*m)*(-E_Na + V)*h*j
# Expressions for the Sodium background current component
i_b_Na = g_bna*(-E_Na + V)
# Expressions for the L_type Ca current component
i_CaL = 4*g_CaL*(F*F)*(-15 + V)*(0.25*Ca_ss*ufl.exp(F*(-30 +\
2*V)/(R*T)) - Ca_o)*d*f*f2*fCass/(R*T*(-1 + ufl.exp(F*(-30 +\
2*V)/(R*T))))
# Expressions for the Calcium background current component
i_b_Ca = g_bca*(-E_Ca + V)
# Expressions for the Transient outward current component
i_to = g_to*(-E_K + V)*r*s
# Expressions for the Sodium potassium pump current component
i_NaK = K_o*P_NaK*Na_i/((K_mNa + Na_i)*(K_mk + K_o)*(1 +\
0.0353*ufl.exp(-F*V/(R*T)) + 0.1245*ufl.exp(-0.1*F*V/(R*T))))
# Expressions for the Sodium calcium exchanger current component
i_NaCa = K_NaCa*(-alpha*(Na_o*Na_o*Na_o)*Ca_i*ufl.exp(F*(-1 +\
gamma)*V/(R*T)) +\
Ca_o*(Na_i*Na_i*Na_i)*ufl.exp(F*gamma*V/(R*T)))/((1 +\
K_sat*ufl.exp(F*(-1 + gamma)*V/(R*T)))*(Km_Ca +\
Ca_o)*((Na_o*Na_o*Na_o) + (Km_Nai*Km_Nai*Km_Nai)))
# Expressions for the Calcium pump current component
i_p_Ca = g_pCa*Ca_i/(Ca_i + K_pCa)
# Expressions for the Potassium pump current component
i_p_K = g_pK*(-E_K + V)/(1 + 65.4052157419*ufl.exp(-0.167224080268*V))
# Expressions for the Membrane component
i_Stim = 0
current[0] = -i_CaL - i_Ks - i_NaCa - i_b_Na - i_Stim - i_Kr - i_p_Ca\
- i_to - i_b_Ca - i_Na - i_p_K - i_NaK - i_K1
# Return results
return current[0]
[docs] def I(self, v, s, time=None):
"""
Transmembrane current
I = -dV/dt
"""
return -self._I(v, s, time)
[docs] def F(self, v, s, time=None):
"""
Right hand side for ODE system
"""
time = time if time else Constant(0.0)
# Assign states
V = v
assert(len(s) == 18)
Xr1, Xr2, Xs, m, h, j, d, f, f2, fCass, s, r, Ca_SR, Ca_i, Ca_ss,\
R_prime, Na_i, K_i = s
# Assign parameters
P_kna = self._parameters["P_kna"]
g_K1 = self._parameters["g_K1"]
g_Kr = self._parameters["g_Kr"]
g_Ks = self._parameters["g_Ks"]
g_Na = self._parameters["g_Na"]
g_bna = self._parameters["g_bna"]
g_CaL = self._parameters["g_CaL"]
g_bca = self._parameters["g_bca"]
g_to = self._parameters["g_to"]
K_mNa = self._parameters["K_mNa"]
K_mk = self._parameters["K_mk"]
P_NaK = self._parameters["P_NaK"]
K_NaCa = self._parameters["K_NaCa"]
K_sat = self._parameters["K_sat"]
Km_Ca = self._parameters["Km_Ca"]
Km_Nai = self._parameters["Km_Nai"]
alpha = self._parameters["alpha"]
gamma = self._parameters["gamma"]
K_pCa = self._parameters["K_pCa"]
g_pCa = self._parameters["g_pCa"]
g_pK = self._parameters["g_pK"]
Buf_c = self._parameters["Buf_c"]
Buf_sr = self._parameters["Buf_sr"]
Buf_ss = self._parameters["Buf_ss"]
Ca_o = self._parameters["Ca_o"]
EC = self._parameters["EC"]
K_buf_c = self._parameters["K_buf_c"]
K_buf_sr = self._parameters["K_buf_sr"]
K_buf_ss = self._parameters["K_buf_ss"]
K_up = self._parameters["K_up"]
V_leak = self._parameters["V_leak"]
V_rel = self._parameters["V_rel"]
V_sr = self._parameters["V_sr"]
V_ss = self._parameters["V_ss"]
V_xfer = self._parameters["V_xfer"]
Vmax_up = self._parameters["Vmax_up"]
k1_prime = self._parameters["k1_prime"]
k2_prime = self._parameters["k2_prime"]
k3 = self._parameters["k3"]
k4 = self._parameters["k4"]
max_sr = self._parameters["max_sr"]
min_sr = self._parameters["min_sr"]
Na_o = self._parameters["Na_o"]
Cm = self._parameters["Cm"]
F = self._parameters["F"]
R = self._parameters["R"]
T = self._parameters["T"]
V_c = self._parameters["V_c"]
K_o = self._parameters["K_o"]
# Init return args
F_expressions = [ufl.zero()]*18
# Expressions for the Reversal potentials component
E_Na = R*T*ufl.ln(Na_o/Na_i)/F
E_K = R*T*ufl.ln(K_o/K_i)/F
E_Ks = R*T*ufl.ln((Na_o*P_kna + K_o)/(K_i + P_kna*Na_i))/F
E_Ca = 0.5*R*T*ufl.ln(Ca_o/Ca_i)/F
# Expressions for the Inward rectifier potassium current component
alpha_K1 = 0.1/(1 + 6.14421235333e-06*ufl.exp(-0.06*E_K + 0.06*V))
beta_K1 = (3.06060402008*ufl.exp(0.0002*V - 0.0002*E_K) +\
0.367879441171*ufl.exp(0.1*V - 0.1*E_K))/(1 + ufl.exp(0.5*E_K -\
0.5*V))
xK1_inf = alpha_K1/(alpha_K1 + beta_K1)
i_K1 = 0.430331482912*g_K1*ufl.sqrt(K_o)*(-E_K + V)*xK1_inf
# Expressions for the Rapid time dependent potassium current component
i_Kr = 0.430331482912*g_Kr*ufl.sqrt(K_o)*(-E_K + V)*Xr1*Xr2
# Expressions for the Xr1 gate component
xr1_inf = 1.0/(1 + ufl.exp(-26/7 - V/7))
alpha_xr1 = 450/(1 + ufl.exp(-9/2 - V/10))
beta_xr1 = 6/(1 + 13.5813245226*ufl.exp(0.0869565217391*V))
tau_xr1 = alpha_xr1*beta_xr1
F_expressions[0] = (xr1_inf - Xr1)/tau_xr1
# Expressions for the Xr2 gate component
xr2_inf = 1.0/(1 + ufl.exp(11/3 + V/24))
alpha_xr2 = 3/(1 + ufl.exp(-3 - V/20))
beta_xr2 = 1.12/(1 + ufl.exp(-3 + V/20))
tau_xr2 = alpha_xr2*beta_xr2
F_expressions[1] = (xr2_inf - Xr2)/tau_xr2
# Expressions for the Slow time dependent potassium current component
i_Ks = g_Ks*(Xs*Xs)*(-E_Ks + V)
# Expressions for the Xs gate component
xs_inf = 1.0/(1 + ufl.exp(-5/14 - V/14))
alpha_xs = 1400/ufl.sqrt(1 + ufl.exp(5/6 - V/6))
beta_xs = 1.0/(1 + ufl.exp(-7/3 + V/15))
tau_xs = 80 + alpha_xs*beta_xs
F_expressions[2] = (xs_inf - Xs)/tau_xs
# Expressions for the Fast sodium current component
i_Na = g_Na*(m*m*m)*(-E_Na + V)*h*j
# Expressions for the m gate component
m_inf = 1.0/((1 + 0.00184221158117*ufl.exp(-0.110741971207*V))*(1 +\
0.00184221158117*ufl.exp(-0.110741971207*V)))
alpha_m = 1.0/(1 + ufl.exp(-12 - V/5))
beta_m = 0.1/(1 + ufl.exp(-1/4 + V/200)) + 0.1/(1 + ufl.exp(7 + V/5))
tau_m = alpha_m*beta_m
F_expressions[3] = (-m + m_inf)/tau_m
# Expressions for the h gate component
h_inf = 1.0/((1 + 15212.5932857*ufl.exp(0.134589502019*V))*(1 +\
15212.5932857*ufl.exp(0.134589502019*V)))
alpha_h = ufl.conditional(ufl.lt(V, -40),\
4.43126792958e-07*ufl.exp(-0.147058823529*V), 0)
beta_h = ufl.conditional(ufl.lt(V, -40), 2.7*ufl.exp(0.079*V) +\
310000*ufl.exp(0.3485*V), 0.77/(0.13 +\
0.0497581410839*ufl.exp(-0.0900900900901*V)))
tau_h = 1.0/(alpha_h + beta_h)
F_expressions[4] = (-h + h_inf)/tau_h
# Expressions for the j gate component
j_inf = 1.0/((1 + 15212.5932857*ufl.exp(0.134589502019*V))*(1 +\
15212.5932857*ufl.exp(0.134589502019*V)))
alpha_j = ufl.conditional(ufl.lt(V, -40), (37.78 +\
V)*(-25428*ufl.exp(0.2444*V) - 6.948e-06*ufl.exp(-0.04391*V))/(1 +\
50262745826.0*ufl.exp(0.311*V)), 0)
beta_j = ufl.conditional(ufl.lt(V, -40),\
0.02424*ufl.exp(-0.01052*V)/(1 +\
0.0039608683399*ufl.exp(-0.1378*V)), 0.6*ufl.exp(0.057*V)/(1 +\
0.0407622039784*ufl.exp(-0.1*V)))
tau_j = 1.0/(alpha_j + beta_j)
F_expressions[5] = (-j + j_inf)/tau_j
# Expressions for the Sodium background current component
i_b_Na = g_bna*(-E_Na + V)
# Expressions for the L_type Ca current component
i_CaL = 4*g_CaL*(F*F)*(-15 + V)*(0.25*Ca_ss*ufl.exp(F*(-30 +\
2*V)/(R*T)) - Ca_o)*d*f*f2*fCass/(R*T*(-1 + ufl.exp(F*(-30 +\
2*V)/(R*T))))
# Expressions for the d gate component
d_inf = 1.0/(1 + 0.344153786865*ufl.exp(-0.133333333333*V))
alpha_d = 0.25 + 1.4/(1 + ufl.exp(-35/13 - V/13))
beta_d = 1.4/(1 + ufl.exp(1 + V/5))
gamma_d = 1.0/(1 + ufl.exp(5/2 - V/20))
tau_d = alpha_d*beta_d + gamma_d
F_expressions[6] = (-d + d_inf)/tau_d
# Expressions for the f gate component
f_inf = 1.0/(1 + ufl.exp(20/7 + V/7))
tau_f = 20 + 1102.5*ufl.exp(-((27 + V)*(27 + V))/225) + 180/(1 +\
ufl.exp(3 + V/10)) + 200/(1 + ufl.exp(13/10 - V/10))
F_expressions[7] = (f_inf - f)/tau_f
# Expressions for the F2 gate component
f2_inf = 0.33 + 0.67/(1 + ufl.exp(5 + V/7))
tau_f2 = 80/(1 + ufl.exp(3 + V/10)) + 562*ufl.exp(-((27 + V)*(27 +\
V))/240) + 31/(1 + ufl.exp(5/2 - V/10))
F_expressions[8] = (-f2 + f2_inf)/tau_f2
# Expressions for the FCass gate component
fCass_inf = 0.4 + 0.6/(1 + 400.0*(Ca_ss*Ca_ss))
tau_fCass = 2 + 80/(1 + 400.0*(Ca_ss*Ca_ss))
F_expressions[9] = (fCass_inf - fCass)/tau_fCass
# Expressions for the Calcium background current component
i_b_Ca = g_bca*(-E_Ca + V)
# Expressions for the Transient outward current component
i_to = g_to*(-E_K + V)*r*s
# Expressions for the s gate component
s_inf = 1.0/(1 + ufl.exp(4 + V/5))
tau_s = 3 + 5/(1 + ufl.exp(-4 + V/5)) + 85*ufl.exp(-((45 + V)*(45 +\
V))/320)
F_expressions[10] = (s_inf - s)/tau_s
# Expressions for the r gate component
r_inf = 1.0/(1 + ufl.exp(10/3 - V/6))
tau_r = 0.8 + 9.5*ufl.exp(-((40 + V)*(40 + V))/1800)
F_expressions[11] = (r_inf - r)/tau_r
# Expressions for the Sodium potassium pump current component
i_NaK = K_o*P_NaK*Na_i/((K_mNa + Na_i)*(K_mk + K_o)*(1 +\
0.0353*ufl.exp(-F*V/(R*T)) + 0.1245*ufl.exp(-0.1*F*V/(R*T))))
# Expressions for the Sodium calcium exchanger current component
i_NaCa = K_NaCa*(-alpha*(Na_o*Na_o*Na_o)*Ca_i*ufl.exp(F*(-1 +\
gamma)*V/(R*T)) +\
Ca_o*(Na_i*Na_i*Na_i)*ufl.exp(F*gamma*V/(R*T)))/((1 +\
K_sat*ufl.exp(F*(-1 + gamma)*V/(R*T)))*(Km_Ca +\
Ca_o)*((Na_o*Na_o*Na_o) + (Km_Nai*Km_Nai*Km_Nai)))
# Expressions for the Calcium pump current component
i_p_Ca = g_pCa*Ca_i/(Ca_i + K_pCa)
# Expressions for the Potassium pump current component
i_p_K = g_pK*(-E_K + V)/(1 + 65.4052157419*ufl.exp(-0.167224080268*V))
# Expressions for the Calcium dynamics component
i_up = Vmax_up/(1 + (K_up*K_up)/(Ca_i*Ca_i))
i_leak = V_leak*(Ca_SR - Ca_i)
i_xfer = V_xfer*(Ca_ss - Ca_i)
kcasr = max_sr - (-min_sr + max_sr)/(1 + (EC*EC)/(Ca_SR*Ca_SR))
Ca_i_bufc = 1.0/(1 + Buf_c*K_buf_c/((Ca_i + K_buf_c)*(Ca_i + K_buf_c)))
Ca_sr_bufsr = 1.0/(1 + Buf_sr*K_buf_sr/((Ca_SR + K_buf_sr)*(Ca_SR +\
K_buf_sr)))
Ca_ss_bufss = 1.0/(1 + Buf_ss*K_buf_ss/((Ca_ss + K_buf_ss)*(Ca_ss +\
K_buf_ss)))
F_expressions[13] = (i_xfer - Cm*(i_b_Ca + i_p_Ca -\
2*i_NaCa)/(2*F*V_c) + V_sr*(-i_up + i_leak)/V_c)*Ca_i_bufc
k1 = k1_prime/kcasr
k2 = k2_prime*kcasr
O = (Ca_ss*Ca_ss)*R_prime*k1/((Ca_ss*Ca_ss)*k1 + k3)
F_expressions[15] = -Ca_ss*R_prime*k2 + k4*(1 - R_prime)
i_rel = V_rel*(Ca_SR - Ca_ss)*O
F_expressions[12] = (i_up - i_leak - i_rel)*Ca_sr_bufsr
F_expressions[14] = (-Cm*i_CaL/(2*F*V_ss) - V_c*i_xfer/V_ss +\
V_sr*i_rel/V_ss)*Ca_ss_bufss
# Expressions for the Sodium dynamics component
F_expressions[16] = Cm*(-i_b_Na - i_Na - 3*i_NaCa - 3*i_NaK)/(F*V_c)
# Expressions for the Membrane component
i_Stim = 0
# Expressions for the Potassium dynamics component
F_expressions[17] = Cm*(2*i_NaK - i_Ks - i_Stim - i_Kr - i_to - i_p_K\
- i_K1)/(F*V_c)
# Return results
return dolfin.as_vector(F_expressions)
[docs] def num_states(self):
return 18
def __str__(self):
return 'Tentusscher_panfilov_2006_M_cell cardiac cell model'