Generated Code
The following is python code generated by the CellML API from this CellML file. (Back to language selection)
The raw code is available.
# Size of variable arrays:
sizeAlgebraic = 29
sizeStates = 9
sizeConstants = 48
from math import *
from numpy import *
def createLegends():
legend_states = [""] * sizeStates
legend_rates = [""] * sizeStates
legend_algebraic = [""] * sizeAlgebraic
legend_voi = ""
legend_constants = [""] * sizeConstants
legend_voi = "time in component environment (millisecond)"
legend_constants[0] = "isotonic_mode in component parameters (dimensionless)"
legend_constants[1] = "alpha_1 in component parameters (per_um)"
legend_constants[2] = "beta_1 in component parameters (mN)"
legend_constants[3] = "alpha_2 in component parameters (per_um)"
legend_constants[4] = "beta_2 in component parameters (mN)"
legend_constants[5] = "alpha_3 in component parameters (per_um)"
legend_constants[6] = "beta_3 in component parameters (mN)"
legend_constants[7] = "lambda in component parameters (mN)"
legend_constants[8] = "A_half in component parameters (dimensionless)"
legend_constants[9] = "mu in component parameters (dimensionless)"
legend_constants[10] = "chi in component parameters (dimensionless)"
legend_constants[11] = "chi_0 in component parameters (dimensionless)"
legend_constants[12] = "m_0 in component parameters (dimensionless)"
legend_constants[13] = "v_max in component parameters (um_per_msec)"
legend_constants[14] = "a in component parameters (dimensionless)"
legend_constants[15] = "d_h in component parameters (dimensionless)"
legend_constants[16] = "alpha_P in component parameters (dimensionless)"
legend_constants[17] = "alpha_PG in component parameters (dimensionless)"
legend_constants[18] = "S_0 in component parameters_izakov_et_al_1991 (um)"
legend_algebraic[3] = "q_v in component parameters_izakov_et_al_1991 (per_millisecond)"
legend_constants[19] = "q_1 in component parameters_izakov_et_al_1991 (per_millisecond)"
legend_constants[20] = "q_2 in component parameters_izakov_et_al_1991 (per_millisecond)"
legend_constants[21] = "q_3 in component parameters_izakov_et_al_1991 (per_millisecond)"
legend_constants[45] = "v_1 in component parameters_izakov_et_al_1991 (um_per_msec)"
legend_constants[22] = "alpha_P in component parameters_izakov_et_al_1991 (per_um)"
legend_constants[23] = "alpha_S in component parameters_izakov_et_al_1991 (per_um)"
legend_constants[24] = "alpha_G in component parameters_izakov_et_al_1991 (dimensionless)"
legend_constants[25] = "a_on in component parameters_izakov_et_al_1991 (per_millisecond)"
legend_constants[26] = "a_off in component parameters_izakov_et_al_1991 (per_millisecond)"
legend_constants[27] = "k_A in component parameters_izakov_et_al_1991 (dimensionless)"
legend_states[0] = "v in component CE_velocity (um_per_msec)"
legend_algebraic[26] = "F_CE in component force (mN)"
legend_algebraic[5] = "F_muscle in component force (mN)"
legend_algebraic[0] = "F_XSE in component force (mN)"
legend_algebraic[1] = "F_SE in component force (mN)"
legend_algebraic[2] = "F_PE in component force (mN)"
legend_states[1] = "N in component crossbridge_kinetics (dimensionless)"
legend_algebraic[13] = "k_P_vis in component CE_velocity (mN)"
legend_algebraic[15] = "k_S_vis in component PE_velocity (mN)"
legend_states[2] = "w in component PE_velocity (um_per_msec)"
legend_states[3] = "l_1 in component length (um)"
legend_states[4] = "l_2 in component length (um)"
legend_states[5] = "l_3 in component length (um)"
legend_algebraic[25] = "p_v in component average_crossbridge_force (dimensionless)"
legend_algebraic[22] = "K_chi in component crossbridge_kinetics (per_millisecond)"
legend_algebraic[6] = "M_A in component crossbridge_kinetics (dimensionless)"
legend_algebraic[7] = "n_1 in component crossbridge_kinetics (dimensionless)"
legend_algebraic[8] = "L_oz in component crossbridge_kinetics (dimensionless)"
legend_algebraic[20] = "k_p_v in component crossbridge_kinetics (per_millisecond)"
legend_algebraic[21] = "k_m_v in component crossbridge_kinetics (per_millisecond)"
legend_states[6] = "A in component calcium_handling (dimensionless)"
legend_algebraic[19] = "G_star in component average_crossbridge_force (dimensionless)"
legend_algebraic[9] = "dl_1_dt in component length (um_per_msec)"
legend_algebraic[11] = "dl_2_dt in component length (um_per_msec)"
legend_algebraic[4] = "dl_3_dt in component length (um_per_msec)"
legend_algebraic[27] = "phi_chi in component CE_velocity (um_per_msec2)"
legend_algebraic[28] = "p_prime_v in component average_crossbridge_force (per_millisecond)"
legend_constants[28] = "alpha_P_lengthening in component CE_velocity (per_um)"
legend_constants[29] = "beta_P_lengthening in component CE_velocity (mN)"
legend_constants[30] = "alpha_P_shortening in component CE_velocity (per_um)"
legend_constants[31] = "beta_P_shortening in component CE_velocity (mN)"
legend_constants[32] = "alpha_S_lengthening in component PE_velocity (per_um)"
legend_constants[33] = "beta_S_lengthening in component PE_velocity (mN)"
legend_constants[34] = "alpha_S_shortening in component PE_velocity (per_um)"
legend_constants[35] = "beta_S_shortening in component PE_velocity (mN)"
legend_algebraic[18] = "P_star in component average_crossbridge_force (dimensionless)"
legend_algebraic[17] = "gamma in component average_crossbridge_force (dimensionless)"
legend_constants[46] = "case_1 in component average_crossbridge_force (per_millisecond)"
legend_algebraic[23] = "case_2 in component average_crossbridge_force (per_millisecond)"
legend_constants[47] = "case_3 in component average_crossbridge_force (per_millisecond)"
legend_algebraic[24] = "case_4 in component average_crossbridge_force (per_millisecond)"
legend_algebraic[14] = "dA_dt in component calcium_handling (per_millisecond)"
legend_algebraic[10] = "N_A in component calcium_handling (dimensionless)"
legend_algebraic[12] = "pi_N_A in component calcium_handling (dimensionless)"
legend_states[7] = "B in component calcium_handling (dimensionless)"
legend_algebraic[16] = "dB_dt in component calcium_handling (per_millisecond)"
legend_states[8] = "Ca_C in component calcium_handling (dimensionless)"
legend_constants[36] = "A_tot in component calcium_handling (dimensionless)"
legend_constants[37] = "B_tot in component calcium_handling (dimensionless)"
legend_constants[38] = "b_on in component calcium_handling (per_millisecond)"
legend_constants[39] = "b_off in component calcium_handling (per_millisecond)"
legend_constants[40] = "a_c in component calcium_handling (per_millisecond2)"
legend_constants[41] = "b_c in component calcium_handling (per_millisecond2)"
legend_constants[42] = "r_Ca in component calcium_handling (per_millisecond)"
legend_constants[43] = "q_Ca in component calcium_handling (dimensionless)"
legend_constants[44] = "t_d in component calcium_handling (millisecond)"
legend_rates[1] = "d/dt N in component crossbridge_kinetics (dimensionless)"
legend_rates[3] = "d/dt l_1 in component length (um)"
legend_rates[4] = "d/dt l_2 in component length (um)"
legend_rates[5] = "d/dt l_3 in component length (um)"
legend_rates[0] = "d/dt v in component CE_velocity (um_per_msec)"
legend_rates[2] = "d/dt w in component PE_velocity (um_per_msec)"
legend_rates[6] = "d/dt A in component calcium_handling (dimensionless)"
legend_rates[7] = "d/dt B in component calcium_handling (dimensionless)"
legend_rates[8] = "d/dt Ca_C in component calcium_handling (dimensionless)"
return (legend_states, legend_algebraic, legend_voi, legend_constants)
def initConsts():
constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
constants[0] = 1
constants[1] = 19
constants[2] = 2.9
constants[3] = 14.6
constants[4] = 0.01
constants[5] = 48
constants[6] = 0.1
constants[7] = 960
constants[8] = 0.6
constants[9] = 3
constants[10] = 0.705
constants[11] = 3
constants[12] = 0.9
constants[13] = 0.0056
constants[14] = 0.25
constants[15] = 0.5
constants[16] = 4
constants[17] = 1
constants[18] = 0.77
constants[19] = 0.017
constants[20] = 0.26
constants[21] = 0.03
constants[22] = 4
constants[23] = 4
constants[24] = 4
constants[25] = 2.9e-2
constants[26] = 0.2
constants[27] = 2.8
states[0] = 0
states[1] = 1
states[2] = 0
states[3] = 1
states[4] = 1
states[5] = 1
states[6] = 0
constants[28] = 16
constants[29] = 15
constants[30] = 16
constants[31] = 15
constants[32] = 39
constants[33] = 80
constants[34] = 46
constants[35] = 60
states[7] = 0
states[8] = 0
constants[36] = 1
constants[37] = 0.4
constants[38] = 2.6
constants[39] = 0.182
constants[40] = 0.005
constants[41] = 0.03
constants[42] = 0.65
constants[43] = 50
constants[44] = 33
constants[45] = constants[13]/10.0000
constants[46] = (constants[14]*(0.400000+0.400000*constants[14]))/(constants[13]*(power((constants[14]+1.00000)*0.400000, 2.00000)))
constants[47] = (0.400000*constants[14]+1.00000)/(constants[14]*constants[13])
return (states, constants)
def computeRates(voi, states, constants):
rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
algebraic[4] = custom_piecewise([equal(constants[0] , 1.00000), 0.00000 , True, -states[2]])
rates[5] = algebraic[4]
algebraic[9] = states[0]
rates[3] = algebraic[9]
algebraic[11] = states[2]
rates[4] = algebraic[11]
algebraic[8] = (states[3]+constants[18])/(0.460000+constants[18])
algebraic[10] = states[1]/(algebraic[8]*states[6])
algebraic[12] = custom_piecewise([greater_equal(algebraic[10] , 1.00000), 1.00000 , True, power(0.0200000, algebraic[10])])
algebraic[14] = constants[25]*(constants[36]-states[6])*states[8]-constants[26]*exp(-constants[27]*states[6])*algebraic[12]*states[6]
rates[6] = algebraic[14]
algebraic[16] = constants[38]*(constants[37]-states[7])*states[8]-constants[39]*states[7]
rates[7] = algebraic[16]
rates[8] = custom_piecewise([less(voi , constants[44]), constants[41]*voi*(1.00000-exp(-constants[40]*(power(voi, 2.00000))))*exp(-constants[40]*(power(voi, 2.00000))) , True, (-algebraic[14]-algebraic[16])-constants[42]*exp(-constants[43]*states[8])*states[8]])
algebraic[6] = (power(states[6], constants[9]))/(power(states[6], constants[9])+power(constants[8], constants[9]))
algebraic[7] = 0.600000*states[3]+0.500000
algebraic[3] = custom_piecewise([less_equal(states[0] , 0.00000), constants[19]-(constants[20]*states[0])/constants[13] , True, constants[21]])
algebraic[17] = (constants[14]*constants[15]*(power(constants[45]/constants[13], 2.00000)))/(3.00000*constants[14]*constants[15]-((constants[14]+1.00000)*states[0])/constants[13])
algebraic[18] = custom_piecewise([less_equal(states[0] , 0.00000), (constants[14]*(1.00000+states[0]/constants[13]))/(constants[14]-states[0]/constants[13]) , True, (1.00000+constants[15])-((power(constants[15], 2.00000))*constants[14])/(((constants[14]*constants[15])/algebraic[17])*(power(states[0]/constants[13], 2.00000))+((constants[14]+1.00000)*states[0])/constants[13]+constants[14]*constants[15])])
algebraic[19] = custom_piecewise([less_equal(-constants[13] , states[0]) & less_equal(states[0] , 0.00000), 1.00000+(0.600000*states[0])/constants[13] , less(0.00000 , states[0]) & less_equal(states[0] , constants[45]), algebraic[18]/((((0.400000*constants[14]+1.00000)/constants[14])*states[0])/constants[13]+1.00000) , True, (algebraic[18]*exp(-constants[24]*(power((states[0]-constants[45])/constants[13], constants[17]))))/((((0.400000*constants[14]+1.00000)/constants[14])*states[0])/constants[13]+1.00000)])
algebraic[20] = constants[10]*constants[11]*algebraic[3]*constants[12]*algebraic[19]
algebraic[21] = constants[11]*algebraic[3]*(1.00000-constants[10]*constants[12]*algebraic[19])
algebraic[22] = algebraic[20]*algebraic[6]*algebraic[7]*algebraic[8]*(1.00000-states[1])-algebraic[21]*states[1]
rates[1] = algebraic[22]
algebraic[13] = custom_piecewise([less_equal(algebraic[9] , 0.00000), constants[29]*exp(constants[28]*states[3]) , True, constants[31]*exp(constants[30]*states[3])])
algebraic[25] = algebraic[18]/algebraic[19]
algebraic[23] = (constants[14]*1.00000*(1.00000+0.400000*constants[14]+(1.20000*states[0])/constants[13]+0.600000*(power(states[0]/constants[13], 2.00000))))/(constants[13]*(power((constants[14]-states[0]/constants[13])*(1.00000+(0.600000*states[0])/constants[13]), 2.00000)))
algebraic[24] = (1.00000/constants[13])*exp(-constants[24]*(power(states[0]/constants[13]-constants[45]/constants[13], constants[17])))*((0.400000*constants[14]+1.00000)/constants[14]+constants[24]*constants[16]*(1.00000+((0.400000*constants[14]+1.00000)*states[0])/(constants[14]*constants[13])))*(power(states[0]/constants[13]-constants[45]/constants[13], constants[17]-1.00000))
rootfind_0(voi, constants, rates, states, algebraic)
rates[0] = algebraic[27]
algebraic[15] = custom_piecewise([less_equal(algebraic[11] , algebraic[9]), constants[33]*exp(constants[32]*(states[4]-states[3])) , True, constants[35]*exp(constants[34]*(states[4]-states[3]))])
rates[2] = custom_piecewise([equal(constants[0] , 1.00000), ((algebraic[15]*(algebraic[27]-constants[23]*(power(states[2]-states[0], 2.00000)))-constants[1]*constants[2]*exp(constants[1]*(states[4]-states[3]))*(states[2]-states[0])*1.00000)-constants[3]*constants[4]*exp(constants[3]*states[4])*states[2]*1.00000)/algebraic[15] , True, ((algebraic[15]*(algebraic[27]-constants[23]*(power(states[2]-states[0], 2.00000)))-constants[1]*constants[2]*exp(constants[1]*(states[4]-states[3]))*(states[2]-states[0])*1.00000)-(constants[3]*constants[4]*exp(constants[3]*states[4])+constants[5]*constants[6]*exp(constants[5]*states[5]))*states[2]*1.00000)/algebraic[15]])
return(rates)
def computeAlgebraic(constants, states, voi):
algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
states = array(states)
voi = array(voi)
algebraic[4] = custom_piecewise([equal(constants[0] , 1.00000), 0.00000 , True, -states[2]])
algebraic[9] = states[0]
algebraic[11] = states[2]
algebraic[8] = (states[3]+constants[18])/(0.460000+constants[18])
algebraic[10] = states[1]/(algebraic[8]*states[6])
algebraic[12] = custom_piecewise([greater_equal(algebraic[10] , 1.00000), 1.00000 , True, power(0.0200000, algebraic[10])])
algebraic[14] = constants[25]*(constants[36]-states[6])*states[8]-constants[26]*exp(-constants[27]*states[6])*algebraic[12]*states[6]
algebraic[16] = constants[38]*(constants[37]-states[7])*states[8]-constants[39]*states[7]
algebraic[6] = (power(states[6], constants[9]))/(power(states[6], constants[9])+power(constants[8], constants[9]))
algebraic[7] = 0.600000*states[3]+0.500000
algebraic[3] = custom_piecewise([less_equal(states[0] , 0.00000), constants[19]-(constants[20]*states[0])/constants[13] , True, constants[21]])
algebraic[17] = (constants[14]*constants[15]*(power(constants[45]/constants[13], 2.00000)))/(3.00000*constants[14]*constants[15]-((constants[14]+1.00000)*states[0])/constants[13])
algebraic[18] = custom_piecewise([less_equal(states[0] , 0.00000), (constants[14]*(1.00000+states[0]/constants[13]))/(constants[14]-states[0]/constants[13]) , True, (1.00000+constants[15])-((power(constants[15], 2.00000))*constants[14])/(((constants[14]*constants[15])/algebraic[17])*(power(states[0]/constants[13], 2.00000))+((constants[14]+1.00000)*states[0])/constants[13]+constants[14]*constants[15])])
algebraic[19] = custom_piecewise([less_equal(-constants[13] , states[0]) & less_equal(states[0] , 0.00000), 1.00000+(0.600000*states[0])/constants[13] , less(0.00000 , states[0]) & less_equal(states[0] , constants[45]), algebraic[18]/((((0.400000*constants[14]+1.00000)/constants[14])*states[0])/constants[13]+1.00000) , True, (algebraic[18]*exp(-constants[24]*(power((states[0]-constants[45])/constants[13], constants[17]))))/((((0.400000*constants[14]+1.00000)/constants[14])*states[0])/constants[13]+1.00000)])
algebraic[20] = constants[10]*constants[11]*algebraic[3]*constants[12]*algebraic[19]
algebraic[21] = constants[11]*algebraic[3]*(1.00000-constants[10]*constants[12]*algebraic[19])
algebraic[22] = algebraic[20]*algebraic[6]*algebraic[7]*algebraic[8]*(1.00000-states[1])-algebraic[21]*states[1]
algebraic[13] = custom_piecewise([less_equal(algebraic[9] , 0.00000), constants[29]*exp(constants[28]*states[3]) , True, constants[31]*exp(constants[30]*states[3])])
algebraic[25] = algebraic[18]/algebraic[19]
algebraic[23] = (constants[14]*1.00000*(1.00000+0.400000*constants[14]+(1.20000*states[0])/constants[13]+0.600000*(power(states[0]/constants[13], 2.00000))))/(constants[13]*(power((constants[14]-states[0]/constants[13])*(1.00000+(0.600000*states[0])/constants[13]), 2.00000)))
algebraic[24] = (1.00000/constants[13])*exp(-constants[24]*(power(states[0]/constants[13]-constants[45]/constants[13], constants[17])))*((0.400000*constants[14]+1.00000)/constants[14]+constants[24]*constants[16]*(1.00000+((0.400000*constants[14]+1.00000)*states[0])/(constants[14]*constants[13])))*(power(states[0]/constants[13]-constants[45]/constants[13], constants[17]-1.00000))
algebraic[15] = custom_piecewise([less_equal(algebraic[11] , algebraic[9]), constants[33]*exp(constants[32]*(states[4]-states[3])) , True, constants[35]*exp(constants[34]*(states[4]-states[3]))])
algebraic[0] = constants[6]*(exp(constants[5]*states[5])-1.00000)
algebraic[1] = constants[2]*(exp(constants[1]*(states[4]-states[3]))-1.00000)
algebraic[2] = constants[4]*(exp(constants[3]*states[4])-1.00000)
algebraic[5] = algebraic[0]
algebraic[26] = constants[7]*algebraic[25]*states[1]
return algebraic
initialGuess0 = None
def rootfind_0(voi, constants, rates, states, algebraic):
"""Calculate values of algebraic variables for DAE"""
from scipy.optimize import fsolve
global initialGuess0
if initialGuess0 is None: initialGuess0 = ones(2)*0.1
if not iterable(voi):
soln = fsolve(residualSN_0, initialGuess0, args=(algebraic, voi, constants, rates, states), xtol=1E-6)
initialGuess0 = soln
algebraic[27] = soln[0]
algebraic[28] = soln[1]
else:
for (i,t) in enumerate(voi):
soln = fsolve(residualSN_0, initialGuess0, args=(algebraic[:,i], voi[i], constants, rates[:i], states[:,i]), xtol=1E-6)
initialGuess0 = soln
algebraic[27][i] = soln[0]
algebraic[28][i] = soln[1]
def residualSN_0(algebraicCandidate, algebraic, voi, constants, rates, states):
resid = array([0.0] * 2)
algebraic[27] = algebraicCandidate[0]
algebraic[28] = algebraicCandidate[1]
resid[0] = (algebraic[27]-(custom_piecewise([equal(constants[0] , 1.00000), (constants[7]*algebraic[22]*algebraic[25]*1.00000+constants[22]*algebraic[13]*(power(states[0], 2.00000))+constants[3]*constants[4]*exp(constants[3]*states[4])*states[2]*1.00000)/(constants[7]*states[1]*algebraic[28]*1.00000+algebraic[13]) , True, (constants[7]*algebraic[22]*algebraic[25]*1.00000+constants[22]*algebraic[13]*(power(states[0], 2.00000))+(constants[3]*constants[4]*exp(constants[3]*states[4])+constants[5]*constants[6]*exp(constants[5]*states[5]))*states[2]*1.00000)/(constants[7]*states[1]*algebraic[28]*1.00000+algebraic[13])])))
resid[1] = (algebraic[28]-(custom_piecewise([less_equal(states[0] , -constants[13]), constants[46]*algebraic[27] , less(-constants[13] , states[0]) & less_equal(states[0] , 0.00000), algebraic[23]*algebraic[27] , less(0.00000 , states[0]) & less_equal(states[0] , constants[45]), constants[47]*algebraic[27] , True, algebraic[24]*algebraic[27]])))
return resid
def custom_piecewise(cases):
"""Compute result of a piecewise function"""
return select(cases[0::2],cases[1::2])
def solve_model():
"""Solve model with ODE solver"""
from scipy.integrate import ode
# Initialise constants and state variables
(init_states, constants) = initConsts()
# Set timespan to solve over
voi = linspace(0, 10, 500)
# Construct ODE object to solve
r = ode(computeRates)
r.set_integrator('vode', method='bdf', atol=1e-06, rtol=1e-06, max_step=1)
r.set_initial_value(init_states, voi[0])
r.set_f_params(constants)
# Solve model
states = array([[0.0] * len(voi)] * sizeStates)
states[:,0] = init_states
for (i,t) in enumerate(voi[1:]):
if r.successful():
r.integrate(t)
states[:,i+1] = r.y
else:
break
# Compute algebraic variables
algebraic = computeAlgebraic(constants, states, voi)
return (voi, states, algebraic)
def plot_model(voi, states, algebraic):
"""Plot variables against variable of integration"""
import pylab
(legend_states, legend_algebraic, legend_voi, legend_constants) = createLegends()
pylab.figure(1)
pylab.plot(voi,vstack((states,algebraic)).T)
pylab.xlabel(legend_voi)
pylab.legend(legend_states + legend_algebraic, loc='best')
pylab.show()
if __name__ == "__main__":
(voi, states, algebraic) = solve_model()
plot_model(voi, states, algebraic)