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 = 64
sizeStates = 19
sizeConstants = 73
from math import *
from numpy import *
def createLegends():
legend_states = [""] * sizeStates
legend_rates = [""] * sizeStates
legend_algebraic = [""] * sizeAlgebraic
legend_voi = ""
legend_constants = [""] * sizeConstants
legend_voi = "t in component environment (ms)"
legend_constants[0] = "R in component environment (mJ_per_mole_kelvin)"
legend_constants[1] = "T in component environment (kelvin)"
legend_constants[2] = "F in component environment (coulomb_per_mole)"
legend_constants[64] = "V_tau in component environment (mV)"
legend_constants[3] = "Ca_o in component environment (mM)"
legend_constants[4] = "Na_o in component environment (mM)"
legend_constants[5] = "K_o in component environment (mM)"
legend_constants[6] = "dia in component environment (cm)"
legend_constants[61] = "vol_cyt in component environment (pl)"
legend_constants[57] = "vol_pmu in component environment (pl)"
legend_constants[7] = "fr_cyt in component environment (dimensionless)"
legend_algebraic[0] = "V in component Membrane (mV)"
legend_algebraic[1] = "VD in component Membrane (dimensionless)"
legend_constants[8] = "C_sp in component Membrane (pF_per_sqcm)"
legend_states[0] = "Ca_i in component Cytosol (mM)"
legend_states[1] = "Na_i in component Cytosol (mM)"
legend_states[2] = "K_i in component Cytosol (mM)"
legend_constants[68] = "anoff in component Membrane (mM)"
legend_algebraic[3] = "V_Ca in component Membrane (dimensionless)"
legend_algebraic[5] = "V_Na in component Membrane (dimensionless)"
legend_algebraic[7] = "V_K in component Membrane (dimensionless)"
legend_constants[66] = "A_pmu in component Membrane (sqcm)"
legend_constants[63] = "SVR_pmu in component Membrane (per_cm)"
legend_constants[9] = "svr in component Membrane (dimensionless)"
legend_constants[69] = "C_m in component Membrane (pF)"
legend_constants[10] = "atp in component Cytosol (mM)"
legend_algebraic[63] = "J_Ca in component calcium_dynamics (mM_per_ms)"
legend_algebraic[62] = "J_Na in component sodium_dynamics (mM_per_ms)"
legend_algebraic[45] = "J_K in component potassium_dynamics (mM_per_ms)"
legend_algebraic[61] = "J_ca in component calcium_dynamics (mM_per_ms)"
legend_algebraic[20] = "I_CaL in component L_type_Ca_channel (pA)"
legend_algebraic[21] = "I_CaT in component T_type_Ca_channel (pA)"
legend_algebraic[22] = "I_CaHVA in component HVA_Ca_channel (pA)"
legend_algebraic[49] = "I_pmca in component PMCA (pA)"
legend_algebraic[59] = "I_xm in component Membrane_NaCa (pA)"
legend_algebraic[16] = "J_calb in component calcium_buffer_dynamics (mM_per_ms)"
legend_algebraic[18] = "J_cam in component calcium_buffer_dynamics (mM_per_ms)"
legend_algebraic[24] = "I_Na in component transient_Na_channel (pA)"
legend_algebraic[25] = "I_Nalk in component Leak_Na_channel (pA)"
legend_algebraic[26] = "I_NaHCN in component HCN_channel (pA)"
legend_algebraic[42] = "I_nk in component sodium_pump (pA)"
legend_algebraic[36] = "I_K in component potassium_dynamics (pA)"
legend_algebraic[29] = "I_Ksk in component SK_K_channel (pA)"
legend_algebraic[31] = "I_Kdr in component DR_K_channel (pA)"
legend_algebraic[33] = "I_Ka in component Atype_K_channel (pA)"
legend_algebraic[35] = "I_Kir in component IR_K_channel (pA)"
legend_algebraic[27] = "I_KHCN in component HCN_channel (pA)"
legend_states[3] = "Calb in component calcium_buffer_dynamics (mM)"
legend_states[4] = "Cam in component calcium_buffer_dynamics (mM)"
legend_constants[11] = "Calbtot in component calcium_buffer_dynamics (mM)"
legend_constants[12] = "Camtot in component calcium_buffer_dynamics (mM)"
legend_algebraic[15] = "CaCalb in component calcium_buffer_dynamics (mM)"
legend_algebraic[17] = "CaCam in component calcium_buffer_dynamics (mM)"
legend_constants[13] = "kcal_1 in component calcium_buffer_dynamics (per_mM_ms)"
legend_constants[14] = "kcal_2 in component calcium_buffer_dynamics (per_ms)"
legend_algebraic[9] = "kcam_cb in component calcium_buffer_dynamics (per_ms)"
legend_constants[15] = "kcam_cd in component calcium_buffer_dynamics (per_ms)"
legend_algebraic[11] = "kcam_nb in component calcium_buffer_dynamics (per_ms)"
legend_constants[16] = "kcam_nd in component calcium_buffer_dynamics (per_ms)"
legend_algebraic[13] = "alpha_cam in component calcium_buffer_dynamics (per_ms)"
legend_algebraic[14] = "beta_cam in component calcium_buffer_dynamics (per_ms)"
legend_states[5] = "m_cal in component L_type_Ca_channel (dimensionless)"
legend_algebraic[19] = "h_cal in component L_type_Ca_channel (dimensionless)"
legend_constants[17] = "g_cal in component L_type_Ca_channel (pA_per_mM)"
legend_states[6] = "m_cat in component T_type_Ca_channel (dimensionless)"
legend_states[7] = "h_cat in component T_type_Ca_channel (dimensionless)"
legend_constants[18] = "g_cat in component T_type_Ca_channel (pA_per_mM)"
legend_states[8] = "m_cah in component HVA_Ca_channel (dimensionless)"
legend_states[9] = "h_cah in component HVA_Ca_channel (dimensionless)"
legend_constants[19] = "g_cah in component HVA_Ca_channel (pA_per_mM)"
legend_constants[20] = "g_na in component transient_Na_channel (pA_per_mM)"
legend_algebraic[23] = "O_na in component transient_Na_channel (dimensionless)"
legend_states[10] = "m_na in component transient_Na_channel (dimensionless)"
legend_states[11] = "h_na in component transient_Na_channel (dimensionless)"
legend_constants[21] = "A_mna in component transient_Na_channel (per_ms)"
legend_constants[22] = "B_mna in component transient_Na_channel (per_ms)"
legend_constants[23] = "A_hna in component transient_Na_channel (per_ms)"
legend_constants[24] = "B_hna in component transient_Na_channel (per_ms)"
legend_constants[25] = "za_mna in component transient_Na_channel (dimensionless)"
legend_constants[26] = "zb_mna in component transient_Na_channel (dimensionless)"
legend_constants[27] = "za_hna in component transient_Na_channel (dimensionless)"
legend_constants[28] = "zb_hna in component transient_Na_channel (dimensionless)"
legend_constants[29] = "g_nalk in component Leak_Na_channel (pA_per_mM)"
legend_constants[30] = "g_nahcn in component HCN_channel (pA_per_mM)"
legend_states[12] = "O_hcn in component HCN_channel (dimensionless)"
legend_constants[31] = "g_khcn in component HCN_channel (pA_per_mM)"
legend_algebraic[8] = "kf_hcn in component HCN_channel (per_ms)"
legend_algebraic[12] = "kr_hcn in component HCN_channel (per_ms)"
legend_algebraic[2] = "kf_free in component HCN_channel (per_ms)"
legend_algebraic[4] = "kr_free in component HCN_channel (per_ms)"
legend_algebraic[6] = "kf_bnd in component HCN_channel (per_ms)"
legend_algebraic[10] = "kr_bnd in component HCN_channel (per_ms)"
legend_constants[67] = "P_c in component HCN_channel (dimensionless)"
legend_constants[70] = "P_o in component HCN_channel (dimensionless)"
legend_constants[32] = "cAMP in component HCN_channel (mM)"
legend_algebraic[28] = "O_sk in component SK_K_channel (dimensionless)"
legend_constants[33] = "g_ksk in component SK_K_channel (pA_per_mM)"
legend_algebraic[30] = "O_kdr in component DR_K_channel (dimensionless)"
legend_states[13] = "m_kdr in component DR_K_channel (dimensionless)"
legend_constants[34] = "g_kdr in component DR_K_channel (pA_per_mV)"
legend_algebraic[32] = "O_ka in component Atype_K_channel (dimensionless)"
legend_states[14] = "p_ka in component Atype_K_channel (dimensionless)"
legend_states[15] = "q_ka in component Atype_K_channel (dimensionless)"
legend_constants[35] = "g_ka in component Atype_K_channel (pA_per_mV)"
legend_algebraic[34] = "O_kir in component IR_K_channel (dimensionless)"
legend_constants[36] = "g_kir in component IR_K_channel (pA_per_mV)"
legend_algebraic[37] = "Na_eff in component sodium_pump (mM)"
legend_states[16] = "y_nk in component sodium_pump (dimensionless)"
legend_algebraic[40] = "alpha_nk in component sodium_pump (per_ms)"
legend_algebraic[46] = "beta_nk in component sodium_pump (per_ms)"
legend_algebraic[38] = "P_E1Snk in component sodium_pump (dimensionless)"
legend_algebraic[41] = "P_E2Snk in component sodium_pump (dimensionless)"
legend_algebraic[39] = "P_E1Dnk in component sodium_pump (dimensionless)"
legend_algebraic[43] = "P_E2Dnk in component sodium_pump (dimensionless)"
legend_constants[58] = "k_1nk in component sodium_pump (per_ms)"
legend_constants[37] = "k_2nk in component sodium_pump (per_ms)"
legend_constants[38] = "k_3nk in component sodium_pump (per_ms)"
legend_constants[39] = "k_4nk in component sodium_pump (per_ms)"
legend_constants[40] = "K_nknai in component sodium_pump (mM)"
legend_constants[41] = "K_nknao in component sodium_pump (mM)"
legend_constants[42] = "K_nkki in component sodium_pump (mM)"
legend_constants[43] = "K_nkko in component sodium_pump (mM)"
legend_constants[44] = "k_nk in component sodium_pump (pA)"
legend_states[17] = "y_pc in component PMCA (dimensionless)"
legend_algebraic[44] = "K_pmca in component PMCA (pA)"
legend_constants[59] = "k_1pc in component PMCA (per_ms)"
legend_constants[45] = "k_2pc in component PMCA (per_ms)"
legend_constants[46] = "k_3pc in component PMCA (per_ms)"
legend_constants[47] = "k_4pc in component PMCA (per_ms)"
legend_algebraic[48] = "P_E1Spc in component PMCA (dimensionless)"
legend_constants[60] = "P_E2Spc in component PMCA (dimensionless)"
legend_algebraic[50] = "P_E1pc in component PMCA (dimensionless)"
legend_constants[62] = "P_E2pc in component PMCA (dimensionless)"
legend_algebraic[52] = "alpha_pc in component PMCA (per_ms)"
legend_constants[65] = "beta_pc in component PMCA (per_ms)"
legend_algebraic[47] = "K_pci in component PMCA (mM)"
legend_constants[48] = "K_pco in component PMCA (mM)"
legend_constants[49] = "k_pmca in component PMCA (dimensionless)"
legend_constants[72] = "P_E2Dxm in component Membrane_NaCa (dimensionless)"
legend_algebraic[53] = "P_E1Dxm in component Membrane_NaCa (dimensionless)"
legend_algebraic[51] = "P_E1Sxm in component Membrane_NaCa (dimensionless)"
legend_constants[71] = "P_E2Sxm in component Membrane_NaCa (dimensionless)"
legend_algebraic[54] = "k_1xm in component Membrane_NaCa (per_ms)"
legend_algebraic[55] = "k_2xm in component Membrane_NaCa (per_ms)"
legend_algebraic[56] = "k_3xm in component Membrane_NaCa (per_ms)"
legend_algebraic[58] = "k_4xm in component Membrane_NaCa (per_ms)"
legend_algebraic[60] = "beta_xm in component Membrane_NaCa (per_ms)"
legend_algebraic[57] = "alpha_xm in component Membrane_NaCa (per_ms)"
legend_constants[50] = "K_xmnai in component Membrane_NaCa (mM)"
legend_constants[51] = "K_xmnao in component Membrane_NaCa (mM)"
legend_constants[52] = "K_xmcai in component Membrane_NaCa (mM)"
legend_constants[53] = "K_xmcao in component Membrane_NaCa (mM)"
legend_constants[54] = "delta_xmca in component Membrane_NaCa (dimensionless)"
legend_constants[55] = "delta_xmna in component Membrane_NaCa (dimensionless)"
legend_states[18] = "y_xm in component Membrane_NaCa (dimensionless)"
legend_constants[56] = "k_xm in component Membrane_NaCa (pA_ms)"
legend_rates[0] = "d/dt Ca_i in component Cytosol (mM)"
legend_rates[1] = "d/dt Na_i in component Cytosol (mM)"
legend_rates[2] = "d/dt K_i in component Cytosol (mM)"
legend_rates[3] = "d/dt Calb in component calcium_buffer_dynamics (mM)"
legend_rates[4] = "d/dt Cam in component calcium_buffer_dynamics (mM)"
legend_rates[5] = "d/dt m_cal in component L_type_Ca_channel (dimensionless)"
legend_rates[6] = "d/dt m_cat in component T_type_Ca_channel (dimensionless)"
legend_rates[7] = "d/dt h_cat in component T_type_Ca_channel (dimensionless)"
legend_rates[8] = "d/dt m_cah in component HVA_Ca_channel (dimensionless)"
legend_rates[9] = "d/dt h_cah in component HVA_Ca_channel (dimensionless)"
legend_rates[10] = "d/dt m_na in component transient_Na_channel (dimensionless)"
legend_rates[11] = "d/dt h_na in component transient_Na_channel (dimensionless)"
legend_rates[12] = "d/dt O_hcn in component HCN_channel (dimensionless)"
legend_rates[13] = "d/dt m_kdr in component DR_K_channel (dimensionless)"
legend_rates[14] = "d/dt p_ka in component Atype_K_channel (dimensionless)"
legend_rates[15] = "d/dt q_ka in component Atype_K_channel (dimensionless)"
legend_rates[16] = "d/dt y_nk in component sodium_pump (dimensionless)"
legend_rates[17] = "d/dt y_pc in component PMCA (dimensionless)"
legend_rates[18] = "d/dt y_xm in component Membrane_NaCa (dimensionless)"
return (legend_states, legend_algebraic, legend_voi, legend_constants)
def initConsts():
constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
constants[0] = 8314.472
constants[1] = 310.15
constants[2] = 96485.30929
constants[3] = 1.8
constants[4] = 137
constants[5] = 5.4
constants[6] = 30e-4
constants[7] = 1
constants[8] = 0.9e6
states[0] = 0.00015
states[1] = 6
states[2] = 140
constants[9] = 6
constants[10] = 2
states[3] = 0.0011
states[4] = 0.0487
constants[11] = 0.002
constants[12] = 0.0489
constants[13] = 10
constants[14] = 2e-3
constants[15] = 0.003
constants[16] = 3
states[5] = 0.0004
constants[17] = 1158.2
states[6] = 0.1099
states[7] = 0.5716
constants[18] = 10
states[8] = 0.3021
states[9] = 0.454
constants[19] = 78.5
constants[20] = 395.14
states[10] = 0.0758
states[11] = 0.2272
constants[21] = 1.9651
constants[22] = 0.0424
constants[23] = 9.566e-5
constants[24] = 0.5296
constants[25] = 1.7127
constants[26] = 1.5581
constants[27] = -2.4317
constants[28] = -1.1868
constants[29] = 0.0039
constants[30] = 3
states[12] = 0
constants[31] = 10
constants[32] = 1e-5
constants[33] = 15
states[13] = 0.0043
constants[34] = 10
states[14] = 0.2577
states[15] = 0.827
constants[35] = 0.2234
constants[36] = 5
states[16] = 0.555
constants[37] = 0.04
constants[38] = 0.01
constants[39] = 0.165
constants[40] = 4.05
constants[41] = 69.8
constants[42] = 32.88
constants[43] = 0.258
constants[44] = 200
states[17] = 0.001
constants[45] = 0.001
constants[46] = 0.001
constants[47] = 1
constants[48] = 2
constants[49] = 10
constants[50] = 8.75
constants[51] = 87.5
constants[52] = 0.00138
constants[53] = 1.38
constants[54] = 0.68
constants[55] = 0.32
states[18] = 0.343
constants[56] = 25
constants[57] = ((( pi*(power(constants[6], 3.00000)))/6.00000)*1.00000e+09)/(1.00000*1.00000*1.00000)
constants[58] = 0.370000/(1.00000+0.0940000/constants[10])
constants[59] = 1.00000/(1.00000+0.100000/constants[10])
constants[60] = 1.00000/(1.00000+constants[48]/constants[3])
constants[61] = constants[7]*constants[57]
constants[62] = 1.00000-constants[60]
constants[63] = constants[9]/constants[6]
constants[64] = (constants[0]*constants[1])/constants[2]
constants[65] = constants[45]*constants[60]+constants[47]*constants[62]
constants[66] = (constants[63]*constants[57]*0.00100000*0.00100000*0.00100000)/1.00000
constants[67] = 1.00000/(1.00000+constants[32]/0.00116300)
constants[68] = (((-52.3100*constants[8]*constants[66])/(constants[2]*constants[61])-2.00000*(0.000150000-constants[3]))-(6.00000-constants[4]))-(140.000-constants[5])
constants[69] = constants[8]*constants[66]
constants[70] = 1.00000/(1.00000+constants[32]/1.45000e-05)
constants[71] = 1.00000/(1.00000+(constants[53]/constants[3])*(1.00000+power(constants[4]/constants[51], 3.00000)))
constants[72] = 1.00000/(1.00000+(power(constants[51]/constants[4], 3.00000))*(1.00000+constants[3]/constants[53]))
return (states, constants)
def computeRates(voi, states, constants):
rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
algebraic[0] = ((constants[2]*constants[61])/(constants[8]*constants[66]))*((((states[2]-constants[5])+2.00000*(states[0]-constants[3])+states[1])-constants[4])+constants[68])
rates[5] = (1.00000/(1.00000+exp(-(algebraic[0]+15.0000)/7.00000))-states[5])/(10.0000*exp(-(power((algebraic[0]+86.4000)/23.2000, 2.00000)))+0.943000)
rates[6] = (1.00000/(1.00000+exp(-(algebraic[0]+63.0000)/1.50000))-states[6])/(65.0000*exp(-(power((algebraic[0]+68.0000)/6.00000, 2.00000)))+12.0000)
rates[7] = (1.00000/(1.00000+exp((algebraic[0]+76.2000)/3.00000))-states[7])/(50.0000*exp(-(power((algebraic[0]+72.0000)/10.0000, 2.00000)))+10.0000)
rates[8] = (1.00000/(1.00000+exp(-(algebraic[0]+10.0000)/10.0000))-states[8])/(0.100000*exp(-(power((algebraic[0]+62.0000)/13.0000, 2.00000)))+0.0500000)
rates[9] = (1.00000/(1.00000+exp((algebraic[0]+48.0000)/5.00000))-states[9])/(0.500000*exp(-(power((algebraic[0]+55.6000)/18.0000, 2.00000)))+0.500000)
rates[13] = (1.00000/(1.00000+exp(-(algebraic[0]+25.0000)/12.0000))-states[13])/(18.0000/(1.00000+exp((algebraic[0]+39.0000)/8.00000))+1.00000)
rates[14] = (1.00000/(1.00000+exp(-(algebraic[0]+43.0000)/24.0000))-states[14])/(2.00000*exp(-(power((algebraic[0]+50.0000)/23.4500, 2.00000)))+1.10000)
rates[15] = (1.00000/(1.00000+exp((algebraic[0]+56.0000)/8.00000))-states[15])/20.0000
algebraic[1] = algebraic[0]/constants[64]
rates[10] = constants[21]*exp(constants[25]*algebraic[1])*(1.00000-states[10])-constants[22]*exp(-constants[26]*algebraic[1])*states[10]
rates[11] = constants[23]*exp(constants[27]*algebraic[1])*(1.00000-states[11])-constants[24]*exp(-constants[28]*algebraic[1])*states[11]
algebraic[2] = 0.00600000/(1.00000+exp((algebraic[0]+87.7000)/6.45000))
algebraic[6] = 0.0268000/(1.00000+exp((algebraic[0]+94.2000)/13.3000))
algebraic[8] = algebraic[2]*constants[67]+algebraic[6]*(1.00000-constants[67])
algebraic[4] = 0.0800000/(1.00000+exp(-(algebraic[0]+51.7000)/7.00000))
algebraic[10] = 0.0800000/(1.00000+exp(-(algebraic[0]+35.5000)/7.00000))
algebraic[12] = algebraic[4]*constants[70]+algebraic[10]*(1.00000-constants[70])
rates[12] = algebraic[8]*(1.00000-states[12])-algebraic[12]*states[12]
algebraic[15] = constants[11]-states[3]
algebraic[16] = constants[13]*states[3]*states[0]-constants[14]*algebraic[15]
rates[3] = -algebraic[16]
algebraic[17] = constants[12]-states[4]
algebraic[9] = 12000.0*(power(states[0], 2.00000))
algebraic[11] = 3.70000e+06*(power(states[0], 2.00000))
algebraic[13] = algebraic[9]*algebraic[11]*(1.00000/(algebraic[9]+constants[16])+1.00000/(constants[15]+constants[16]))
algebraic[14] = constants[15]*constants[16]*(1.00000/(algebraic[9]+constants[16])+1.00000/(constants[15]+constants[16]))
algebraic[18] = algebraic[13]*states[4]-algebraic[14]*algebraic[17]
rates[4] = -algebraic[18]
algebraic[38] = 1.00000/(1.00000+(constants[40]/states[1])*(1.00000+states[2]/constants[42]))
algebraic[37] = constants[4]*exp(-0.820000*algebraic[1])
algebraic[41] = 1.00000/(1.00000+(constants[41]/algebraic[37])*(1.00000+constants[5]/constants[43]))
algebraic[42] = constants[44]*(constants[58]*algebraic[38]*states[16]-constants[37]*algebraic[41]*(1.00000-states[16]))*1.00000
algebraic[7] = log(constants[5]/states[2])
algebraic[28] = (power(states[0], 4.20000))/(power(0.000350000, 4.20000)+power(states[0], 4.20000))
algebraic[29] = (constants[33]*algebraic[28]*(power(states[2]*constants[5], 1.0/2))*sinh(0.500000*(algebraic[1]-algebraic[7])))/(sinh(0.500000*algebraic[1])/(0.500000*algebraic[1]))
algebraic[30] = power(states[13], 3.00000)
algebraic[31] = constants[34]*algebraic[30]*(algebraic[0]-algebraic[7]*constants[64])
algebraic[32] = (power(states[14], 3.00000))*states[15]
algebraic[33] = constants[35]*algebraic[32]*(algebraic[0]-algebraic[7]*constants[64])
algebraic[34] = 1.00000/(1.00000+exp((algebraic[0]+90.0000)/12.1000))
algebraic[35] = constants[36]*algebraic[34]*(algebraic[0]-algebraic[7]*constants[64])
algebraic[27] = (constants[31]*states[12]*(power(states[2]*constants[5], 1.0/2))*sinh(0.500000*(algebraic[1]-algebraic[7])))/(sinh(0.500000*algebraic[1])/(0.500000*algebraic[1]))
algebraic[36] = algebraic[29]+algebraic[27]+algebraic[33]+algebraic[31]+algebraic[35]
algebraic[45] = (-1.00000/(constants[2]*constants[61]))*(algebraic[36]-2.00000*algebraic[42])
rates[2] = algebraic[45]
algebraic[39] = 1.00000/(1.00000+(constants[42]/states[2])*(1.00000+states[1]/constants[40]))
algebraic[40] = constants[58]*algebraic[38]+constants[38]*algebraic[39]
algebraic[43] = 1.00000/(1.00000+(constants[43]/constants[5])*(1.00000+algebraic[37]/constants[41]))
algebraic[46] = constants[37]*algebraic[41]+constants[39]*algebraic[43]
rates[16] = algebraic[46]*(1.00000-states[16])-algebraic[40]*states[16]
algebraic[47] = (173.600/(1.00000+algebraic[17]/5.00000e-05)+6.40000)*1.00000e-05
algebraic[48] = 1.00000/(1.00000+algebraic[47]/states[0])
algebraic[50] = 1.00000-algebraic[48]
algebraic[52] = constants[59]*algebraic[48]+constants[46]*algebraic[50]
rates[17] = constants[65]*(1.00000-states[17])-algebraic[52]*states[17]
algebraic[55] = 1.00000*exp((1.00000-constants[54])*algebraic[1])
algebraic[58] = 1.00000*exp(-constants[55]*algebraic[1])
algebraic[60] = algebraic[55]*constants[71]+algebraic[58]*constants[72]
algebraic[53] = 1.00000/(1.00000+(power(constants[50]/states[1], 3.00000))*(1.00000+states[0]/constants[52]))
algebraic[51] = 1.00000/(1.00000+(constants[52]/states[0])*(1.00000+power(states[1]/constants[50], 3.00000)))
algebraic[54] = 1.00000*exp(-constants[54]*algebraic[1])
algebraic[56] = 1.00000*exp((1.00000-constants[55])*algebraic[1])
algebraic[57] = algebraic[54]*algebraic[51]+algebraic[56]*algebraic[53]
rates[18] = algebraic[60]*(1.00000-states[18])-algebraic[57]*states[18]
algebraic[59] = constants[56]*(algebraic[56]*algebraic[53]*states[18]-algebraic[58]*constants[72]*(1.00000-states[18]))
algebraic[5] = log(constants[4]/states[1])
algebraic[23] = (power(states[10], 3.00000))*states[11]
algebraic[24] = (constants[20]*algebraic[23]*(power(states[1]*constants[4], 1.0/2))*sinh(0.500000*(algebraic[1]-algebraic[5])))/(sinh(0.500000*algebraic[1])/(0.500000*algebraic[1]))
algebraic[25] = (constants[29]*(power(states[1]*constants[4], 1.0/2))*sinh(0.500000*(algebraic[1]-algebraic[5])))/(sinh(0.500000*algebraic[1])/(0.500000*algebraic[1]))
algebraic[26] = (constants[30]*states[12]*(power(states[1]*constants[4], 1.0/2))*sinh(0.500000*(algebraic[1]-algebraic[5])))/(sinh(0.500000*algebraic[1])/(0.500000*algebraic[1]))
algebraic[62] = (-1.00000/(constants[2]*constants[61]))*(3.00000*algebraic[42]+3.00000*algebraic[59]+algebraic[24]+algebraic[25]+algebraic[26])
rates[1] = algebraic[62]
algebraic[3] = 0.500000*log(constants[3]/states[0])
algebraic[19] = 0.000450000/(0.000450000+states[0])
algebraic[20] = (constants[17]*states[5]*algebraic[19]*(power(states[0]*constants[3], 1.0/2))*sinh(algebraic[1]-algebraic[3]))/(sinh(algebraic[1])/algebraic[1])
algebraic[21] = (constants[18]*states[6]*states[7]*(power(states[0]*constants[3], 1.0/2))*sinh(algebraic[1]-algebraic[3]))/(sinh(algebraic[1])/algebraic[1])
algebraic[22] = (constants[19]*states[8]*states[9]*(power(states[0]*constants[3], 1.0/2))*sinh(algebraic[1]-algebraic[3]))/(sinh(algebraic[1])/algebraic[1])
algebraic[44] = constants[49]*((10.5600*algebraic[17])/(algebraic[17]+5.00000e-05)+1.20000)
algebraic[49] = algebraic[44]*(constants[59]*algebraic[48]*states[17]-constants[45]*constants[60]*(1.00000-states[17]))*1.00000
algebraic[61] = (-1.00000/(2.00000*constants[2]*constants[61]))*((algebraic[20]+algebraic[21]+algebraic[22]+2.00000*algebraic[49])-2.00000*algebraic[59])
algebraic[63] = algebraic[61]-(algebraic[16]+4.00000*algebraic[18])
rates[0] = algebraic[63]
return(rates)
def computeAlgebraic(constants, states, voi):
algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
states = array(states)
voi = array(voi)
algebraic[0] = ((constants[2]*constants[61])/(constants[8]*constants[66]))*((((states[2]-constants[5])+2.00000*(states[0]-constants[3])+states[1])-constants[4])+constants[68])
algebraic[1] = algebraic[0]/constants[64]
algebraic[2] = 0.00600000/(1.00000+exp((algebraic[0]+87.7000)/6.45000))
algebraic[6] = 0.0268000/(1.00000+exp((algebraic[0]+94.2000)/13.3000))
algebraic[8] = algebraic[2]*constants[67]+algebraic[6]*(1.00000-constants[67])
algebraic[4] = 0.0800000/(1.00000+exp(-(algebraic[0]+51.7000)/7.00000))
algebraic[10] = 0.0800000/(1.00000+exp(-(algebraic[0]+35.5000)/7.00000))
algebraic[12] = algebraic[4]*constants[70]+algebraic[10]*(1.00000-constants[70])
algebraic[15] = constants[11]-states[3]
algebraic[16] = constants[13]*states[3]*states[0]-constants[14]*algebraic[15]
algebraic[17] = constants[12]-states[4]
algebraic[9] = 12000.0*(power(states[0], 2.00000))
algebraic[11] = 3.70000e+06*(power(states[0], 2.00000))
algebraic[13] = algebraic[9]*algebraic[11]*(1.00000/(algebraic[9]+constants[16])+1.00000/(constants[15]+constants[16]))
algebraic[14] = constants[15]*constants[16]*(1.00000/(algebraic[9]+constants[16])+1.00000/(constants[15]+constants[16]))
algebraic[18] = algebraic[13]*states[4]-algebraic[14]*algebraic[17]
algebraic[38] = 1.00000/(1.00000+(constants[40]/states[1])*(1.00000+states[2]/constants[42]))
algebraic[37] = constants[4]*exp(-0.820000*algebraic[1])
algebraic[41] = 1.00000/(1.00000+(constants[41]/algebraic[37])*(1.00000+constants[5]/constants[43]))
algebraic[42] = constants[44]*(constants[58]*algebraic[38]*states[16]-constants[37]*algebraic[41]*(1.00000-states[16]))*1.00000
algebraic[7] = log(constants[5]/states[2])
algebraic[28] = (power(states[0], 4.20000))/(power(0.000350000, 4.20000)+power(states[0], 4.20000))
algebraic[29] = (constants[33]*algebraic[28]*(power(states[2]*constants[5], 1.0/2))*sinh(0.500000*(algebraic[1]-algebraic[7])))/(sinh(0.500000*algebraic[1])/(0.500000*algebraic[1]))
algebraic[30] = power(states[13], 3.00000)
algebraic[31] = constants[34]*algebraic[30]*(algebraic[0]-algebraic[7]*constants[64])
algebraic[32] = (power(states[14], 3.00000))*states[15]
algebraic[33] = constants[35]*algebraic[32]*(algebraic[0]-algebraic[7]*constants[64])
algebraic[34] = 1.00000/(1.00000+exp((algebraic[0]+90.0000)/12.1000))
algebraic[35] = constants[36]*algebraic[34]*(algebraic[0]-algebraic[7]*constants[64])
algebraic[27] = (constants[31]*states[12]*(power(states[2]*constants[5], 1.0/2))*sinh(0.500000*(algebraic[1]-algebraic[7])))/(sinh(0.500000*algebraic[1])/(0.500000*algebraic[1]))
algebraic[36] = algebraic[29]+algebraic[27]+algebraic[33]+algebraic[31]+algebraic[35]
algebraic[45] = (-1.00000/(constants[2]*constants[61]))*(algebraic[36]-2.00000*algebraic[42])
algebraic[39] = 1.00000/(1.00000+(constants[42]/states[2])*(1.00000+states[1]/constants[40]))
algebraic[40] = constants[58]*algebraic[38]+constants[38]*algebraic[39]
algebraic[43] = 1.00000/(1.00000+(constants[43]/constants[5])*(1.00000+algebraic[37]/constants[41]))
algebraic[46] = constants[37]*algebraic[41]+constants[39]*algebraic[43]
algebraic[47] = (173.600/(1.00000+algebraic[17]/5.00000e-05)+6.40000)*1.00000e-05
algebraic[48] = 1.00000/(1.00000+algebraic[47]/states[0])
algebraic[50] = 1.00000-algebraic[48]
algebraic[52] = constants[59]*algebraic[48]+constants[46]*algebraic[50]
algebraic[55] = 1.00000*exp((1.00000-constants[54])*algebraic[1])
algebraic[58] = 1.00000*exp(-constants[55]*algebraic[1])
algebraic[60] = algebraic[55]*constants[71]+algebraic[58]*constants[72]
algebraic[53] = 1.00000/(1.00000+(power(constants[50]/states[1], 3.00000))*(1.00000+states[0]/constants[52]))
algebraic[51] = 1.00000/(1.00000+(constants[52]/states[0])*(1.00000+power(states[1]/constants[50], 3.00000)))
algebraic[54] = 1.00000*exp(-constants[54]*algebraic[1])
algebraic[56] = 1.00000*exp((1.00000-constants[55])*algebraic[1])
algebraic[57] = algebraic[54]*algebraic[51]+algebraic[56]*algebraic[53]
algebraic[59] = constants[56]*(algebraic[56]*algebraic[53]*states[18]-algebraic[58]*constants[72]*(1.00000-states[18]))
algebraic[5] = log(constants[4]/states[1])
algebraic[23] = (power(states[10], 3.00000))*states[11]
algebraic[24] = (constants[20]*algebraic[23]*(power(states[1]*constants[4], 1.0/2))*sinh(0.500000*(algebraic[1]-algebraic[5])))/(sinh(0.500000*algebraic[1])/(0.500000*algebraic[1]))
algebraic[25] = (constants[29]*(power(states[1]*constants[4], 1.0/2))*sinh(0.500000*(algebraic[1]-algebraic[5])))/(sinh(0.500000*algebraic[1])/(0.500000*algebraic[1]))
algebraic[26] = (constants[30]*states[12]*(power(states[1]*constants[4], 1.0/2))*sinh(0.500000*(algebraic[1]-algebraic[5])))/(sinh(0.500000*algebraic[1])/(0.500000*algebraic[1]))
algebraic[62] = (-1.00000/(constants[2]*constants[61]))*(3.00000*algebraic[42]+3.00000*algebraic[59]+algebraic[24]+algebraic[25]+algebraic[26])
algebraic[3] = 0.500000*log(constants[3]/states[0])
algebraic[19] = 0.000450000/(0.000450000+states[0])
algebraic[20] = (constants[17]*states[5]*algebraic[19]*(power(states[0]*constants[3], 1.0/2))*sinh(algebraic[1]-algebraic[3]))/(sinh(algebraic[1])/algebraic[1])
algebraic[21] = (constants[18]*states[6]*states[7]*(power(states[0]*constants[3], 1.0/2))*sinh(algebraic[1]-algebraic[3]))/(sinh(algebraic[1])/algebraic[1])
algebraic[22] = (constants[19]*states[8]*states[9]*(power(states[0]*constants[3], 1.0/2))*sinh(algebraic[1]-algebraic[3]))/(sinh(algebraic[1])/algebraic[1])
algebraic[44] = constants[49]*((10.5600*algebraic[17])/(algebraic[17]+5.00000e-05)+1.20000)
algebraic[49] = algebraic[44]*(constants[59]*algebraic[48]*states[17]-constants[45]*constants[60]*(1.00000-states[17]))*1.00000
algebraic[61] = (-1.00000/(2.00000*constants[2]*constants[61]))*((algebraic[20]+algebraic[21]+algebraic[22]+2.00000*algebraic[49])-2.00000*algebraic[59])
algebraic[63] = algebraic[61]-(algebraic[16]+4.00000*algebraic[18])
return algebraic
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)