00001
00012 #include "BackwardEulerFoxModel2002Modified.hpp"
00013
00014 #include <cmath>
00015 #include <cassert>
00016 #include "CardiacNewtonSolver.hpp"
00017 #include "Exception.hpp"
00018 #include "OdeSystemInformation.hpp"
00019
00020 BackwardEulerFoxModel2002Modified::BackwardEulerFoxModel2002Modified(
00021 boost::shared_ptr<AbstractStimulusFunction> pIntracellularStimulus)
00022 : AbstractBackwardEulerCardiacCell<3>(13, 0, pIntracellularStimulus)
00023 {
00024
00025 mpSystemInfo = OdeSystemInformation<BackwardEulerFoxModel2002Modified>::Instance();
00026 Init();
00027 }
00028
00032 BackwardEulerFoxModel2002Modified::BackwardEulerFoxModel2002Modified(
00033 boost::shared_ptr<AbstractIvpOdeSolver> ,
00034 boost::shared_ptr<AbstractStimulusFunction> pIntracellularStimulus)
00035 : AbstractBackwardEulerCardiacCell<3>(13, 0, pIntracellularStimulus)
00036 {
00037
00038 mpSystemInfo = OdeSystemInformation<BackwardEulerFoxModel2002Modified>::Instance();
00039 Init();
00040 }
00041
00042 double BackwardEulerFoxModel2002Modified::GetIIonic()
00043 {
00044 std::vector<double>& rY = rGetStateVariables();
00045 double var_membrane__V = rY[0];
00046
00047 double var_fast_sodium_current_m_gate__m = rY[1];
00048
00049 double var_fast_sodium_current_h_gate__h = rY[2];
00050
00051 double var_fast_sodium_current_j_gate__j = rY[3];
00052
00053 double var_rapid_activating_delayed_rectifiyer_K_current_X_kr_gate__X_kr = rY[4];
00054
00055 double var_slow_activating_delayed_rectifiyer_K_current_X_ks_gate__X_ks = rY[5];
00056
00057 double var_transient_outward_potassium_current_X_to_gate__X_to = rY[6];
00058
00059 double var_transient_outward_potassium_current_Y_to_gate__Y_to = rY[7];
00060
00061 double var_L_type_Ca_current_f_gate__f = rY[8];
00062
00063 double var_L_type_Ca_current_d_gate__d = rY[9];
00064
00065 double var_L_type_Ca_current_f_Ca_gate__f_Ca = rY[10];
00066
00067 double var_calcium_dynamics__Ca_i = rY[11];
00068
00069
00070 const double var_membrane__R = 8.314;
00071 const double var_membrane__T = 310.0;
00072 const double var_membrane__F = 96.5;
00073 double var_fast_sodium_current__h = var_fast_sodium_current_h_gate__h;
00074 const double var_fast_sodium_current__g_Na = 12.8;
00075 double var_fast_sodium_current__j = var_fast_sodium_current_j_gate__j;
00076 double var_fast_sodium_current__T = var_membrane__T;
00077 double var_fast_sodium_current__R = var_membrane__R;
00078 const double var_standard_ionic_concentrations__Na_i = 10.0;
00079 double var_fast_sodium_current__Na_i = var_standard_ionic_concentrations__Na_i;
00080 const double var_standard_ionic_concentrations__Na_o = 138.0;
00081 double var_fast_sodium_current__Na_o = var_standard_ionic_concentrations__Na_o;
00082 double var_fast_sodium_current__F = var_membrane__F;
00083 double var_fast_sodium_current__E_Na = ((var_fast_sodium_current__R * var_fast_sodium_current__T) / var_fast_sodium_current__F) * log(var_fast_sodium_current__Na_o / var_fast_sodium_current__Na_i);
00084 double var_fast_sodium_current__V = var_membrane__V;
00085 double var_fast_sodium_current__m = var_fast_sodium_current_m_gate__m;
00086 double var_fast_sodium_current__i_Na = var_fast_sodium_current__g_Na * pow(var_fast_sodium_current__m, 3.0) * var_fast_sodium_current__h * var_fast_sodium_current__j * (var_fast_sodium_current__V - var_fast_sodium_current__E_Na);
00087 double var_membrane__i_Na = var_fast_sodium_current__i_Na;
00088 const double var_L_type_Ca_current__P_Ca = 1.26e-05;
00089 double var_L_type_Ca_current__V = var_membrane__V;
00090 const double var_standard_ionic_concentrations__Ca_o = 2000.0;
00091 double var_L_type_Ca_current__Ca_o = var_standard_ionic_concentrations__Ca_o;
00092 double var_L_type_Ca_current__T = var_membrane__T;
00093 const double var_L_type_Ca_current__C_sc = 1.0;
00094 double var_L_type_Ca_current__Ca_i = var_calcium_dynamics__Ca_i;
00095 double var_L_type_Ca_current__R = var_membrane__R;
00096 double var_L_type_Ca_current__F = var_membrane__F;
00097 double var_L_type_Ca_current__i_Ca_max = ((((var_L_type_Ca_current__P_Ca / var_L_type_Ca_current__C_sc) * 4.0 * var_L_type_Ca_current__V * pow(var_L_type_Ca_current__F, 2.0)) / (var_L_type_Ca_current__R * var_L_type_Ca_current__T)) * ((var_L_type_Ca_current__Ca_i * exp((2.0 * var_L_type_Ca_current__V * var_L_type_Ca_current__F) / (var_L_type_Ca_current__R * var_L_type_Ca_current__T))) - (0.341 * var_L_type_Ca_current__Ca_o))) / (exp((2.0 * var_L_type_Ca_current__V * var_L_type_Ca_current__F) / (var_L_type_Ca_current__R * var_L_type_Ca_current__T)) - 1.0);
00098 double var_L_type_Ca_current__d = var_L_type_Ca_current_d_gate__d;
00099 double var_L_type_Ca_current__f = var_L_type_Ca_current_f_gate__f;
00100 double var_L_type_Ca_current__f_Ca = var_L_type_Ca_current_f_Ca_gate__f_Ca;
00101 double var_L_type_Ca_current__i_Ca = var_L_type_Ca_current__i_Ca_max * var_L_type_Ca_current__f * var_L_type_Ca_current__d * var_L_type_Ca_current__f_Ca;
00102 double var_membrane__i_Ca = var_L_type_Ca_current__i_Ca;
00103 const double var_standard_ionic_concentrations__K_o = 4.0;
00104 double var_L_type_Ca_current__K_o = var_standard_ionic_concentrations__K_o;
00105 const double var_L_type_Ca_current__i_Ca_half = -0.265;
00106 const double var_L_type_Ca_current__P_CaK = 5.79e-07;
00107 const double var_standard_ionic_concentrations__K_i = 149.4;
00108 double var_L_type_Ca_current__K_i = var_standard_ionic_concentrations__K_i;
00109 double var_L_type_Ca_current__i_CaK = ((((((var_L_type_Ca_current__P_CaK / var_L_type_Ca_current__C_sc) * var_L_type_Ca_current__f * var_L_type_Ca_current__d * var_L_type_Ca_current__f_Ca) / (1.0 + (var_L_type_Ca_current__i_Ca_max / var_L_type_Ca_current__i_Ca_half))) * 1000.0 * var_L_type_Ca_current__V * pow(var_L_type_Ca_current__F, 2.0)) / (var_L_type_Ca_current__R * var_L_type_Ca_current__T)) * ((var_L_type_Ca_current__K_i * exp((var_L_type_Ca_current__V * var_L_type_Ca_current__F) / (var_L_type_Ca_current__R * var_L_type_Ca_current__T))) - var_L_type_Ca_current__K_o)) / (exp((var_L_type_Ca_current__V * var_L_type_Ca_current__F) / (var_L_type_Ca_current__R * var_L_type_Ca_current__T)) - 1.0);
00110 double var_membrane__i_CaK = var_L_type_Ca_current__i_CaK;
00111 double var_rapid_activating_delayed_rectifiyer_K_current__V = var_membrane__V;
00112 double var_rapid_activating_delayed_rectifiyer_K_current__R_V = 1.0 / (1.0 + (2.5 * exp(0.1 * (var_rapid_activating_delayed_rectifiyer_K_current__V + 28.0))));
00113 double var_rapid_activating_delayed_rectifiyer_K_current__X_kr = var_rapid_activating_delayed_rectifiyer_K_current_X_kr_gate__X_kr;
00114 double var_rapid_activating_delayed_rectifiyer_K_current__R = var_membrane__R;
00115 double var_rapid_activating_delayed_rectifiyer_K_current__K_o = var_standard_ionic_concentrations__K_o;
00116 double var_rapid_activating_delayed_rectifiyer_K_current__T = var_membrane__T;
00117 double var_rapid_activating_delayed_rectifiyer_K_current__K_i = var_standard_ionic_concentrations__K_i;
00118 double var_rapid_activating_delayed_rectifiyer_K_current__F = var_membrane__F;
00119 double var_rapid_activating_delayed_rectifiyer_K_current__E_K = ((var_rapid_activating_delayed_rectifiyer_K_current__R * var_rapid_activating_delayed_rectifiyer_K_current__T) / var_rapid_activating_delayed_rectifiyer_K_current__F) * log(var_rapid_activating_delayed_rectifiyer_K_current__K_o / var_rapid_activating_delayed_rectifiyer_K_current__K_i);
00120 const double var_rapid_activating_delayed_rectifiyer_K_current__g_Kr = 0.0136;
00121 double var_rapid_activating_delayed_rectifiyer_K_current__i_Kr = var_rapid_activating_delayed_rectifiyer_K_current__g_Kr * var_rapid_activating_delayed_rectifiyer_K_current__R_V * var_rapid_activating_delayed_rectifiyer_K_current__X_kr * sqrt(var_rapid_activating_delayed_rectifiyer_K_current__K_o / 4.0) * (var_rapid_activating_delayed_rectifiyer_K_current__V - var_rapid_activating_delayed_rectifiyer_K_current__E_K);
00122 double var_membrane__i_Kr = var_rapid_activating_delayed_rectifiyer_K_current__i_Kr;
00123 const double var_slow_activating_delayed_rectifiyer_K_current__g_Ks = 0.0245;
00124 double var_slow_activating_delayed_rectifiyer_K_current__V = var_membrane__V;
00125 double var_slow_activating_delayed_rectifiyer_K_current__K_i = var_standard_ionic_concentrations__K_i;
00126 double var_slow_activating_delayed_rectifiyer_K_current__F = var_membrane__F;
00127 double var_slow_activating_delayed_rectifiyer_K_current__K_o = var_standard_ionic_concentrations__K_o;
00128 double var_slow_activating_delayed_rectifiyer_K_current__T = var_membrane__T;
00129 double var_slow_activating_delayed_rectifiyer_K_current__Na_o = var_standard_ionic_concentrations__Na_o;
00130 double var_slow_activating_delayed_rectifiyer_K_current__R = var_membrane__R;
00131 double var_slow_activating_delayed_rectifiyer_K_current__Na_i = var_standard_ionic_concentrations__Na_i;
00132 double var_slow_activating_delayed_rectifiyer_K_current__E_Ks = ((var_slow_activating_delayed_rectifiyer_K_current__R * var_slow_activating_delayed_rectifiyer_K_current__T) / var_slow_activating_delayed_rectifiyer_K_current__F) * log((var_slow_activating_delayed_rectifiyer_K_current__K_o + (0.01833 * var_slow_activating_delayed_rectifiyer_K_current__Na_o)) / (var_slow_activating_delayed_rectifiyer_K_current__K_i + (0.01833 * var_slow_activating_delayed_rectifiyer_K_current__Na_i)));
00133 double var_slow_activating_delayed_rectifiyer_K_current__X_ks = var_slow_activating_delayed_rectifiyer_K_current_X_ks_gate__X_ks;
00134 double var_slow_activating_delayed_rectifiyer_K_current__i_Ks = var_slow_activating_delayed_rectifiyer_K_current__g_Ks * pow(var_slow_activating_delayed_rectifiyer_K_current__X_ks, 2.0) * (var_slow_activating_delayed_rectifiyer_K_current__V - var_slow_activating_delayed_rectifiyer_K_current__E_Ks);
00135 double var_membrane__i_Ks = var_slow_activating_delayed_rectifiyer_K_current__i_Ks;
00136 const double var_transient_outward_potassium_current__g_to = 0.23815;
00137 double var_transient_outward_potassium_current__V = var_membrane__V;
00138 double var_transient_outward_potassium_current__X_to = var_transient_outward_potassium_current_X_to_gate__X_to;
00139 double var_transient_outward_potassium_current__E_K = var_rapid_activating_delayed_rectifiyer_K_current__E_K;
00140 double var_transient_outward_potassium_current__Y_to = var_transient_outward_potassium_current_Y_to_gate__Y_to;
00141 double var_transient_outward_potassium_current__i_to = var_transient_outward_potassium_current__g_to * var_transient_outward_potassium_current__X_to * var_transient_outward_potassium_current__Y_to * (var_transient_outward_potassium_current__V - var_transient_outward_potassium_current__E_K);
00142 double var_membrane__i_to = var_transient_outward_potassium_current__i_to;
00143 const double var_time_independent_potassium_current__g_K1 = 2.8;
00144 double var_time_independent_potassium_current__F = var_membrane__F;
00145 double var_time_independent_potassium_current_K1_gate__F = var_time_independent_potassium_current__F;
00146 double var_time_independent_potassium_current__V = var_membrane__V;
00147 double var_time_independent_potassium_current_K1_gate__V = var_time_independent_potassium_current__V;
00148 double var_time_independent_potassium_current__T = var_membrane__T;
00149 double var_time_independent_potassium_current_K1_gate__T = var_time_independent_potassium_current__T;
00150 double var_time_independent_potassium_current__R = var_membrane__R;
00151 double var_time_independent_potassium_current_K1_gate__R = var_time_independent_potassium_current__R;
00152 double var_time_independent_potassium_current__E_K = var_rapid_activating_delayed_rectifiyer_K_current__E_K;
00153 double var_time_independent_potassium_current_K1_gate__E_K = var_time_independent_potassium_current__E_K;
00154 double var_time_independent_potassium_current_K1_gate__K1_infinity = 1.0 / (2.0 + exp(((1.62 * var_time_independent_potassium_current_K1_gate__F) / (var_time_independent_potassium_current_K1_gate__R * var_time_independent_potassium_current_K1_gate__T)) * (var_time_independent_potassium_current_K1_gate__V - var_time_independent_potassium_current_K1_gate__E_K)));
00155 double var_time_independent_potassium_current__K1_infinity = var_time_independent_potassium_current_K1_gate__K1_infinity;
00156 double var_time_independent_potassium_current__K_o = var_standard_ionic_concentrations__K_o;
00157 const double var_time_independent_potassium_current__K_mK1 = 13.0;
00158 double var_time_independent_potassium_current__i_K1 = ((var_time_independent_potassium_current__g_K1 * var_time_independent_potassium_current__K1_infinity * var_time_independent_potassium_current__K_o) / (var_time_independent_potassium_current__K_o + var_time_independent_potassium_current__K_mK1)) * (var_time_independent_potassium_current__V - var_time_independent_potassium_current__E_K);
00159 double var_membrane__i_K1 = var_time_independent_potassium_current__i_K1;
00160 double var_plateau_potassium_current__V = var_membrane__V;
00161 double var_plateau_potassium_current__E_K = var_rapid_activating_delayed_rectifiyer_K_current__E_K;
00162 const double var_plateau_potassium_current__g_Kp = 0.002216;
00163 double var_plateau_potassium_current_Kp_gate__V = var_plateau_potassium_current__V;
00164 double var_plateau_potassium_current_Kp_gate__Kp_V = 1.0 / (1.0 + exp((7.488 - var_plateau_potassium_current_Kp_gate__V) / 5.98));
00165 double var_plateau_potassium_current__Kp_V = var_plateau_potassium_current_Kp_gate__Kp_V;
00166 double var_plateau_potassium_current__i_Kp = var_plateau_potassium_current__g_Kp * var_plateau_potassium_current__Kp_V * (var_plateau_potassium_current__V - var_plateau_potassium_current__E_K);
00167 double var_membrane__i_Kp = var_plateau_potassium_current__i_Kp;
00168 double var_Na_Ca_exchanger__Na_o = var_standard_ionic_concentrations__Na_o;
00169 const double var_Na_Ca_exchanger__K_NaCa = 1500.0;
00170 double var_Na_Ca_exchanger__V = var_membrane__V;
00171 double var_Na_Ca_exchanger__Ca_o = var_standard_ionic_concentrations__Ca_o;
00172 const double var_Na_Ca_exchanger__eta = 0.35;
00173 double var_Na_Ca_exchanger__Na_i = var_standard_ionic_concentrations__Na_i;
00174 double var_Na_Ca_exchanger__T = var_membrane__T;
00175 double var_Na_Ca_exchanger__R = var_membrane__R;
00176 const double var_Na_Ca_exchanger__K_sat = 0.2;
00177 const double var_Na_Ca_exchanger__K_mCa = 1380.0;
00178 double var_Na_Ca_exchanger__F = var_membrane__F;
00179 const double var_Na_Ca_exchanger__K_mNa = 87.5;
00180 double var_Na_Ca_exchanger__Ca_i = var_calcium_dynamics__Ca_i;
00181 double var_Na_Ca_exchanger__i_NaCa = (var_Na_Ca_exchanger__K_NaCa / ((pow(var_Na_Ca_exchanger__K_mNa, 3.0) + pow(var_Na_Ca_exchanger__Na_o, 3.0)) * (var_Na_Ca_exchanger__K_mCa + var_Na_Ca_exchanger__Ca_o) * (1.0 + (var_Na_Ca_exchanger__K_sat * exp(((var_Na_Ca_exchanger__eta - 1.0) * var_Na_Ca_exchanger__V * var_Na_Ca_exchanger__F) / (var_Na_Ca_exchanger__R * var_Na_Ca_exchanger__T)))))) * ((exp((var_Na_Ca_exchanger__eta * var_Na_Ca_exchanger__V * var_Na_Ca_exchanger__F) / (var_Na_Ca_exchanger__R * var_Na_Ca_exchanger__T)) * pow(var_Na_Ca_exchanger__Na_i, 3.0) * var_Na_Ca_exchanger__Ca_o) - (exp(((var_Na_Ca_exchanger__eta - 1.0) * var_Na_Ca_exchanger__V * var_Na_Ca_exchanger__F) / (var_Na_Ca_exchanger__R * var_Na_Ca_exchanger__T)) * pow(var_Na_Ca_exchanger__Na_o, 3.0) * var_Na_Ca_exchanger__Ca_i));
00182 double var_membrane__i_NaCa = var_Na_Ca_exchanger__i_NaCa;
00183 double var_sodium_potassium_pump__Na_i = var_standard_ionic_concentrations__Na_i;
00184 double var_sodium_potassium_pump__K_o = var_standard_ionic_concentrations__K_o;
00185 const double var_sodium_potassium_pump__i_NaK_max = 0.693;
00186 const double var_sodium_potassium_pump__K_mNai = 10.0;
00187 double var_sodium_potassium_pump__T = var_membrane__T;
00188 double var_sodium_potassium_pump__R = var_membrane__R;
00189 double var_sodium_potassium_pump__Na_o = var_standard_ionic_concentrations__Na_o;
00190 double var_sodium_potassium_pump__sigma = (1.0 / 7.0) * (exp(var_sodium_potassium_pump__Na_o / 67.3) - 1.0);
00191 double var_sodium_potassium_pump__V = var_membrane__V;
00192 double var_sodium_potassium_pump__F = var_membrane__F;
00193 double var_sodium_potassium_pump__f_NaK = 1.0 / (1.0 + (0.1245 * exp(((-0.1) * var_sodium_potassium_pump__V * var_sodium_potassium_pump__F) / (var_sodium_potassium_pump__R * var_sodium_potassium_pump__T))) + (0.0365 * var_sodium_potassium_pump__sigma * exp(((-var_sodium_potassium_pump__V) * var_sodium_potassium_pump__F) / (var_sodium_potassium_pump__R * var_sodium_potassium_pump__T))));
00194 const double var_sodium_potassium_pump__K_mKo = 1.5;
00195 double var_sodium_potassium_pump__i_NaK = (((var_sodium_potassium_pump__i_NaK_max * var_sodium_potassium_pump__f_NaK) / (1.0 + pow(var_sodium_potassium_pump__K_mNai / var_sodium_potassium_pump__Na_i, 1.5))) * var_sodium_potassium_pump__K_o) / (var_sodium_potassium_pump__K_o + var_sodium_potassium_pump__K_mKo);
00196 double var_membrane__i_NaK = var_sodium_potassium_pump__i_NaK;
00197 const double var_sarcolemmal_calcium_pump__i_pCa_max = 0.05;
00198 double var_sarcolemmal_calcium_pump__Ca_i = var_calcium_dynamics__Ca_i;
00199 const double var_sarcolemmal_calcium_pump__K_mpCa = 0.05;
00200 double var_sarcolemmal_calcium_pump__i_p_Ca = (var_sarcolemmal_calcium_pump__i_pCa_max * var_sarcolemmal_calcium_pump__Ca_i) / (var_sarcolemmal_calcium_pump__K_mpCa + var_sarcolemmal_calcium_pump__Ca_i);
00201 double var_membrane__i_p_Ca = var_sarcolemmal_calcium_pump__i_p_Ca;
00202 const double var_calcium_background_current__g_Cab = 0.0003842;
00203 double var_calcium_background_current__R = var_membrane__R;
00204 double var_calcium_background_current__Ca_i = var_calcium_dynamics__Ca_i;
00205 double var_calcium_background_current__F = var_membrane__F;
00206 double var_calcium_background_current__Ca_o = var_standard_ionic_concentrations__Ca_o;
00207 double var_calcium_background_current__T = var_membrane__T;
00208 double var_calcium_background_current__E_Ca = ((var_calcium_background_current__R * var_calcium_background_current__T) / (2.0 * var_calcium_background_current__F)) * log(var_calcium_background_current__Ca_o / var_calcium_background_current__Ca_i);
00209 double var_calcium_background_current__V = var_membrane__V;
00210 double var_calcium_background_current__i_Ca_b = var_calcium_background_current__g_Cab * (var_calcium_background_current__V - var_calcium_background_current__E_Ca);
00211 double var_membrane__i_Ca_b = var_calcium_background_current__i_Ca_b;
00212 double var_sodium_background_current__V = var_membrane__V;
00213 const double var_sodium_background_current__g_Nab = 0.0031;
00214 double var_sodium_background_current__E_Na = var_fast_sodium_current__E_Na;
00215 double var_sodium_background_current__i_Na_b = var_sodium_background_current__g_Nab * (var_sodium_background_current__V - var_sodium_background_current__E_Na);
00216 double var_membrane__i_Na_b = var_sodium_background_current__i_Na_b;
00217
00218 return var_membrane__i_Na+var_membrane__i_Ca+var_membrane__i_CaK+var_membrane__i_Kr+var_membrane__i_Ks+var_membrane__i_to+var_membrane__i_K1+var_membrane__i_Kp+var_membrane__i_NaCa+var_membrane__i_NaK+var_membrane__i_p_Ca+var_membrane__i_Ca_b+var_membrane__i_Na_b;
00219 }
00220
00221 void BackwardEulerFoxModel2002Modified::ComputeResidual(double var_environment__time, const double rCurrentGuess[3], double rResidual[3])
00222 {
00223 std::vector<double>& rY = rGetStateVariables();
00224 double var_membrane__V = rY[0];
00225
00226
00227 double var_L_type_Ca_current_f_gate__f = rY[8];
00228
00229 double var_L_type_Ca_current_d_gate__d = rY[9];
00230
00231
00232 double var_L_type_Ca_current_f_Ca_gate__f_Ca = rCurrentGuess[0];
00233 double var_calcium_dynamics__Ca_SR = rCurrentGuess[1];
00234 double var_calcium_dynamics__Ca_i = rCurrentGuess[2];
00235
00236 const double var_membrane__R = 8.314;
00237 const double var_membrane__T = 310.0;
00238 const double var_membrane__F = 96.5;
00239 const double var_standard_ionic_concentrations__Na_i = 10.0;
00240 const double var_standard_ionic_concentrations__Na_o = 138.0;
00241 const double var_L_type_Ca_current__P_Ca = 1.26e-05;
00242 double var_L_type_Ca_current__V = var_membrane__V;
00243 const double var_standard_ionic_concentrations__Ca_o = 2000.0;
00244 double var_L_type_Ca_current__Ca_o = var_standard_ionic_concentrations__Ca_o;
00245 double var_L_type_Ca_current__T = var_membrane__T;
00246 const double var_L_type_Ca_current__C_sc = 1.0;
00247 double var_L_type_Ca_current__Ca_i = var_calcium_dynamics__Ca_i;
00248 double var_L_type_Ca_current__R = var_membrane__R;
00249 double var_L_type_Ca_current__F = var_membrane__F;
00250 double var_L_type_Ca_current__i_Ca_max = ((((var_L_type_Ca_current__P_Ca / var_L_type_Ca_current__C_sc) * 4.0 * var_L_type_Ca_current__V * pow(var_L_type_Ca_current__F, 2.0)) / (var_L_type_Ca_current__R * var_L_type_Ca_current__T)) * ((var_L_type_Ca_current__Ca_i * exp((2.0 * var_L_type_Ca_current__V * var_L_type_Ca_current__F) / (var_L_type_Ca_current__R * var_L_type_Ca_current__T))) - (0.341 * var_L_type_Ca_current__Ca_o))) / (exp((2.0 * var_L_type_Ca_current__V * var_L_type_Ca_current__F) / (var_L_type_Ca_current__R * var_L_type_Ca_current__T)) - 1.0);
00251 double var_L_type_Ca_current__d = var_L_type_Ca_current_d_gate__d;
00252 double var_L_type_Ca_current__f = var_L_type_Ca_current_f_gate__f;
00253 double var_L_type_Ca_current__f_Ca = var_L_type_Ca_current_f_Ca_gate__f_Ca;
00254 double var_L_type_Ca_current__i_Ca = var_L_type_Ca_current__i_Ca_max * var_L_type_Ca_current__f * var_L_type_Ca_current__d * var_L_type_Ca_current__f_Ca;
00255 double var_Na_Ca_exchanger__Na_o = var_standard_ionic_concentrations__Na_o;
00256 const double var_Na_Ca_exchanger__K_NaCa = 1500.0;
00257 double var_Na_Ca_exchanger__V = var_membrane__V;
00258 double var_Na_Ca_exchanger__Ca_o = var_standard_ionic_concentrations__Ca_o;
00259 const double var_Na_Ca_exchanger__eta = 0.35;
00260 double var_Na_Ca_exchanger__Na_i = var_standard_ionic_concentrations__Na_i;
00261 double var_Na_Ca_exchanger__T = var_membrane__T;
00262 double var_Na_Ca_exchanger__R = var_membrane__R;
00263 const double var_Na_Ca_exchanger__K_sat = 0.2;
00264 const double var_Na_Ca_exchanger__K_mCa = 1380.0;
00265 double var_Na_Ca_exchanger__F = var_membrane__F;
00266 const double var_Na_Ca_exchanger__K_mNa = 87.5;
00267 double var_Na_Ca_exchanger__Ca_i = var_calcium_dynamics__Ca_i;
00268 double var_Na_Ca_exchanger__i_NaCa = (var_Na_Ca_exchanger__K_NaCa / ((pow(var_Na_Ca_exchanger__K_mNa, 3.0) + pow(var_Na_Ca_exchanger__Na_o, 3.0)) * (var_Na_Ca_exchanger__K_mCa + var_Na_Ca_exchanger__Ca_o) * (1.0 + (var_Na_Ca_exchanger__K_sat * exp(((var_Na_Ca_exchanger__eta - 1.0) * var_Na_Ca_exchanger__V * var_Na_Ca_exchanger__F) / (var_Na_Ca_exchanger__R * var_Na_Ca_exchanger__T)))))) * ((exp((var_Na_Ca_exchanger__eta * var_Na_Ca_exchanger__V * var_Na_Ca_exchanger__F) / (var_Na_Ca_exchanger__R * var_Na_Ca_exchanger__T)) * pow(var_Na_Ca_exchanger__Na_i, 3.0) * var_Na_Ca_exchanger__Ca_o) - (exp(((var_Na_Ca_exchanger__eta - 1.0) * var_Na_Ca_exchanger__V * var_Na_Ca_exchanger__F) / (var_Na_Ca_exchanger__R * var_Na_Ca_exchanger__T)) * pow(var_Na_Ca_exchanger__Na_o, 3.0) * var_Na_Ca_exchanger__Ca_i));
00269 const double var_sarcolemmal_calcium_pump__i_pCa_max = 0.05;
00270 double var_sarcolemmal_calcium_pump__Ca_i = var_calcium_dynamics__Ca_i;
00271 const double var_sarcolemmal_calcium_pump__K_mpCa = 0.05;
00272 double var_sarcolemmal_calcium_pump__i_p_Ca = (var_sarcolemmal_calcium_pump__i_pCa_max * var_sarcolemmal_calcium_pump__Ca_i) / (var_sarcolemmal_calcium_pump__K_mpCa + var_sarcolemmal_calcium_pump__Ca_i);
00273 const double var_calcium_background_current__g_Cab = 0.0003842;
00274 double var_calcium_background_current__R = var_membrane__R;
00275 double var_calcium_background_current__Ca_i = var_calcium_dynamics__Ca_i;
00276 double var_calcium_background_current__F = var_membrane__F;
00277 double var_calcium_background_current__Ca_o = var_standard_ionic_concentrations__Ca_o;
00278 double var_calcium_background_current__T = var_membrane__T;
00279 double var_calcium_background_current__E_Ca = ((var_calcium_background_current__R * var_calcium_background_current__T) / (2.0 * var_calcium_background_current__F)) * log(var_calcium_background_current__Ca_o / var_calcium_background_current__Ca_i);
00280 double var_calcium_background_current__V = var_membrane__V;
00281 double var_calcium_background_current__i_Ca_b = var_calcium_background_current__g_Cab * (var_calcium_background_current__V - var_calcium_background_current__E_Ca);
00282 double var_L_type_Ca_current_f_Ca_gate__tau_f_Ca = 30.0;
00283 double var_L_type_Ca_current_f_Ca_gate__Ca_i = var_L_type_Ca_current__Ca_i;
00284 const double var_L_type_Ca_current_f_Ca_gate__K_mfCa = 0.18;
00285 double var_L_type_Ca_current_f_Ca_gate__f_Ca_infinity = 1.0 / (1.0 + pow(var_L_type_Ca_current_f_Ca_gate__Ca_i / var_L_type_Ca_current_f_Ca_gate__K_mfCa, 3.0));
00286 const double var_calcium_dynamics__K_mCMDN = 2.0;
00287 const double var_calcium_dynamics__CMDN_tot = 10.0;
00288 double var_calcium_dynamics__beta_i = 1.0 / (1.0 + ((var_calcium_dynamics__CMDN_tot * var_calcium_dynamics__K_mCMDN) / pow(var_calcium_dynamics__K_mCMDN + var_calcium_dynamics__Ca_i, 2.0)));
00289 const double var_calcium_dynamics__V_myo = 2.584e-05;
00290 double var_calcium_dynamics__F = var_membrane__F;
00291 double var_calcium_dynamics__C_sc = var_L_type_Ca_current__C_sc;
00292 const double var_calcium_dynamics__A_Cap = 0.0001534;
00293 double var_calcium_dynamics__d = var_L_type_Ca_current__d;
00294 double var_calcium_dynamics__V = var_membrane__V;
00295 const double var_calcium_dynamics__P_rel = 6.0;
00296 double var_calcium_dynamics__gamma = 1.0 / (1.0 + pow(2000.0 / var_calcium_dynamics__Ca_SR, 3.0));
00297 double var_calcium_dynamics__f = var_L_type_Ca_current__f;
00298 double var_calcium_dynamics__f_Ca = var_L_type_Ca_current__f_Ca;
00299 double var_calcium_dynamics__J_rel = (var_calcium_dynamics__P_rel * var_calcium_dynamics__f * var_calcium_dynamics__d * var_calcium_dynamics__f_Ca * ((var_calcium_dynamics__gamma * var_calcium_dynamics__Ca_SR) - var_calcium_dynamics__Ca_i)) / (1.0 + (1.65 * exp(var_calcium_dynamics__V / 20.0)));
00300 const double var_calcium_dynamics__P_leak = 1e-06;
00301 double var_calcium_dynamics__J_leak = var_calcium_dynamics__P_leak * (var_calcium_dynamics__Ca_SR - var_calcium_dynamics__Ca_i);
00302 const double var_calcium_dynamics__V_up = 0.1;
00303 const double var_calcium_dynamics__K_mup = 0.32;
00304 double var_calcium_dynamics__J_up = var_calcium_dynamics__V_up / (1.0 + pow(var_calcium_dynamics__K_mup / var_calcium_dynamics__Ca_i, 2.0));
00305 double var_calcium_dynamics__i_Ca = var_L_type_Ca_current__i_Ca;
00306 double var_calcium_dynamics__i_Ca_b = var_calcium_background_current__i_Ca_b;
00307 double var_calcium_dynamics__i_p_Ca = var_sarcolemmal_calcium_pump__i_p_Ca;
00308 double var_calcium_dynamics__i_NaCa = var_Na_Ca_exchanger__i_NaCa;
00309 const double var_calcium_dynamics__K_mCSQN = 600.0;
00310 const double var_calcium_dynamics__CSQN_tot = 10000.0;
00311 const double var_calcium_dynamics__V_SR = 2e-06;
00312 double var_calcium_dynamics__beta_SR = 1.0 / (1.0 + ((var_calcium_dynamics__CSQN_tot * var_calcium_dynamics__K_mCSQN) / pow(var_calcium_dynamics__K_mCSQN + var_calcium_dynamics__Ca_SR, 2.0)));
00313 double d_dt_L_type_Ca_current_f_Ca_gate__f_Ca = (var_L_type_Ca_current_f_Ca_gate__f_Ca_infinity - var_L_type_Ca_current_f_Ca_gate__f_Ca) / var_L_type_Ca_current_f_Ca_gate__tau_f_Ca;
00314 double d_dt_calcium_dynamics__Ca_SR = (var_calcium_dynamics__beta_SR * ((var_calcium_dynamics__J_up - var_calcium_dynamics__J_leak) - var_calcium_dynamics__J_rel) * var_calcium_dynamics__V_myo) / var_calcium_dynamics__V_SR;
00315 double d_dt_calcium_dynamics__Ca_i = var_calcium_dynamics__beta_i * (((var_calcium_dynamics__J_rel + var_calcium_dynamics__J_leak) - var_calcium_dynamics__J_up) - (((var_calcium_dynamics__A_Cap * var_calcium_dynamics__C_sc) / (2.0 * var_calcium_dynamics__F * var_calcium_dynamics__V_myo)) * ((var_calcium_dynamics__i_Ca + var_calcium_dynamics__i_Ca_b + var_calcium_dynamics__i_p_Ca) - (2.0 * var_calcium_dynamics__i_NaCa))));
00316
00317 rResidual[0] = rCurrentGuess[0] - rY[10] - mDt*d_dt_L_type_Ca_current_f_Ca_gate__f_Ca;
00318 rResidual[2] = rCurrentGuess[2] - rY[11] - mDt*d_dt_calcium_dynamics__Ca_i;
00319 rResidual[1] = rCurrentGuess[1] - rY[12] - mDt*d_dt_calcium_dynamics__Ca_SR;
00320 }
00321
00322 void BackwardEulerFoxModel2002Modified::ComputeJacobian(double var_environment__time, const double rCurrentGuess[3], double rJacobian[3][3])
00323 {
00324 std::vector<double>& rY = rGetStateVariables();
00325 double var_membrane__V = rY[0];
00326
00327 double var_L_type_Ca_current_f_gate__f = rY[8];
00328
00329 double var_L_type_Ca_current_d_gate__d = rY[9];
00330
00331
00332 double var_L_type_Ca_current_f_Ca_gate__f_Ca = rCurrentGuess[0];
00333 double var_calcium_dynamics__Ca_SR = rCurrentGuess[1];
00334 double var_calcium_dynamics__Ca_i = rCurrentGuess[2];
00335
00336 const double var_membrane__R = 8.314;
00337 const double var_membrane__T = 310.0;
00338 const double var_membrane__F = 96.5;
00339 const double var_standard_ionic_concentrations__Na_i = 10.0;
00340 const double var_standard_ionic_concentrations__Na_o = 138.0;
00341 const double var_L_type_Ca_current__P_Ca = 1.26e-05;
00342 const double var_standard_ionic_concentrations__Ca_o = 2000.0;
00343 const double var_L_type_Ca_current__C_sc = 1.0;
00344 const double var_Na_Ca_exchanger__K_NaCa = 1500.0;
00345 const double var_Na_Ca_exchanger__eta = 0.35;
00346 const double var_Na_Ca_exchanger__K_sat = 0.2;
00347 const double var_Na_Ca_exchanger__K_mCa = 1380.0;
00348 const double var_Na_Ca_exchanger__K_mNa = 87.5;
00349 const double var_sarcolemmal_calcium_pump__i_pCa_max = 0.05;
00350 const double var_sarcolemmal_calcium_pump__K_mpCa = 0.05;
00351 const double var_calcium_background_current__g_Cab = 0.0003842;
00352 const double var_L_type_Ca_current_f_Ca_gate__K_mfCa = 0.18;
00353 const double var_calcium_dynamics__K_mCMDN = 2.0;
00354 const double var_calcium_dynamics__CMDN_tot = 10.0;
00355 const double var_calcium_dynamics__V_myo = 2.584e-05;
00356 const double var_calcium_dynamics__A_Cap = 0.0001534;
00357 const double var_calcium_dynamics__P_rel = 6.0;
00358 const double var_calcium_dynamics__P_leak = 1e-06;
00359 const double var_calcium_dynamics__V_up = 0.1;
00360 const double var_calcium_dynamics__K_mup = 0.32;
00361 const double var_calcium_dynamics__K_mCSQN = 600.0;
00362 const double var_calcium_dynamics__CSQN_tot = 10000.0;
00363 const double var_calcium_dynamics__V_SR = 2e-06;
00364
00365 rJacobian[0][0] = 1.0 + ((1.0 / 30.0) * mDt);
00366 rJacobian[0][1] = 0.0;
00367 rJacobian[0][2] = ((((1.0 / 10.0) * mDt) / pow(1.0 + (pow(var_calcium_dynamics__Ca_i, 3.0) / pow(var_L_type_Ca_current_f_Ca_gate__K_mfCa, 3.0)), 2.0)) * pow(var_calcium_dynamics__Ca_i, 2.0)) / pow(var_L_type_Ca_current_f_Ca_gate__K_mfCa, 3.0);
00368 rJacobian[1][0] = (((((((mDt / (1.0 + ((var_calcium_dynamics__CSQN_tot * var_calcium_dynamics__K_mCSQN) / pow(var_calcium_dynamics__K_mCSQN + var_calcium_dynamics__Ca_SR, 2.0)))) * var_calcium_dynamics__P_rel) * var_L_type_Ca_current_f_gate__f) * var_L_type_Ca_current_d_gate__d) * (((1.0 / (1.0 + (8000000000.0 / pow(var_calcium_dynamics__Ca_SR, 3.0)))) * var_calcium_dynamics__Ca_SR) - var_calcium_dynamics__Ca_i)) / (1.0 + (1.65 * exp((1.0 / 20.0) * var_membrane__V)))) * var_calcium_dynamics__V_myo) / var_calcium_dynamics__V_SR;
00369 rJacobian[1][1] = (1.0 - ((((((((2.0 * mDt) / pow(1.0 + ((var_calcium_dynamics__CSQN_tot * var_calcium_dynamics__K_mCSQN) / pow(var_calcium_dynamics__K_mCSQN + var_calcium_dynamics__Ca_SR, 2.0)), 2.0)) * (((var_calcium_dynamics__V_up / (1.0 + (pow(var_calcium_dynamics__K_mup, 2.0) / pow(var_calcium_dynamics__Ca_i, 2.0)))) - (var_calcium_dynamics__P_leak * (var_calcium_dynamics__Ca_SR - var_calcium_dynamics__Ca_i))) - (((((var_calcium_dynamics__P_rel * var_L_type_Ca_current_f_gate__f) * var_L_type_Ca_current_d_gate__d) * var_L_type_Ca_current_f_Ca_gate__f_Ca) * (((1.0 / (1.0 + (8000000000.0 / pow(var_calcium_dynamics__Ca_SR, 3.0)))) * var_calcium_dynamics__Ca_SR) - var_calcium_dynamics__Ca_i)) / (1.0 + (1.65 * exp((1.0 / 20.0) * var_membrane__V)))))) * var_calcium_dynamics__V_myo) / var_calcium_dynamics__V_SR) * var_calcium_dynamics__CSQN_tot) * var_calcium_dynamics__K_mCSQN) / pow(var_calcium_dynamics__K_mCSQN + var_calcium_dynamics__Ca_SR, 3.0))) - ((((mDt / (1.0 + ((var_calcium_dynamics__CSQN_tot * var_calcium_dynamics__K_mCSQN) / pow(var_calcium_dynamics__K_mCSQN + var_calcium_dynamics__Ca_SR, 2.0)))) * ((-var_calcium_dynamics__P_leak) - (((((var_calcium_dynamics__P_rel * var_L_type_Ca_current_f_gate__f) * var_L_type_Ca_current_d_gate__d) * var_L_type_Ca_current_f_Ca_gate__f_Ca) * (((24000000000.0 / pow(1.0 + (8000000000.0 / pow(var_calcium_dynamics__Ca_SR, 3.0)), 2.0)) / pow(var_calcium_dynamics__Ca_SR, 3.0)) + (1.0 / (1.0 + (8000000000.0 / pow(var_calcium_dynamics__Ca_SR, 3.0)))))) / (1.0 + (1.65 * exp((1.0 / 20.0) * var_membrane__V)))))) * var_calcium_dynamics__V_myo) / var_calcium_dynamics__V_SR);
00370 rJacobian[1][2] = ((((-mDt) / (1.0 + ((var_calcium_dynamics__CSQN_tot * var_calcium_dynamics__K_mCSQN) / pow(var_calcium_dynamics__K_mCSQN + var_calcium_dynamics__Ca_SR, 2.0)))) * ((((((2.0 * var_calcium_dynamics__V_up) / pow(1.0 + (pow(var_calcium_dynamics__K_mup, 2.0) / pow(var_calcium_dynamics__Ca_i, 2.0)), 2.0)) * pow(var_calcium_dynamics__K_mup, 2.0)) / pow(var_calcium_dynamics__Ca_i, 3.0)) + var_calcium_dynamics__P_leak) + ((((var_calcium_dynamics__P_rel * var_L_type_Ca_current_f_gate__f) * var_L_type_Ca_current_d_gate__d) * var_L_type_Ca_current_f_Ca_gate__f_Ca) / (1.0 + (1.65 * exp((1.0 / 20.0) * var_membrane__V)))))) * var_calcium_dynamics__V_myo) / var_calcium_dynamics__V_SR;
00371 rJacobian[2][0] = ((-mDt) / (1.0 + ((var_calcium_dynamics__CMDN_tot * var_calcium_dynamics__K_mCMDN) / pow(var_calcium_dynamics__K_mCMDN + var_calcium_dynamics__Ca_i, 2.0)))) * (((((var_calcium_dynamics__P_rel * var_L_type_Ca_current_f_gate__f) * var_L_type_Ca_current_d_gate__d) * (((1.0 / (1.0 + (8000000000.0 / pow(var_calcium_dynamics__Ca_SR, 3.0)))) * var_calcium_dynamics__Ca_SR) - var_calcium_dynamics__Ca_i)) / (1.0 + (1.65 * exp((1.0 / 20.0) * var_membrane__V)))) - (((((((((((2.0 * var_calcium_dynamics__A_Cap) * var_membrane__F) / var_calcium_dynamics__V_myo) * var_L_type_Ca_current__P_Ca) * var_membrane__V) / var_membrane__R) / var_membrane__T) * ((var_calcium_dynamics__Ca_i * exp((((2.0 * var_membrane__V) * var_membrane__F) / var_membrane__R) / var_membrane__T)) - (0.341 * var_standard_ionic_concentrations__Ca_o))) / (exp((((2.0 * var_membrane__V) * var_membrane__F) / var_membrane__R) / var_membrane__T) - 1.0)) * var_L_type_Ca_current_f_gate__f) * var_L_type_Ca_current_d_gate__d));
00372 rJacobian[2][1] = ((-mDt) / (1.0 + ((var_calcium_dynamics__CMDN_tot * var_calcium_dynamics__K_mCMDN) / pow(var_calcium_dynamics__K_mCMDN + var_calcium_dynamics__Ca_i, 2.0)))) * ((((((var_calcium_dynamics__P_rel * var_L_type_Ca_current_f_gate__f) * var_L_type_Ca_current_d_gate__d) * var_L_type_Ca_current_f_Ca_gate__f_Ca) * (((24000000000.0 / pow(1.0 + (8000000000.0 / pow(var_calcium_dynamics__Ca_SR, 3.0)), 2.0)) / pow(var_calcium_dynamics__Ca_SR, 3.0)) + (1.0 / (1.0 + (8000000000.0 / pow(var_calcium_dynamics__Ca_SR, 3.0)))))) / (1.0 + (1.65 * exp((1.0 / 20.0) * var_membrane__V)))) + var_calcium_dynamics__P_leak);
00373 rJacobian[2][2] = (1.0 - ((((((2.0 * mDt) / pow(1.0 + ((var_calcium_dynamics__CMDN_tot * var_calcium_dynamics__K_mCMDN) / pow(var_calcium_dynamics__K_mCMDN + var_calcium_dynamics__Ca_i, 2.0)), 2.0)) * ((((((((var_calcium_dynamics__P_rel * var_L_type_Ca_current_f_gate__f) * var_L_type_Ca_current_d_gate__d) * var_L_type_Ca_current_f_Ca_gate__f_Ca) * (((1.0 / (1.0 + (8000000000.0 / pow(var_calcium_dynamics__Ca_SR, 3.0)))) * var_calcium_dynamics__Ca_SR) - var_calcium_dynamics__Ca_i)) / (1.0 + (1.65 * exp((1.0 / 20.0) * var_membrane__V)))) + (var_calcium_dynamics__P_leak * (var_calcium_dynamics__Ca_SR - var_calcium_dynamics__Ca_i))) - (var_calcium_dynamics__V_up / (1.0 + (pow(var_calcium_dynamics__K_mup, 2.0) / pow(var_calcium_dynamics__Ca_i, 2.0))))) - ((((((1.0 / 2.0) * var_calcium_dynamics__A_Cap) * var_L_type_Ca_current__C_sc) / var_membrane__F) / var_calcium_dynamics__V_myo) * ((((((((((((((4.0 * var_L_type_Ca_current__P_Ca) / var_L_type_Ca_current__C_sc) * var_membrane__V) * pow(var_membrane__F, 2.0)) / var_membrane__R) / var_membrane__T) * ((var_calcium_dynamics__Ca_i * exp((((2.0 * var_membrane__V) * var_membrane__F) / var_membrane__R) / var_membrane__T)) - (0.341 * var_standard_ionic_concentrations__Ca_o))) / (exp((((2.0 * var_membrane__V) * var_membrane__F) / var_membrane__R) / var_membrane__T) - 1.0)) * var_L_type_Ca_current_f_gate__f) * var_L_type_Ca_current_d_gate__d) * var_L_type_Ca_current_f_Ca_gate__f_Ca) + (var_calcium_background_current__g_Cab * (var_membrane__V - (((((1.0 / 2.0) * var_membrane__R) * var_membrane__T) / var_membrane__F) * log(var_standard_ionic_concentrations__Ca_o / var_calcium_dynamics__Ca_i))))) + ((var_sarcolemmal_calcium_pump__i_pCa_max * var_calcium_dynamics__Ca_i) / (var_sarcolemmal_calcium_pump__K_mpCa + var_calcium_dynamics__Ca_i))) - (((((2.0 * var_Na_Ca_exchanger__K_NaCa) / (pow(var_Na_Ca_exchanger__K_mNa, 3.0) + pow(var_standard_ionic_concentrations__Na_o, 3.0))) / (var_Na_Ca_exchanger__K_mCa + var_standard_ionic_concentrations__Ca_o)) / (1.0 + (var_Na_Ca_exchanger__K_sat * exp(((((var_Na_Ca_exchanger__eta - 1.0) * var_membrane__V) * var_membrane__F) / var_membrane__R) / var_membrane__T)))) * (((exp((((var_Na_Ca_exchanger__eta * var_membrane__V) * var_membrane__F) / var_membrane__R) / var_membrane__T) * pow(var_standard_ionic_concentrations__Na_i, 3.0)) * var_standard_ionic_concentrations__Ca_o) - ((exp(((((var_Na_Ca_exchanger__eta - 1.0) * var_membrane__V) * var_membrane__F) / var_membrane__R) / var_membrane__T) * pow(var_standard_ionic_concentrations__Na_o, 3.0)) * var_calcium_dynamics__Ca_i))))))) * var_calcium_dynamics__CMDN_tot) * var_calcium_dynamics__K_mCMDN) / pow(var_calcium_dynamics__K_mCMDN + var_calcium_dynamics__Ca_i, 3.0))) - ((mDt / (1.0 + ((var_calcium_dynamics__CMDN_tot * var_calcium_dynamics__K_mCMDN) / pow(var_calcium_dynamics__K_mCMDN + var_calcium_dynamics__Ca_i, 2.0)))) * ((((((((-var_calcium_dynamics__P_rel) * var_L_type_Ca_current_f_gate__f) * var_L_type_Ca_current_d_gate__d) * var_L_type_Ca_current_f_Ca_gate__f_Ca) / (1.0 + (1.65 * exp((1.0 / 20.0) * var_membrane__V)))) - var_calcium_dynamics__P_leak) - ((((2.0 * var_calcium_dynamics__V_up) / pow(1.0 + (pow(var_calcium_dynamics__K_mup, 2.0) / pow(var_calcium_dynamics__Ca_i, 2.0)), 2.0)) * pow(var_calcium_dynamics__K_mup, 2.0)) / pow(var_calcium_dynamics__Ca_i, 3.0))) - ((((((1.0 / 2.0) * var_calcium_dynamics__A_Cap) * var_L_type_Ca_current__C_sc) / var_membrane__F) / var_calcium_dynamics__V_myo) * (((((((((((((((4.0 * var_L_type_Ca_current__P_Ca) / var_L_type_Ca_current__C_sc) * var_membrane__V) * pow(var_membrane__F, 2.0)) / var_membrane__R) / var_membrane__T) * exp((((2.0 * var_membrane__V) * var_membrane__F) / var_membrane__R) / var_membrane__T)) / (exp((((2.0 * var_membrane__V) * var_membrane__F) / var_membrane__R) / var_membrane__T) - 1.0)) * var_L_type_Ca_current_f_gate__f) * var_L_type_Ca_current_d_gate__d) * var_L_type_Ca_current_f_Ca_gate__f_Ca) + ((((((1.0 / 2.0) * var_calcium_background_current__g_Cab) * var_membrane__R) * var_membrane__T) / var_membrane__F) / var_calcium_dynamics__Ca_i)) + (var_sarcolemmal_calcium_pump__i_pCa_max / (var_sarcolemmal_calcium_pump__K_mpCa + var_calcium_dynamics__Ca_i))) - ((var_sarcolemmal_calcium_pump__i_pCa_max * var_calcium_dynamics__Ca_i) / pow(var_sarcolemmal_calcium_pump__K_mpCa + var_calcium_dynamics__Ca_i, 2.0))) + ((((((2.0 * var_Na_Ca_exchanger__K_NaCa) / (pow(var_Na_Ca_exchanger__K_mNa, 3.0) + pow(var_standard_ionic_concentrations__Na_o, 3.0))) / (var_Na_Ca_exchanger__K_mCa + var_standard_ionic_concentrations__Ca_o)) / (1.0 + (var_Na_Ca_exchanger__K_sat * exp(((((var_Na_Ca_exchanger__eta - 1.0) * var_membrane__V) * var_membrane__F) / var_membrane__R) / var_membrane__T)))) * exp(((((var_Na_Ca_exchanger__eta - 1.0) * var_membrane__V) * var_membrane__F) / var_membrane__R) / var_membrane__T)) * pow(var_standard_ionic_concentrations__Na_o, 3.0))))));
00374 }
00375
00376 void BackwardEulerFoxModel2002Modified::UpdateTransmembranePotential(double var_environment__time)
00377 {
00378
00379 std::vector<double>& rY = rGetStateVariables();
00380 double var_membrane__V = rY[0];
00381
00382 double var_fast_sodium_current_m_gate__m = rY[1];
00383
00384 double var_fast_sodium_current_h_gate__h = rY[2];
00385
00386 double var_fast_sodium_current_j_gate__j = rY[3];
00387
00388 double var_rapid_activating_delayed_rectifiyer_K_current_X_kr_gate__X_kr = rY[4];
00389
00390 double var_slow_activating_delayed_rectifiyer_K_current_X_ks_gate__X_ks = rY[5];
00391
00392 double var_transient_outward_potassium_current_X_to_gate__X_to = rY[6];
00393
00394 double var_transient_outward_potassium_current_Y_to_gate__Y_to = rY[7];
00395
00396 double var_L_type_Ca_current_f_gate__f = rY[8];
00397
00398 double var_L_type_Ca_current_d_gate__d = rY[9];
00399
00400 double var_L_type_Ca_current_f_Ca_gate__f_Ca = rY[10];
00401
00402 double var_calcium_dynamics__Ca_i = rY[11];
00403
00404
00405 const double var_membrane__R = 8.314;
00406 const double var_membrane__T = 310.0;
00407 const double var_membrane__F = 96.5;
00408 double var_membrane__time = var_environment__time;
00409 double var_fast_sodium_current__h = var_fast_sodium_current_h_gate__h;
00410 const double var_fast_sodium_current__g_Na = 12.8;
00411 double var_fast_sodium_current__j = var_fast_sodium_current_j_gate__j;
00412 double var_fast_sodium_current__T = var_membrane__T;
00413 double var_fast_sodium_current__R = var_membrane__R;
00414 const double var_standard_ionic_concentrations__Na_i = 10.0;
00415 double var_fast_sodium_current__Na_i = var_standard_ionic_concentrations__Na_i;
00416 const double var_standard_ionic_concentrations__Na_o = 138.0;
00417 double var_fast_sodium_current__Na_o = var_standard_ionic_concentrations__Na_o;
00418 double var_fast_sodium_current__F = var_membrane__F;
00419 double var_fast_sodium_current__E_Na = ((var_fast_sodium_current__R * var_fast_sodium_current__T) / var_fast_sodium_current__F) * log(var_fast_sodium_current__Na_o / var_fast_sodium_current__Na_i);
00420 double var_fast_sodium_current__V = var_membrane__V;
00421 double var_fast_sodium_current__m = var_fast_sodium_current_m_gate__m;
00422 double var_fast_sodium_current__i_Na = var_fast_sodium_current__g_Na * pow(var_fast_sodium_current__m, 3.0) * var_fast_sodium_current__h * var_fast_sodium_current__j * (var_fast_sodium_current__V - var_fast_sodium_current__E_Na);
00423 double var_membrane__i_Na = var_fast_sodium_current__i_Na;
00424 const double var_L_type_Ca_current__P_Ca = 1.26e-05;
00425 double var_L_type_Ca_current__V = var_membrane__V;
00426 const double var_standard_ionic_concentrations__Ca_o = 2000.0;
00427 double var_L_type_Ca_current__Ca_o = var_standard_ionic_concentrations__Ca_o;
00428 double var_L_type_Ca_current__T = var_membrane__T;
00429 const double var_L_type_Ca_current__C_sc = 1.0;
00430 double var_L_type_Ca_current__Ca_i = var_calcium_dynamics__Ca_i;
00431 double var_L_type_Ca_current__R = var_membrane__R;
00432 double var_L_type_Ca_current__F = var_membrane__F;
00433 double var_L_type_Ca_current__i_Ca_max = ((((var_L_type_Ca_current__P_Ca / var_L_type_Ca_current__C_sc) * 4.0 * var_L_type_Ca_current__V * pow(var_L_type_Ca_current__F, 2.0)) / (var_L_type_Ca_current__R * var_L_type_Ca_current__T)) * ((var_L_type_Ca_current__Ca_i * exp((2.0 * var_L_type_Ca_current__V * var_L_type_Ca_current__F) / (var_L_type_Ca_current__R * var_L_type_Ca_current__T))) - (0.341 * var_L_type_Ca_current__Ca_o))) / (exp((2.0 * var_L_type_Ca_current__V * var_L_type_Ca_current__F) / (var_L_type_Ca_current__R * var_L_type_Ca_current__T)) - 1.0);
00434 double var_L_type_Ca_current__d = var_L_type_Ca_current_d_gate__d;
00435 double var_L_type_Ca_current__f = var_L_type_Ca_current_f_gate__f;
00436 double var_L_type_Ca_current__f_Ca = var_L_type_Ca_current_f_Ca_gate__f_Ca;
00437 double var_L_type_Ca_current__i_Ca = var_L_type_Ca_current__i_Ca_max * var_L_type_Ca_current__f * var_L_type_Ca_current__d * var_L_type_Ca_current__f_Ca;
00438 double var_membrane__i_Ca = var_L_type_Ca_current__i_Ca;
00439 const double var_standard_ionic_concentrations__K_o = 4.0;
00440 double var_L_type_Ca_current__K_o = var_standard_ionic_concentrations__K_o;
00441 const double var_L_type_Ca_current__i_Ca_half = -0.265;
00442 const double var_L_type_Ca_current__P_CaK = 5.79e-07;
00443 const double var_standard_ionic_concentrations__K_i = 149.4;
00444 double var_L_type_Ca_current__K_i = var_standard_ionic_concentrations__K_i;
00445 double var_L_type_Ca_current__i_CaK = ((((((var_L_type_Ca_current__P_CaK / var_L_type_Ca_current__C_sc) * var_L_type_Ca_current__f * var_L_type_Ca_current__d * var_L_type_Ca_current__f_Ca) / (1.0 + (var_L_type_Ca_current__i_Ca_max / var_L_type_Ca_current__i_Ca_half))) * 1000.0 * var_L_type_Ca_current__V * pow(var_L_type_Ca_current__F, 2.0)) / (var_L_type_Ca_current__R * var_L_type_Ca_current__T)) * ((var_L_type_Ca_current__K_i * exp((var_L_type_Ca_current__V * var_L_type_Ca_current__F) / (var_L_type_Ca_current__R * var_L_type_Ca_current__T))) - var_L_type_Ca_current__K_o)) / (exp((var_L_type_Ca_current__V * var_L_type_Ca_current__F) / (var_L_type_Ca_current__R * var_L_type_Ca_current__T)) - 1.0);
00446 double var_membrane__i_CaK = var_L_type_Ca_current__i_CaK;
00447 double var_rapid_activating_delayed_rectifiyer_K_current__V = var_membrane__V;
00448 double var_rapid_activating_delayed_rectifiyer_K_current__R_V = 1.0 / (1.0 + (2.5 * exp(0.1 * (var_rapid_activating_delayed_rectifiyer_K_current__V + 28.0))));
00449 double var_rapid_activating_delayed_rectifiyer_K_current__X_kr = var_rapid_activating_delayed_rectifiyer_K_current_X_kr_gate__X_kr;
00450 double var_rapid_activating_delayed_rectifiyer_K_current__R = var_membrane__R;
00451 double var_rapid_activating_delayed_rectifiyer_K_current__K_o = var_standard_ionic_concentrations__K_o;
00452 double var_rapid_activating_delayed_rectifiyer_K_current__T = var_membrane__T;
00453 double var_rapid_activating_delayed_rectifiyer_K_current__K_i = var_standard_ionic_concentrations__K_i;
00454 double var_rapid_activating_delayed_rectifiyer_K_current__F = var_membrane__F;
00455 double var_rapid_activating_delayed_rectifiyer_K_current__E_K = ((var_rapid_activating_delayed_rectifiyer_K_current__R * var_rapid_activating_delayed_rectifiyer_K_current__T) / var_rapid_activating_delayed_rectifiyer_K_current__F) * log(var_rapid_activating_delayed_rectifiyer_K_current__K_o / var_rapid_activating_delayed_rectifiyer_K_current__K_i);
00456 const double var_rapid_activating_delayed_rectifiyer_K_current__g_Kr = 0.0136;
00457 double var_rapid_activating_delayed_rectifiyer_K_current__i_Kr = var_rapid_activating_delayed_rectifiyer_K_current__g_Kr * var_rapid_activating_delayed_rectifiyer_K_current__R_V * var_rapid_activating_delayed_rectifiyer_K_current__X_kr * sqrt(var_rapid_activating_delayed_rectifiyer_K_current__K_o / 4.0) * (var_rapid_activating_delayed_rectifiyer_K_current__V - var_rapid_activating_delayed_rectifiyer_K_current__E_K);
00458 double var_membrane__i_Kr = var_rapid_activating_delayed_rectifiyer_K_current__i_Kr;
00459 const double var_slow_activating_delayed_rectifiyer_K_current__g_Ks = 0.0245;
00460 double var_slow_activating_delayed_rectifiyer_K_current__V = var_membrane__V;
00461 double var_slow_activating_delayed_rectifiyer_K_current__K_i = var_standard_ionic_concentrations__K_i;
00462 double var_slow_activating_delayed_rectifiyer_K_current__F = var_membrane__F;
00463 double var_slow_activating_delayed_rectifiyer_K_current__K_o = var_standard_ionic_concentrations__K_o;
00464 double var_slow_activating_delayed_rectifiyer_K_current__T = var_membrane__T;
00465 double var_slow_activating_delayed_rectifiyer_K_current__Na_o = var_standard_ionic_concentrations__Na_o;
00466 double var_slow_activating_delayed_rectifiyer_K_current__R = var_membrane__R;
00467 double var_slow_activating_delayed_rectifiyer_K_current__Na_i = var_standard_ionic_concentrations__Na_i;
00468 double var_slow_activating_delayed_rectifiyer_K_current__E_Ks = ((var_slow_activating_delayed_rectifiyer_K_current__R * var_slow_activating_delayed_rectifiyer_K_current__T) / var_slow_activating_delayed_rectifiyer_K_current__F) * log((var_slow_activating_delayed_rectifiyer_K_current__K_o + (0.01833 * var_slow_activating_delayed_rectifiyer_K_current__Na_o)) / (var_slow_activating_delayed_rectifiyer_K_current__K_i + (0.01833 * var_slow_activating_delayed_rectifiyer_K_current__Na_i)));
00469 double var_slow_activating_delayed_rectifiyer_K_current__X_ks = var_slow_activating_delayed_rectifiyer_K_current_X_ks_gate__X_ks;
00470 double var_slow_activating_delayed_rectifiyer_K_current__i_Ks = var_slow_activating_delayed_rectifiyer_K_current__g_Ks * pow(var_slow_activating_delayed_rectifiyer_K_current__X_ks, 2.0) * (var_slow_activating_delayed_rectifiyer_K_current__V - var_slow_activating_delayed_rectifiyer_K_current__E_Ks);
00471 double var_membrane__i_Ks = var_slow_activating_delayed_rectifiyer_K_current__i_Ks;
00472 const double var_transient_outward_potassium_current__g_to = 0.23815;
00473 double var_transient_outward_potassium_current__V = var_membrane__V;
00474 double var_transient_outward_potassium_current__X_to = var_transient_outward_potassium_current_X_to_gate__X_to;
00475 double var_transient_outward_potassium_current__E_K = var_rapid_activating_delayed_rectifiyer_K_current__E_K;
00476 double var_transient_outward_potassium_current__Y_to = var_transient_outward_potassium_current_Y_to_gate__Y_to;
00477 double var_transient_outward_potassium_current__i_to = var_transient_outward_potassium_current__g_to * var_transient_outward_potassium_current__X_to * var_transient_outward_potassium_current__Y_to * (var_transient_outward_potassium_current__V - var_transient_outward_potassium_current__E_K);
00478 double var_membrane__i_to = var_transient_outward_potassium_current__i_to;
00479 const double var_time_independent_potassium_current__g_K1 = 2.8;
00480 double var_time_independent_potassium_current__F = var_membrane__F;
00481 double var_time_independent_potassium_current_K1_gate__F = var_time_independent_potassium_current__F;
00482 double var_time_independent_potassium_current__V = var_membrane__V;
00483 double var_time_independent_potassium_current_K1_gate__V = var_time_independent_potassium_current__V;
00484 double var_time_independent_potassium_current__T = var_membrane__T;
00485 double var_time_independent_potassium_current_K1_gate__T = var_time_independent_potassium_current__T;
00486 double var_time_independent_potassium_current__R = var_membrane__R;
00487 double var_time_independent_potassium_current_K1_gate__R = var_time_independent_potassium_current__R;
00488 double var_time_independent_potassium_current__E_K = var_rapid_activating_delayed_rectifiyer_K_current__E_K;
00489 double var_time_independent_potassium_current_K1_gate__E_K = var_time_independent_potassium_current__E_K;
00490 double var_time_independent_potassium_current_K1_gate__K1_infinity = 1.0 / (2.0 + exp(((1.62 * var_time_independent_potassium_current_K1_gate__F) / (var_time_independent_potassium_current_K1_gate__R * var_time_independent_potassium_current_K1_gate__T)) * (var_time_independent_potassium_current_K1_gate__V - var_time_independent_potassium_current_K1_gate__E_K)));
00491 double var_time_independent_potassium_current__K1_infinity = var_time_independent_potassium_current_K1_gate__K1_infinity;
00492 double var_time_independent_potassium_current__K_o = var_standard_ionic_concentrations__K_o;
00493 const double var_time_independent_potassium_current__K_mK1 = 13.0;
00494 double var_time_independent_potassium_current__i_K1 = ((var_time_independent_potassium_current__g_K1 * var_time_independent_potassium_current__K1_infinity * var_time_independent_potassium_current__K_o) / (var_time_independent_potassium_current__K_o + var_time_independent_potassium_current__K_mK1)) * (var_time_independent_potassium_current__V - var_time_independent_potassium_current__E_K);
00495 double var_membrane__i_K1 = var_time_independent_potassium_current__i_K1;
00496 double var_plateau_potassium_current__V = var_membrane__V;
00497 double var_plateau_potassium_current__E_K = var_rapid_activating_delayed_rectifiyer_K_current__E_K;
00498 const double var_plateau_potassium_current__g_Kp = 0.002216;
00499 double var_plateau_potassium_current_Kp_gate__V = var_plateau_potassium_current__V;
00500 double var_plateau_potassium_current_Kp_gate__Kp_V = 1.0 / (1.0 + exp((7.488 - var_plateau_potassium_current_Kp_gate__V) / 5.98));
00501 double var_plateau_potassium_current__Kp_V = var_plateau_potassium_current_Kp_gate__Kp_V;
00502 double var_plateau_potassium_current__i_Kp = var_plateau_potassium_current__g_Kp * var_plateau_potassium_current__Kp_V * (var_plateau_potassium_current__V - var_plateau_potassium_current__E_K);
00503 double var_membrane__i_Kp = var_plateau_potassium_current__i_Kp;
00504 double var_Na_Ca_exchanger__Na_o = var_standard_ionic_concentrations__Na_o;
00505 const double var_Na_Ca_exchanger__K_NaCa = 1500.0;
00506 double var_Na_Ca_exchanger__V = var_membrane__V;
00507 double var_Na_Ca_exchanger__Ca_o = var_standard_ionic_concentrations__Ca_o;
00508 const double var_Na_Ca_exchanger__eta = 0.35;
00509 double var_Na_Ca_exchanger__Na_i = var_standard_ionic_concentrations__Na_i;
00510 double var_Na_Ca_exchanger__T = var_membrane__T;
00511 double var_Na_Ca_exchanger__R = var_membrane__R;
00512 const double var_Na_Ca_exchanger__K_sat = 0.2;
00513 const double var_Na_Ca_exchanger__K_mCa = 1380.0;
00514 double var_Na_Ca_exchanger__F = var_membrane__F;
00515 const double var_Na_Ca_exchanger__K_mNa = 87.5;
00516 double var_Na_Ca_exchanger__Ca_i = var_calcium_dynamics__Ca_i;
00517 double var_Na_Ca_exchanger__i_NaCa = (var_Na_Ca_exchanger__K_NaCa / ((pow(var_Na_Ca_exchanger__K_mNa, 3.0) + pow(var_Na_Ca_exchanger__Na_o, 3.0)) * (var_Na_Ca_exchanger__K_mCa + var_Na_Ca_exchanger__Ca_o) * (1.0 + (var_Na_Ca_exchanger__K_sat * exp(((var_Na_Ca_exchanger__eta - 1.0) * var_Na_Ca_exchanger__V * var_Na_Ca_exchanger__F) / (var_Na_Ca_exchanger__R * var_Na_Ca_exchanger__T)))))) * ((exp((var_Na_Ca_exchanger__eta * var_Na_Ca_exchanger__V * var_Na_Ca_exchanger__F) / (var_Na_Ca_exchanger__R * var_Na_Ca_exchanger__T)) * pow(var_Na_Ca_exchanger__Na_i, 3.0) * var_Na_Ca_exchanger__Ca_o) - (exp(((var_Na_Ca_exchanger__eta - 1.0) * var_Na_Ca_exchanger__V * var_Na_Ca_exchanger__F) / (var_Na_Ca_exchanger__R * var_Na_Ca_exchanger__T)) * pow(var_Na_Ca_exchanger__Na_o, 3.0) * var_Na_Ca_exchanger__Ca_i));
00518 double var_membrane__i_NaCa = var_Na_Ca_exchanger__i_NaCa;
00519 double var_sodium_potassium_pump__Na_i = var_standard_ionic_concentrations__Na_i;
00520 double var_sodium_potassium_pump__K_o = var_standard_ionic_concentrations__K_o;
00521 const double var_sodium_potassium_pump__i_NaK_max = 0.693;
00522 const double var_sodium_potassium_pump__K_mNai = 10.0;
00523 double var_sodium_potassium_pump__T = var_membrane__T;
00524 double var_sodium_potassium_pump__R = var_membrane__R;
00525 double var_sodium_potassium_pump__Na_o = var_standard_ionic_concentrations__Na_o;
00526 double var_sodium_potassium_pump__sigma = (1.0 / 7.0) * (exp(var_sodium_potassium_pump__Na_o / 67.3) - 1.0);
00527 double var_sodium_potassium_pump__V = var_membrane__V;
00528 double var_sodium_potassium_pump__F = var_membrane__F;
00529 double var_sodium_potassium_pump__f_NaK = 1.0 / (1.0 + (0.1245 * exp(((-0.1) * var_sodium_potassium_pump__V * var_sodium_potassium_pump__F) / (var_sodium_potassium_pump__R * var_sodium_potassium_pump__T))) + (0.0365 * var_sodium_potassium_pump__sigma * exp(((-var_sodium_potassium_pump__V) * var_sodium_potassium_pump__F) / (var_sodium_potassium_pump__R * var_sodium_potassium_pump__T))));
00530 const double var_sodium_potassium_pump__K_mKo = 1.5;
00531 double var_sodium_potassium_pump__i_NaK = (((var_sodium_potassium_pump__i_NaK_max * var_sodium_potassium_pump__f_NaK) / (1.0 + pow(var_sodium_potassium_pump__K_mNai / var_sodium_potassium_pump__Na_i, 1.5))) * var_sodium_potassium_pump__K_o) / (var_sodium_potassium_pump__K_o + var_sodium_potassium_pump__K_mKo);
00532 double var_membrane__i_NaK = var_sodium_potassium_pump__i_NaK;
00533 const double var_sarcolemmal_calcium_pump__i_pCa_max = 0.05;
00534 double var_sarcolemmal_calcium_pump__Ca_i = var_calcium_dynamics__Ca_i;
00535 const double var_sarcolemmal_calcium_pump__K_mpCa = 0.05;
00536 double var_sarcolemmal_calcium_pump__i_p_Ca = (var_sarcolemmal_calcium_pump__i_pCa_max * var_sarcolemmal_calcium_pump__Ca_i) / (var_sarcolemmal_calcium_pump__K_mpCa + var_sarcolemmal_calcium_pump__Ca_i);
00537 double var_membrane__i_p_Ca = var_sarcolemmal_calcium_pump__i_p_Ca;
00538 const double var_calcium_background_current__g_Cab = 0.0003842;
00539 double var_calcium_background_current__R = var_membrane__R;
00540 double var_calcium_background_current__Ca_i = var_calcium_dynamics__Ca_i;
00541 double var_calcium_background_current__F = var_membrane__F;
00542 double var_calcium_background_current__Ca_o = var_standard_ionic_concentrations__Ca_o;
00543 double var_calcium_background_current__T = var_membrane__T;
00544 double var_calcium_background_current__E_Ca = ((var_calcium_background_current__R * var_calcium_background_current__T) / (2.0 * var_calcium_background_current__F)) * log(var_calcium_background_current__Ca_o / var_calcium_background_current__Ca_i);
00545 double var_calcium_background_current__V = var_membrane__V;
00546 double var_calcium_background_current__i_Ca_b = var_calcium_background_current__g_Cab * (var_calcium_background_current__V - var_calcium_background_current__E_Ca);
00547 double var_membrane__i_Ca_b = var_calcium_background_current__i_Ca_b;
00548 double var_sodium_background_current__V = var_membrane__V;
00549 const double var_sodium_background_current__g_Nab = 0.0031;
00550 double var_sodium_background_current__E_Na = var_fast_sodium_current__E_Na;
00551 double var_sodium_background_current__i_Na_b = var_sodium_background_current__g_Nab * (var_sodium_background_current__V - var_sodium_background_current__E_Na);
00552 double var_membrane__i_Na_b = var_sodium_background_current__i_Na_b;
00553 double var_membrane__i_Stim = GetStimulus(var_membrane__time);
00554 double d_dt_membrane__V = -(var_membrane__i_Na + var_membrane__i_Ca + var_membrane__i_CaK + var_membrane__i_Kr + var_membrane__i_Ks + var_membrane__i_to + var_membrane__i_K1 + var_membrane__i_Kp + var_membrane__i_NaCa + var_membrane__i_NaK + var_membrane__i_p_Ca + var_membrane__i_Na_b + var_membrane__i_Ca_b + var_membrane__i_Stim);
00555
00556 rY[0] += mDt * d_dt_membrane__V;
00557 }
00558
00559 void BackwardEulerFoxModel2002Modified::ComputeOneStepExceptVoltage(double var_environment__time)
00560 {
00561
00562 std::vector<double>& rY = rGetStateVariables();
00563 double var_membrane__V = rY[0];
00564
00565
00566 double var_fast_sodium_current__V = var_membrane__V;
00567 double var_L_type_Ca_current__V = var_membrane__V;
00568 double var_rapid_activating_delayed_rectifiyer_K_current__V = var_membrane__V;
00569 double var_slow_activating_delayed_rectifiyer_K_current__V = var_membrane__V;
00570 double var_transient_outward_potassium_current__V = var_membrane__V;
00571 double var_fast_sodium_current_m_gate__V = var_fast_sodium_current__V;
00572 double var_fast_sodium_current_m_gate__E0_m = var_fast_sodium_current_m_gate__V + 47.13;
00573 double var_fast_sodium_current_m_gate__alpha_m = (0.32 * var_fast_sodium_current_m_gate__E0_m) / (1.0 - exp((-0.1) * var_fast_sodium_current_m_gate__E0_m));
00574 double var_fast_sodium_current_m_gate__beta_m = 0.08 * exp((-var_fast_sodium_current_m_gate__V) / 11.0);
00575 double var_fast_sodium_current_h_gate__V = var_fast_sodium_current__V;
00576 double var_fast_sodium_current_h_gate__alpha_h = 0.135 * exp((var_fast_sodium_current_h_gate__V + 80.0) / (-6.8));
00577 double var_fast_sodium_current_h_gate__beta_h = 7.5 / (1.0 + exp((-0.1) * (var_fast_sodium_current_h_gate__V + 11.0)));
00578 double var_fast_sodium_current_j_gate__V = var_fast_sodium_current__V;
00579 double var_fast_sodium_current_j_gate__alpha_j = (0.175 * exp((var_fast_sodium_current_j_gate__V + 100.0) / (-23.0))) / (1.0 + exp(0.15 * (var_fast_sodium_current_j_gate__V + 79.0)));
00580 double var_fast_sodium_current_j_gate__beta_j = 0.3 / (1.0 + exp((-0.1) * (var_fast_sodium_current_j_gate__V + 32.0)));
00581 double var_rapid_activating_delayed_rectifiyer_K_current_X_kr_gate__V = var_rapid_activating_delayed_rectifiyer_K_current__V;
00582 double var_rapid_activating_delayed_rectifiyer_K_current_X_kr_gate__X_kr_inf = 1.0 / (1.0 + exp((-2.182) - (0.1819 * var_rapid_activating_delayed_rectifiyer_K_current_X_kr_gate__V)));
00583 double var_rapid_activating_delayed_rectifiyer_K_current_X_kr_gate__tau_X_kr = 43.0 + (1.0 / (exp((-5.495) + (0.1691 * var_rapid_activating_delayed_rectifiyer_K_current_X_kr_gate__V)) + exp((-7.677) - (0.0128 * var_rapid_activating_delayed_rectifiyer_K_current_X_kr_gate__V))));
00584 double var_slow_activating_delayed_rectifiyer_K_current_X_ks_gate__V = var_slow_activating_delayed_rectifiyer_K_current__V;
00585 double var_slow_activating_delayed_rectifiyer_K_current_X_ks_gate__tau_X_ks = 1.0 / (((7.19e-05 * (var_slow_activating_delayed_rectifiyer_K_current_X_ks_gate__V - 10.0)) / (1.0 - exp((-0.148) * (var_slow_activating_delayed_rectifiyer_K_current_X_ks_gate__V - 10.0)))) + ((0.000131 * (var_slow_activating_delayed_rectifiyer_K_current_X_ks_gate__V - 10.0)) / (exp(0.0687 * (var_slow_activating_delayed_rectifiyer_K_current_X_ks_gate__V - 10.0)) - 1.0)));
00586 double var_slow_activating_delayed_rectifiyer_K_current_X_ks_gate__X_ks_infinity = 1.0 / (1.0 + exp((var_slow_activating_delayed_rectifiyer_K_current_X_ks_gate__V - 16.0) / (-13.6)));
00587 double var_transient_outward_potassium_current_X_to_gate__V = var_transient_outward_potassium_current__V;
00588 double var_transient_outward_potassium_current_X_to_gate__alpha_X_to = 0.04516 * exp(0.03577 * var_transient_outward_potassium_current_X_to_gate__V);
00589 double var_transient_outward_potassium_current_X_to_gate__beta_X_to = 0.0989 * exp((-0.06237) * var_transient_outward_potassium_current_X_to_gate__V);
00590 double var_transient_outward_potassium_current_Y_to_gate__V = var_transient_outward_potassium_current__V;
00591 double var_transient_outward_potassium_current_Y_to_gate__alpha_Y_to = (0.005415 * exp((var_transient_outward_potassium_current_Y_to_gate__V + 33.5) / (-5.0))) / (1.0 + (0.051335 * exp((var_transient_outward_potassium_current_Y_to_gate__V + 33.5) / (-5.0))));
00592 double var_transient_outward_potassium_current_Y_to_gate__beta_Y_to = (0.005415 * exp((var_transient_outward_potassium_current_Y_to_gate__V + 33.5) / 5.0)) / (1.0 + (0.051335 * exp((var_transient_outward_potassium_current_Y_to_gate__V + 33.5) / 5.0)));
00593 double var_L_type_Ca_current_f_gate__V = var_L_type_Ca_current__V;
00594 double var_L_type_Ca_current_f_gate__f_infinity = 1.0 / (1.0 + exp((var_L_type_Ca_current_f_gate__V + 12.5) / 5.0));
00595 double var_L_type_Ca_current_f_gate__tau_f = 30.0 + (200.0 / (1.0 + exp((var_L_type_Ca_current_f_gate__V + 20.0) / 9.5)));
00596 double var_L_type_Ca_current_d_gate__V = var_L_type_Ca_current__V;
00597 double var_L_type_Ca_current_d_gate__d_infinity = 1.0 / (1.0 + exp((var_L_type_Ca_current_d_gate__V + 10.0) / (-6.24)));
00598 double var_L_type_Ca_current_d_gate__E0_m = var_L_type_Ca_current_d_gate__V + 40.0;
00599 double var_L_type_Ca_current_d_gate__tau_d = 1.0 / (((0.25 * exp((-0.01) * var_L_type_Ca_current_d_gate__V)) / (1.0 + exp((-0.07) * var_L_type_Ca_current_d_gate__V))) + ((0.07 * exp((-0.05) * var_L_type_Ca_current_d_gate__E0_m)) / (1.0 + exp(0.05 * var_L_type_Ca_current_d_gate__E0_m))));
00600
00601 const double _g_0 = var_L_type_Ca_current_d_gate__d_infinity / var_L_type_Ca_current_d_gate__tau_d;
00602 const double _h_0 = (-1.0) / var_L_type_Ca_current_d_gate__tau_d;
00603 const double _g_1 = var_L_type_Ca_current_f_gate__f_infinity / var_L_type_Ca_current_f_gate__tau_f;
00604 const double _h_1 = (-1.0) / var_L_type_Ca_current_f_gate__tau_f;
00605 const double _g_2 = var_fast_sodium_current_h_gate__alpha_h * 1.0;
00606 const double _h_2 = (var_fast_sodium_current_h_gate__alpha_h * (-1.0)) - (var_fast_sodium_current_h_gate__beta_h * 1.0);
00607 const double _g_3 = var_fast_sodium_current_j_gate__alpha_j * 1.0;
00608 const double _h_3 = (var_fast_sodium_current_j_gate__alpha_j * (-1.0)) - (var_fast_sodium_current_j_gate__beta_j * 1.0);
00609 const double _g_4 = var_fast_sodium_current_m_gate__alpha_m * 1.0;
00610 const double _h_4 = (var_fast_sodium_current_m_gate__alpha_m * (-1.0)) - (var_fast_sodium_current_m_gate__beta_m * 1.0);
00611 const double _g_5 = var_rapid_activating_delayed_rectifiyer_K_current_X_kr_gate__X_kr_inf / var_rapid_activating_delayed_rectifiyer_K_current_X_kr_gate__tau_X_kr;
00612 const double _h_5 = (-1.0) / var_rapid_activating_delayed_rectifiyer_K_current_X_kr_gate__tau_X_kr;
00613 const double _g_6 = var_slow_activating_delayed_rectifiyer_K_current_X_ks_gate__X_ks_infinity / var_slow_activating_delayed_rectifiyer_K_current_X_ks_gate__tau_X_ks;
00614 const double _h_6 = (-1.0) / var_slow_activating_delayed_rectifiyer_K_current_X_ks_gate__tau_X_ks;
00615 const double _g_7 = var_transient_outward_potassium_current_X_to_gate__alpha_X_to * 1.0;
00616 const double _h_7 = (var_transient_outward_potassium_current_X_to_gate__alpha_X_to * (-1.0)) - (var_transient_outward_potassium_current_X_to_gate__beta_X_to * 1.0);
00617 const double _g_8 = var_transient_outward_potassium_current_Y_to_gate__alpha_Y_to * 1.0;
00618 const double _h_8 = (var_transient_outward_potassium_current_Y_to_gate__alpha_Y_to * (-1.0)) - (var_transient_outward_potassium_current_Y_to_gate__beta_Y_to * 1.0);
00619
00620 rY[1] = (rY[1] + _g_4*mDt) / (1 - _h_4*mDt);
00621 rY[2] = (rY[2] + _g_2*mDt) / (1 - _h_2*mDt);
00622 rY[3] = (rY[3] + _g_3*mDt) / (1 - _h_3*mDt);
00623 rY[4] = (rY[4] + _g_5*mDt) / (1 - _h_5*mDt);
00624 rY[5] = (rY[5] + _g_6*mDt) / (1 - _h_6*mDt);
00625 rY[6] = (rY[6] + _g_7*mDt) / (1 - _h_7*mDt);
00626 rY[7] = (rY[7] + _g_8*mDt) / (1 - _h_8*mDt);
00627 rY[8] = (rY[8] + _g_1*mDt) / (1 - _h_1*mDt);
00628 rY[9] = (rY[9] + _g_0*mDt) / (1 - _h_0*mDt);
00629
00630 double _guess[3] = {rY[10],rY[11],rY[12]};
00631 CardiacNewtonSolver<3> *_solver = CardiacNewtonSolver<3>::Instance();
00632 _solver->Solve(*this, var_environment__time, _guess);
00633 rY[10] = _guess[0];
00634 rY[12] = _guess[1];
00635 rY[11] = _guess[2];
00636 }
00637
00638
00639 template<>
00640 void OdeSystemInformation<BackwardEulerFoxModel2002Modified>::Initialise(void)
00641 {
00642 this->mVariableNames.push_back("V");
00643 this->mVariableUnits.push_back("millivolt");
00644 this->mInitialConditions.push_back(-94.7);
00645
00646 this->mVariableNames.push_back("m");
00647 this->mVariableUnits.push_back("dimensionless");
00648 this->mInitialConditions.push_back(0.00024676);
00649
00650 this->mVariableNames.push_back("h");
00651 this->mVariableUnits.push_back("dimensionless");
00652 this->mInitialConditions.push_back(0.99869);
00653
00654 this->mVariableNames.push_back("j");
00655 this->mVariableUnits.push_back("dimensionless");
00656 this->mInitialConditions.push_back(0.99887);
00657
00658 this->mVariableNames.push_back("X_kr");
00659 this->mVariableUnits.push_back("dimensionless");
00660 this->mInitialConditions.push_back(0.229);
00661
00662 this->mVariableNames.push_back("X_ks");
00663 this->mVariableUnits.push_back("dimensionless");
00664 this->mInitialConditions.push_back(0.0001);
00665
00666 this->mVariableNames.push_back("X_to");
00667 this->mVariableUnits.push_back("dimensionless");
00668 this->mInitialConditions.push_back(0.00003742);
00669
00670 this->mVariableNames.push_back("Y_to");
00671 this->mVariableUnits.push_back("dimensionless");
00672 this->mInitialConditions.push_back(1);
00673
00674 this->mVariableNames.push_back("f");
00675 this->mVariableUnits.push_back("dimensionless");
00676 this->mInitialConditions.push_back(0.983);
00677
00678 this->mVariableNames.push_back("d");
00679 this->mVariableUnits.push_back("dimensionless");
00680 this->mInitialConditions.push_back(0.0001);
00681
00682 this->mVariableNames.push_back("f_Ca");
00683 this->mVariableUnits.push_back("dimensionless");
00684 this->mInitialConditions.push_back(0.942);
00685
00686 this->mVariableNames.push_back("CaI");
00687 this->mVariableUnits.push_back("micromolar");
00688 this->mInitialConditions.push_back(0.0472);
00689
00690 this->mVariableNames.push_back("Ca_SR");
00691 this->mVariableUnits.push_back("micromolar");
00692 this->mInitialConditions.push_back(320);
00693
00694 this->mInitialised = true;
00695 }
00696
00697
00698
00699 #include "SerializationExportWrapperForCpp.hpp"
00700 CHASTE_CLASS_EXPORT(BackwardEulerFoxModel2002Modified)
