Generated Code
The following is matlab code generated by the CellML API from this CellML file. (Back to language selection)
The raw code is available.
function [VOI, STATES, ALGEBRAIC, CONSTANTS] = mainFunction()
% This is the "main function". In Matlab, things work best if you rename this function to match the filename.
[VOI, STATES, ALGEBRAIC, CONSTANTS] = solveModel();
end
function [algebraicVariableCount] = getAlgebraicVariableCount()
% Used later when setting a global variable with the number of algebraic variables.
% Note: This is not the "main method".
algebraicVariableCount =18;
end
% There are a total of 8 entries in each of the rate and state variable arrays.
% There are a total of 10 entries in the constant variable array.
%
function [VOI, STATES, ALGEBRAIC, CONSTANTS] = solveModel()
% Create ALGEBRAIC of correct size
global algebraicVariableCount; algebraicVariableCount = getAlgebraicVariableCount();
% Initialise constants and state variables
[INIT_STATES, CONSTANTS] = initConsts;
% Set timespan to solve over
tspan = [0, 10];
% Set numerical accuracy options for ODE solver
options = odeset('RelTol', 1e-06, 'AbsTol', 1e-06, 'MaxStep', 1);
% Solve model with ODE solver
[VOI, STATES] = ode15s(@(VOI, STATES)computeRates(VOI, STATES, CONSTANTS), tspan, INIT_STATES, options);
% Compute algebraic variables
[RATES, ALGEBRAIC] = computeRates(VOI, STATES, CONSTANTS);
ALGEBRAIC = computeAlgebraic(ALGEBRAIC, CONSTANTS, STATES, VOI);
% Plot state variables against variable of integration
[LEGEND_STATES, LEGEND_ALGEBRAIC, LEGEND_VOI, LEGEND_CONSTANTS] = createLegends();
figure();
plot(VOI, STATES);
xlabel(LEGEND_VOI);
l = legend(LEGEND_STATES);
set(l,'Interpreter','none');
end
function [LEGEND_STATES, LEGEND_ALGEBRAIC, LEGEND_VOI, LEGEND_CONSTANTS] = createLegends()
LEGEND_STATES = ''; LEGEND_ALGEBRAIC = ''; LEGEND_VOI = ''; LEGEND_CONSTANTS = '';
LEGEND_VOI = strpad('time in component environment (ms)');
LEGEND_STATES(:,1) = strpad('V in component membrane (mV)');
LEGEND_CONSTANTS(:,1) = strpad('C in component membrane (uF_per_mm2)');
LEGEND_ALGEBRAIC(:,1) = strpad('i_Na in component sodium_current (uA_per_mm2)');
LEGEND_ALGEBRAIC(:,15) = strpad('i_s in component slow_inward_current (uA_per_mm2)');
LEGEND_ALGEBRAIC(:,16) = strpad('i_x1 in component time_dependent_outward_current (uA_per_mm2)');
LEGEND_ALGEBRAIC(:,17) = strpad('i_K1 in component time_independent_outward_current (uA_per_mm2)');
LEGEND_ALGEBRAIC(:,18) = strpad('Istim in component stimulus_protocol (uA_per_mm2)');
LEGEND_CONSTANTS(:,2) = strpad('g_Na in component sodium_current (mS_per_mm2)');
LEGEND_CONSTANTS(:,3) = strpad('E_Na in component sodium_current (mV)');
LEGEND_CONSTANTS(:,4) = strpad('g_Nac in component sodium_current (mS_per_mm2)');
LEGEND_STATES(:,2) = strpad('m in component sodium_current_m_gate (dimensionless)');
LEGEND_STATES(:,3) = strpad('h in component sodium_current_h_gate (dimensionless)');
LEGEND_STATES(:,4) = strpad('j in component sodium_current_j_gate (dimensionless)');
LEGEND_ALGEBRAIC(:,2) = strpad('alpha_m in component sodium_current_m_gate (per_ms)');
LEGEND_ALGEBRAIC(:,9) = strpad('beta_m in component sodium_current_m_gate (per_ms)');
LEGEND_ALGEBRAIC(:,3) = strpad('alpha_h in component sodium_current_h_gate (per_ms)');
LEGEND_ALGEBRAIC(:,10) = strpad('beta_h in component sodium_current_h_gate (per_ms)');
LEGEND_ALGEBRAIC(:,4) = strpad('alpha_j in component sodium_current_j_gate (per_ms)');
LEGEND_ALGEBRAIC(:,11) = strpad('beta_j in component sodium_current_j_gate (per_ms)');
LEGEND_CONSTANTS(:,5) = strpad('g_s in component slow_inward_current (mS_per_mm2)');
LEGEND_ALGEBRAIC(:,8) = strpad('E_s in component slow_inward_current (mV)');
LEGEND_STATES(:,5) = strpad('Cai in component slow_inward_current (concentration_units)');
LEGEND_STATES(:,6) = strpad('d in component slow_inward_current_d_gate (dimensionless)');
LEGEND_STATES(:,7) = strpad('f in component slow_inward_current_f_gate (dimensionless)');
LEGEND_ALGEBRAIC(:,5) = strpad('alpha_d in component slow_inward_current_d_gate (per_ms)');
LEGEND_ALGEBRAIC(:,12) = strpad('beta_d in component slow_inward_current_d_gate (per_ms)');
LEGEND_ALGEBRAIC(:,6) = strpad('alpha_f in component slow_inward_current_f_gate (per_ms)');
LEGEND_ALGEBRAIC(:,13) = strpad('beta_f in component slow_inward_current_f_gate (per_ms)');
LEGEND_STATES(:,8) = strpad('x1 in component time_dependent_outward_current_x1_gate (dimensionless)');
LEGEND_ALGEBRAIC(:,7) = strpad('alpha_x1 in component time_dependent_outward_current_x1_gate (per_ms)');
LEGEND_ALGEBRAIC(:,14) = strpad('beta_x1 in component time_dependent_outward_current_x1_gate (per_ms)');
LEGEND_CONSTANTS(:,6) = strpad('IstimStart in component stimulus_protocol (ms)');
LEGEND_CONSTANTS(:,7) = strpad('IstimEnd in component stimulus_protocol (ms)');
LEGEND_CONSTANTS(:,8) = strpad('IstimAmplitude in component stimulus_protocol (uA_per_mm2)');
LEGEND_CONSTANTS(:,9) = strpad('IstimPeriod in component stimulus_protocol (ms)');
LEGEND_CONSTANTS(:,10) = strpad('IstimPulseDuration in component stimulus_protocol (ms)');
LEGEND_RATES(:,1) = strpad('d/dt V in component membrane (mV)');
LEGEND_RATES(:,2) = strpad('d/dt m in component sodium_current_m_gate (dimensionless)');
LEGEND_RATES(:,3) = strpad('d/dt h in component sodium_current_h_gate (dimensionless)');
LEGEND_RATES(:,4) = strpad('d/dt j in component sodium_current_j_gate (dimensionless)');
LEGEND_RATES(:,5) = strpad('d/dt Cai in component slow_inward_current (concentration_units)');
LEGEND_RATES(:,6) = strpad('d/dt d in component slow_inward_current_d_gate (dimensionless)');
LEGEND_RATES(:,7) = strpad('d/dt f in component slow_inward_current_f_gate (dimensionless)');
LEGEND_RATES(:,8) = strpad('d/dt x1 in component time_dependent_outward_current_x1_gate (dimensionless)');
LEGEND_STATES = LEGEND_STATES';
LEGEND_ALGEBRAIC = LEGEND_ALGEBRAIC';
LEGEND_RATES = LEGEND_RATES';
LEGEND_CONSTANTS = LEGEND_CONSTANTS';
end
function [STATES, CONSTANTS] = initConsts()
VOI = 0; CONSTANTS = []; STATES = []; ALGEBRAIC = [];
STATES(:,1) = -84.624;
CONSTANTS(:,1) = 0.01;
CONSTANTS(:,2) = 4e-2;
CONSTANTS(:,3) = 50;
CONSTANTS(:,4) = 3e-5;
STATES(:,2) = 0.011;
STATES(:,3) = 0.988;
STATES(:,4) = 0.975;
CONSTANTS(:,5) = 9e-4;
STATES(:,5) = 1e-4;
STATES(:,6) = 0.003;
STATES(:,7) = 0.994;
STATES(:,8) = 0.0001;
CONSTANTS(:,6) = 10;
CONSTANTS(:,7) = 50000;
CONSTANTS(:,8) = 0.5;
CONSTANTS(:,9) = 1000;
CONSTANTS(:,10) = 1;
if (isempty(STATES)), warning('Initial values for states not set');, end
end
function [RATES, ALGEBRAIC] = computeRates(VOI, STATES, CONSTANTS)
global algebraicVariableCount;
statesSize = size(STATES);
statesColumnCount = statesSize(2);
if ( statesColumnCount == 1)
STATES = STATES';
ALGEBRAIC = zeros(1, algebraicVariableCount);
utilOnes = 1;
else
statesRowCount = statesSize(1);
ALGEBRAIC = zeros(statesRowCount, algebraicVariableCount);
RATES = zeros(statesRowCount, statesColumnCount);
utilOnes = ones(statesRowCount, 1);
end
ALGEBRAIC(:,2) = ( - 1.00000.*(STATES(:,1)+47.0000))./(exp( - 0.100000.*(STATES(:,1)+47.0000)) - 1.00000);
ALGEBRAIC(:,9) = 40.0000.*exp( - 0.0560000.*(STATES(:,1)+72.0000));
RATES(:,2) = ALGEBRAIC(:,2).*(1.00000 - STATES(:,2)) - ALGEBRAIC(:,9).*STATES(:,2);
ALGEBRAIC(:,3) = 0.126000.*exp( - 0.250000.*(STATES(:,1)+77.0000));
ALGEBRAIC(:,10) = 1.70000./(exp( - 0.0820000.*(STATES(:,1)+22.5000))+1.00000);
RATES(:,3) = ALGEBRAIC(:,3).*(1.00000 - STATES(:,3)) - ALGEBRAIC(:,10).*STATES(:,3);
ALGEBRAIC(:,4) = ( 0.0550000.*exp( - 0.250000.*(STATES(:,1)+78.0000)))./(exp( - 0.200000.*(STATES(:,1)+78.0000))+1.00000);
ALGEBRAIC(:,11) = 0.300000./(exp( - 0.100000.*(STATES(:,1)+32.0000))+1.00000);
RATES(:,4) = ALGEBRAIC(:,4).*(1.00000 - STATES(:,4)) - ALGEBRAIC(:,11).*STATES(:,4);
ALGEBRAIC(:,5) = ( 0.0950000.*exp( - (STATES(:,1) - 5.00000)./100.000))./(1.00000+exp( - (STATES(:,1) - 5.00000)./13.8900));
ALGEBRAIC(:,12) = ( 0.0700000.*exp( - (STATES(:,1)+44.0000)./59.0000))./(1.00000+exp((STATES(:,1)+44.0000)./20.0000));
RATES(:,6) = ALGEBRAIC(:,5).*(1.00000 - STATES(:,6)) - ALGEBRAIC(:,12).*STATES(:,6);
ALGEBRAIC(:,6) = ( 0.0120000.*exp( - (STATES(:,1)+28.0000)./125.000))./(1.00000+exp((STATES(:,1)+28.0000)./6.67000));
ALGEBRAIC(:,13) = ( 0.00650000.*exp( - (STATES(:,1)+30.0000)./50.0000))./(1.00000+exp( - (STATES(:,1)+30.0000)./5.00000));
RATES(:,7) = ALGEBRAIC(:,6).*(1.00000 - STATES(:,7)) - ALGEBRAIC(:,13).*STATES(:,7);
ALGEBRAIC(:,7) = ( 0.000500000.*exp((STATES(:,1)+50.0000)./12.1000))./(1.00000+exp((STATES(:,1)+50.0000)./17.5000));
ALGEBRAIC(:,14) = ( 0.00130000.*exp( - (STATES(:,1)+20.0000)./16.6700))./(1.00000+exp( - (STATES(:,1)+20.0000)./25.0000));
RATES(:,8) = ALGEBRAIC(:,7).*(1.00000 - STATES(:,8)) - ALGEBRAIC(:,14).*STATES(:,8);
ALGEBRAIC(:,8) = - 82.3000 - 13.0287.*log( STATES(:,5).*0.00100000);
ALGEBRAIC(:,15) = CONSTANTS(:,5).*STATES(:,6).*STATES(:,7).*(STATES(:,1) - ALGEBRAIC(:,8));
RATES(:,5) = ( - 0.0100000.*ALGEBRAIC(:,15))./1.00000+ 0.0700000.*(0.000100000 - STATES(:,5));
ALGEBRAIC(:,1) = ( CONSTANTS(:,2).*power(STATES(:,2), 3.00000).*STATES(:,3).*STATES(:,4)+CONSTANTS(:,4)).*(STATES(:,1) - CONSTANTS(:,3));
ALGEBRAIC(:,16) = ( STATES(:,8).*0.00800000.*(exp( 0.0400000.*(STATES(:,1)+77.0000)) - 1.00000))./exp( 0.0400000.*(STATES(:,1)+35.0000));
ALGEBRAIC(:,17) = 0.00350000.*(( 4.00000.*(exp( 0.0400000.*(STATES(:,1)+85.0000)) - 1.00000))./(exp( 0.0800000.*(STATES(:,1)+53.0000))+exp( 0.0400000.*(STATES(:,1)+53.0000)))+( 0.200000.*(STATES(:,1)+23.0000))./(1.00000 - exp( - 0.0400000.*(STATES(:,1)+23.0000))));
ALGEBRAIC(:,18) = piecewise({VOI>=CONSTANTS(:,6)&VOI<=CONSTANTS(:,7)&(VOI - CONSTANTS(:,6)) - floor((VOI - CONSTANTS(:,6))./CONSTANTS(:,9)).*CONSTANTS(:,9)<=CONSTANTS(:,10), CONSTANTS(:,8) }, 0.00000);
RATES(:,1) = (ALGEBRAIC(:,18) - (ALGEBRAIC(:,1)+ALGEBRAIC(:,15)+ALGEBRAIC(:,16)+ALGEBRAIC(:,17)))./CONSTANTS(:,1);
RATES = RATES';
end
% Calculate algebraic variables
function ALGEBRAIC = computeAlgebraic(ALGEBRAIC, CONSTANTS, STATES, VOI)
statesSize = size(STATES);
statesColumnCount = statesSize(2);
if ( statesColumnCount == 1)
STATES = STATES';
utilOnes = 1;
else
statesRowCount = statesSize(1);
utilOnes = ones(statesRowCount, 1);
end
ALGEBRAIC(:,2) = ( - 1.00000.*(STATES(:,1)+47.0000))./(exp( - 0.100000.*(STATES(:,1)+47.0000)) - 1.00000);
ALGEBRAIC(:,9) = 40.0000.*exp( - 0.0560000.*(STATES(:,1)+72.0000));
ALGEBRAIC(:,3) = 0.126000.*exp( - 0.250000.*(STATES(:,1)+77.0000));
ALGEBRAIC(:,10) = 1.70000./(exp( - 0.0820000.*(STATES(:,1)+22.5000))+1.00000);
ALGEBRAIC(:,4) = ( 0.0550000.*exp( - 0.250000.*(STATES(:,1)+78.0000)))./(exp( - 0.200000.*(STATES(:,1)+78.0000))+1.00000);
ALGEBRAIC(:,11) = 0.300000./(exp( - 0.100000.*(STATES(:,1)+32.0000))+1.00000);
ALGEBRAIC(:,5) = ( 0.0950000.*exp( - (STATES(:,1) - 5.00000)./100.000))./(1.00000+exp( - (STATES(:,1) - 5.00000)./13.8900));
ALGEBRAIC(:,12) = ( 0.0700000.*exp( - (STATES(:,1)+44.0000)./59.0000))./(1.00000+exp((STATES(:,1)+44.0000)./20.0000));
ALGEBRAIC(:,6) = ( 0.0120000.*exp( - (STATES(:,1)+28.0000)./125.000))./(1.00000+exp((STATES(:,1)+28.0000)./6.67000));
ALGEBRAIC(:,13) = ( 0.00650000.*exp( - (STATES(:,1)+30.0000)./50.0000))./(1.00000+exp( - (STATES(:,1)+30.0000)./5.00000));
ALGEBRAIC(:,7) = ( 0.000500000.*exp((STATES(:,1)+50.0000)./12.1000))./(1.00000+exp((STATES(:,1)+50.0000)./17.5000));
ALGEBRAIC(:,14) = ( 0.00130000.*exp( - (STATES(:,1)+20.0000)./16.6700))./(1.00000+exp( - (STATES(:,1)+20.0000)./25.0000));
ALGEBRAIC(:,8) = - 82.3000 - 13.0287.*log( STATES(:,5).*0.00100000);
ALGEBRAIC(:,15) = CONSTANTS(:,5).*STATES(:,6).*STATES(:,7).*(STATES(:,1) - ALGEBRAIC(:,8));
ALGEBRAIC(:,1) = ( CONSTANTS(:,2).*power(STATES(:,2), 3.00000).*STATES(:,3).*STATES(:,4)+CONSTANTS(:,4)).*(STATES(:,1) - CONSTANTS(:,3));
ALGEBRAIC(:,16) = ( STATES(:,8).*0.00800000.*(exp( 0.0400000.*(STATES(:,1)+77.0000)) - 1.00000))./exp( 0.0400000.*(STATES(:,1)+35.0000));
ALGEBRAIC(:,17) = 0.00350000.*(( 4.00000.*(exp( 0.0400000.*(STATES(:,1)+85.0000)) - 1.00000))./(exp( 0.0800000.*(STATES(:,1)+53.0000))+exp( 0.0400000.*(STATES(:,1)+53.0000)))+( 0.200000.*(STATES(:,1)+23.0000))./(1.00000 - exp( - 0.0400000.*(STATES(:,1)+23.0000))));
ALGEBRAIC(:,18) = piecewise({VOI>=CONSTANTS(:,6)&VOI<=CONSTANTS(:,7)&(VOI - CONSTANTS(:,6)) - floor((VOI - CONSTANTS(:,6))./CONSTANTS(:,9)).*CONSTANTS(:,9)<=CONSTANTS(:,10), CONSTANTS(:,8) }, 0.00000);
end
% Compute result of a piecewise function
function x = piecewise(cases, default)
set = [0];
for i = 1:2:length(cases)
if (length(cases{i+1}) == 1)
x(cases{i} & ~set,:) = cases{i+1};
else
x(cases{i} & ~set,:) = cases{i+1}(cases{i} & ~set);
end
set = set | cases{i};
if(set), break, end
end
if (length(default) == 1)
x(~set,:) = default;
else
x(~set,:) = default(~set);
end
end
% Pad out or shorten strings to a set length
function strout = strpad(strin)
req_length = 160;
insize = size(strin,2);
if insize > req_length
strout = strin(1:req_length);
else
strout = [strin, blanks(req_length - insize)];
end
end