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 =8;
end
% There are a total of 3 entries in each of the rate and state variable arrays.
% There are a total of 22 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('u in component membrane (dimensionless)');
LEGEND_CONSTANTS(:,1) = strpad('Cm in component membrane (uF_per_cm2)');
LEGEND_ALGEBRAIC(:,1) = strpad('Vm in component membrane (mV)');
LEGEND_CONSTANTS(:,2) = strpad('V_0 in component membrane (mV)');
LEGEND_CONSTANTS(:,3) = strpad('V_fi in component membrane (mV)');
LEGEND_ALGEBRAIC(:,3) = strpad('J_fi in component fast_inward_current (per_ms)');
LEGEND_ALGEBRAIC(:,5) = strpad('J_so in component slow_outward_current (per_ms)');
LEGEND_ALGEBRAIC(:,7) = strpad('J_si in component slow_inward_current (per_ms)');
LEGEND_ALGEBRAIC(:,8) = strpad('Istim in component stimulus_protocol (per_ms)');
LEGEND_ALGEBRAIC(:,2) = strpad('p in component p (dimensionless)');
LEGEND_CONSTANTS(:,4) = strpad('u_c in component p (dimensionless)');
LEGEND_ALGEBRAIC(:,4) = strpad('q in component q (dimensionless)');
LEGEND_CONSTANTS(:,5) = strpad('u_v in component q (dimensionless)');
LEGEND_CONSTANTS(:,22) = strpad('tau_d in component fast_inward_current (ms)');
LEGEND_CONSTANTS(:,6) = strpad('g_fi_max in component fast_inward_current (mS_per_cm2)');
LEGEND_STATES(:,2) = strpad('v in component fast_inward_current_v_gate (dimensionless)');
LEGEND_ALGEBRAIC(:,6) = strpad('tau_v_minus in component fast_inward_current_v_gate (ms)');
LEGEND_CONSTANTS(:,7) = strpad('tau_v1_minus in component fast_inward_current_v_gate (ms)');
LEGEND_CONSTANTS(:,8) = strpad('tau_v2_minus in component fast_inward_current_v_gate (ms)');
LEGEND_CONSTANTS(:,9) = strpad('tau_v_plus in component fast_inward_current_v_gate (ms)');
LEGEND_CONSTANTS(:,10) = strpad('tau_0 in component slow_outward_current (ms)');
LEGEND_CONSTANTS(:,11) = strpad('tau_r in component slow_outward_current (ms)');
LEGEND_CONSTANTS(:,12) = strpad('tau_si in component slow_inward_current (ms)');
LEGEND_CONSTANTS(:,13) = strpad('u_csi in component slow_inward_current (dimensionless)');
LEGEND_CONSTANTS(:,14) = strpad('k in component slow_inward_current (dimensionless)');
LEGEND_STATES(:,3) = strpad('w in component slow_inward_current_w_gate (dimensionless)');
LEGEND_CONSTANTS(:,15) = strpad('tau_w_minus in component slow_inward_current_w_gate (ms)');
LEGEND_CONSTANTS(:,16) = strpad('tau_w_plus in component slow_inward_current_w_gate (ms)');
LEGEND_CONSTANTS(:,17) = strpad('IstimStart in component stimulus_protocol (ms)');
LEGEND_CONSTANTS(:,18) = strpad('IstimEnd in component stimulus_protocol (ms)');
LEGEND_CONSTANTS(:,19) = strpad('IstimAmplitude in component stimulus_protocol (per_ms)');
LEGEND_CONSTANTS(:,20) = strpad('IstimPeriod in component stimulus_protocol (ms)');
LEGEND_CONSTANTS(:,21) = strpad('IstimPulseDuration in component stimulus_protocol (ms)');
LEGEND_RATES(:,1) = strpad('d/dt u in component membrane (dimensionless)');
LEGEND_RATES(:,2) = strpad('d/dt v in component fast_inward_current_v_gate (dimensionless)');
LEGEND_RATES(:,3) = strpad('d/dt w in component slow_inward_current_w_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) = 0;
CONSTANTS(:,1) = 1;
CONSTANTS(:,2) = -85;
CONSTANTS(:,3) = 15;
CONSTANTS(:,4) = 0.13;
CONSTANTS(:,5) = 0.04;
CONSTANTS(:,6) = 4;
STATES(:,2) = 1;
CONSTANTS(:,7) = 1250;
CONSTANTS(:,8) = 19.6;
CONSTANTS(:,9) = 3.33;
CONSTANTS(:,10) = 12.5;
CONSTANTS(:,11) = 33.33;
CONSTANTS(:,12) = 29;
CONSTANTS(:,13) = 0.85;
CONSTANTS(:,14) = 10;
STATES(:,3) = 1;
CONSTANTS(:,15) = 41;
CONSTANTS(:,16) = 870;
CONSTANTS(:,17) = 10;
CONSTANTS(:,18) = 50000;
CONSTANTS(:,19) = -0.2;
CONSTANTS(:,20) = 1000;
CONSTANTS(:,21) = 1;
CONSTANTS(:,22) = CONSTANTS(:,1)./CONSTANTS(:,6);
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) = piecewise({STATES(:,1)<CONSTANTS(:,4), 0.00000 }, 1.00000);
RATES(:,3) = ( (1.00000 - ALGEBRAIC(:,2)).*(1.00000 - STATES(:,3)))./CONSTANTS(:,15) - ( ALGEBRAIC(:,2).*STATES(:,3))./CONSTANTS(:,16);
ALGEBRAIC(:,4) = piecewise({STATES(:,1)<CONSTANTS(:,5), 0.00000 }, 1.00000);
ALGEBRAIC(:,6) = ALGEBRAIC(:,4).*CONSTANTS(:,7)+ (1.00000 - ALGEBRAIC(:,4)).*CONSTANTS(:,8);
RATES(:,2) = ( (1.00000 - ALGEBRAIC(:,2)).*(1.00000 - STATES(:,2)))./ALGEBRAIC(:,6) - ( ALGEBRAIC(:,2).*STATES(:,2))./CONSTANTS(:,9);
ALGEBRAIC(:,3) = ( - STATES(:,2).*ALGEBRAIC(:,2).*(1.00000 - STATES(:,1)).*(STATES(:,1) - CONSTANTS(:,4)))./CONSTANTS(:,22);
ALGEBRAIC(:,5) = ( STATES(:,1).*(1.00000 - ALGEBRAIC(:,2)))./CONSTANTS(:,10)+ALGEBRAIC(:,2)./CONSTANTS(:,11);
ALGEBRAIC(:,7) = ( - STATES(:,3).*(1.00000+ tanh( CONSTANTS(:,14).*(STATES(:,1) - CONSTANTS(:,13)))))./( 2.00000.*CONSTANTS(:,12));
ALGEBRAIC(:,8) = piecewise({VOI>=CONSTANTS(:,17)&VOI<=CONSTANTS(:,18)&(VOI - CONSTANTS(:,17)) - floor((VOI - CONSTANTS(:,17))./CONSTANTS(:,20)).*CONSTANTS(:,20)<=CONSTANTS(:,21), CONSTANTS(:,19) }, 0.00000);
RATES(:,1) = - (ALGEBRAIC(:,3)+ALGEBRAIC(:,5)+ALGEBRAIC(:,7)+ALGEBRAIC(:,8));
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) = piecewise({STATES(:,1)<CONSTANTS(:,4), 0.00000 }, 1.00000);
ALGEBRAIC(:,4) = piecewise({STATES(:,1)<CONSTANTS(:,5), 0.00000 }, 1.00000);
ALGEBRAIC(:,6) = ALGEBRAIC(:,4).*CONSTANTS(:,7)+ (1.00000 - ALGEBRAIC(:,4)).*CONSTANTS(:,8);
ALGEBRAIC(:,3) = ( - STATES(:,2).*ALGEBRAIC(:,2).*(1.00000 - STATES(:,1)).*(STATES(:,1) - CONSTANTS(:,4)))./CONSTANTS(:,22);
ALGEBRAIC(:,5) = ( STATES(:,1).*(1.00000 - ALGEBRAIC(:,2)))./CONSTANTS(:,10)+ALGEBRAIC(:,2)./CONSTANTS(:,11);
ALGEBRAIC(:,7) = ( - STATES(:,3).*(1.00000+ tanh( CONSTANTS(:,14).*(STATES(:,1) - CONSTANTS(:,13)))))./( 2.00000.*CONSTANTS(:,12));
ALGEBRAIC(:,8) = piecewise({VOI>=CONSTANTS(:,17)&VOI<=CONSTANTS(:,18)&(VOI - CONSTANTS(:,17)) - floor((VOI - CONSTANTS(:,17))./CONSTANTS(:,20)).*CONSTANTS(:,20)<=CONSTANTS(:,21), CONSTANTS(:,19) }, 0.00000);
ALGEBRAIC(:,1) = CONSTANTS(:,2)+ STATES(:,1).*(CONSTANTS(:,3) - CONSTANTS(:,2));
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