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 =16;
end
% There are a total of 4 entries in each of the rate and state variable arrays.
% There are a total of 32 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_CONSTANTS(:,1) = strpad('epi in component environment (dimensionless)');
LEGEND_CONSTANTS(:,2) = strpad('endo in component environment (dimensionless)');
LEGEND_CONSTANTS(:,3) = strpad('mcell in component environment (dimensionless)');
LEGEND_STATES(:,1) = strpad('u in component membrane (dimensionless)');
LEGEND_ALGEBRAIC(:,1) = strpad('Vm in component membrane (mV)');
LEGEND_CONSTANTS(:,4) = strpad('V_0 in component membrane (mV)');
LEGEND_CONSTANTS(:,5) = strpad('V_fi in component membrane (mV)');
LEGEND_ALGEBRAIC(:,9) = strpad('J_fi in component fast_inward_current (per_ms)');
LEGEND_ALGEBRAIC(:,15) = strpad('J_so in component slow_outward_current (per_ms)');
LEGEND_ALGEBRAIC(:,16) = strpad('J_si in component slow_inward_current (per_ms)');
LEGEND_ALGEBRAIC(:,2) = strpad('J_stim in component membrane (per_ms)');
LEGEND_ALGEBRAIC(:,3) = strpad('m in component m (dimensionless)');
LEGEND_CONSTANTS(:,6) = strpad('u_m in component m (dimensionless)');
LEGEND_ALGEBRAIC(:,5) = strpad('p in component p (dimensionless)');
LEGEND_CONSTANTS(:,7) = strpad('u_p in component p (dimensionless)');
LEGEND_ALGEBRAIC(:,4) = strpad('q in component q (dimensionless)');
LEGEND_CONSTANTS(:,14) = strpad('u_q in component q (dimensionless)');
LEGEND_ALGEBRAIC(:,6) = strpad('r in component r (dimensionless)');
LEGEND_CONSTANTS(:,16) = strpad('u_r in component r (dimensionless)');
LEGEND_CONSTANTS(:,17) = strpad('tau_fi in component fast_inward_current (ms)');
LEGEND_CONSTANTS(:,18) = strpad('u_u in component fast_inward_current (dimensionless)');
LEGEND_STATES(:,2) = strpad('v in component fast_inward_current_v_gate (dimensionless)');
LEGEND_ALGEBRAIC(:,7) = strpad('v_inf in component fast_inward_current_v_gate (dimensionless)');
LEGEND_ALGEBRAIC(:,10) = strpad('tau_v_minus in component fast_inward_current_v_gate (ms)');
LEGEND_CONSTANTS(:,31) = strpad('tau_v1_minus in component fast_inward_current_v_gate (ms)');
LEGEND_CONSTANTS(:,13) = strpad('tau_v2_minus in component fast_inward_current_v_gate (ms)');
LEGEND_CONSTANTS(:,8) = strpad('tau_v_plus in component fast_inward_current_v_gate (ms)');
LEGEND_ALGEBRAIC(:,12) = strpad('tau_o in component slow_outward_current (ms)');
LEGEND_CONSTANTS(:,15) = strpad('tau_o1 in component slow_outward_current (ms)');
LEGEND_CONSTANTS(:,32) = strpad('tau_o2 in component slow_outward_current (ms)');
LEGEND_ALGEBRAIC(:,14) = strpad('tau_so in component slow_outward_current (ms)');
LEGEND_CONSTANTS(:,19) = strpad('tau_so1 in component slow_outward_current (ms)');
LEGEND_CONSTANTS(:,20) = strpad('tau_so2 in component slow_outward_current (ms)');
LEGEND_CONSTANTS(:,21) = strpad('k_so in component slow_outward_current (dimensionless)');
LEGEND_CONSTANTS(:,22) = strpad('u_so in component slow_outward_current (dimensionless)');
LEGEND_CONSTANTS(:,23) = strpad('tau_si in component slow_inward_current (ms)');
LEGEND_STATES(:,3) = strpad('w in component slow_inward_current_w_gate (dimensionless)');
LEGEND_STATES(:,4) = strpad('s in component slow_inward_current_s_gate (dimensionless)');
LEGEND_ALGEBRAIC(:,11) = strpad('w_inf in component slow_inward_current_w_gate (dimensionless)');
LEGEND_CONSTANTS(:,24) = strpad('tau_winf in component slow_inward_current_w_gate (ms)');
LEGEND_CONSTANTS(:,25) = strpad('wstar_inf in component slow_inward_current_w_gate (dimensionless)');
LEGEND_ALGEBRAIC(:,13) = strpad('tau_w_minus in component slow_inward_current_w_gate (ms)');
LEGEND_CONSTANTS(:,26) = strpad('tau_w1_minus in component slow_inward_current_w_gate (ms)');
LEGEND_CONSTANTS(:,27) = strpad('tau_w2_minus in component slow_inward_current_w_gate (ms)');
LEGEND_CONSTANTS(:,28) = strpad('k_w_minus in component slow_inward_current_w_gate (dimensionless)');
LEGEND_CONSTANTS(:,29) = strpad('u_w_minus in component slow_inward_current_w_gate (dimensionless)');
LEGEND_CONSTANTS(:,30) = strpad('tau_w_plus in component slow_inward_current_w_gate (ms)');
LEGEND_ALGEBRAIC(:,8) = strpad('tau_s in component slow_inward_current_s_gate (ms)');
LEGEND_CONSTANTS(:,9) = strpad('tau_s1 in component slow_inward_current_s_gate (ms)');
LEGEND_CONSTANTS(:,12) = strpad('tau_s2 in component slow_inward_current_s_gate (ms)');
LEGEND_CONSTANTS(:,10) = strpad('k_s in component slow_inward_current_s_gate (dimensionless)');
LEGEND_CONSTANTS(:,11) = strpad('u_s in component slow_inward_current_s_gate (dimensionless)');
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_RATES(:,4) = strpad('d/dt s in component slow_inward_current_s_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 = [];
CONSTANTS(:,1) = 1;
CONSTANTS(:,2) = 0;
CONSTANTS(:,3) = 0;
STATES(:,1) = 0;
CONSTANTS(:,4) = -83;
CONSTANTS(:,5) = 2.7;
CONSTANTS(:,6) = 0.3;
CONSTANTS(:,7) = 0.13;
STATES(:,2) = 1;
CONSTANTS(:,8) = 1.45;
STATES(:,3) = 1;
STATES(:,4) = 0;
CONSTANTS(:,9) = 2.7342;
CONSTANTS(:,10) = 2.0994;
CONSTANTS(:,11) = 0.9087;
CONSTANTS(:,12) = piecewise({CONSTANTS(:,1)==1.00000, 16.0000 , CONSTANTS(:,2)==1.00000, 2.00000 }, 4.00000);
CONSTANTS(:,13) = piecewise({CONSTANTS(:,1)==1.00000, 1150.00 , CONSTANTS(:,2)==1.00000, 10.0000 }, 1.45000);
CONSTANTS(:,14) = piecewise({CONSTANTS(:,1)==1.00000, 0.00600000 , CONSTANTS(:,2)==1.00000, 0.0240000 }, 0.100000);
CONSTANTS(:,15) = piecewise({CONSTANTS(:,1)==1.00000, 400.000 , CONSTANTS(:,2)==1.00000, 470.000 }, 410.000);
CONSTANTS(:,16) = piecewise({CONSTANTS(:,1)==1.00000, 0.00600000 , CONSTANTS(:,2)==1.00000, 0.00600000 }, 0.00500000);
CONSTANTS(:,17) = piecewise({CONSTANTS(:,1)==1.00000, 0.110000 , CONSTANTS(:,2)==1.00000, 0.104000 }, 0.0780000);
CONSTANTS(:,18) = piecewise({CONSTANTS(:,1)==1.00000, 1.55000 , CONSTANTS(:,2)==1.00000, 1.56000 }, 1.61000);
CONSTANTS(:,19) = piecewise({CONSTANTS(:,1)==1.00000, 30.0200 , CONSTANTS(:,2)==1.00000, 40.0000 }, 91.0000);
CONSTANTS(:,20) = piecewise({CONSTANTS(:,1)==1.00000, 0.996000 , CONSTANTS(:,2)==1.00000, 1.20000 }, 0.800000);
CONSTANTS(:,21) = piecewise({CONSTANTS(:,1)==1.00000, 2.04600 , CONSTANTS(:,2)==1.00000, 2.00000 }, 2.10000);
CONSTANTS(:,22) = piecewise({CONSTANTS(:,1)==1.00000, 0.650000 , CONSTANTS(:,2)==1.00000, 0.650000 }, 0.600000);
CONSTANTS(:,23) = piecewise({CONSTANTS(:,1)==1.00000, 1.88750 , CONSTANTS(:,2)==1.00000, 2.90130 }, 3.38490);
CONSTANTS(:,24) = piecewise({CONSTANTS(:,1)==1.00000, 0.0700000 , CONSTANTS(:,2)==1.00000, 0.0273000 }, 0.0100000);
CONSTANTS(:,25) = piecewise({CONSTANTS(:,1)==1.00000, 0.940000 , CONSTANTS(:,2)==1.00000, 0.780000 }, 0.500000);
CONSTANTS(:,26) = piecewise({CONSTANTS(:,1)==1.00000, 60.0000 , CONSTANTS(:,2)==1.00000, 6.00000 }, 70.0000);
CONSTANTS(:,27) = piecewise({CONSTANTS(:,1)==1.00000, 15.0000 , CONSTANTS(:,2)==1.00000, 140.000 }, 8.00000);
CONSTANTS(:,28) = piecewise({CONSTANTS(:,1)==1.00000, 65.0000 , CONSTANTS(:,2)==1.00000, 200.000 }, 200.000);
CONSTANTS(:,29) = piecewise({CONSTANTS(:,1)==1.00000, 0.0300000 , CONSTANTS(:,2)==1.00000, 0.0160000 }, 0.0160000);
CONSTANTS(:,30) = piecewise({CONSTANTS(:,1)==1.00000, 200.000 , CONSTANTS(:,2)==1.00000, 280.000 }, 280.000);
CONSTANTS(:,31) = piecewise({CONSTANTS(:,1)==1.00000, 60.0000 , CONSTANTS(:,2)==1.00000, 75.0000 }, 80.0000);
CONSTANTS(:,32) = piecewise({CONSTANTS(:,1)==1.00000, 6.00000 , CONSTANTS(:,2)==1.00000, 6.00000 }, 7.00000);
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(:,5) = piecewise({STATES(:,1)<CONSTANTS(:,7), 0.00000 }, 1.00000);
ALGEBRAIC(:,8) = (1.00000 - ALGEBRAIC(:,5)).*CONSTANTS(:,9)+ ALGEBRAIC(:,5).*CONSTANTS(:,12);
RATES(:,4) = ((1.00000+ tanh( CONSTANTS(:,10).*(STATES(:,1) - CONSTANTS(:,11))))./2.00000 - STATES(:,4))./ALGEBRAIC(:,8);
ALGEBRAIC(:,3) = piecewise({STATES(:,1)<CONSTANTS(:,6), 0.00000 }, 1.00000);
ALGEBRAIC(:,7) = piecewise({STATES(:,1)<CONSTANTS(:,14), 1.00000 }, 0.00000);
ALGEBRAIC(:,4) = piecewise({STATES(:,1)<CONSTANTS(:,14), 0.00000 }, 1.00000);
ALGEBRAIC(:,10) = ALGEBRAIC(:,4).*CONSTANTS(:,13)+ (1.00000 - ALGEBRAIC(:,4)).*CONSTANTS(:,31);
RATES(:,2) = ( (1.00000 - ALGEBRAIC(:,3)).*(ALGEBRAIC(:,7) - STATES(:,2)))./ALGEBRAIC(:,10) - ( ALGEBRAIC(:,3).*STATES(:,2))./CONSTANTS(:,8);
ALGEBRAIC(:,6) = piecewise({STATES(:,1)<CONSTANTS(:,16), 0.00000 }, 1.00000);
ALGEBRAIC(:,11) = (1.00000 - ALGEBRAIC(:,6)).*(1.00000 - ( STATES(:,1).*1.00000)./CONSTANTS(:,24))+ ALGEBRAIC(:,6).*CONSTANTS(:,25);
ALGEBRAIC(:,13) = CONSTANTS(:,26)+( (CONSTANTS(:,27) - CONSTANTS(:,26)).*(1.00000+ tanh( CONSTANTS(:,28).*(STATES(:,1) - CONSTANTS(:,29)))))./2.00000;
RATES(:,3) = ( (1.00000 - ALGEBRAIC(:,6)).*(ALGEBRAIC(:,11) - STATES(:,3)))./ALGEBRAIC(:,13) - ( ALGEBRAIC(:,6).*STATES(:,3))./CONSTANTS(:,30);
ALGEBRAIC(:,9) = ( - ALGEBRAIC(:,3).*STATES(:,2).*(STATES(:,1) - CONSTANTS(:,6)).*(CONSTANTS(:,18) - STATES(:,1)))./CONSTANTS(:,17);
ALGEBRAIC(:,12) = (1.00000 - ALGEBRAIC(:,6)).*CONSTANTS(:,15)+ ALGEBRAIC(:,6).*CONSTANTS(:,32);
ALGEBRAIC(:,14) = CONSTANTS(:,19)+( (CONSTANTS(:,20) - CONSTANTS(:,19)).*(1.00000+ tanh( CONSTANTS(:,21).*(STATES(:,1) - CONSTANTS(:,22)))))./2.00000;
ALGEBRAIC(:,15) = ( STATES(:,1).*(1.00000 - ALGEBRAIC(:,5)))./ALGEBRAIC(:,12)+ALGEBRAIC(:,5)./ALGEBRAIC(:,14);
ALGEBRAIC(:,16) = ( - ALGEBRAIC(:,5).*STATES(:,3).*STATES(:,4))./CONSTANTS(:,23);
ALGEBRAIC(:,2) = piecewise({VOI>=100.000&VOI<=101.000, - 1.00000 }, 0.00000);
RATES(:,1) = - (ALGEBRAIC(:,9)+ALGEBRAIC(:,15)+ALGEBRAIC(:,16)+ALGEBRAIC(:,2));
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(:,5) = piecewise({STATES(:,1)<CONSTANTS(:,7), 0.00000 }, 1.00000);
ALGEBRAIC(:,8) = (1.00000 - ALGEBRAIC(:,5)).*CONSTANTS(:,9)+ ALGEBRAIC(:,5).*CONSTANTS(:,12);
ALGEBRAIC(:,3) = piecewise({STATES(:,1)<CONSTANTS(:,6), 0.00000 }, 1.00000);
ALGEBRAIC(:,7) = piecewise({STATES(:,1)<CONSTANTS(:,14), 1.00000 }, 0.00000);
ALGEBRAIC(:,4) = piecewise({STATES(:,1)<CONSTANTS(:,14), 0.00000 }, 1.00000);
ALGEBRAIC(:,10) = ALGEBRAIC(:,4).*CONSTANTS(:,13)+ (1.00000 - ALGEBRAIC(:,4)).*CONSTANTS(:,31);
ALGEBRAIC(:,6) = piecewise({STATES(:,1)<CONSTANTS(:,16), 0.00000 }, 1.00000);
ALGEBRAIC(:,11) = (1.00000 - ALGEBRAIC(:,6)).*(1.00000 - ( STATES(:,1).*1.00000)./CONSTANTS(:,24))+ ALGEBRAIC(:,6).*CONSTANTS(:,25);
ALGEBRAIC(:,13) = CONSTANTS(:,26)+( (CONSTANTS(:,27) - CONSTANTS(:,26)).*(1.00000+ tanh( CONSTANTS(:,28).*(STATES(:,1) - CONSTANTS(:,29)))))./2.00000;
ALGEBRAIC(:,9) = ( - ALGEBRAIC(:,3).*STATES(:,2).*(STATES(:,1) - CONSTANTS(:,6)).*(CONSTANTS(:,18) - STATES(:,1)))./CONSTANTS(:,17);
ALGEBRAIC(:,12) = (1.00000 - ALGEBRAIC(:,6)).*CONSTANTS(:,15)+ ALGEBRAIC(:,6).*CONSTANTS(:,32);
ALGEBRAIC(:,14) = CONSTANTS(:,19)+( (CONSTANTS(:,20) - CONSTANTS(:,19)).*(1.00000+ tanh( CONSTANTS(:,21).*(STATES(:,1) - CONSTANTS(:,22)))))./2.00000;
ALGEBRAIC(:,15) = ( STATES(:,1).*(1.00000 - ALGEBRAIC(:,5)))./ALGEBRAIC(:,12)+ALGEBRAIC(:,5)./ALGEBRAIC(:,14);
ALGEBRAIC(:,16) = ( - ALGEBRAIC(:,5).*STATES(:,3).*STATES(:,4))./CONSTANTS(:,23);
ALGEBRAIC(:,2) = piecewise({VOI>=100.000&VOI<=101.000, - 1.00000 }, 0.00000);
ALGEBRAIC(:,1) = CONSTANTS(:,4)+ STATES(:,1).*(CONSTANTS(:,5) - CONSTANTS(:,4));
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