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 =23;
end
% There are a total of 5 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 (millisecond)');
LEGEND_STATES(:,1) = strpad('V in component membrane (millivolt)');
LEGEND_CONSTANTS(:,1) = strpad('RToF in component membrane (millivolt)');
LEGEND_CONSTANTS(:,2) = strpad('K_c in component membrane (millimolar)');
LEGEND_CONSTANTS(:,3) = strpad('K_i in component membrane (millimolar)');
LEGEND_CONSTANTS(:,4) = strpad('Na_c in component membrane (millimolar)');
LEGEND_CONSTANTS(:,5) = strpad('Na_i in component membrane (millimolar)');
LEGEND_ALGEBRAIC(:,6) = strpad('i_ns in component non_specific_current (picoA_per_picoF)');
LEGEND_ALGEBRAIC(:,11) = strpad('i_to in component transient_outward_K_current (picoA_per_picoF)');
LEGEND_ALGEBRAIC(:,21) = strpad('i_K1 in component inward_rectifier (picoA_per_picoF)');
LEGEND_ALGEBRAIC(:,16) = strpad('i_Kur in component ultra_rapid_K_current (picoA_per_picoF)');
LEGEND_ALGEBRAIC(:,22) = strpad('i_b_Na in component background_currents (picoA_per_picoF)');
LEGEND_ALGEBRAIC(:,23) = strpad('i_NaK in component sodium_potassium_pump (picoA_per_picoF)');
LEGEND_ALGEBRAIC(:,1) = strpad('i_Stim in component membrane (picoA_per_picoF)');
LEGEND_CONSTANTS(:,6) = strpad('stim_start in component membrane (millisecond)');
LEGEND_CONSTANTS(:,7) = strpad('stim_end in component membrane (millisecond)');
LEGEND_CONSTANTS(:,8) = strpad('stim_period in component membrane (millisecond)');
LEGEND_CONSTANTS(:,9) = strpad('stim_duration in component membrane (millisecond)');
LEGEND_CONSTANTS(:,10) = strpad('stim_amplitude in component membrane (picoA_per_picoF)');
LEGEND_CONSTANTS(:,11) = strpad('g_ns in component non_specific_current (nanoS_per_picoF)');
LEGEND_CONSTANTS(:,21) = strpad('E_K in component transient_outward_K_current (millivolt)');
LEGEND_CONSTANTS(:,12) = strpad('g_to in component transient_outward_K_current (nanoS_per_picoF)');
LEGEND_STATES(:,2) = strpad('oa in component transient_outward_K_current_oa_gate (dimensionless)');
LEGEND_STATES(:,3) = strpad('oi in component transient_outward_K_current_oi_gate (dimensionless)');
LEGEND_ALGEBRAIC(:,2) = strpad('alpha_oa in component transient_outward_K_current_oa_gate (per_millisecond)');
LEGEND_ALGEBRAIC(:,7) = strpad('beta_oa in component transient_outward_K_current_oa_gate (per_millisecond)');
LEGEND_ALGEBRAIC(:,17) = strpad('tau_oa in component transient_outward_K_current_oa_gate (millisecond)');
LEGEND_ALGEBRAIC(:,12) = strpad('oa_inf in component transient_outward_K_current_oa_gate (dimensionless)');
LEGEND_ALGEBRAIC(:,3) = strpad('alpha_oi in component transient_outward_K_current_oi_gate (per_millisecond)');
LEGEND_ALGEBRAIC(:,8) = strpad('beta_oi in component transient_outward_K_current_oi_gate (per_millisecond)');
LEGEND_ALGEBRAIC(:,18) = strpad('tau_oi in component transient_outward_K_current_oi_gate (millisecond)');
LEGEND_ALGEBRAIC(:,13) = strpad('oi_inf in component transient_outward_K_current_oi_gate (dimensionless)');
LEGEND_CONSTANTS(:,13) = strpad('g_Kur in component ultra_rapid_K_current (nanoS_per_picoF)');
LEGEND_STATES(:,4) = strpad('ua in component ultra_rapid_K_current_ua_gate (dimensionless)');
LEGEND_STATES(:,5) = strpad('ui in component ultra_rapid_K_current_ui_gate (dimensionless)');
LEGEND_ALGEBRAIC(:,4) = strpad('alpha_ua in component ultra_rapid_K_current_ua_gate (per_millisecond)');
LEGEND_ALGEBRAIC(:,9) = strpad('beta_ua in component ultra_rapid_K_current_ua_gate (per_millisecond)');
LEGEND_ALGEBRAIC(:,19) = strpad('tau_ua in component ultra_rapid_K_current_ua_gate (millisecond)');
LEGEND_ALGEBRAIC(:,14) = strpad('ua_inf in component ultra_rapid_K_current_ua_gate (dimensionless)');
LEGEND_ALGEBRAIC(:,5) = strpad('alpha_ui in component ultra_rapid_K_current_ui_gate (per_millisecond)');
LEGEND_ALGEBRAIC(:,10) = strpad('beta_ui in component ultra_rapid_K_current_ui_gate (per_millisecond)');
LEGEND_ALGEBRAIC(:,20) = strpad('tau_ui in component ultra_rapid_K_current_ui_gate (millisecond)');
LEGEND_ALGEBRAIC(:,15) = strpad('ui_inf in component ultra_rapid_K_current_ui_gate (dimensionless)');
LEGEND_CONSTANTS(:,14) = strpad('g_K1 in component inward_rectifier (nanoS_per_picoF)');
LEGEND_CONSTANTS(:,15) = strpad('g_b_Na in component background_currents (nanoS_per_picoF)');
LEGEND_CONSTANTS(:,22) = strpad('E_Na in component background_currents (millivolt)');
LEGEND_CONSTANTS(:,16) = strpad('k_NaK_K in component sodium_potassium_pump (millimolar)');
LEGEND_CONSTANTS(:,17) = strpad('k_NaK_Na in component sodium_potassium_pump (millimolar)');
LEGEND_CONSTANTS(:,18) = strpad('i_NaK_max in component sodium_potassium_pump (picoA_per_picoF)');
LEGEND_CONSTANTS(:,19) = strpad('V_rev in component sodium_potassium_pump (millivolt)');
LEGEND_CONSTANTS(:,20) = strpad('B in component sodium_potassium_pump (millivolt)');
LEGEND_RATES(:,1) = strpad('d/dt V in component membrane (millivolt)');
LEGEND_RATES(:,2) = strpad('d/dt oa in component transient_outward_K_current_oa_gate (dimensionless)');
LEGEND_RATES(:,3) = strpad('d/dt oi in component transient_outward_K_current_oi_gate (dimensionless)');
LEGEND_RATES(:,4) = strpad('d/dt ua in component ultra_rapid_K_current_ua_gate (dimensionless)');
LEGEND_RATES(:,5) = strpad('d/dt ui in component ultra_rapid_K_current_ui_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) = -80;
CONSTANTS(:,1) = 26.54;
CONSTANTS(:,2) = 5.4;
CONSTANTS(:,3) = 139;
CONSTANTS(:,4) = 140;
CONSTANTS(:,5) = 11.2;
CONSTANTS(:,6) = 100;
CONSTANTS(:,7) = 10000;
CONSTANTS(:,8) = 5000;
CONSTANTS(:,9) = 2;
CONSTANTS(:,10) = -100;
CONSTANTS(:,11) = 0.018;
CONSTANTS(:,12) = 0.01652;
STATES(:,2) = 0.2488;
STATES(:,3) = 0.1866;
CONSTANTS(:,13) = 0.6;
STATES(:,4) = 0.9933;
STATES(:,5) = 0.0999;
CONSTANTS(:,14) = 0.03;
CONSTANTS(:,15) = 0.00607;
CONSTANTS(:,16) = 1;
CONSTANTS(:,17) = 11;
CONSTANTS(:,18) = 2.002;
CONSTANTS(:,19) = -150;
CONSTANTS(:,20) = -200;
CONSTANTS(:,21) = CONSTANTS(:,1).*log(CONSTANTS(:,2)./CONSTANTS(:,3));
CONSTANTS(:,22) = CONSTANTS(:,1).*log(CONSTANTS(:,4)./CONSTANTS(:,5));
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) = 0.650000./(exp((STATES(:,1)+10.0000)./ - 8.50000)+exp((STATES(:,1) - 30.0000)./ - 59.0000));
ALGEBRAIC(:,7) = 0.650000./(2.50000+exp((STATES(:,1)+82.0000)./17.0000));
ALGEBRAIC(:,17) = 15.0000./(ALGEBRAIC(:,2)+ALGEBRAIC(:,7));
ALGEBRAIC(:,12) = 1.00000./(1.00000+exp((STATES(:,1)+20.4700)./ - 17.5400));
RATES(:,2) = (ALGEBRAIC(:,12) - STATES(:,2))./ALGEBRAIC(:,17);
ALGEBRAIC(:,3) = 1.00000./(18.5300+exp((STATES(:,1)+113.700)./10.9500));
ALGEBRAIC(:,8) = 1.00000./(35.5600+exp((STATES(:,1)+1.26000)./ - 7.44000));
ALGEBRAIC(:,18) = 15.0000./(ALGEBRAIC(:,3)+ALGEBRAIC(:,8));
ALGEBRAIC(:,13) = 1.00000./(1.00000+exp((STATES(:,1)+43.1000)./5.30000));
RATES(:,3) = (ALGEBRAIC(:,13) - STATES(:,3))./ALGEBRAIC(:,18);
ALGEBRAIC(:,4) = 0.650000./(exp((STATES(:,1)+10.0000)./ - 8.50000)+exp((STATES(:,1) - 30.0000)./ - 59.0000));
ALGEBRAIC(:,9) = 0.650000./(2.50000+exp((STATES(:,1)+82.0000)./17.0000));
ALGEBRAIC(:,19) = 1.00000./(ALGEBRAIC(:,4)+ALGEBRAIC(:,9));
ALGEBRAIC(:,14) = 1.00000./(1.00000+exp((STATES(:,1)+33.3000)./ - 9.60000));
RATES(:,4) = (ALGEBRAIC(:,14) - STATES(:,4))./ALGEBRAIC(:,19);
ALGEBRAIC(:,5) = 1.00000./(21.0000+exp((STATES(:,1) - 185.000)./28.0000));
ALGEBRAIC(:,10) = 1.00000./exp((STATES(:,1) - 158.000)./ - 16.0000);
ALGEBRAIC(:,20) = 5.00000./(ALGEBRAIC(:,5)+ALGEBRAIC(:,10));
ALGEBRAIC(:,15) = 1.00000./(1.00000+exp((STATES(:,1) - 99.4500)./27.4800));
RATES(:,5) = (ALGEBRAIC(:,15) - STATES(:,5))./ALGEBRAIC(:,20);
ALGEBRAIC(:,6) = CONSTANTS(:,11).*STATES(:,1);
ALGEBRAIC(:,11) = CONSTANTS(:,12).*power(STATES(:,2), 3.00000).*STATES(:,3).*(STATES(:,1) - CONSTANTS(:,21));
ALGEBRAIC(:,21) = ( CONSTANTS(:,14).*(STATES(:,1)+86.7500))./(1.00000+exp((STATES(:,1)+20.0000)./20.0000));
ALGEBRAIC(:,16) = ( CONSTANTS(:,13).*0.00500000+0.0500000./(1.00000+exp( - (STATES(:,1) - 15.0000)./13.0000))).*power(STATES(:,4), 3.00000).*STATES(:,5).*(STATES(:,1) - CONSTANTS(:,21));
ALGEBRAIC(:,22) = CONSTANTS(:,15).*(STATES(:,1) - CONSTANTS(:,22));
ALGEBRAIC(:,23) = ( (( (( CONSTANTS(:,18).*CONSTANTS(:,2))./(CONSTANTS(:,2)+CONSTANTS(:,16))).*power(CONSTANTS(:,5), 1.50000))./(power(CONSTANTS(:,5), 1.50000)+power(CONSTANTS(:,17), 1.50000))).*(STATES(:,1) - CONSTANTS(:,19)))./(STATES(:,1) - CONSTANTS(:,20));
ALGEBRAIC(:,1) = piecewise({VOI>=CONSTANTS(:,6)&VOI<=CONSTANTS(:,7)&(VOI - CONSTANTS(:,6)) - floor((VOI - CONSTANTS(:,6))./CONSTANTS(:,8)).*CONSTANTS(:,8)<=CONSTANTS(:,9), CONSTANTS(:,10) }, 0.00000);
RATES(:,1) = - (ALGEBRAIC(:,6)+ALGEBRAIC(:,16)+ALGEBRAIC(:,11)+ALGEBRAIC(:,21)+ALGEBRAIC(:,22)+ALGEBRAIC(:,23)+ALGEBRAIC(:,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) = 0.650000./(exp((STATES(:,1)+10.0000)./ - 8.50000)+exp((STATES(:,1) - 30.0000)./ - 59.0000));
ALGEBRAIC(:,7) = 0.650000./(2.50000+exp((STATES(:,1)+82.0000)./17.0000));
ALGEBRAIC(:,17) = 15.0000./(ALGEBRAIC(:,2)+ALGEBRAIC(:,7));
ALGEBRAIC(:,12) = 1.00000./(1.00000+exp((STATES(:,1)+20.4700)./ - 17.5400));
ALGEBRAIC(:,3) = 1.00000./(18.5300+exp((STATES(:,1)+113.700)./10.9500));
ALGEBRAIC(:,8) = 1.00000./(35.5600+exp((STATES(:,1)+1.26000)./ - 7.44000));
ALGEBRAIC(:,18) = 15.0000./(ALGEBRAIC(:,3)+ALGEBRAIC(:,8));
ALGEBRAIC(:,13) = 1.00000./(1.00000+exp((STATES(:,1)+43.1000)./5.30000));
ALGEBRAIC(:,4) = 0.650000./(exp((STATES(:,1)+10.0000)./ - 8.50000)+exp((STATES(:,1) - 30.0000)./ - 59.0000));
ALGEBRAIC(:,9) = 0.650000./(2.50000+exp((STATES(:,1)+82.0000)./17.0000));
ALGEBRAIC(:,19) = 1.00000./(ALGEBRAIC(:,4)+ALGEBRAIC(:,9));
ALGEBRAIC(:,14) = 1.00000./(1.00000+exp((STATES(:,1)+33.3000)./ - 9.60000));
ALGEBRAIC(:,5) = 1.00000./(21.0000+exp((STATES(:,1) - 185.000)./28.0000));
ALGEBRAIC(:,10) = 1.00000./exp((STATES(:,1) - 158.000)./ - 16.0000);
ALGEBRAIC(:,20) = 5.00000./(ALGEBRAIC(:,5)+ALGEBRAIC(:,10));
ALGEBRAIC(:,15) = 1.00000./(1.00000+exp((STATES(:,1) - 99.4500)./27.4800));
ALGEBRAIC(:,6) = CONSTANTS(:,11).*STATES(:,1);
ALGEBRAIC(:,11) = CONSTANTS(:,12).*power(STATES(:,2), 3.00000).*STATES(:,3).*(STATES(:,1) - CONSTANTS(:,21));
ALGEBRAIC(:,21) = ( CONSTANTS(:,14).*(STATES(:,1)+86.7500))./(1.00000+exp((STATES(:,1)+20.0000)./20.0000));
ALGEBRAIC(:,16) = ( CONSTANTS(:,13).*0.00500000+0.0500000./(1.00000+exp( - (STATES(:,1) - 15.0000)./13.0000))).*power(STATES(:,4), 3.00000).*STATES(:,5).*(STATES(:,1) - CONSTANTS(:,21));
ALGEBRAIC(:,22) = CONSTANTS(:,15).*(STATES(:,1) - CONSTANTS(:,22));
ALGEBRAIC(:,23) = ( (( (( CONSTANTS(:,18).*CONSTANTS(:,2))./(CONSTANTS(:,2)+CONSTANTS(:,16))).*power(CONSTANTS(:,5), 1.50000))./(power(CONSTANTS(:,5), 1.50000)+power(CONSTANTS(:,17), 1.50000))).*(STATES(:,1) - CONSTANTS(:,19)))./(STATES(:,1) - CONSTANTS(:,20));
ALGEBRAIC(:,1) = piecewise({VOI>=CONSTANTS(:,6)&VOI<=CONSTANTS(:,7)&(VOI - CONSTANTS(:,6)) - floor((VOI - CONSTANTS(:,6))./CONSTANTS(:,8)).*CONSTANTS(:,8)<=CONSTANTS(:,9), CONSTANTS(:,10) }, 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