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 =9;
end
% There are a total of 1 entries in each of the rate and state variable arrays.
% There are a total of 6 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 (minute)');
LEGEND_CONSTANTS(:,1) = strpad('BFN in component non_muscle_O2_delivery (L_per_minute)');
LEGEND_CONSTANTS(:,2) = strpad('OVA in component non_muscle_O2_delivery (mL_per_L)');
LEGEND_CONSTANTS(:,3) = strpad('HM in component non_muscle_O2_delivery (dimensionless)');
LEGEND_CONSTANTS(:,4) = strpad('AOM in component non_muscle_O2_delivery (dimensionless)');
LEGEND_CONSTANTS(:,6) = strpad('O2ARTN in component NM_O2_blood_supply (mL_per_minute)');
LEGEND_ALGEBRAIC(:,5) = strpad('DOB in component delivery_of_O2_to_NM_tissues (mL_per_minute)');
LEGEND_ALGEBRAIC(:,6) = strpad('POV in component NM_venous_O2_content (mmHg)');
LEGEND_ALGEBRAIC(:,7) = strpad('OSV in component NM_venous_O2_content (dimensionless)');
LEGEND_ALGEBRAIC(:,2) = strpad('POT in component pressure_of_O2_in_NM_tissue_cells (mmHg)');
LEGEND_ALGEBRAIC(:,4) = strpad('MO2 in component O2_consumption_by_NM_tissue (mL_per_minute)');
LEGEND_CONSTANTS(:,5) = strpad('O2M in component parameter_values (mL_per_minute)');
LEGEND_ALGEBRAIC(:,3) = strpad('P1O in component O2_consumption_by_NM_tissue (mmHg)');
LEGEND_ALGEBRAIC(:,1) = strpad('QO2 in component volume_of_O2_in_NM_tissue (mL)');
LEGEND_ALGEBRAIC(:,9) = strpad('DO2N in component volume_of_O2_in_NM_tissue (mL_per_minute)');
LEGEND_ALGEBRAIC(:,8) = strpad('DO2N1 in component volume_of_O2_in_NM_tissue (mL_per_minute)');
LEGEND_STATES(:,1) = strpad('QO2T in component volume_of_O2_in_NM_tissue (mL)');
LEGEND_RATES(:,1) = strpad('d/dt QO2T in component volume_of_O2_in_NM_tissue (mL)');
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) = 2.79521;
CONSTANTS(:,2) = 204.497;
CONSTANTS(:,3) = 40.0381;
CONSTANTS(:,4) = 1.00002;
CONSTANTS(:,5) = 164;
STATES(:,1) = 72.2362;
CONSTANTS(:,6) = CONSTANTS(:,2).*CONSTANTS(:,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(:,1) = piecewise({STATES(:,1)<0.00000, 0.00000 }, STATES(:,1));
ALGEBRAIC(:,2) = ALGEBRAIC(:,1).*0.486110;
[CONSTANTS, STATES, ALGEBRAIC] = rootfind_0(VOI, CONSTANTS, STATES, ALGEBRAIC);
ALGEBRAIC(:,3) = piecewise({ALGEBRAIC(:,2)>35.0000, 35.0000 }, ALGEBRAIC(:,2));
ALGEBRAIC(:,4) = CONSTANTS(:,4).*CONSTANTS(:,5).*(1.00000 - power(35.0001 - ALGEBRAIC(:,3), 3.00000)./42875.0);
ALGEBRAIC(:,8) = ALGEBRAIC(:,5) - ALGEBRAIC(:,4);
ALGEBRAIC(:,9) = piecewise({ALGEBRAIC(:,1)<6.00000&ALGEBRAIC(:,8)<0.00000, ALGEBRAIC(:,8).*0.100000 }, ALGEBRAIC(:,8));
RATES(:,1) = ALGEBRAIC(:,9);
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(:,1) = piecewise({STATES(:,1)<0.00000, 0.00000 }, STATES(:,1));
ALGEBRAIC(:,2) = ALGEBRAIC(:,1).*0.486110;
ALGEBRAIC(:,3) = piecewise({ALGEBRAIC(:,2)>35.0000, 35.0000 }, ALGEBRAIC(:,2));
ALGEBRAIC(:,4) = CONSTANTS(:,4).*CONSTANTS(:,5).*(1.00000 - power(35.0001 - ALGEBRAIC(:,3), 3.00000)./42875.0);
ALGEBRAIC(:,8) = ALGEBRAIC(:,5) - ALGEBRAIC(:,4);
ALGEBRAIC(:,9) = piecewise({ALGEBRAIC(:,1)<6.00000&ALGEBRAIC(:,8)<0.00000, ALGEBRAIC(:,8).*0.100000 }, ALGEBRAIC(:,8));
end
% Functions required for solving differential algebraic equation
function [CONSTANTS, STATES, ALGEBRAIC] = rootfind_0(VOI, CONSTANTS_IN, STATES_IN, ALGEBRAIC_IN)
ALGEBRAIC = ALGEBRAIC_IN;
CONSTANTS = CONSTANTS_IN;
STATES = STATES_IN;
global initialGuess_0;
if (length(initialGuess_0) ~= 3), initialGuess_0 = [0.1,0.1,0.1];, end
options = optimset('Display', 'off', 'TolX', 1E-6);
if length(VOI) == 1
residualfn = @(algebraicCandidate)residualSN_0(algebraicCandidate, ALGEBRAIC, VOI, CONSTANTS, STATES);
soln = fsolve(residualfn, initialGuess_0, options);
initialGuess_0 = soln;
ALGEBRAIC(:,5) = soln(1);
ALGEBRAIC(:,6) = soln(2);
ALGEBRAIC(:,7) = soln(3);
else
SET_ALGEBRAIC(:,5) = logical(1);
SET_ALGEBRAIC(:,6) = logical(1);
SET_ALGEBRAIC(:,7) = logical(1);
for i=1:length(VOI)
residualfn = @(algebraicCandidate)residualSN_0(algebraicCandidate, ALGEBRAIC(i,:), VOI(i), CONSTANTS, STATES(i,:));
soln = fsolve(residualfn, initialGuess_0, options);
initialGuess_0 = soln;
TEMP_ALGEBRAIC(:,5) = soln(1);
TEMP_ALGEBRAIC(:,6) = soln(2);
TEMP_ALGEBRAIC(:,7) = soln(3);
ALGEBRAIC(i,SET_ALGEBRAIC) = TEMP_ALGEBRAIC(SET_ALGEBRAIC);
end
end
end
function resid = residualSN_0(algebraicCandidate, ALGEBRAIC, VOI, CONSTANTS, STATES)
ALGEBRAIC(:,5) = algebraicCandidate(1);
ALGEBRAIC(:,6) = algebraicCandidate(2);
ALGEBRAIC(:,7) = algebraicCandidate(3);
resid(1) = ALGEBRAIC(:,7) - (CONSTANTS(:,6) - ALGEBRAIC(:,5))./( CONSTANTS(:,3).*5.25000.*CONSTANTS(:,1));
resid(2) = ALGEBRAIC(:,6) - ALGEBRAIC(:,7).*57.1400;
resid(3) = ALGEBRAIC(:,5) - (ALGEBRAIC(:,6) - ALGEBRAIC(:,2)).*12.8570.*CONSTANTS(:,1);
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