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 4 entries in each of the rate and state variable arrays. % There are a total of 14 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 (second)'); LEGEND_STATES(:,1) = strpad('HCO3_int in component concentrations (mM)'); LEGEND_STATES(:,2) = strpad('HCO3_ext in component concentrations (mM)'); LEGEND_STATES(:,3) = strpad('Cl_int in component concentrations (mM)'); LEGEND_STATES(:,4) = strpad('Cl_ext in component concentrations (mM)'); LEGEND_ALGEBRAIC(:,13) = strpad('J_AE1_HCO3 in component AE1 (mM_per_s)'); LEGEND_ALGEBRAIC(:,18) = strpad('J_AE1_Cl in component AE1 (mM_per_s)'); LEGEND_ALGEBRAIC(:,14) = strpad('J_HCO3_influx in component AE1 (mM_per_s)'); LEGEND_ALGEBRAIC(:,15) = strpad('J_Cl_influx in component AE1 (mM_per_s)'); LEGEND_CONSTANTS(:,1) = strpad('K_HCO3_ext in component AE1 (mM)'); LEGEND_CONSTANTS(:,2) = strpad('K_HCO3_int in component AE1 (mM)'); LEGEND_CONSTANTS(:,3) = strpad('K_Cl_ext in component AE1 (mM)'); LEGEND_CONSTANTS(:,4) = strpad('K_Cl_int in component AE1 (mM)'); LEGEND_CONSTANTS(:,5) = strpad('P_HCO3_ext in component AE1 (per_s)'); LEGEND_CONSTANTS(:,6) = strpad('P_HCO3_int in component AE1 (per_s)'); LEGEND_CONSTANTS(:,7) = strpad('P_Cl_ext in component AE1 (per_s)'); LEGEND_CONSTANTS(:,8) = strpad('P_Cl_int in component AE1 (per_s)'); LEGEND_ALGEBRAIC(:,2) = strpad('beta_ext in component AE1 (dimensionless)'); LEGEND_ALGEBRAIC(:,9) = strpad('beta_int in component AE1 (dimensionless)'); LEGEND_ALGEBRAIC(:,10) = strpad('gamma_ext in component AE1 (dimensionless)'); LEGEND_ALGEBRAIC(:,11) = strpad('gamma_int in component AE1 (dimensionless)'); LEGEND_ALGEBRAIC(:,12) = strpad('sigma in component AE1 (per_s)'); LEGEND_CONSTANTS(:,9) = strpad('x_Tmax in component AE1 (mM)'); LEGEND_CONSTANTS(:,10) = strpad('K_I in component AE1 (mM)'); LEGEND_ALGEBRAIC(:,1) = strpad('x_T in component AE1 (mM)'); LEGEND_ALGEBRAIC(:,16) = strpad('x_ext in component AE1 (mM)'); LEGEND_ALGEBRAIC(:,17) = strpad('x_int in component AE1 (mM)'); LEGEND_ALGEBRAIC(:,3) = strpad('Jo_bm in component AE1 (mM_per_s)'); LEGEND_ALGEBRAIC(:,4) = strpad('Ji_bm in component AE1 (mM_per_s)'); LEGEND_ALGEBRAIC(:,5) = strpad('Js_bm in component AE1 (mM_per_s)'); LEGEND_ALGEBRAIC(:,6) = strpad('Jo_cm in component AE1 (mM_per_s)'); LEGEND_ALGEBRAIC(:,7) = strpad('Ji_cm in component AE1 (mM_per_s)'); LEGEND_ALGEBRAIC(:,8) = strpad('Js_cm in component AE1 (mM_per_s)'); LEGEND_RATES(:,1) = strpad('d/dt HCO3_int in component concentrations (mM)'); LEGEND_RATES(:,2) = strpad('d/dt HCO3_ext in component concentrations (mM)'); LEGEND_RATES(:,3) = strpad('d/dt Cl_int in component concentrations (mM)'); LEGEND_RATES(:,4) = strpad('d/dt Cl_ext in component concentrations (mM)'); 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) = 165.0; STATES(:,2) = 0.0; STATES(:,3) = 0.0; STATES(:,4) = 0.0; CONSTANTS(:,1) = 198; CONSTANTS(:,2) = 198; CONSTANTS(:,3) = 50; CONSTANTS(:,4) = 50; CONSTANTS(:,5) = 1247; CONSTANTS(:,6) = 135; CONSTANTS(:,7) = 562; CONSTANTS(:,8) = 61; CONSTANTS(:,9) = 1; CONSTANTS(:,10) = 172; CONSTANTS(:,10) = 0.00000; CONSTANTS(:,11) = 1.00000; CONSTANTS(:,12) = 0.00000; CONSTANTS(:,13) = 0.00000; 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 RATES(:,1) = CONSTANTS(:,10); RATES(:,2) = CONSTANTS(:,11); RATES(:,3) = CONSTANTS(:,12); RATES(:,4) = CONSTANTS(:,13); 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) = CONSTANTS(:,9)./(1.00000+STATES(:,1)./CONSTANTS(:,10)); ALGEBRAIC(:,2) = STATES(:,2)./CONSTANTS(:,1); ALGEBRAIC(:,3) = power( (1.00000./ALGEBRAIC(:,1)).*(1.00000./CONSTANTS(:,5)+1.00000./CONSTANTS(:,6)+CONSTANTS(:,2)./( CONSTANTS(:,6).*STATES(:,1))), - 1.00000); ALGEBRAIC(:,4) = power( (1.00000./ALGEBRAIC(:,1)).*(1.00000./CONSTANTS(:,5)+1.00000./CONSTANTS(:,6)+CONSTANTS(:,1)./( CONSTANTS(:,5).*STATES(:,2))), - 1.00000); ALGEBRAIC(:,5) = power( (1.00000./ALGEBRAIC(:,1)).*(1.00000./CONSTANTS(:,5)+1.00000./CONSTANTS(:,6)), - 1.00000); ALGEBRAIC(:,6) = power( (1.00000./ALGEBRAIC(:,1)).*(1.00000./CONSTANTS(:,7)+1.00000./CONSTANTS(:,8)+CONSTANTS(:,4)./( CONSTANTS(:,8).*STATES(:,3))), - 1.00000); ALGEBRAIC(:,7) = power( (1.00000./ALGEBRAIC(:,1)).*(1.00000./CONSTANTS(:,7)+1.00000./CONSTANTS(:,8)+CONSTANTS(:,3)./( CONSTANTS(:,7).*STATES(:,4))), - 1.00000); ALGEBRAIC(:,8) = power( (1.00000./ALGEBRAIC(:,1)).*(1.00000./CONSTANTS(:,7)+1.00000./CONSTANTS(:,8)), - 1.00000); ALGEBRAIC(:,9) = STATES(:,1)./CONSTANTS(:,2); ALGEBRAIC(:,10) = STATES(:,4)./CONSTANTS(:,3); ALGEBRAIC(:,11) = STATES(:,3)./CONSTANTS(:,4); ALGEBRAIC(:,12) = (1.00000+ALGEBRAIC(:,2)+ALGEBRAIC(:,10)).*( CONSTANTS(:,6).*ALGEBRAIC(:,9)+ CONSTANTS(:,8).*ALGEBRAIC(:,11))+ (1.00000+ALGEBRAIC(:,9)+ALGEBRAIC(:,11)).*( CONSTANTS(:,5).*ALGEBRAIC(:,2)+ CONSTANTS(:,7).*ALGEBRAIC(:,10)); ALGEBRAIC(:,13) = (ALGEBRAIC(:,1)./ALGEBRAIC(:,12)).*( CONSTANTS(:,6).*ALGEBRAIC(:,9).*CONSTANTS(:,7).*ALGEBRAIC(:,10) - CONSTANTS(:,5).*ALGEBRAIC(:,2).*CONSTANTS(:,8).*ALGEBRAIC(:,11)); ALGEBRAIC(:,14) = (ALGEBRAIC(:,1)./ALGEBRAIC(:,12)).*CONSTANTS(:,5).*ALGEBRAIC(:,2).*( CONSTANTS(:,6).*ALGEBRAIC(:,9)+ CONSTANTS(:,8).*ALGEBRAIC(:,11)); ALGEBRAIC(:,15) = (ALGEBRAIC(:,1)./ALGEBRAIC(:,12)).*CONSTANTS(:,7).*ALGEBRAIC(:,10).*( CONSTANTS(:,6).*ALGEBRAIC(:,9)+ CONSTANTS(:,8).*ALGEBRAIC(:,11)); ALGEBRAIC(:,16) = ( ALGEBRAIC(:,1).*( CONSTANTS(:,6).*ALGEBRAIC(:,9)+ CONSTANTS(:,8).*ALGEBRAIC(:,11)))./ALGEBRAIC(:,12); ALGEBRAIC(:,17) = ( ALGEBRAIC(:,1).*( CONSTANTS(:,5).*ALGEBRAIC(:,2)+ CONSTANTS(:,7).*ALGEBRAIC(:,10)))./ALGEBRAIC(:,12); ALGEBRAIC(:,18) = - ALGEBRAIC(:,13); 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