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) = 0.055; CONSTANTS(:,6) = 4; STATES(:,2) = 1; CONSTANTS(:,7) = 1000; CONSTANTS(:,8) = 19.2; CONSTANTS(:,9) = 3.33; CONSTANTS(:,10) = 8.3; CONSTANTS(:,11) = 50; CONSTANTS(:,12) = 44.84; CONSTANTS(:,13) = 0.85; CONSTANTS(:,14) = 10; STATES(:,3) = 1; CONSTANTS(:,15) = 11; CONSTANTS(:,16) = 667; 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(:,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(:,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