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)=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)=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