% =============================================================== % == Single Cell Minimal Model (4 state variables) == % == == % == Supplement for the CMACS Workshop == % == == % == == % == Author: == % == == % == E. Bartocci == % == == % == Date: 11/05/10 == % == == % == Free distribution with authors permission == % == == % == SUNY Stony Brook, Stony Brook, NY == % == == % =============================================================== % The following are the parameters that you can find in the paper % A. Bueno-Orovio, M. Cherry, and F. Fenton, ?Minimal model for % human ventricular action potentials in tissue,? Journal of % Theoretical Biology, no. 253, pp. 544?560, 2008. % Questions: % % What is the maximum dt such that I can still observe the solution ? % Modify the parameters in order to increase the action potential duration. % Modify the parameters in order to obtain alternans % Find the range of the parameters such that the cell is still excitable % Modify the parameters in order to increase the length of the peak of the upstroke. % Eliminate divisions from the Minimal Resistor using the Sigmoid Closure function [out] = single_cell_mm4V () global EPI_TVP; global EPI_TV1M; global EPI_TV2M; global EPI_TWP; global EPI_TW1P; %200 global EPI_TW2P; %200 global EPI_TW1M; %190 global EPI_TW2M; global EPI_TS1; global EPI_TS2; global EPI_TFI; global EPI_TO1; global EPI_TO2; global EPI_TSO1; global EPI_TSO2; global EPI_TSI; % TSI1 1.8875 % TSI2 1.8875 global EPI_TWINF; global EPI_THV; global EPI_THVM; global EPI_THVINF; global EPI_THW; global EPI_THWINF; global EPI_THSO; global EPI_THSI; global EPI_THO; % KWP 5.7 global EPI_KWM; global EPI_KS; global EPI_KSO; % KSI 97.8 global EPI_UWM; global EPI_US; global EPI_UO; global EPI_UU; global EPI_USO; global EPI_SC; % WCP 0.15 global EPI_WINFSTAR; global EPI_TW2M_TW1M; global EPI_TSO2_TSO1; global EPI_TW2M_TW1M_DIVBY2; global EPI_TSO2_TSO1_DIVBY2; EPI_TVP = 1.4506; EPI_TV1M = 60.; EPI_TV2M = 1150.; EPI_TWP = 200.0; EPI_TW1P = 60.0; %200 EPI_TW2P = 15.0; %200 EPI_TW1M = 60.0; %190 EPI_TW2M = 15.; %190 %The same with Flavio's paper EPI_TS1 = 2.7342; %The same with Flavio's paper EPI_TS2 = 16.; %The same with Flavio's paper EPI_TFI = 0.11; %The same with Flavio's paper EPI_TO1 = 400.; %The same with Flavio's paper EPI_TO2 = 6. ; %The same with Flavio's paper EPI_TSO1 = 30.0181; %The same with Flavio's paper EPI_TSO2 = 0.9957; %The same with Flavio's paper EPI_TSI = 1.8875; % We have TSI1 and TSI2 = TSI in Flavio's paper % TSI1 1.8875 % TSI2 1.8875 EPI_TWINF = 0.07; %The same with Flavio's paper EPI_THV = 0.3; %EPUM % The same of Flavio's paper EPI_THVM = 0.006; %EPUQ % The same of Flavio's paper EPI_THVINF = 0.006; %EPUQ % The same of Flavio's paper EPI_THW = 0.13; %EPUP % The same of Flavio's paper EPI_THWINF = 0.006; %EPURR % In Flavio's paper 0.13 EPI_THSO = 0.13; %EPUP % The same of Flavio's paper EPI_THSI = 0.13; %EPUP % The same of Flavio's paper EPI_THO = 0.006; %EPURR % The same of Flavio's paper % KWP 5.7 EPI_KWM = 65.; %The same of Flavio's paper EPI_KS = 2.0994; %The same of Flavio's paper EPI_KSO = 2.0458; %The same of Flavio's paper % KSI 97.8 EPI_UWM = 0.03; %The same of Flavio's paper EPI_US = 0.9087; %The same of Flavio's paper EPI_UO = 0.; % The same of Flavio's paper EPI_UU = 1.55; % The same of Flavio's paper EPI_USO = 0.65; % The same of Flavio's paper EPI_SC = 0.007; % WCP 0.15 EPI_WINFSTAR = 0.94; % The same of Flavio's paper EPI_TW2M_TW1M = -45.0; EPI_TSO2_TSO1 = -29.0224; EPI_TW2M_TW1M_DIVBY2 = -22.5; EPI_TSO2_TSO1_DIVBY2 = -14.5112; ut1 = []; vt1 = []; wt1 = []; st1 = []; stimt1 = []; u = 0.0; v = 1.0; w = 1.0; s = 0.0; t1 = 0; t2 = 0; for i=1:20000 [u,v,w,s, t1, t2, stim] = nextStepNonlinear (u,v,w,s, t1, t2, 0.1); ut1(i) = u; vt1(i) = v; wt1(i) = w; st1(i) = s; stimt1(i)= stim; end %hold off; plot(linspace(0,2000, 20000), [ut1; vt1; wt1; st1; stimt1]); %plot(linspace(0,30, 30000), ut3); end function [u,v,w,s, t1, t2, stim] = nextStepNonlinear (u,v,w,s, t1, t2, dt) global EPI_TVP; global EPI_TV1M; global EPI_TV2M; global EPI_TWP; global EPI_TW1P; %200 global EPI_TW2P; %200 global EPI_TW1M; %190 global EPI_TW2M; global EPI_TS1; global EPI_TS2; global EPI_TFI; global EPI_TO1; global EPI_TO2; global EPI_TSO1; global EPI_TSO2; global EPI_TSI; % TSI1 1.8875 % TSI2 1.8875 global EPI_TWINF; global EPI_THV; global EPI_THVM; global EPI_THVINF; global EPI_THW; global EPI_THWINF; global EPI_THSO; global EPI_THSI; global EPI_THO; % KWP 5.7 global EPI_KWM; global EPI_KS; global EPI_KSO; % KSI 97.8 global EPI_UWM; global EPI_US; global EPI_UO; global EPI_UU; global EPI_USO; global EPI_SC; % WCP 0.15 global EPI_WINFSTAR; global EPI_TW2M_TW1M; global EPI_TSO2_TSO1; global EPI_TW2M_TW1M_DIVBY2; global EPI_TSO2_TSO1_DIVBY2; t1 = t1 + dt; t2 = t2 + dt; stim = HEAVISIDE(t1 - 0)*(1 - HEAVISIDE(t2 - 1)) + HEAVISIDE(t1 - 350)*(1 - HEAVISIDE(t2 - 351)) + HEAVISIDE(t1 - 700)*(1 - HEAVISIDE(t2 - 701)) + HEAVISIDE(t1 - 1100)*(1 - HEAVISIDE(t2 - 1101)); jfi = 0.0; jso = 0.0; jsi = 0.0; if u < 0.006 %w = w + (1.0 -(u/EPI_TWINF) - w) * (0.04166666666666667 + 0.025 * tanh(EPI_KWM*(u- 0.0406638027778453)))*dt; w = w + ((1.0 -(u/EPI_TWINF) - w)/(EPI_TW1M + (EPI_TW2M - EPI_TW1M) * 0.5 * (1.+tanh(EPI_KWM*(u-EPI_UWM)))))*dt; v = v + ((1.0-v)/EPI_TV1M)*dt; s = s + ((((1.+tanh(EPI_KS*(u - EPI_US))) * 0.5) - s)/EPI_TS1)*dt; jfi = 0.0; jso = u/EPI_TO1; jsi = 0.0; elseif u < 0.13 %w = w + ((0.94-w) * (0.04166666666666667 + 0.025 * tanh(EPI_KWM*(u- 0.0406638027778453 ))))*dt; w = w + ((0.94-w)/(EPI_TW1M + (EPI_TW2M - EPI_TW1M) * 0.5 * (1.+tanh(EPI_KWM*(u-EPI_UWM)))))*dt; v = v + (-v/EPI_TV2M)*dt; s = s +((((1.+tanh(EPI_KS*(u-EPI_US))) * 0.5) - s)/EPI_TS1)*dt; jfi = 0.0; jso = u/EPI_TO2; jsi = 0.0; elseif u < 0.3 w = w + (-w/EPI_TWP)*dt; v = v + (-v/EPI_TV2M)*dt; s = s + ((((1.+tanh(EPI_KS*(u-EPI_US))) * 0.5) - s)/EPI_TS2)*dt; jfi = 0.0; jso = 0.518815902099483 + 0.485502667750873 * tanh(EPI_KSO * (u - 1.48246402499052 )); jsi = -w * s/EPI_TSI; else w = w + (-w/EPI_TWP)*dt; v = v + (-v/EPI_TVP)*dt; s = s +((((1.+tanh(EPI_KS*(u - EPI_US))) * 0.5) - s)/EPI_TS2)*dt; jfi = -v * (u - EPI_THV) * (EPI_UU - u)/EPI_TFI; jso = 0.518815902099483 + 0.485502667750873 * tanh(EPI_KSO * (u - 1.48246402499052 )); jsi = -w * s/EPI_TSI; end u = u - (jfi+jso+jsi-stim)*dt; end