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Figure1_proof_of_principal.m
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Figure1_proof_of_principal.m
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%% proof of principal of the accuracy of the steady-state analytical solution
clear
close all
%% example 1: Pseudo
close all
f=.45;
U=0;
F=.300;
D=.800;
Tsyn=1e-4;
pulse_num=50;
for F_DBS=1:200
I_infinity_analytical(F_DBS)=infinity_current_Tsyn(f, U, F, D,Tsyn, F_DBS);
I=DBS_profile(f, U, F, D,0.0001, F_DBS,pulse_num);
I_infinity_computational(F_DBS)=I(end);
end
F_DBS=1:200;
figure;
plot(F_DBS,I_infinity_computational);
hold on
F_DBS_sparse=[1,5,20,30,50,100,130,200];
plot(F_DBS,I_infinity_analytical);
figure('Position',[100 100 900 300])
plot(F_DBS,I_infinity_analytical,'b','LineWidth',2);
hold on
F_DBS_sparse=[1,5,10,20,30,50,100,130,200];
title('Frequency response')
xlabel('F_{DBS}')
ylabel('Steady-state value')
p=plot(F_DBS_sparse,I_infinity_computational(F_DBS_sparse),'or','MarkerSize',6,'MarkerFaceColor','r');
legend('Analytical formula','100th EPSC')
% for i=F_DBS_sparse
% figure('position',[100,100,300,200]);
%
% plot(DBS_profile(f,U,F,D,i,pulse_num))
% hold on
% plot(ones(1,pulse_num)*infinity_current(f,U,F,D,i))
% ylim([0 0.4])
% title(['F_{DBS}=',num2str(i),'Hz'])
% xlabel('stimulation number')
% ylabel('EPSC')
% end
figure('Position',[100 100 900 400])
n=0;
for i=F_DBS_sparse(2:end)
n=n+1;
s=subplot(2,4,n);
I=zeros(1,floor(pulse_num*10000/i)+1);
I(floor(10000*(1:pulse_num)./i))=DBS_profile(f,U,F,D,0,i,pulse_num);
h=exp(-1*(0:5000)./30);
I=conv(I,h);
plot((1:length(I))/floor(10000./i),I); hold on
% plot(DBS_profile(f,U,F,D,i,pulse_num),'--b')
hold on
% plot([1:pulse_num;1:pulse_num],[zeros(1,pulse_num);DBS_profile(f,U,F,D,i,pulse_num)],'b')
plot(DBS_profile(f,U,F,D,0.0001,i,pulse_num),'.b','LineWidth',2)
hold on
plot(ones(1,pulse_num)*infinity_current_Tsyn(f,U,F,D,Tsyn,i),'--r','LineWidth',1)
ylim([0 .4])
xlim([0 30])
title(['F_{DBS}=',num2str(i),'Hz'])
if n>4; xlabel('stimulation number');set(s,'XTick',[0,10,20,30]); else; set(s,'XTick',''); end
if n==1 || n==5; ylabel('EPSC');set(s,'YTick',[0,.4]); else; set(s,'YTick',''); end
end
%% example 2:
close all
f=.05;
U=0.1;
F=.600;
D=.080;
pulse_num=100;
for F_DBS=1:200
I_infinity_analytical(F_DBS)=infinity_current_Tsyn(f, U, F, D,Tsyn, F_DBS);
I=DBS_profile(f, U, F, D,Tsyn, F_DBS,pulse_num);
I_infinity_computational(F_DBS)=I(end);
end
F_DBS=1:200;
figure;
plot(F_DBS,I_infinity_computational);
hold on
F_DBS_sparse=[1,5,20,30,50,100,130,200];
plot(F_DBS,I_infinity_analytical);
figure('Position',[100 100 900 300])
s=subplot(1,1,1);
plot(F_DBS,I_infinity_analytical,'b','LineWidth',2);
hold on
F_DBS_sparse=[1,5,10,20,30,50,100,130,200];
title('Frequency response')
xlabel('F_{DBS}')
ylabel('Steady-state value')
p=plot(F_DBS_sparse,I_infinity_computational(F_DBS_sparse),'or','MarkerSize',6,'MarkerFaceColor','r');
legend('Analytical formula','100th EPSC')
Ticks=[1,5:5:200];
LABELS={};
for i=1:length(Ticks)
if sum(Ticks(i)==F_DBS_sparse)
LABELS{i}=num2str(Ticks(i));
else
LABELS{i}=''
end
end
set(s,'XTick',Ticks,'XTickLabel',LABELS,'BOX','off','XScale','log')
% for i=F_DBS_sparse
% figure('position',[100,100,300,200]);
%
% plot(DBS_profile(f,U,F,D,i,pulse_num))
% hold on
% plot(ones(1,pulse_num)*infinity_current_Tsyn(f,U,F,D,i))
% ylim([0 0.4])
% title(['F_{DBS}=',num2str(i),'Hz'])
% xlabel('stimulation number')
% ylabel('EPSC')
% end
figure('Position',[100 100 900 400])
n=0;
for i=F_DBS_sparse(2:end)
n=n+1;
s=subplot(2,4,n);
I=zeros(1,floor(pulse_num*10000/i)+1);
I(floor(10000*(1:pulse_num)./i))=DBS_profile(f,U,F,D,Tsyn,i,pulse_num);
h=exp(-1*(0:5000)./30);
I=conv(I,h);
p(1)=plot(0:pulse_num-1,ones(1,pulse_num)*infinity_current_Tsyn(f,U,F,D,Tsyn,i),'--r','LineWidth',1); hold on
p(2)=plot((1:length(I))/floor(10000./1),I,'Color','k'); hold on
% plot(DBS_profile(f,U,F,D,i,pulse_num),'--b')
hold on
% plot([1:pulse_num;1:pulse_num],[zeros(1,pulse_num);DBS_profile(f,U,F,D,i,pulse_num)],'b')
p(3)=plot((1:pulse_num)/i,DBS_profile(f,U,F,D,Tsyn,i,pulse_num),'.b','LineWidth',2);
hold on
ylim([0 .4])
xlim([0 20/i])
title(['F_{DBS}=',num2str(i),'Hz'],'VerticalAlignment','top')
% if n==4; legend(p,{'Analytical formula','TM','DTM'}, 'Location','northeastoutside'); end
if n>4; xlabel('Time(sec)'); end
if n==1 || n==5; ylabel('EPSC');set(s,'YTick',[0,.2,.4],'BOX','off'); else; set(s,'YTick','','BOX','off','YColor','w'); end
end
%% example 3: Depression
f=.95;
U=0.;
F=.010;
D=.080;
pulse_num=50;
for F_DBS=1:200
I_infinity_analytical(F_DBS)=infinity_current_Tsyn(f, U, F, D,Tsyn, F_DBS);
I=DBS_profile(f, U, F, D,Tsyn, F_DBS,pulse_num);
I_infinity_computational(F_DBS)=I(end);
end
F_DBS=1:200;
figure;
plot(F_DBS,I_infinity_computational);
hold on
F_DBS_sparse=[1,5,20,30,50,100,130,200];
plot(F_DBS,I_infinity_analytical);
figure('Position',[100 100 900 300])
plot(F_DBS,I_infinity_analytical,'b','LineWidth',2);
hold on
F_DBS_sparse=[1,5,10,20,30,50,100,130,200];
title('Frequency response')
xlabel('F_{DBS}')
ylabel('Steady-state value')
p=plot(F_DBS_sparse,I_infinity_computational(F_DBS_sparse),'or','MarkerSize',6,'MarkerFaceColor','r');
legend('Analytical formula','100th EPSC')
% for i=F_DBS_sparse
% figure('position',[100,100,300,200]);
%
% plot(DBS_profile(f,U,F,D,i,pulse_num))
% hold on
% plot(ones(1,pulse_num)*infinity_current_Tsyn(f,U,F,D,i))
% ylim([0 0.4])
% title(['F_{DBS}=',num2str(i),'Hz'])
% xlabel('stimulation number')
% ylabel('EPSC')
% end
figure('Position',[100 100 900 400])
n=0;
for i=F_DBS_sparse(2:end)
n=n+1;
s=subplot(2,4,n);
I=zeros(1,floor(pulse_num*10000/i)+1);
I(floor(10000*(1:pulse_num)./i))=DBS_profile(f,U,F,D,Tsyn,i,pulse_num);
h=exp(-1*(0:5000)./30);
I=conv(I,h);
plot((1:length(I))/floor(10000./i),I); hold on
% plot(DBS_profile(f,U,F,D,i,pulse_num),'--b')
hold on
% plot([1:pulse_num;1:pulse_num],[zeros(1,pulse_num);DBS_profile(f,U,F,D,i,pulse_num)],'b')
plot(DBS_profile(f,U,F,D,Tsyn,i,pulse_num),'.b','LineWidth',2)
hold on
plot(ones(1,pulse_num)*infinity_current_Tsyn(f,U,F,D,Tsyn,i),'--r','LineWidth',1)
ylim([0 1.2])
xlim([0 30])
title(['F_{DBS}=',num2str(i),'Hz'])
if n>4; xlabel('stimulation number');set(s,'XTick',[0,10,20,30]); else; set(s,'XTick',''); end
if n==1 || n==5; ylabel('EPSC');set(s,'YTick',[0,.4,.8,1.2]); else; set(s,'YTick',''); end
end