Plateau followed by one phase decay
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Good morning, I am trying to figure out how to compute tau constants from my data
My data could be be fitted by such plateau followed by one phase decay function:
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1627558/image.png)
I tried to implement it in MATLAB as follows:
x = 0:0.5:20; % time in seconds
Y0 = -0.6; % signal baseline value
Plateau = -1; % singnal plateu after trigger/stimulus, maximum change from baseline
tau = 0.6; % exponenential decay constant
K = 1/tau; % rate constant in units reciprocal of the x-axis units
X0 = 5; % trigger time
y = Plateau+(Y0-Plateau)*exp(-K*(x-X0));
figure;plot(x,y,'k');
However, I get the following result:
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1627563/image.png)
I would have 2 questions:
1) why cant I reproduce the one phase decay function?
2) would you know how to use the matlab funciton "fit" for such data with plateau followed by one phase decay function?
Thanks community for your kind support,
Best regards.
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Réponses (2)
Alan Stevens
le 26 Fév 2024
Like this?
x = 0:0.5:20; % time in seconds
Y0 = -0.6; % signal baseline value
Plateau = -1; % singnal plateu after trigger/stimulus, maximum change from baseline
tau = 0.6; % exponenential decay constant
K = 1/tau; % rate constant in units reciprocal of the x-axis units
X0 = 5; % trigger time
y = Y0*(x<=X0)+(Plateau+(Y0-Plateau)*exp(-K*(x-X0))).*(x>X0);
figure;plot(x,y,'k');
5 commentaires
Alan Stevens
le 26 Fév 2024
Here's a quick fit of tau and Y0. I'll leave you to tidy it up and extend it to fit X0 as well.
x = 0:0.5:20;
y = [-0.137055262721364 -0.118841612584876 -0.274602636741299 -0.117324828772196 ...
-0.173528150754918 -0.280491919000118 -0.244300356226590 -0.367583069701879 ...
-0.423274105143034 -0.529129050767333 -0.774173830727337 -0.676677606159725 ...
-0.730062482232667 -0.863905715495076 -0.831675679632950 -0.987303352625066 ...
-0.949979744575626 -0.865710605996821 -0.901728879393798 -0.877082148456042 ...
-0.944693953430828 -1.07404346760035 -0.915521627715257 -0.901789963321291 ...
-0.955365771797851 -0.941530617721837 -0.945983148775748 -1.01735658137382 ...
-0.965635004813717 -1.06321643780048 -0.956807780654745 -1.09208906741553 ...
-1.04341265165344 -1.08982901817714 -1.07984413818039 -0.934740294823467 ...
-0.960591807908718 -1.03623550995537 -0.909687220130007 -1.09290177705358 ...
-1.01208835337351];
Plateau = -1;
X0 = 2;
fn = @(x,tau,Y0)Y0*(x<=X0)+(Plateau+(Y0-Plateau)*exp(-(x-X0)/tau)).*(x>X0);
tauY0 = [1, -0.1]; % Initial guess
tauY = fminsearch(@(tauY) F(tauY,x,y), tauY0);
tau = tauY(1); Y0 = tauY(2);
yfit = fn(x,tau,Y0);
plot(x,y,'.',x,yfit), grid
xlabel('x'), ylabel('y')
text(12,-0.25,['tau = ' num2str(tau)])
text(12,-0.35,['Y0 = ' num2str(Y0)])
function Z = F(tauY,x,y)
tau = tauY(1); Y0 = tauY(2);
Plateau = -1;
X0 = 2;
yvals = zeros(1,numel(x));
for i = 1:numel(x)
t = x(i) - X0;
yvals(i) = Y0*(t<=0)+(Plateau+(Y0-Plateau)*exp(-t/tau)).*(t>0);
end
Z = norm(yvals-y);
end
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