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a code that works before started working so why
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%% Description
% This Matlab cod simulates the membrane potential of the neuronal membrane (here, squid giant axon)
% using parameter predetermined in the Hodgkin-Huxley model. Users can set
% the stimulation current intensity, stimulation timing 't_start' and
% 't_end' which we inject the current into the neuron. User also should
% define the total simulation time.
%%
clc
clear all
%% simulation conditions
I_sti = 90e-12; % stimulation current intensity [A]
t_start = 0.001; % start time of current injection [ms]
t_end = 0.002; % end time of current injection [ms]
simulationTime = 0.005; % total simulation time [ms]
temp = 20; % body temperature [degC]
q_ten = 3; % Q_10 value
baseTemp = 6.3; % base temperature [degC]
%% timing
deltaT=0.001*1e-3; % time interval between each euler method.[s]
t=0:deltaT:simulationTime; % total time span.
t = t(1:end-1);
%% stimulation current
currentLevels = [I_sti]; % current intensity [A]
I(1:t_start/deltaT+1) = 0;
Warning: Integer operands are required for colon operator when used as index.
I(t_start/deltaT+1:t_end/deltaT) = currentLevels;
Warning: Integer operands are required for colon operator when used as index.
I(t_end/deltaT+1:numel(t)) = 0; % square shaped current
Warning: Integer operands are required for colon operator when used as index.
radi=1e-5; % [m] current injection area [m^2]
figure(1)
plot(t,I)
%% membrane constants
gbar_K = 360; gbar_Na = 1200; g_L = 3; % [S/m^2] conductance of Na+ and K+ ion channels and leakage pathway.
E_K = -0.077; E_Na = 0.05; E_L = -0.0544; % [V] equilibrium potential
C = 1e-2; % [F/m^2] membrane capacitance
%% initial value (to solve the equation using euler's fomulation)
x(1) = -0.065; % V
V(1) =x(1);
alpha_n = 1000 * 0.01*((10-1000*(V+0.065))/(exp((10-1000*(V+0.065))/10)-1)).*q_ten.^((temp-baseTemp)/10);
beta_n = 1000 * 0.125*exp(-1000*(V+0.065)/80).*q_ten.^((temp-baseTemp)/10);
alpha_m = 1000 * 0.1*((25-1000*(V+0.065))/(exp((25-1000*(V+0.065))/10)-1)).*q_ten.^((temp-baseTemp)/10);
beta_m = 1000 * 4*exp(-1000*(V+0.065)/18).*q_ten.^((temp-baseTemp)/10);
alpha_h = 1000 * 0.07*exp(-1000*(V+0.065)/20).*q_ten.^((temp-baseTemp)/10);
beta_h = 1000 * 1/(exp((30-1000*(V+0.065))/10)+1).*q_ten.^((temp-baseTemp)/10);
x(2) = alpha_n/(alpha_n+beta_n); n(1) = x(2); % n
x(3) = alpha_m/(alpha_m+beta_m); m(1) = x(3); % m
x(4) = alpha_h/(alpha_h+beta_h); h(1) = x(4); % h
x0 = zeros(1,4);
options2 = optimoptions('fsolve','StepTolerance',1e-20,'MaxIterations',100000,'MaxFunctionEvaluations',40000);
%% Calculate V, n, m, and h for entire time points
for i = 1:numel(t)-1
% Coefficients
alpha_n = 1000 * 0.01*((10-1000*(V(i)+0.065))/(exp((10-1000*(V(i)+0.065))/10)-1)).*q_ten.^((temp-baseTemp)/10);
beta_n = 1000 * 0.125*exp(-1000*(V(i)+0.065)/80).*q_ten.^((temp-baseTemp)/10);
alpha_m = 1000 * 0.1*((25-1000*(V(i)+0.065))/(exp((25-1000*(V(i)+0.065))/10)-1)).*q_ten.^((temp-baseTemp)/10);
beta_m = 1000 * 4*exp(-1000*(V(i)+0.065)/18).*q_ten.^((temp-baseTemp)/10);
alpha_h = 1000 * 0.07*exp(-1000*(V(i)+0.065)/20).*q_ten.^((temp-baseTemp)/10);
beta_h = 1000 * 1/(exp((30-1000*(V(i)+0.065))/10)+1).*q_ten.^((temp-baseTemp)/10);
% Currents
I_Na(i) = (m(i)^3)*gbar_Na*h(i)*(V(i)-E_Na);
I_K(i) = (n(i)^4)*gbar_K*(V(i)-E_K);
I_L(i) = g_L*(V(i)-E_L);
I_ion(i) = I(i)/(pi()*radi^2) - I_K(i) - I_Na(i) - I_L(i);
if i == 1
VV=V(1); N=n(1); M=m(1); H=h(1);
end
dT = baseTemp - 6.3;
func1 = @(x) HH(x,VV,N,M,H,alpha_n,beta_n, alpha_m,beta_m,alpha_h,beta_h,I_ion(i),deltaT,C);
[x(i,:),fval(i,:),exitflag(i),output(i)] = fsolve(func1,x0(i,:),options2);
VV = x(i,1); N = x(i,2); M = x(i,3); H = x(i,4);
x0(i+1,:) = x(i,:);
V(i+1) = x(i,1);
n(i+1) = x(i,2); % n
m(i+1) = x(i,3); % m
h(i+1) = x(i,4); % h
end
Equation solved.
fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.
Solver stopped prematurely.
fsolve stopped because it exceeded the function evaluation limit,
options.MaxFunctionEvaluations = 4.000000e+04.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.
No solution found.
fsolve stopped because the relative size of the current step is less than the
value of the step siz...
%%
I_Na(end+1)=I_Na(end);
I_K(end+1)=I_K(end);
I_L(end+1)=I_L(end);
I_ion(end+1)=I_ion(end);
%% plot graph
figure(2)
subplot(1,2,1)
plot(1000.*t,V,'LineWidth',2,'Color','k');
hold on
xlabel('Time (ms)');
ylabel('Membrane Potential (V)');
set(gca,'fontsize',15);
subplot(1,2,2)
hold on;
plot(1000.*t,I_Na,1000.*t,I_K,1000.*t,I_K+I_Na);
xlabel('Time (ms)');
ylabel('Total Current (mA)');
set(gca,'fontsize',15);
legend('Na','K')
hold off
the above code work for the whole day and now i run it it does not work the same why
Edit by Dyuman Joshi - Attached the function file - HH.m provided by OP in the commets and code has been executed.
6 Commenti
dpb
il 14 Ott 2023
type HH_Run
%% Description
% This Matlab cod simulates the membrane potential of the neuronal membrane (here, squid giant axon)
% using parameter predetermined in the Hodgkin-Huxley model. Users can set
% the stimulation current intensity, stimulation timing 't_start' and
% 't_end' which we inject the current into the neuron. User also should
% define the total simulation time.
%%
clc
clear all
%% simulation conditions
I_sti = 90e-12; % stimulation current intensity [A]
t_start = 0.001; % start time of current injection [ms]
t_end = 0.002; % end time of current injection [ms]
simulationTime = 0.005; % total simulation time [ms]
temp = 20; % body temperature [degC]
q_ten = 3; % Q_10 value
baseTemp = 6.3; % base temperature [degC]
%% timing
deltaT=0.001*1e-3; % time interval between each euler method.[s]
t=0:deltaT:simulationTime; % total time span.
t = t(1:end-1);
%% stimulation current
currentLevels = [I_sti]; % current intensity [A]
I(1:t_start/deltaT+1) = 0; I(t_start/deltaT+1:t_end/deltaT) = currentLevels; I(t_end/deltaT+1:numel(t)) = 0; % square shaped current
radi=1e-5; % [m] current injection area [m^2]
figure(1)
plot(t,I)
%% membrane constants
gbar_K = 360; gbar_Na = 1200; g_L = 3; % [S/m^2] conductance of Na+ and K+ ion channels and leakage pathway.
E_K = -0.077; E_Na = 0.05; E_L = -0.0544; % [V] equilibrium potential
C = 1e-2; % [F/m^2] membrane capacitance
%% initial value (to solve the equation using euler's fomulation)
x(1) = -0.065; % V
V(1) =x(1);
alpha_n = 1000 * 0.01*((10-1000*(V+0.065))/(exp((10-1000*(V+0.065))/10)-1)).*q_ten.^((temp-baseTemp)/10);
beta_n = 1000 * 0.125*exp(-1000*(V+0.065)/80).*q_ten.^((temp-baseTemp)/10);
alpha_m = 1000 * 0.1*((25-1000*(V+0.065))/(exp((25-1000*(V+0.065))/10)-1)).*q_ten.^((temp-baseTemp)/10);
beta_m = 1000 * 4*exp(-1000*(V+0.065)/18).*q_ten.^((temp-baseTemp)/10);
alpha_h = 1000 * 0.07*exp(-1000*(V+0.065)/20).*q_ten.^((temp-baseTemp)/10);
beta_h = 1000 * 1/(exp((30-1000*(V+0.065))/10)+1).*q_ten.^((temp-baseTemp)/10);
x(2) = alpha_n/(alpha_n+beta_n); n(1) = x(2); % n
x(3) = alpha_m/(alpha_m+beta_m); m(1) = x(3); % m
x(4) = alpha_h/(alpha_h+beta_h); h(1) = x(4); % h
x0 = zeros(1,4);
options2 = optimoptions('fsolve','StepTolerance',1e-20,'MaxIterations',100000,'MaxFunctionEvaluations',40000);
%% Calculate V, n, m, and h for entire time points
for i = 1:numel(t)-1
% Coefficients
alpha_n = 1000 * 0.01*((10-1000*(V(i)+0.065))/(exp((10-1000*(V(i)+0.065))/10)-1)).*q_ten.^((temp-baseTemp)/10);
beta_n = 1000 * 0.125*exp(-1000*(V(i)+0.065)/80).*q_ten.^((temp-baseTemp)/10);
alpha_m = 1000 * 0.1*((25-1000*(V(i)+0.065))/(exp((25-1000*(V(i)+0.065))/10)-1)).*q_ten.^((temp-baseTemp)/10);
beta_m = 1000 * 4*exp(-1000*(V(i)+0.065)/18).*q_ten.^((temp-baseTemp)/10);
alpha_h = 1000 * 0.07*exp(-1000*(V(i)+0.065)/20).*q_ten.^((temp-baseTemp)/10);
beta_h = 1000 * 1/(exp((30-1000*(V(i)+0.065))/10)+1).*q_ten.^((temp-baseTemp)/10);
% Currents
I_Na(i) = (m(i)^3)*gbar_Na*h(i)*(V(i)-E_Na);
I_K(i) = (n(i)^4)*gbar_K*(V(i)-E_K);
I_L(i) = g_L*(V(i)-E_L);
I_ion(i) = I(i)/(pi()*radi^2) - I_K(i) - I_Na(i) - I_L(i);
if i == 1
VV=V(1); N=n(1); M=m(1); H=h(1);
end
dT = baseTemp - 6.3;
func1 = @(x) HH(x,VV,N,M,H,alpha_n,beta_n, alpha_m,beta_m,alpha_h,beta_h,I_ion(i),deltaT,C);
[x(i,:),fval(i,:),exitflag(i),output(i)] = fsolve(func1,x0(i,:),options2);
VV = x(i,1); N = x(i,2); M = x(i,3); H = x(i,4);
x0(i+1,:) = x(i,:);
V(i+1) = x(i,1);
n(i+1) = x(i,2); % n
m(i+1) = x(i,3); % m
h(i+1) = x(i,4); % h
end
%%
I_Na(end+1)=I_Na(end);
I_K(end+1)=I_K(end);
I_L(end+1)=I_L(end);
I_ion(end+1)=I_ion(end);
%% plot graph
figure(2)
subplot(1,2,1)
plot(1000.*t,V,'LineWidth',2,'Color','k');
hold on
xlabel('Time (ms)');
ylabel('Membrane Potential (V)');
set(gca,'fontsize',15);
subplot(1,2,2)
hold on;
plot(1000.*t,I_Na,1000.*t,I_K,1000.*t,I_K+I_Na);
xlabel('Time (ms)');
ylabel('Total Current (mA)');
set(gca,'fontsize',15);
legend('Na','K')
hold off
There's no function HH in that file, either.
Somewhere you had to have had another m-file named "HH.m" that contained the missing HH function. Hopefully you can get it back from wherever you got this code; clearly it isn't something you wrote yourself or you would know all about it.
But, you've either deleted, moved, or renamed the HH.m file you had when it did work; you'll have to get it back in some fashion or another for it to run again...
Risposte (1)
William Rose
il 14 Ott 2023
This method makes things look a lot more complicated than necessary.
The state vector x() has the usual components for the HH model: x=[V,n,m,h]. You want to solve by forward Euler method - that is fine. Funciton HH(x,V,n,m,h,...) returns the difference between x and the value you would expect x to have based on the forward Euler projection from the previous time step. On each pass, the code uses fsolve() to find the value of x which, if passed to HH(x,...), will give HH=[0,0,0,0], i.e. no difference between x() and the first order Euler esitmate. This is unnecessarily complex. Since you have the formulas for the first order Euler estimates built into HH, just use them to advance the solution, and delete the call to fsolve() on each time step.
By the way, you say
radi=1e-5; % [m] current injection area [m^2]
But the usage later in the code
I_ion(i) = I(i)/(pi()*radi^2) - I_K(i) - I_Na(i) - I_L(i);
indicates that radi is radius in m, not area in m^2. The line above divides I(i) by the injection area. This is reasonable, because currents I_ion, I_K, I_Na,I_L are measured in amps per unit area, and I is in amps. Therefore it is correct to to divide I(i) by the area, before adding I to I_K, I_Na, I_L.
The values
gbar_K = 360; gbar_Na = 1200; g_L = 3; % [S/m^2] conductance of Na+, K+, and leak
are consistent with the values in column 2 of Table 3 of the 1952 paper. H&H used units of milli-mhos per cm^2. You have correctly multiplied by 10 to convert their conductances to units of S/m^2.
The resulting current plots have units of mA/m^2. The y-axis labels do not include the "/m^2" part.
5 Commenti
Min Khant
il 14 Ott 2023
my assignment is to remove the part where fsolve function was used and modify it by writing my own code of euler method directly. but i dunt know the correct code to write although i understand the assignment .:(
Min Khant
il 14 Ott 2023
1. Calculate the differential equation numerically by applying Euler’s law to lines 70 to 83 of the attached Matlab file (HH_run). 2. Find the stimulation threshold (stimulation resolution 1pA) of the Hodgkin-Huxley model. Stimulus duration was fixed at 1ms. 3. Plot the voltage gated Na+, K+ current at the stimulation threshold and explain what characteristics it has. 4. The current Matlab code is a code that checks the response when only one stimulus is applied. Modify the code so that two stimulations are applied and calculate the refractory period (interval between the first and second stimulations).
I would be so greatful if you could teach me how to code to get my assignment done :(
Im in a very helpless situation because im a complete beginner to matlab who jus started recently by finishing matlab onramp tuto. But my knowledge is not enough to fulfill the tast im given TT
it would also be helpful if you could guide me where i should start to study to have the knowledge you have in Matlab.
William Rose
il 14 Ott 2023
The exact part of your code which I said should be changed is the part you are suposed to change.
This not a homework service. As I said above, you can remove func1(), remove the call to fsolve(), and delete all reference to HH.m. Use the formulas in HH to update x(:). For example,
x(1) = V + deltaT*I_ion/C;
and so on.
You said "it would also be helpful if you could guide me where i should start to study to have the knowledge you have in Matlab". I learned about Matlab by looking at examples, by trying things, and by reading the help pages. It has taken a while, since I am not the fastest learner.
Min Khant
il 15 Ott 2023
dV = deltaT * I_ion(i) / C;
dn = deltaT * (alpha_n*(1-n(i)) - beta_n*n(i));
dm = deltaT * (alpha_m*(1-m(i)) - beta_m*m(i));
dh = deltaT * (alpha_h*(1-h(i)) - beta_h*h(i));
V(i+1) = V(i) + dV;
n(i+1) = n(i) + dn;
m(i+1) = m(i) + dm;
h(i+1) = h(i) + dh;
i modified my code this way and it worked surprisingly hehe
can you tell me if there is any differene from the code you suggested sir
William Rose
il 15 Ott 2023
@Min Khant, That looks good to me! Well done!
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