function Is = AxonThresh(depth,diam)
% calculate axon thresholds based on all combinations of depth and diameter
% depth: length M
% diam: length N
% Is: size MxN
L = 400; % length of axon field (cm)
dVmt = 10; % depolarization threshold (mV)
dAC = 2.5; % distance between anode and cathode (cm)
dz = 0.01; % axial spatial resolution (cm)
zA = L/2 + dAC/2; % anode position (cm)
zC = zA - dAC; % cathode position (cm)
z = 0:dz:L; % vector of axial positions (cm)
Rm = 5000; % specific membrane resistance (ohm.cm^2)
Ra = 70; % specific axial resistance (ohm.cm)
re = 350; % extracellular resistance (ohm.cm)
Is = zeros(length(depth),length(diam));
for j = 1: length(diam)
r = diam(j) / 1e4 / 2; % axon radius (cm)
rm = Rm./(2*pi.*r); % membrane resistance (ohm.cm)
ra = Ra./(pi.*r.^2); % axial resistance (ohm/cm)
k = sqrt(ra/rm); % spatial frequency of intracellular potential
% 1/um
for i = 1 : length(depth)
d = depth(i) / 1e4; % convert depth to cm
dA = sqrt( (d-r)^2 + (zA-z).^2 ); % absolute distances from electrodes
dC = sqrt( (d-r)^2 + (zC-z).^2 ); % to axon surface coordinates (cm)
VA = re./(4*pi*dA); % potential outside membrane due to 1mA anode (mV)
VC = re./(4*pi*dC); % potential outside membrane due to 1mA cathode (mV)
Ve = VA - VC; % potential applied to membrane (mV)
dVi = Visolve(Ve,rm,ra,dz);
dVm1 = max(dVi - Ve);
Is(i,j) = dVmt ./ dVm1;
end
end
return