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Conductivity.m
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Conductivity.m
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%physical constants
clear all;
close all;
c0 = 2.998e8;
eta0 = 120*pi;
mu0 = pi*4e-7;
eps0 = 1e-9/(36*pi);
%box dimensions
width = 0.05; % cm
height = 0.05;
length = 0.002; % cm
%source parameters
f0 = 2e9; % GHz
tw = 1e-8/pi;
t0 = 4*tw;
%spatial discretization
adipose = 10;
tumor = 60;
sigma = 1;
epsr = tumor;
w = 2 * pi * f0;
k = (w/c0)*sqrt(epsr-1j*sigma/(w*eps0));
beta = real(k);
c = w / beta;
lambda = c/f0;
dxmax = lambda / 10;
dx = dxmax;
dy = dxmax;
dz = dxmax;
nx = round(width/dx);
ny = round(height/dy);
nz = round(length/dz);
%source position
srcx = round(nx / 2);
srcy = round(ny / 2);
srcz = round(3 * nz / 4);
%material
mx = 3 * nx / 8;
my = ny / 8;
mz = nz / 8;
mw = nx / 4; % width
mh = ny / 4; % height
ml = nz / 4; % length
al = ny / 2;
eps = ones(nx,ny,nz) * eps0 * adipose;
sigma = ones(nx,ny,nz) * f0 * 1e-9 * 0.5 - 0.5;;
for i=1:1:nx
for j=1:1:ny
for k=1:1:nz
% adipose tissue is located under z < al
if (k<al)
eps(i,j,k) = eps0 * adipose ;
sigma(i,j,k) = f0 * 1e-9 * 0.5 - 0.5;
end
if (i>mx && i<(mw+mx) && j>my && j<(mh+my) && k>mz && k<(ml+mz))
eps(i,j,k) = eps0 * tumor;
sigma(i,j,k) = f0 * 1e-9 - 0.5;
end
end
end
end
%time discretization
dt = 0.99/(c0*sqrt(dx^-2+dy^-2+dz^-2));
n_iter = 10000;
%receivers
nrec = round(nx / 3)-1;
recdy = round(ny / nrec);
recx = srcx;
recz = srcz;
rec = zeros(nrec,n_iter);
%EM field dimensions
Hx = zeros(nx,ny,nz);
Hy = zeros(nx,ny,nz);
Hz = zeros(nx,ny,nz);
Ex = zeros(nx,ny,nz);
Ey = zeros(nx,ny,nz);
Ez = zeros(nx,ny,nz);
%iteration
i = 0;
for n=1:1:n_iter
%magnetic field derivatives
Hxy = diff(Hx,1,2);
Hxz = diff(Hx,1,3);
Hzx = diff(Hz,1,1);
Hzy = diff(Hz,1,2);
Hyx = diff(Hy,1,1);
Hyz = diff(Hy,1,3);
%electric field maxwell equations
epsi = eps(:,2:end-1,2:nz-1);
ksi = (dt * sigma(:,2:end-1,2:nz-1)) ./ ( 2 * epsi );
c2 = (1./(1+ksi)).*(dt./epsi);
c1 = (1-ksi)./(1+ksi);
Ex(:,2:end-1,2:end-1) = c1.*Ex(:,2:end-1,2:nz-1) + c2.*((1/dy)*Hzy(:,1:end-1,2:end-1) - (1/dz)*Hyz(:,2:ny-1,1:end-1));
epsi = eps(2:end-1,:,2:end-1);
ksi = (dt * sigma(2:end-1,:,2:end-1)) ./ ( 2 * epsi );
c2 = (1./(1+ksi)).*(dt./epsi);
c1 = (1-ksi)./(1+ksi);
Ey(2:end-1,:,2:end-1) = c1.*Ey(2:end-1,:,2:end-1) + c2.*((1/dz)*Hxz(2:end-1,:,1:end-1) - (1/dx)*Hzx(1:end-1,:,2:end-1));
epsi = eps(2:end-1,2:end-1,:);
ksi = (dt * sigma(2:end-1,2:end-1,:)) ./ ( 2 * epsi );
c2 = (1./(1+ksi)).*(dt./epsi);
c1 = (1-ksi)./(1+ksi);
Ez(2:end-1,2:end-1,:) = c1.*Ez(2:end-1,2:end-1,:) + c2.*((1/dx)*Hyx(1:end-1,2:end-1,:) - (1/dy)*Hxy(2:end-1,1:end-1,:));
%gaussian source
f = sin(2*pi*f0*n*dt)*exp(-(n*dt-t0)^2/(tw^2))/dy;
Ez(srcx,srcy,srcz) = Ez(srcx,srcy,srcz) + f;
%Ezn(n)=Ez(srcx,srcy,srcz);
%electric field derivatives
Exy = diff(Ex,1,2);
Exz = diff(Ex,1,3);
Ezx = diff(Ez,1,1);
Ezy = diff(Ez,1,2);
Eyx = diff(Ey,1,1);
Eyz = diff(Ey,1,3);
%magnetic field maxwell equations
Hx(:,1:end-1,1:end-1) = Hx(:,1:end-1,1:end-1) - (dt/(mu0*dy))*Ezy(:,:,1:end-1) + (dt/(mu0*dz))*Eyz(:,1:end-1,:);
Hy(1:end-1,:,1:end-1) = Hy(1:end-1,:,1:end-1) - (dt/(mu0*dz))*Exz(1:end-1,:,:) + (dt/(mu0*dx))*Ezx(:,:,1:end-1);
Hz(1:end-1,1:end-1,:) = Hz(1:end-1,1:end-1,:) - (dt/(mu0*dx))*Eyx(:,1:end-1,:) + (dt/(mu0*dy))*Exy(1:end-1,:,:);
for k=1:1:nrec
rec(k,n) = Ez(recx,recdy * k ,recz);
end
%display
if (mod(i,5)==0)
slice(:,:)=Ez(:,:,round(nz/2));
pcolor(slice');
colorbar;
drawnow
end
i = i+1;
disp(i)
end
close all
hold on
for k=1:1:nrec
plot(rec(k,:))
end
save('conductive-receivers.mat','rec','nrec','n_iter','recx','recdy','recz')