EIDORS: Electrical Impedance Tomography and Diffuse Optical Tomography Reconstruction Software

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Using Netgen to simulate fwd and inverse solutions

Model a 2D tank with 8 electrodes

% Netgen simulation $Id: netgen_sims01.m 3273 2012-06-30 18:00:35Z aadler $

extra={'ball','solid ball = cylinder(0.2,0.2,0;0.2,0.2,1;0.2) and orthobrick(-1,-1,0;1,1,0.05);'};
fmdl= ng_mk_cyl_models(0,[9],[0.2,0,0.05],extra); 
ctr = interp_mesh(fmdl); ctr=(ctr(:,1)-0.2).^2 + (ctr(:,2)-0.2).^2;
img= mk_image(fmdl, 1 + 0.1*(ctr < 0.2^2));

subplot(221)
show_fem(img);

print_convert netgen_sims01a.png '-density 100'

Simulate a 2D tank with 8 electrodes with adjacent patterns

% Netgen simulation $Id: netgen_sims02.m 3791 2013-04-04 15:48:25Z aadler $

% Calculate stimulation pattern adjacent
stim = mk_stim_patterns(9,1,[0,1],[0,1],{},1);
img.fwd_model.stimulation = stim;

% Get all voltages so we can plot it
img.fwd_solve.get_all_meas = 1;

% Homogeneous model
img.elem_data(:) = 1;

vh = fwd_solve(img);

% Show Voltage for stim pattern #1
imgn = rmfield(img,'elem_data');
imgn.node_data = vh.volt(:,1);

h1= subplot(221);
show_fem(imgn);

% Show Voltage for stim pattern #2
imgn = rmfield(img,'elem_data');
imgn.node_data = vh.volt(:,2);

h2= subplot(222);
show_fem(imgn);

imgn.calc_colours.cb_shrink_move = [0.5,0.8,-.02];
common_colourbar([h1,h2],imgn);
print_convert netgen_sims02a.png '-density 100'

Figure: Voltage pattens for two adjacent simulation patterns

Simulate a 2D tank with 8 electrodes with different current patterns

% Netgen simulation $Id: netgen_sims03.m 3792 2013-04-04 16:01:34Z aadler $
clf;subplot(221);

% Calculate stimulation pattern adjacent
img.fwd_model.stimulation = mk_stim_patterns(9,1,[0,1],[0,1],{},1);
vh = fwd_solve(img);
imgn.node_data = vh.volt(:,1);

show_fem(imgn); axis equal; axis tight;
print_convert netgen_sims03a.png '-density 100'

% Calculate stimulation pattern offset-2
img.fwd_model.stimulation = mk_stim_patterns(9,1,[0,2],[0,1],{},1);
vh = fwd_solve(img);
imgn.node_data = vh.volt(:,1);

show_fem(imgn); axis equal; axis tight;
print_convert netgen_sims03b.png '-density 100'

% Calculate stimulation pattern offset-3
img.fwd_model.stimulation = mk_stim_patterns(9,1,[0,3],[0,1],{},1);
vh = fwd_solve(img);
imgn.node_data = vh.volt(:,1);

show_fem(imgn); axis equal; axis tight;
print_convert netgen_sims03c.png '-density 100'

% Calculate stimulation pattern offset-4
img.fwd_model.stimulation = mk_stim_patterns(9,1,[0,4],[0,1],{},1);
vh = fwd_solve(img);
imgn.node_data = vh.volt(:,1);

show_fem(imgn); axis equal; axis tight;
print_convert netgen_sims03d.png '-density 100'

Figure: Voltage pattens for two adjacent simulation patterns

Simulate a voltages for a change in conductivity

% Netgen simulation $Id: netgen_sims04.m 3792 2013-04-04 16:01:34Z aadler $

% Calculate stimulation pattern offset-4
img.fwd_model.stimulation = mk_stim_patterns(9,1,[0,4],[0,1],{},1);

% Set homogeneous phantom
img.elem_data(:) = 1;
vh = fwd_solve(img);
imgn.node_data = vh.volt(:,1);
imgn.calc_colours.cb_shrink_move = [0.3,0.7,0.02];
imgn.calc_colours.ref_level = 0;

clf; subplot(221);
show_fem(imgn,1); axis equal; axis tight;
print_convert netgen_sims04a.png '-density 100'

% Set inhomogeneity very insulating
img.elem_data = 1 - 0.99*(ctr < 0.2^2);
vi = fwd_solve(img);
imgn.node_data = vi.volt(:,1);

clf; subplot(221);
show_fem(imgn,1); axis equal; axis tight;
print_convert netgen_sims04b.png '-density 100'

% Difference in voltages
imgn.node_data = vh.volt(:,1) - vi.volt(:,1);

clf; subplot(221);
show_fem(imgn,1); axis equal; axis tight;
print_convert netgen_sims04c.png '-density 100'

Figure: Voltage pattens without (left) and with (middle) non-conductive target. Right is the difference in voltage pattern.

Voltage patterns for a change in conductivity

% Netgen simulation $Id: netgen_sims05.m 2787 2011-07-14 21:52:22Z bgrychtol $

subplot(211)
plot([vh.meas, vi.meas, vi.meas-vh.meas]);
print_convert netgen_sims05a.png '-density 100'

Figure: Voltage pattens without (green) and with (blue) non-conductive target. Red is the difference in voltage pattern.

Simple image reconstruction

% Netgen simulation $Id: netgen_sims06.m 4839 2015-03-30 07:44:50Z aadler $
subplot(221)

% Get a basic inverse model - replace the fwd model part
imdl = mk_common_model('a2c2',16); % the parameters aren't important because we replace it
imdl.fwd_model = img.fwd_model;

imgr = inv_solve(imdl, vh, vi);
show_fem(imgr);
axis equal; axis tight; print_convert netgen_sims06a.png '-density 100'

% Change the hyperparameter
imdl.hyperparameter.value = .05;
imgr = inv_solve(imdl, vh, vi);
show_fem(imgr);
axis equal; axis tight; print_convert netgen_sims06b.png '-density 100'

Figure: Image reconstructed with large (left) and smaller (right) hyperparameter value. Note that the expected resolution with nine electrodes isn't particularly good.