EIDORS: Electrical Impedance Tomography and Diffuse Optical Tomography Reconstruction Software

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Using EIDORS to image gastric emptying

2D EIT for imaging of gastric emptying

Trudelle, Stéphane, Évaluation de la vidange gastrique par tomographie d'impédance électrique, Thesis (M.Sc.A.)--École polytechnique de Montréal

A. Adler, R. Guardo, Y. Berthiaume Imaging of Gastric Emptying with Electrical Impedance Tomography Canadian Medical and Biolological Eng. Soc., Vancouver, Canada, May 1994. 20:14-15.

Step 1: Create models

% Lung images
% $Id: tutorial410a.m 1535 2008-07-26 15:36:27Z aadler $

% 2D Model
imdl= mk_common_model('c2t3',16);


% most EIT systems image best with normalized difference
imdl.fwd_model.normalize_measurements= 1;
imdl.RtR_prior= @gaussian_HPF_prior;

% electrodes start on back (dorsal), then do this
imdl.fwd_model.electrode([9:16,1:8])=  ...
   imdl.fwd_model.electrode;


subplot(221);
show_fem(imdl.fwd_model);

axis equal
print -r100 -dpng tutorial410a.png;

Figure: 2D FEM of thorax (units in mm). Electrode #1 (o) and electrode #2 (o) are shown in different colours than the others (o).

Image reconstruction

% Lung images
% $Id: tutorial410b.m 1535 2008-07-26 15:36:27Z aadler $

load montreal_data_1995
imdl.hyperparameter.value=5e-2;
vh= zc_h_stomach_pre; % abdomen before fluid
vi= zc_stomach_0_5_60min; % each 5 minutes after drink
img= inv_solve(imdl, vh, vi);

clf; show_slices(img)
axis equal

print -r100 -dpng tutorial410b.png;

Figure: Image slices of the abdomen every five minutes after drink. Image progression is from left to right, top to bottom.

Calculate signal as a function of time

% Lung images
% $Id: tutorial410c.m 1535 2008-07-26 15:36:27Z aadler $

raster_img= calc_slices(img);
raster_img(isnan(raster_img))=0;
% define roi as whole image
s_ri = size(raster_img);
roi = ones(s_ri(1:2));

for i= 1:s_ri(3)
  sig(i)= sum(sum(raster_img(:,:,i) .* roi));
end

subplot(221)
plot( ((1:s_ri(3))-1)*5, sig/sig(1))
xlabel('minutes after drink')
ylabel('normalized conductivity');

print -r125 -dpng tutorial410c.png;

Figure: Normalized image in stomach as a function of time.

Different algorithms for stomach images

% Lung images
% $Id: tutorial410d.m 1535 2008-07-26 15:36:27Z aadler $

load montreal_data_1995
vh= zc_h_stomach_pre; % abdomen before fluid
vi= zc_stomach_0_5_60min(:,1); % right after drink

% GN solution - Gaussian prior
imdl.RtR_prior= @gaussian_HPF_prior;
imdl.solve=     @aa_inv_solve;
imdl.hyperparameter.value=1e-2;
img= inv_solve(imdl, vh, vi);

subplot(221); show_fem(img); axis equal; axis off

% GN solution - Noser prior
imdl.RtR_prior= @noser_image_prior;
imdl.solve=     @aa_inv_solve;
imdl.hyperparameter.value=8e-2;
img= inv_solve(imdl, vh, vi);

subplot(222); show_fem(img); axis equal; axis off

% GN solution - Noser prior
imdl= rmfield(imdl,'RtR_prior');
imdl.R_prior=   @ab_calc_tv_prior;
imdl.solve=     @ab_tv_diff_solve;
imdl.hyperparameter.value=1e-2;
img= inv_solve(imdl, vh, vi);

subplot(223); show_fem(img); axis equal; axis off

% GN solution - Noser prior
imdl.R_prior=   @ab_calc_tv_prior;
imdl.solve=     @ab_tv_diff_solve;
imdl.hyperparameter.value=1e-1;
img= inv_solve(imdl, vh, vi);

subplot(224); show_fem(img); axis equal; axis off


print -r100 -dpng tutorial410d.png;

Figure: Top Left: Gauss-Newton Reconstruction with Gaussian HPF prior Top Right: Gauss-Newton Reconstruction with Laplacian filter Bottom Left: Total Variation Reconstruction (hp=1e-3) Bottom Right: Total Variation Reconstruction (hp=1e-4)