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 3340 2012-07-01 21:25:30Z bgrychtol $

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


% most EIT systems image best with normalized difference
imdl.fwd_model = mdl_normalize(imdl.fwd_model, 1);
imdl.RtR_prior= @prior_gaussian_HPF;

% 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_convert 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

% Abdomen Images  $Id: tutorial410b.m 4839 2015-03-30 07:44:50Z aadler $

load montreal_data_1995
imdl.hyperparameter.value=.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_convert 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

% Abdomen Images  $Id: tutorial410c.m 3273 2012-06-30 18:00:35Z 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_convert tutorial410c.png '-density 150';

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

Different algorithms for stomach images

% Abdomen Images $Id: tutorial410d.m 4839 2015-03-30 07:44:50Z 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= @prior_gaussian_HPF;
imdl.solve=     @inv_solve_diff_GN_one_step;
imdl.hyperparameter.value=.1;
img= inv_solve(imdl, vh, vi);

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

% GN solution - Noser prior
imdl.RtR_prior= @prior_noser;
imdl.solve=     @inv_solve_diff_GN_one_step;
imdl.hyperparameter.value=.3;
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=   @prior_TV;
imdl.solve=     @inv_solve_TV_pdipm;
imdl.hyperparameter.value=3e-4;
img= inv_solve(imdl, vh, vi);

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

% GN solution - Noser prior
imdl.R_prior=   @prior_TV;
imdl.solve=     @inv_solve_TV_pdipm;
imdl.hyperparameter.value=3e-3;
img= inv_solve(imdl, vh, vi);

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


print_convert tutorial410d.png '-density 150';

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)