Image Reconstruction for 3D Lung Imaging - Department of Systems ...

while the lung conductivity (σL) was varied. Simulation data were calculated to model the
EIT difference measurements due to introduction of a small tidal volume (∆V ) at different
levels of baseline σL. Since the relationship between σL and lung volume (VL) is not precisely
known in vivo [94], we model lung conductivity as inversely proportional to VL. For a small
∆V we make the following approximation:
σL
σ =
1 + ∆V/VL
≈ σLe −∆V /VL
Using this approximation, tidal volume, ∆V , constitutes a constant decrease in log conductivity.
Difference measurements are simulated for inspiration and expiration as:
vinsp = F(σLe −∆V /VL )
vexp i = F(σL)
Simulations were conducted for ∆V/VL = 10% over a range of 20 values from 5 mS/m to
2000 mS/m. This large non-physiological range was simulated in order to clarify the trend
of the results. The reference frame was taken at the background lung conductivity.
A.2.3 Evaluation Procedure
Six sets of reconstructions were calculated using a 1968 element 2D finite element model.
Images were reconstructed from the simulated data and using three different reconstruction
algorithms: 1) using a homogeneous σ0, 2) using σ0 with physiological values and σ0 at its
inspiration value (60 mS/m) (∆VEIT,Inspi), and 3) using σ0 with physiological values and
σL matching σL that was used to simulate the data ∆VEIT,Simul. In the third algorithm
the area of the non-homogenous region, AσL of the FEM was varied; thus four sets of
reconstructions were calculated with areas of AσL = 33%, AσL = 51%, AσL = 73%, and
AσL = 86% as shown in figure A.2. Thus the single set of 20 simulated measurements was
used to reconstruct six sets of 20 images.
An EIT estimate of tidal volume, ∆VEIT, was then calculated by summing all pixels of
the 2D FEM weighted by the pixel’s area. ∆VEIT = E�
Aiσi where Ai is the area/volume
of element i and σi is the conductivity of element i.
A.3 Results
Figure A.3 shows four plots of image amplitude vs baseline lung conductivity, σL, for each
algorithm. The different subplots correspond to non-homogenous Jacobians of differing
area. The two curves for the homogenous Jacobian algorithms (blue and black lines) are
the same in each of the subplots.
The results for ∆VEIT −Homo (black curve) are consistent with those of Kunst et al
[83]. Image amplitude for the same proportional volume change increases dramatically with
increasing baseline (starting/initial) lung conductivity; there is a large increase in image
amplitude as σL increases from 60 mS/m to 120 mS/m. Use of constant but physiologically
realistic values reduces the dependence only slightly (blue curve). The use of parameters
that match the simulation (red curve) results in significant decrease in the dependence on
σL. However the effect is strongly dependent on the area of the inhomogeneity of the reconstruction
mesh used to calculate the Jacobian. Figure 8.3(a), in which the inhomogeneous
area, Aσˆ L is 33%, shows a strong dependence on σL for σL < 120 mS/m but becomes
121
i=1