# DYNAMIC MODEL OF THE THORAX
FOR ECG AND ICG STUDIES

J. Hyttinen^{1}, J.Lötjönen^{2},
P. Kauppinen^{1}, M. Saarilampi^{1}, R-K Mäenpää.^{1},
M Jerosch-Herold^{3}, J. Zhang^{3}, R. Patterson^{3},
J. Malmivuo^{1}

^{1}Ragnar Granit Institute, Tampere University of Technology

PO Box 692, 33101 Tampere, Finland

^{2 }VTT Information Technology, Human
Interaction Technologies, Tampere, Finland

^{3}University of Minnesota, Minneapolis, MN 55455,
USA

*Abstract: ***
A 3D model of the thorax as a volume conductor representing 18 time instances
of the cardiac cycle was constructed. The model is based on 18 sets of MR images
representing 56 slices with 0.5 cm slice distance. The image sets were segmented
on a two-stage process. The first time set of images was segmented based on
2D semiautomatic region growing method. The volumes occupied by 28 tissue types
were determined. In the second phase mapping of the voxels between the other
time instances were calculated based on deformable geometry models extending
the first segmentation to all 18 time instances. The segmentation is directly
useable for finite difference model. The model providing the dynamic properties
of the thorax will be applied for forward and inverse problem of electrocardiography
and simulation of the impedance cardiography and tomography.**

##### INTRODUCTION

The shape and the inhomogeneities of the human
thorax as a volume conductor affect the electric field generated by the heart.
Previously models of the thorax as a volume conductor has mainly been based
on static sets of thorax images. The dynamic changes of the geometry due to
the function of the heart, namely the changes of the geometry of the heart muscle
and the blood masses may be of importance in ECG simulation and inverse problem.
Lately the effects of diastole and systole have been studied. The effects of
these changes on ECG forward problem are substantial [1], however the inverse
localization of equivalent dipolar sources is less affected [2].
On the other hand, the inverse solution of the epicardial potential distribution
may largely be affected by the changes of the epicardial surface geometry.

Likewise, the impedance cardiography is based on
the measurement of the changes in the geometry and tissue impedance of the volume
conductor affected by the heart function. The properties of the measurement
systems can be estimated with static models [3], however, for the simulation
of the ICG signals a dynamic model is required.

**METHODS**

A Siemens Sonata scanner operating at a field strength
of 1.5 T (Tesla) located at University of Minnesota was employed for imaging.
This devise provides magnetic field gradients with a maximum amplitude of 40
mT/m, with a maximum slew rate of 200 mT/m/ms. The high quality full thorax
56 slice cine MRI images with 18 time frames were acquired with an ECG-gated,
gradient echo sequence, with steady-state free precession. The resolution was 256x256 with field of view 46x46cm. Due to the relatively
small size of the test person the 56 slices with 0.5 cm separation reached from
the neck to below the heart.

The images were segmented with a two-stage procedure.
At the first stage the first timeframe (T=1) of the 56 slice image sets was
segmented using the semiautomatic IARD method [4]. Altogether 28 distinct tissue
types were determined assigning a tissue code for every voxel (3D volume element).
Five MR slices and corresponding segmentations from the first time instant are
shown in Fig. 1 a) and b), respectively.

*Figure 1. Five MR slices a) and corresponding
semiautomatic IARD segmentations b) from the first time instant. The result
contains 28 compartments.*

At second stage a method based on deformable models
[5] utilizing the segmentation result of the first time instant was used to
segment the rest 17 phases. Deformable model is a volumetric template consisting
of two components: a gray-scale volume and triangulated surfaces of objects
of interest. The model is deformed using a non-rigid spatial transformation
in such a way that a similarity measure between the model and data to be segmented
is maximized. The transformation preserves the topology of the model. The similarity
measure consists of three terms: 1) the absolute value of the voxel-by-voxel
gray-scale difference between the model and data, 2) the overlap of similarly
oriented edges in the model and data and 3) the change of the model shape from
its original shape, which is used to regulate the maximization process. The
deformation is accomplished by optimizing the transformation locally inside
sphere shaped regions changing the location of the sphere and minimizing the
size of the sphere in this multiresolution maximization process.

In this study, the model is composed of MR slices
from one time instant (Fig. 1a) and the triangulated surfaces extracted from
the corresponding segmentation result (Fig. 1 b). The model built from the time
instant one (T=1) is matched to the second set (T=2). This spatial transformation
is applied to the IARD segmented set producing a segmentation for the set (T=2).
While segmenting the set (T=3), the set (T=2) is regarded as a model. The procedure
is repeated until all sets (T=1,..,18) have been segmented.

*Figure 2. A segmentation at time step T=5. a) The transformed model and the original MR volume are shown using a chess-board visualization, b) the transformation is visualized by an elastic grid superimposed on the data. c) the result.*

**RESULTS**

Fig. 2 demonstrates a segmentation result for the
set (T=5). The transformed model and the original MR set are shown using a chess-board
visualization technique in Fig. 2a, i.e. the areas shown from the deformed model
and from the original data vary as the black and white areas in the chessboard.
The length of a block edge is 10 voxels. If the match was not good, it would
be seen as discontinuous edges in the picture. Because the deformations between
consecutive time instants are small compared to the size of the thorax, Fig.
2a demonstrates actually the sum of four transformations from T=1 to T=5, when
the model was the volume T=1. Nevertheless, discontinuities are hardly visible
in the result. The transformation is visualized in Fig. 2b by an elastic grid
superimposed on the data. The segmentation result is shown in Fig. 2c. The segmented
voxels are directly applicable to form an FDM model of the thorax as a volume
conductor.

**CONCLUSION **

The whole data consists of 18 different time instances,
thus as many models with small changes in geometry were constructed. The material
with 18 models will provide computational challenges. However, since the outer
surface of the model is unchanged and thus element structure of the FDM cubic
grid is unchanged, the FDM solver can use the results from the previous time
step as an initial value to calculate the next step. This sequential calculation
will evidently improve the otherwise relatively slow computational method.

The voxel based segmentation provides an excellent data
to form an FDM model. However, the deformable model based 3D segmentation produce
triangulated surface data as well. This would serve well for construction of
boundary of finite difference models.

In near future the data will be available for the research
community via DYNAMO web page (www.tut.fi/dynamo).

*Acknowledgments:*** **Work supported by Academy
of Finland, Emil Aaltonen Foundation, Finnish Cultural Foundation and Ragnar
Granit Foundation.

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