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International Journal of Bioelectromagnetism
Vol. 4, No. 2, pp. 81-82, 2002.

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J. Hyttinen1, J.Lötjönen2, P. Kauppinen1, M. Saarilampi1,  R-K Mäenpää.1, M Jerosch-Herold3, J. Zhang3, R. Patterson3, J. Malmivuo1

1Ragnar Granit Institute, Tampere University of Technology
PO Box 692, 33101 Tampere, Finland
2 VTT Information  Technology, Human Interaction Technologies, Tampere, Finland
3University 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.


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.


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.


 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.


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.


 [1] Puurtinen H-G, Hyttinen J, Kauppinen P, et al.. ”Including Anatomical Changes Due to Cardiac Function into a Model of a Human Thorax as Volume Conductor,” Med. & Biol. Eng. & Comput., 1999; vol 37 Suppl 1: 234-235

[2] Puurtinen H-G, Hyttinen J, Kauppinen P, et al.. ”Dependency of the Inverse ECG Solutions on the Number of Electrodes - Effects of Modeling Error and Measurement Noise,”  in Proceedings of the 3rd International Conference on Bioelectromagnetism, 7-8.9.2000: 65-66.

[3] Kauppinen P, Kööbi T, Kaukinen S,et al..”Application of Computer Modelling and Lead Field Theory In Developing Multiple Aimed Impedance Cardiography Measurements,” J. of Med. Eng.& Techn., 1999; vol 23: 169-177.

 [4] Heinonen T, Eskola H, Dastidar et al.. ”Segmentation of T1 scans for reconstruction of resistive head models”. Comp Methods Prog Biomed 54:173, 1997.

[5] Lötjönen J.  “Segmentation of MR Images using Deformable Models: Application to Cardiac Images, ”  IJBEM, 2001;vol3 num 3. (http://www.ee.tut.fi/rgi/ijbem/).


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