Effects of Reducing the Full-Body Surface to a Torso Model in Forward and Inverse Electrocardiography

R. Martin Arthur^a, Krisha J. Timbadia^a, Ali Rauf^a, and Jason W. Trobaugh^ab

^aElectronic Signals and Systems Research Laboratory, School of Engineering and Applied Science,
^bDepartment of Medicine, School of Medicine, Washington University in St. Louis, USA

Correspondence: RM Arthur, Department of Electrical Engineering, Washington University in St. Louis, Campus Box 1127,
One Brookings Drive, St. Louis, MO 63130. E-mail: rma@ee.wustl.edu, phone +001 314 935 6167, fax +001 314 935 7500

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1.  Introduction

Torso models are used to study forward and inverse problems in electrocardiography. Previously, we showed that those models should be individualized [Arthur et al., 1999]. Here we report the effects on both forward and inverse solutions of reducing the full-body surface to a torso model. Our objective was to find the increase, if any, in relative error that could be attributed to surface-reduction practices that are commonly employed.

2.  Material and Methods

To generate full-body and torso models for comparison we segmented color images of the Visible Human Male [Spitzer et al., 1996] in 1-cm steps from head to toe as shown in Fig. 1. This surface was systematically reduced to form the torso models shown in Fig. 2. Positions of 163 simulated electrodes are shown in Fig. 2. They were at the same position in all torso models, as well as on the full body. The heart of the Visible Human Male was also segmented at 1-cm intervals to form the heart model shown in Fig. 2.

Transfer-coefficients were calculated for the 93-node heart surface to all body surfaces using the method of Barr and coworkers [Barr et al., 1977]. Transfer coefficients were compared at the electrode sites to assess forward-problem effects of full-body reduction to torso models.

To assess effects on the inverse problem, inferred potentials were compared to known values. Known heart-surface potentials were taken from 90-electrode sock recordings in an adult male during normal sinus rhythm. Sock-electrode recording were mapped to the heart model using methods described previously [Arthur et al., 1999].

Body-surface potentials were calculated, rather than recorded, at the designated electrode locations in the full body. Body-surface potentials, , were found from the known heart-surface potentials, , using the forward-problem expression (see Fig. 1),

                                                                                                                                                   (1)

Inferred heart-surface potentials were found using zero-order Tikhonov regularization.

Figure 1. The Visible Human Male with calculated ECG distribution near the peak of the QRS complex.

      (2) 

where t, the regularization parameter, was the optimal value and noise  was added to the calculated surface potentials. The noise level was 1 % of the rms value of the surface potentials over the QRS complex.

3.  Results

Relative errors of forward-problem solutions compared to the full-body results at the same 163 electrode sites were 0.024, 0.026, and 0.027 for models with successive removal of arms and legs (TM#1), head and pelvis (TM#2), and shoulders (TM#3), respectively. Relative errors of inverse solutions near the peak of the QRS complex with 1 % noise added to body-surface potentials increased from 0.34 for the full body, to 0.40, 0.42, and 0.42 in the reduced-surface models. Over the QRS complex the relative error increased from 0.46 for the full body, to 0.56 in all three reduced-surface models.

4.  Discussion

Figure 2. Torso models. TM#1 is the full body without arms and legs. TM#2 is TM#1 without head, neck and pelvis. TM#3 is TM#2 without shoulders. TM#2 shows the electrode sites used on all models. TM#3 includes the heart model used in all body models.

The increase in relative error of the inverse solutions due to reduction of the body surface to form torso models was about 20%. Most of this increase occurred with the removal of arms and legs and did not significantly increase with the additional removal of head, pelvis, and shoulders. Presumably modeling the torso surface in the vicinity of the heart has the greatest impact and should be the subject of further study. These findings also suggest that in addition to the need for individualizing torso models as shown previously [Arthur et al., 1999], care must be taken in the process of extracting the torso model from the full body for each subject.

Acknowledgements

This work was supported in part by National Institute of Health grant R01-50295 and by the Wilkinson Trust at Washington University.

References

[1] Arthur RM, Beetner DG, Ambos HD, Cain ME. Improved estimation of pericardial potentials from body-surface maps using individualized torso models. J. of Electrocardiology, 31(Suppl): 106-113, 1999.

[2] Spitzer V, Ackerman ML, Scherzinger AL, Whitlock D. The visible human male: A technical report. J Am Med Inform Assoc, 3(2): 118-130, 1996.

[3] Barr RC, Ramsey III M, Spach MS. Relating epicardial to body surface potential distributions by means of transfer coefficients based on geometry measurements. IEEE Trans on Biomed Eng, BME-24: 1-11, 1977.