The Determination of Integral Epicardial Potential Maps by Non-Invasive Method

Alina Czerwinska

Institute of Biocybernetics and Biomedical Engineering PAS, Warsaw, Poland

Correspondence: A Czerwińska, Institute of Biocybernetics and Biomedical Engineering PAS, Ks.Trojdena 4, 02-109 Warsaw, Poland.
E-mail: Marek.Doros@ibib.waw.pl, phone +48 22 6599143 ex 411, fax +48 22 6597030

1.  Introduction

The aim of the researches of the heart field carried out by the computer simulation method is to provide the information supporting the cardiac diagnosis. The solved inverse problem of the electrical heart field allows, in non-invasive way, to determine the potentials on the heart surface i.e. the epicardial potentials for a given instant of ECG cycle [Czerwińska et al., 1998] or integrals of epicardial potentials calculated for the selected sections of ECG of examined patient. In works [Czerwińska, 2000, Czerwińska, 2002] there have been presented the results of investigations regarding the section QRS and ST of ECG. However, the current clinical investigations confirmed, that more information is obtained through analysis of the QRST section [Jagielski, 1998], therefore in this work the results just of that section of ECG are described.

2.  Applied Mathematical Model and Clinical Data

In the carried out investigations of the heart field using the simulation method there has been applied the mathematical model described below.

The examined field is described by following equation:

(1)

and boundary conditions:

(2)

 where:    - region between the heart surface and torso surface,   - potential generated by the heart, S  - torso surface, H  - heart surface,  - integral calculated for the assumed period of time t₁, t₂ of ECG cycle (section QRST), x    - vector of coordinates in .

Posed Inverse problem leads to the determining of the function (H), which will generate on the surface S the function (S). From a mathematical point of view there is searched the boundary condition, fulfilling the assumed (obtained from measurements and calculations) distribution of function  (S). For solving the problem posed such a way there has been elaborated the FEM method with non-linear regularization, described in [Demenko et al., 1995].

Applying above method there have been calculated the isointegral potential maps for 12 healthy patients and for 12 patients with confirmed ischemia disease. The measurements of the isointegral maps of surface potentials (using the HP 7100 system) have been carried out in the Department of Pathophysiology (the head – professor J Jagielski) of Medical Academy in Wrocław.

3.  Results and Conclusions

On a basis of carried out examinations, in which the isointegral maps have been applied there has been confirmed that:

-     in calculated isointegral maps of epicardial potentials for the healthy patients the two extremes occur,

-     in calculated isointegral maps of epicardial potentials for patients with myocardial ischemia concerning the non-proper kinesis there occur more then two extremes.

Also on a basis of examinations there have been observed the differences in regions of epicardial surface with decreased values of calculated integrals for healthy patients (~10%) and diseased patients (~30%). In cardiac practice the presented method is useful for:

-           preliminary examinations classifying the patients to further (invasive) examinations,

-           examinations during the drug therapy, monitoring the patient state, screening examinations.

As the example, in Fig.1 there have been presented the maps of the healthy patient: a) measured isointegral map of surface potentials, b) calculated as a result of simulation the isointegral map of surface potentials, c) calculated isointegral map of epicardial potentials. Analogously, in Fig.2 there have been presented the maps for the patient with ischemia disease.

Acknowledgements

This work was supported by National CSR Research Project No 4 T11E 014 24

References

Czerwińska A., Doros M., Kolebska K. Myocardially generated electrical field for non-invasive cardiac diagnosis”, Automedica, Vol. 16 pp. 245-261, 1998. 

Czerwińska A. Inverse problem of elektrocardiology with integral boundary conditions”, Proc. XXII Int. Workshop ASIS 2000, Sv. Hostyn (Czech Republic), pp. 9-13, September 2000.

Czerwińska A. The Laplacian Inverse Problem of Electrocardiology, Proc. XXIV Int. Workshop ASIS 2002, Krnov (Czech Republic), pp. 97-101, September 2002.

Demenko A., Czerwińska A. The finite element method with non-linear regularization to solve the inverse problem of electrocardiology (in Polish), Works of IBIB PAN, no 39, 1995.

Jagielski D. Usefulness of body surface potential maps for estimation of patients with post-infarcted aneurism of left ventricle (in Polish). PhD thesis, Medical Academy, Wrocław 1998.