The forward problem in fetal electro/magnetocardiography

J. G. Stinstra and M.J. Peters
Twente University, Faculty of Applied Physics, Low temperature department,
PO Box 217, 7500AE Enschede, The Netherlands

Abstract: In order to estimate the influence of the volume conductor on fetal ECG and MCG, simulations with realistically-shaped models have been performed. The simulations show a large dependence of both the fetal ECG and the MCG on the individual volume conductor even when the fetus is located in a similar position.

INTRODUCTION

A fetal electrocardiogram is obtained by measuring the potential difference between two electrodes attached to the abdomen of a pregnant woman. A fetal magnetocardiogram is the recording of the magnetic field somewhere over the maternal abdomen. Fetal MCGs can be used to classify arrhythmia and to study congenital heart diseases. Currently, the detection and classification of fetal cardiac diseases using fetal MCGs is based on the cardiac rhythm and the time intervals within a fetal cardiac complex [1]. In order to use the amplitudes of the cardiac waves for diagnostic purposes, the influence of the volume conductor needs to be studied. Not only the amplitude of a complex is affected by the volume conduction process, but also the shape, the polarity and the ratios of the various peaks. In this paper, simulations are described that are used to estimate the influence of the volume conductor on a fetal MCG and ECG. One layer that is thought to influence the volume conductor problem is the layer of vernix caseosa, a fatty layer surrounding the fetus. This poorly conducting layer is segregated from the fetal skin and covers the fetus. Thence, the volume conduction problem will be divided into two, one for the period before the segregation of vernix caseosa and one for the period it covers the fetus. There is no solid evidence that the vernix caseosa is completely covering the fetus, as it seems unlikely that the fetus keeps its mouth closed. Fetal ECG measurements in combination with simulations suggest that likely candidates for holes in the layer vernix caseosa are the oronasal cavities and the onset of the umbilical cord [1]. These holes act as preferred pathways for currents. Hence, for the third trimester these holes have been included into the model.

METHOD

To compute the electric potential and the magnetic field, the boundary element method is used. A drawback of the boundary element method is the difficulty in producing accurate solutions when there is a thin, poor conducting, inhomogeneous layer involved, such as the vernix caseosa. To overcome the numerical problems a hybrid method is chosen, which combines the boundary element method with the finite difference method [1]. The division of the fetoabdominal volume into homogeneous compartments is based on knowledge of the conductivities. The highest conductivity in the abdominal volume is found in the amniotic fluid and the lowest in the vernix caseosa. In the present study, the abdominal volume conductor is split into four compartments the fetus (0.5S/m), the layer of vernix caseosa (10^-5S/m), the amniotic fluid (1.6S/m), and the remainder of the maternal abdomen (0.2S/m). To define the geometry of these four compartments, MR-images of pregnant women are used. In order to avoid the use of large amounts of elements the volume of arms and legs of the fetus are divided up into the fetal and amniotic fluid compartment.

RESULTS

In order to estimate the influence of inter-individual differences, the magnetic field and the surface potential have been computed for seven models. In Fig. 1 the results of the simulations are depicted for three models, two of the third trimester (both fetuses are in approximately the same position within the maternal abdomen) and one of the second. In the figure both the potential and the magnetic field (x-component) are depicted for three unitary dipoles. A frontal view of the model is given as well. The potential maps show that in the third trimester a dipole in the z-direction gives a much higher contribution than dipoles in the x- or y-direction.  The magnetic maps display a wide variety of patterns. For dipoles oriented along the y- and z-axis the overall pattern is the same, whereas for a dipole along the x-axis the patterns seem to be rotated over a wide variety of angles. Not only do the patterns change, the strengths of the fields vary over a wide range. For instance, the strength of the field generated by a current dipole along the z-axis in model 1B differs from those in model 1A and 2 by at least a factor 10.

		Unitary X-dipole	Unitary Y-dipole	Unitary Z-dipole
Model 1A Third trimester of pregnancy, including layer of vernix caseosa with holes near fetal mouth and onset of umbilical cord.	Potential
	Magnetic field
Model 1B Third trimester of pregnancy, including layer of vernix caseosa with holes near fetal mouth and onset of umbilical cord.	Potential
	Magnetic field
Model 2 Second trimester of pregnancy, without vernix caseosa present. Note potential is ten times larger	Potential	10X	10X	10X
	Magnetic field

Fig. 1: Simulations of the electric potential at the abdominal surface and the magnetic field component perpendicular to the abdomen at a distance of 2cm. For each of the models the mesh is depicted as well. The white lines in the figure indicate the position of the fetus and the uterus filled with amniotic fluid. The white dot indicates the position of the fetal heart. All figures depict a frontal view of the maternal abdomen. In the model without the layer of vernix caseosa, the surface potential is ten times as large as in the models which include this layer.

DISCUSSION

The ultimate goal of creating a model of the fetoabdominal volume conduction is to reconstruct the source(s) within the fetal heart. From our calculations it follows that both the layer of vernix caseosa and the volume of amniotic fluid play a dominant role in the volume conduction and should be incorporated in the models. As the conductivity of the amniotic fluid is higher than that of the other tissues, currents are restrained within the uterus. Only a small part of the volume currents will reach the surface of the abdomen generating fetal ECGs that may be too weak to be measurable. This effect is reinforced by the presence of a layer of vernix caseosa, restricting the currents even further.

REFERENCE

[1] Stinstra JG, The reliability of the fetal magnetocardiogram, PhD thesis, University of Twente. Enschede: Twente University Press, The Netherlands, 2001.