Blind source separation (BSS) techniques are widely used to extract signals of interest from a mixture with other signals, such as extracting fetal electrocardiogram (ECG) signals from noninvasive recordings on the maternal abdomen. These BSS techniques, however, typically lack possibilities to incorporate any prior knowledge on the mixing of the source signals. Particularly for fetal ECG signals, knowledge on the mixing is available based on the origin and propagation properties of these signals. In this paper, a novel source separation method is developed that combines the strengths and accuracy of BSS techniques with the robustness of an underlying physiological model of the fetal ECG. The method is developed within a probabilistic framework and yields an iterative convergence of the separation matrix towards a maximum a posteriori estimation, where in each iteration the latest estimate of the separation matrix is corrected towards a tradeoff between the BSS technique and the physiological model. The method is evaluated by comparing its performance with that of FastICA on both simulated and real multichannel fetal ECG recordings, demonstrating that the developed method outperforms FastICA in extracting the fetal ECG source signals.

Current fetal monitoring mainly relies on the cardiotocogram (CTG); the simultaneous registration of fetal heart rate; and uterine activity. Unfortunately, in many cases the information provided by the CTG is insufficient. In these cases, obstetricians have to rely on other sources of information or on their intuition and experience to make the optimal treatment plan. A valuable complementary source of information is provided by the fetal electrocardiogram (ECG) [

Although these abdominal recordings are a promising candidate for use in fetal monitoring, their widespread use is impeded by the quality of the fetal ECG signals which is typically poor. Specifically, each signal recorded from the maternal abdomen consists of a mixture of signals, including the fetal ECG, maternal ECG, activity of abdominal muscles and uterus, and interferences from external sources. Several methods to extract the fetal ECG from such mixtures have been proposed in the literature [

One of the reasons for poor robustness with respect to signal quality lies in the fact that ICA assumes no

In this paper, we follow the approach by Knuth and develop a probabilistic framework to derive a generic source separation technique. This technique allows for inclusion of

In Section

When we assume a fetal ECG recording of

Using Bayes’ rule, the probability that the source model of (

The expression in the denominator of (

As mentioned previously, the goal of the source separation method is to obtain the source signals

In the context of this probabilistic description, the challenge of source separation methods is to infer

Until here, we have followed the descriptions of Knuth [

When recorded relatively far away from the heart, the electrical activity of the heart can be approximated by an electrical dipole

The electrical dipole

We can rewrite (

Finally, to facilitate an analytical solution to the source separation problem, we ignore the dependence of the scaling

We can express our belief in the mixing model of (

When, for reasons of mathematical simplification, we assume the elements of the mixing matrix to be mutually independent, we can write

For the other conditional probability distribution in (

Combining (

As mentioned in Section

When we consider the posterior probability distribution of (

As a first step to solve the inference problem, we follow Bell and Sejnowski [

Taking logarithms on either side gives

For clarity, we introduce the estimated sources

The optimal unmixing matrix

When implementing the proposed source separation method, singularities can arise due to a finite numerical accuracy in estimating the error functions in the denominator of (

To avoid such singularities, we can approximate the error function by [

Implementation of this approximation in MATLAB resolves the issue with finite numerical accuracy of the error function, no longer yielding zero difference when both

In Section

For fetal ECG recordings, inaccuracies in the prior model arise from noise in the ECG signals or from erroneous assumptions with respect to the uniform propagation properties of the volume conductor or with respect to the sphere-like shape of the pregnant abdomen with the fetal heart in the center. These model inaccuracies can be tested by using the prior model to estimate

The difference signal

This expression implicitly assumes that

To account for changes in the circumstances during the fetal ECG recording, for example, when the mother is having uterine contractions, the variance is determined within a sliding window of 2 seconds.

The developed probabilistic source separation method is evaluated by assessing its performance in extracting fetal ECG source signals from noninvasive recordings. The performance is evaluated by comparing it with that of a widely used ICA method: FastICA [

Example of a simulated 6-channel fetal ECG recording.

To evaluate the developed source separation method for various degrees of signal quality, the signal to noise ratio (SNR) is varied between −10 and +30 dB. For each SNR, the evaluation is repeated 20 times to suppress the influence of the randomly determined mixing matrix. That is, in each repetition the mixing matrix is determined by picking its coefficients from a Gaussian distribution with unit variance.

Example of real 8-channel fetal ECG recording. In this recording, the maternal ECG has already been removed using an adaptive template subtraction method [

In our simulations, the performance of the source separation methods is quantified in terms of the normalized mean squared error

The performance in separating sources in actual fetal ECG recordings is determined by assessing the ability of a peak detection algorithm to determine the fetal heart rate. The employed peak detection algorithm is based on a continuous wavelet transform [

With fetal heart rate detected, further enhancement of the fetal ECG can be achieved by (adaptively) averaging various consecutive ECG complexes, for example, as described in [

In Figure

Results of source separation by the developed ISS method and FastICA for SNR of 6 dB. Each panel represents one of the three orthogonal ECG sources. In each panel, the top line represents the ECG source used in the simulation, the center line represents the corresponding source extracted by the ISS method, and the bottom line represents the corresponding source extracted by FastICA. The simulated fetal ECG recording used in the source extraction was depicted in Figure

In Figure

Performance of both source separation methods as a function of the SNR of the simulated recordings. Each depicted data point is the mean over 20 simulations with random mixing matrix. The standard deviations over these 20 simulations, although often too small to see in the graph, are also plotted.

In Figure

The upper plot shows a recorded and annotated fetal ECG signal. This depicted signal was preprocessed as described in Section

In total, 1532 ECG peaks have been annotated by the clinical expert in the 10-minute long abdominal recording. The performance of the employed peak detection algorithm in finding all these peaks in the ISS estimated fetal ECG source signal is

As mentioned in Section

The abovementioned tradeoff between ICA and physiology can also be regarded as a tradeoff between accuracy and robustness. We have illustrated this by applying our method to high-quality, yet realistic, (simulated) fetal ECG recordings and to lower-quality, but commonly more frequently encountered, (real) fetal ECG recordings. The statement of lower quality for the real recordings is based on visual comparison of Figures

In this paper, the developed ISS method was applied to extract fetal ECG sources from preprocessed abdominal recordings. This preprocessing includes suppression of the maternal ECG and in this paper we used a template-based method to do this. As an alternative approach, others have used BSS techniques to extract fetal ECG sources directly from (unprocessed) abdominal recordings [

In this paper, a source separation technique for fetal ECG signals was developed that exploits prior knowledge on the signal mixing. When critically examining the presented solution to the source separation problem, it shows that the developed technique is similar to the Bell and Sejnowski [

With respect to FastICA, the developed method performs better in retrieving the ECG sources in simulated and real fetal ECG recordings. More extensive evaluation of the developed method is however required to conclusively state about its performance, for example, in case of poorly determined electrode positions.

This work was supported by the Dutch Technology Foundation STW.