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Fetal ECG Recovery Using Dynamic Neural
Networks with FIR Synapses

G. Camps, M. Martínez, E. Soria, L. Gómez,
J. Calpe, J. Guerrero, J. Muñoz

Grupo de Procesado Digital de Señales, Universidad de Valencia, España

RESUMEN

SUMMARY
Introduction: Non-invasive electrocardiography reveals itself as a very interesting method to obtain reliable information about the fetus' state thus assuring his well being during pregnancy.
Objectives: In this communication a Finite Impulse Response (FIR) neural network is included in the familiar Adaptive Noise Cancellation (ANC) scheme in order to provide with highly non-linear dynamic capabilities to the recovery model. Results from its application to both simulated and real registers are shown and benchmarked with classical algorithms (LMS and NLMS). Since the maternal contribution to the abdominal signal is obviously unknown in real registers, a method to generate simulated signals can be adopted and a novel methodology for models' identification is also presented.
Methods: The ability of this network to deal with temporal patterns led us to consider its inclusion in the familiar ANC scheme. In this approach, the FIR neural network models the maternal abdominal component from a thoracic reference. The error reference constitutes the recovered fetal signal. The FIR network models each weight as a basic FIR linear filter that can be modeled with a tapped delay line. The popular cross-validation method has been used to select the optimal network structure and the correlation coefficient has been adopted as a measure of fit.
Results: In Figure 1A and 1B performance with synthetic and real registers is shown.

Figure 1A and 1B. Synthetic registers: (a) SNRfm=-5, SNRfn=100 (b) SNRfm=-20, SNRfn=10. Real registers (c) y (d). Arrow markers indicate some maternal contributions that are not completely removed by the NLMS algorithm.

The best topology identified using synthetic registers has not proven to be exactly the optimal one to use with real registers and therefore, simulations of some other real conditions become necessary.
Conclusions and Discussion: In this communication an FIR neural network was included in the familiar ANC structure for the FECG extraction. A methodology for topology selection was also presented. This network has solved complex situations more reliably than classical adaptive methods.

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INTRODUCTION
   Since the early work of Cremer in 1906 [1], various methods for foetal monitoring have been proposed to obtain information about the foetal heart status. Non-invasive fetal electrocardiography reveals itself as a very interesting method to obtain reliable information about the fetus' state and thus assure his well being during pregnancy. This technique has the additional advantage that no energy is supplied to the fetus and thus long-term studies can be accomplished. The main noise contribution is the maternal electrical activity since its amplitude is much higher than that of the fetus. In addition, the spectra of both maternal and foetal signals overlap; it is consequently not possible to separate them through conventional frequency selective filtering. Numerous methods have been used for the maternal signal cancellation: substraction of an averaged pattern [2], adaptive filters [3], etc. An early approach to the use of classical neural networks to FECG extraction was presented in [4] but only a single register was used.

OBJECTIVES
   In this communication a Finite Impulse Response (FIR) neural network is included in the familiar Adaptive Noise Cancellation (ANC) scheme in order to provide with highly non-linear dynamic capabilities to the recovery model. Results from its application to both simulated and real registers are shown and benchmarked with classical algorithms (LMS and NLMS). Since the maternal contribution to the abdominal signal is obviously unknown in real registers, a method to generate simulated signals can be adopted and a novel methodology for models' identification is also presented.

METHODS
   One of the most commonly used approaches to FECG recovery is based on adaptive filters and uses an ANC structure as illustrated in Figure 1.

  The reference input, x(i), is a thoracic maternal signal which is assumed to be free from foetal contributions, while the desired signal, d(i), is the abdominal signal. In this way, all the correlated components (maternal signal) vanish and the FECG register is obtained as the error signal, e(i). The essence of such a scheme is the principle of orthogonality [5].

   An extension to this basic adaptive structure is provided by the use of neural networks. A multilayer perceptron extends the use of the static neuron and forms a complex mapping from the input of the first layer to the output of the last layer [6]. It is, nevertheless, a static mapping; there are no internal dynamics. In order to introduce dynamic capabilities in a static neural network we have substituted the static synaptic weights by dynamic connections (FIR synapses).

The FIR Neural Network
   The ability of this network to deal with temporal patterns led us to consider its inclusion in the familiar ANC scheme. In this approach, the FIR neural network models the maternal abdominal component from a thoracic reference. The FIR network models each weight as a basic FIR linear filter [7]. This filter can be modeled with a tapped delay line as illustrated in Figure 2a.

   In a FIR filter, the output y(k) corresponds to a weighted sum of past delayed values of the input (Figure 2b).

    The coefficients for the synaptic filter connecting neuron i to neuron j in layer l are specified by the vector wijl=[wi,jl(0), wi,jl(1),..., wi,jl(Tl)]. Similarly xil(k)= [xil(k), xil(k)1,..., xil(k-Tl)] denotes the vector of delayed states along the synaptic filter. This allows us to express the operation of a filter by a vector dot product wijl · xil(k), where time relations are now implicit in the notation. The output xjl +1(k) of a neuron in layer l at time k is now taken as the sigmoid function of the sum of all the filter outputs which feed the neuron (Figure 3)

   (Figure 4) There are striking similarities in appearance between this equation and that of a static model. Notationally, scalars are replaced by vectors and multiplications by vector products. These simple analogies carry through when comparing standard backpropagation for static networks with temporal backpropagation for FIR networks [6,8].

Identification methodology
   It is a common practice to evaluate a FECG recovery model through visual inspection of the algorithm performance. Since the maternal contribution to the abdominal signal is obviously unknown in real registers, a method to generate simulated signals can be adopted. This constitutes a novel methodology for the identification of the model and allows interesting advantages: (1) to define accuracy measures in order to benchmark different models and decide, over a wide range of situations, which one can offer a more robust solution and (2) A great many trainings are thus done and useful information about the range of optimal free parameters can be obtained. Synthetic signals, nevertheless, are intended to represent a wide range of real-life registers but extrapolation to real registers must be verified. This will allow assessment, in principle, of whether the simulated signals are useful or not in the identification of a model.

Synthetic registers
   A MATLAB™ function has been developed to generate two different abdominal composite signals and a reference thoracic signal from two real registers with two leads each. Its programmable parameters are the foetal/maternal (SNRfm), the foetal/Gaussian noise (SNRfn) and the foetal/electromyogram (SNRfe) signal-to-noise ratios together with the addition of base-line wander (BW) and power line interference (PLI). Twenty-four registers have been generated with the following adjustable parameters. SNRfm was varied from -5 to -30 dB with a -5 dB step and the following discrete values of SNRfn were used: {100, 15, 10, 5} dB. A wide range of real-like situations can nevertheless be afforded varying the SNRfm and SNRfn parameters. In addition to these simulated signals, we have also used two real registers to validate the methodology.

RESULTS
  Table 1 shows the best results for different synthetic situations (registers).

   A slight improvement can be appreciated using the FIR neural network compared to the NLMS algorithm, specially significant with low values of SNRfm. However, this improvement locates precisely on the maternal elimination and thus, the recovered signal appears rather cleared from spurious peaks. Figure 5A and 5B shows performance with synthetic and real registers.

   The best topology identified using synthetic registers has not proven to be exactly the optimal one to use with real registers and therefore, simulations of some other real conditions become necessary.

CONCLUSIONS AND DISCUSSION
   In this communication an FIR neural network was included in the familiar ANC structure for the FECG extraction. A methodology for topology selection was also presented. This network has solved complex situations more reliably than classical adaptive methods.

REFERENCES

1. Deam A. The use of foetal electrocardiogram. Am J Obstet Gynecol. 1994;101:9-17.

2. Budin N, Abbound S. Real-Time multichannel abdominal foetal ECG monitor using a digital signal coprocessor. Comp Biol Med 1994;24:451-462.

3. Widrow B, Glover J, MacCool J, Kaunitz J, Williams C, Hearn R, Zeidler J, Dong E, Goodlin R. Adaptive Noise Cancelling: Principles and Applications. Proc IEEE. 1975;63(12):1692-1716.

4. Lin J-H, Chang J-S, Chiueh, T-D. Heterogeneous Recurrent Neural Networks. IEICE Transactions on Fundamentals. 1998:E81-A(3):489-499.

5. Haykin S. Adaptive Filter Theory. In Prentice Hall, Englewood Cliffs, N. J. 1991.

6. Rumelhart DE, McClelland JL, PDP Research Group. Parallel Distributed Processing: Explorations in the Microstructure of Cognition. In Cambridge, MA: MIT Press, 1986.

7. Wan EA. Finite Impulse Response Neural Networks with Applications in Time Series Prediction. PhD Thesis. Department of Electrical Engineering. Stanford University. 1993. Available at http://www.ece.ogi.edu/~ericwan/

8. Weigend AS, Gershenfeld NA Time Series Prediction. Forecasting the Future and Understanding the Past. In Proceedings of the NATO Advanced Research Workshop on Comparative Time Series Analysis held in Santa Fe, New Mexico, May 14-17, 1992. Proceedings Volume XV. 1994. Addison-Wesley.

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Extracción del ECG Fetal Mediante Redes Neuronales Dinámicas con Sinapsis FIR

RESUMEN
Introducción: La electrocardiografía fetal no invasiva se presenta como un método muy interesante en la monitorización del estado del feto, ya que, de dicha señal, se puede extraer información no sólo de su ritmo cardíaco sino que además es posible la medida de parámetros morfológicos que reflejen sus cambios metabólicos. La principal interferencia a cancelar presente en las señales adquiridas es la contribución de la actividad eléctrica materna.
Objetivos: En esta comunicación se propone la inclusión de una red neuronal FIR en la popular estructura del cancelador activo de ruido adaptativo (ANC) como nuevo método de extracción del electrocardiograma fetal. Los resultados se comparan con los obtenidos mediante métodos clásicos (LMS y NLMS). Se describe el procedimiento utilizado para fijar los parámetros de funcionamiento del modelo y los resultados obtenidos al aplicarlo sobre registros simulados y reales.
Método: La red FIR deberá modelizar la componente materna abdominal a partir de una referencia torácica. Para la identificación de la mejor arquitectura se han empleado como guía los resultados obtenidos mediante validación cruzada al emplear registros simulados en los que se puede variar las relaciones señal-ruido fetal-materna (SNRfm) y fetal-ruido (SNRfn). El mismo proceso se ha realizado con las señales reales para comprobar la validez de la identificación.
Resultados: En la Figura 1A y 1B mostramos la actuación sobre registros reales y simulados.

Figura 1A y 1B. Registros sintéticos: (a) SNRfm=-5, SNRfn=100 (b) SNRfm=-20, SNRfn=10. Registros reales (c) y (d) donde las flechas indican errores de algoritmo NLMS en la cancelación de la señal materna.

Aunque la metodología ha sido de gran ayuda para reducir el coste computacional, la mejor topología identificada no es la idónea al aplicarla sobre registros reales.
Conclusiones y Discusión: La utilización de redes neuronales dinámicas para la cancelación de la interferencia materna supone una generalización de la estructura del cancelador activo de ruido. Este método proporciona buenos niveles de cancelación materna, mejorando los obtenidos con métodos clásicos como el NLMS.


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2nd Virtual Congress of Cardiology

Dr. Florencio Garófalo
Steering Committee
President
Dr. Raúl Bretal
Scientific Committee
President
Dr. Armando Pacher
Technical Committee - CETIFAC
President
fgaro@fac.org.ar
fgaro@satlink.com
rbretal@fac.org.ar
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