W. Zgallai

Higher-order ambulatory electrocardiogram identification and motion artifact suppression with adaptive second- and third-order Volterra filters

The objective of this paper is to demonstrate how, in a few seconds, a relatively simple ECG monitor, PC and advanced signal processing algorithms could pinpoint microvolts - late potentials - result from an infarct zone in the heart and is used as an indicator in identifying patients prone to ventricular tachycardia which, if left untreated, leads to ventricular fibrillation. We will characterize recorded ECG data obtained from the standard three vector electrodes during exercise in terms of their higher-order statistical features. Essentially we use adaptive LMS- and Kalman-based second- and third-order Volterra filters to model the non- linear low-frequency P and T waves and motion artifacts which might overlap with the QRS complex and lead to false positive QRS detection. We will illustrate the effectiveness of this new approach by mapping out bispectral regions with a strong bicoherence manifestation and showing their corresponding temporal/spatial origins. Furthermore, we will present a few examples of our own application of these non-invasive techniques to illustrate what we see as their promise for analysis of heart abnormality.

Third-order cumulant signature matching technique for non-invasive fetal heart beat identification

This paper utilises the distinctive transient pulse feature of the third-order cumulant diagonal slice (TOCDS) of ECG signals to detect the number of occurrences of fetal heart beats during each of the maternal cycles. The fetal ECG signal is a comparatively weak signal (less than 20 percent of the mother ECG) and often embedded in noise. The fetal heart rate (FHR) lies in the range from 1.3 Hz to 3.5 Hz and it is possible for the mother and some of the fetal ECG signals to be closely overlapping. The paper also addresses the problem of false alarm situations often arising in diagonal-cumulant-slice recording during labour due to non-Gaussian impulsive or transient noise types and shows some results obtained after Volterra noise whitening and interpolation of the neighbouring fetal TOCDS samples.

Virtues and vices of source separation using linear independent component analysis for blind source separation of non-linearly coupled and synchronised fetal and mother ECGs

In this paper, we address the imminent problem which arises when researchers unjudiciously use a linear and instantaneous (memoryless) model for the source mixing structures of independent component analysis (ICA), also known as blind source separation (BSS), in pursuit of separating noisy and frequently nonstationary combined mother and fetal electrocardiogram (ECG) signals from cutaneous measurements under the following false assumptions. (1) Sensors (electrodes) are instantaneous linear mixtures of mother and fetal source signals. (2) Noise is an additive Gaussian perturbation. (3) Mother and fetal ECG signals are assumed to be stationary and linear, mutually statistically independent and statistically independent from noise. (4) Most of the second-order (SO) and fourth-order (FO) blind source separation (BSS) methods developed this last decade assume that third-order cumulants vanish hence the need to use FO. All these assumptions are not valid and will be challenged. We will expose these vices without providing any significant contributions for overcoming them. Rather, we provide a framework for investigations which are based on conformal mapping of nonlinear mixtures and novel dynamic nonlinear structures with time-variant memory to cater for quadratic coupling between mother and fetal which is quasi-periodical and the concomitant (quasi) cyclostationarity. Results given here show linear ICA shortfalls in nonstationary environment which is precipitated by quadratic coupling between mother and fetal ECGs during events of synchronised QRS complexes and P-waves and account for more than 20% of the 100,000 maternal cardiac cycles obtained from several clinical trials.

Highly accurate higher order statistics based neural network classifier of specific abnormality in electrocardiogram signals

The paper describes a simple yet highly accurate multilayer feed-forward neural network classifier (based on the backpropagation algorithm) specifically designed to successfully distinguish between normal and abnormal higher-order statistics features of electrocardiogram (EGG) signals. The concerned abnormality in ECG is associated with ventricular late potentials (LPs) indicative of life threatening heart diseases. The LPs are defined as signals from areas of delayed conduction which outlast the normal QRS period (80-100 msec). The QRS along with the P and T waves constitute the heart beat cycle. This classifier incorporates both preprocessing and adaptive weight adjustments across the input layer during the training phase of the network to enhance extraction of features pertinent to LPs found in 1-D cumulants. The latter is deemed necessary to offset the low S/N ratio in the cumulant domains concomitant to performing short data segmentation in order to capture the LPs transient appearance. We summarize the procedures of feature selection for neural network training, modification to the backpropagation algorithm to speed its rate of conversion, and the pilot trial results of the neural ECG classifier.

Novel Volterra predictor based on state-space equilibrium of nonlinear single- or multifractal signals

It has been quite common in the analysis of single- or multi- fractal signals originating from complex nonlinear systems to make a time-delayed construction of the state space attractor in which the dynamics can be qualitatively viewed. This involves the calculations of the embedding dimension and an appropriate time delay based on the signal nonlinear correlation behavioral pattern. This is usually followed by a sub-optimal short-term linear prediction in the signal time/subspace domain instead of the optimal nonlinear prediction in the time/frequency domain. In this paper, we propose to alleviate the sub-optimality problem and exploit the nonlinear signal dynamics embedded in the attractor and integrate them in the design of a new family of temporal multiple- step Volterra predictors. Essentially, this is done by including relevant past information preserved in the signal up to a time td equals the embedded dimension X embedded time delay, and sampled at instances coincident with the embedded time delays, to predict one-step ahead, adaptively, using the LMS criteria. The results obtained using several nonlinear (chaotic or non-chaotic) synthetic and measured biomedical signals and performing the novel quadratic- and cubic-Volterra predictions show superior MSE performance, of as much as 30 dB, over those obtained using an optimized conventional one-step Volterra predictor of the same order, particularly in the case of electrocardiogram signals. This is not achieved at the expense of any increase in the CPU time as the algorithm is designed to cater for new parallel Volterra structures, with progressive delayed inputs.

Multifractility in labor contraction dynamics

Recently, we presented evidence that electromyographic signals during healthy uterine contractions may have a fractal temporal structure [M. Sabry-Rizk et al., Transactions of the Institute of Measurement and Control, Vol. 22, No. 3, p. 243-70, 2000]. We also uncovered a loss of chaoticity in very early segments of uterine contractions for typical cases of failure to progress in the first stage of labor and ending with surgical procedure (Caesarean section). In both healthy and unhealthy labor contractions, quadratic Volterra structures were used to estimate non-linearity in their respective measured time series. Healthy uterine contractions start from the 16/sup th/ week of the human pregnancy. These contractions become more and more frequent and increase in strength up to the end of pregnancy. In this paper, we use the Hurst analysis algorithm to detect fractility in abdominal electromyographic signals (AEMG), and show that the multi-fractal character and nonlinear properties of the healthy contractions are encoded in the Fourier phases. Results are shown for representatives of the following groups: (i) healthy pregnancy, spontaneous labor and parturition, and (ii) full term at 40 weeks, prolonged labor (arbitrarily defined as lasting more than 12 hours) and ending with Caesarean section. Our ongoing study is aimed at exploiting the aforementioned method to characterize potentially pre-term labor (less than 37 weeks) by analyzing electromyographic signals as early as 16 weeks gestation.