Prediction of Pulsatile Physiological Signals Using a Negative ... - wseas

1st WSEAS International Conference on BIOMEDICAL ELECTRONICS and BIOMEDICAL INFORMATICS (BEBI '08) Rhodes, Greece, August 20-22, 2008

Prediction of Pulsatile Physiological Signals Using a Negative Group Delay Circuit HILMI R. DAJANI, JONATHAN C. H. LAM School of Information Technology and Engineering (SITE) University of Ottawa 161 Louis Pasteur, Ottawa, K1N 6N5 CANADA

Abstract: - Prediction of pulsatile physiological signals is demonstrated using a negative group delay electronic circuit. The peak of the pulse leaves the output port of the circuit before it enters the input port. Analog and digital circuit simulations with simulated neural pulses show that prediction of the entire waveform is possible 50 µsec in advance (relative to a pulse-width of around 1 msec). With a blood pressure pulse, prediction is possible 20 msec in advance (relative to a pulse-width of around 1 sec). In all cases, there is minimal distortion in the morphology of the predicted pulse. Prediction of pulsatile physiological activity could be used to compensate for processing and mechanical delays that compromise real-time performance and stability in assistive biomedical devices. Key-Words: - Negative group delay circuit, Superluminal propagation, Pulsatile signals, Predictive signal processing, Predictive filtering, Predictive control of the pulse bandwidth, the negative group delay of the circuit results in a minimally distorted output signal appearing earlier than the input. It is important to stress that this phenomenon does not violate the principle of causality, since there is sufficient information in the early portion of an analytic signal to reproduce the entire waveform earlier in time [3],[7]. Garrison et al. have shown that causality is connected to “front” and “back” discontinuities, which are not present in smooth analytic signals [8]. In the case of the electronic demonstration mentioned above, the initial discontinuous rectangular pulse may be considered as the causal starting point [3]. The low-pass filter then introduces a delay on the input side, which can be counteracted by the negative delay circuit. So while it possible for the output pulse to precede the input low-pass filtered pulse, it is not possible to push the output pulse further back in time to precede the rectangular pulse, and any attempt to do that results in severe signal distortion. Earlier work with negative delay circuits has been restricted to highly smoothed artificial pulses [1],[2], so the question arises as to the applicability of these circuits to natural pulsatile signals which are not very smooth and which posses a more complex morphology. In physiological systems, pulsatile signals are common and are often highly functionally significant. Examples include neural pulstile signals that range from the action potential

1 Introduction Mitchell and Chiao have demonstrated an RLC operational amplifier circuit in which the peak of a pulse leaves the exit port of the circuit before the peak of the input pulse enters the input port [1]. Nakanishi et al. showed that a simpler RC circuit could also achieve this result [2],[3]. Using a bandlimited pulse obtained by low-pass filtering a rectangular waveform, they were able to experimentally obtain strikingly large negative delays (on the order of the width of the pulse) between the input and output. In this circuit, the output LED (light-emitting diode) could easily be observed to light earlier than the input LED. This counter-intuitive phenomenon had been observed earlier in the propagation of analytic pulses in optical and other transmission media where it has been described as superluminal (faster-than-light) propagation [4],[5]. For example, the peak of a laser pulse has been shown to leave the output face of a cesium vapour cell before the peak of the input pulse enters the input face of the cell [6]. In the case of electronic circuits, the interpretation of negative delay between the input and the output is relatively straightforward. The group delay is equal to the negative of the slope of the phase curve, and the circuit is designed to have an approximately linear rising phase response over the range of the pulse bandwidth. When the gain of the circuit is approximately constant over the range

ISSN: 1790-5125

91

ISBN: 978-960-6766-93-0

1st WSEAS International Conference on BIOMEDICAL ELECTRONICS and BIOMEDICAL INFORMATICS (BEBI '08) Rhodes, Greece, August 20-22, 2008

in individual neurons to slower neural activation in large groupings of nerve cells [9], pulsatile motor unit activation during movement [10], and pressure pulses in the vasculature caused by the beating heart [11]. This paper will explore the use of a simple negative group delay circuit for the prediction of three pulsatile physiological signals (two neural pulses and the blood pressure pulse waveform). It will also demonstrate a digital implementation of this circuit, and discuss possible applications in physiological control systems.

high frequency noise and high frequency signal features, and so leads to signal distortion. In this study, negative group delay is investigated using analog circuit simulations in the Multisim environment (National Instruments, Austin, Texas), which facilitates examination of the effects of adjusting the different circuit parameters. The pulsatile physiological signals tested are two nerve action potentials generated using the Simulator for Neural Networks and Action Potentials (SNNAP) (University of Texas, Houston, Texas), and a blood pressure pulse waveform collected from a normal individual using digital photoplethysmography (Finapres 2300, Ohmeda, Englewood, Colorado). The action potentials were simulated at a sampling frequency of 1 MHz. The blood pressure signal was digitised at a sampling frequency of 50 Hz, spline-interpolated, and then resampled at 4 kHz. In a real-time application, the signal should be digitised at a frequency much higher than the Nyquist rate (e.g. 4 kHz for the blood pressure pulse) because although smoothness is a fuzzy and application specific concept, a signal is considered smooth if it is slowly changing compared to the sampling rate [12]. The blood pressure and action potential signal amplitudes were not calibrated. The circuit parameters used for the three signals are shown in Table 1.

2 Negative group delay The group delay signifies the time-shift of the envelope of a band-limited signal passing through a system [3]. It is defined as: Td =

− dφ dω ω 0

(1)

where φ (ω ) is the frequency dependent phase response. A simple electronic circuit that achieves a satisfactory negative group delay is proposed in [3] and is shown in Fig. 1. The transfer function of the circuit is given by: H (ω ) = 1 +

jω RC (1 + jω RC ')(1 + jω R ' C )

(2)

3 Prediction of pulsatile physiological signals The action potential (or nerve pulse) is thought to be the primary communication signal between neurons [9]. Although there is a large diversity of action potential shapes, rise and fall times, widths etc., in neural circuits it is believed that neural information is primarily carried in the timing (and temporal patterns) of nerve activity [13],[14]. The action potential is characterized by a sudden depolarisation across the membrane of a nerve fiber followed by a typically slower repolarization (Fig. 3a). However, while nerve membrane depolarisation may be rapid, it is not instantaneous. The change in membrane potential proceeds smoothly, governed by electrochemical dynamics such as those described in the Hodgkin and Huxley equations [15]. The negative delay circuit is capable of predicting the entire course of the action potential as shown in Figures 3a and 3b. With a nerve pulse based on the standard Hodgkin and Huxley model, it is possible to obtain a negative delay of approximately 55 µsec (relative to a pulse width of approximately 1.5 msec) without substantial distortion in the shape of the

If RC’