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# Introduction

The electrocardiogram (ECG) is a time-varying signal reflecting the ionic current flow which causes the cardiac fibres to contract and subsequently relax. The surface ECG is obtained by recording the potential difference between two electrodes placed on the surface of the skin. A single normal cycle of the ECG represents the successive atrial depolarisation/repolarisation and ventricular depolarisation/repolarisation which occurs with every heart beat. These can be approximately associated with the peaks and troughs of the ECG waveform labelled P,Q,R,S and T as shown in Fig. 1. Extracting useful clinical information from the real (noisy) ECG requires reliable signal processing techniques [1]. These include R-peak detection [2,3], QT-interval detection [4] and the derivation of heart rate and respiration rate from the ECG [5,6]. The RR-interval is the time between successive R-peaks, the inverse of this time interval gives the instantaneous heart rate. A series of RR-intervals is known as a RR tachogram and variability of these RR-intervals reveals important information about the physiological state of the subject [7]. At present, new biomedical signal processing algorithms are usually evaluated by applying them to ECGs in a large database such as the Physionet database [8]. While this gives the operator an indication of the accuracy of a given algorithm when applied to real data, it is difficult to infer how the performance would vary in different clinical settings with a range of noise levels and sampling frequencies. Having access to realistic artificial ECG signals may facilitate this evaluation.

Figure 1: Morphology of a mean PQRST-complex of an ECG recorded from a normal human.

This paper presents a model for generating a synthetic ECG signal with realistic PQRST morphology and prescribed heart rate dynamics. The aim of this model is to provide a standard realistic ECG signal with known characteristics, which can be generated with specific statistics such as the mean and standard deviation of the heart rate and frequency-domain characteristics of heart rate variability (HRV), such as the LF/HF ratio, defined as the ratio of power between 0.015 and 0.15 Hz and 0.15 and 0.4 Hz in the RR tachogram [7]. By generating a signal which represents a typical human ECG, this facilitates a comparison of different signal processing techniques. A synthetic ECG can be generated with different sampling frequencies and different noise levels in order to establish the performance of a given technique. This performance can be presented, for example, as the number of true positives, false positives, true negatives and false negatives for each test. Such performance assessment could be used as a ``standard'' and would enable clinicians to ascertain which biomedical signal processing techniques were best for a given application. The layout of this paper is as follows; section II summarises the physiological mechanisms underlying the cardiac cycle and reviews the morphological variability which is reflected in the ECG signal. A brief review of HRV is presented in section III. The dynamical model is introduced in section IV and investigated in section V. Section VI concludes and discusses extensions to the model which may be useful for simulating specific disorders.

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