Attractor reconstruction analysis has previously been applied to analyse arterial blood pressure and photoplethysmogram signals. This study extends this novel technique to ECG signals. We show that the method gives high accuracy in identifying gender from ECG signals, performing significantly better than the same classification by interval measures. IntroductionTraditional analysis of electrocardiogram (ECG) signals consists of identifying particular points and deriving lengths of various intervals from these points [1]. For instance, Heart Rate Variability (HRV) methods are used to analyse beat-to-beat intervals [2]. However, such approaches exclude the wealth of diagnostic information contained in the remainder of the waveform shape.Our novel attractor reconstruction (AR) method uses all of the available data and so retains the underlying waveform information. It therefore goes "beyond HRV" and can characterise changes in signal morphology that are not detected by HRV [3]. AR analysis has previously been applied to arterial blood pressure (ABP) [3,4] and photoplethysmogram (PPG) [5] signals, where it has been shown to supplement standard cardiovascular assessment.The aim of this study is to demonstrate how the AR method can be applied to ECG signals. We illustrate this by comparing the performance of our AR method with standard interval analysis for identifying gender from ECG signals, both in a normal state and when dosed with drugs that impact ventricular repolarisation. It is well known that there are significant differences in various ECG parameters between females and males, including the PR interval, QRS duration and QT interval [6,7]. Normal interval ranges may be gender-specific and certain cardiovascular diseases have a higher prevalence in one sex. Differences in ventricular repolarisation are of key interest, especially in the development and application of drugs that have a QT-prolonging effect [8]. Attractor Reconstruction AnalysisThe attractor reconstruction method has been described previously [3][4][5], so only an overview is given here. The AR approach provides a means of analysing approximately periodic signals that may be irregular, strongly nonstationary and noisy, supporting its application to ECG signals. Moreover, it uses all of the data and so can detect changes in the morphology of the signal.The first step of the AR method consists of embedding the one-dimensional ECG time series, which we denote by x(t), in a three-dimensional phase space by using Takens' delay coordinate method [9]. From the original time series, we generate two further time series y(t) = x(t − τ ) and z(t) = x(t − 2τ ), where τ > 0 is a fixed time delay, taken as one third of the average cycle length of the data, (i.e. one third of the cardiac cycle duration). A plot of (x, y, z) gives the reconstructed attractor in the bounded three-dimensional phase space (see Fig. 1(ii)).Baseline variation, e.g. due to respiration or motion, in x(t) is removed by projecting the attractor onto a plane perpendicular to the...

Tumours that are low in oxygen (hypoxic) tend to be more aggressive and respond less well to treatment. Knowing the spatial distribution of oxygen within a tumour could therefore play an important role in treatment planning, enabling treatment to be targeted in such a way that higher doses of radiation are given to the more radioresistant tissue. Mapping the spatial distribution of oxygen in vivo is difficult. Radioactive tracers that are sensitive to different levels of oxygen are under development and in the early stages of clinical use. The concentration of these tracer chemicals can be detected via positron emission tomography resulting in a time dependent concentration profile known as a tissue activity curve (TAC). Pharmaco-kinetic models have then been used to deduce oxygen concentration from TACs. Some such models have included the fact that the spatial distribution of oxygen is often highly inhomogeneous and some have not. We show that the oxygen distribution has little impact on the form of a TAC; it is only the mean oxygen concentration that matters. This has significant consequences both in terms of the computational power needed, and in the amount of information that can be deduced from TACs.

Knowledge of how a population of cancerous cells progress through the cell cycle is vital if the population is to be treated effectively, as treatment outcome is dependent on the phase distributions of the population. Estimates on the phase distribution may be obtained experimentally however the errors present in these estimates may effect treatment efficacy and planning. If mathematical models are to be used to make accurate, quantitative predictions concerning treatments, whose efficacy is phase dependent, knowledge of the phase distribution is crucial. In this paper it is shown that two different transition rates at the - checkpoint provide a good fit to a growth curve obtained experimentally. However, the different transition functions predict a different phase distribution for the population, but both lying within the bounds of experimental error. Since treatment outcome is effected by the phase distribution of the population this difference may be critical in treatment planning. Using an age-structured population balance approach the cell cycle is modelled with particular emphasis on the - checkpoint. By considering the probability of cells transitioning at the - checkpoint, different transition functions are obtained. A suitable finite difference scheme for the numerical simulation of the model is derived and shown to be stable. The model is then fitted using the different probability transition functions to experimental data and the effects of the different probability transition functions on the model's results are discussed.

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