The photoplethysmogram (PPG) signal is widely used in pulse oximeters and smartwatches. A fundamental step in analysing the PPG is the detection of heartbeats. Several PPG beat detection algorithms have been proposed, although it is not clear which performs best. Objective: This study aimed to: (i) develop a framework with which to design and test PPG beat detectors; (ii) assess the performance of PPG beat detectors in different use cases; and (iii) investigate how their performance is affected by patient demographics and physiology. Approach: Fifteen beat detectors were assessed against electrocardiogram-derived heartbeats using data from eight datasets. Performance was assessed using the F ₁ score, which combines sensitivity and positive predictive value. Main results: Eight beat detectors performed well in the absence of movement with F ₁ scores of ≥90% on hospital data and wearable data collected at rest. Their performance was poorer during exercise with F ₁ scores of 55%–91%; poorer in neonates than adults with F ₁ scores of 84%–96% in neonates compared to 98%–99% in adults; and poorer in atrial fibrillation (AF) with F ₁ scores of 92%–97% in AF compared to 99%–100% in normal sinus rhythm. Significance: Two PPG beat detectors denoted ‘MSPTD’ and ‘qppg’ performed best, with complementary performance characteristics. This evidence can be used to inform the choice of PPG beat detector algorithm. The algorithms, datasets, and assessment framework are freely available.

Advances in monitoring technology allow blood pressure waveforms to be collected at sampling frequencies of 250-1000 Hz for long time periods. However, much of the raw data are under-analysed. Heart rate variability (HRV) methods, in which beat-to-beat interval lengths are extracted and analysed, have been extensively studied. However, this approach discards the majority of the raw data. Our aim is to detect changes in the shape of the waveform in long streams of blood pressure data. Our approach involves extracting key features from large complex data sets by generating a reconstructed attractor in a three-dimensional phase space using delay coordinates from a window of the entire raw waveform data. The naturally occurring baseline variation is removed by projecting the attractor onto a plane from which new quantitative measures are obtained. The time window is moved through the data to give a collection of signals which relate to various aspects of the waveform shape. This approach enables visualisation and quantification of changes in the waveform shape and has been applied to blood pressure data collected from conscious unrestrained mice and to human blood pressure data. The interpretation of the attractor measures is aided by the analysis of simple artificial waveforms. We have developed and analysed a new method for analysing blood pressure data that uses all of the waveform data and hence can detect changes in the waveform shape that HRV methods cannot, which is confirmed with an example, and hence our method goes 'beyond HRV'.

Current arterial pulse monitoring systems capture data at high frequencies (100-1000 Hz). However, they typically report averaged or low frequency summary data such as heart rate and systolic, mean and diastolic blood pressure. In doing so, a potential wealth of information contained in the high-fidelity waveform data is discarded, data which has long been known to contain useful information on cardiovascular performance. Here we summarise a new mathematical method, attractor reconstruction, which enables the quantification of arterial waveform shape and variability in real-time. The method can handle long streams of non-stationary data and does not require preprocessing of the raw physiological data by the end user. Whilst the detailed mathematical proofs have been described elsewhere (Aston et al 2008 Physiol. Meas. 39), the authors were motivated to write a summary of the method and its potential utility for biomedical researchers, physiologists and clinician readers. Here we illustrate how this new method may supplement and potentially enhance the sensitivity of detecting cardiovascular disturbances, to aid with biomedical research and clinical decision making.

Background: The electrocardiogram (ECG) is a key tool in patient management. Automated ECG analysis supports clinical decision-making, but traditional fiducial point identification discards much of the time-series data that captures the morphology of the whole waveform. Our Symmetric Projection Attractor Reconstruction (SPAR) method uses all the available data to provide a new visualization and quantification of the morphology and variability of any approximately periodic signal. We therefore applied SPAR to ECG signals to ascertain whether this more detailed investigation of ECG morphology adds clinical value.Methods: Our aim was to demonstrate the accuracy of the SPAR method in discriminating between two biologically distinct groups. As sex has been shown to influence the waveform appearance, we investigated sex differences in normal sinus rhythm ECGs. We applied the SPAR method to 9,007 10 second 12-lead ECG recordings from Physionet, which comprised; Dataset 1: 104 subjects (40% female), Dataset 2: 8,903 subjects (54% female).Results: SPAR showed clear visual differences between female and male ECGs (Dataset 1). A stacked machine learning model achieved a cross-validation sex classification accuracy of 86.3% (Dataset 2) and an unseen test accuracy of 91.3% (Dataset 1). The mid-precordial leads performed best in classification individually, but the highest overall accuracy was achieved with all 12 leads. Classification accuracy was highest for young adults and declined with older age.Conclusions: SPAR allows quantification of the morphology of the ECG without the need to identify conventional fiducial points, whilst utilizing of all the data reduces inadvertent bias. By intuitively re-visualizing signal morphology as two-dimensional images, SPAR accurately discriminated ECG sex differences in a small dataset. We extended the approach to a machine learning classification of sex for a larger dataset, and showed that the SPAR method provided a means of visualizing the similarities of subjects given the same classification. This proof-of-concept study therefore provided an implementation of SPAR using existing data and showed that subtle differences in the ECG can be amplified by the attractor. SPAR's supplementary analysis of ECG morphology may enhance conventional automated analysis in clinically important datasets, and improve patient stratification and risk management.

Radioactive decay of an unstable isotope is widely believed to be exponential. This view is supported by experiments on rapidly decaying isotopes but is more difficult to verify for slowly decaying isotopes. The decay of ¹⁴C can be calibrated over a period of 12550 years by comparing radiocarbon dates with dates obtained from dendrochronology. It is well known that this approach shows that radiocarbon dates of over 3000 years are in error, which is generally attributed to past variation in atmospheric levels of ¹⁴C. We note that predicted atmospheric variation (assuming exponential decay) does not agree with results from modelling, and that theoretical quantum mechanics does not predict exact exponential decay. We give mathematical arguments that non-exponential decay should be expected for slowly decaying isotopes and explore the consequences of non-exponential decay. We propose an experimental test of this prediction of non-exponential decay for ¹⁴C. If confirmed, a foundation stone of current dating methods will have been removed, requiring a radical reappraisal both of radioisotope dating methods and of currently predicted dates obtained using these methods.