Extracting new information from old waveforms: Symmetric projection attractor reconstruction: Where maths meets medicine.

Abstract

What is the topic of this review? Symmetric Projection Attractor Reconstruction (SPAR) is a relatively new mathematical method that can extract additional information pertaining to the morphology and variability of physiological waveforms, such as arterial pulse pressure. Herein, we describe the potential utility of the method for more sensitive quantification of cardiovascular changes. What advances does it highlight? We use a simple example of a human tilt table to illustrate these concepts. SPAR can be used on any approximately periodic waveform and may add value to experimental and clinical settings, where such signals are collected routinely. Periodic physiological waveform data, such as blood pressure, pulse oximetry and ECG, are routinely sampled between 100 and 1000Hz in preclinical research and in the clinical setting from a wide variety of implantable, bedside and wearable monitoring devices. Despite the underlying numerical waveform data being captured at such high fidelity, conventional analysis tends to reside in reporting only averages of minimum, maximum, amplitude and rate, as single point averages. Although these averages are undoubtedly of value, simplification of the data in this way means that most of the available numerical data are discarded. In turn, this may lead to subtle physiological changes being missed when investigating the cardiovascular system over time. We have developed a mathematical method (symmetric projection attractor reconstruction) that uses all the numerical data, replotting and revisualizing them in a manner that allows unique quantification of multiple changes in waveform morphology and variability. We propose that the additional quantification of these features will allow the complex behaviour of the cardiovascular system to be mapped more sensitively in different physiological and pathophysiological settings.