Complex systems and the technology of variability analysis

Abstract

Characteristic patterns of variation over time, namely rhythms, represent a defining feature of complex systems, one that is synonymous with life. Despite the intrinsic dynamic, interdependent and nonlinear relationships of their parts, complex biological systems exhibit robust systemic stability. Applied to critical care, it is the systemic properties of the host response to a physiological insult that manifest as health or illness and determine outcome in our patients. Variability analysis provides a novel technology with which to evaluate the overall properties of a complex system. This review highlights the means by which we scientifically measure variation, including analyses of overall variation (time domain analysis, frequency distribution, spectral power), frequency contribution (spectral analysis), scale invariant (fractal) behaviour (detrended fluctuation and power law analysis) and regularity (approximate and multiscale entropy). Each technique is presented with a definition, interpretation, clinical application, advantages, limitations and summary of its calculation. The ubiquitous association between altered variability and illness is highlighted, followed by an analysis of how variability analysis may significantly improve prognostication of severity of illness and guide therapeutic intervention in critically ill patients.

Detection of Paroxysmal Atrial Fibrillation in Acute Stroke Patients

“…It performs time series analysis which includes 6 mostly nonlinear mathematical parameters. These parameters are derived from principle component analysis, RR difference plots, the ratio between shortest and longest interval of maximum 6 consecutive RR intervals, the number of atrial premature complexes, complexes without sinus nodal reset and approximate entropy of RR interval data [25,26,27,28]. Based on this ASA analysis, the risk of pAF was estimated by the software and each patient was assigned to 1 of 5 predefined categories: (1) continuous sinus rhythm; (2) ventricular rhythm disorders; (3) intermediate risk of pAF; (4) high risk of pAF; (5) manifest episodes of AF.…”

Characterization of Seepage Velocity beneath a Complex Rock Mass Dam Based on Entropy Theory

“…In other words, states tend to evolve from ordered, statistically-unlikely configurations, to less-ordered and statistically more probable. The spontaneous reverse occurrence is statistically improbable to the point of impossibility [21]. Based on the Second Law of Thermodynamics, the information entropy theory was developed in the late 1940s, followed by the principle of maximum entropy (POME) in the late 1950s.…”

“…Entropy reflects system complexity, that is, smaller values of entropy indicate greater regularity, and greater values convey more disorder, or randomness [21]. As a measure of information or uncertainty, it is associated with a random variable or probability distribution.…”

Multiscale, multiorgan and multivariate complexity analyses of cardiovascular regulation

“…(c ) Risk assessment in multiple organ dysfunction syndrome Multiple organ dysfunction syndrome (MODS) is a multiple systems illness, representing a common end-stage pathway of inflammation, infection, dysfunctional host response and organ failure in critically ill patients, frequently leading to death (Marshall 2000;Seely & Christou 2000;Seely & Macklem 2004). A MODS is a sequential failure of several organ systems after a trigger event, such as cardiogenic shock or decompensated CHF, whereby the associated autonomic dysfunction may substantially contribute to the development of MODS.…”