Analysis of patterns of variation of time-series, termed variability analysis, represents a rapidly evolving discipline with increasing applications in different fields of science. In medicine and in particular critical care, efforts have focussed on evaluating the clinical utility of variability. However, the growth and complexity of techniques applicable to this field have made interpretation and understanding of variability more challenging. Our objective is to provide an updated review of variability analysis techniques suitable for clinical applications. We review more than 70 variability techniques, providing for each technique a brief description of the underlying theory and assumptions, together with a summary of clinical applications. We propose a revised classification for the domains of variability techniques, which include statistical, geometric, energetic, informational, and invariant. We discuss the process of calculation, often necessitating a mathematical transform of the time-series. Our aims are to summarize a broad literature, promote a shared vocabulary that would improve the exchange of ideas, and the analyses of the results between different studies. We conclude with challenges for the evolving science of variability analysis.

Introduction: Prolonged ventilation and failed extubation are associated with increased harm and cost. The added value of heart and respiratory rate variability (HRV and RRV) during spontaneous breathing trials (SBTs) to predict extubation failure remains unknown. Methods: We enrolled 721 patients in a multicenter (12 sites), prospective, observational study, evaluating clinical estimates of risk of extubation failure, physiologic measures recorded during SBTs, HRV and RRV recorded before and during the last SBT prior to extubation, and extubation outcomes. We excluded 287 patients because of protocol or technical violations, or poor data quality. Measures of variability (97 HRV, 82 RRV) were calculated from electrocardiogram and capnography waveforms followed by automated cleaning and variability analysis using Continuous Individualized Multiorgan Variability Analysis (CIMVA™) software. Repeated randomized subsampling with training, validation, and testing were used to derive and compare predictive models. Results: Of 434 patients with high-quality data, 51 (12%) failed extubation. Two HRV and eight RRV measures showed statistically significant association with extubation failure (P 0.5 in patients with RSBI >105 and perceived high risk of failure yielded a fold increase in risk of extubation failure of 3.0 (95% confidence interval (CI) 1.2 to 5.2) and 3.5 (95% CI 1.9 to 5.4), respectively. Conclusions: Altered HRV and RRV (during the SBT prior to extubation) are significantly associated with extubation failure. A predictive model using RRV during the last SBT provided optimal accuracy of prediction in all patients, with improved accuracy when combined with clinical impression or RSBI. This model requires a validation cohort to evaluate accuracy and generalizability. Trial registration: ClinicalTrials.gov NCT01237886. Registered 13 October 2010.

Learning the spatial organization of the environment is essential for most animals’ survival. This requires the animal to derive allocentric spatial information from egocentric sensory and motor experience. The neural mechanisms underlying this transformation are mostly unknown. We addressed this problem in electric fish, which can precisely navigate in complete darkness and whose brain circuitry is relatively simple. We conducted the first neural recordings in the preglomerular complex, the thalamic region exclusively connecting the optic tectum with the spatial learning circuits in the dorsolateral pallium. While tectal topographic information was mostly eliminated in preglomerular neurons, the time-intervals between object encounters were precisely encoded. We show that this reliable temporal information, combined with a speed signal, can permit accurate estimation of the distance between encounters, a necessary component of path-integration that enables computing allocentric spatial relations. Our results suggest that similar mechanisms are involved in sequential spatial learning in all vertebrates.

Neural tissue injuries render voltage-gated Na⁺ channels (Nav) leaky, thereby altering excitability, disrupting propagation and causing neuropathic pain related ectopic activity. In both recombinant systems and native excitable membranes, membrane damage causes the kinetically-coupled activation and inactivation processes of Nav channels to undergo hyperpolarizing shifts. This damage-intensity dependent change, called coupled left-shift (CLS), yields a persistent or “subthreshold” Nav window conductance. Nodes of Ranvier simulations involving various degrees of mild CLS showed that, as the system’s channel/pump fluxes attempt to re-establish ion homeostasis, the CLS elicits hyperexcitability, subthreshold oscillations and neuropathic type action potential (AP) bursts. CLS-induced intermittent propagation failure was studied in simulations of stimulated axons, but pump contributions were ignored, leaving open an important question: does mild-injury (small CLS values, pumps functioning well) render propagation-competent but still quiescent axons vulnerable to further impairments as the system attempts to cope with its normal excitatory inputs? We probe this incipient diffuse axonal injury scenario using a 10-node myelinated axon model. Fully restabilized nodes with mild damage can, we show, become ectopic signal generators (“ectopic nodes”) because incoming APs stress Na⁺/K⁺ gradients, thereby altering spike thresholds. Comparable changes could contribute to acquired sodium channelopathies as diverse as epileptic phenomena and to the neuropathic amplification of normally benign sensory inputs. Input spike patterns, we found, propagate with good fidelity through an ectopically firing site only when their frequencies exceed the ectopic frequency. This “propagation window” is a robust phenomenon, occurring despite Gaussian noise, large jitter and the presence of several consecutive ectopic nodes.

Brain rhythms recorded in vivo, such as gamma oscillations, are notoriously variable both in amplitude and frequency. They are characterized by transient epochs of higher amplitude known as bursts. It has been suggested that, despite their short-life and random occurrence, bursts in gamma and other rhythms can efficiently contribute to working memory or communication tasks. Abnormalities in bursts have also been associated with e.g. motor and psychiatric disorders. It is thus crucial to understand how single cell and connectivity parameters influence burst statistics and the corresponding brain states. To address this problem, we consider a generic stochastic recurrent network of Pyramidal Interneuron Network Gamma (PING) type. Using the stochastic averaging method, we derive dynamics for the phase and envelope of the amplitude process, and find that they depend on only two meta-parameters that combine all the model parameters. This allows us to identify an optimal parameter regime of healthy variability with similar statistics to those seen in vivo; in this regime, oscillations and bursts are supported by synaptic noise. The probability density for the rhythm’s envelope as well as the mean burst duration are then derived using first passage time analysis. Our analysis enables us to link burst attributes, such as duration and frequency content, to system parameters. Our general approach can be extended to different frequency bands, network topologies and extra populations. It provides the much needed insight into the biophysical determinants of rhythm burst statistics, and into what needs to be changed to correct rhythms with pathological statistics.