The heart-rate dynamics are one of the most analyzed physiological interactions. Many mathematical methods were proposed to evaluate heart-rate variability. These methods have been successfully applied in research to expand knowledge concerning the cardiovascular dynamics in healthy as well as in pathological conditions. Notwithstanding, they are still far from clinical practice. In this paper, we aim to review the nonlinear methods most used to assess heart-rate dynamics. We focused on methods based on concepts of chaos, fractality, and complexity: Poincaré plot, recurrence plot analysis, fractal dimension (and the correlation dimension), detrended fluctuation analysis, Hurst exponent, Lyapunov exponent entropies (Shannon, conditional, approximate, sample entropy, and multiscale entropy), and symbolic dynamics. We present the description of the methods along with their most notable applications.

About 160 years ago, the concept of entropy was introduced in thermodynamics by Rudolf Clausius. Since then, it has been continually extended, interpreted, and applied by researchers in many scientific fields, such as general physics, information theory, chaos theory, data mining, and mathematical linguistics. This paper presents The Entropy Universe, which aims to review the many variants of entropies applied to time-series. The purpose is to answer research questions such as: How did each entropy emerge? What is the mathematical definition of each variant of entropy? How are entropies related to each other? What are the most applied scientific fields for each entropy? We describe in-depth the relationship between the most applied entropies in time-series for different scientific fields, establishing bases for researchers to properly choose the variant of entropy most suitable for their data. The number of citations over the past sixteen years of each paper proposing a new entropy was also accessed. The Shannon/differential, the Tsallis, the sample, the permutation, and the approximate entropies were the most cited ones. Based on the ten research areas with the most significant number of records obtained in the Web of Science and Scopus, the areas in which the entropies are more applied are computer science, physics, mathematics, and engineering. The universe of entropies is growing each day, either due to the introducing new variants either due to novel applications. Knowing each entropy’s strengths and of limitations is essential to ensure the proper improvement of this research field.

Diabetes mellitus (DM) is one of the world's most prevalent medical conditions. Contemporary management focuses on lowering mean blood glucose values toward a normal range, but largely ignores the dynamics of glucose fluctuations. We probed analyte time series obtained from continuous glucose monitor (CGM) sensors. We show that the fluctuations in CGM values sampled every 5 min are not uncorrelated noise. Next, using multiscale entropy analysis, we quantified the complexity of the temporal structure of the CGM time series from a group of elderly subjects with type 2 DM and age-matched controls. We further probed the structure of these CGM time series using detrended fluctuation analysis. Our findings indicate that the dynamics of glucose fluctuations from control subjects are more complex than those of subjects with type 2 DM over time scales ranging from about 5 min to 5 h. These findings support consideration of a new framework, dynamical glucometry, to guide mechanistic research and to help assess and compare therapeutic interventions, which should enhance complexity of glucose fluctuations and not just lower mean and variance of blood glucose levels.

Poincaré delay maps are widely used in the analysis of cardiac interbeat interval (RR) dynamics. To facilitate visualization of the structure of these time series, we introduce multiscale Poincaré (MSP) plots. Starting with the original RR time series, the method employs a coarse-graining procedure to create a family of time series, each of which represents the system’s dynamics in a different time scale. Next, the Poincaré plots are constructed for the original and the coarse-grained time series. Finally, as an optional adjunct, color can be added to each point to represent its normalized frequency. We illustrate the MSP method on simulated Gaussian white and 1/f noise time series. The MSP plots of 1/f noise time series reveal relative conservation of the phase space area over multiple time scales, while those of white noise show a marked reduction in area. We also show how MSP plots can be used to illustrate the loss of complexity when heartbeat time series from healthy subjects are compared with those from patients with chronic (congestive) heart failure syndrome or with atrial fibrillation. This generalized multiscale approach to Poincaré plots may be useful in visualizing other types of time series.

Pharyngocutaneous fistula is considered one of the major complications in the postoperative period after total laryngectomy/pharyngolaryngectomy, leading to a severe adverse impact for the patient and society. This study aimed to identify all the described pharyngocutaneous fistula predictive factors and risk classifications. Research was conducted to identify all the studies assessing predictive factors and risk classification for pharyngocutaneous fistula development published until April of 2012 (n = 846). The included studies were analyzed and data regarding their identification, methodological quality and results were recorded. A total of 39 studies were included. The variables consistently reported as associated with fistula development were nutritional deficiency, American Society of Anesthesiologists (ASA) classification, high consumption of alcohol, anemia and hypoalbuminemia, co-morbidities, advanced N stage, location and extent of primary tumor, pre-radiotherapy and pre-chemoradiotherapy treatment, emergency tracheotomy, surgical margin status, surgery's duration, surgeon's experience, local complications of the wound, performance of intraoperative blood transfusion and relationship between nasogastric tube and oral feeding. Several risk factors were associated with pharyngocutaneous fistula formation in the included studies. However, there is still no consensus in the most pertinent selection. Only two classification systems were retrieved and they were not able to accurately predict pharyngocutaneous fistula.