The fractal nature of blood glucose fluctuations

Hierarchical network structure as the source of hierarchical dynamics (power-law frequency spectra) in living and non-living systems: How state-trait continua (body plans, personalities) emerge from first principles in biophysics

Living systems are hierarchical control systems that display a small world network structure. In such structures, many smaller clusters are nested within fewer larger ones, producing a fractal-like structure with a 'power-law' cluster size distribution (a mereology). Just like their structure, the dynamics of living systems shows fractal-like qualities: the timeseries of inner message passing and overt behavior contain high frequencies or 'states' (treble) that are nested within lower frequencies or 'traits' (bass), producing a power-law frequency spectrum that is known as a 'state-trait continuum' in the behavioral sciences. Here, we argue that the power-law dynamics of living systems results from their power-law network structure: organisms 'vertically encode' the deep spatiotemporal structure of their (anticipated) environments, to the effect that many small clusters near the base of the hierarchy produce high frequency signal changes and fewer larger clusters at its top produce ultra-low frequencies. Such ultra-low frequencies exert a tonic regulatory pressure that produces morphological as well as behavioral traits (i.e., body plans and personalities). Nested-modular structure causes higher frequencies to be embedded within lower frequencies, producing a power-law state-trait continuum. At the heart of such dynamics lies the need for efficient energy dissipation through networks of coupled oscillators, which also governs the dynamics of non-living systems (e.q., earthquakes, stock market fluctuations). Since hierarchical structure produces hierarchical dynamics, the development and collapse of hierarchical structure (e.g., during maturation and disease) should leave specific traces in system dynamics (shifts in lower frequencies, i.e. morphological and behavioral traits) that may serve as early warning signs to system failure. The applications of this idea range from (bio)physics and phylogenesis to ontogenesis and clinical medicine.

Scale-Free Coupled Dynamics in Brain Networks Captured by Bivariate Focus-Based Multifractal Analysis

While most connectivity studies investigate functional connectivity (FC) in a scale-dependent manner, coupled neural processes may also exhibit broadband dynamics, manifesting as power-law scaling of their measures of interdependence. Here we introduce the bivariate focus-based multifractal (BFMF) analysis as a robust tool for capturing such scale-free relations and use resting-state electroencephalography (EEG) recordings of 12 subjects to demonstrate its performance in reconstructing physiological networks. BFMF was employed to characterize broadband FC between 62 cortical regions in a pairwise manner, with all investigated connections being tested for true bivariate multifractality. EEG channels were also grouped to represent the activity of six resting-state networks (RSNs) in the brain, thus allowing for the analysis of within- and between- RSNs connectivity, separately. Most connections featured true bivariate multifractality, which could be attributed to the genuine scale-free coupling of neural dynamics. Bivariate multifractality showed a characteristic topology over the cortex that was highly concordant among subjects. Long-term autocorrelation was higher in within-RSNs, while the degree of multifractality was generally found stronger in between-RSNs connections. These results offer statistical evidence of the bivariate multifractal nature of functional coupling in the brain and validate BFMF as a robust method to capture such scale-independent coupled dynamics.

Analyzing Complexity and Fractality of Glucose Dynamics in a Pregnant Woman with Type 2 Diabetes under Treatment

Currently, the rapid development of continuous glucose monitoring (CGM) device brings new insights into the treatment of diabetic patients including those during pregnancy. Complexity and fractality have recently under fast development for extracting information embodied in glucose dynamics measured using CGM. Although scientists have investigated the difference of complexity in glucose dynamics between diabetes and non-diabetes in order to discover better approaches for diabetes care, no one has analyzed the complexity and fractality of glucose dynamics during the process of adopting CGM to successfully treat pregnant women with type 2 diabetes. Thus, we analyzed the complexity and fractality using power spectral density (PSD), multi-scale sample entropy (MSE) and multifractal detrended fluctuation analysis (MF-DFA) in a clinical case. Our results show that (i) there exists multifractal behavior in blood glucose dynamics; (ii) the alpha stable distribution fits to the glucose increment data better than the Gaussian distribution; and (iii) the "global" complexity indicated by multiscale entropy, spectrum exponent and Hurst exponent increase and the "local" complexity indicated by multifractal spectrum decrease after the successful therapy. Our results offer findings that may bring value to health care providers for managing glucose levels of pregnant women with type 2 diabetes as well as provide scientists a reference on applying complexity and fractality in the clinical practice of treating diabetes.

NMR-based metabolomics in real-time monitoring of treatment induced toxicity and cachexia in head and neck cancer: a method for early detection of high risk patients

INTRODUCTION

Nutritional treatment in head and neck squamous cell carcinoma cancer (HNSCC) patients undergoing radio-/chemo-radiotherapy (RT/CHRT) is complex and requires a multidisciplinary approach. In this study the real-time dynamic changes in serum metabolome during RT/CHRT in HNSCC patients were monitored using NMR-based metabolomics.

OBJECTIVES

The main goal was to find the metabolic markers that could help prevent of acute radiation sequelae (ARS) escalation.

METHODS

170 HNSCC patients were treated radically with RT/CHRT. Blood samples were collected weekly, starting from the day before the treatment and stopping within the week after the RT/CHRT completion, resulting in a total number of 1328 samples. 1H NMR spectra were acquired on Bruker 400 MHz spectrometer at 310 K and analyzed using principal component analysis (PCA) and orthogonal partial least squares discriminant analysis (OPLS-DA). Additional statistical analyses were performed on the quantified metabolites.

RESULTS

PCA has detected a group of distinct outliers corresponding to ketone bodies (3HB, Ace, AceAce). These outliers were found to identify the individuals at high risk of weight loss, mainly by the 3HB changes, which was confirmed by the patients' medical data. In the OPLS-DA models a transition from the lowest to the highest weight loss is seen, defining the metabolic time trajectories for the patients from the studied groups during RT/CHRT. 3HB is a relatively sensitive marker that allows earlier identification of the patients at higher risk of > 10% weight loss.

CONCLUSION

Our findings indicate that metabolic alterations, characteristic for malnutrition or cachexia, can be detected already at the beginning of the treatment, making it possible to monitor the patients with a higher risk of weight loss.

Applications of Variability Analysis Techniques for Continuous Glucose Monitoring Derived Time Series in Diabetic Patients

Methods from non-linear dynamics have enhanced understanding of functional dysregulation in various diseases but received less attention in diabetes. This retrospective cross-sectional study evaluates and compares relationships between indices of non-linear dynamics and traditional glycemic variability, and their potential application in diabetes control. Continuous glucose monitoring provided data for 177 subjects with type 1 (n = 22), type 2 diabetes (n = 143), and 12 non-diabetic subjects. Each time series comprised 576 glucose values. We calculated Poincaré plot measures (SD1, SD2), shape (SFE) and area of the fitting ellipse (AFE), multiscale entropy (MSE) index, and detrended fluctuation exponents (α1, α2). The glycemic variability metrics were the coefficient of variation (%CV) and standard deviation. Time of glucose readings in the target range (TIR) defined the quality of glycemic control. The Poincaré plot indices and α exponents were higher (p < 0.05) in type 1 than in the type 2 diabetes; SD1 (mmol/l): 1.64 ± 0.39 vs. 0.94 ± 0.35, SD2 (mmol/l): 4.06 ± 0.99 vs. 2.12 ± 1.04, AFE (mmol²/l²): 21.71 ± 9.82 vs. 7.25 ± 5.92, and α1: 1.94 ± 0.12 vs. 1.75 ± 0.12, α2: 1.38 ± 0.11 vs. 1.30 ± 0.15. The MSE index decreased consistently from the non-diabetic to the type 1 diabetic group (5.31 ± 1.10 vs. 3.29 ± 0.83, p < 0.001); higher indices correlated with lower %CV values (r = -0.313, p < 0.001). In a subgroup of type 1 diabetes patients, insulin pump therapy significantly decreased SD1 (-0.85 mmol/l), SD2 (-1.90 mmol/l), and AFE (-16.59 mmol²/l²), concomitantly with %CV (-15.60). The MSE index declined from 3.09 ± 0.94 to 1.93 ± 0.40 (p = 0.001), whereas the exponents α1 and α2 did not. On multivariate regression analyses, SD1, SD2, SFE, and AFE emerged as dominant predictors of TIR (β = -0.78, -1.00, -0.29, and -0.58) but %CV as a minor one, though α1 and MSE failed. In the regression models, including SFE, AFE, and α2 (β = -0.32), %CV was not a significant predictor. Poincaré plot descriptors provide additional information to conventional variability metrics and may complement assessment of glycemia, but complexity measures produce mixed results.