The Gini coefficient: a methodological pilot study to assess fetal brain development employing postmortem diffusion MRI

Theil Entropy as a Non-Lineal Analysis for Spectral Inequality of Physiological Oscillations

Theil entropy is a statistical measure used in economics to quantify income inequalities. However, it can be applied to any data distribution including biological signals. In this work, we applied different spectral methods on heart rate variability signals and cellular calcium oscillations previously to Theil entropy analysis. The behavior of Theil entropy and its decomposable property was investigated using exponents in the range of [−1, 2], on the spectrum of synthetic and physiological signals. Our results suggest that the best spectral decomposition method to analyze the spectral inequality of physiological oscillations is the Lomb–Scargle method, followed by Theil entropy analysis. Moreover, our results showed that the exponents that provide more information to describe the spectral inequality in the tested signals were zero, one, and two. It was also observed that the intra-band component is the one that contributes the most to total inequality for the studied oscillations. More in detail, we found that in the state of mental stress, the inequality determined by the Theil entropy analysis of heart rate increases with respect to the resting state. Likewise, the same analytical approach shows that cellular calcium oscillations present on developing interneurons display greater inequality distribution when inhibition of a neurotransmitter system is in place. In conclusion, we propose that Theil entropy is useful for analyzing spectral inequality and to explore its origin in physiological signals.

Glycine Receptor Inhibition Differentially Affect Selected Neuronal Populations of the Developing Embryonic Cortex, as Evidenced by the Analysis of Spontaneous Calcium Oscillations

The embryonic developing cerebral cortex is characterized by the presence of distinctive cell types such as progenitor pools, immature projection neurons and interneurons. Each of these cell types is diverse on itself, but they all take part of the developmental process responding to intrinsic and extrinsic cues that can affect their calcium oscillations. Importantly, calcium activity is crucial for controlling cellular events linked to cell cycle progression, cell fate determination, specification, cell positioning, morphological development and maturation. Therefore, in this work we measured calcium activity in control conditions and in response to neurotransmitter inhibition. Different data analysis methods were applied over the experimental measurements including statistical methods entropy and fractal calculations, and spectral and principal component analyses. We found that developing projection neurons are differentially affected by classic inhibitory neurotransmission as a cell type and at different places compared to migrating interneurons, which are also heterogeneous in their response to neurotransmitter inhibition. This reveals important insights into the developmental role of neurotransmitters and calcium oscillations in the forming brain cortex. Moreover, we present an improved analysis proposing a Gini coefficient-based inequality distribution and principal component analysis as mathematical tools for understanding the earliest patterns of brain activity.