The Gini coefficient is a statistical tool generally used by economists to quantify income inequality. However, it can be applied to any kind of data with unequal distribution, including heart rate variability (HRV). To assess the application of the Gini coefficient to measure inequality in power spectral density of RR intervals, and to use this application as a psychophysiological indicator of mental stress. Thirteen healthy subjects (19 ± 1.5 years) participated in this study, and their RR intervals were obtained by electrocardiogram during rest (five minutes) and during mental stress (arithmetic challenge; five minutes). These RR intervals were used to obtain the estimates of power spectral densities (PSD). The limits for the PSD bands were defined from 0.15 to 0.40 Hz for high frequency band (HF), from 0.04 to 0.15 Hz for low frequency band (LF), from 0.04 to 0.085 Hz for first low frequency sub-band (LF1) and from 0.085 to 0.15 Hz for second low frequency sub-band (LF2). The spectral Gini coefficient (SpG) was proposed to measure the inequality in the power distribution of the RR intervals in each of above-mentioned HRV bands. SpG from each band was compared with its respective traditional index of HRV during the conditions of rest and mental stress. All the differences were considered statistically significant for p < 0.05. There was a significant decrease in HF power (p = 0.046), as well as significant increases in heart rate (p = 0.004), LF power (p = 0.033), LF2 power (p = 0.019) and LF/HF (p = 0.002) during mental stress. There was also a significant increase in SpG(LF) (p = 0.009) and SpG(LF2) (p = 0.033) during mental stress. Coefficient of variation showed SpG has more homogeneity compared to the traditional index of HRV during mental stress. This pilot study suggested that spectral inequality of Heart Rate Variability analyzed using the Gini coefficient seems to be an independent and homogeneous psychophysiological indicator of mental stress. Also, HR, LF/HF, SpG(LF) of HRV are possibly important, reliable and valid indicators of mental stress.

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.

Introduction: Gini coefficient (Gini index or Gini ratio) is a parameter that is normally used in economy to measure the income distribution in a country or in the whole wide world, but it can be used to measure any kind of distribution. In the present study it is exposed an innovative proposal of application of the Gini coefficient to Heart Rate Variability (HRV) like a psychophysiological indicator of mental stress.Objective: To assess the application of the Gini coefficient as a psychophysiological indicator of mental stress.Methods: A non-observational crossover study, carried out in the biomedical laboratory of the Medical University of Santiago de Cuba. The involved participants are 13 healthy individuals (age 19 ± 1.5 years). Heart rate was continuously recorded at rest (5 minutes) and during a mental stress (5 minutes). Linear and nonlinear methods of heart rate variability were assessed, and 2 new indicators (Sequential and Non-Sequential Gini) were calculated and proposed to measure HRV differences between states.Results: When comparing rest and mental stress conditions, a sensible decrease of the traditional indicators of the HRV was founded (p<0,05), an increase of the heart rate (p=0,004) and of the Sequential Gini (p=0,004) and Non-Sequential Gini (p=0,04).Conclusions: The results suggest that temporary inequality of the RR intervals analyzed from the Gini coefficient could be an adequate indicator of sympathetic activity present during the mental stress. Introducción: El coeficiente de Gini o índice de Gini es un parámetro que normalmente se usa en economía para medir la distribución del ingreso en un país o en todo el mundo, pero puede usarse para medir cualquier tipo de distribución. En el presente estudio se expone una propuesta innovadora de aplicación del coeficiente de Gini a la Variabilidad de la Frecuencia Cardíaca (VFC) como indicador psicofisiológico del estrés mental.Objetivo: Evaluar la aplicación del coeficiente de Gini como indicador psicofisiológico de estrés mental.Métodos: Estudio no observacional de corte transversal, llevado a cabo en el laboratorio de estudios biomédicos de la Universidad Médica de Santiago Cuba. Los participantes involucrados fueron 13 individuos sanos (edad 19 ± 1,5 años). La frecuencia cardíaca se registró continuamente en reposo (5 minutos) y durante un estrés mental (5 minutos). Se evaluaron métodos lineales y no lineales de variabilidad de la frecuencia cardíaca, y se calcularon y propusieron 2 nuevos indicadores (Gini secuencial y no secuencial) para medir las diferencias de VFC entre estados.Resultados: Al comparar las condiciones de reposo y estrés mental, se encontró una sensible disminución de los indicadores tradicionales de la VFC (p<0,05), un aumento de la frecuencia cardiaca (p=0,004) y del Gini Secuencial (p=0,004) y Gini no secuencial (p=0,04).Conclusiones: Los resultados sugieren que la desigualdad temporal de los intervalos RR analizados a partir del coeficiente de Gini podría ser un indicador adecuado de la actividad simpática presente durante el estrés mental.