Use of the Gini Coefficient for the Analysis of Heart Rate Variability in Sick and Healthy Individuals

Abstract

The Gini Coefficient (GC) is a statistical tool widely used in Economics to quantify the degree of variation of values belonging to a group, ranging from zero to one. The closer to zero, the less unequal the country. We proposed to evaluate GC in the analysis of Heart Rate Variability in different groups of individuals hypothesizing that groups with more similar conditions and better stationarity (healthy individuals) should be the groups with lower differences among them and among the aged, diseased, or premature individuals. Time series of normal RR intervals were analyzed in eight groups of individuals: premature (G1) or healthy newborns (G2), healthy children (G3), healthy young adults (G4), elderly adults (G5), patients with chronic liver (G6) or kidney disease (G7) and individuals with a state of brain death or who died in the short term after the initial evaluation (G8). GC distinguished the less unequal groups (G2, G3 and G4) from all other groups. Was identified, graphically, a parabolic behavior with near similarity among equivalent homeostatic levels. GC is a useful tool for characterizing the stationarity and the homeostatic level of clinical groups (by lower GC values) and to interpret more adequately the results.

1. Introduction

1.1 Autonomic nervous system

The autonomic nervous system (ANS) is the portion of the central nervous system that controls most of the body’s visceral functions, such as breathing, blood circulation, body temperature, and digestion. It is activated by centers located in the spinal cord, brainstem, and hypothalamus, which transmit signals to lower centers such as baroreceptors, chemoreceptors, atrial receptors, ventricular receptors, the vasomotor system, the renin-angiotensin-aldosterone system, and the thermoregulatory system [1]. These efferent autonomic signals are transmitted to the visceral organs by two subdivisions: the sympathetic nervous system and the parasympathetic nervous system, which differ anatomically and physiologically, the first being organized in the form of a thoracolumbar paravertebral ganglionic chain, while the second consists of in a chain of craniosacral conformation.

The sympathetic autonomic nervous system is responsible for increasing the global activity of the heart, through the release of epinephrine and norepinephrine, favoring three mechanisms: increased heart rate (HR), increased conduction velocity, and increased myocardial contraction force. On the other hand, parasympathetic stimulation - from the release of acetylcholine in the sinoatrial (SA) and atrioventricular (AV) nodes - causes effects essentially opposite to those observed in sympathetic stimulation, decreasing the rhythm of the sinus node and the speed of transmission of impulses to the ventricles. Thus, when vagal inhibition occurs, there is a relative predominance of the sympathetic over the parasympathetic, with an increase in HR. The decrease in HR is related to the predominance of vagal (parasympathetic) activity. In this sense, in healthy individuals, the cardiac rhythm is constantly controlled by the sympathetic stimulation, accelerating it, and by the parasympathetic stimulation, decelerating it. This dynamic balance, throughout the day, undergoes variability according to breathing, hemodynamic changes, mental stress, metabolic changes, physical exercises, sleep, and orthostatism, among others.

The study of heart rate fluctuations throughout the day reflects the functioning of the ANS and is called Heart Rate Variability (HRV). In this sense, the ability of the heart to adapt to the body’s needs is based on high variability and is directly related to the individual’s health. Thus, healthy patients with good ANS functioning have high HRV, while individuals with low HRV denote insufficient and abnormal physiological functioning of this system.

HRV is usually analyzed using time and frequency domains. Its measurement is made from the oscillations of the distances between the consecutive peaks on the electrocardiogram, the normal R-R intervals (RRi), graphically represented by the tachograms below (Figure 1).

Figure 1.

Note the tachograms, in [A], of a healthy young adult, while, in [B], the tachogram of a healthy newborn. There is less variability in B relative to A.

In Figure 1, the tachogram shows in [A] the HRV of a healthy adult, while in [B] the HRV of a healthy newborn is recorded.

In this context, it is known that changes in HRV have predictive and anticipated value in the analysis of an individual’s health. Thus, the decrease in HRV is an important indicator both for the appearance of diseases in previously healthy patients and for the appearance of complications in individuals who already have alterations [2]. This reduction in HRV is usually due to relative hyperactivity of the adrenergic system and a decrease in parasympathetic activity.

HRV quantification has been, in recent years, increasingly used, since it is easy to acquire data, it is a non-invasive method, easy to perform, reproducible, and, mainly, of wide clinical applicability. There is a large literature regarding the monitoring of various morbid conditions, such as coronary artery disease [3, 4], cardiomyopathies [5], systemic arterial hypertension [6, 7], renal failure [8], diabetes [9], among others.

1.2 Lorenz curve

The Lorenz curve is a graph used to study the relative distribution of a variable in a given domain. It is widely used in economics, where the “y-axis (ordinate)” corresponds to the income variability of a society, and the “x-axis (abscissa)” to the cumulative percentage of the population with that income [10].

In a perfectly egalitarian society, all citizens receive the same income, and the Lorenz curve would be represented as the black line in Figure 2, where y = x, is called the line of equality. However, most societies are not economically egalitarian, and the Lorenz curve is represented by the red line (Figure 2).

Figure 2.

Lorenz curve.

1.3 Gini coefficient

The Gini coefficient was created in 1931 by the Italian mathematician Conrado Gini to measure the degree of income concentration in a given society, based on the Lorenz curve. The coefficient consists of the difference between the equal distribution (black curve, Figure 2) and the Lorenz curve (red curve, Figure 2). The measurement of the Gini coefficient follows a scale that goes from 0 (when there is no inequality) to 1 (with maximum inequality), representing ideal extremes.

In this sense, a Gini coefficient equal to 1 would represent a society in which a single individual stores all income, and a Gini coefficient equal to 0, a society in which all people have the same income.

This coefficient has been used, however, not only in the economic area but also in social studies, such as the suicide rate related to income [11]; cell transport markers [12] and gene expression [13]; bacterial aggregation rates [14]; health access distribution rates [15]; screening for pathologies, such as central nervous system tumors in children [16] and perinatal mortality [17]. Therefore, it is understood that this coefficient can be used in any analysis of a variable that manifests itself through a time series.

The purpose of the present study is to use the Gini coefficient in a time series of heartbeats in healthy individuals and in those with different degrees of homeostatic impairment in a wide range of age groups, considering, that will be possible to characterize the variation degree of each group and, by extension, the variation degree relatively among groups hypothesizing that conditions with the worst homeostatic level should present higher coefficients than states with better homeostatic level.

2. Casuistic and method

Time series of normal RR intervals were analyzed in eight groups of individuals: 29 premature newborns admitted to the ICU (G1), 21 healthy newborns (G2), 31 healthy children (G3), 32 healthy young adults (G4), 27 elderly adults hospitalized in nursing homes (G5), 40 patients with chronic liver disease (G6), 22 patients with chronic kidney disease on hemodialysis program (G7) and 9 individuals with a state of brain death or who died in the short term after carrying out the initial evaluation (G8).

2.1 Gini coefficient formula

The Gini Coefficient (GC) was calculated from Brown’s formula, based on the Lorenz curve (Equation):

$$G=\frac{2}{n^2\overline{x}}{\displaystyle \sum _{i=1}^{n}i}\left(x_i-\overline{x}\right)$$E1

Where,

1. G = Gini coefficient.

2. P = accumulated proportion of the variable “population”.

3. R = accumulated proportion of the variable “income” (in this study “income” is understood as the numerical value of the RR interval in milliseconds.

2.2 Statistical analysis

Concomitant comparative analyses between the eight groups were carried out using the non-parametric Kruskal-Wallis test and, in case of detection of a statistically significant difference in the set, post-test comparisons were made of all pairs using the Conover-Iman test. An alpha error of 5% was admitted, with P values less than or equal to 0.05 being considered significant. The statistical software used was StatsDirect version 3.3.6 of May 23, 2023.

3. Results

Descriptive statistics values for groups G1 to G8 are shown in Table 1.

Variables	G1	G2	G3	G4	G5	G6	G7	G8
Valid data	29	21	31	32	27	40	22	9
Mean	0.0079	0.0048	0.0033	0.0031	0.0091	0.0065	0.0105	0.0265
SD	0.0097	0.0055	0.0033	0.0023	0.0122	0.0065	0.0130	0.0217
Maximum	0.0418	0.0224	0.0153	0.0108	0.0503	0.0277	0.0462	0.0713
UpperQuart	0.0089	0.0054	0.0046	0.0041	0.0115	0.0098	0.0146	0.0249
Median	0.0047	0.0026	0.0023	0.0032	0.0051	0.0049	0.0054	0.0191
LowerQuart	0.0019	0.0016	0.0010	0.0011	0.0024	0.0010	0.0021	0.0172
InterqRange	0.0070	0.0038	0.0036	0.0029	0.0091	0.0087	0.0125	0.0077
Minimum	0.0004	0.0003	0.0003	0.0000	0.0002	0.0000	0.0008	0.0037
Range	0.0414	0.0221	0.0150	0.0108	0.0501	0.0277	0.0454	0.0676

Table 1.

Descriptive statistics of the intragroup (G1 to G8) Gini coefficient values.

Legend. G1 (29 premature newborns admitted to the ICU); G2 (21 healthy newborns); G3 (31 healthy children); G4 (32 healthy young adults); G5 (27 elderly adults hospitalized in nursing homes); G6 (40 patients with chronic liver disease); G7 (22 patients with chronic kidney disease on hemodialysis program); G8 (9 individuals with a state of brain death or who died in the short term after carrying out the initial evaluation).

The graphic distribution by Box-Plot graphs is shown in Figure 3.

Figure 3.

Box-plot graph distribution of Gini coefficient descriptive values in groups G1 to G8. G1 (29 premature newborns admitted to the ICU); G2 (21 healthy newborns); G3 (31 healthy children); G4 (32 healthy young adults); G5 (27 elderly adults hospitalized in nursing homes); G6 (40 patients with chronic liver disease); G7 (22 patients with chronic kidney disease on hemodialysis program); G8 (9 individuals with a state of brain death or who died in the short term after carrying out the initial evaluation).

Table 2 shows the pairwise statistical comparisons.

	G1	G2	G3	G4	G5	G6	G7	G8
G1	XXX	0.1629	0.0186	0.0228	0.9280	0.6185	0.6308	0.0023
G2		XXX	0.4544	0.5069	0.1452	0.3007	0.0797	<0.0001
G3			XXX	0.9208	0.0164	0.0413	0.0078	<0.0001
G4				XXX	0.0201	0.0506	0.0096	<0.0001
G5					XXX	0.5589	0.6972	0.0030
G6						XXX	0.3327	0.0005
G7							XXX	0.0090
G8								XXX

Table 2.

Pair-to-pair statistical comparisons (P values) were performed using the Kruskal-Wallis non-parametric test and the Conover-Iman post-test.

Legend. G1 (29 premature newborns admitted to the ICU); G2 (21 healthy newborns); G3 (31 healthy children); G4 (32 healthy young adults); G5 (27 elderly adults hospitalized in nursing homes); G6 (40 patients with chronic liver disease); G7 (22 patients with chronic kidney disease on hemodialysis program); G8 (9 individuals with a state of brain death or who died in the short term after carrying out the initial evaluation). Statistical test: Kruskal-Wallis: all pairwise comparisons (Conover-Iman); significant P-values are in bold.

Was identified, graphically, as a parabolic behavior with near similarity of values among equivalent homeostatic levels. (The lower the Gini Coefficient values, the greater the uniformity between the intragroup measures); Figures 4 and 5.

Figure 4.

Distribution of mean global Gini coefficient values [A] and maximum global Gini coefficient values [B], according to the clinical groups. G1 (29 premature newborns admitted to the ICU); G2 (21 healthy newborns); G3 (31 healthy children); G4 (32 healthy young adults); G5 (27 elderly adults hospitalized in nursing homes); G6 (40 patients with chronic liver disease); G7 (22 patients with chronic kidney disease on hemodialysis program); G8 (9 individuals with a state of brain death or who died in the short term after carrying out the initial evaluation). Y-axis [A] = mean values of intragroup Gini Coefficients; Y-axis [B] = maximum values of intragroup Gini Coefficients.

Figure 5.

Parabolic behavior with near similarity of values among equivalent homeostatic levels of the clinical groups. G1 (29 premature newborns admitted to the ICU); G2 (21 healthy newborns); G3 (31 healthy children); G4 (32 healthy young adults); G5 (27 elderly adults hospitalized in nursing homes); G6 (40 patients with chronic liver disease); G7 (22 patients with chronic kidney disease on hemodialysis program); G8 (9 individuals with a state of brain death or who died in the short term after carrying out the initial evaluation).

4. Discussion

Different behavior of the Gini coefficient was observed between the groups of patients studied. Firstly, when analyzing the Gini coefficients in the intragroup mode, that is, evaluating the values of the Gini coefficient in relation to the inequality of the RR intervals of each patient, it was found that the global means for the groups G2, G3, and G4 were the lowest (closer to zero) indicating similarity of behavior in these three groups. It is noteworthy that the three groups mentioned involve healthy individuals (newborns, children, and young adults). In addition, the groups corresponding to cases with potential for greater clinical impairment or lower homeostatic level (premature newborns, elderly hospitalized in nursing homes, chronic, liver and kidney disease, and, mainly, cases with ongoing brain death or in a state of imminent death), exhibited progressively higher mean values.

It is important to remember that the Gini Coefficient here is not assessing the heart rate variability, which is repeatedly lower in the presence of more important clinical impairment, but the intragroup variability of the GC values for the individual RR intervals. This can be translated as healthy individuals being more homogeneous among themselves. The groups composed of premature, senile, or severely ill individuals, on the other hand, contain individuals with more heterogeneous clinical characteristics, hence the GINI coefficients have higher mean values. The same behavior was seen when considering the median and maximum values for the GC (Figures 4 and 5).

This clinical heterogeneity, within each group, is based on the concept of nonstationarity. Stationarity means that the statistical properties of the signal remain the same throughout the period of recording and refers to the invariance of its distributional characteristics over time, being essential for HRV measurements in the frequency domain [18, 19, 20].

Nonstationarity translates into the presence of values that are more different from each other and leads, consequently, to higher Gini Coefficient values. In agreement, in groups G1, G5, G6, G7, and G8, higher overall values were found.

It is convenient to emphasize again that high or low heart rate variability may be independent of higher or lower CG values, as it all depends on the degree of present stationarity.

The allocation in parabolic distribution shown in Figure 5 is quite illustrative as it is consistent with the behavior of homeostatic levels, which are still reduced in view of the present autonomic immaturity (G1), become higher from healthy newborns to children and to young adults when it reached the point of greatest autonomic maturity and continuous regression begins with the concurrence of progressively more serious illnesses until death occurs [21].

It is concluded that the Gini Coefficient, in addition to being a useful tool in the sense of assessing the inequality within a time series of any HRV variable, was also useful in characterizing the parabolic spatial distribution of the different groups studied, suggesting that in premature infants, elderly individuals and patients with severe diseases there is a significantly greater presence of non-stationarity.

Acknowledgments

This work has been supported by the Brazilian research agency (FAPESP).

The second author was funded by the grant 2021/04472-0 Sao Paulo Research Foundation.