Major depressive disorder (MDD) is a relatively common illness which is characterized by low mood, negative attitude, cognitive impairment, and physical impairment (Air et al., 2015). Studies have shown that its lifetime prevalence is approximately 15% (Hasin et al., 2005), making it a major source of disease burden worldwide (Ferrari et al., 2013). However, psychotherapy and pharmacotherapy are only successful in two-thirds of MDD patients and do not provide rapid recovery (Anand et al., 2005). For severe MDD, electroconvulsive therapy (ECT) is one of the most effective and fast therapies (Kellner et al., 2012; Lisanby, 2007). Studies have shown that ECT is more effective than antidepressants in the treatment of patients which has severe depression and drug resistance, with an effective recovery rate of approximately 60%-80% (Haq et al., 2015), few side effects, short duration, fast onset of action (Stippl et al., 2020), and good effects (Loureiro et al., 2020). Therefore, it is highly recommended for treating MDD.

Functional magnetic resonance imaging (fMRI) is one of the most commonly tools which is used to study the brain today. Besides, it is also one of the most powerful tools for the non-invasive assessment of behavioral, cognitive, and psychiatric disorders. It uses signals dependent on blood oxygen levels to record and analyze neural activity in the brain. It serves as an indirect tool for providing information about neural activity. (Biswal et al., 2010). Since its inception in 1990, fMRI has been used in numerous studies in cognitive neuroscience, psychology, clinical psychiatry, and preoperative planning (Hasin et al., 2005). Resting state fMRI (rs-fMRI) is easy to perform and provides ample opportunities to evaluate brain circuits, thus, it was used in more and more MDD research (Wang et al., 2012). Studies also have shown that blood-oxygen-level-dependent (BOLD) signals have nonlinear characteristics (Friston et al., 2000). Most of rs-fMRI studies for MDD patients have focused on linear features. However, both activity and connectivity can be investigated using linear and nonlinear metrics. such as resting-state functional connectivity (RSFC), and only few studies have investigated the nonlinear characteristics of brain signals as indicators for the diagnosis of MDD. As more and more attention has been paid to the nonlinear and complex analysis of rs-fMRI data, an increasing number of researchers have begun to use entropy analysis, a nonlinear statistical calculation method, for the analysis of fMRI time series (Lin et al., 2019).

In general, entropy is defined as the lack of order or predictability in a system, which is independent of the value of a random variable and it only depends on the distribution of values, In contrast to commonly used linear activity metrics, entropy represents a nonlinear metric, more adept at capturing complex and irregular patterns of neural activity(Akdeniz, 2017). In medical imaging processing applications, entropy is utilized as a tool to measure the heterogeneity of data distribution within image matrices, facilitating the extraction of meaningful results from research, particularly when analyzing complex imaging data(Akdeniz, 2017). Its variant, sample entropy (SampEn), is determined by the time coherence of the time series (Richman and Moorman, 2000) and is currently used in many medical fields, including electroencephalography (EEG), electrocardiography, heart rate variability, blood pressure, and hormone release irregularities (Lin et al., 2019). General-purpose algorithms for establishing entropy require a large number of datasets; however, the less number of time points of rs-fMRI studies makes it difficult to estimate the probability distribution function accurately, and SampEn can provide a good solution to this problem. Complexity models are the basis for SampEn (Wang et al., 2014), which can be evaluated with small datasets (Shalit, 2009). Therefore, it is suited for the analysis of rs-fMRI data, where the number of time points is relatively small compared to the number of voxels (Nezafati et al., 2020). The brain is a complex, nonlinear system (Saxe et al., 2018), and it is difficult to directly determine the state of the brain; however, brain entropy (BEN) can provide a means of quantifying rs-fMRI data, which can help us understand the continuous fluctuating activity in the brain (Saxe et al., 2018), which in turn facilitates further research into the underlying structural functions of the brain. Therefore, we considered a nonlinear method for analysis, that is, BEN.

RSFC, which refers to the temporal consistency of BOLD signals within or between human brain regions or networks at rest, (Mulders et al., 2015; Takamura and Hanakawa, 2017). Compared with healthy controls (HCs), studies have shown that RSFC increases or decreases in the ventrolateral prefrontal cortex, insular lobe, caudate nucleus, middle and upper temporal areas, cerebellum, amygdala, striatum, anterior cingulate gyrus, and other areas in patients with MDD (Gong et al., 2018; Kim et al., 2016; Wang et al., 2018; Wu et al., 2016). However, current research on RSFC is dominated by linear studies, which ignore the complex nonlinear features of the brain. Our objective is to integrate RSFC, a linear indicator, with BEN, a nonlinear indicator, to explore the psychobiological mechanisms underlying MDD and brain alterations before and after ECT treatment.

In this study, We performed a comparative analysis of the nonlinear measurement results of SampEn at baseline in 42 HC and at two time points before and after ECT in 42 patients with MDD, in order to identify brain regions exhibiting significant differences. Spheroids centered on the peak coordinates of the identified brain regions were used as seeds for whole-brain RSFC analysis to identify linear features of MDD. By combining linear and nonlinear indicators, we hypothesized that the combination of BEN and RSFC could be used as a new psychobiological indicator to future explore the mechanism of ECT in treating MDD patients.