Sample entropy (SampEn) differentiate patients with Major Depressive Disorder (MDD) from healthy controls and explores mechanism of MDD
Kai Wang1, Yunwen Shao1, Tongxin Chen1, Chuangjian Cai1, Yan Zhu2, and Kui Ying3,4

1Department of Biomedical Engineering, Tsinghua University, Beijing, China, People's Republic of, 2Psychiatry Department, Yu Quan Hospital, Tsinghua University, Beijing, China, People's Republic of, 3Department of Engineering Physics, Tsinghua University, Beijing, China, People's Republic of, 4Key Laboratory of Particle and Radiation Imaging, Ministry of Education, Beijing, China, People's Republic of


Entropy indicates system irregularity. Sample Entropy (SampEn), an estimation of entropy in a relatively robust way, was used to differentiate patients with Major Depressive Disorder (MDD) from healthy controls and to explore the mechanism of MDD. In this work, we found five clusters with significantly different SampEn in MDD group from that of control group, located in left frontal lobe, left parietal lobe, left temporal lobe, cerebellum and occipital lobe respectively, and the overall accuracy obtained with linear support vector machine formed by SampEn of those regions was 86.7%(p=0.000).


Psychologists, behaviorists, fMRI investigators, neuroimaging scientists, and clinicians.


Entropy indicates system irregularity. The system with high entropy has a high level of uncertainty and randomness. In this work, we proposed a method by use of the sample entropy (SampEn), an estimation of entropy in a relatively robust way [1], to differentiate medication-free patients with Major Depressive Disorder from healthy controls and explore the mechanism of MDD.


Subjects 14 patients diagnosed with MDD and 16 demographically similar healthy participants (male, right-handed, Chinese speaker, aged from 20 to 25, no history of drugs) were recruited with approval from local ethics committee and signed consent forms from the subjects. Resting state fMRI (rs-fMRI) images were acquired using a 3T scanner (SIEMENS MAGNETOM Trio) with following parameters: GRE-EPI sequence, TR/TE=2000/30ms, 30 slices, slice thickness=4mm, FOV=210mmX210mm, and matrix=64X64, lasting for seven minutes per subject.

Image preprocessing The preprocessing included DICOM to NIFTI conversion, slice timing correction, realignment, normalization and spatial smoothing (Gaussian kernel=4mm). Nuisance covariates including six motion parameters, global mean signal, white matter and cerebrospinal fluid signal were regressed out. Resultant data was further detrended and filtered (0.01Hz~0.08Hz) using DPARSF (Yan & Zang, 2010,

Parameter Evaluation for Entropy Calculation The algorithm to calculate SampEn was described by [2]. According to previous SampEn studies of biomedical signals (Z Wang el at., 2014; M Costa el at., 2002; P R Norris el at., 2009), m=2, 3 and r from 0.2 to 0.7std (standard variation of the time course) with the interval 0.05std were evaluated. After traversing all pairs of m and r to calculate a set of SampEn values for time course of every AAL region and every subject, two sample T-test was performed between MDD group and control groups to identify regions with a significantly different SampEn. Then SPSS ( was used to calculate areas under ROC curves for those regions identified by T-tests. The maximum area of ROC appeared at m=2 and r=0.55std, which obtained the most precise classification of the two groups, so the corresponding m and r were used in further analysis.

Statistical analysis using atlas of 950 regions In order to obtain a higher spatial accuracy, parameters of m=2 and r=0.55std were used to calculate SampEn of 950 regions [2]. Then two-sample T-test was performed for each of the 950 regions, with significance level =0.01 (alpha-sim multicomparison correction).

Evaluation by linear support vector machine (SVM) Linear SVM was used to evaluate the T-test results. SampEn of regions identified by the T-tests was used to form a classifier, and leave-one-out algorithm was adopted to examine the accuracy rate for both MDD group (sensitivity) and control group (specificity), and the generalization rate (the overall accuracy), noted as GR0. Also, the generalization rate GR was used as a statistics in a permutation test to calculate the significance level, which repeated permutation for 100,000 times where labels of training data were randomly permuted prior to training and generalization rate was calculated by cross-validation with the original labels.


In this study, we found that MDD patients had higher SampEn values in left frontal lobe, left parietal lobe, left temporal lobe, and cerebellum than those in controls, while the SampEn in occipital lobe in MDD was lower than that in control subjects (shown in fig. 2). With leave-one-out algorithm, the SVM classifier achieved an accuracy of 86.7% (78.6% for patients, and 93.8% for controls, p=0.000).


To the best of our knowledge, this is the first study using SampEn of rs-fMRI signals to differentiate MDD patients from healthy controls. In the current study, patients with MDD showed higher SampEn in the left prefrontal cortex, which is consistent with what was discovered by previous studies (K.L. Phan, T. Wager, S.F. Taylor, & I. Liberzon, 2002). Cerebellum has been underemphasized in neuropsychiatric research, but a growing confluence of scientific data indicates that cerebellum and its neural connections may be relevant to neuropsychiatric disorders (J.Z. Konarski, 2005). Abnormalities of occipital lobe (L Wang et al., 2008) of MDD group were discovered, and decreased temporal lobe activation may be a specific marker of limbic dysfunction (M.M. Machulda, 2003), implying that these regions can both be involved in emotional processing (IM Veer et al., 2010). Results of this study were in good accordance with previous studies. Sample entropy is a quantitative measure, making a potentially useful index for studying MDD.


This work was supported by Capital Medical Development and Scientific Research Grant.


[1] Richman, J.S., etc. American Journal of Physiology. Heart and Circulatory Physiology. 2000. 278 (6). (47-6).

[2] Wang Z, etc. PloS one, 2014, 9(3): e89948. [2] R. Cameron Craddock, etc. Human Brain Mapping. A whole brain fMRI atlas generated via spatially constraint spectral clustering. 2012. 33(8): doi:10.1002/hbm.21333.


Fig.1 Plot of area of ROC vs. Value of m and r.

Fig. 2 Clusters discovered by two-sample T-test. a, b, c, d, e are clusters found in left frontal lobe, left parietal lobe, left temporal lobe, cerebellum, and occipital lobe. Red indicates higher SampEn in MDD than that in the control group, and blue indicates lower SampEn in MDD.

Fig.3 Result of permutation test As GR0=86.7%, the significance level (p) was calculated as the frequency of tests whose GR is larger than GR0. Thus it is confirmed that the classifier learned the relationship between the data and the labels with the probability of being wrong p=0.000.

Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)