Frequency-dependent Alterations in Complexity in Parkinson’s Disease and Prodromal Parkinson’s Disease: A Resting-State fMRI Study


 Parkinson’s disease manifests principally as resting tremor, rigidity, akinesia and postural instability and exhibits deficits in information-processing tasks and abnormalities in the striatum. Human brain is one of the most complex information processing systems and resting-state fMRI signals, which possess complex nonlinear dynamic properties, have been extensively applied to study changes in brain function. However, it remains unclear whether patients with Parkinson’s disease and prodromal Parkinson’s disease have an abnormal complexity in resting-state fMRI signals and whether the abnormalities are frequency band dependent. Therefore, we investigated the complexity of signals in 47 patients with Parkinson’s disease, 26 patients with prodromal Parkinson’s disease and 21 normal controls within four frequency bands with Fuzzy Entropy. After preprocessing, entropy maps of the whole brain were extracted within four different frequency bands. Then we performed a one-way analysis of variance and results in slow-2 and slow-3 bands revealed that Parkinson’s disease patients exhibited higher complexity than those with prodromal Parkinson’s disease and normal controls. Prodromal Parkinson’s disease patients exhibited lower complexity than normal controls. Significant differences were observed mainly in the precentral gyrus , precuneus, caudate, thalamus and superior frontal gyrus. Significant correlations were found between the Fuzzy Entropy and clinical characteristics, regional homogeneity, gray matter volume and gray matter density. The results indicated that Parkinson’s disease and prodromal Parkinson’s disease patients had abnormal intrinsic neural oscillations, mainly in slow-3 and slow-2 bands, depending on frequency bands. Complexity analysis of resting-state fMRI signals in multiple bands can help probe brain activity and pathophysiology of neurodegenerative diseases.

Entropy measures the uncertainty about the information source and can describe a system's complexity (Ma, Shi, Peng, & Yang, 2018).Approximate entropy (AE) (Pincus, 1991) was introduced to assess the irregularity of the time sequence data and sample entropy (SE) (Richman, Randall, & Physiology, 2000) was developed to solve the shortcomings of AE.
Fuzzy entropy (FE) was developed to solve the flaws of Heaviside function in AE and SE and more powerful to analyze complexity and irregularity of short time series contaminated by noise than AE and SE (Chen et al., 2009;Ma et al., 2018).
Different frequency bands may reflect different spontaneous brain activities and are generated by different mechanisms and serve different physiological functions (Hoptman et al., 2010;Penttonen, 2003).Some studies eliminated slow-3 and slow-2 signals (Zuo et al., 2010), but new researches showed that spontaneous brain activity may occur in the frequency band higher than 0.1 Hz (Gohel & Biswal, 2015;Niazy, Xie, Miller, Beckmann, & Smith, 2011;Wu et al., 2008).However, few studies have performed complexity analysis on rs-fMRI signals (C.Y. Liu et al., 2013), and the complexity of brain signals from PD and PPD patients (PPD patients are the people at high risk for developing PD) in multiple frequency bands is not well understood.
This study aims to investigate the problems mentioned above.Firstly, we determined four frequency bands (slow-5: 0.01-0.027Hz, slow-4: 0.027-0.073Hz,.The division of multiple distinct frequency bands was based on earlier neurophysiological studies and the higher frequency boundary was determined by the Nyquist theorem (Y.Han et al., 2011;Nyquist & AIEE, 1928;Zuo et al., 2010).Then FE maps from three groups in four frequency bands were extracted and one-way analysis of variance (ANOVA) was performed to identify significantly different clusters.Then FE values of regions of interest (ROIs) were obtained and Spearman's correlation analysis between FE and clinical scores was analyzed.Moreover, we examined the relationships between FE and regional homogeneity (ReHo) and fractional Amplitude of Low Frequency Fluctuation (fALFF).Finally, we obtained gray matter volume (GMV), white matter volume (WMV), gray matter density (GMD) and white matter density (WMD) using a voxel-based morphometry (VBM) method and studied the relationships between FE and GMV, WMV, GMD and WMD.

Data Acquisition
Three-dimensional T1-weighted MR images were obtained with the following parameters:

Data Preprocessing
The

Voxel-based Morphometry Analysis
GM atrophy in PD has been reported (Blair et al., 2019;Fioravanti et al., 2015;Lewis et al., 2016;Mak, Bergsland, Dwyer, Zivadinov, & Kandiah, 2014;L. Zhang et al., 2018), to explore more information about brain atrophy and its effects, a VBM analysis of structural images was performed using SPM12.Individual structural images were first co-registered using a linear transformation and then segmented into GM, WM, and cerebrospinal fluid (CSF) using a unified segmentation algorithm.The warped GMV, GMD, WMV and WMD maps were affine-transformed into MNI space.Finally, the resultant GMV, GMD, WMV and WMD maps were smoothed with a Gaussian kernel of 6 mm full width at half maximum (FWHM).

Fuzzy Entropy Algorithm
Computation process of FE is as follows (M.-a.Li, Liu, Zhu, & Yang, 2017): Assume a time series is X = {x (i): 1 ≤ i ≤ N}, where N is the length of the time series. Then where m is called the embedding dimension, {x (i), x (i + 1), ..., x (i + m -1)} represents the value of N consecutive x starting from the j-th point.
x0 (i) is the mean of m consecutive values, which can be calculated as follows: The maximum distance between and is defined as which can be calculated The similarity degree between and can be calculated by a fuzzy function μ where exp () is the exponential function, n is the boundary gradient, and r is the boundary width of exponential function respectively.
Ф m (n, r) function is defined as follows: Repeat steps (1) -( 5) to reconstruct m+1 dimensional vector +1 : The FE of time series can be calculated as follows:

Statistical Analysis
We performed one-way ANOVA on FE maps using rs-fMRI Data Analysis Toolkit (REST 1.8) (Song et al., 2011) after adjusting for age and sex differences.We chose a False Discovery Rate (FDR) correction and a strict statistical significance level was set with p < 0.01.There were no significant differences in slow-4 and slow-5.So we only discuss the results in slow-2 and slow-3.We defined ROIs according to the peak MNI coordinates.GMV, WMV, GMD, WMD and FE of ROIs were obtained using DPABI.Finally, spearman's correlation analysis was performed using Statistical Package for Social Sciences (SPSS, IBM Corporation, New York).

ROI Analysis
We extracted 10 ROIs from 6 clusters in slow-2 and 14 ROIs from 7 clusters in slow-3 (Table 2).The results show a significantly increased complexity in the PD group compared to the PPD group, and a decreased complexity in the PPD group compared to the NCs.
UPDRS-Ⅲ concerns "motor examination" (Goetz et al., 2008).The results of the correlations between FE and UPDRS-Ⅲ and corresponding axial image slices are shown in  3.

Relationships between FE and GMV, WMV, GMD and WMD
Eight ROIs in slow-2 and nine ROIs in slow-3 exhibit significant negative correlations between FE and GMV (r < -0.2, P < 0.05), and only one ROI in slow-2 exhibit significant negative correlation between FE and WMV (r = -0.239,P < 0.05).Six ROIs in slow-2 and eleven ROIs in slow-3 exhibit significant negative correlations between FE and GMD (r < -0.2, P < 0.05), and one ROI in slow-2 and two ROIs in slow-3 exhibit significant positive correlations between FE and WMD (r > 0.2, P < 0.05).Results are presented in Table 5.

Discussion
PD and PPD patients have abnormal intrinsic neural oscillations depending on frequency bands.In the slow-2 and slow-3 frequency bands, a significantly increased complexity of PD patients may be related to abnormal brain activity and significantly decreased complexity of PPD patients may be related with compensatory mechanisms.Significant correlations between FE and ReHo, fALFF and clinical scores mean that alterations of complexity may be related to alterations in ReHo and fALFF.

Complexity alteration of PD and PPD patients
In several brain regions (i.e.CAU in slow-3, PCUN and THA in slow-2 and slow-3), a significantly increased complexity is detected in PD patients, which is consistent with previous research that PD patients show a significant higher entropy over the global frequency domain (C.X. Han et al., 2013).Some studies found that PD exhibited abnormal dynamic brain activity in PCUN and striatum where CAU is included (Fearnley & Lees, 1991;M. G. Li et al., 2020;C. Y. Liu et al., 2013;Samii, Nutt, & Ransom, 2004;Wang et al., 2020;C. Zhang et al., 2019).PCUN is interrelated to cognitive measures of executive and memory and CAU is associated with numerous cognitive processes (Hirano, 2021;Nobili et al., 2011;Sarbu et al., 2019).Deep brain stimulation (DBS) could treat advanced PD by changing neuronal activity in THA (Xu, Russo, Hashimoto, Zhang, & Vitek, 2008), which means PD patients had abnormal dynamic brain activity in THA.THA plays a role in sensory and motor functions and multiple cognitive functions, including memory, attention, perception, motor planning, and language processing (Lewis et al., 2016;Moustafa, McMullan, Rostron, Hewedi, & Haladjian, 2017).All of these brain regions (PCUN, CAU and THA) are of great importance in cognitive processes and PD patients exhibit cognitive impairment and decline (Hirano, 2021;Lewis et al., 2016;Mak et al., 2014;Moustafa et al., 2017;Nobili et al., 2011;Sarbu et al., 2019;L. Zhang et al., 2018), which implies increased complexity may be related to cognitive deficits in PD patients.
Our results reveal lower complexity in PPD patients compared to NCs (especially in CAU.L in slow-2 and SFGmed.L in both slow-2 and slow-3), which is similar to previous study that RBD patients have diminished complexity compared to NCs (RBD is a state of PPD) (Holtbernd et al., 2021;Ruffini et al., 2019).Lesion of cortical surface in SFGmed.L would result in declined control of eye movements (Deng et al., 2016).The physiological striatal dopamine function, especially in the CAU.L, is associated with executive and verbal functions (Hirano, 2021).So decreased complexity may be associated with deficits of executive function and language disturbances in PPD patients.

Potential Explanations for the Altered Complexity in PD and PPD
The substantia nigra pars compacta of PD patients contains high amounts of oxidised and nitrated proteins that are resistant to proteasomal degradation and then abnormal protein accumulation leads to neuronal death (Halliwell & Jenner, 1998;Samii et al., 2004).These changes lead to cognitive deficits that affect multiple domains and behavioral disturbances (Mak et al., 2014;L. Zhang et al., 2018).PD reveals selective loss of neurons and brain atrophy, especially in gray matter, and some subcortical regions have declined GMV and GMD (Blair et al., 2019;Fioravanti et al., 2015;Lewis et al., 2016;Mak et al., 2014;Samii et al., 2004).We examined relationships between FE and GMV, GMD, WMV and WMD and the results are consistent with previous studies.A significantly negative correlation between GMV and FE in CAU.L in both slow-2 and slow-3 bands implies an increase on GMV with decreasing brain activity complexity in CAU.L. PPD patients have significantly lower brain activity complexity than NCs in CAU.L in slow-2, which means PPD patients have increased volume of CAU.L than NCs.Previous study found RBD individuals (RBD is a state of PPD) showed increased volume of the right caudate nucleus compared to NCs (Holtbernd et al., 2021).These results hint at a compensation mechanism in the progression of Parkinson's disease.GMD can be regarded as a downstream proxy for potential mechanisms of neurodegeneration in PD (Blair et al., 2019) and GM atrophy may be indirect evidence for altered complexity in PD and PPD patients.
ReHo that calculates the coherence of the BOLD signal in a given voxel with those of its nearest neighbors can be used to explore resting-state functional homogeneity and to reveal complexity of human brain function (Zang, Jiang, Lu, He, & Tian, 2004;Zeng et al., 2017).
Study found ReHo is increased in PD in several brain regions (i.e., PCUN.R, SPG.R, SMA and THA) (X.Liu, Liu, Chen, & Chen, 2011;Zeng et al., 2017;J. Zhang, Hu, Liu, Wu, & Gan, 2016).fALFF could detect spontaneous brain activities and study found different alterations in different brain regions in fALFF in PD (Possin et al., 2013;Tang et al., 2017;Zou et al., 2008).Our research found similar but not exactly identical results.Higher ReHo and altered fALFF may be related to altered complexity in PD and PPD patients and may be helpful in the development of disease diagnoses.

Correlation of FE with Clinical Characteristics
Some brain regions show significant correlations between FE and clinical scores (i.e., PCUN and PreCG).Precentral gyrus is responsible for providing relief from drug-resistant neurogenic pain (Lefaucheur, Drouot, Keravel, & Nguyen, 2001;Z. Li et al., 2019;Yu et al., 2019).Precuneus plays a role in obtaining visuospatial imagery and somatosensory information (Culham et al., 1998;Lefaucheur et al., 2001;Z. Li et al., 2019;Malouin, Richards, Jackson, Dumas, & Doyon, 2003;Nicastro, Eger, Assal, & Garibotto, 2020;Yu et al., 2019).Positive correlations between FE and UPDRS-II and UPDRS-Ⅲ reveal higher scores with increasing FE.This means a worse motor performance may be related to increased complexity.RBDSQ scores are significantly lower in NC and PD groups than the PPD group, which means that the PPD patients have more serious parasomnia.

Different degrees of change in complexity in four frequency bands
There are no significant differences in slow-4 and slow-5, but significant differences in slow-2 and slow-3.For the two frequency bands, the distribution of FE maps in the whole brain is basically the same in patients and normal subjects but various in different frequency bands.Higher complexity and more significant differences are found in slow-3, which is consistent with previous findings that slow oscillators involve larger neuronal areas but higher frequency oscillations are more localized (Buzsaki & Draguhn, 2004;Y. Han et al., 2011;Penttonen, 2003).Significantly positive correlations were found in GM between FE and UPDRS-II and UPDRS-Ⅲ scores in slow-3 but there are no correlations in slow-2, so

Limitations
Due to the higher age and fewer female in PPD patients, we were not able to achieve a perfect matching of age and sex between the three groups but we eliminated the effect by adjusting for age and sex differences.Another limitation is that the number of subjects is not a lot.
at participating PPMI sites.

Ethical Approval
The Clinical Trials Coordination Center (CTCC) submitted the protocol and consent forms to the Institutional Review Board/Independent Ethics Committee (IRB/IEC) for review and obtained appropriate IRB/IEC approval.The Investigator agrees to provide the IRB/IEC all appropriate material.

Figures
Figure 1 The FE maps in slow-2 and slow-3 bands.
The differences in FE of GM and WM in slow-2 and slow-3 bands between the three groups.*P < 0.05, **P < 0.01 and ***P < 0.001.The error bars show the standard deviation and each small black dot represents a subject.
Axial image slices of regions that show signi cant differences between the three groups.

Supplementary Files
This is a list of supplementary les associated with this preprint.Click to download.

table.pdf
Checklist.pdf

FE
maps in each frequency band are shown in Figure 1.The FE values of GM are significantly smaller in PPD and NC groups than in the PD group.The FE values of WM are significantly lower in the NC group than the PD group.Similar results in slow-2 and slow-3 are shown in Figure 2. At the regional level, 6 clusters in slow-2 and 7 clusters in slow-3 show significant differences between the three groups.Axial image slices are shown in Figure 3.

Figure 5 .
Figure 5.All results are presented in Table3.
abnormal complexity in GM may depend on frequency bands.More significant correlations between FE and GMV, GMD, WMV, WMD, ReHo and fALFF in slow-3 band than slow-2 band means that slow-2 band may be affected by high-frequency noise signals to a certain extent.Each of oscillatory bands are generated by different mechanisms and serve different physiological functions(Penttonen, 2003), which is matched different degrees of change shown in four frequency bands.These results indicate that it is necessary to study brain signals in different frequency bands, and more significant results can be found in slow-2 and slow-3 frequency bands.ConclusionsPD and PPD patients have abnormal intrinsic neural oscillations, mainly in slow-3 band, and the abnormalities depend on frequency bands.Alterations of complexity are significantly correlated to altered ReHo, fALFF, GMV and GMD.Complexity analysis using FE in rs-fMRI signals in multiple bands can provide a new insight into brain activity and pathophysiology of PD and other neurodegenerative diseases.

Table 1 .
Three parameters must be fixed, including the embedding dimension m, boundary gradient n and boundary width r of exponential function.Larger m means a reconstructed sequence contains more states, but a too large m is inadvisable.A too narrow boundary will lead to greater influence from noise, while a too broad boundary may cause information loss (Escudero, Abasolo, Hornero, Espino, & Lopez, 2006;r = 0.25 × standard deviation of the original dataset, referring to previous researchers(Escudero, Abasolo, Hornero, Espino, & Lopez, 2006; M.-a.Li et al., 2017).