Parkinson’s disease (PD) is a clinically degenerative disorder disease of the nervous system with motor and non-motor symptoms. The disease mainly affects people’s motor function, such as bradykinesia, tremor, muscle stiffness or rigidity, abnormal walking gait, etc. In addition, it will also affect non-motor function, such as cognitive impairment, insomnia, depression, autonomic nerve dysfunction, and so on. The cause of PD is unclear. In the early premotor stages, the diagnosis of this disease is still difficult (Aarsland et al., 2017). Anatomical magnetic resonance imaging could not detect the loss of dopamine neurons. With the development of molecular biology, neural structure, and functional imaging technology, more and more biomarkers of PD can be discovered, providing the possibility for early diagnosis, disease monitoring, and differential diagnosis, thus achieving accurate early intervention and efficacy evaluation of the disease. Dopamine transporter single photon emission computed tomography (DAT-SPECT) and resting state functional magnetic resonance imaging (rsfMRI) are potential techniques for detecting the survival status of neurons in PD (Wang et al., 2012). Among them, DAT-SPECT can provide quantitative information about dopamine neurons, which is very useful for assessing disease severity and monitoring treatment effectiveness. However, it is expensive and carries the risk of radioactive tracer. On the other hand, rsfMRI is a non-invasive imaging technique that is relatively inexpensive and can avoid ionizing radiation. It can provide information about brain activity, which is very useful for studying the neural mechanisms of PD and evaluating treatment effectiveness.

Therefore, the study of functional connectivity (FC) based on rsfMRI is a promising method. Based on the correlation of time series, FC was preliminary explored and studied through rsfMRI (Aarsland et al., 2017). With rsfMRI, FC can be used to detect a variety of diseases such as Alzheimer’s disease, PD, schizophrenia, and so on (Lee et al., 2013). Some studies have shown that motor and cognitive impairment in PD are related to abnormal functional connections (Putcha et al., 2015; Zhang et al., 2015). Graph theory-based approaches used in PD research have shown that topological properties of brain networks are disrupted, which can help identify this type of disease (Luo et al., 2015). Specifically, abnormal local and global network efficiency changes suggest clinical phenomena in PD. The above methods assume that the functional network is stable and does not change over time. A dynamic FC based method was used in recent research. For example, previous studies used rsfMRI and sliding windows to assess differences in dynamic connectivity between normal control (NC) and PD (Kim et al., 2017). Huang et al. (2020) proposed a regression method to model the dynamic correlation matrices as a linear combination of symmetric positive definite matrix to smooth the image acquisition and physiological noise. Pang et al. (2021) distinguished different motor subtypes of PD based on multilevel indices of rsfMRI and Support Vector Machine (SVM).

However, the graph theory analysis method can not describe the characteristics of higher-level complex brain networks. To study the topological characteristics of complex brain networks on a larger scale, researchers began to study Vietoris-Rips (VR) complex filtration based on persistent homology in brain networks. In topological data analysis (TDA), persistent homology is an effective tool to explore the nonlinear structure of the data. Compared with the common methods such as principal component analysis (PCA), cluster analysis, and graph theory (Li et al., 2009), TDA can effectively capture the topological information of high-dimensional data space. This kind of algorithm adopts a free threshold and solves the problem of threshold selection. It measures the topological characteristics of brain network under all possible thresholds (Choi et al., 2014; Chung et al., 2015; Lee et al., 2017). These approaches mainly associate the 0-dimensional Betti numbers β₀ with current varying thresholds. A connected component-based aggregation cost model called Integrated Persistence Features (IPF) was proposed in previous research (Kuang et al., 2019). Different from the above persistent homology feature which based on 0-dimensional Betti numbers, this paper proposes a persistent homology feature based on the 1-dimensional Betti number β₁. To our knowledge, there is little literature investigating the 1-dimensional Betti number β₁ in PD. Our main contributions of this paper are as follows: (1) The VR complex filtering model was established based on the relationship matrix of the human brain network. The persistent homology method was used to calculate VR filtered barcodes. And then the functional connectivity neural circuits (FCNC) at different thresholds are calculated from the barcodes. (2) Two-sample Mann–Whitney U test and FDR correction are used for statistical analysis to investigate the FCNC changes between PD and NC groups. (3) Through the statistical tests on the number of FCNC in PD and NC groups, our results show that there is a significant statistical difference between the PD group and the NC group.

The VR complex is established under multiple scales. The 0-dimensional Betti number β₀ and the 1-dimensional Betti number β₁ under each scale are calculated using Javaplex software. Figure 3 plots show the 0-dimensional and 1-dimensional Betti number curves between PD and NC. As depicted from the 0-dimensional Betti number diagram (Figure 3A), with the increase of threshold δ, the number of connected branches of PD and NC gradually decrease from the initial 90. Until the threshold δ = 0.7, they tend to be consistent and gradually decreased to 1. But β₀ in PD is always greater than that in NC when δ ≤ 0.7. In the 1-dimensional Betti number curves (Figure 3B), the topological features was significantly different between the PD brain network and the NC brain network under different thresholds.

In Table 2, two sample Kolmogorov Smirnov (K-S) tests were also conducted from Figures 3A,B to compare whether there is a significant difference in distribution between the PD group and the NC group. From Table 2, it can be seen that the maximum absolute differences in the cumulative probability of Betti numbers in 0-dimension and 1-dimension are 0.049 and 0.082, respectively. Assuming a significance level of 0.05, as the probability p-values (both 0.000) are less than the significance level, it can be concluded that there is a significant difference in the Betti number curve between the PD group and the NC group, regardless of whether it is 0-dimensional or 1-dimensional. Therefore, by comparing the Betti numbers at all scales, the differences between these two groups can be detected.

To more intuitively show the difference between PD and NC groups, comparison of the 1-dimention FCNC in the PD group and the NC group with δ = 0.4 in the Neurocon dataset are shown in Figure 4. Among them, the coronal and sagittal views are shown in Figure 4A and Figure 4B respectively, and their corresponding relationship matrices are given in Figure 4C. Note that, the different colors in Figure 4 only represent different FCNC.

The number of FCNC in 90 brain regions was analyzed and a histogram was drawn in Figure 5. It can be seen intuitively, the average number of FCNC in PD and NC groups is significantly different in some brain regions. To further analyze these differences, the mean and standard deviation of the number of FCNC in each brain region were calculated for the PD and NC groups under thresholds of 0.7, 0.8, and 0.9 in Neurocon dataset, respectively. Then, two sample Mann Whitney U test and false discovery rate (FDR) correction were performed to detect differences between the two groups. The brain regions with statistical differences are shown in Table 3. In PD group, under threshold of 0.7, the number of FCNC involved was significantly differences and these brain regions include the Cuneus_R, Lingual_R, Fusiform_R and Heschl_R. In addition to the aforementioned brain regions, there are also significant differences in brain regions in the Frontal_Inf_Orb_R and Pallidum_R, when the threshold increases to 0.8 and 0.9 (p < 0.05 and FDR correction).

We also analyzed the statistical differences in the number of FCNC with medium lengths in the Neurocon and PPMI datasets (Table 4). From Table 4, it can be seen that there is a significant difference between the PD group and the NC group for medium length of FCNC. Specifically, at thresholds of 0.8 and 0.9, there was a significant difference between the two groups in the Neurocon dataset (length = 8). When the thresholds are 0.7, 0.8, and 0.9, there was a significant difference between the two groups in the PPMI dataset (length = 9). All results were corrected through FDR correction. In these two datasets, at different thresholds, the mean of the PD group is always greater than that of the NC group.

At different thresholds, we can also visually see the significant differences between the two groups through the box-plot in the Neurocon dataset. From the box-plot Figure 6, it can be seen that when the threshold is 0.7, there is no significant difference in the median between the two groups. However, when the thresholds are increased to 0.8 and 0.9, the median of the PD group are significantly higher than that of the NC group. The above results show that there are significant differences in the characteristics of FCNC in some brain regions, and the medium length of FCNC in PD patients show significant changes.

According to the functional classification of the brain, Woo et al. (2014) divided the AAL brain regions into 7 sub networks. That is dorsal attention network (DAN), default mode network (DMN), the visual network (VSN), ventral attention network (VAN), limbic network (LBN), fronto parietal network (FPN) and somatomotor network (SMN) (Esposito et al., 2013; Baum et al., 2017).

By analyzing the FCNC, we found significant statistical difference in the Frontal_Inf_Orb, Cuneus, Lingual gyrus, Fusiform, Pallidum and Heschl areas. A similar result was obtained in previous studies regarding the function connectivity strength of the SMN and VAN (Caspers et al., 2021; Tsuboi et al., 2021) and our findings provide guidance for further studies on the pathogenesis of early PD. Interestingly, increases in FC within SMN (Pang et al., 2021) have been observed upon a dopaminergic challenge in PD patients. Both anterior central gyrus and transverse Nie gyrus belong to SMN. Caspers et al. (2021) pointed out that PD is accompanied by the loss of functional connection of SMN, whether within the network or in the interaction with other networks. The lesions of globus pallidus can have symptoms such as increased muscle tension, decreased movement and static tremor (such as Parkinson’s syndrome). Globus pallidus plays an important role in the regulation of motor function. It is not only the relay nucleus between the caudate putamen (CPU) and subthalamic nucleus (STN), but also integrates the inhibitory afferent from CPU and the excitatory afferent from STN, neocortex and thalamus, thus affecting the efferent signal of basal ganglia (Esposito et al., 2013). Globus pallidus stimulation can be used to improve the brain connectivity in order to treat advanced PD (Tsuboi et al., 2021).

This study applies persistent homology to the brain functional networks of PD. This work provides some new insights into the evolution of functional network in the progression of PD and may provide evidence for the study of preclinical biomarkers of PD. We observed that there are significant differences in the characteristics of FCNC in some brain regions, and the medium length of FCNC in PD patients show significant changes. Topological analysis based on rsfMRI data may provide comprehensive information about the changes of FCNC and may provide an alternative for clinical differential diagnosis.

Publicly available datasets were analyzed in this study. The Neurocon dataset can be found at: http://fcon_1000.projects.nitrc.org/indi/retro/parkinsons.html. The PPMI dataset can be found at: https://www.ppmi-info.org/.

WZ, SX, and XZ designed the research study. DL performed the research. XT and YW wrote the manuscript. All authors contributed to editorial changes in the manuscript, read, and approved the final manuscript.

This work was supported by the Natural Science Foundation of Shandong Province of China (ZR2020ZD25) and the Autonomous Innovation Team Foundation for “20 Items of the New University” of Jinan City (No. 202228087).

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

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