Simulated brain networks reflecting progression of Parkinson's disease

Abstract

The neurodegenerative progression of Parkinson's disease affects brain structure and function and, concomitantly, alters the topological properties of brain networks. The network alteration accompanied by motor impairment and the duration of the disease has not yet been clearly demonstrated in the disease progression. In this study, we aim to resolve this problem with a modeling approach using the reduced Jansen-Rit model applied to large-scale brain networks derived from cross-sectional MRI data. Optimizing whole-brain simulation models allows us to discover brain networks showing unexplored relationships with clinical variables. We observe that the simulated brain networks exhibit significant differences between healthy controls (n = 51) and patients with Parkinson's disease (n = 60) and strongly correlate with disease severity and disease duration of the patients. Moreover, the modeling results outperform the empirical brain networks in these clinical measures. Consequently, this study demonstrates that utilizing the simulated brain networks provides an enhanced view of network alterations in the progression of motor impairment and identifies potential biomarkers for clinical indices.

Keywords: Brain network; Parkinson’s disease; Progressive disease; Whole-brain model.

Figure 1.

Workflow of the study. (A) Individual WBT calculated from dwMRI data was used to extract parcellation-based empirical SC (streamline counts and streamline path lengths) that was then utilized for derivation of the whole-brain dynamical model, simulation of the resting-state brain activity, and calculation of simulated FC for varying model parameters. For every subject, a few parameter landscapes were obtained, representing the properties of the simulated FC networks, for example, network modularity and efficiency versus model parameters. (B) Individual parameter landscapes of network properties were used for a group-level analysis to obtain a parameter landscape of statistics of simulated network properties across subjects, for example, group differences between patients and healthy controls and correlation between disease severity and network properties. (C) The statistical parameter landscapes and results of the behavioral model fitting were employed for investigation of the relationships between the simulated network properties and clinical variables, for example, disease severity and duration.

Figure 2.

Parameter landscapes of behavioral model fitting of the whole-brain dynamical model of the Jansen-Rit type. The network modularity and network efficiency of simulated FC were used to calculate (A–B) landscapes of the effect size of the group difference between healthy controls (HC) and patients with PD and (C–E) landscapes of Pearson’s correlation (across PD patients) between simulated network properties and severity of the disease, as given by the unified PD rating scales (UPDRS III medication On). The calculations were performed for the Schaefer and the Desikan-Killiany (Desikan) brain atlases indicated in the titles of plots together with the respective network properties. The color depicts the effect size and correlation in plots (A–B) and (C–E), respectively. The vertical lines bound an approximate range of biologically plausible delays; the magenta-white squares indicate the optimal parameter points of the largest effect size or correlation in the parameter domain bounded by the black contour curves of intersection between significant areas thresholded by the random-field theory for multiple tests and areas of high intersubject variance of the respective network properties (> third quartile). See the rightmost plot in the upper row for explanation. Abbreviation: arbitrary unit (a.u.).

Figure 3.

Group difference between healthy controls (HC, n = 51) and patients with PD (n = 60) for two brain parcellations and several comparison conditions. (A–C) The group differences of the network modularity and efficiency between HC and PD for (A) empirical FC, (B) empirical SC, and (C) optimal simulated FC. The empty circles in the plots correspond to individual subjects. The brain parcellations are indicated in the plots, and the values under the plots are the effect sizes of the group difference (positive for HC > PD and negative for PD > HC) and their statistics (p values of the Wilcoxon rank-sum two-tail test). The p values with asterisks indicate significant results (p < 0.05). The middle thick lines in the interquartile boxes indicate the medians of distributions, and the red crosses are the outliers.

Figure 4.

Correlation between severity of the disease of individual PD patients as given by the UPDRS (UPDRS III medication On, horizontal axes) and modularity and efficiency network properties (vertical axes) of empirical and simulated brain connectomes for (A–B) empirical FC, (C–D) empirical SC, and (E–G) simulated FC calculated for the optimal parameters of maximal correlations indicated by the dashed arrows from the optimal model parameter points from Figure 2C–E. The depicting triangles and squares in the plots denote that the two considered brain parcellations correspond to individual PD patients. The used brain parcellations, calculated Pearson’s correlation coefficient, and its statistical test (p value) are indicated in the legends.

Figure 5.

Correlations between disease severity as given by the unified PD rating scales (UPDRS III, medication On) and simulated FC. The latter was simulated for the optimal model parameters of the strongest positive and negative correlations between the disease severity and network efficiency of simulated FC obtained for large and small optimal delays, respectively (Figure 2D–E, square marks). (A–B) Results of statistical tests (p values corrected by the Benjamini-Hochberg false discovery rate) of Pearson’s correlation (across patients) between the disease severity and the edges of the simulated FC for the optimal model parameters of small (lower triangles) and large (upper triangles) delays for each parcellation indicated at the left. (C–D) Histograms of the differences of significant FC edges from lower triangles of the corrected p matrices (A–B) between the large and small optimal delays of each patient and parcellation scheme. The color shading of the histograms indicates the severity of the disease of corresponding patients. (E–F) Scatterplots of the relationships between the disease severity and the differences between the values for the large and small delays of (E) the medians of the histograms in (C–D) and (F) the network efficiency. The depicting triangles and squares in the plots denote the two considered brain parcellations correspond to individual PD patients. The amount of correlation of the depicted relationships are indicated in the plots together with the results of its statistical tests (p values) of Pearson’s correlation for both considered parcellation schemes. In the scatterplot (F, left side), the boxplots depict the distributions of the respective values of the efficiency differences (vertical axes) for 51 healthy controls, where the middle lines in the interquartile boxes indicate the medians of distributions, and the red crosses are outliers. Both distributions were normally distributed according to the Kolmogorov-Smirnov normal distribution test and significantly different from zero (one-sample, two-tail t test).

Figure 6.

Relationships between network efficiency of simulated FC and disease duration. (A) Parameter landscape of Pearson’s correlation coefficients between the simulated network efficiency and the disease duration for the Desikan-Killiany (Desikan) atlas. The vertical lines with “small delay” and “large delay” indicate optimal parameter points for negative and positive correlations, respectively. (B–C) Scatterplots for (B) negative and (C) positive correlations between disease duration and network efficiency of the simulated FC at the optimal parameter points with small and large delay, respectively. The lines are linear fitting between simulated network efficiency and the disease duration. The depicting triangles and squares in the plots denote the two considered brain parcellations and correspond to individual PD patients. The amount of correlation of the depicted relationships are indicated in the plots together with results of statistical tests (p values) for both considered parcellation schemes. (D) Ratio of the optimal simulated network efficiency of large delay to that of small delay for individual patients (vertical axes) sorted according to the ratio of the network efficiency indicated by the horizontal bars with color depicting the disease durations of the corresponding patients. The inserts show medians of the disease duration corresponding to the moving average along the patients in ascending order of the efficiency ratio. The gray shadow indicates interquartile ranges (IQR) of the disease duration. (E) Barplots of the median values of the efficiency ratio with error bars indicating IQR of ratios in five intervals splitting the range from 0 to 1.25. The amount of correlation of the depicted relationships between the efficiency ratio and the disease duration is denoted in the plots together with results of statistical tests (p values) of the Pearson’s correlation and the Spearman’s correlation, respectively.