A Novel Method to Assess Motor Cortex Connectivity and Event Related Desynchronization Based on Mass Models

Abstract

Knowledge of motor cortex connectivity is of great value in cognitive neuroscience, in order to provide a better understanding of motor organization and its alterations in pathological conditions. Traditional methods provide connectivity estimations which may vary depending on the task. This work aims to propose a new method for motor connectivity assessment based on the hypothesis of a task-independent connectivity network, assuming nonlinear behavior. The model considers six cortical regions of interest (ROIs) involved in hand movement. The dynamics of each region is simulated using a neural mass model, which reproduces the oscillatory activity through the interaction among four neural populations. Parameters of the model have been assigned to simulate both power spectral densities and coherences of a patient with left-hemisphere stroke during resting condition, movement of the affected, and movement of the unaffected hand. The presented model can simulate the three conditions using a single set of connectivity parameters, assuming that only inputs to the ROIs change from one condition to the other. The proposed procedure represents an innovative method to assess a brain circuit, which does not rely on a task-dependent connectivity network and allows brain rhythms and desynchronization to be assessed on a quantitative basis.

Keywords: EEG; brain rhythms; excitatory/inhibitory synaptic connections; model–based connectivity; motor cortex after stroke; network model; non–linear coupling.

Figure 1

Block diagram of the neural mass model (upper panel) used to simulate activity in a single region of interest (ROI). Continuous lines denote excitatory synapses (from pyramidal neurons, blue lines, or from excitatory interneurons, green lines), magenta dotted lines denote slow inhibitory synapses, and red dash-dotted lines denote fast inhibitory synapses. The bottom panels show two exempla of connections among ROIs: excitatory (pyramidal-pyramidal) in the left and bi-synaptic inhibitory (pyramidal–fast inhibitory–pyramidal) in the right.

Figure 2

General structure of the connections used to fit the neural mass model to the experimental data. It is evident the presence of feedback connections between the SMAps and the PMDs, and the presence of feedforward connections towards the M1hs. Black lines denote excitatory pyramidal-pyramidal connections, whereas red lines denote inhibitory bi-synaptic connections (pyramidal–fast inhibitory–pyramidal).

Figure 3

Functional connectivity networks obtained using model-free connectivity estimation methods. All the displayed networks are obtained by averaging the estimates over the three tasks. Coherence (upper left panel) is a symmetrical quantity (i.e., it is the same in both directions), therefore, all connections are bidirectional: only connections with maximum coherence value (averaged over the tasks) above 0.3 within the beta band are shown. Thick lines denote a maximum coherence greater than 0.5, medium lines a maximum coherence in the range 0.4–0.5, and thin lines a maximum coherence in the range 0.3–0.4.; gPDC (upper right panel) is a directional quantity: only connections with a gPDC value higher than 0.01 (averaged over the three trials) within the beta band are shown. Line thickness is proportional to the mean gPDC level (thin lines: gPDC < 0. 1; medium lines: 0.1 < gPDC < 0.3; thick lines: gPDC > 0.3). TE (bottom left panel) is also a directional quantity: only connections with TE value (on average) higher than 20% of the maximum TE (maxTE = 0.023) are shown. Line thickness is proportional to the mean TE level (thin lines: TE between 20% and 30% of maxTE; medium lines: TE between 30% and 50% of maxTE; thick lines: TE greater than 50% of maxTE). Pearson’s linear correlation (bottom right panel) is a symmetrical quantity; therefore, all connections are bidirectional: only connections with correlation coefficient absolute value above 0.3 are shown. Here, colors specify whether the bidirectional connection is excitatory (blue, positive correlation coefficient) or inhibitory (red, negative correlation coefficient). It is worth noting that the sign of the correlation never changed from one task to another. Thick lines denote a Pearson correlation coefficient greater than 0.5, medium lines a correlation coefficient in the range 0.4–0.5, and thin lines a correlation coefficient in the range 0.3–0.4.

Figure 4

Connectivity strengths obtained by fitting the neural mass model to the normalized power spectra and coherence of the experimental data (see Section 2.2.2)). Since the fitting procedure has been divided in two main steps (Step 1 and Step 2), results of Step 1 (concerning the SMAp L, SMAp R, PMD L, PMD R) are reported in the upper panel, while results of Step 2 (concerning the connection strengths entering into the M1h L and M1h R) are reported in the second panel, although a single network should be considered in the reality. Black lines denote excitatory pyramidal–pyramidal connections, whereas red lines denote inhibitory bi-synaptic connections (pyramidal–fast inhibitory–pyramidal). Continuous lines are used to denote the higher synapses, dashed lines intermediate synapses, and dotted lines the smaller synapses. All remaining synapses are set at zero. The other parameters of the fitting procedure (internal constants within each ROI and inputs to the SMAps and PMDs) can be found in Table 2 and Table 3.

Figure 5

Normalized power spectral densities in the SMAp L (upper left panel), SMAp R (upper right panel), PMD L (bottom left panel) and PMD R (bottom right panel) obtained in basal condition (green lines) and during movement of the affected (red line) and unaffected (blue lines) hands. In each panel, the left part represents model simulation results with optimal parameter values, and the right part the spectra computed from the experimental data. The model after fitting is able to reproduce the main aspects of the experimental data in a satisfactory way, as confirmed by the analysis of the SD of errors (Supplementary Materials, Table S2).

Figure 6

Coherences among the SMAp L, SMAp R, PMD L and PMD R obtained in basal conditions (green lines) and during movement of the affected (red lines) and unaffected (blue lines) hands. The continuous lines represent model simulation results with optimal parameter values, and the dashed lines the values computed from the experimental data. The model can simulate coherences in the range 10–30 Hz quite satisfactorily in all conditions (as shown by SDs of errors in Supplementary Materials, Table S3), but does not incorporate coherence in the gamma range (>30 Hz). It is worth noting that only the coherences in basal conditions were used in the cost function of the fitting procedure. The others are posterior predictions.

Figure 7

Normalized power spectral densities in the M1h L (left panel) and in the M1h R (right panel), obtained in basal condition (green lines) and during movement of the affected (red lines) and unaffected (blue lines) hands. In each panel, the left figure represents model simulation results with optimal parameter values, and the right figure the spectra computed from the experimental data. The model can simulate the power spectral density, and ERD in a satisfactory way in all conditions, as shown by SDs of errors in Supplementary Materials, Table S2), with the exception of the basal M1h R.

Figure 8

Coherences among the M1h L and all other ROIs obtained in basal conditions (green lines) and during movement of the affected (red lines) and unaffected (blue lines) hands. The continuous lines represent model simulation results with optimal parameter values, and the dashed lines the values computed from the experimental data. It is worth noting that only the coherence M1h L–M1hR in basal conditions was used in the cost function of the fitting procedure. All the others are posterior predictions.

Figure 9

Coherences among the M1h R and all other ROIs obtained in basal conditions (green lines) and during movement of the affected (red lines) and unaffected (blue lines) hands. The continuous lines represent model simulation results with optimal parameter values, and the dashed lines the values computed from the experimental data. It is worth noting that these coherences were not used in the cost function of the fitting procedure, hence are posterior predictions.