Differential Dynamic Causal Nets: Model Construction, Identification and Group Comparisons

TL;DR

The paper introduces Differential Dynamic Causal Nets (NccDCM), a data-driven, EEG-based framework that constructs a heterogeneous network of conditionally coupled neural mass units to model brain dynamics across subjects. By solving the nonlinear Jansen–Rit equations with Chen-Fliess expansions and optimizing via an evolutionary JADE method, the authors obtain subject-specific within- and between-channel parameters, which are then analyzed with mixed-effects modeling to identify differential causal nets between cases and controls and between preictal and ictal periods. The work demonstrates that certain edges and biophysically informed parameters differentiate epileptic patients from controls, particularly in frontal regions and DMN-related pathways, and shows systematic parameter shifts around seizure onset. Simulation studies validate identifiability of key ratios (e.g., excitation/inhibition) and reveal bifurcation behavior under varying parameters, supporting the method’s ability to capture both normal and pathological dynamics. Overall, the framework enables data-driven, whole-brain, differential connectivity analyses with explicit biophysical meaning, offering a path toward better understanding and predicting epileptic networks from EEG data.

Abstract

Pathophysiolpgical modelling of brain systems from microscale to macroscale remains difficult in group comparisons partly because of the infeasibility of modelling the interactions of thousands of neurons at the scales involved. Here, to address the challenge, we present a novel approach to construct differential causal networks directly from electroencephalogram (EEG) data. The proposed network is based on conditionally coupled neuronal circuits which describe the average behaviour of interacting neuron populations that contribute to observed EEG data. In the network, each node represents a parameterised local neural system while directed edges stand for node-wise connections with transmission parameters. The network is hierarchically structured in the sense that node and edge parameters are varying in subjects but follow a mixed-effects model. A novel evolutionary optimisation algorithm for parameter inference in the proposed method is developed using a loss function derived from Chen-Fliess expansions of stochastic differential equations. The method is demonstrated by application to the fitting of coupled Jansen-Rit local models. The performance of the proposed method is evaluated on both synthetic and real EEG data. In the real EEG data analysis, we track changes in the parameters that characterise dynamic causality within brains that demonstrate epileptic activity. We show evidence of network functional disruptions, due to imbalance of excitatory-inhibitory interneurons and altered epileptic brain connectivity, before and during seizure periods.

Figures (33)

• Figure 1: A schematic diagram of NccDCM of five channels. The bigger circles stand for channels, each described by a Jansen-Rit neural mass equation with the hidden states $x_0$, $x_1$, and $x_2$. Parameters $C_{\cdot}^{(i|\cdot)}$, $A^{(i|\cdot)}$, and $B^{(i|\cdot)}$ denote the within-channel parameters in channel $i$, taking into account the regressive effects of signal transmission from other channels. Parameter $K^{(i|j)}$ defines a regressive coupling from a designated input channel $j$ to output channel $i$.
• Figure 4: Networks for significant parameters changes after the corrections for multiple testing in the function of inhibitory connections (e.g., in the frontal cortex in psychosis) disrupt normal circuit operations and network dynamics. $A^{(i|j)k}_{nq}/B^{(ilj)k}_{nq}, A^{(i|j)k}_{nq}*C^{(i|j)k}_{nq}, A^{(i|j)k}_{nq}*K^{(i|j)k}_{nq}$ and $v^{(i|j)k}_{0nq}$. Dashed lines stand for edges where the case mean is smaller than the control mean, while solid lines represent edges where the case mean is larger than the control mean.
• Figure 5: Differential causal nets in variation for parameters after the adjustments for multiple testing: (a) $A^{(i|j)k}_{nq}/B^{(ilj)k}_{nq}$, (b) $A^{(i|j)k}_{nq}*C^{(i|j)k}_{nq}$ and (c) $A^{(i|j)k}_{nq}*K^{(i|j)k}_{nq}$ in case-control groups. No significant differential causal nets in variation found in $v^{(i|j)k}_{0nq}$. By dashed (solid) lines, we meant the case mean of variation was smaller (larger) than the control mean of variation. For a comaprison, the maximum lagged correlations-based functional connectivity was also plotted in (d). There were no significant lagged correlations left after the adjustments for multiple testing.
• Figure 6: The percentages of uncertainty in the data which was explained by the NccDCM-based mixed-effects models, $R^2$. See Anderson2017 for the definition of $R^2$.
• Figure 7: Networks for parameters $A^{(i|j)k}_{nq}/B^{(ilj)k}_{nq}, A^{(i|j)k}_{nq}*C^{(i|j)k}_{nq} , A^{(i|j)k}_{nq}*K^{(i|j)k}_{nq}$ and $v^{(i|j)k}_{0nq}$