Reservoir Computing Model For Multi-Electrode Electrophysiological Data Analysis

TL;DR

This work addresses decoding spatio-temporal electrophysiological data to infer macroscopic neuronal connectivity. It introduces a two-domain reservoir computing framework in which each MEA electrode couples to a micro-reservoir, forming a macro-dynamics operator $\hat{\mathcal{O}}$ that maps $\mathbf{y}[n]$ to $\mathbf{y}[n+1]$, and trains only the linear output layer via $\ell_1$-regularized regression. By analyzing the linearized regime, it derives transfer matrices $\mathcal{T}_p$ (with $\mathcal{T}_0 = \mathcal{W}_{out}\hat{\mathcal{S}}\mathcal{W}_{in}$) to recover intrinsic connectivity and higher-order corrections, yielding a functional connectivity map of neuronal populations from MEA data. The approach is demonstrated on mouse cortical MEA recordings, enabling visualization of connectivity graphs and enabling predictions of network responses to localized stimuli, with ongoing benchmarking against synthetic data (NEST) and future experimental validation. Overall, the method offers a computationally efficient, data-driven pathway to map and simulate neural network connectivity and dynamics at the macroscopic level. $\mathcal{T}_0$ and $\mathcal{T}_p$ provide interpretable links between electrode measurements and underlying circuit interactions, facilitating applications in culture studies and stimulus-response analysis.

Abstract

In this paper we present a computational model which decodes the spatio-temporal data from electro-physiological measurements of neuronal networks and reconstructs the network structure on a macroscopic domain, representing the connectivity between neuronal units. The model is based on reservoir computing network (RCN) approach, where experimental data is used as training and validation data. Consequently, the model can be used to study the functionality of different neuronal cultures and simulate the network response to external stimuli.

Figures (4)

• Figure 1: A general description of reservoir computing network (RCN). Time-sequence $u[n]$ is processed in a higher dimensional space by a non-linear reservoir operator, which updates in recurrent manner, via complex interconnections, a reservoir state $\mathbf{x}[n]$ according to the history of the input. This reservoir state is then transformed in an output $y[n]$.
• Figure 2: A scheme of data processing for each time step of the data sequence $\mathbf{y}[n],\mathbf{y}[n+1], \mathbf{y}[n+2] \ldots$ At each time step $n$ a state $\mathbf{y}[n]$, representing the instantaneous activity of the macro-domain network (here encoded in color-scale), is processed by three layers: input, reservoir and output (detailed below) and eventually transformed to the next state of the network, $\mathbf{y}[n+1]$. The whole process is described by the operator $\hat{\mathcal{O}}$ as was defined in \ref{['Eq: Operator']}.
• Figure 3: An example of a connectivity map (or a graph) obtained by the ANN model discussed in this paper. The map corresponds to 60 electrode MEA layout (of $8\times 8$ matrix), where each node represents an electrode in the measurement. Each electrode samples signals from a population of neurons. The connections presented in the figure are taken from the intrinsic connectivity matrix $\mathcal{T}_0$\ref{['eq: intrinsic conn matrix']}, associated with the linearized model (Section \ref{['sec: Linear model']}). The model has been trained on data from microelectrode array (MEA) measurements auslender2023integrated. Note that positive weights assigned to excitatory connections and negative to inhibitory. Threshold of $|\mathcal{T}_0| > 0.05$ was applied for visualization.
• Figure 4: Simulation of network response to a local stimulus. The model has been trained on basal spontaneous activity of the culture and was tested on a response to a stimulus at electrode (node) 45 (lightning symbol on the left figure). Left: Map corresponding to $8\times 8$ MEA. Each pixel represents an electrode, the colorscale indicates the time-integrated response to the stimulus. Right: instantaneous spike rate (ISR) as a function of time (time-bin = $5ms$) of the four most responsive electrode in the network. The figures describe the time evolution of the network (response) following an initial state $\mathbf{y}[1]$ (stimulus).