Introduction

Intracranial electrical stimulation (iES) has long been used in patients with epilepsy, whether for pre-surgical functional mapping, measuring tissue excitability, or mitigating seizures. Despite this massive clinical use, however, our understanding of how iES activates neural circuits has remained greatly limited. Particularly missing is a precise, quantitative understanding that goes beyond phenomenology, to a level where we can predict how the brain will respond to an unseen iES event. Such an understanding is critical for an optimal predictive approach to responsive neurostimulation design, where the brain’s response to iES with various settings and parameters is simulated in silico in real time and optimized to find the best parameters for the next iES event. Valuable progress has been made through detailed biophysical modeling with geometrically well-defined neuron models, but the results are limited to the local effects of iES on the surrounding tissue and hardly translate to a global understanding of how iES propagates through the entire brain. This gap has been the main motivation behind the present study.

As hinted, our main interest in this problem is from a controls engineering perspective. Over the years, various research groups have sought to improve and automate the design of closed-loop neurostimulation for a variety of conditions, including epilepsy. The results are promising in silico, but have hardly ever been translated into clinical practice. We believe one major factor here has been how the iES itself is modeled. Quite often, the iES is either modeled locally, with extensive biophysical detail, or globally, with no biophysical detail—simply as a linear additive input to a baseline network model. This study sought to find the sweet spot between these extremes: global network models that are complex enough to be empirically accurate, and simple enough to be theoretically tractable.

Our work: Data-Driven Modeling of Evoked Neural Response

The present study was designed to provide a global network model that starts with minimal assumptions and generalizes how iES spreads throughout the brain directly from subject-specific data. Starting with minimal assumptions is critical, especially given that our previous work on resting-state dynamics challenges the expectation that large-scale networks of nonlinear neurons must, by necessity, be modeled using intricate nonlinear approaches. In fact, linear auto-regressive models have shown unexpectedly strong performance in explaining the dynamics under these conditions. Here we pursued a similar approach for data-driven modeling of the brain's response under stimulation. Considering that the system may exhibit stimulation-induced nonlinear effects, we compared a family of linear (AR, ARX) and nonlinear autoregressive models (ANN, LSTM) in our analysis. We focus specifically on bilinear autoregressive models —the simplest nonlinear extension of linear models—which maintain much of the interpretability of linear approaches and have been extensively studied in the context of control design.

The core of our study involves using acute intracranial EEG (iEEG) recordings from patients with epilepsy who underwent iES to train various machine learning models (e.g., bilinear autoregressive) capable of predicting global brain responses to iES. We optimized each model to forecast evoked activity across various brain regions, selected the ones that were most predictive for each subject and channel, and then analyzed these most accurate models to understand how the effects of stimulation ripple through the broader network. We used data from 13 subjects in the Restoring Active Memory (RAM) dataset, each including iEEG across different brain regions under a range of stimulation frequencies and amplitudes. An extremely important feature of this dataset is sweeping over stimulation parameters. This is critical for the generalizability of data-driven models, since without which the models can merely ‘memorize’ the iEEG response to a single stimulation setting without necessarily learning much about the causal flow of evoked response through the network.

Key Findings

The results of our modeling experiments demonstrate that it is indeed possible to predict brain-wide responses to iES using a data-driven, bilinear network model. By comparing our model’s predictions to actual iEEG recordings of brain activity during iES, we found a significant correlation between the predicted and observed responses. Interestingly, we discovered that a specific type of nonlinear model, namely, the switched-linear autoregressive model, outperforms both more complex nonlinear models as well as simpler linear ones. When compared against more sophisticated artificial neural networks (ANNs), we did find the latter to be more accurate, though at the cost of more computational power and memory which are important considerations for future implementations in implantable devices. Furthermore, we found non-smooth, switched-linear ANNs (using ReLU activation) to be more accurate than smooth ANNs (using sigmoidal activation) with similar architecture, a finding that interestingly resonates with the greater accuracy of switch-linear autoregressive models compared to fully bilinear ones noted earlier.

Data-driven models, in addition to serving as ‘digital twins’ for engineering-oriented purposes, can also be used for a purely scientific understanding of how different variables in the system interact—in this case, how stimulation propagates throughout the brain. As expected, we found that stimulation has the strongest impact on areas closest to the electrode, with its influence gradually weakening over distance. However, we found the causal flow of evoked response through the network to follow a non-monotonic, inverted-U-shaped pattern. Specifically, the iES-evoked response in nearby regions has minimal reliance on network connections (e.g., through ephaptic coupling and volume conduction), whereas evoked response in medium-distance areas exhibited the strongest network contribution, and distant regions exhibited minimal evoked response through all means. This observation is crucial for optimizing electrode placement and improving the controllability of brain networks, as it helps refine how stimulation can be targeted to achieve the desired therapeutic effects.

Conclusion

The study we present here represents a significant advancement in our ability to model and predict the effects of iES on brain-wide neural dynamics. However, there is still much work to be done. While our model has shown promise in predicting brain responses to iES in a controlled research setting, further validation in clinical trials will be necessary before it can be implemented in practice. This may require richer datasets with a larger set of stimulation patterns—a costly procedure that yet needs to be carried out in large cohorts of human subjects. Additionally, future work will need to focus on improving the computational efficiency of the model to ensure that it can be integrated into real-time neurostimulation systems. Specifically, we can prune the network-related terms based on functional connectivity, eliminating connections that contribute minimally to the brain's response.

In conclusion, our work lays the foundation for a new paradigm in neurostimulation design, one that is grounded in a deeper understanding of how the brain responds to iES and is driven by patient-specific data. By continuing to refine and validate this model, we hope to bring the benefits of predictive, personalized neurostimulation to patients with epilepsy and beyond.