Evolving Network Dynamics Reveal Critical Nodes in the Epileptic Brain

Epilepsy is a neurological condition characterized by persistent and unprovoked seizures that affects nearly 50 million people worldwide, making it one of the most prevalent neurological disorders. About one-third of patients experience drug-resistant epilepsy, in which seizures persist despite pharmacological interventions. For these individuals, surgical resection remains the most effective therapeutic option, particularly in focal epilepsy where seizure activity arises from a localized cortical region. The clinical goal of such interventions is to accurately delineate and remove the cortical area where seizures originate, otherwise known as seizure onset zone (SOZ). The lack of a universally accepted biomarker for the SOZ hampers surgical efficacy, often leading to less-than-optimal results, with long-term successful outcomes varying between 16 and 66 percent depending on the type of epilepsy and surgical intervention [7].

Intracranial electroencephalogram (iEEG) recordings offer a window into the dynamics of the epileptic brain, thus researchers have begun looking to iEEGs to explore potential SOZ biomarkers. Techniques span a broad range, from reconstructing functional brain networks [4] and analyzing their graph-theoretic properties [3], to modeling seizure dynamics through personalized virtual patients [8]. Among these methods, the concept of neural fragility has garnered recent attention by quantifying how easily a patient’s brain network can be destabilized to predict surgical outcomes [5]. 

Despite these advances, significant challenges remain. Many existing techniques rely on static representations of brain networks that average across seizure epochs, often overlooking the rapid, local transitions that define seizure onset. Others achieve impressive predictive performance but act as black boxes, making them difficult to interpret or validate in a clinical setting. These limitations highlight the need for biomarkers that are computationally efficient and transparent enough to integrate seamlessly into surgical planning.

In our recent work [6], we proposed a new biomarker called node degree volatility, which quantifies the rate of change in a node’s functional connectivity over time. We borrowed the term volatility from other disciplines, but in this context it reflects rapid shifts within evolving brain networks. The method begins by reconstructing time-resolved directed functional networks from iEEG recordings using Granger causality [1], this allows for a representation of the brain’s regions as nodes and causal influences as edges. Traditional graph-theoretic measures, such as node degree, count the total number of connections for each node, summarizing its structural importance within the network. Node degree volatility extends this concept by measuring how quickly these connections change, capturing the dynamic local features that static metrics inherently miss. An overview of the study design and computational pipeline is shown in Figure 1.

This focus on rapid changes is motivated by dynamics observed around seizure onset. Seizures are often associated with sudden transitions in neural activity, and one hypothesis is that these transitions involve transient reconfigurations in how regions interact functionally. While the underlying structural wiring of the brain is largely stable on these timescales, evolving functional connectivity patterns may reflect these temporary shifts in network organization. Node degree volatility is designed to capture exactly this: identifying how quickly a node’s connections strengthen, weaken, appear, or disappear, highlights regions that may play dynamically critical roles during seizure initiation.

Figure 2 illustrates the overall framework using data from a patient treated at Emory University Hospital, referred to here as Patient 0. In this case, clinicians had high confidence in the SOZ localization based on distinctive seizure symptoms and responsive neural stimulation that led to long-term seizure freedom. Using this patient as a benchmark, node degree volatility was computed across multiple recorded seizures. Channels clinically identified as part of the SOZ exhibited dramatic peaks in volatility centered around seizure onset, distinguishing them sharply from surrounding non-SOZ regions. 

To test the method’s generalizability, we evaluated it on a diverse cohort of 80 patients with drug-resistant epilepsy across two large datasets, encompassing 82 seizures in total. Using a stringent criterion that required at least one clinically labeled SOZ channel to fall within the top five percent of volatility values, node degree volatility successfully identified SOZ candidates in 75 percent of cases with favorable surgical outcomes. These cases correspond to Engel class I on the Engel Epilepsy Surgical Outcome Scale, where patients experience long-term seizure freedom. Across the analyzed datasets, node degree volatility consistently outperformed existing approaches used to identify SOZs, including neural fragility, static node degree, and betweenness centrality.

An equally important finding is that node degree volatility tends not to reinforce the original SOZ hypothesis in cases with unsuccessful surgical outcomes (Engel classes II–IV). In patients who continued to have seizures after resection, clinically hypothesized SOZ regions often did not rank highly by volatility; instead, the metric highlighted alternative candidate contacts. Across Engel II–IV cases, node degree volatility produced a 30.8 percent false-positive rate, lower than the comparative methods. This pattern suggests that the approach may be useful not only for supporting SOZ hypotheses in successful cases, but also for informing post-operative re-evaluation when initial localization is unsuccessful.

 Beyond its performance, node degree volatility is notable for being computationally efficient and interpretable. Unlike many machine learning (ML) models, it requires no training datasets and operates directly on reconstructed functional networks, making it accessible for integration into clinical workflows. Its formulation also provides physiological intuition: regions that play dynamically critical roles during seizure initiation exhibit rapid reconfiguration of their network connectivity, a signature naturally captured by the volatility measure.

Looking forward, node degree volatility complements rather than replaces existing biomarkers. It can be combined with spectral and structural features or used as a transparent, physiologically grounded input to ML frameworks. Prospective multicenter validation and real-time applications represent promising next steps.

Beyond its utility for epilepsy surgery, the concept of node degree volatility has broader implications for understanding rapid reconfigurations in functional brain networks. Because the metric isolates nodes that undergo abrupt changes in effective connectivity during critical state transitions, it provides a principled and scalable framework for identifying dynamically influential regions across neurological disorders and common brain imaging modalities, including magnetoencephalography and functional magnetic resonance imaging. More generally, this dynamical perspective on nodal influence extends to other complex systems in which transient network reorganization is central to large-scale behavior, suggesting that similar volatility-based approaches may prove valuable for detecting critical elements in evolving biological, social, and engineered networks [2].

Kelley Smith delivered a poster presentation on this research at the 2025 SIAM Conference on Applications of Dynamical Systems (DS25), which took place in Denver, Colo., last year. Kelley Smith and Marrium Shamshad received funding to attend DS25 through a SIAM Student Travel Award. To learn more about Early Career Travel Awards and submit an application, visit the online page.  

Acknowledgments: This work was supported by the Brains and Behavior Program at Georgia State University.

References  
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