arXiv subjects

Christoffer G. Alexandersen

Publications and source records attributed to Christoffer G. Alexandersen.

4 recordsLinked to original sources

arXiv2026

Hysteresis and multistability in network spreading with neuronal activity feedback

Spreading processes on networks often interact with other dynamics on the same nodes. Neurodegenerative disease provides one example: pathological proteins spread through anatomical connections, while neuronal activity influences and is altered by their spread, forming a spreading-activity feedback loop. However, models coupling pathological protein spreading and neuronal activity have largely focused on linear feedback between the two processes. Here we show that nonlinear feedback can fundamentally change the invasion dynamics in a susceptible--infected--susceptible spreading process coupled to a co-evolving activity process. On general weighted networks, the strength and shape of the feedback may generate finite-amplitude invasion thresholds, hysteresis, and endemic multistability. On regular graphs with homogeneous dynamics, we rule out periodic solutions and show that the degrees of polynomial coupling functions bound the number of endemic states, while monotone couplings require reinforcing feedback for multistability. We test these predictions in simulations of a stochastic spiking neuronal network described by quadratic integrate-and-fire dynamics, where we recover both finite-amplitude invasion thresholds and endemic bistability. These results show that feedback from activity processes can create hysteresis and multistability in network spreading dynamics. In neuroscientific applications, our work suggests that neuronal dynamics may act as a control point in neurodegenerative disease, with even transient changes in activity capable of tipping the brain between health and disease.

q-bio.NC↗

arXiv2026

Activity-dependent epidemic spreading on multiscale brain networks predicts Alzheimer's disease progression

Neurodegenerative diseases can be viewed as spreading processes on brain networks, in which pathological proteins propagate between anatomically connected brain regions. Mathematical models have been used to study this process, but they generally ignore the influence of neuronal activity, even though experimental studies show that neuronal firing promotes protein transmission. Here, we couple a general node-activity process to susceptible--infected--susceptible dynamics. In this framework, an epidemic threshold determines whether small pathological seeds can grow, while a dominant network mode determines where growth begins. We derive approximations showing how neuronal activity shifts this threshold and redirects spreading by mixing structural network modes. For networks with multiscale structure, we decompose these changes into contributions from regional mean activity and within-region activity variation, allowing us to account for activity heterogeneity that is not resolved by brain imaging. Stochastic simulations validate the theoretical results across synthetic networks. We next use longitudinal human positron emission tomography to test whether neuronal activity predicts where and how broadly pathology spreads. Regional glucose metabolism serves as a proxy for neuronal activity, while tau accumulation measures disease progression. Adding neuronal activity to the network model captures spatial patterns of disease progression that are not explained by structural connectivity and established disease markers alone. Across individuals, predicted epidemic thresholds are also associated with how broadly pathology spreads through the brain. Together, these results connect epidemic theory to neurodegeneration, implicate neuronal activity as a driver of Alzheimer's disease progression, and motivate activity-modulating therapies to slow or prevent pathological spread.

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arXiv2026

QUIET: Quantifying Underutilized Influential Edges for Targeted Synchronization

Network control theory can be used to model intrinsic and extrinsic strategies to steer neural dynamics. Standard approaches are node-centric, structural, and focused on achieving desired instantaneous states. Here, we develop an edge-centric approach which incorporates both structure and function to achieve extended patterns of neural dynamics characterized by desired synchronization states. Our method, Quantifying Underutilized Influential Edges for Targeted Synchronization (QUIET), is an edge-centric framework that integrates structural controllability of individual white matter connections and mutual information between pairwise functional timeseries to identify energy-efficient synchronization pathways. QUIET identifies quiet highways, edges that are structurally influential but functionally underutilized, to optimize regional synchronization. We validated QUIET across 75 synthetic configurations, where QUIET-ranked edge sets significantly outperformed random selection in 93% of cases (p<0.01). The framework, tested on Human Connectome Project participants, revealed that the control energy required for synchronization of the salience network correlates with fluid intelligence. QUIET, applied to healthy adults undergoing dexmedetomidine-induced unresponsiveness, showed that the frontoparietal and default-mode networks exhibited the largest control energy required for synchronization in both awake and sedated states. QUIET is released as a stand-alone software to be used to study theoretically-defined synchronization pathways, which in turn could inform testable hypotheses in perturbative studies.

eess.SY↗

arXiv2025

Network Models of Neurodegeneration: Bridging Neuronal Dynamics and Disease Progression

Neurodegenerative diseases are characterized by the accumulation of misfolded proteins and widespread disruptions in brain function. Computational modeling has advanced our understanding of these processes, but efforts have traditionally focused on either neuronal dynamics or the underlying biological mechanisms of disease. One class of models uses neural mass and whole-brain frameworks to simulate changes in oscillations, connectivity, and network stability. A second class focuses on biological processes underlying disease progression, particularly prion-like propagation through the connectome, and glial responses and vascular mechanisms. Each modeling tradition has provided important insights, but experimental evidence shows these processes are interconnected: neuronal activity modulates protein release and clearance, while pathological burden feeds back to disrupt circuit function. Modeling these domains in isolation limits our understanding. To determine where and why disease emerges, how it spreads, and how it might be altered, we must develop integrated frameworks that capture feedback between neuronal dynamics and disease biology. In this review, we survey the two modeling approaches and highlight efforts to unify them. We argue that such integration is necessary to address key questions in neurodegeneration and to inform interventions, from targeted stimulation to control-theoretic strategies that slow progression and restore function.

q-bio.NC↗