A Mathematical Network Model of Ischemic Stroke

To work on this thesis, I received a $5,000 undergraduate research scholarship from Arts and Sciences (ASC) HonorsStroke is a major cause of morbidity and mortality in the United States, with one stoke occurring every forty seconds. About eighty-seven percent of all stokes are ischemic, in which a blood vessel to the brain is blocked, resulting in an energy crisis and subsequent disruption of ion gradients. As a result, waves of recurrent spreading depolarizations (RSDs) start to spread throughout the penumbra. Eventually, extracellular glutamate builds up and leads to excitotoxicity, swelling and death of brain cells. The purpose of this research is to better understand the dynamics of the RSDs that have been associated with glutamate accumulation and growth of brain lesions. We have constructed a functioning model of 25 astrocytes and 25 neurons that incorporates membrane potentials, ion currents, cell receptors, sodium-potassium pumps and glial sodium-glutamate transporters. The network model is then reduced to 15 neuron-astrocyte pairs, so that the effect of parameters, such as neuron Na+-K+ ATPase strength and astrocytic Na+-K+ ATPase strength, on RSDs can be determined. Gap junctions between astrocytes are also included in the reduced model to understand how the number of gap junction connections and strength of gap junction impact RSDs.OSU ASC HonorsNo embargoAcademic Major: Neuroscienc

A reaction-diffusion model of cholinergic retinal waves

Prior to receiving visual stimuli, spontaneous, correlated activity called retinal waves drives activity-dependent developmental programs. Early-stage waves mediated by acetylcholine (ACh) manifest as slow, spreading bursts of action potentials. They are believed to be initiated by the spontaneous firing of Starburst Amacrine Cells (SACs), whose dense, recurrent connectivity then propagates this activity laterally. Their extended inter-wave intervals and shifting wave boundaries are the result of the slow after-hyperpolarization of the SACs creating an evolving mosaic of recruitable and refractory cells, which can and cannot participate in waves, respectively. Recent evidence suggests that cholinergic waves may be modulated by the extracellular concentration of ACh. Here, we construct a simplified, biophysically consistent, reaction-diffusion model of cholinergic retinal waves capable of recapitulating wave dynamics observed in mice retina recordings. The dense, recurrent connectivity of SACs is modeled through local, excitatory coupling occurring via the volume release and diffusion of ACh. In contrast with previous, simulation-based models, we are able to use non-linear wave theory to connect wave features to underlying physiological parameters, making the model useful in determining appropriate pharmacological manipulations to experimentally produce waves of a prescribed spatiotemporal character. The model is used to determine how ACh mediated connectivity may modulate wave activity, and how the noise rate and sAHP refractory period contributes to critical wave size variability.Comment: 38 pages, 10 figure

Neuroprotective Role of Gap Junctions in a Neuron Astrocyte Network Model

A detailed biophysical model for a neuron/astrocyte network is developed to explore mechanisms responsible for the initiation and propagation of cortical spreading depolarizations and the role of astrocytes in maintaining ion homeostasis, thereby preventing these pathological waves. Simulations of the model illustrate how properties of spreading depolarizations, such as wave speed and duration of depolarization, depend on several factors, including the neuron and astrocyte Na+-K+ ATPase pump strengths. In particular, we consider the neuroprotective role of astrocyte gap junction coupling. The model demonstrates that a syncytium of electrically coupled astrocytes can maintain a physiological membrane potential in the presence of an elevated extracellular K+ concentration and efficiently distribute the excess K+ across the syncytium. This provides an effective neuroprotective mechanism for delaying or preventing the initiation of spreading depolarizations.Postprint (author's final draft

The Critical Role of Spreading Depolarizations in Early Brain Injury: Consensus and Contention

Background: When a patient arrives in the emergency department following a stroke, a traumatic brain injury, or sudden cardiac arrest, there is no therapeutic drug available to help protect their jeopardized neurons. One crucial reason is that we have not identified the molecular mechanisms leading to electrical failure, neuronal swelling, and blood vessel constriction in newly injured gray matter. All three result from a process termed spreading depolarization (SD). Because we only partially understand SD, we lack molecular targets and biomarkers to help neurons survive after losing their blood flow and then undergoing recurrent SD. Methods: In this review, we introduce SD as a single or recurring event, generated in gray matter following lost blood flow, which compromises the Na/K pump. Electrical recovery from each SD event requires so much energy that neurons often die over minutes and hours following initial injury, independent of extracellular glutamate. Results: We discuss how SD has been investigated with various pitfalls in numerous experimental preparations, how overtaxing the Na/K ATPase elicits SD. Elevated K or glutamate are unlikely natural activators of SD. We then turn to the properties of SD itself, focusing on its initiation and propagation as well as on computer modeling. Conclusions: Finally, we summarize points of consensus and contention among the authors as well as where SD research may be heading. In an accompanying review, we critique the role of the glutamate excitotoxicity theory, how it has shaped SD research, and its questionable importance to the study of early brain injury as compared with SD theory.This work was supported by grants from the Heart and Stroke Foundation of Canada and the National Science and Engineering Research Council of Canada to RDA, an NIH grant (NS106901) to CWS, a National Research, Development and Innovation Office of Hungary grant (K1343777) and EU Horizon 2020 research and innovation program (739953) to EF and from DFG Deutsche Forschungsgemeinschaft (German Research Council) (DFG DR 323/5-1), DFG DR 323/10-1, and BMBF Bundesministerium fuer Bildung und Forschung (EraNet Neuron EBio2, with funds from BMBF 01EW2004) to JPD

Recording, analysis, and interpretation of spreading depolarizations in neurointensive care: Review and recommendations of the COSBID research group.

Spreading depolarizations (SD) are waves of abrupt, near-complete breakdown of neuronal transmembrane ion gradients, are the largest possible pathophysiologic disruption of viable cerebral gray matter, and are a crucial mechanism of lesion development. Spreading depolarizations are increasingly recorded during multimodal neuromonitoring in neurocritical care as a causal biomarker providing a diagnostic summary measure of metabolic failure and excitotoxic injury. Focal ischemia causes spreading depolarization within minutes. Further spreading depolarizations arise for hours to days due to energy supply-demand mismatch in viable tissue. Spreading depolarizations exacerbate neuronal injury through prolonged ionic breakdown and spreading depolarization-related hypoperfusion (spreading ischemia). Local duration of the depolarization indicates local tissue energy status and risk of injury. Regional electrocorticographic monitoring affords even remote detection of injury because spreading depolarizations propagate widely from ischemic or metabolically stressed zones; characteristic patterns, including temporal clusters of spreading depolarizations and persistent depression of spontaneous cortical activity, can be recognized and quantified. Here, we describe the experimental basis for interpreting these patterns and illustrate their translation to human disease. We further provide consensus recommendations for electrocorticographic methods to record, classify, and score spreading depolarizations and associated spreading depressions. These methods offer distinct advantages over other neuromonitoring modalities and allow for future refinement through less invasive and more automated approaches

The Critical Role of Spreading Depolarizations in Early Brain Injury: Consensus and Contention

Background: When a patient arrives in the emergency department following a stroke, a traumatic brain injury, or sudden cardiac arrest, there is no therapeutic drug available to help protect their jeopardized neurons. One crucial reason is that we have not identified the molecular mechanisms leading to electrical failure, neuronal swelling, and blood vessel constriction in newly injured gray matter. All three result from a process termed spreading depolarization (SD). Because we only partially understand SD, we lack molecular targets and biomarkers to help neurons survive after losing their blood flow and then undergoing recurrent SD. Methods: In this review, we introduce SD as a single or recurring event, generated in gray matter following lost blood flow, which compromises the Na+/K+ pump. Electrical recovery from each SD event requires so much energy that neurons often die over minutes and hours following initial injury, independent of extracellular glutamate. Results: We discuss how SD has been investigated with various pitfalls in numerous experimental preparations, how overtaxing the Na+/K+ ATPase elicits SD. Elevated K+ or glutamate are unlikely natural activators of SD. We then turn to the properties of SD itself, focusing on its initiation and propagation as well as on computer modeling. Conclusions: Finally, we summarize points of consensus and contention among the authors as well as where SD research may be heading. In an accompanying review, we critique the role of the glutamate excitotoxicity theory, how it has shaped SD research, and its questionable importance to the study of early brain injury as compared with SD theory. © 2022, The Author(s)

Towards dynamical network biomarkers in neuromodulation of episodic migraine

Computational methods have complemented experimental and clinical neursciences and led to improvements in our understanding of the nervous systems in health and disease. In parallel, neuromodulation in form of electric and magnetic stimulation is gaining increasing acceptance in chronic and intractable diseases. In this paper, we firstly explore the relevant state of the art in fusion of both developments towards translational computational neuroscience. Then, we propose a strategy to employ the new theoretical concept of dynamical network biomarkers (DNB) in episodic manifestations of chronic disorders. In particular, as a first example, we introduce the use of computational models in migraine and illustrate on the basis of this example the potential of DNB as early-warning signals for neuromodulation in episodic migraine.Comment: 13 pages, 5 figure

Migraine Aura, Transient Ischemic Attacks, Stroke, and Dying of the Brain Share the Same Key Pathophysiological Process in Neurons Driven by Gibbs–Donnan Forces, Namely Spreading Depolarization

Neuronal cytotoxic edema is the morphological correlate of the near-complete neuronal battery breakdown called spreading depolarization, or conversely, spreading depolarization is the electrophysiological correlate of the initial, still reversible phase of neuronal cytotoxic edema. Cytotoxic edema and spreading depolarization are thus different modalities of the same process, which represents a metastable universal reference state in the gray matter of the brain close to Gibbs-Donnan equilibrium. Different but merging sections of the spreading-depolarization continuum from short duration waves to intermediate duration waves to terminal waves occur in a plethora of clinical conditions, including migraine aura, ischemic stroke, traumatic brain injury, aneurysmal subarachnoid hemorrhage (aSAH) and delayed cerebral ischemia (DCI), spontaneous intracerebral hemorrhage, subdural hematoma, development of brain death, and the dying process during cardio circulatory arrest. Thus, spreading depolarization represents a prime and simultaneously the most neglected pathophysiological process in acute neurology. Aristides Leao postulated as early as the 1940s that the pathophysiological process in neurons underlying migraine aura is of the same nature as the pathophysiological process in neurons that occurs in response to cerebral circulatory arrest, because he assumed that spreading depolarization occurs in both conditions. With this in mind, it is not surprising that patients with migraine with aura have about a twofold increased risk of stroke, as some spreading depolarizations leading to the patient percept of migraine aura could be caused by cerebral ischemia. However, it is in the nature of spreading depolarization that it can have different etiologies and not all spreading depolarizations arise because of ischemia. Spreading depolarization is observed as a negative direct current (DC) shift and associated with different changes in spontaneous brain activity in the alternating current (AC) band of the electrocorticogram. These are non-spreading depression and spreading activity depression and epileptiform activity. The same spreading depolarization wave may be associated with different activity changes in adjacent brain regions. Here, we review the basal mechanism underlying spreading depolarization and the associated activity changes. Using original recordings in animals and patients, we illustrate that the associated changes in spontaneous activity are by no means trivial, but pose unsolved mechanistic puzzles and require proper scientific analysis

Spreading dynamics on spatially constrained complex brain networks

The study of dynamical systems defined on complex networks provides a natural framework with which to investigate myriad features of neural dynamics and has been widely undertaken. Typically, however, networks employed in theoretical studies bear little relation to the spatial embedding or connectivity of the neural networks that they attempt to replicate. Here, we employ detailed neuroimaging data to define a network whose spatial embedding represents accurately the folded structure of the cortical surface of a rat brain and investigate the propagation of activity over this network under simple spreading and connectivity rules. By comparison with standard network models with the same coarse statistics, we show that the cortical geometry influences profoundly the speed of propagation of activation through the network. Our conclusions are of high relevance to the theoretical modelling of epileptic seizure events and indicate that such studies which omit physiological network structure risk simplifying the dynamics in a potentially significant way

Transient localized wave patterns and their application to migraine

Transient dynamics is pervasive in the human brain and poses challenging problems both in mathematical tractability and clinical observability. We investigate statistical properties of transient cortical wave patterns with characteristic forms (shape, size, duration) in a canonical reaction-diffusion model with mean field inhibition. The patterns are formed by a ghost near a saddle-node bifurcation in which a stable traveling wave (node) collides with its critical nucleation mass (saddle). Similar patterns have been observed with fMRI in migraine. Our results support the controversial idea that waves of cortical spreading depression (SD) have a causal relationship with the headache phase in migraine and therefore occur not only in migraine with aura (MA) but also in migraine without aura (MO), i.e., in the two major migraine subforms. We suggest a congruence between the prevalence of MO and MA with the statistical properties of the traveling waves' forms, according to which (i) activation of nociceptive mechanisms relevant for headache is dependent upon a sufficiently large instantaneous affected cortical area anti-correlated to both SD duration and total affected cortical area such that headache would be less severe in MA than in MO (ii) the incidence of MA is reflected in the distance to the saddle-node bifurcation, and (iii) the contested notion of MO attacks with silent aura is resolved. We briefly discuss model-based control and means by which neuromodulation techniques may affect pathways of pain formation.Comment: 14 pages, 11 figure