How does spreading depression spread? Physiology and modeling

Uncertainty quantification and sensitivity analysis of neuron models with ion concentration dynamics

This paper provides a comprehensive and computationally efficient case study for uncertainty quantification (UQ) and global sensitivity analysis (GSA) in a neuron model incorporating ion concentration dynamics. We address how challenges with UQ and GSA in this context can be approached and solved, including challenges related to computational cost, parameters affecting the system's resting state, and the presence of both fast and slow dynamics. Specifically, we analyze the electrodiffusive neuron-extracellular-glia (edNEG) model, which captures electrical potentials, ion concentrations (Na+, K+, Ca2+, and Cl-), and volume changes across six compartments. Our methodology includes a UQ procedure assessing the model's reliability and susceptibility to input uncertainty and a variance-based GSA identifying the most influential input parameters. To mitigate computational costs, we employ surrogate modeling techniques, optimized using efficient numerical integration methods. We propose a strategy for isolating parameters affecting the resting state and analyze the edNEG model dynamics under both physiological and pathological conditions. The influence of uncertain parameters on model outputs, particularly during spiking dynamics, is systematically explored. Rapid dynamics of membrane potentials necessitate a focus on informative spiking features, while slower variations in ion concentrations allow a meaningful study at each time point. Our study offers valuable guidelines for future UQ and GSA investigations on neuron models with ion concentration dynamics, contributing to the broader application of such models in computational neuroscience.

Noninvasive and reliable automated detection of spreading depolarization in severe traumatic brain injury using scalp EEG

BACKGROUND

Spreading depolarizations (SDs) are a biomarker and a potentially treatable mechanism of worsening brain injury after traumatic brain injury (TBI). Noninvasive detection of SDs could transform critical care for brain injury patients but has remained elusive. Current methods to detect SDs are based on invasive intracranial recordings with limited spatial coverage. In this study, we establish the feasibility of automated SD detection through noninvasive scalp electroencephalography (EEG) for patients with severe TBI.

METHODS

Building on our recent WAVEFRONT algorithm, we designed an automated SD detection method. This algorithm, with learnable parameters and improved velocity estimation, extracts and tracks propagating power depressions using low-density EEG. The dataset for testing our algorithm contains 700 total SDs in 12 severe TBI patients who underwent decompressive hemicraniectomy (DHC), labeled using ground-truth intracranial EEG recordings. We utilize simultaneously recorded, continuous, low-density (19 electrodes) scalp EEG signals, to quantify the detection accuracy of WAVEFRONT in terms of true positive rate (TPR), false positive rate (FPR), as well as the accuracy of estimating SD frequency.

RESULTS

WAVEFRONT achieves the best average validation accuracy using Delta band EEG: 74% TPR with less than 1.5% FPR. Further, preliminary evidence suggests WAVEFRONT can estimate how frequently SDs may occur.

CONCLUSIONS

We establish the feasibility, and quantify the performance, of noninvasive SD detection after severe TBI using an automated algorithm. The algorithm, WAVEFRONT, can also potentially be used for diagnosis, monitoring, and tailoring treatments for worsening brain injury. Extension of these results to patients with intact skulls requires further study.

Interneuronal dynamics facilitate the initiation of spike block in cortical microcircuits

Pyramidal cell spike block is a common occurrence in migraine with aura and epileptic seizures. In both cases, pyramidal cells experience hyperexcitation with rapidly increasing firing rates, major changes in electrochemistry, and ultimately spike block that temporarily terminates neuronal activity. In cortical spreading depression (CSD), spike block propagates as a slowly traveling wave of inactivity through cortical pyramidal cells, which is thought to precede migraine attacks with aura. In seizures, highly synchronized cortical activity can be interspersed with, or terminated by, spike block. While the identifying characteristic of CSD and seizures is the pyramidal cell hyperexcitation, it is currently unknown how the dynamics of the cortical microcircuits and inhibitory interneurons affect the initiation of hyperexcitation and subsequent spike block.We tested the contribution of cortical inhibitory interneurons to the initiation of spike block using a cortical microcircuit model that takes into account changes in ion concentrations that result from neuronal firing. Our results show that interneuronal inhibition provides a wider dynamic range to the circuit and generally improves stability against spike block. Despite these beneficial effects, strong interneuronal firing contributed to rapidly changing extracellular ion concentrations, which facilitated hyperexcitation and led to spike block first in the interneuron and then in the pyramidal cell. In all cases, a loss of interneuronal firing triggered pyramidal cell spike block. However, preventing interneuronal spike block was insufficient to rescue the pyramidal cell from spike block. Our data thus demonstrate that while the role of interneurons in cortical microcircuits is complex, they are critical to the initiation of pyramidal cell spike block. We discuss the implications that localized effects on cortical interneurons have beyond the isolated microcircuit and their contribution to CSD and epileptic seizures.

Migraine Visual Aura and Cortical Spreading Depression-Linking Mathematical Models to Empirical Evidence

This review describes the subjective experience of visual aura in migraine, outlines theoretical models of this phenomenon, and explores how these may be linked to neurochemical, electrophysiological, and psychophysical differences in sensory processing that have been reported in migraine with aura. Reaction-diffusion models have been used to model the hallucinations thought to arise from cortical spreading depolarisation and depression in migraine aura. One aim of this review is to make the underlying principles of these models accessible to a general readership. Cortical spreading depolarisation and depression in these models depends on the balance of the diffusion rate between excitation and inhibition and the occurrence of a large spike in activity to initiate spontaneous pattern formation. We review experimental evidence, including recordings of brain activity made during the aura and attack phase, self-reported triggers of migraine, and psychophysical studies of visual processing in migraine with aura, and how these might relate to mechanisms of excitability that make some people susceptible to aura. Increased cortical excitability, increased neural noise, and fluctuations in oscillatory activity across the migraine cycle are all factors that are likely to contribute to the occurrence of migraine aura. There remain many outstanding questions relating to the current limitations of both models and experimental evidence. Nevertheless, reaction-diffusion models, by providing an integrative theoretical framework, support the generation of testable experimental hypotheses to guide future research.

A mathematical model for persistent post-CSD vasoconstriction

Cortical spreading depression (CSD) is the propagation of a relatively slow wave in cortical brain tissue that is linked to a number of pathological conditions such as stroke and migraine. Most of the existing literature investigates the dynamics of short term phenomena such as the depolarization and repolarization of membrane potentials or large ion shifts. Here, we focus on the clinically-relevant hour-long state of neurovascular malfunction in the wake of CSDs. This dysfunctional state involves widespread vasoconstriction and a general disruption of neurovascular coupling. We demonstrate, using a mathematical model, that dissolution of calcium that has aggregated within the mitochondria of vascular smooth muscle cells can drive an hour-long disruption. We model the rate of calcium clearance as well as the dynamical implications on overall blood flow. Based on reaction stoichiometry, we quantify a possible impact of calcium phosphate dissolution on the maintenance of F0F1-ATP synthase activity.

An electrodiffusive, ion conserving Pinsky-Rinzel model with homeostatic mechanisms

In most neuronal models, ion concentrations are assumed to be constant, and effects of concentration variations on ionic reversal potentials, or of ionic diffusion on electrical potentials are not accounted for. Here, we present the electrodiffusive Pinsky-Rinzel (edPR) model, which we believe is the first multicompartmental neuron model that accounts for electrodiffusive ion concentration dynamics in a way that ensures a biophysically consistent relationship between ion concentrations, electrical charge, and electrical potentials in both the intra- and extracellular space. The edPR model is an expanded version of the two-compartment Pinsky-Rinzel (PR) model of a hippocampal CA3 neuron. Unlike the PR model, the edPR model includes homeostatic mechanisms and ion-specific leakage currents, and keeps track of all ion concentrations (Na⁺, K⁺, Ca²⁺, and Cl⁻), electrical potentials, and electrical conductivities in the intra- and extracellular space. The edPR model reproduces the membrane potential dynamics of the PR model for moderate firing activity. For higher activity levels, or when homeostatic mechanisms are impaired, the homeostatic mechanisms fail in maintaining ion concentrations close to baseline, and the edPR model diverges from the PR model as it accounts for effects of concentration changes on neuronal firing. We envision that the edPR model will be useful for the field in three main ways. Firstly, as it relaxes commonly made modeling assumptions, the edPR model can be used to test the validity of these assumptions under various firing conditions, as we show here for a few selected cases. Secondly, the edPR model should supplement the PR model when simulating scenarios where ion concentrations are expected to vary over time. Thirdly, being applicable to conditions with failed homeostasis, the edPR model opens up for simulating a range of pathological conditions, such as spreading depression or epilepsy.

Neurons generate their electrical signals by letting ions pass through their membranes. Despite this fact, most models of neurons apply the simplifying assumption that ion concentrations remain effectively constant during neural activity. This assumption is often quite good, as neurons contain a set of homeostatic mechanisms that make sure that ion concentrations vary quite little under normal circumstances. However, under some conditions, these mechanisms can fail, and ion concentrations can vary quite dramatically. Standard models are thus not able to simulate such conditions. Here, we present what to our knowledge is the first multicompartmental neuron model that accounts for ion concentration variations in a way that ensures complete and consistent ion concentration and charge conservation. In this work, we use the model to explore under which activity conditions the ion concentration variations become important for predicting the neurodynamics. We expect the model to be of great value for the field of neuroscience, as it can be used to simulate a range of pathological conditions, such as spreading depression or epilepsy, which are associated with large changes in extracellular ion concentrations.

A computational study on the role of glutamate and NMDA receptors on cortical spreading depression using a multidomain electrodiffusion model

Cortical spreading depression (SD) is a spreading disruption of ionic homeostasis in the brain during which neurons experience complete and prolonged depolarizations. SD is the basis of migraine aura and is increasingly associated with many other brain pathologies. Here, we study the role of glutamate and NMDA receptor dynamics in the context of an ionic electrodiffusion model. We perform simulations in one (1D) and two (2D) spatial dimension. Our 1D simulations reproduce the "inverted saddle" shape of the extracellular voltage signal for the first time. Our simulations suggest that SD propagation depends on two overlapping mechanisms; one dependent on extracellular glutamate diffusion and NMDA receptors and the other dependent on extracellular potassium diffusion and persistent sodium channel conductance. In 2D simulations, we study the dynamics of spiral waves. We study the properties of the spiral waves in relation to the planar 1D wave, and also compute the energy expenditure associated with the recurrent SD spirals.

Modeling cortical spreading depression induced by the hyperactivity of interneurons

Cortical spreading depression (CSD) is a wave of transient intense neuronal firing leading to a long lasting depolarizing block of neuronal activity. It is a proposed pathological mechanism of migraine with aura. Some forms of migraine are associated with a genetic mutation of the Na_v1.1 channel, resulting in its gain of function and implying hyperexcitability of interneurons. This leads to the counterintuitive hypothesis that intense firing of interneurons can cause CSD ignition. To test this hypothesis in silico, we developed a computational model of an E-I pair (a pyramidal cell and an interneuron), in which the coupling between the cells in not just synaptic, but takes into account also the effects of the accumulation of extracellular potassium caused by the activity of the neurons and of the synapses. In the context of this model, we show that the intense firing of the interneuron can lead to CSD. We have investigated the effect of various biophysical parameters on the transition to CSD, including the levels of glutamate or GABA, frequency of the interneuron firing and the efficacy of the KCC2 co-transporter. The key element for CSD ignition in our model was the frequency of interneuron firing and the related accumulation of extracellular potassium, which induced a depolarizing block of the pyramidal cell. This constitutes a new mechanism of CSD ignition.

Altered Brain Glucose Metabolism Assessed by 18F-FDG PET Imaging Is Associated with the Cognitive Impairment of CADASIL

Recurrent stroke and cognitive impairment are the primary features of patients with cerebral autosomal dominant arteriopathy with subcortical infarcts and leukoencephalopathy (CADASIL). The cognitive deficits in these patients are known to be correlated with structural brain changes, such as white matter lesions and lacunae, and resting-state functional connectivity in brain networks. However, the associations between changes in brain glucose metabolism based on ¹⁸F-2-fluoro-2-deoxy-D-glucose (¹⁸F-FDG) positron emission tomography (PET) imaging and cognitive scores in CADASIL patients remain unclear. In the present study, 24 CADASIL patients and 24 matched healthy controls underwent ¹⁸F-FDG PET imaging. Brain glucose metabolism was measured in all subjects and Pearson's correlation analyses were performed to evaluate relationships between abnormal glucose metabolism in various brain areas and cognitive scores. Compared to controls, CADASIL patients exhibited significantly lower metabolism in the right cerebellar posterior lobe, left cerebellar anterior lobe, bilateral thalamus and left limbic lobe. Additionally, hypermetabolism was observed in the left precentral and postcentral gyri. Importantly, glucose metabolism in the left limbic lobe was positively associated with cognitive scores on the Mini-Mental State Examination (MMSE). Furthermore, glucose metabolism in the left precentral gyri was negatively correlated with cognitive scores on the Montreal Cognitive Assessment (MoCA). The present findings provide strong support for the presence of altered brain glucose metabolism in CADASIL patients as well as the associations between abnormal metabolism and cognitive scales in this population. The present findings suggest that patterns of brain glucose metabolism may become useful markers of cognitive impairment in CADASIL patients.

An Algorithm for Automated, Noninvasive Detection of Cortical Spreading Depolarizations Based on EEG Simulations

OBJECTIVE

We present a novel signal processing algorithm for automated, noninvasive detection of cortical spreading depolarizations (CSDs) using electroencephalography (EEG) signals and validate the algorithm on simulated EEG signals. CSDs are waves of neurochemical changes that suppress the neuronal activity as they propagate across the brain's cortical surface. CSDs are believed to mediate secondary brain damage after brain trauma and cerebrovascular diseases like stroke. We address the following two key challenges in detecting CSDs from EEG signals: i) attenuation and loss of high spatial resolution information; and ii) cortical folds, which complicate tracking CSD waves.

METHODS

Our algorithm detects and tracks "wavefronts" of a CSD wave, and stitch together data across space and time to make a detection. To test our algorithm, we provide different models of CSD waves, including different widths of CSD suppressions and different patterns, and use them to simulate scalp EEG signals using head models of four subjects.

RESULTS AND CONCLUSION

Our results suggest that low-density EEG grids (40 electrodes) can detect CSD widths of 1.1 cm on average, while higher density EEG grids (340 electrodes) can detect CSD patterns as thin as 0.43 cm (less than minimum widths reported in prior works), among which single-gyrus CSDs are the hardest to detect because of their small suppression area.

SIGNIFICANCE

The proposed algorithm is a first step toward noninvasive, automated detection of CSDs, which can help in reducing secondary brain damages.

Cytotoxic Swelling of Sick Excitable Cells - Impaired Ion Homeostasis and Membrane Tension Homeostasis in Muscle and Neuron

When they become simultaneously leaky to both Na⁺ and Cl^-, excitable cells are vulnerable to potentially lethal cytotoxic swelling. Swelling ensues in spite of an isosmotic milieu because the entering ions add osmolytes to the cytoplasm's high concentration of impermeant anionic osmolytes. An influx of osmotically-obliged water is unavoidable. A cell that cannot stanch at least one the leaks will succumb to death by Donnan effect. "Sick excitable cells" are those injured through ischemia, trauma, inflammation, hyperactivity, genetically-impaired membrane skeletons and other insults, all of which foster bleb-damage to regions of the plasma membrane. Nav channels resident in damaged membrane exhibit left-shifted kinetics; the corresponding Nav window conductance constitutes a Na⁺-leak. In cortical neurons, sustained depolarization to ∼-20mV elicits a sustained lethal gCl. Underlying V_rest in skeletal muscle is a constitutively active gCl; not surprisingly therefore, dystrophic muscle fibers, which are prone to bleb damage and which exhibit Nav-leak and Na⁺-overload, are prone to cytotoxic swelling. To restore viability in cytotoxically swelling neurons and muscle, the imperative of fully functional ion homeostasis is well-recognized. However, as emphasized here, in a healthy excitable cell, fully functional membrane tension homeostasis is also imperative. ATPase-pumps keep plasma membrane batteries charged, and ATPase-motor proteins maintain membrane tone. In sick excitable cells, neither condition prevails.

Understanding Spreading Depression from Headache to Sudden Unexpected Death

Spreading depression (SD) is a neurophysiological phenomenon characterized by abrupt changes in intracellular ion gradients and sustained depolarization of neurons. It leads to loss of electrical activity, changes in the synaptic architecture, and an altered vascular response. Although SD is often described as a unique phenomenon with homogeneous characteristics, it may be strongly affected by the particular triggering event and by genetic background. Furthermore, SD may contribute differently to the pathogenesis of widely heterogeneous clinical conditions. Indeed, clinical disorders related to SD vary in their presentation and severity, ranging from benign headache conditions (migraine syndromes) to severely disabling events, such as cerebral ischemia, or even death in people with epilepsy. Although the characteristics and mechanisms of SD have been dissected using a variety of approaches, ranging from cells to human models, this phenomenon remains only partially understood because of its complexity and the difficulty of obtaining direct experimental data. Currently, clinical monitoring of SD is limited to patients who require neurosurgical interventions and the placement of subdural electrode strips. Significantly, SD events recorded in humans display electrophysiological features that are essentially the same as those observed in animal models. Further research using existing and new experimental models of SD may allow a better understanding of its core mechanisms, and of their differences in different clinical conditions, fostering opportunities to identify and develop targeted therapies for SD-related disorders and their worst consequences.

Detecting Cortical Spreading Depolarization with Full Band Scalp Electroencephalography: An Illusion?

Introduction

There is strong evidence suggesting detrimental effects of cortical spreading depolarization (CSD) in patients with acute ischemic stroke and severe traumatic brain injury. Previous studies implicated scalp electroencephalography (EEG) features to be correlates of CSD based on retrospective analysis of EEG epochs after having detected “CSD” in time aligned electrocorticography. We studied the feasibility of CSD detection in a prospective cohort study with continuous EEG in 18 patients with acute ischemic stroke and 18 with acute severe traumatic brain injury.

Methods

Full band EEG with 21 silver/silver chloride electrodes was started within 48 h since symptom onset. Five additional electrodes were used above the infarct. We visually analyzed all raw EEG data in epochs of 1 h. Inspection was directed at detection of the typical combination of CSD characteristics, i.e., (i) a large slow potential change (SPC) accompanied by a simultaneous amplitude depression of >1Hz activity, (ii) focal presentation, and (iii) spread reflected as appearance on neighboring electrodes with a delay.

Results

In 3,035 one-hour EEG epochs, infraslow activity (ISA) was present in half to three quarters of the registration time. Typically, activity was intermittent with amplitudes of 40–220 µV, approximately half was oscillatory. There was no specific spatial distribution. Relevant changes of ISA were always visible in multiple electrodes, and not focal, as expected in CSD. ISA appearing as “SPC” was mostly associated with an amplitude increase of faster activities, and never with suppression. In all patients, depressions of spontaneous brain activity occurred. However, these were not accompanied by simultaneous SPC, occurred simultaneously on all channels, and were not focal, let alone spread, as expected in CSD.

Conclusion

With full band scalp EEG in patients with cortical ischemic stroke or traumatic brain injury, we observed various ISA, probably modulating cortical excitability. However, we were unable to identify unambiguous characteristics of CSD.

Patient-specific computational modeling of cortical spreading depression via diffusion tensor imaging

Cortical spreading depression, a depolarization wave originating in the visual cortex and traveling towards the frontal lobe, is commonly accepted as a correlate of migraine visual aura. As of today, little is known about the mechanisms that can trigger or stop such phenomenon. However, the complex and highly individual characteristics of the brain cortex suggest that the geometry might have a significant impact in supporting or contrasting the propagation of cortical spreading depression. Accurate patient-specific computational models are fundamental to cope with the high variability in cortical geometries among individuals, but also with the conduction anisotropy induced in a given cortex by the complex neuronal organisation in the grey matter. In this paper, we integrate a distributed model for extracellular potassium concentration with patient-specific diffusivity tensors derived locally from diffusion tensor imaging data.

Heterogeneous propagation of spreading depolarizations in the lissencephalic and gyrencephalic brain

In the recently published article, "Heterogeneous incidence and propagation of spreading depolarizations," it is shown, in vivo and in vitro, how KCl-induced spreading depolarizations in mouse and rat brains can be highly variable, and that they are not limited, as once thought, to a concentric, isotropic, or homogenous depolarization wave in space or in time. The reported results serve as a link between the different species, and this paper contributes to changing the way in which SD expansion is viewed in the lissencephalic brain. Here, we discuss their results with our previous observations made in the gyrencephalic swine brain, in computer simulations, and in the human brain.

Effects of Glia in a Triphasic Continuum Model of Cortical Spreading Depression

Cortical spreading depression (SD) is a spreading disruption in brain ionic homeostasis during which neurons experience complete and prolonged depolarizations. SD is generally believed to be the physiological substrate of migraine aura and is associated with many other brain pathologies. Here, we perform simulations with a model of SD treating brain tissue as a triphasic continuum of neurons, glia and the extracellular space. A thermodynamically consistent incorporation of the major biophysical effects, including ionic electrodiffusion and osmotic water flow, allows for the computation of important physiological variables including the extracellular voltage (DC) shift. A systematic parameter study reveals that glia can act as both a disperser and buffer of potassium in SD propagation. Furthermore, we show that the timing of the DC shift with respect to extracellular [Formula: see text] rise is highly dependent on glial parameters, a result with implications for the identification of the propagating mechanism of SD.

Multistability in Large Scale Models of Brain Activity

Noise driven exploration of a brain network’s dynamic repertoire has been hypothesized to be causally involved in cognitive function, aging and neurodegeneration. The dynamic repertoire crucially depends on the network’s capacity to store patterns, as well as their stability. Here we systematically explore the capacity of networks derived from human connectomes to store attractor states, as well as various network mechanisms to control the brain’s dynamic repertoire. Using a deterministic graded response Hopfield model with connectome-based interactions, we reconstruct the system’s attractor space through a uniform sampling of the initial conditions. Large fixed-point attractor sets are obtained in the low temperature condition, with a bigger number of attractors than ever reported so far. Different variants of the initial model, including (i) a uniform activation threshold or (ii) a global negative feedback, produce a similarly robust multistability in a limited parameter range. A numerical analysis of the distribution of the attractors identifies spatially-segregated components, with a centro-medial core and several well-delineated regional patches. Those different modes share similarity with the fMRI independent components observed in the “resting state” condition. We demonstrate non-stationary behavior in noise-driven generalizations of the models, with different meta-stable attractors visited along the same time course. Only the model with a global dynamic density control is found to display robust and long-lasting non-stationarity with no tendency toward either overactivity or extinction. The best fit with empirical signals is observed at the edge of multistability, a parameter region that also corresponds to the highest entropy of the attractors.

Recent developments in non-invasive brain imaging allow reconstructing axonal tracts in the human brain and building realistic network models of the human brain. These models resemble brain systems in their network character and allow deciphering how different regions share signals and process information. Inspired by the metastable dynamics of the spin glass model in statistical physics, we systematically explore the brain network’s capacity to process information and investigate novel avenues how to enhance it. In particular, we study how the brain activates and switches between different functional networks across time. Such non-stationary behavior has been observed in human brain imaging data and hypothesized to be linked to information processsing. To shed light on the conditions under which large-scale brain network models exhibit such dynamics, we characterize the principal network patterns and confront them with modular structures observed both in graph theoretical analysis and resting-state functional Magnetic Resonance Imaging (rs-fMRI).

Computational modeling of neurostimulation in brain diseases

Neurostimulation as a therapeutic tool has been developed and used for a range of different diseases such as Parkinson's disease, epilepsy, and migraine. However, it is not known why the efficacy of the stimulation varies dramatically across patients or why some patients suffer from severe side effects. This is largely due to the lack of mechanistic understanding of neurostimulation. Hence, theoretical computational approaches to address this issue are in demand. This chapter provides a review of mechanistic computational modeling of brain stimulation. In particular, we will focus on brain diseases, where mechanistic models (e.g., neural population models or detailed neuronal models) have been used to bridge the gap between cellular-level processes of affected neural circuits and the symptomatic expression of disease dynamics. We show how such models have been, and can be, used to investigate the effects of neurostimulation in the diseased brain. We argue that these models are crucial for the mechanistic understanding of the effect of stimulation, allowing for a rational design of stimulation protocols. Based on mechanistic models, we argue that the development of closed-loop stimulation is essential in order to avoid inference with healthy ongoing brain activity. Furthermore, patient-specific data, such as neuroanatomic information and connectivity profiles obtainable from neuroimaging, can be readily incorporated to address the clinical issue of variability in efficacy between subjects. We conclude that mechanistic computational models can and should play a key role in the rational design of effective, fully integrated, patient-specific therapeutic brain stimulation.

Cortical hot spots and labyrinths: why cortical neuromodulation for episodic migraine with aura should be personalized

Stimulation protocols for medical devices should be rationally designed. For episodic migraine with aura we outline model-based design strategies toward preventive and acute therapies using stereotactic cortical neuromodulation. To this end, we regard a localized spreading depression (SD) wave segment as a central element in migraine pathophysiology. To describe nucleation and propagation features of the SD wave segment, we define the new concepts of cortical hot spots and labyrinths, respectively. In particular, we firstly focus exclusively on curvature-induced dynamical properties by studying a generic reaction-diffusion model of SD on the folded cortical surface. This surface is described with increasing level of details, including finally personalized simulations using patient's magnetic resonance imaging (MRI) scanner readings. At this stage, the only relevant factor that can modulate nucleation and propagation paths is the Gaussian curvature, which has the advantage of being rather readily accessible by MRI. We conclude with discussing further anatomical factors, such as areal, laminar, and cellular heterogeneity, that in addition to and in relation to Gaussian curvature determine the generalized concept of cortical hot spots and labyrinths as target structures for neuromodulation. Our numerical simulations suggest that these target structures are like fingerprints, they are individual features of each migraine sufferer. The goal in the future will be to provide individualized neural tissue simulations. These simulations should predict the clinical data and therefore can also serve as a test bed for exploring stereotactic cortical neuromodulation.