A Continuum Neuronal Model for the Instigation and Propagation of Cortical Spreading Depression

Yao, Wei; Huang, Huaxiong; Miura, Robert M.

doi:10.1007/s11538-011-9647-3

Cited by 44 publications

(66 citation statements)

References 15 publications

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“…Reaction-diffusion models for SD with varying amounts of physiological detail have been proposed (Tuckwell and Miura, 1978;Tuckwell, 1981;Shapiro, 2001;Yao et al, 2011). However, the complexity of these models does not allow for analytical solutions.…”

Section: Methodsmentioning

confidence: 99%

Diffusing Substances during Spreading Depolarization: Analytical Expressions for Propagation Speed, Triggering, and Concentration Time Courses

2013

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Spreading depolarization (SD) is an important phenomenon in stroke and migraine. However, the processes underlying the propagation of SD are still poorly understood, and an elementary model that is both physiological and quantitative is lacking. We show that, during the onset and propagation of SD, the concentration time courses of excitatory substances such as potassium and glutamate can be described with a reaction-diffusion equation. This equation contains four physiological parameters: (1) a concentration threshold for excitation; (2) a release rate; (3) a removal rate; and (4) an effective diffusion constant. Solving this equation yields expressions for the propagation velocity, concentration time courses, and the minimum stimulus that can trigger SD. This framework allows for analyzing experimental results in terms of these four parameters. The derived time courses are validated with measurements of potassium in rat brain tissue.

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Section: Methodsmentioning

confidence: 99%

Diffusing Substances during Spreading Depolarization: Analytical Expressions for Propagation Speed, Triggering, and Concentration Time Courses

2013

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“…For a more detailed description, we refer the readers to Bennett et al 4 , Huang et al27 , and Yao et al60 …”

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confidence: 99%

Mathematical approaches to modeling of cortical spreading depression

Miura

Huang

Wylie

2013

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Migraine with aura (MwA) is a debilitating disease that afflicts about 25%-30% of migraine sufferers. During MwA, a visual illusion propagates in the visual field, then disappears, and is followed by a sustained headache. MwA was conjectured by Lashley to be related to some neurological phenomenon. A few years later, Leão observed electrophysiological waves in the brain that are now known as cortical spreading depression (CSD). CSD waves were soon conjectured to be the neurological phenomenon underlying MwA that had been suggested by Lashley. However, the confirmation of the link between MwA and CSD was not made until 2001 by Hadjikhani et al. [Proc. Natl. Acad. Sci. U.S.A. 98, 4687-4692 (2001)] using functional MRI techniques. Despite the fact that CSD has been studied continuously since its discovery in 1944, our detailed understandings of the interactions between the mechanisms underlying CSD waves have remained elusive. The connection between MwA and CSD makes the understanding of CSD even more compelling and urgent. In addition to all of the information gleaned from the many experimental studies on CSD since its discovery, mathematical modeling studies provide a general and in some sense more precise alternative method for exploring a variety of mechanisms, which may be important to develop a comprehensive picture of the diverse mechanisms leading to CSD wave instigation and propagation. Some of the mechanisms that are believed to be important include ion diffusion, membrane ionic currents, osmotic effects, spatial buffering, neurotransmitter substances, gap junctions, metabolic pumps, and synaptic connections. Discrete and continuum models of CSD consist of coupled nonlinear differential equations for the ion concentrations. In this review of the current quantitative understanding of CSD, we focus on these modeling paradigms and various mechanisms that are felt to be important for CSD.

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“…During propagation, the front of the SD wave extends over several 100 μm in the longitudinal direction, and hence, SD propagation is a smooth process, rather than a chain reaction from neuron to neuron (Yao et al, 2011).…”

Section: Diffusion Of Potassium and Glutamate Can Propagate Sdmentioning

confidence: 99%

How does spreading depression spread? Physiology and modeling

Zandt

Haken

Putten³

et al. 2015

Reviews in the Neurosciences

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AbstractSpreading depression (SD) is a wave phenomenon in gray matter tissue. Locally, it is characterized by massive redistribution of ions across cell membranes. As a consequence, there is sustained membrane depolarization and tissue polarization that depress any normal electrical activity. Despite these dramatic events, SD remains difficult to observe in humans noninvasively, which, for long, has slowed advances in this field. The growing appreciation of its clinical importance in migraine and stroke is therefore consistent with an increasing need for computational methods that tackle the complexity of the problem at multiple levels. In this review, we focus on mathematical tools to investigate the question of spread and its two complementary aspects: What are the physiological mechanisms and what is the spatial extent of SD in the cortex? This review discusses two types of models used to study these two questions, namely, Hodgkin-Huxley type and generic activator-inhibitor models, and the recent advances in techniques to link them.

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A Continuum Neuronal Model for the Instigation and Propagation of Cortical Spreading Depression

Cited by 44 publications

References 15 publications

Diffusing Substances during Spreading Depolarization: Analytical Expressions for Propagation Speed, Triggering, and Concentration Time Courses

Diffusing Substances during Spreading Depolarization: Analytical Expressions for Propagation Speed, Triggering, and Concentration Time Courses

Mathematical approaches to modeling of cortical spreading depression

How does spreading depression spread? Physiology and modeling

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