A steady-state model of spreading depression predicts the importance of an unknown conductance in specific dendritic domains

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 Leão 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.

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.

Mechanisms of the negative potential associated with Leão's spreading depolarization: A history of brain electrogenesis

Spreading depolarization (SD) is a self-propagated wave that provokes transient disorder of numerous cell and tissue functions, and that may kill neurons in metabolically compromised tissue. We examined the mechanisms underlying the main hallmark of SD, a giant extracellular potential (ΔVo) for which multiple electromotive forces have been proposed. The end-point is that neurons and not glia, dendritic channels and not spatial currents, and increased sodium conductance rather than potassium gradients, appear to be the main actors in the generation of the negative ΔVo. Neuronal currents are established by two mechanisms, a voltage independent dendritic current, and the differential polarization along the neuron membranes. Notably, despite of a marked drop of ion gradients, these evolve significantly during SD, and yet the membrane potential remains clamped at zero no matter how much inward current is present. There may be substantial inward current or none in function of the evolving portion of the neuron dendrites with SD-activated channels. We propose that the ΔVo promotes swelling-induced dendritic damage. Understanding SD electrogenesis requires all elements relevant for membrane potential, action currents, field potentials and volume conduction to be jointly considered, and it has already encouraged the search for new targets to limit SD-related pathology.

Neural shutdown under stress: an evolutionary perspective on spreading depolarization

Neural function depends on maintaining cellular membrane potentials as the basis for electrical signaling. Yet, in mammals and insects, neuronal and glial membrane potentials can reversibly depolarize to zero, shutting down neural function by the process of spreading depolarization (SD) that collapses the ion gradients across membranes. SD is not evident in all metazoan taxa with centralized nervous systems. We consider the occurrence and similarities of SD in different animals and suggest that it is an emergent property of nervous systems that have evolved to control complex behaviors requiring energetically expensive, rapid information processing in a tightly regulated extracellular environment. Whether SD is beneficial or not in mammals remains an open question. However, in insects, it is associated with the response to harsh environments and may provide an energetic advantage that improves the chances of survival. The remarkable similarity of SD in diverse taxa supports a model systems approach to understanding the mechanistic underpinning of human neuropathology associated with migraine, stroke, and traumatic brain injury.

How does spreading depression spread? Physiology and modeling

Spreading 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.

Activity-dependent calcium, oxygen, and vascular responses in a mouse model of familial hemiplegic migraine type 1

OBJECTIVE

Familial hemiplegic migraine type 1 (FHM1) is a subtype of migraine with aura caused by a gain-of-function mutation in the pore-forming α1 subunit of CaV 2.1 (P/Q-type) calcium channels. However, the mechanisms underlying how the disease is brought about and the prolonged aura remain incompletely understood.

METHODS

In the anesthetized FHM1 mouse model in vivo, we used two-photon microscopy to measure calcium changes in neurons and astrocytes during somatosensory stimulations and cortical spreading depression (CSD), the putative mechanism of the migraine aura. We combined it with assessment of local field potentials by electrophysiological recordings, cerebral blood flow by laser Doppler flowmetry, and oxygen consumption with measurement of the oxygen tissue tension.

RESULTS

During spreading depression, the evoked increase in cytosolic Ca(2+) was larger and faster in FHM1 mice than wild-type (WT) mice. It was accompanied by larger increases in oxygen consumption in FHM1 mice, leading to tissue anoxia, but moderate hypoxia, in WT mice. In comparison, before CSD, Ca(2+) and hemodynamic responses to somatosensory stimulations were smaller in FHM1 mice than WT mice and almost abolished after CSD. The CSD-induced Ca(2+) changes were mitigated by the CaV 2.1 gating modifier, tert-butyl dihydroquinone.

INTERPRETATION

Our findings suggest that tissue anoxia might be a mechanism for prolonged aura in FHM1. Reduced Ca(2+) signals during normal network activity in FHM1 as compared to WT mice may explain impaired neurovascular responses in the mutant, and these alterations could contribute to brain frailty in FHM1 patients. Ann Neurol 2016;80:219-232.

How spreading depolarization can be the pathophysiological correlate of both migraine aura and stroke

The term spreading depolarization describes a mechanism of abrupt, massive ion translocation between neurons and the interstitial space, which leads to a cytotoxic edema in the gray matter of the brain. In energy-compromised tissue, spreading depolarization is preceded by a nonspreading silencing (depression of spontaneous activity) because of a neuronal hyperpolarization. By contrast, in tissue that is not energy compromised, spreading depolarization is accompanied by a spreading silencing (spreading depression) of spontaneous activity caused by a depolarization block. It is assumed that the nonspreading silencing translates into the initial clinical symptoms of ischemic stroke and the spreading silencing (spreading depression) into the symptoms of migraine aura. In energy-compromised tissue, spreading depolarization facilitates neuronal death, whereas, in healthy tissue, it is relatively innocuous. Therapies targeting spreading depolarization in metabolically compromised tissue may potentially treat conditions of acute cerebral injury such as aneurysmal subarachnoid hemorrhage.

Determining the true polarity and amplitude of synaptic currents underlying gamma oscillations of local field potentials

Fluctuations in successive waves of oscillatory local field potentials (LFPs) reflect the ongoing processing of neuron populations. However, their amplitude, polarity and synaptic origin are uncertain due to the blending of electric fields produced by multiple converging inputs, and the lack of a baseline in standard AC-coupled recordings. Consequently, the estimation of underlying currents by laminar analysis yields spurious sequences of inward and outward currents. We devised a combined analytical/experimental approach that is suitable to study laminated structures. The approach was essayed on an experimental oscillatory LFP as the Schaffer-CA1 gamma input in anesthetized rats, and it was verified by parallel processing of model LFPs obtained through a realistic CA1 aggregate of compartmental units. This approach requires laminar LFP recordings and the isolation of the oscillatory input from other converging pathways, which was achieved through an independent component analysis. It also allows the spatial and temporal components of pathway-specific LFPs to be separated. While reconstructed Schaffer-specific LFPs still show spurious inward/outward current sequences, these were clearly stratified into distinct subcellular domains. These spatial bands guided the localized delivery of neurotransmitter blockers in experiments. As expected, only Glutamate but not GABA blockers abolished Schaffer LFPs when applied to the active but not passive subcellular domains of pyramidal cells. The known chemical nature of the oscillatory LFP allowed an empirical offset of the temporal component of Schaffer LFPs, such that following reconstruction they yield only sinks or sources at the appropriate sites. In terms of number and polarity, some waves increased and others decreased proportional to the concomitant inputs in native multisynaptic LFPs. Interestingly, the processing also retrieved the initiation time for each wave, which can be used to discriminate afferent from postsynaptic cells in standard spike-phase correlations. The applicability of this approach to other pathways and structures is discussed.

Sequential changes in neuronal activity in single neocortical neurons after spreading depression

BACKGROUND

Cortical spreading depression (CSD) has an important role in migraine with aura. Prolonged neuronal depression is followed by a late excitatory synaptic plasticity after CSD.

METHOD

Intra- and extracellular recordings were performed to investigate the effect of CSD on intracellular properties of mouse neocortical tissues in the late excitatory period.

RESULTS

During CSD, changes in the membrane potentials usually began with a relatively short hyperpolarization followed by an abrupt depolarization. These changes occurred roughly at the same time point after CSD as the beginning of the negative extracellular deflection. Forty-five minutes after CSD, neurons showed significantly smaller amplitude of afterhyperpolarization and a reduced input resistance. Depolarization and hyperpolarization of the cells by constant intracellular current injections in this period significantly changed the frequency of the action potentials.

CONCLUSION

These data indicate higher excitability of the neocortical neurons after CSD, which can be assumed to contribute to hyperexcitability of neocortical tissues in patients suffering from migraine.

Parallel readout of pathway-specific inputs to laminated brain structures

Local field potentials (LFPs) capture the electrical activity produced by principal cells during integration of converging synaptic inputs from multiple neuronal populations. However, since synaptic currents mix in the extracellular volume, LFPs have complex spatiotemporal structure, making them hard to exploit. Here we propose a biophysical framework to identify and separate LFP-generators. First we use a computational multineuronal model that scales up single cell electrogenesis driven by several synaptic inputs to realistic aggregate LFPs. This approach relies on the fixed but distinct locations of synaptic inputs from different presynaptic populations targeting a laminated brain structure. Thus the LFPs are contributed by several pathway-specific LFP-generators, whose electrical activity is defined by the spatial distribution of synaptic terminals and the time course of synaptic currents initiated in target cells by the corresponding presynaptic population. Then we explore the efficacy of independent component analysis to blindly separate converging sources and reconstruct pathway-specific LFP-generators. This approach can optimally locate synaptic inputs with subcellular accuracy while the reconstructed time course of pathway-specific LFP-generators is reliable in the millisecond scale. We also describe few cases where the non-linear intracellular interaction of strongly overlapping LFP-generators may lead to a significant cross-contamination and the appearance of derivative generators. We show that the approach reliably disentangle ongoing LFPs in the hippocampus into contribution of several LFP-generators. We were able to readout in parallel the pathway-specific presynaptic activity of projection cells in the entorhinal cortex and pyramidal cells in the ipsilateral and contralateral CA3. Thus we provide formal mathematical and experimental support for parallel readout of the activity of converging presynaptic populations in working neuronal circuits from common LFPs.

Generation of Sustained Field Potentials by Gradients of Polarization Within Single Neurons: A Macroscopic Model of Spreading Depression

Spreading depression (SD) is a pathological wave of depolarization of the neural tissue producing a negative macroscopic field potential ( Vo), used as a marker for diagnostic purposes. The cellular basis of SD and neuronal mechanisms of generation of Vo at the microscopic level are poorly understood. Using a CA1 mathematical model and experimental verification, we examined how transmembrane currents in single cells scale up in the extracellular space shaping Vo. The model includes an array of 17,000 realistically modeled neurons (responsible for generating transmembrane currents) dynamically coupled to a virtual aggregate/extracellular space (responsible for Vo). The SD wave in different tissue bands is simulated by imposing membrane shunts in the corresponding dendritic elements as suggested by experimentally assessed drop in membrane resistance. We show that strong isopotential depolarization of wide domains (as in the main SD phase) produce broad central cancellation of axial and transmembrane currents in single cells. When depolarization is restricted to narrow dendritic domains (as in the late SD phase), the internal cancellation shrinks and the transmembrane current increases. This explains why in the laminated CA1 the Vo is smaller in the main phase of SD, when both dendritic layers are seized, than in the SD tail restricted to an apical band. Moreover, scattering of the neuronal somatas (as in cortical regions) further decreases the aggregate Vo due to the volume averaging. Although mechanistically the Vo associated to SD is similar to customary transient fields, its changes maybe related to spatial factors in single cells rather than cell number or depolarization strength.

Migraine aura: retracting particle-like waves in weakly susceptible cortex

Cortical spreading depression (SD) has been suggested to underlie migraine aura. Despite a precise match in speed, the spatio-temporal patterns of SD observed in animal cortex and aura symptoms mapped to the cortical surface ordinarily differ in aspects of size and shape. We show that this mismatch is reconciled by utilizing that both pattern types bifurcate from an instability point of generic reaction-diffusion models. To classify these spatio-temporal pattern we suggest a susceptibility scale having the value sigma = 1 at the instability point. We predict that human cortex is only weakly susceptible to SD (sigma<1), and support this prediction by directly matching visual aura symptoms with anatomical landmarks using fMRI retinotopic mapping. Moreover, we use retinal SD to give a proof of concept of the existence of this instability point and describe how cortical susceptibility to SD must be adjusted for migraine drug testing. Close to the instability point at sigma = 1 the dynamical repertoire of cortical tissue is increased. As a consequence, the picture of an engulfing SD that became paradigmatic for migraine with aura needs to be modified in most cases towards a more spatially confined pattern that remains within the originating major gyrus or sulcus. Furthermore, we discuss the resulting implications on migraine pharmacology that is hitherto tested in the regime (sigma>1), and potentially silent aura occurring below a second bifurcation point at sigma = 0 on the susceptible scale.

A quantitative model of cortical spreading depression due to purinergic and gap-junction transmission in astrocyte networks

Spreading depression (SD), a propagating wave of electrical silence in the cortex and archicortex, involves depolarization of neurons and astrocytes for approximately 1 min, due principally to a large increase in extracellular K+. SD is accompanied by large increases in extracellular ATP and is blocked by glutamate N-methyl-D-aspartate receptor antagonists. As a principal means of transmission between astrocytes is through their release of ATP, we have investigated if a model in which SD is driven by the effects of astrocyte waves of ATP interacting with waves of glutamate release from neurons and astrocytes can give a quantitative account of experimental observations on SD. We show that the characteristics of SD and the accompanying extracellular ionic changes can be accommodated by such a model-whether astrocyte transmission is principally through the release of ATP, as in archicortex (hippocampus) and spinal cord, or via gap junctions, as in the neocortex. Furthermore, these models give quantitative accounts of the effects on the characteristics of SD of agents toxic for astrocytes and of gap-junction blockers. Finally, an additional series of critical tests of the model is suggested.

Variations in tissue resistivity and in the extension of activated neuron domains shape the voltage signal during spreading depression in the CA1 in vivo

Spreading depression (SD), a wave of neuron activity related to migraine and the ischaemic penumbra, features a moving shell of extracellular negative potential shift (V(o)) whose generators are poorly understood. We investigated its subcellular correlates in the hippocampal CA1 in vivo by localizing the neuron domains that generate transmembrane current (I(m)) using field analysis, and the local changes of tissue resistivity, a major determinant of extracellular current flow. A large increase of tissue resistivity occurred in times and dendritic strata displaying large V(o), albeit with different rates. Typically, SD is composed of basal and apical dendritic components. The apical SD lasts much longer, while it becomes gradually restricted to a narrow dendritic region. Strikingly, pyramidal cells displayed a strong surge of inward current only when SD affected a small dendritic region. However, when the V(o) signal covered most of the main neuron axis, only smaller surges of inward current developed at the outer dendritic rims of a wide null current zone. Computational reconstruction showed that this effect was due to strong spatial cancellation of the inward and outward currents in SD-activated isopotential and shunted regions of individual neurons. Consequently, despite former accounts of large conductance increase, the net I(m) is small and the large DeltaV(o) amplitude mostly due to increased tissue resistivity. The particular subcellular evolution indicates an initial explosive opening of conductance along most of the pyramidal neuron followed by a wave-like centripetal closure towards the apical dendrites. The applicability of these mechanisms to SD in other brain regions is discussed.