Ion and transmitter movements during spreading cortical depression

A model of neurovascular coupling and its application to cortical spreading depolarization

Cortical spreading depolarization (CSD) is a neuropathological condition involving propagating waves of neuronal silence, and is related to multiple diseases, such as migraine aura, traumatic brain injury (TBI), stroke, and cardiac arrest, as well as poor outcome of patients. While CSDs of different severity share similar roots on the ion exchange level, they can lead to different vascular responses (namely spreading hyperemia and spreading ischemia). In this paper, we propose a mathematical model relating neuronal activities to predict vascular changes as measured with near-infrared spectroscopy (NIRS) and fMRI recordings, and apply it to the extreme case of CSD, where sustained near-complete neuronal depolarization is seen. We utilize three serially connected models (namely, ion exchange, neurovascular coupling, and hemodynamic model) which are described by differential equations. Propagating waves of ion concentrations, as well as the associated vasodynamics and hemodynamics, are simulated by solving these equations. Our proposed model predicts vasodynamics and hemodynamics that agree both qualitatively and quantitatively with experimental literature. Mathematical modeling and simulation offer a powerful tool to help understand the underlying mechanisms of CSD and help interpret the data. In addition, it helps develop novel monitoring techniques prior to data collection. Our simulated results strongly suggest that fMRI is unable to reliably distinguish between spreading hyperemia and spreading ischemia, while NIRS signals are substantially distinct in the two cases.

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.

Cortical spreading depression as a target for anti-migraine agents

Spreading depression (SD) is a slowly propagating wave of neuronal and glial depolarization lasting a few minutes, that can develop within the cerebral cortex or other brain areas after electrical, mechanical or chemical depolarizing stimulations. Cortical SD (CSD) is considered the neurophysiological correlate of migraine aura. It is characterized by massive increases in both extracellular K⁺ and glutamate, as well as rises in intracellular Na⁺ and Ca²⁺. These ionic shifts produce slow direct current (DC) potential shifts that can be recorded extracellularly. Moreover, CSD is associated with changes in cortical parenchymal blood flow. CSD has been shown to be a common therapeutic target for currently prescribed migraine prophylactic drugs. Yet, no effects have been observed for the antiepileptic drugs carbamazepine and oxcarbazepine, consistent with their lack of efficacy on migraine. Some molecules of interest for migraine have been tested for their effect on CSD. Specifically, blocking CSD may play an enabling role for novel benzopyran derivative tonabersat in preventing migraine with aura. Additionally, calcitonin gene-related peptide (CGRP) antagonists have been recently reported to inhibit CSD, suggesting the contribution of CGRP receptor activation to the initiation and maintenance of CSD not only at the classic vascular sites, but also at a central neuronal level. Understanding what may be lying behind this contribution, would add further insights into the mechanisms of actions for "gepants", which may be pivotal for the effectiveness of these drugs as anti-migraine agents. CSD models are useful tools for testing current and novel prophylactic drugs, providing knowledge on mechanisms of action relevant for migraine.

Self-terminating wave patterns and self-organized pacemakers in a phenomenological model of spreading depression

A simple reaction-diffusion model of spreading depression (SD) is presented. Its local dynamics are governed by two activator and two inhibitor variables that provide an extremely simplified description of the mutual interaction between the neurons and extracellular space. This interaction is realized by the substances in the extracellular space that are increasing excitability of the neurons that have released them and are diffusing to the neighboring neurons, thereby spreading this excitation. Typical dynamic patterns of simulated activity are presented. The focus is laid on the case where response of the extracellular medium is relatively fast, and retracting waves, spiral-shaped waves, and autonomous pacemakers are observed, which is in good agreement with experimental observations. The underlying mechanisms are found to be related to switching between the local bi-stable, excitable, and self-sustained dynamics in the simulated medium. This article is part of a Special Issue entitled: Neural Coding.

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

Spreading depression (SD) is a pathological wave of transient neuronal inactivation. We recently reported that the characteristic sustained complete depolarization is restricted to specific cell domains where the input resistance (R(in)) first becomes negligible before achieving partial recovery, whereas in adjacent, more polarized membranes it drops by much less. The experimental study of the participating membrane channels is hindered by their mixed contribution and heterogeneous distribution. Therefore, we derived a biophysical model to analyze the conductances that replicate the subcellular profile of R(in) during SD. Systematic variation of conductance densities far beyond the ranges reported failed to fit the experimental values. Besides standard potassium, sodium, and Glu-mediated conductances, the initial opening and gradual closing of an as yet undetermined large conductance is required to account for the evolution of R(in). Potassium conductances follow in the relative contribution and their closing during the late phase is also predicted. Large intracellular potential gradients from zero to rest are readily sustained between shunted and adjacent SD-spared membranes, which remain electroregenerative. The gradients are achieved by a combination of high-conductance subcellular domains and transmembrane ion redistribution in extended but discrete dendritic domains. We conclude that the heterogeneous subcellular behavior is due to local membrane properties, some of which may be specifically activated under extreme SD conditions.

Simulation of the effect of Na+ and Cl- on the velocity of a spreading depression wave using a simplified electrochemical model of synaptic terminals

In the study of the spreading depression (SD) wave phenomenon and its dynamics, it is necessary to describe the ionic movements along the extracellular space, as well as between this and the intracellular space. In both cases, the ionic movement includes a double coupling involving the concentration and the potential gradients and hence must be described by electrodiffusion mechanisms. Based on this, the effects of the ionic composition on the characteristics of the wave propagation can be predicted. The influence of varying extracellular sodium and chloride concentrations on the velocity of propagation of the SD wave was investigated by simulation. The results achieved are close to the experimental measurement from the literature. These findings suggest the potentiality of the model proposed in supporting the interpretation of experimental data in neuronal tissues, particularly the SD.

Osmotic forces and gap junctions in spreading depression: a computational model

In a computational model of spreading depression (SD), ionic movement through a neuronal syncytium of cells connected by gap junctions is described electrodiffusively. Simulations predict that SD will not occur unless cells are allowed to expand in response to osmotic pressure gradients and K+ is allowed to move through gap junctions. SD waves of [K+]out approximately 25 to approximately 60 mM moving at approximately 2 to approximately 18 mm/min are predicted over the range of parametric values reported in gray matter, with extracellular space decreasing up to approximately 50%. Predicted waveform shape is qualitatively similar to laboratory reports. The delayed-rectifier, NMDA, BK, and Na+ currents are predicted to facilitate SD, while SK and A-type K+ currents and glial activity impede SD. These predictions are consonant with recent findings that gap junction poisons block SD and support the theories that cytosolic diffusion via gap junctions and osmotic forces are important mechanisms underlying SD.

Cortical potential distributions and information processing

The use of sets of spatiotemporal cortical potential distributions (CPDs) as the basis for cognitive information processing results in a very large space of cognitive elements with natural metrics. Results obtained from current source density (CSD) analysis suggest that in the CPD picture, action potentials may make only a relatively minor contribution to the brain's code. In order to establish if two CPDs are close, we consider standard metrics in spaces of continuous functions, and these may be employed to ascertain if two stimuli will be identified as the same. The correspondence between the electrical activity within brain regions, including not only action potentials but all postsynaptic potentials (PSPs), and CPDs is considered. We examine the possibility of using the CSD approach to find potential distributions using the descriptive approach in which precise sets of times are ascribed to the occurrence of action potentials and PSPs. Using metrics in the multidimensional space of paths of collections of point processes, we show that closeness of CPDs is implied by closeness of sets of spike times and PSP times if a certain metric is used but not others. We also set forth a dynamical model consisting of a system of reaction-dif fusion equations for ionic concentrations coupled with nerve membrane potential equations and active transport systems. Making the approximation of a descriptive approach, the correspondence between sets of spike times and PSP times and CPDs is obtained as with the CSD method. However, since it is not possible to ascribe precise times to the occurrence of PSPs and action potentials, the descriptive approach cannot be used to describe the configuration of electrical activity in cortical regions accurately. We also discuss how the CPD framework relates to the binding problem and submillisecond timing.

Functional imaging of the brain by infrared radiation (thermoencephaloscopy)

A technique for thermal imaging of the animal and human brain cortex using an infrared optical system is described. Thermoencephaloscopy (TES) is based on improved thermovision and image processing techniques and allows two-dimensional, contact-free, dynamic and non-invasive recording of background and evoked cortical activity through an unopened skull. Activated (heated) and deactivated (cooled) zones of the cerebral cortex are revealed. The instrumental temporal resolution of TES is 40 msec (25 maps sec-1), the spatial resolution is up to 70 x 70 microns pixel-1. The diameter of the smallest recordable active region of the cortex is 200-300 microns. TES allows to detect the position, size and sequence of activation of precisely located specific cortical zones, and to measure their dynamics before, during and after sensory and direct cortical stimulation, motor acts and conditioning (associative learning). TES effects were recorded in rats, rabbits, cats, monkeys and humans. Waves were found spreading over the cortex with a speed up to 33 mm sec-1 along trajectories specific for the sensory modality and the site of stimulation. Some pathological processes in the brain are detectable by TES: spreading depression; stress; catalepsy; experimental tumors; and epileptic focuses. The main mechanisms of thermal responses recorded by TES are discussed: neural activity; local metabolism of units; local cerebral blood flow; and thermoconductivity in the activated zones of the cortex. Thermoencephaloscopy is a dynamic, non-invasive, contact-free, comparatively cheap, simple and inexpensive method of neuroimaging with a relatively high temporal and spatial resolution and sensitivity. It can be a useful tool in basic neuroscience and medicine.

Continuum models in neurobiology and information processing

Continuum models have been used with considerable success for single neurons but have been neglected in the study of neuronal populations. In more popular discrete neuronal network models, the geometric details of the neuronal centers are usually neglected. We here give a continuum nonlinear dynamical model and an approximate model which admits the possibility of ascertaining the roles of the various connectivity patterns from center to center in the central nervous system. Frequency transfer characteristics are used to incorporate the nonlinear dynamics of single neurons. Simple examples are evaluated both analytically and numerically and the results presented graphically.

Penetration of substances into tumor tissue: a methodological study with microelectrodes and cellular spheroids

A new method was tested for studies of penetration of substances into tumorlike tissue. The penetration of the ions K+, Cl-, and Ca2+ through several layers of tumor cells was demonstrated by using double barrelled, ion sensitive microelectrodes with extra thin tip diameters. Spheroids consisting of human glioma, U-118 MG, and human thyroid cancer, HTh-7, cells were used as models of tumor tissue. A microelectrode was inserted into the center of a spheroid. Thereafter, the concentration of the test substance was increased in the surrounding medium. The change in concentration inside the spheroid was recorded and the penetration pattern evaluated. All three types of tested ions penetrated easily through the spheroids. The K+ ions penetrated most efficiently, and the Ca2+ ions showed the slowest penetration. The Ca2+ ions penetrated somewhat more slowly in the U-118 MG spheroids (which had rather small extracellular spaces) than in the HTh-7 spheroids (which had larger extracellular spaces). Ion sensitive electrodes, which are easily available, were used in this study only to demonstrate the principle. We hope that the method described can be used for penetration studies of various substances. For example, all substances that can be detected by enzyme microelectrodes could be studied. The main advantage of the method is that the complete penetration pattern can be studied as a function of time in individual spheroids. Previously described methods require histological procedures for each analyzed penetration time.