Low-Dimensional Models of “Neuro-Glio-Vascular Unit” for Describing Neural Dynamics under Normal and Energy-Starved Conditions

Stroke causes massive energy starvation in the brain so your doctor should be able to use this to create interventions during that starvation time period.
http://journal.frontiersin.org/article/10.3389/fneur.2016.00024/full?

Karishma Chhabria and V. Srinivasa Chakravarthy*

• Computational Biophysics and Neurosciences Laboratory, Department of Biotechnology, Bhupat and Jyoti Mehta School of Biosciences, Indian Institute of Technology Madras, Chennai, India

The motivation of developing simple minimal models for neuro-glio-vascular (NGV) system arises from a recent modeling study elucidating the bidirectional information flow within the NGV system having 89 dynamic equations (1). While this was one of the first attempts at formulating a comprehensive model for neuro-glio-vascular system, it poses severe restrictions in scaling up to network levels. On the contrary, low-­dimensional models are convenient devices in simulating large networks that also provide an intuitive understanding of the complex interactions occurring within the NGV system. The key idea underlying the proposed models is to describe the glio-vascular system as a lumped system, which takes neural firing rate as input and returns an “energy” variable (analogous to ATP) as output. To this end, we present two models: biophysical neuro-energy (Model 1 with five variables), comprising K_ATP channel activity governed by neuronal ATP dynamics, and the dynamic threshold (Model 2 with three variables), depicting the dependence of neural firing threshold on the ATP dynamics. Both the models show different firing regimes, such as continuous spiking, phasic, and tonic bursting depending on the ATP production coefficient, ɛ_p, and external current. We then demonstrate that in a network comprising such energy-dependent neuron units, ɛ_p could modulate the local field potential (LFP) frequency and amplitude. Interestingly, low-frequency LFP dominates under low ɛ_p conditions, which is thought to be reminiscent of seizure-like activity observed in epilepsy. The proposed “neuron-energy” unit may be implemented in building models of NGV networks to simulate data obtained from multimodal neuroimaging systems, such as functional near infrared spectroscopy coupled to electroencephalogram and functional magnetic resonance imaging coupled to electroencephalogram. Such models could also provide a theoretical basis for devising optimal neurorehabilitation strategies, such as non-invasive brain stimulation for stroke patients.

1. Introduction

A key tenet of the contemporary neuroscience states that neurons constitute the primary units of brain’s information processing networks. However, there is growing evidence suggesting an imperative role of the “other brain” in sustaining the brain’s physiological activity (2–4). This other brain comprises the glial cells that occupy around half of the brain’s volume, though the exact numbers and neuron/glia ratio vary across the brain (5–8). Developments in glial research over the last two decades reveal the immense and extensive contributions of this system to brain functions, such as neurotransmitter homeostasis, potassium siphoning, and shuttling the energy substrates across the blood–brain barrier among others (2, 9–18). Interestingly, glial cells also sense and modulate the synaptic activity (19, 20) in addition to the above-mentioned maintenance functions. There are significant studies speculating on the contributions of glial cells in brain’s computations (21, 22).

Neural activity is constantly sensed by a type of glial cells called the astrocytes, whose perisynaptic processes eavesdrop on ongoing neurotransmission events (23–25). The end-feet of astrocytes also wrap around the blood vessels, thereby forming the blood–brain barrier (26). This configuration is known to facilitate the transmission of “hunger signals” from the neurons to the cerebral blood vessels through the glial interface (27, 28). The possibility of reverse influence from the vessels to the neurons is generally neglected, though there are experimental grounds supporting the role of vasomotion in various diseases, such as diabetes, hypertension, and even Alzheimer’s disease (29, 30). Recent studies present substantial evidence supporting the role of glio-vascular dysfunction in cognitive impairments, such as epilepsy, neurodegenerative disorders, and migraine (31–33). Furthermore, some recent proposals postulate a role for the glio-vascular system in neural information processing (1, 34–36).

These significant developments in glial and cerebrovascular research indicate a need to incorporate both the glial and vascular systems in an expanded theory of brain’s computations. Hence, it seems pragmatic to investigate further the role of glial cells and the cerebral vasculature in information processing in the brain. Therefore, we hypothesize that the neural activity also has an obligate dependence on the spatiotemporal vascular dynamics governed by the astrocyte activity.

Chander and Chakravarthy (1) proposed a model of the neuro-glio-vascular (NGV) system, in which a single neuron interacts with a single astrocyte and single microvessel. The model is a detailed biophysical model consisting of 89 dynamic equations. In order to explore, using computational models, the possible role of NGV system as a fundamental unit in brain’s information processing, it is essential to develop network models of the NGV system. However, with a model that is significantly complex at single-unit level, it is difficult to scale up to the network level. Therefore, the main objective of the present study was to formulate simple models of the NGV system whose rationale is inspired by the behaviors observed in more complex models like that of Chander and Chakravarthy (1). Considering the serious challenges involved in systematically reducing an 89-dimensional system to a five-variable system, we begin with a simple five-variable biophysical neuron model that captures the dependence of neural firing on ATP. This five-variable biophysical model is constructed by modifying the neuron model of Ching et al. (37).

In an attempt to develop a more generic, low-dimensional model that shows the effects of varying energy (ATP) levels in a spiking neuron model as a function of vessel dynamics, we have developed two models (Figure 1). Our approach to development of the proposed simplified model of the NGV system is as follows: instead of treating the astrocyte and the vessels as independent, isolated entities, we represent the entire glial-vascular system as a single, lumped system, which represents a source of energy substrates for the neurons. Thus, the proposed system has two modules: a neuron module and an “energy” module. The output of the neuron module is its firing activity, which is sensed by the energy module. In turn, the energy module supplies “energy” to the neuron module to fuel its firing activity. Since the neuron module is characterized by the fast neural dynamics, it is considered the fast subsystem. The “energy” module, which represents the slower glial and vascular dynamics, is the slow subsystem. The energy module takes the firing activity output of the neuron module and releases energy in the form of ATP. It must be noted that the firing activity of the neuron has a dual impact on the ATP dynamics: on the one hand, neural firing activity leads to the consumption of ATP via the activity of Na⁺–K⁺ ATPase pump, while on the other hand, it acts as a trigger to induce the energy module to release more energy in the form of ATP (38). Based on this paradigm, we first present the two minimal models for NGV. The first minimal model (Model 1 with five dynamic variables) described in the present study is biophysical and elucidates the effect of intracellular [ATP] on the excitability of a mammalian cortical pyramidal neuron by modulating the K_ATP channel activity. The first model reproduces most of the dynamical behaviors (such as tonic spiking and tonic bursting) of the detailed model. We then propose that this regulatory effect of [ATP] changes the neuronal firing threshold and thereby governs its excitability. Accordingly, we propose the second model (Model 2 with three dynamic variables), which comprises a quadratic integrate-and-fire neuron with a dynamic threshold, governed by intracellular [ATP].

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