Low-Dimensional Models of “Neuro-Glio-Vascular Unit” for Describing Neural Dynamics under Normal and Energy-Starved Conditions - Chhabria, Karishma; Chakravarthy, V. Srinivasa (Frontiers in Neurology, 2016)
The motivation of developing simple minimal models for neuro-glio-vascular system arises from a recent modeling study elucidating the bidirectional information flow within the neuro-glio-vascular system having 89 dynamic equations (Chander and Chakravarthy 2012). While this was one of the first attempts at formulating a comprehensive model for neuro-glia-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 neuro-glio-vascular 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 5 variables), comprising of KATP channel activity governed by neuronal ATP dynamics and the Dynamic threshold (Model #2 with 3 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, εp and external current. We then demonstrate that in a network comprising of such energy-dependent neuron units, εp could modulate the Local field potential (LFP) frequency and amplitude. Interestingly, low frequency LFP dominates under low εp 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 neuro-glio-vascular networks to simulate data obtained from multimodal neuroimaging systems such as fNIRS-EEG and fMRI-EEG. Such models could also provide a theoretical basis for devising optimal neurorehabilitation strategies such as non-invasive brain stimulation for stroke patients.