Cortical network models of impulse firing in the resting and active states predict cortical energetics

Abstract

Measurements of the cortical metabolic rate of glucose oxidation [CMR glc(ox) ] have provided a number of interesting and, in some cases, surprising observations. One is the decline in CMR glc(ox) during anesthesia and non-rapid eye movement (NREM) sleep, and another, the inverse relationship between the resting-state CMR glc(ox) and the transient following input from the thalamus. The recent establishment of a quantitative relationship between synaptic and action potential activity on the one hand and CMR glc(ox) on the other allows neural network models of such activity to probe for possible mechanistic explanations of these phenomena. We have carried out such investigations using cortical models consisting of networks of modules with excitatory and inhibitory neurons, each receiving excitatory inputs from outside the network in addition to intermodular connections. Modules may be taken as regions of cortical interest, the inputs from outside the network as arising from the thalamus, and the intermodular connections as long associational fibers. The model shows that the impulse frequency of different modules can differ from each other by less than 10%, consistent with the relatively uniform CMR glc(ox) observed across different regions of cortex. The model also shows that, if correlations of the average impulse rate between different modules decreases, there is a concomitant decrease in the average impulse rate in the modules, consistent with the observed drop in CMR glc(ox) in NREM sleep and under anesthesia. The model also explains why a transient thalamic input to sensory cortex gives rise to responses with amplitudes inversely dependent on the resting-state frequency, and therefore resting-state CMR glc(ox) .cortical networks | resting-state networks | impulse firing | cortical energetic C lassical measures of cortical activity, using cortical metabolic rate of glucose oxidation [CMR glc(ox) ], give results that are yet to be related in a mechanistic way with the underlying cortical excitability. There is a strict quantitative relationship between impulse and synaptic potential activity and CMR glc(ox) necessary to maintain this activity (1). The recent establishment of this relationship allows for an inquiry into how cortical excitability might give rise to observed changes in CMR glc(ox) in a number of different physiological conditions. Variation in impulse activity between modules in some networks would be expected to reflect the observed variation in CMR glc (ox) . Maximal reported differences of about 32% have been reported between different regions of cortex (2-4), but most cortical regions show much lower variations than this (3). The differences that do exist are not due to variations in thickness of cortex under consideration, nor to differences in the density of neurons (3). However, the differences may reflect that differences in the extent of cortico-cortical associational fiber connections for these are highest in posterior medial and parietal cortex (5), which have a relatively high oxida...

Cortical Network Models of Firing Rates in the Resting and Active States Predict BOLD Responses

“…The projections within these modular networks are illustrated here by two networks with different levels of intermodular connectivity, designated network I (NI) and network II (NII), given in Fig 1B and 1C respectively, from which the external modules have been removed for clarity (for a more detailed description of these networks see [ 15 ]. NI consists of 8 modules (one in isolation for comparison with the rest), with each of these receiving between a single associational input from another module (modules 2 and 8), or inputs from 2 to 3 modules (module 6), with most (63%) of these inputs synapsing on excitatory neurons within modules, the rest on inhibitory neurons ( Fig 1B ).…”

“…The strengths of these connections provided an excitatory to inhibitory ratio of strengths of 0.33 which may be compared with that reported in the literature of 0.5 [ 17 ] to 1.0 [ 18 ]. It should be noted that no attempt has been made in this work to reproduce the wide range of intermodular neuronal types and their connectivity that might lead to more appropriate patterns of firing than that observed in the present and previous modeling studies [ 6 , 15 ]. The overall extent of intramodular connections, their absolute strengths and the total number of neurons per module were selected, given the above restrictions, so that the firing rates of isolated modules were neither continuous nor collapsed to zero.…”

“…The network models we have used in this work have been described in detail in our recent publications [ 6 , 15 ] and are only briefly described here. Modules in the networks, representing cortical areas, possess relatively large numbers of excitatory and inhibitory neurons (75% of the former and 25% of the latter, in agreement with observations of [ 16 ]) with recurrent synaptic connections.…”

“…The formalism for the network in a single isolated module, follows that of [ 6 , 15 ], which in turn was based on [ 28 ] and [ 29 ]. The time evolution of the network is initiated by trains of independent but identically distributed Poisson inputs applied to each neuron.…”

“…Large scale networks of cortico-cortical anatomical connectivity have been used to analyze resting-state cortical activity [ 11 – 14 ] although phenomenological models of lower complexity are very useful in order to reveal important mechanisms responsible for the dynamics of cortical activity [ 11 ]. We have used such phenomenological models [ 15 ], described in the Methods and illustrated in Fig 1 , in order to illuminate the mechanisms relating BOLD activity to the underlying firing rate in the different experiments outlined above.…”