Artificial neurovascular network (ANVN) to study the accuracy vs. efficiency trade-off in an energy dependent neural network

Artificial feedforward neural networks perform a wide variety of classification and function approximation tasks with high accuracy. Unlike their artificial counterparts, biological neural networks require a supply of adequate energy delivered to single neurons by a network of cerebral microvessels. Since energy is a limited resource, a natural question is whether the cerebrovascular network is capable of ensuring maximum performance of the neural network while consuming minimum energy? Should the cerebrovascular network also be trained, along with the neural network, to achieve such an optimum? In order to answer the above questions in a simplified modeling setting, we constructed an Artificial Neurovascular Network (ANVN) comprising a multilayered perceptron (MLP) connected to a vascular tree structure. The root node of the vascular tree structure is connected to an energy source, and the terminal nodes of the vascular tree supply energy to the hidden neurons of the MLP. The energy delivered by the terminal vascular nodes to the hidden neurons determines the biases of the hidden neurons. The "weights" on the branches of the vascular tree depict the energy distribution from the parent node to the child nodes. The vascular weights are updated by a kind of "backpropagation" of the energy demand error generated by the hidden neurons. We observed that higher performance was achieved at lower energy levels when the vascular network was also trained along with the neural network. This indicates that the vascular network needs to be trained to ensure efficient neural performance. We observed that below a certain network size, the energetic dynamics of the network in the per capita energy consumption vs. classification accuracy space approaches a fixed-point attractor for various initial conditions. Once the number of hidden neurons increases beyond a threshold, the fixed point appears to vanish, giving place to a line of attractors. The model also showed that when there is a limited resource, the energy consumption of neurons is strongly correlated to their individual contribution to the network's performance.

A Network Architecture for Bidirectional Neurovascular Coupling in Rat Whisker Barrel Cortex

Neurovascular coupling is typically considered as a master-slave relationship between the neurons and the cerebral vessels: the neurons demand energy which the vessels supply in the form of glucose and oxygen. In the recent past, both theoretical and experimental studies have suggested that the neurovascular coupling is a bidirectional system, a loop that includes a feedback signal from the vessels influencing neural firing and plasticity. An integrated model of bidirectionally connected neural network and the vascular network is hence required to understand the relationship between the informational and metabolic aspects of neural dynamics. In this study, we present a computational model of the bidirectional neurovascular system in the whisker barrel cortex and study the effect of such coupling on neural activity and plasticity as manifest in the whisker barrel map formation. In this model, a biologically plausible self-organizing network model of rate coded, dynamic neurons is nourished by a network of vessels modeled using the biophysical properties of blood vessels. The neural layer which is designed to simulate the whisker barrel cortex of rat transmits vasodilatory signals to the vessels. The feedback from the vessels is in the form of available oxygen for oxidative metabolism whose end result is the adenosine triphosphate (ATP) necessary to fuel neural firing. The model captures the effect of the feedback from the vascular network on the neuronal map formation in the whisker barrel model under normal and pathological (Hypoxia and Hypoxia-Ischemia) conditions.

A Computational Model of Loss of Dopaminergic Cells in Parkinson's Disease Due to Glutamate-Induced Excitotoxicity

Parkinson's disease (PD) is a neurodegenerative disease associated with progressive and inexorable loss of dopaminergic cells in Substantia Nigra pars compacta (SNc). Although many mechanisms have been suggested, a decisive root cause of this cell loss is unknown. A couple of the proposed mechanisms, however, show potential for the development of a novel line of PD therapeutics. One of these mechanisms is the peculiar metabolic vulnerability of SNc cells compared to other dopaminergic clusters; the other is the SubThalamic Nucleus (STN)-induced excitotoxicity in SNc. To investigate the latter hypothesis computationally, we developed a spiking neuron network-model of SNc-STN-GPe system. In the model, prolonged stimulation of SNc cells by an overactive STN leads to an increase in ‘stress' variable; when the stress in a SNc neuron exceeds a stress threshold, the neuron dies. The model shows that the interaction between SNc and STN involves a positive-feedback due to which, an initial loss of SNc cells that crosses a threshold causes a runaway-effect, leading to an inexorable loss of SNc cells, strongly resembling the process of neurodegeneration. The model further suggests a link between the two aforementioned mechanisms of SNc cell loss. Our simulation results show that the excitotoxic cause of SNc cell loss might initiate by weak-excitotoxicity mediated by energy deficit, followed by strong-excitotoxicity, mediated by a disinhibited STN. A variety of conventional therapies were simulated to test their efficacy in slowing down SNc cell loss. Among them, glutamate inhibition, dopamine restoration, subthalamotomy and deep brain stimulation showed superior neuroprotective-effects in the proposed model.

A computational model of neuro-glio-vascular loop interactions

We present a computational, biophysical model of neuron-astrocyte-vessel interaction. Unlike other cells, neurons convey “hunger” signals to the vascular network via an intervening layer of glial cells (astrocytes); vessels dilate and release glucose which fuels neuronal firing. Existing computational models focus on only parts of this loop (neuron→astrocyte→vessel→neuron), whereas the proposed model describes the entire loop. Neuronal firing causes release of a neurotransmitter like glutamate which triggers release of vasodilator by astrocytes via a cascade of biochemical events. Vasodilators released from astrocytic endfeet cause blood vessels to dilate and release glucose into the interstitium, part of which is taken up by the astrocyticendfeet. Glucose is converted into lactate in the astrocyte and transported into the neuron. Glucose from the interstitium and lactate (produced from glucose) influx from astrocyte are converted into ATP in the neuron. Neuronal ATP is used to drive the Na⁺/K⁺ATPase pumps, which maintain ionic gradients necessary for neuronal firing. When placed in the metabolic loop, the neuron exhibits sustained firing only when the stimulation current is more than a minimum threshold. For various combinations of initial neuronal [ATP] and external current, the neuron exhibits a variety of firing patterns including sustained firing, firing after an initial pause, burst firing etc. Neurovascular interactions under conditions of constricted vessels are also studied. Most models of cerebral circulation describe neurovascular interactions exclusively in the “forward” neuron→vessel direction. The proposed model indicates possibility of “reverse” influence also, with vasomotion rhythms influencing neural firing patterns. Another idea that emerges out of the proposed work is that brain's computations may be more comprehensively understood in terms of neuro-glial-vascular dynamics and not in terms of neural firing alone.

Informational dynamics of vasomotion in microvascular networks: a review

Vasomotion refers to spontaneous oscillation of small vessels observed in many microvascular beds. It is an intrinsic phenomenon unrelated to cardiac rhythm or neural and hormonal regulation. Vasomotion is found to be particularly prominent under conditions of metabolic stress. In spite of a significant existent literature on vasomotion, its physiological and pathophysiological roles are not clear. It is thought that modulation of vasomotion by vasoactive substances released by metabolizing tissue plays a role in ensuring optimal delivery of nutrients to the tissue. Vasomotion rhythms exhibit a great variety of temporal patterns from regular oscillations to chaos. The nature of vasomotion rhythm is believed to be significant to its function, with chaotic vasomotion offering several physiological advantages over regular, periodic vasomotion. In this article, we emphasize that vasomotion is best understood as a network phenomenon. When there is a local metabolic demand in tissue, an ideal vascular response should extend beyond local microvasculature, with coordinated changes over multiple vascular segments. Mechanisms of information transfer over a vessel network have been discussed in the literature. The microvascular system may be regarded as a network of dynamic elements, interacting, either over the vascular anatomical network via gap junctions, or physiologically by exchange of vasoactive substances. Drawing analogies with spatiotemporal patterns in neuronal networks of central nervous system, we ask if properties like synchronization/desynchronization of vasomotors have special significance to microcirculation. Thus the contemporary literature throws up a novel view of microcirculation as a network that exhibits complex, spatiotemporal and informational dynamics.