A model of neurovascular coupling and the BOLD response PART II

The Reversal Characteristics of GABAergic Neurons: A Neurovascular Model

Neurovascular coupling (NVC) is the ability to locally adjust vascular resistance as a function of neuronal activity. Recent experiments have illustrated that NVC is partially independent of metabolic signals. In addition, nitric oxide (NO) has been shown in some instances to provide an important mechanism in altering vascular resistance. An extension to the original model of NVC [1] has been developed to include the activation of both somatosensory neurons and GABAergic interneurons and to investigate the role of NO and the delicate balance of GABA and neuronal peptide enzymes (NPY) pathways. The numerical model is compared to murine experimental data that provides time-dependent profiles of oxy, de-oxy, and total-hemoglobin. The results indicate a delicate balance that exists between GABA and NPY when nNOS interneurons are activated mediated by NO. Whereas somatosensory neurons (producing potassium into the extracellular space) do not seem to be effected by the inhibition of NO. Further work will need to be done to investigate the role of NO when stimulation periods are increased substantially from the short pulses of 2 s as used in the above experiments.

Inverse neurovascular coupling and associated spreading depolarization models for traumatic brain injury

The paper presents the mathematical model of cortical spreading depolarisation and its effect on inverse neurovascular coupling. The paper considers the potassium ion channels present in the neuron-astrocyte blood vascular network to access the role of potassium ions during spreading depolarisation and associated inverse neurovascular coupling. Simulation of our proposed mathematical model confirms the experimental results that an increase in concentration of potassium ions beyond 20mM in the perivascular space essentially leads to vasoconstriction and hence inverse neurovascular coupling. The propagatory nature of depolarizing potassium waves has been unraveled though our proposed mathematical model.

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.

Elevation of intracranial pressure affects the relationship between hemoglobin concentration and neuronal activation in human somatosensory cortex

During neuronal activation, a local decrease of deoxygenated hemoglobin concentration (deoxy‐Hb) occurs which is the basis of functional brain imaging with blood oxygenation level dependent functional magnetic resonance imaging (BOLD‐fMRI). Elevated intracranial pressure (eICP) has been shown to impair functional deoxy‐Hb changes. This study investigated this effect and its relation to the underlying neuronal activity in the human primary somatosensory cortex (SI). Functional near‐infrared spectroscopy (fNIRS) during somatosensory evoked potentials (SEP) monitoring was performed on 75 subjects during conditions of median nerve stimulation (MNS) and resting state, combined with normal breathing (NB) and eICP by escalating breathing maneuvers (breath holding [BH], Valsalva maneuver with 15 mmHg [V15] and 35 mmHg expiratory pressure [V35]). During NB, fNIRS revealed a typical oxygenated hemoglobin concentration (oxy‐Hb) increase with deoxy‐Hb decrease during MNS enabling SI brain mapping. Breathing maneuvers associated eICP produced a known global change of oxy‐Hb and deoxy‐Hb with and without MNS. When subtracting measurements during resting state from measurements during MNS, neither functional oxy‐Hb nor deoxy‐Hb changes could be recovered while SEPs remained unchanged. In conclusion, Valsalva‐induced eICP prevents oxy‐Hb and deoxy‐Hb changes during neuronal activation in SI. This finding raises questions on the validity of oxy‐Hb‐ and deoxy‐Hb‐based brain imaging (e.g., BOLD‐fMRI) during eICP.

Global Sensitivity Analysis of High-Dimensional Neuroscience Models: An Example of Neurovascular Coupling

The complexity and size of state-of-the-art cell models have significantly increased in part due to the requirement that these models possess complex cellular functions which are thought-but not necessarily proven-to be important. Modern cell models often involve hundreds of parameters; the values of these parameters come, more often than not, from animal experiments whose relationship to the human physiology is weak with very little information on the errors in these measurements. The concomitant uncertainties in parameter values result in uncertainties in the model outputs or quantities of interest (QoIs). Global sensitivity analysis (GSA) aims at apportioning to individual parameters (or sets of parameters) their relative contribution to output uncertainty thereby introducing a measure of influence or importance of said parameters. New GSA approaches are required to deal with increased model size and complexity; a three-stage methodology consisting of screening (dimension reduction), surrogate modeling, and computing Sobol' indices, is presented. The methodology is used to analyze a physiologically validated numerical model of neurovascular coupling which possess 160 uncertain parameters. The sensitivity analysis investigates three quantities of interest, the average value of [Formula: see text] in the extracellular space, the average volumetric flow rate through the perfusing vessel, and the minimum value of the actin/myosin complex in the smooth muscle cell. GSA provides a measure of the influence of each parameter, for each of the three QoIs, giving insight into areas of possible physiological dysfunction and areas of further investigation.

Existence of Initial Dip for BCI: An Illusion or Reality

A tight coupling between the neuronal activity and the cerebral blood flow (CBF) is the motivation of many hemodynamic response (HR)-based neuroimaging modalities. The increase in neuronal activity causes the increase in CBF that is indirectly measured by HR modalities. Upon functional stimulation, the HR is mainly categorized in three durations: (i) initial dip, (ii) conventional HR (i.e., positive increase in HR caused by an increase in the CBF), and (iii) undershoot. The initial dip is a change in oxygenation prior to any subsequent increase in CBF and spatially more specific to the site of neuronal activity. Despite additional evidence from various HR modalities on the presence of initial dip in human and animal species (i.e., cat, rat, and monkey); the existence/occurrence of an initial dip in HR is still under debate. This article reviews the existence and elusive nature of the initial dip duration of HR in intrinsic signal optical imaging (ISOI), functional magnetic resonance imaging (fMRI), and functional near-infrared spectroscopy (fNIRS). The advent of initial dip and its elusiveness factors in ISOI and fMRI studies are briefly discussed. Furthermore, the detection of initial dip and its role in brain-computer interface using fNIRS is examined in detail. The best possible application for the initial dip utilization and its future implications using fNIRS are provided.

Impaired Cerebral Perfusion in Multiple Sclerosis: Relevance of Endothelial Factors

Magnetic resonance imaging techniques measuring in vivo brain perfusion and integrity of the blood-brain barrier have developed rapidly in the past decade, resulting in a wide range of available methods. This review first discusses their principles, possible pitfalls, and potential for quantification and outlines clinical application in neurological disorders. Then, we focus on the endothelial cells of the blood-brain barrier, pointing out their contribution in regulating vascular tone by production of vasoactive substances. Finally, the role of these substances in brain hypoperfusion in multiple sclerosis is discussed.