A model of neurovascular coupling and the BOLD response: PART I

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.

A quantitative model for human neurovascular coupling with translated mechanisms from animals

Neurons regulate the activity of blood vessels through the neurovascular coupling (NVC). A detailed understanding of the NVC is critical for understanding data from functional imaging techniques of the brain. Many aspects of the NVC have been studied both experimentally and using mathematical models; various combinations of blood volume and flow, local field potential (LFP), hemoglobin level, blood oxygenation level-dependent response (BOLD), and optogenetics have been measured and modeled in rodents, primates, or humans. However, these data have not been brought together into a unified quantitative model. We now present a mathematical model that describes all such data types and that preserves mechanistic behaviors between experiments. For instance, from modeling of optogenetics and microscopy data in mice, we learn cell-specific contributions; the first rapid dilation in the vascular response is caused by NO-interneurons, the main part of the dilation during longer stimuli is caused by pyramidal neurons, and the post-peak undershoot is caused by NPY-interneurons. These insights are translated and preserved in all subsequent analyses, together with other insights regarding hemoglobin dynamics and the LFP/BOLD-interplay, obtained from other experiments on rodents and primates. The model can predict independent validation-data not used for training. By bringing together data with complementary information from different species, we both understand each dataset better, and have a basis for a new type of integrative analysis of human data.

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.

Grey-box modeling and hypothesis testing of functional near-infrared spectroscopy-based cerebrovascular reactivity to anodal high-definition tDCS in healthy humans

Transcranial direct current stimulation (tDCS) has been shown to evoke hemodynamics response; however, the mechanisms have not been investigated systematically using systems biology approaches. Our study presents a grey-box linear model that was developed from a physiologically detailed multi-compartmental neurovascular unit model consisting of the vascular smooth muscle, perivascular space, synaptic space, and astrocyte glial cell. Then, model linearization was performed on the physiologically detailed nonlinear model to find appropriate complexity (Akaike information criterion) to fit functional near-infrared spectroscopy (fNIRS) based measure of blood volume changes, called cerebrovascular reactivity (CVR), to high-definition (HD) tDCS. The grey-box linear model was applied on the fNIRS-based CVR during the first 150 seconds of anodal HD-tDCS in eleven healthy humans. The grey-box linear models for each of the four nested pathways starting from tDCS scalp current density that perturbed synaptic potassium released from active neurons for Pathway 1, astrocytic transmembrane current for Pathway 2, perivascular potassium concentration for Pathway 3, and voltage-gated ion channel current on the smooth muscle cell for Pathway 4 were fitted to the total hemoglobin concentration (tHb) changes from optodes in the vicinity of 4x1 HD-tDCS electrodes as well as on the contralateral sensorimotor cortex. We found that the tDCS perturbation Pathway 3 presented the least mean square error (MSE, median <2.5%) and the lowest Akaike information criterion (AIC, median -1.726) from the individual grey-box linear model fitting at the targeted-region. Then, minimal realization transfer function with reduced-order approximations of the grey-box model pathways was fitted to the ensemble average tHb time series. Again, Pathway 3 with nine poles and two zeros (all free parameters), provided the best Goodness of Fit of 0.0078 for Chi-Square difference test of nested pathways. Therefore, our study provided a systems biology approach to investigate the initial transient hemodynamic response to tDCS based on fNIRS tHb data. Future studies need to investigate the steady-state responses, including steady-state oscillations found to be driven by calcium dynamics, where transcranial alternating current stimulation may provide frequency-dependent physiological entrainment for system identification. We postulate that such a mechanistic understanding from system identification of the hemodynamics response to transcranial electrical stimulation can facilitate adequate delivery of the current density to the neurovascular tissue under simultaneous portable imaging in various cerebrovascular diseases.

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.

Locus Coeruleus and neurovascular unit: From its role in physiology to its potential role in Alzheimer's disease pathogenesis

Locus coeruleus (LC) is the main noradrenergic (NA) nucleus of the central nervous system. LC degenerates early during Alzheimer's disease (AD) and NA loss might concur to AD pathogenesis. Aside from neurons, LC terminals provide dense innervation of brain intraparenchymal arterioles/capillaries, and NA modulates astrocyte functions. The term neurovascular unit (NVU) defines the strict anatomical/functional interaction occurring between neurons, glial cells, and brain vessels. NVU plays a fundamental role in coupling the energy demand of activated brain regions with regional cerebral blood flow, it includes the blood-brain barrier (BBB), plays an active role in neuroinflammation, and participates also to the glymphatic system. NVU alteration is involved in AD pathophysiology through several mechanisms, mainly related to a relative oligoemia in activated brain regions and impairment of structural and functional BBB integrity, which contributes also to the intracerebral accumulation of insoluble amyloid. We review the existing data on the morphological features of LC-NA innervation of the NVU, as well as its contribution to neurovascular coupling and BBB proper functioning. After introducing the main experimental data linking LC with AD, which have repeatedly shown a key role of neuroinflammation and increased amyloid plaque formation, we discuss the potential mechanisms by which the loss of NVU modulation by LC might contribute to AD pathogenesis. Surprisingly, thus far not so many studies have tested directly these mechanisms in models of AD in which LC has been lesioned experimentally. Clarifying the interaction of LC with NVU in AD pathogenesis may disclose potential therapeutic targets for AD.

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.