Mechanistic Mathematical Modeling Tests Hypotheses of the Neurovascular Coupling in fMRI

An interaction graph approach to gain new insights into mechanisms that modulate cerebrovascular tone

Mechanisms to modulate cerebrovascular tone are numerous, interconnected, and spatially dependent, increasing the complexity of experimental study design, interpretation of action-effect pathways, and mechanistic modelling. This difficulty is exacerbated when there is an incomplete understanding of these pathways. We propose interaction graphs to break down this complexity, while still maintaining a holistic view of mechanisms to modulate cerebrovascular tone. These graphs highlight the competing processes of neurovascular coupling, cerebral autoregulation, and cerebral reactivity. Subsequent analysis of these interaction graphs provides new insights and suggest potential directions for research on neurovascular coupling, modelling, and dementia.

Mechanistic model for human brain metabolism and its connection to the neurovascular coupling

The neurovascular and neurometabolic couplings (NVC and NMC) connect cerebral activity, blood flow, and metabolism. This interconnection is used in for instance functional imaging, which analyses the blood-oxygen-dependent (BOLD) signal. The mechanisms underlying the NVC are complex, which warrants a model-based analysis of data. We have previously developed a mechanistically detailed model for the NVC, and others have proposed detailed models for cerebral metabolism. However, existing metabolic models are still not fully utilizing available magnetic resonance spectroscopy (MRS) data and are not connected to detailed models for NVC. Therefore, we herein present a new model that integrates mechanistic modelling of both MRS and BOLD data. The metabolic model covers central metabolism, using a minimal set of interactions, and can describe time-series data for glucose, lactate, aspartate, and glutamate, measured after visual stimuli. Statistical tests confirm that the model can describe both estimation data and predict independent validation data, not used for model training. The interconnected NVC model can simultaneously describe BOLD data and can be used to predict expected metabolic responses in experiments where metabolism has not been measured. This model is a step towards a useful and mechanistically detailed model for cerebral blood flow and metabolism, with potential applications in both basic research and clinical applications.

A system identification analysis of optogenetically evoked electrocorticography and cerebral blood flow responses

OBJECTIVE

The main objective of this research was to study the coupling between neural circuits and the vascular network in the cortex of small rodents from system engineering point of view and generate a mathematical model for the dynamics of neurovascular coupling. The model was adopted to implement closed-loop blood flow control algorithms.

APPROACH

We used a combination of advanced technologies including optogenetics, electrocorticography, and optical coherence tomography to stimulate selected populations of neurons and simultaneously record induced electrocorticography and hemodynamic signals. We adopted system identification methods to analyze the acquired data and investigate the relation between optogenetic neural activation and consequential electrophysiology and blood flow responses.

MAIN RESULTS

We showed that the developed model, once trained by the acquired data, could successfully regenerate subtle spatio-temporal features of evoked electrocorticography and cerebral blood flow responses following an onset of optogenetic stimulation.

SIGNIFICANCE

The long term goal of this research is to open a new line for computational analysis of neurovascular coupling particularly in pathologies where the normal process of blood flow regulation in the central nervous system is disrupted including Alzheimer's disease.

Physiological Gaussian process priors for the hemodynamics in fMRI analysis

BACKGROUND

Inference from fMRI data faces the challenge that the hemodynamic system that relates neural activity to the observed BOLD fMRI signal is unknown.

NEW METHOD

We propose a new Bayesian model for task fMRI data with the following features: (i) joint estimation of brain activity and the underlying hemodynamics, (ii) the hemodynamics is modeled nonparametrically with a Gaussian process (GP) prior guided by physiological information and (iii) the predicted BOLD is not necessarily generated by a linear time-invariant (LTI) system. We place a GP prior directly on the predicted BOLD response, rather than on the hemodynamic response function as in previous literature. This allows us to incorporate physiological information via the GP prior mean in a flexible way, and simultaneously gives us the nonparametric flexibility of the GP.

RESULTS

Results on simulated data show that the proposed model is able to discriminate between active and non-active voxels also when the GP prior deviates from the true hemodynamics. Our model finds time varying dynamics when applied to real fMRI data.

COMPARISON WITH EXISTING METHOD(S)

The proposed model is better at detecting activity in simulated data than standard models, without inflating the false positive rate. When applied to real fMRI data, our GP model in several cases finds brain activity where previously proposed LTI models does not.

CONCLUSIONS

We have proposed a new non-linear model for the hemodynamics in task fMRI, that is able to detect active voxels, and gives the opportunity to ask new kinds of questions related to hemodynamics.

A quantitative analysis of cell-specific contributions and the role of anesthetics to the neurovascular coupling

The neurovascular coupling (NVC) connects neuronal activity to hemodynamic responses in the brain. This connection is the basis for the interpretation of functional magnetic resonance imaging data. Despite the central role of this coupling, we lack detailed knowledge about cell-specific contributions and our knowledge about NVC is mainly based on animal experiments performed during anesthesia. Anesthetics are known to affect neuronal excitability, but how this affects the vessel diameters is not known. Due to the high complexity of NVC data, mathematical modeling is needed for a meaningful analysis. However, neither the relevant neuronal subtypes nor the effects of anesthetics are covered by current models. Here, we present a mathematical model including GABAergic interneurons and pyramidal neurons, as well as the effect of an anesthetic agent. The model is consistent with data from optogenetic experiments from both awake and anesthetized animals, and it correctly predicts data from experiments with different pharmacological modulators. The analysis suggests that no downstream anesthetic effects are necessary if one of the GABAergic interneuron signaling pathways include a Michaelis-Menten expression. This is the first example of a quantitative model that includes both the cell-specific contributions and the effect of an anesthetic agent on the NVC.

Computational singular perturbation analysis of brain lactate metabolism

Lactate in the brain is considered an important fuel and signalling molecule for neuronal activity, especially during neuronal activation. Whether lactate is shuttled from astrocytes to neurons or from neurons to astrocytes leads to the contradictory Astrocyte to Neuron Lactate Shuttle (ANLS) or Neuron to Astrocyte Lactate Shuttle (NALS) hypotheses, both of which are supported by extensive, but indirect, experimental evidence. This work explores the conditions favouring development of ANLS or NALS phenomenon on the basis of a model that can simulate both by employing the two parameter sets proposed by Simpson et al. (J Cereb. Blood Flow Metab., 27:1766, 2007) and Mangia et al. (J of Neurochemistry, 109:55, 2009). As most mathematical models governing brain metabolism processes, this model is multi-scale in character due to the wide range of time scales characterizing its dynamics. Therefore, we utilize the Computational Singular Perturbation (CSP) algorithm, which has been used extensively in multi-scale systems of reactive flows and biological systems, to identify components of the system that (i) generate the characteristic time scale and the fast/slow dynamics, (ii) participate to the expressions that approximate the surfaces of equilibria that develop in phase space and (iii) control the evolution of the process within the established surfaces of equilibria. It is shown that a decisive factor on whether the ANLS or NALS configuration will develop during neuronal activation is whether the lactate transport between astrocytes and interstitium contributes to the fast dynamics or not. When it does, lactate is mainly generated in astrocytes and the ANLS hypothesis is realised, while when it doesn't, lactate is mainly generated in neurons and the NALS hypothesis is realised. This scenario was tested in exercise conditions.

Perivascular neurotransmitters: Regulation of cerebral blood flow and role in primary headaches

In order to understand the nature of the relationship between cerebral blood flow (CBF) and primary headaches, we have conducted a literature review with particular emphasis on the role of perivascular neurotransmitters. Primary headaches are in general considered complex polygenic disorders (genetic and environmental influence) with pathophysiological neurovascular alterations. Identified candidate headache genes are associated with neuro- and gliogenesis, vascular development and diseases, and regulation of vascular tone. These findings support a role for the vasculature in primary headache disorders. Moreover, neuronal hyperexcitability and other abnormalities have been observed in primary headaches and related to changes in hemodynamic factors. In particular, this relates to migraine aura and spreading depression. During headache attacks, ganglia such as trigeminal and sphenopalatine (located outside the blood-brain barrier) are variably activated and sensitized which gives rise to vasoactive neurotransmitter release. Sympathetic, parasympathetic and sensory nerves to the cerebral vasculature are activated. During migraine attacks, altered CBF has been observed in brain regions such as the somatosensory cortex, brainstem and thalamus. In regulation of CBF, the individual roles of neurotransmitters are partly known, but much needs to be unraveled with respect to headache disorders.

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.

Dynamic 23Na MRI - A non-invasive window on neuroglial-vascular mechanisms underlying brain function

A novel magnetic resonance imaging (MRI) acquisition and reconstruction method for obtaining a series of dynamic sodium ²³Na-MRI acquisitions was designed to non-invasively assess the signal variations of brain sodium during a hand motor task in 14 healthy human volunteers on an ultra high field (7T) MR scanner. Regions undergoing activation and deactivation were identified with reference to conventional task-related BOLD functional MRI (fMRI). Activation observed in the left central regions, the supplementary motor areas and the left cerebellum induced an increase in the sodium signal observed at ultra short echo time and a decrease in the ²³Na signal observed at long echo time. Based on a simple model of two distinct sodium pools (namely, restricted and mobile sodium), the ultra short echo time measures the totality of sodium whereas the long echo time is mainly sensitive to mobile sodium. This activation pattern is consistent with previously described processes related to an influx of Na⁺ into the intracellular compartments and a moderate increase in the cerebral blood volume (CBV). In contrast, deactivation observed in the right central regions ipsilateral to the movement, the precuneus and the left cerebellum induced a slight decrease in sodium signal at ultra short echo time and an increase of sodium signal at longer echo times. This inhibitory pattern is compatible with a slight decrease in CBV and an efflux of intracellular Na⁺ to the extracellular compartments that may reflect neural dendritic spine and astrocytic shrinkage, and an increase of sodium in the extracellular fraction. In conclusion, cerebral dynamic ²³Na MRI experiments can provide access to the ionic transients following a functional task occurring within the neuro-glial-vascular ensemble. This has the potential to open up a novel non-invasive window on the mechanisms underlying brain function.

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.

Mitochondrial calcium homeostasis: Implications for neurovascular and neurometabolic coupling

Mitochondrial function is critical to maintain high rates of oxidative metabolism supporting energy demands of both spontaneous and evoked neuronal activity in the brain. Mitochondria not only regulate energy metabolism, but also influence neuronal signaling. Regulation of "energy metabolism" and "neuronal signaling" (i.e. neurometabolic coupling), which are coupled rather than independent can be understood through mitochondria's integrative functions of calcium ion (Ca²⁺) uptake and cycling. While mitochondrial Ca²⁺ do not affect hemodynamics directly, neuronal activity changes are mechanistically linked to functional hyperemic responses (i.e. neurovascular coupling). Early in vitro studies lay the foundation of mitochondrial Ca²⁺ homeostasis and its functional roles within cells. However, recent in vivo approaches indicate mitochondrial Ca²⁺ homeostasis as maintained by the role of mitochondrial Ca²⁺ uniporter (mCU) influences system-level brain activity as measured by a variety of techniques. Based on earlier evidence of subcellular cytoplasmic Ca²⁺ microdomains and cellular bioenergetic states, a mechanistic model of Ca²⁺ mobilization is presented to understand systems-level neurovascular and neurometabolic coupling. This integrated view from molecular and cellular to the systems level, where mCU plays a major role in mitochondrial and cellular Ca²⁺ homeostasis, may explain the wide range of activation-induced coupling across neuronal activity, hemodynamic, and metabolic responses.