A model of the coupling between brain electrical activity, metabolism, and hemodynamics: application to the interpretation of functional neuroimaging

Numerical simulation and fast method for the 0D-1D multi-scale coupled model and its application in ischemic brain tissue blood flow problems

As living standards rise, more and more people are paying attention to their own health, especially issues such as cerebral thrombosis, cerebral infarction, and other cerebral blood flow problems. An accurate simulation of blood flow within cerebral vessels has emerged as a crucial area of research. In this study, we focus on microcirculatory blood flow in ischemic brain tissue and employ a 0D-1D geometric multi-scale coupled model to characterize this process. Given the intricate nature of human cerebral vessels, we apply a numerical method combining the finite element method and the third-order Runge-Kutta method to resolve the coupled model. To enhance computational efficiency, we introduce a fast method based on the reduced-order extrapolation algorithm. Our numerical example underscores the stability of the method and convergence accuracy to O h 3 + τ 3 , while significantly improving the accuracy and efficiency of blood flow simulation, making the mechanism analysis more accurate. Additionally, we present examples detailing variations and distribution of intracranial pressure and blood flow in ischemic brain tissue throughout a cardiac cycle. Both reduced vascular compliance and vascular stenosis can have adverse effects on intracranial cerebral pressure and blood flow, leading to insufficient local oxygen supply and negative effects on brain function. Meanwhile, there will also be corresponding changes in volume flow and pulsatile blood pressure.

Brain FDG PET for visualizing the relation between impaired lung function and cognitive decline in lung cancer: a preliminary study

OBJECTIVE

Impaired lung function is associated with an increased risk for cognitive decline. F-18 fluorodeoxyglucose (FDG) PET is a well-known neurodegenerative biomarker for dementia. We investigated the association between lung and brain function using FDG PET in patients with lung cancer.

METHODS

A random sub-sample of 102 patients with lung cancer and without a self-reported history of neuropsychiatric disorders were recruited and underwent both lung function tests and FDG PET scans before treatment. Lung function was analyzed as the percentage predicted value (% pred) of forced vital capacity (FVC) and forced expiratory volume in the first second (FEV1). FDG uptake was measured as standardized uptake values (SUVs) in the frontal, parietal, temporal, and occipital cortices and cognition-related regions. Regional SUV ratios (SUVRs) were calculated by dividing the SUV in each region by the whole-brain SUV and were then evaluated against lung function indices and clinical variables.

RESULTS

After excluding five patients with brain metastases, 97 patients were included in the final analysis (mean age, 67.7 ± 10.3 years). Mean FVC and mean FEV1 were 80.0% ± 15.4% and 77.6% ± 17.8%, respectively. Both FVC and FEV1 were positively correlated with SUVRs in all brain regions after adjusting the data for clinical variables. The degree of decrease in SUVRs related to lung function was not significantly different between cognition-related regions and other regions.

CONCLUSION

Impaired lung function was associated with decreased glucose metabolism in all regions of the brain, indicating that cognitive decline related to decreased glucose metabolism may be due to reduced perfusion.

Resting-state coupling between HbO and Hb measured by fNIRS in autism spectrum disorder

To distinguish between children with autism spectrum disorder (ASD) and typically developing (TD) children, we have uncovered a new discriminative feature, hemoglobin coupling. Functional near-infrared spectroscopy (fNIRS) was used to record resting-state hemodynamic fluctuations in the bilateral temporal lobes in 25 children with ASD and 22 TD children, in which the coupling between low frequency oxygenated hemoglobin (HbO) and deoxygenated hemoglobin (Hb) fluctuations was evaluated by Pearson correlation coefficient. The results showed significantly weak coupling in children with ASD in both the left and right, and throughout the whole temporal cortex. To explain this observation, a simulation study was performed using a balloon model, in which we found four related parameters could impact the coupling. This study suggested that hemoglobin coupling might be applied as a new cerebral hemodynamic characteristic for ASD screening or diagnostics.

Altered cerebral blood flow and white matter during wakeful rest in patients with obstructive sleep apnea: a population-based retrospective study

OBJECTIVES

To explore changes in cerebral blood flow (CBF) and white matter during wakeful rest in patients with obstructive sleep apnea (OSA).

METHODS

The subjects comprised OSA patients and age- and sex-matched non-sleep apnea (NSA) subjects from December 2020 to December 2021. All subjects underwent structural and arterial spin labeling MRI examinations using a 3.0 T MRI scanner. Intergroup differences in regional and global CBF and white matter hyperintensities (WMHs) were analyzed.

RESULTS

In this study, 100 (74 males) of 750 (439 males) subjects were diagnosed with OSA, so the prevalence of OSA in the general population was 13.3% (100/750), with 16.9% (74/439) in males and 8.4% (26/311) in females. Excluding four patients with incomplete imaging data, 96 OSA patients and 103 age- and sex-matched NSA subjects were included. At global level, OSA patients showed significantly decreased CBF values in gray matter and whole brain compared to NSA subjects (gray matter: p = 0.010; whole brain: p = 0.021). No significant difference in CBF values was found in WM between the two groups (p = 0.250). At regional level, compared with NSA subjects, patients with OSA exhibited significantly decreased regional CBF values mainly in right parietal lobe and right temporal lobe. Moreover, OSA patients had significantly higher WMHs burden than NSA subjects (p = 0.017).

CONCLUSIONS

OSA patients exhibit decreased global and regional CBF values and increased WMHs burden.

ADVANCES IN KNOWLEDGE

These findings provide a basis for exploring neuropathological changes of OSA and for early and appropriate treatment.

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.

Altered Neurovascular Coupling in Unilateral Pulsatile Tinnitus

Objective

Altered cerebral blood flow (CBF) and regional homogeneity (ReHo) have been reported in pulsatile tinnitus (PT) patients. We aimed to explore regional neurovascular coupling changes in PT patients.

Materials and Methods

Twenty-four right PT patients and 25 sex- and age-matched normal controls were included in this study. All subjects received arterial spin labeling imaging to measure CBF and functional MRI to compute ReHo. CBF/ReHo ratio was used to assess regional neurovascular coupling between the two groups. We also analyzed the correlation between CBF/ReHo ratio and clinical data from the PT patients.

Results

PT patients exhibited increased CBF/ReHo ratio in left middle temporal gyrus and right angular gyrus than normal controls, and no decreased CBF/ReHo ratio was found. CBF/ReHo ratio in the left middle temporal gyrus of PT patients was positively correlated with Tinnitus Handicap Inventory score (r = 0.433, p = 0.035).

Conclusion

These findings indicated that patients with PT exhibit abnormal neurovascular coupling, which provides new information for understanding the neuropathological mechanisms underlying PT.

Perfusion CT imaging as a diagnostic and prognostic tool for dementia: prospective case-control study

BACKGROUND

As functional changes precede structural changes in dementia, we aimed to elucidate changes on cerebral perfusion CT (PCT) for early diagnosis of dementia; and to differentiate Alzheimer's disease (AD) from vascular dementia (VaD). We also aimed to study correlation between Montreal Cognitive Assessment (MOCA) score and PCT parameters.

METHODS

We conducted a prospective case-control study enrolling 25 dementia patients (15 cases of VaD, 10 cases of AD) and 25 age-matched controls. PCT was performed on a 256-slice CT scanner. Using perfusion software, colour maps were generated for cerebral blood flow (CBF), cerebral blood volume (CBV), mean transit time and time-to-peak. These colour maps were first visually inspected for any abnormalities. Subsequently, quantitative assessment of perfusion parameters was done using symmetrical freehand region of interests drawn in bilateral frontal, temporal, parietal regions, basal ganglia and hippocampi.

RESULTS

Strategic infarcts were present in 93.3% cases and white matter ischaemic changes in 100% cases of VaD. A global reduction in CBF and CBV was also observed in cases of VaD; whereas these parameters were significantly lower mainly in temporoparietal regions and hippocampi of patients with AD. There was significant positive correlation between MOCA score and various perfusion parameters in both forms of dementia.

CONCLUSION

PCT is a reliable imaging modality for early diagnosis of dementia and in differentiating VaD from AD. As perfusion parameters show positive correlation with MOCA score, they could be used as a surrogate marker of cognitive status in the follow-up of patients with dementia.

Brain energetics, mitochondria, and traumatic brain injury

We review current thinking about, and draw connections between, brain energetics and metabolism, and between mitochondria and traumatic brain injury. Energy is fundamental to proper brain function. Its creation in a useful form for neurons and glia, and consistently in response to the brain's high energy needs, is critical for physiological pathways. Dysfunction in the mechanisms of energy production is at the center of neurological and neuropsychiatric pathologies. We examine the connections between energetics and mitochondria - the organelle responsible for almost all the energy production in the cell - and how secondary pathologies in traumatic brain injury result from energetic dysfunction. This paper interweaves these topics, a necessity since they are closely coupled, and identifies where there exist a lack of understanding and of data. In addition to summarizing current thinking in these disciplines, our goal is to suggest a framework for the mathematical modeling of mechanisms and pathways based on optimal energetic decisions.

Brain mitochondrial dysfunction and driving simulator performance in untreated obstructive sleep apnea

It is challenging to determine which patients with obstructive sleep apnea (OSA) have impaired driving ability. Vulnerability to this neurobehavioral impairment may be explained by lower brain metabolites levels involved in mitochondrial metabolism. This study compared markers of brain energy metabolism in OSA patients identified as vulnerable vs resistant to driving impairment following extended wakefulness. 44 patients with moderate-severe OSA underwent 28hr extended wakefulness with three 90min driving simulation assessments. Using a two-step cluster analysis, objective driving data (steering deviation and crashes) from the 2nd driving assessment (22.5 h awake) was used to categorise patients into vulnerable (poor driving, n = 21) or resistant groups (good driving, n = 23). ¹ H magnetic resonance spectra were acquired at baseline using two scan sequences (short echo PRESS and longer echo-time asymmetric PRESS), focusing on key metabolites, creatine, glutamate, N-acetylaspartate (NAA) in the hippocampus, anterior cingulate cortex and left orbito-frontal cortex. Based on cluster analysis, the vulnerable group had impaired driving performance compared with the resistant group and had lower levels of creatine (PRESS p = ns, APRESS p = 0.039), glutamate, (PRESS p < 0.01, APRESS p < 0.01), NAA (PRESS p = 0.038, APRESS p = 0.035) exclusively in the left orbito-frontal cortex. Adjusted analysis, higher glutamate was associated with a 21% (PRESS) and 36% (APRESS) reduced risk of vulnerable classification. Brain mitochondrial bioenergetics in the frontal brain regions are impaired in OSA patients who are vulnerable to driving impairment following sleep loss. These findings provide a potential way to identify at risk OSA phenotype when assessing fitness to drive, but this requires confirmation in larger future studies.

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.

The thermodynamics of thinking: connections between neural activity, energy metabolism and blood flow

Several current functional neuroimaging methods are sensitive to cerebral metabolism and cerebral blood flow (CBF) rather than the underlying neural activity itself. Empirically, the connections between metabolism, flow and neural activity are complex and somewhat counterintuitive: CBF and glycolysis increase more than seems to be needed to provide oxygen and pyruvate for oxidative metabolism, and the oxygen extraction fraction is relatively low in the brain and decreases when oxygen metabolism increases. This work lays a foundation for the idea that this unexpected pattern of physiological changes is consistent with basic thermodynamic considerations related to metabolism. In the context of this thermodynamic framework, the apparent mismatches in metabolic rates and CBF are related to preserving the entropy change of oxidative metabolism, specifically the O₂/CO₂ ratio in the mitochondria. However, the mechanism supporting this CBF response is likely not owing to feedback from a hypothetical O₂ sensor in tissue, but rather is consistent with feed-forward control by signals from both excitatory and inhibitory neural activity. Quantitative predictions of the thermodynamic framework, based on models of O₂ and CO₂ transport and possible neural drivers of CBF control, are in good agreement with a wide range of experimental data, including responses to neural activation, hypercapnia, hypoxia and high-altitude acclimatization. This article is part of the theme issue 'Key relationships between non-invasive functional neuroimaging and the underlying neuronal activity'.

Cerebral Blood Flow Alterations in High Myopia: An Arterial Spin Labeling Study

Objective

The aim of this study was to explore cerebral blood flow (CBF) alterations in subjects with high myopia (HM) using three-dimensional pseudocontinuous arterial spin labeling (3D-pcASL).

Methods

A total of sixteen patients with bilateral HM and sixteen age- and sex-matched healthy controls (HCs) were recruited. All subjects were right-handed. Image data preprocessing was performed using SPM8 and the DPABI toolbox. Clinical parameters were acquired in the HM group. Two-sample t-tests and Pearson correlation analysis were applied in this study.

Results

Compared to HCs, patients with HM exhibited significantly increased CBF in the bilateral cerebellum, and no decreases in CBF were detected in the brain. However, no relationship was found between the mean CBF values in the different brain areas and the disease duration (P > 0.05).

Conclusions

Using ASL analysis, we detected aberrant blood perfusion in the cerebellum in HM patients, contributing to a better understanding of brain abnormalities and brain plasticity through a different perspective.

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.

A Bayesian framework for the analysis of systems biology models of the brain

Systems biology models are used to understand complex biological and physiological systems. Interpretation of these models is an important part of developing this understanding. These models are often fit to experimental data in order to understand how the system has produced various phenomena or behaviour that are seen in the data. In this paper, we have outlined a framework that can be used to perform Bayesian analysis of complex systems biology models. In particular, we have focussed on analysing a systems biology of the brain using both simulated and measured data. By using a combination of sensitivity analysis and approximate Bayesian computation, we have shown that it is possible to obtain distributions of parameters that can better guard against misinterpretation of results, as compared to a maximum likelihood estimate based approach. This is done through analysis of simulated and experimental data. NIRS measurements were simulated using the same simulated systemic input data for the model in a ‘healthy’ and ‘impaired’ state. By analysing both of these datasets, we show that different parameter spaces can be distinguished and compared between different physiological states or conditions. Finally, we analyse experimental data using the new Bayesian framework and the previous maximum likelihood estimate approach, showing that the Bayesian approach provides a more complete understanding of the parameter space.

Systems biology models are mathematical representations of biological processes that reproduce the overall behaviour of a biological system. They are comprised by a number of parameters representing biological information. We use them to understand the behaviour of biological systems, such as the brain. We do this by fitting the model’s parameter to observed or simulated data; and by looking at how these values change during the fitting process we investigate the behaviour of our system. We are interested in understanding differences between a healthy and an injured brain. Here we outline a statistical framework that uses a Bayesian approach during the fitting process that can provide us with a distribution of parameters rather than single parameter number. We apply this method when simulating the physiological responses between a healthy and a vascular compromised brain to a drop in oxygenation. We then use experimental data that demonstrates the healthy brain response to an increase in arterial CO2 and fit our brain model predictions to the measurements. In both instances we show that our approach provides more information about the overlap between healthy and unhealthy brain states than a fitting process that provides a single value parameter estimate.

A Process for Digitizing and Simulating Biologically Realistic Oligocellular Networks Demonstrated for the Neuro-Glio-Vascular Ensemble

One will not understand the brain without an integrated exploration of structure and function, these attributes being two sides of the same coin: together they form the currency of biological computation. Accordingly, biologically realistic models require the re-creation of the architecture of the cellular components in which biochemical reactions are contained. We describe here a process of reconstructing a functional oligocellular assembly that is responsible for energy supply management in the brain and creating a computational model of the associated biochemical and biophysical processes. The reactions that underwrite thought are both constrained by and take advantage of brain morphologies pertaining to neurons, astrocytes and the blood vessels that deliver oxygen, glucose and other nutrients. Each component of this neuro-glio-vasculature ensemble (NGV) carries-out delegated tasks, as the dynamics of this system provide for each cell-type its own energy requirements while including mechanisms that allow cooperative energy transfers. Our process for recreating the ultrastructure of cellular components and modeling the reactions that describe energy flow uses an amalgam of state-of the-art techniques, including digital reconstructions of electron micrographs, advanced data analysis tools, computational simulations and in silico visualization software. While we demonstrate this process with the NGV, it is equally well adapted to any cellular system for integrating multimodal cellular data in a coherent framework.

Is visual activation associated with changes in cerebral high-energy phosphate levels?

Phosphorus magnetic resonance spectroscopy (³¹P MRS) has been employed before to assess phosphocreatine (PCr) and other high-energy phosphates in the visual cortex during visual stimulation with inconsistent results. We performed functional ³¹P MRS imaging in the visual cortex and control regions during a visual stimulation paradigm at an unprecedented sensitivity, exploiting a dedicated RF coil design at a 7 T MR system. Visual stimulation in a 3 min 24 s on–off paradigm in eight young healthy adults generated a clear BOLD effect with traditional ¹H functional MRI in the visual cortex (average z score 9.9 ± 0.2). However, no significant event-related changes in any of the ³¹P metabolite concentrations, linewidths (7.9 ± 1.8 vs 7.8 ± 1.9 Hz) or tissue pH (7.07 ± 0.13 vs 7.06 ± 0.07) were detectable. Overall, our study of ³¹P MRSI in 15 cm³ voxels had a detection threshold for changes in PCr, Pi and γ-ATP between stimulation and rest of 5, 17 and 10%, respectively. In individual subjects, the mean coefficients of variance for PCr and Pi levels of control voxels were 6 ± 3 and 19 ± 8% (three time point average of 3 min 24 s). Altogether this indicates that energy supply for neuronal activation at this temporal resolution does not drain global PCr resources.

A computational model integrating brain electrophysiology and metabolism highlights the key role of extracellular potassium and oxygen

The human brain is a small organ which uses a disproportionate amount of the total metabolic energy production in the body. While it is well understood that the most significant energy sink is the maintenance of the neuronal membrane potential during the brain signaling activity, the role of astrocytes in the energy balance continues to be the topic of a lot of research. A key function of astrocytes, besides clearing glutamate from the synaptic clefts, is the potassium clearing after neuronal activation. Extracellular potassium plays a significant role in triggering neuronal firing, and elevated concentration of potassium may lead to abnormal firing patterns, e.g., seizures, thus emphasizing the importance of the glial K⁺ buffering role. The predictive mathematical model proposed in this paper elucidates the role of glial potassium clearing in brain energy metabolism, integrating a detailed model of the ion dynamics which regulates neuronal firing with a four compartment metabolic model. Because of the very different characteristic time scales of electrophysiology and metabolism, care must be taken when coupling the two models to ensure that the predictions, e.g., neuronal firing frequencies and the oxygen-glucose index (OGI) of the brain during activation and rest, are in agreement with empirical observations. The temporal multi-scale nature of the problem requires the design of new computational tools to ensure a stable and accurate numerical treatment. The model predictions for different protocols, including combinations of elevated activation and ischemic episodes, are in good agreement with experimental observations reported in the literature.

Mathematical analysis of the influence of brain metabolism on the BOLD signal in Alzheimer's disease

Blood oxygen level-dependent functional magnetic resonance imaging (BOLD-fMRI) is a standard clinical tool for the detection of brain activation. In Alzheimer's disease (AD), task-related and resting state fMRI have been used to detect brain dysfunction. It has been shown that the shape of the BOLD response is affected in early AD. To correctly interpret these changes, the mechanisms responsible for the observed behaviour need to be known. The parameters of the canonical hemodynamic response function (HRF) commonly used in the analysis of fMRI data have no direct biological interpretation and cannot be used to answer this question. We here present a model that allows relating AD-specific changes in the BOLD shape to changes in the underlying energy metabolism. According to our findings, the classic view that differences in the BOLD shape are only attributed to changes in strength and duration of the stimulus does not hold. Instead, peak height, peak timing and full width at half maximum are sensitive to changes in the reaction rate of several metabolic reactions. Our systems-theoretic approach allows the use of patient-specific clinical data to predict dementia-driven changes in the HRF, which can be used to improve the results of fMRI analyses in AD patients.

The roadmap for estimation of cell-type-specific neuronal activity from non-invasive measurements

The computational properties of the human brain arise from an intricate interplay between billions of neurons connected in complex networks. However, our ability to study these networks in healthy human brain is limited by the necessity to use non-invasive technologies. This is in contrast to animal models where a rich, detailed view of cellular-level brain function with cell-type-specific molecular identity has become available due to recent advances in microscopic optical imaging and genetics. Thus, a central challenge facing neuroscience today is leveraging these mechanistic insights from animal studies to accurately draw physiological inferences from non-invasive signals in humans. On the essential path towards this goal is the development of a detailed 'bottom-up' forward model bridging neuronal activity at the level of cell-type-specific populations to non-invasive imaging signals. The general idea is that specific neuronal cell types have identifiable signatures in the way they drive changes in cerebral blood flow, cerebral metabolic rate of O2 (measurable with quantitative functional Magnetic Resonance Imaging), and electrical currents/potentials (measurable with magneto/electroencephalography). This forward model would then provide the 'ground truth' for the development of new tools for tackling the inverse problem-estimation of neuronal activity from multimodal non-invasive imaging data.This article is part of the themed issue 'Interpreting BOLD: a dialogue between cognitive and cellular neuroscience'.

Arterial Spin Labeling Perfusion of the Brain: Emerging Clinical Applications

Arterial spin labeling (ASL) is a magnetic resonance (MR) imaging technique used to assess cerebral blood flow noninvasively by magnetically labeling inflowing blood. In this article, the main labeling techniques, notably pulsed and pseudocontinuous ASL, as well as emerging clinical applications will be reviewed. In dementia, the pattern of hypoperfusion on ASL images closely matches the established patterns of hypometabolism on fluorine 18 fluorodeoxyglucose (FDG) positron emission tomography (PET) images due to the close coupling of perfusion and metabolism in the brain. This suggests that ASL might be considered as an alternative for FDG, reserving PET to be used for the molecular disease-specific amyloid and tau tracers. In stroke, ASL can be used to assess perfusion alterations both in the acute and the chronic phase. In arteriovenous malformations and dural arteriovenous fistulas, ASL is very sensitive to detect even small degrees of shunting. In epilepsy, ASL can be used to assess the epileptogenic focus, both in peri- and interictal period. In neoplasms, ASL is of particular interest in cases in which gadolinium-based perfusion is contraindicated (eg, allergy, renal impairment) and holds promise in differentiating tumor progression from benign causes of enhancement. Finally, various neurologic and psychiatric diseases including mild traumatic brain injury or posttraumatic stress disorder display alterations on ASL images in the absence of visualized structural changes. In the final part, current limitations and future developments of ASL techniques to improve clinical applicability, such as multiple inversion time ASL sequences to assess alterations of transit time, reproducibility and quantification of cerebral blood flow, and to measure cerebrovascular reserve, will be reviewed. ^© RSNA, 2016 Online supplemental material is available for this article.

The impact of high grade glial neoplasms on human cortical electrophysiology

Objective

The brain’s functional architecture of interconnected network-related oscillatory patterns in discrete cortical regions has been well established with functional magnetic resonance imaging (fMRI) studies or direct cortical electrophysiology from electrodes placed on the surface of the brain, or electrocorticography (ECoG). These resting state networks exhibit a robust functional architecture that persists through all stages of sleep and under anesthesia. While the stability of these networks provides a fundamental understanding of the organization of the brain, understanding how these regions can be perturbed is also critical in defining the brain’s ability to adapt while learning and recovering from injury.

Methods

Patients undergoing an awake craniotomy for resection of a tumor were studied as a unique model of an evolving injury to help define how the cortical physiology and the associated networks were altered by the presence of an invasive brain tumor.

Results

This study demonstrates that there is a distinct pattern of alteration of cortical physiology in the setting of a malignant glioma. These changes lead to a physiologic sequestration and progressive synaptic homogeneity suggesting that a de-learning phenomenon occurs within the tumoral tissue compared to its surroundings.

Significance

These findings provide insight into how the brain accommodates a region of “defunctionalized” cortex. Additionally, these findings may have important implications for emerging techniques in brain mapping using endogenous cortical physiology.

The Impact of Mathematical Modeling in Understanding the Mechanisms Underlying Neurodegeneration: Evolving Dimensions and Future Directions

Neurodegenerative diseases are a heterogeneous group of disorders that are characterized by the progressive dysfunction and loss of neurons. Here, we distil and discuss the current state of modeling in the area of neurodegeneration, and objectively compare the gaps between existing clinical knowledge and the mechanistic understanding of the major pathological processes implicated in neurodegenerative disorders. We also discuss new directions in the field of neurodegeneration that hold potential for furthering therapeutic interventions and strategies.

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.

Lactate and glutamate dynamics during prolonged stimulation of the rat barrel cortex suggest adaptation of cerebral glucose and oxygen metabolism

A better understanding of BOLD responses stems from a better characterization of the brain's ability to metabolize glucose and oxygen. Non-invasive techniques such as functional magnetic resonance spectroscopy (fMRS) have thus been developed allowing for the reproducible assessment of metabolic changes during barrel cortex (S1BF) activations in rats. The present study aimed at further exploring the role of neurotransmitters on local and temporal changes in vascular and metabolic function in S1BF. fMRS and fMRI data were acquired sequentially in α-chloralose anesthetized rats during 32-min rest and trigeminal nerve stimulation periods. During stimulation, concentrations of lactate (Lac) and glutamate (Glu) increased in S1BF by 0.23±0.05 and 0.34±0.05μmol/g respectively in S1BF. Dynamic analysis of metabolite concentrations allowed estimating changes in cerebral metabolic rates of glucose (ΔCMR_Glc) and oxygen (ΔCMR_O2). Findings confirmed a prevalence of oxidative metabolism during prolonged S1BF activation. Habituation led to a significant BOLD magnitude decline as a function of time while both total ΔCMR_Glc and ΔCMR_O2 remained constant revealing adaptation of glucose and oxygen metabolisms to support ongoing trigeminal nerve stimulation.

A Theoretical Study on the Role of Astrocytic Activity in Neuronal Hyperexcitability by a Novel Neuron-Glia Mass Model

Recent experimental evidence on the clustering of glutamate and GABA transporters on astrocytic processes surrounding synaptic terminals pose the question of the functional relevance of the astrocytes in the regulation of neural activity. In this perspective, we introduce a new computational model that embeds recent findings on neuron-astrocyte coupling at the mesoscopic scale intra- and inter-layer local neural circuits. The model consists of a mass model for the neural compartment and an astrocyte compartment which controls dynamics of extracellular glutamate and GABA concentrations. By arguments based on bifurcation theory, we use the model to study the impact of deficiency of astrocytic glutamate and GABA uptakes on neural activity. While deficient astrocytic GABA uptake naturally results in increased neuronal inhibition, which in turn results in a decreased neuronal firing, deficient glutamate uptake by astrocytes may either decrease or increase neuronal firing either transiently or permanently. Given the relevance of neuronal hyperexcitability (or lack thereof) in the brain pathophysiology, we provide biophysical conditions for the onset identifying different physiologically relevant regimes of operation for astrocytic uptake transporters.

Low-Dimensional Models of "Neuro-Glio-Vascular Unit" for Describing Neural Dynamics under Normal and Energy-Starved Conditions

The motivation of developing simple minimal models for neuro-glio-vascular (NGV) system arises from a recent modeling study elucidating the bidirectional information flow within the NGV system having 89 dynamic equations (1). While this was one of the first attempts at formulating a comprehensive model for neuro-glio-vascular system, it poses severe restrictions in scaling up to network levels. On the contrary, low-­dimensional models are convenient devices in simulating large networks that also provide an intuitive understanding of the complex interactions occurring within the NGV system. The key idea underlying the proposed models is to describe the glio-vascular system as a lumped system, which takes neural firing rate as input and returns an “energy” variable (analogous to ATP) as output. To this end, we present two models: biophysical neuro-energy (Model 1 with five variables), comprising K_ATP channel activity governed by neuronal ATP dynamics, and the dynamic threshold (Model 2 with three variables), depicting the dependence of neural firing threshold on the ATP dynamics. Both the models show different firing regimes, such as continuous spiking, phasic, and tonic bursting depending on the ATP production coefficient, ɛ_p, and external current. We then demonstrate that in a network comprising such energy-dependent neuron units, ɛ_p could modulate the local field potential (LFP) frequency and amplitude. Interestingly, low-frequency LFP dominates under low ɛ_p conditions, which is thought to be reminiscent of seizure-like activity observed in epilepsy. The proposed “neuron-energy” unit may be implemented in building models of NGV networks to simulate data obtained from multimodal neuroimaging systems, such as functional near infrared spectroscopy coupled to electroencephalogram and functional magnetic resonance imaging coupled to electroencephalogram. Such models could also provide a theoretical basis for devising optimal neurorehabilitation strategies, such as non-invasive brain stimulation for stroke patients.

A New Computational Model for Neuro-Glio-Vascular Coupling: Astrocyte Activation Can Explain Cerebral Blood Flow Nonlinear Response to Interictal Events

Developing a clear understanding of the relationship between cerebral blood flow (CBF) response and neuronal activity is of significant importance because CBF increase is essential to the health of neurons, for instance through oxygen supply. This relationship can be investigated by analyzing multimodal (fMRI, PET, laser Doppler…) recordings. However, the important number of intermediate (non-observable) variables involved in the underlying neurovascular coupling makes the discovery of mechanisms all the more difficult from the sole multimodal data. We present a new computational model developed at the population scale (voxel) with physiologically relevant but simple equations to facilitate the interpretation of regional multimodal recordings. This model links neuronal activity to regional CBF dynamics through neuro-glio-vascular coupling. This coupling involves a population of glial cells called astrocytes via their role in neurotransmitter (glutamate and GABA) recycling and their impact on neighboring vessels. In epilepsy, neuronal networks generate epileptiform discharges, leading to variations in astrocytic and CBF dynamics. In this study, we took advantage of these large variations in neuronal activity magnitude to test the capacity of our model to reproduce experimental data. We compared simulations from our model with isolated epileptiform events, which were obtained in vivo by simultaneous local field potential and laser Doppler recordings in rats after local bicuculline injection. We showed a predominant neuronal contribution for low level discharges and a significant astrocytic contribution for higher level discharges. Besides, neuronal contribution to CBF was linear while astrocytic contribution was nonlinear. Results thus indicate that the relationship between neuronal activity and CBF magnitudes can be nonlinear for isolated events and that this nonlinearity is due to astrocytic activity, highlighting the importance of astrocytes in the interpretation of regional recordings.

Investigating Human Neurovascular Coupling Using Functional Neuroimaging: A Critical Review of Dynamic Models

The mechanisms that link a transient neural activity to the corresponding increase of cerebral blood flow (CBF) are termed neurovascular coupling (NVC). They are possibly impaired at early stages of small vessel or neurodegenerative diseases. Investigation of NVC in humans has been made possible with the development of various neuroimaging techniques based on variations of local hemodynamics during neural activity. Specific dynamic models are currently used for interpreting these data that can include biophysical parameters related to NVC. After a brief review of the current knowledge about possible mechanisms acting in NVC we selected seven models with explicit integration of NVC found in the literature. All these models were described using the same procedure. We compared their physiological assumptions, mathematical formalism, and validation. In particular, we pointed out their strong differences in terms of complexity. Finally, we discussed their validity and their potential applications. These models may provide key information to investigate various aspects of NVC in human pathology.

Arterial Spin-Labeling Parameters Influence Signal Variability and Estimated Regional Relative Cerebral Blood Flow in Normal Aging and Mild Cognitive Impairment: FAIR versus PICORE Techniques

BACKGROUND AND PURPOSE

Arterial spin-labeling is a noninvasive method to map cerebral blood flow, which might be useful for early diagnosis of neurodegenerative diseases. We directly compared 2 arterial spin-labeling techniques in healthy elderly controls and individuals with mild cognitive impairment.

MATERIALS AND METHODS

This prospective study was approved by the local ethics committee and included 198 consecutive healthy controls (mean age, 73.65 ± 4.02 years) and 43 subjects with mild cognitive impairment (mean age, 73.38 ± 5.85 years). Two pulsed arterial spin-labeling sequences were performed at 3T: proximal inversion with a control for off-resonance effects (PICORE) and flow-sensitive alternating inversion recovery technique (FAIR). Relative cerebral blood flow maps were calculated by using commercial software and standard parameters. Data analysis included spatial normalization of gray matter-corrected relative CBF maps, whole-brain average, and voxelwise comparison of both arterial spin-labeling sequences.

RESULTS

Overall, FAIR yielded higher relative CBF values compared with PICORE (controls, 32.7 ± 7.1 versus 30.0 ± 13.1 mL/min/100 g, P = .05; mild cognitive impairment, 29.8 ± 5.4 versus 26.2 ± 8.6 mL/min/100 g, P < .05; all, 32.2 ± 6.8 versus 29.3 ± 12.3 mL/min/100 g, P < .05). FAIR had lower variability (controls, 36.2% versus 68.8%, P < .00001; mild cognitive impairment, 18.9% versus 22.9%, P < .0001; all, 34.4% versus 64.9% P < .00001). The detailed voxelwise analysis revealed a higher signal for FAIR, notably in both convexities, while PICORE had higher signal predominantly in deep cerebral regions.

CONCLUSIONS

Overall, FAIR had higher estimated relative CBF and lower interindividual variability than PICORE. In more detail, there were regional differences between both arterial spin-labeling sequences. In summary, these results highlight the need to calibrate arterial spin-labeling sequences.

The genetic absence epilepsy rat from Strasbourg as a model to decipher the neuronal and network mechanisms of generalized idiopathic epilepsies

First characterized in 1982, the genetic absence epilepsy rat from Strasbourg (GAERS) has emerged as an animal model highly reminiscent of a specific form of idiopathic generalized epilepsy. Both its electrophysiological (spike-and-wave discharges) and behavioral (behavioral arrest) features fit well with those observed in human patients with typical absence epilepsy and required by clinicians for diagnostic purposes. In addition, its sensitivity to antiepileptic drugs closely matches what has been described in the clinic, making this model one of the most predictive. Here, we report how the GAERS, thanks to its spontaneous, highly recurrent and easily recognizable seizures on electroencephalographic recordings, allows to address several key-questions about the pathophysiology and genetics of absence epilepsy. In particular, it offers the unique possibility to explore simultaneously the neural circuits involved in the generation of seizures at different levels of integration, using multiscale methodologies, from intracellular recording to functional magnetic resonance imaging. In addition, it has recently allowed to perform proofs of concept for innovative therapeutic strategies such as responsive deep brain stimulation or synchrotron-generated irradiation based radiosurgery.

A mathematical model relating cortical oxygenated and deoxygenated hemoglobin flows and volumes to neural activity

OBJECTIVE

To describe a toolkit of components for mathematical models of the relationship between cortical neural activity and space-resolved and time-resolved flows and volumes of oxygenated and deoxygenated hemoglobin motivated by optical intrinsic signal imaging (OISI).

APPROACH

Both blood flow and blood volume and both oxygenated and deoxygenated hemoglobin and their interconversion are accounted for. Flow and volume are described by including analogies to both resistive and capacitive electrical circuit elements. Oxygenated and deoxygenated hemoglobin and their interconversion are described by generalization of Kirchhoff's laws based on well-mixed compartments.

MAIN RESULTS

Mathematical models built from this toolkit are able to reproduce experimental single-stimulus OISI results that are described in papers from other research groups and are able to describe the response to multiple-stimuli experiments as a sublinear superposition of responses to the individual stimuli.

SIGNIFICANCE

The same assembly of tools from the toolkit but with different parameter values is able to describe effects that are considered distinctive, such as the presence or absence of an initial decrease in oxygenated hemoglobin concentration, indicating that the differences might be due to unique parameter values in a subject rather than different fundamental mechanisms.

A spatially distributed computational model of brain cellular metabolism

This paper develops a three-dimensional spatially distributed model of brain cellular metabolism and investigates how the locus of the synaptic activity in reference to the capillaries and diffusion affects the behavior of the model, a type of analysis which is impossible to carry out in spatially lumped models, which are shown to be consistent spatially averaged approximations of the distributed model. To avoid a geometrically detailed modeling of the complex structure of the tissue consisting of different cell types and the extracellular space, the distributed model is based on a novel multi-domain formulation of reaction-diffusion equations, accounting also for separate mitochondria. The model reduction relating the spatially distributed model and lower dimensional reduced models, including the well-mixed spatially lumped compartment model, is carefully explained. We illustrate the effects of losing the spatial resolution with a computed example which is based on a reduced one-dimensional distributed radial model, and look into how the model behaves when the locus of the synaptic activity in reference to the capillaries is changed. By averaging the fluxes and concentrations in the distributed radial model to correspond to quantities in a lumped model, and further by estimating the parameters in the lumped, we conclude that varying the locus of the synaptic activity in reference to the capillaries alters significantly the lumped model parameters. This observation seems to be consequential for parameter estimation procedures from data when the spatial resolution is insufficient to determine the locus of the activity, indicating that the model uncertainty is an inherent feature of lumped models.

On a minimal model for hemodynamics and metabolism of lactate: application to low grade glioma and therapeutic strategies

WHO II low grade glioma evolves inevitably to anaplastic transformation. Magnetic resonance imaging is a good non-invasive way to watch it, by hemodynamic and metabolic modifications, thanks to multinuclear spectroscopy (1)H/(31)P. In this work we study a multi-scale minimal model of hemodynamics and metabolism applied to the study of gliomas. This mathematical analysis leads us to a fast-slow system. The control of the position of the stationary point brings to the concept of domain of viability. Starting from this system, the equations bring to light the parameters that push glioma cells out of their domain of viability. Four fundamental factors are highlighted. The first two are cerebral blood flow and the rate of lactate transport through monocarboxylate transporters, which must be reduced in order to push glioma out of its domain of viability. Another factor is the intra arterial lactate, which must be increased. The last factor is pH, indeed a decrease of intra cellular pH could interfere with glioma growth. These reflections suggest that these four parameters could lead to new therapeutic strategies for the management of low grade gliomas.

The metabolism of neurons and astrocytes through mathematical models

Mathematical modeling of the energy metabolism of brain cells plays a central role in understanding data collected with different imaging modalities, and in making predictions based on them. During the last decade, several sophisticated brain metabolism models have appeared. Unfortunately, the picture of the metabolic details that emerges from them is far from coherent: while each model has its justification and is in agreement with some experimental data, some of the predictions of different models can diverge from each other significantly. In this article, we review some of the recent published models, emphasizing similarities and differences between them to understand where the differences in predictions stem from. In that context we present a probabilistic approach, which rather than assigning fixed values to the model parameters, regard them as random variables whose distributions are inferred on in the light of stoichiometric information and different observations. The probabilistic approach reveals how much intrinsic variability a metabolic system may contain, which in turn may be a valid explanation of the different findings.

3-T proton magnetic spectroscopy in unmedicated first episode psychosis: a focus on creatine

Different lines of evidence suggest an abnormal cerebral energy metabolism as being critical to the pathophysiology of schizophrenia. However, it is unknown as to whether levels of creatine (Cr) would be involved in these anomalies. The study involved 33 unmedicated first episode psychosis patients and 41 healthy controls. Proton magnetic resonance spectroscopy ((1) H-MRS) was performed at 3 T using a long TE (TE/TM/TR of 240/27/3000 ms) such that within the total phosphocreatine (PCr) plus Cr signal (tCr(240)), mainly Cr was detectable. The target region was an 18 cm(3) prefrontal volume. A negative association was found between age of patients and tCr(240) levels referenced to internal water, with 20% of the variance in tCr(240) accounted for by Age. A secondary finding revealed 16% reduction of tCr(240) levels in patients, solely when comparing participants older than the median age of patients. No association existed between tCr(240) levels and clinical variables. These findings support previous data reporting abnormalities in brain creatine kinase isoenzymes involved with the maintenance of energy pools in schizophrenia. The implications of using a long TE are discussed in terms of the relative proportions of Cr and PCr within the tCr(240) signal, and of potential group differences in T(2) times.

HRF estimation in fMRI data with an unknown drift matrix by iterative minimization of the Kullback-Leibler divergence

Hemodynamic response function (HRF) estimation in noisy functional magnetic resonance imaging (fMRI) plays an important role when investigating the temporal dynamic of a brain region response during activations. Nonparametric methods which allow more flexibility in the estimation by inferring the HRF at each time sample have provided improved performance in comparison to the parametric methods. In this paper, the mixed-effects model is used to derive a new algorithm for nonparametric maximum likelihood HRF estimation. In this model, the random effect is used to better account for the variability of the drift. Contrary to the usual approaches, the proposed algorithm has the benefit of considering an unknown and therefore flexible drift matrix. This allows the effective representation of a broader class of drift signals and therefore the reduction of the error in approximating the drift component. Estimates of the HRF and the hyperparameters are derived by iterative minimization of the Kullback-Leibler divergence between a model family of probability distributions defined using the mixed-effects model and a desired family of probability distributions constrained to be concentrated on the observed data. The performance of proposed method is demonstrated on simulated and real fMRI data, the latter originating from both event-related and block design fMRI experiments.

Dynamic models of BOLD contrast

This personal recollection looks at the evolution of ideas about the dynamics of the blood oxygenation level dependent (BOLD) signal, with an emphasis on the balloon model. From the first detection of the BOLD response it has been clear that the signal exhibits interesting dynamics, such as a pronounced and long-lasting post-stimulus undershoot. The BOLD response, reflecting a change in local deoxyhemoglobin, is a combination of a hemodynamic response, related to changes in blood flow and venous blood volume, and a metabolic response related to oxygen metabolism. Modeling is potentially a way to understand the complex path from changes in neural activity to the BOLD signal. In the early days of fMRI it was hoped that the hemodynamic/metabolic response could be modeled in a unitary way, with blood flow, oxygen metabolism, and venous blood volume-the physiological factors that affect local deoxyhemoglobin-all tightly linked. The balloon model was an attempt to do this, based on the physiological ideas of limited oxygen delivery at baseline and a slow recovery of venous blood volume after the stimulus (the balloon effect), and this simple model of the physiology worked well to simulate the BOLD response. However, subsequent experiments suggest a more complicated picture of the underlying physiology, with blood flow and oxygen metabolism driven in parallel, possibly by different aspects of neural activity. In addition, it is still not clear whether the post-stimulus undershoot is a hemodynamic or a metabolic phenomenon, although the original venous balloon effect is unlikely to be the full explanation, and a flow undershoot is likely to be important. Although our understanding of the physics of the BOLD response is now reasonably solid, our understanding of the underlying physiological relationships is still relatively poor, and this is the primary hurdle for future models of BOLD dynamics.