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

The mechanisms with which neurons communicate with the vasculature to increase blood flow, termed neurovascular coupling is still unclear primarily due to the complex interactions between many parameters and the difficulty in accessing, monitoring and measuring them in the highly heterogeneous brain. Hence a solid theoretical framework based on existing experimental knowledge is necessary to study the relation between neural activity, the associated vasoactive factors released and their effects on the vasculature. Such a framework should also be related to experimental data so that it can be validated against repetitive experiments and generate verifiable hypothesis. We have developed a mathematical model which describes a signaling mechanism of neurovascular coupling with a model of pyramidal neuron and its corresponding fMRI BOLD response. In the first part of two papers we describe the integration of the neurovascular coupling unit extended to include a complex neuron model, which includes the important Na/K ATPase pump, with a model that provides a BOLD signal taking its input from the cerebral blood flow and the metabolic rate of oxygen consumption. We show that this produces a viable signal in terms of initial dip, positive and negative BOLD signals.     

A model of neurovascular coupling and the BOLD response PART II

A mathematical model is developed which describes a signalling mechanism of neurovascular coupling with a model of a pyramidal neuron and its corresponding fMRI BOLD response. In the first part of two papers (Part I) we described the integration of the neurovascular coupling unit extended to include a complex neuron model, which includes the important Na/K ATPase pump, with a model that provides a BOLD signal taking its input from the cerebral blood flow and the metabolic rate of oxygen consumption. We showed that this produced a viable signal in terms of initial dip, positive and negative BOLD signals. In this paper (PART II) our model predicts the variations of the BOLD response due to variations in neuronal activity and indicates that the BOLD signal could be used as an initial biomarker for neuronal dysfunction or variations in the perfusion of blood to the cerebral tissue. We have compared the simulated hypoxic BOLD response to experimental BOLD signals observed in the hippocampus during hypoxia showing good agreement. This approach of combined quantitative modelling of neurovascular coupling response and its BOLD response will enable more specific assessment of a brain region.     

Bayesian comparison of neurovascular coupling models using EEG-fMRI

Functional magnetic resonance imaging (fMRI), with blood oxygenation level-dependent (BOLD) contrast, is a widely used technique for studying the human brain. However, it is an indirect measure of underlying neuronal activity and the processes that link this activity to BOLD signals are still a topic of much debate. In order to relate findings from fMRI research to other measures of neuronal activity it is vital to understand the underlying neurovascular coupling mechanism. Currently, there is no consensus on the relative roles of synaptic and spiking activity in the generation of the BOLD response. Here we designed a modelling framework to investigate different neurovascular coupling mechanisms. We use Electroencephalographic (EEG) and fMRI data from a visual stimulation task together with biophysically informed mathematical models describing how neuronal activity generates the BOLD signals. These models allow us to non-invasively infer the degree of local synaptic and spiking activity in the healthy human brain. In addition, we use Bayesian model comparison to decide between neurovascular coupling mechanisms. We show that the BOLD signal is dependent upon both the synaptic and spiking activity but that the relative contributions of these two inputs are dependent upon the underlying neuronal firing rate. When the underlying neuronal firing is low then the BOLD response is best explained by synaptic activity. However, when the neuronal firing rate is high then both synaptic and spiking activity are required to explain the BOLD signal.     

Modeling of pathophysiological coupling between brain electrical activation,energy metabolism and hemodynamics: insights for the interpretation of intracerebral tumor imaging

Gliomas can display marked changes in the concentrations of energy metabolism molecules such as creatine (Cr), phosphocreatine (PCr) and lactate, as measured using magnetic resonance spectroscopy (MRS). Moreover, the BOLD (blood oxygen level dependent) contrast enhancement in functional magnetic resonance imaging (fMRI) can be reduced or missing within or near gliomas, while neural activity is not significantly reduced (so-called neurovascular decoupling), so that the location of functionally eloquent areas using fMRI can be erroneous. In this paper, we adapt a previously developed model of the coupling between neural activation, energy metabolism and hemodynamics, by including the venous dilatation Balloon model of Buxton and Frank. We show that decreasing the cerebral blood flow (CBF) baseline value, or the CBF increase fraction, results in a decrease of the BOLD signal and an increase of the lactate peak during a sustained activation. Baseline lactate and PCr levels are not significantly affected by CBF baseline reduction, but are altered even by a moderate decrease of mitochondrial respiration. Decreasing the total Cr and PCr concentration reduces the BOLD signal after the initial overshoot. In conclusion, we suggest that the coupled use of BOLD fMRI and MRS could contribute to a better understanding of the neurovascular and metabolic decoupling in gliomas.     

Abnormal brain activation to visual stimulation in cocaine abusers

Chronic cocaine abuse has been associated with cerebrovascular pathology. This is likely to reflect its vasoactive effects; cocaine produces vasoconstriction and reduces cerebral blood flow. We propose that cerebrovascular pathology in chronic cocaine abusers would result in abnormal BOLD [blood oxygenation level dependent] responses to activation stimuli. Here, we used fMRI to compared the BOLD response to photic visual stimulation in neurologically intact active cocaine abusers to that in non-drug-using healthy controls. Cocaine abusers showed a significantly enhanced positive BOLD response to photic stimulation when compared to control subjects. The enhanced activation in the cocaine abusers could result from low resting cerebral blood flow secondary to increased vasoconstriction and/or from low oxidative metabolism during activation. Alternatively, the larger signal intensity in the cocaine abusers could result from inefficient neuronal processing as has been shown to occur in other conditions of cerebral pathology. These findings provide evidence of cerebral dysfunction with chronic cocaine abuse, which could reflect cerebral blood flow or neuronal changes. Further studies are required to determine if the cerebrovascular changes we observed in the cocaine abusers recover with detoxification and to assess their functional consequences.     

A New Functional MRI Approach for Investigating Modulations of Brain Oxygen Metabolism

Functional MRI (fMRI) using the blood oxygenation level dependent (BOLD) signal is a common technique in the study of brain function. The BOLD signal is sensitive to the complex interaction of physiological changes including cerebral blood flow (CBF), cerebral blood volume (CBV), and cerebral oxygen metabolism (CMRO₂). A primary goal of quantitative fMRI methods is to combine BOLD imaging with other measurements (such as CBF measured with arterial spin labeling) to derive information about CMRO₂. This requires an accurate mathematical model to relate the BOLD signal to the physiological and hemodynamic changes; the most commonly used of these is the Davis model. Here, we propose a new nonlinear model that is straightforward and shows heuristic value in clearly relating the BOLD signal to blood flow, blood volume and the blood flow-oxygen metabolism coupling ratio. The model was tested for accuracy against a more detailed model adapted for magnetic fields of 1.5, 3 and 7T. The mathematical form of the heuristic model suggests a new ratio method for comparing combined BOLD and CBF data from two different stimulus responses to determine whether CBF and CMRO₂ coupling differs. The method does not require a calibration experiment or knowledge of parameter values as long as the exponential parameter describing the CBF-CBV relationship remains constant between stimuli. The method was found to work well for 1.5 and 3T but is prone to systematic error at 7T. If more specific information regarding changes in CMRO₂ is required, then with accuracy similar to that of the Davis model, the heuristic model can be applied to calibrated BOLD data at 1.5T, 3T and 7T. Both models work well over a reasonable range of blood flow and oxygen metabolism changes but are less accurate when applied to a simulated caffeine experiment in which CBF decreases and CMRO₂ increases.     

Separating vascular and neuronal effects of age on fMRI BOLD signals

Accurate identification of brain function is necessary to understand the neurobiology of cognitive ageing, and thereby promote well-being across the lifespan. A common tool used to investigate neurocognitive ageing is functional magnetic resonance imaging (fMRI). However, although fMRI data are often interpreted in terms of neuronal activity, the blood oxygenation level-dependent (BOLD) signal measured by fMRI includes contributions of both vascular and neuronal factors, which change differentially with age. While some studies investigate vascular ageing factors, the results of these studies are not well known within the field of neurocognitive ageing and therefore vascular confounds in neurocognitive fMRI studies are common. Despite over 10 000 BOLD-fMRI papers on ageing, fewer than 20 have applied techniques to correct for vascular effects. However, neurovascular ageing is not only a confound in fMRI, but an important feature in its own right, to be assessed alongside measures of neuronal ageing. We review current approaches to dissociate neuronal and vascular components of BOLD-fMRI of regional activity and functional connectivity. We highlight emerging evidence that vascular mechanisms in the brain do not simply control blood flow to support the metabolic needs of neurons, but form complex neurovascular interactions that influence neuronal function in health and disease.This article is part of the theme issue ‘Key relationships between non-invasive functional neuroimaging and the underlying neuronal activity’.     

Spatiotemporal BOLD dynamics from a poroelastic hemodynamic model

A quantitative theory is developed for the relationship between stimulus and the resulting blood oxygen level dependent (BOLD) functional magnetic resonance imaging (fMRI) signal, including both spatial and temporal dynamics for the first time. The brain tissue is modeled as a porous elastic medium, whose interconnected pores represent the vasculature. The model explicitly incorporates conservation of blood mass, interconversion of oxygenated and deoxygenated hemoglobin, force balance within the blood and of blood pressure with vessel walls, and blood flow modulation due to neuronal activity. In appropriate limits it is shown to reproduce prior Balloon models of hemodynamic response, which do not include spatial variations. The regime of validity of such models is thereby clarified by elucidating their assumptions, and when these break down, for example when voxel sizes become small.     

Self-regulation of local brain activity using real-time functional magnetic resonance imaging (fMRI)

Functional magnetic resonance imaging (fMRI) measures the blood oxygen level-dependent (BOLD) signal related to neuronal activity. So far, this technique has been limited by time-consuming data analysis impeding on-line analysis. In particular, no brain-computer interface (BCI) was available which provided on-line feedback to learn physiological self-regulation of the BOLD signal. Recently, studies have shown that fMRI feedback is feasible and facilitates voluntary control of brain activity. Here we review these studies to make the fMRI feedback methodology accessible to a broader scientific community such as researchers concerned with functional brain imaging and the neurobiology of learning. Methodological and conceptual limitations were substantially reduced by artefact control, sensitivity improvements, real-time algorithms, and adapted experimental designs. Physiological self-regulation of the local BOLD response is a new paradigm for cognitive neuroscience to study brain plasticity and the functional relevance of regulated brain areas by modification of behaviour. Voluntary control of abnormal activity in circumscribed brain areas may even be applied as psychophysiological treatment.     

Linear and nonlinear relationships between neuronal activity, oxygen metabolism, and hemodynamic responses

We investigated the relationship between neuronal activity, oxygen metabolism, and hemodynamic responses in rat somatosensory cortex with simultaneous optical intrinsic signal imaging and spectroscopy, laser Doppler flowmetry, and local field potential recordings. Changes in cerebral oxygen consumption increased linearly with synaptic activity but with a threshold effect consistent with the existence of a tissue oxygen buffer. Modeling analysis demonstrated that the coupling between neuronal activity and hemodynamic response magnitude may appear linear over a narrow range but incorporates nonlinear effects that are better described by a threshold or power law relationship. These results indicate that caution is required in the interpretation of perfusion-based indicators of brain activity, such as functional magnetic resonance imaging (fMRI), and may help to refine quantitative models of neurovascular coupling.     

Functional magnetic resonance imaging: imaging techniques and contrast mechanisms.

Functional magnetic resonance imaging (fMRI) is a widely used technique for generating images or maps of human brain activity. The applications of the technique are widespread in cognitive neuroscience and it is hoped they will eventually extend into clinical practice. The activation signal measured with fMRI is predicated on indirectly measuring changes in the concentration of deoxyhaemoglobin which arise from an increase in blood oxygenation in the vicinity of neuronal firing. The exact mechanisms of this blood oxygenation level dependent (BOLD) contrast are highly complex. The signal measured is dependent on both the underlying physiological events and the imaging physics. BOLD contrast, although sensitive, is not a quantifiable measure of neuronal activity. A number of different imaging techniques and parameters can be used for fMRI, the choice of which depends on the particular requirements of each functional imaging experiment. The high-speed MRI technique, echo-planar imaging provides the basis for most fMRI experiments. The problems inherent to this method and the ways in which these may be overcome are particularly important in the move towards performing functional studies on higher field MRI systems. Future developments in techniques and hardware are also likely to enhance the measurement of brain activity using MRI.     

Positive Allosteric Modulator of GABA Lowers BOLD Responses in the Cingulate Cortex

Knowledge about the neural underpinnings of the negative blood oxygen level dependent (BOLD) responses in functional magnetic resonance imaging (fMRI) is still limited. We hypothesized that pharmacological GABAergic modulation attenuates BOLD responses, and that blood concentrations of a positive allosteric modulator of GABA correlate inversely with BOLD responses in the cingulate cortex. We investigated whether or not pure task-related negative BOLD responses were co-localized with pharmacologically modulated BOLD responses. Twenty healthy adults received either 5 mg diazepam or placebo in a double blind, randomized design. During fMRI the subjects performed a working memory task. Results showed that BOLD responses in the cingulate cortex were inversely correlated with diazepam blood concentrations; that is, the higher the blood diazepam concentration, the lower the BOLD response. This inverse correlation was most pronounced in the pregenual anterior cingulate cortex and the anterior mid-cingulate cortex. For subjects with diazepam plasma concentration > 0.1 mg/L we observed negative BOLD responses with respect to fixation baseline. There was minor overlap between cingulate regions with task-related negative BOLD responses and regions where the BOLD responses were inversely correlated with diazepam concentration. We interpret that the inverse correlation between the BOLD response and diazepam was caused by GABA-related neural inhibition. Thus, this study supports the hypothesis that GABA attenuates BOLD responses in fMRI. The minimal overlap between task-related negative BOLD responses and responses attenuated by diazepam suggests that these responses might be caused by different mechanisms.     

Functional magnetic resonance study of deliberate deception

The goal of the study was analysis of the cerebral mechanisms of deliberate deception. The eventrelated functional magnetic resonance (ER fMRI) imaging technique was used to assess the changes in the functional brain activity by means of recording the blood oxygen level-dependent (BOLD) signal. Twelve right-handed healthy volunteers aged 19–44 years participated in the study. The BOLD images were obtained during three experimental trials: deliberate deception, manipulative honest and control truthful trials (catch trials). The deliberate deception and manipulative honest actions were characterized by a BOLD signal increase in the anterior cingulate (Brodmann’s area (BA) 32), frontal (BAs 9/10, 6), and parietal (BA 40) cortices as compared with a truthful response. Comparison of the ER fMRI data with the results of earlier studies where event-related potentials (ERPs) were recorded under similar conditions indicates the involvement of the brain mechanism of error detection in deliberate deception.     

Negative BOLD fMRI response in the visual cortex carries precise stimulus-specific information

Sustained positive BOLD (blood oxygen level-dependent) activity is employed extensively in functional magnetic resonance imaging (fMRI) studies as evidence for task or stimulus-specific neural responses. However, the presence of sustained negative BOLD activity (i.e., sustained responses that are lower than the fixation baseline) has remained more difficult to interpret. Some studies suggest that it results from local "blood stealing" wherein blood is diverted to neurally active regions without a concomitant change of neural activity in the negative BOLD regions. However, other evidence suggests that negative BOLD is a result of local neural suppression. In both cases, regions of negative BOLD response are usually interpreted as carrying relatively little, if any, stimulus-specific information (hence the predominant reliance on positive BOLD activity in fMRI). Here we show that the negative BOLD response resulting from visual stimulation can carry high information content that is stimulus-specific. Using a general linear model (GLM), we contrasted standard flickering stimuli to a fixation baseline and found regions of the visual cortex that displayed a sustained negative BOLD response, consistent with several previous studies. Within these negative BOLD regions, we compared patterns of fMRI activity generated by flickering Gabors that were systematically shifted in position. As the Gabors were shifted further from each other, the correlation in the spatial pattern of activity across a population of voxels (such as the population of V1 voxels that displayed a negative BOLD response) decreased significantly. Despite the fact that the BOLD signal was significantly negative (lower than fixation baseline), these regions were able to discriminate objects separated by less than 0.5 deg (at approximately 10 deg eccentricity). The results suggest that meaningful, stimulus-specific processing occurs even in regions that display a strong negative BOLD response.     

Simultaneous BOLD fMRI and fiber-optic calcium recording in rat neocortex

Functional magnetic resonance imaging (fMRI) based on blood oxygen level-dependent (BOLD) contrast is widely used for probing brain activity, but its relationship to underlying neural activity remains elusive. Here, we combined fMRI with fiber-optic recordings of fluorescent calcium indicator signals to investigate this relationship in rat somatosensory cortex. Electrical forepaw stimulation (1-10 Hz) evoked fast calcium signals of neuronal origin that showed frequency-dependent adaptation. Additionally, slower calcium signals occurred in astrocyte networks, as verified by astrocyte-specific staining and two-photon microscopy. Without apparent glia activation, we could predict BOLD responses well from simultaneously recorded fiber-optic signals, assuming an impulse response function and taking into account neuronal adaptation. In cases with glia activation, we uncovered additional prolonged BOLD signal components. Our findings highlight the complexity of fMRI BOLD signals, involving both neuronal and glial activity. Combined fMRI and fiber-optic recordings should help to clarify cellular mechanisms underlying BOLD signals.     

A cerebrovascular response model for functional neuroimaging including dynamic cerebral autoregulation

Functional neuroimaging techniques such as functional magnetic resonance imaging (fMRI) and near-infrared spectroscopy (NIRS) can be used to isolate an evoked response to a stimulus from significant background physiological fluctuations. Data analysis approaches typically use averaging or linear regression to remove this physiological baseline with varying degrees of success. Biophysical model-based analysis of the functional hemodynamic response has also been advanced previously with the Balloon and Windkessel models. In the present work, a biophysical model of systemic and cerebral circulation and gas exchange is applied to resting state NIRS neuroimaging data from 10 human subjects. The model further includes dynamic cerebral autoregulation, which modulates the cerebral arteriole compliance to control cerebral blood flow. This biophysical model allows for prediction, from noninvasive blood pressure measurements, of the background hemodynamic fluctuations in the systemic and cerebral circulations. Significantly higher correlations with the NIRS data were found using the biophysical model predictions compared to blood pressure regression and compared to transfer function analysis (multifactor ANOVA, p < 0.0001). This finding supports the further development and use of biophysical models for removing baseline activity in functional neuroimaging analysis. Future extensions of this work could model changes in cerebrovascular physiology that occur during development, aging, and disease.     

Cerebral oxygen demand for short-lived and steady-state events

Because of the importance of oxidative energetics for cerebral function, extraction of oxygen consumption (CMR_O2) from blood oxygenation level-dependent (BOLD) signal using multi-modal measurements of blood flow (CBF) and volume (CBV) has become an accepted functional magnetic resonance imaging (fMRI) technique. This approach, termed calibrated fMRI, is based on a biophysical model which describes tissue oxygen extraction at steady-state. A problem encountered for calculating dynamic CMR_O2 relates to concerns whether the conventional BOLD model can be applied transiently. In particular, it is unclear whether calculation of CMR_O2 differs between short and long stimuli. Linearity was experimentally demonstrated between BOLD-related components and neural activity, thereby making it possible to use calibrated fMRI in a dynamic manner. We used multi-modal fMRI and electrophysiology, in α-chloralose anesthetized rats during forepaw stimulation to show that respective transfer functions (of BOLD, CBV, CBF) generated by deconvolution with neural activity are time invariant, for events in the millisecond to minute range. These results allowed extraction of a significant component of the BOLD signal that can be ascribed to CMR_O2 transients. We discuss the importance of minimizing residual signal, represented by the difference between modeled and raw signals, in convolution analysis of multi-modal signals.     

Developmental Switch in Neurovascular Coupling in the Immature Rodent Barrel Cortex

Neurovascular coupling (NVC) in the adult central nervous system (CNS) is a mechanism that provides regions of the brain with more oxygen and glucose upon increased levels of neural activation. Hemodynamic changes that go along with neural activation evoke a blood oxygen level-dependent (BOLD) signal in functional magnetic resonance imaging (fMRI) that can be used to study brain activity non-invasively. A correct correlation of the BOLD signal to neural activity is pivotal to understand this signal in neuronal development, health and disease. However, the function of NVC during development is largely unknown. The rodent whisker-to-barrel cortex is an experimentally well established model to study neurovascular interdependences. Using extracellular multi-electrode recordings and laser-Doppler-flowmetry (LDF) we show in the murine barrel cortex of postnatal day 7 (P7) and P30 mice in vivo that NVC undergoes a physiological shift during the first month of life. In the mature CNS it is well accepted that cortical sensory processing results in a rise in regional cerebral blood flow (rCBF). We show in P7 animals that rCBF decreases during prolonged multi-whisker stimulation and goes along with multi unit activity (MUA) fatigue. In contrast at P30, MUA remains stable during repetitive stimulation and is associated with an increase in rCBF. Further we characterize in both age groups the responses in NVC to single sensory stimuli. We suggest that the observed shift in NVC is an important process in cortical development that may be of high relevance for the correct interpretation of brain activity e.g. in fMRI studies of the immature central nervous system (CNS).     

Assessment of single-vessel cerebral blood velocity by phase contrast fMRI

Current approaches to high-field functional MRI (fMRI) provide 2 means to map hemodynamics at the level of single vessels in the brain. One is through changes in deoxyhemoglobin in venules, i.e., blood oxygenation level–dependent (BOLD) fMRI, while the second is through changes in arteriole diameter, i.e., cerebral blood volume (CBV) fMRI. Here, we introduce cerebral blood flow–related velocity-based fMRI, denoted CBFv-fMRI, which uses high-resolution phase contrast (PC) MRI to form velocity measurements of flow. We use CBFv-fMRI in measure changes in blood velocity in single penetrating microvessels across rat parietal cortex. In contrast to the venule-dominated BOLD and arteriole-dominated CBV fMRI signals, CBFv-fMRI is comparable from both arterioles and venules. A single fMRI platform is used to map changes in blood pO₂ (BOLD), volume (CBV), and velocity (CBFv). This combined high-resolution single-vessel fMRI mapping scheme enables vessel-specific hemodynamic mapping in animal models of normal and diseased states and further has translational potential to map vascular dementia in diseased or injured human brains with ultra–high-field fMRI.

This study presents a phase contrast-based, high field MRI-based approach for the functional mapping of cerebral blood velocity in individual cortical arterioles and venules in the rat cortex; this approach can be combined with previously established approaches to map BOLD, CBV, and blood velocity from penetrating microvessels.     

Dynamic activation model for a glutamatergic neurovascular unit

This article considers a dynamic spatially lumped model for brain energy metabolism and proposes to use the results of a Markov chain Monte Carlo (MCMC) based flux balance analysis to estimate the kinetic model parameters. By treating steady state reaction fluxes and transport rates as random variables we are able to propagate the uncertainty in the steady state configurations to the predictions of the dynamic model, whose responses are no longer individual but ensembles of time courses. The kinetic model consists of five compartments and is governed by kinetic mass balance equations with Michaelis-Menten type expressions for reaction rates and transports between the compartments. The neuronal activation is implemented in terms of the effect of neuronal activity on parameters controlling the blood flow and neurotransmitter transport, and a feedback mechanism coupling the glutamate concentration in the synaptic cleft and the ATP hydrolysis, thus accounting for the energetic cost of the membrane potential restoration in the postsynaptic neurons. The changes in capillary volume follow the balloon model developed for BOLD MRI. The model follows the time course of the saturation levels of the blood hemoglobin, which link metabolism and BOLD FMRI signal. Analysis of the model predictions suggest that stoichiometry alone is not enough to determine glucose partitioning between neuron and astrocyte. Lactate exchange between neuron and astrocyte is supported by the model predictions, but the uncertainty on the direction and rate is rather elevated. By and large, the model suggests that astrocyte produces and effluxes lactate, while neuron may switch from using to producing lactate. The level of ATP hydrolysis in astrocyte is substantially higher than strictly required for neurotransmitter cycling, in agreement with the literature.