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

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.

Modeling the contribution of neuron-astrocyte cross talk to slow blood oxygenation level-dependent signal oscillations

A consistent and prominent feature of brain functional magnetic resonance imaging (fMRI) data is the presence of low-frequency (<0.1 Hz) fluctuations of the blood oxygenation level-dependent (BOLD) signal that are thought to reflect spontaneous neuronal activity. In this report we provide modeling evidence that cyclic physiological activation of astroglial cells produces similar BOLD oscillations through a mechanism mediated by intracellular Ca(2+) signaling. Specifically, neurotransmission induces pulses of Ca(2+) concentration in astrocytes, resulting in increased cerebral perfusion and neuroactive transmitter release by these cells (i.e., gliotransmission), which in turn stimulates neuronal activity. Noticeably, the level of neuron-astrocyte cross talk regulates the periodic behavior of the Ca(2+) wave-induced BOLD fluctuations. Our results suggest that the spontaneous ongoing activity of neuroglial networks is a potential source of the observed slow fMRI signal oscillations.

A parametric empirical Bayesian framework for fMRI-constrained MEG/EEG source reconstruction

We describe an asymmetric approach to fMRI and MEG/EEG fusion in which fMRI data are treated as empirical priors on electromagnetic sources, such that their influence depends on the MEG/EEG data, by virtue of maximizing the model evidence. This is important if the causes of the MEG/EEG signals differ from those of the fMRI signal. Furthermore, each suprathreshold fMRI cluster is treated as a separate prior, which is important if fMRI data reflect neural activity arising at different times within the EEG/MEG data. We present methodological considerations when mapping from a 3D fMRI Statistical Parametric Map to a 2D cortical surface and thence to the covariance components used within our Parametric Empirical Bayesian framework. Our previous introduction of a canonical (inverse‐normalized) cortical mesh also allows deployment of fMRI priors that live in a template space; for example, from a group analysis of different individuals. We evaluate the ensuing scheme with MEG and EEG data recorded simultaneously from 12 participants, using the same face‐processing paradigm under which independent fMRI data were obtained. Because the fMRI priors become part of the generative model, we use the model evidence to compare (i) multiple versus single, (ii) valid versus invalid, (iii) binary versus continuous, and (iv) variance versus covariance fMRI priors. For these data, multiple, valid, binary, and variance fMRI priors proved best for a standard Minimum Norm inversion. Interestingly, however, inversion using Multiple Sparse Priors benefited little from additional fMRI priors, suggesting that they already provide a sufficiently flexible generative model. Hum Brain Mapp, 2010. © 2010 Wiley‐Liss, Inc.

Incorporating FMRI functional networks in EEG source imaging: a Bayesian model comparison approach

Brain functional networks extracted from fMRI can improve the accuracy of EEG source localization. However, the coupling between EEG and fMRI remains poorly understood, i.e., whether fMRI networks provide information about the magnitude of neural activity, and whether neural sources demonstrate temporal correlations within each network. In this paper, we present an improved version of the NEtwork-based SOurce Imaging method (iNESOI) through Bayesian model comparison. Different models correspond to various matching between EEG and fMRI, and the appropriate one is selected by data with the model evidence. Synthetic and real data tests show that iNESOI has potential to select the appropriate fMRI priors to reach a better source reconstruction than some other typical approaches.

ATP consumption and neural electrical activity: a physiological model for brain imaging

The relation between neural electrical activity and oxygen consumption is the key issue in almost all brain image modalities based on perfusion. Despite the large amount of physiological information available in the literature about the processes involved in neural activation, a practical, tractable and simultaneously accurate mathematical model to describe this relation is needed.

Reduced medial prefrontal N-acetyl-aspartate levels in pediatric major depressive disorder: a multi-voxel in vivo(1)H spectroscopy study

There is increasing evidence of a reciprocal fronto-limbic network in the pathogenesis of mood disorders. Prior in vivo proton ((1)H) spectroscopy studies provide evidence of abnormal neurochemical levels in the cingulate and dorsolateral prefrontal cortex (DLPFC) of adult subjects with major depressive disorder (MDD). We examined whether similar abnormalities occur in children and adolescents with MDD. We collected two-dimensional multi-voxel in vivo (1)H spectroscopy data at 1.5 Tesla to quantify levels of N-acetyl-aspartate (NAA), glycerolphosphocholine plus phosphocholine (GPC+PC), and phosphocreatine plus creatine (PCr+Cr) in the DLPFC, medial prefrontal cortex (MPFC), and anterior cingulate (AC) of children and adolescents aged 8-17 years with MDD (n=16) compared with healthy control subjects (n=38). Analysis of covariance with age and gender as covariates was performed. MDD subjects showed significantly lower levels of NAA in the right MPFC and right AC than controls. MDD subjects also had significantly lower levels of GPC+PC in the right AC than control subjects. There were no significant differences in other metabolites in the studied regions. Pediatric patients with MDD exhibit neurochemical alterations in prefrontal cortex regions that are important in the monitoring and regulation of emotional states.

Simulation study of brain blood flow regulation by intra-cortical arterioles in an anatomically accurate large human vascular network. Part II: flow variations induced by global or localized modifications of arteriolar diameters

In a companion paper (Lorthois et al., Neuroimage, in press), we perform the first simulations of blood flow in an anatomically accurate large human intra-cortical vascular network (~10000 segments), using a 1D non-linear model taking into account the complex rheological properties of blood flow in microcirculation. This model predicts blood pressure, blood flow and hematocrit distributions, volumes of functional vascular territories, regional flow at voxel and network scales, etc. Using the same approach, we study flow reorganizations induced by global arteriolar vasodilations (an isometabolic global increase in cerebral blood flow). For small to moderate global vasodilations, the relationship between changes in volume and changes in flow is in close agreement with Grubb's law, providing a quantitative tool for studying the variations of its exponent with underlying vascular architecture. A significant correlation between blood flow and vascular structure at the voxel scale, practically unchanged with respect to baseline, is demonstrated. Furthermore, the effects of localized arteriolar vasodilations, representative of a local increase in metabolic demand, are analyzed. In particular, localized vasodilations induce flow changes, including vascular steal, in the neighboring arteriolar trunks at small distances (<300 μm), while their influence in the neighboring veins is much larger (about 1 mm), which provides an estimate of the vascular point spread function. More generally, for the first time, the hemodynamic component of various functional neuroimaging techniques has been isolated from metabolic and neuronal components, and a direct relationship with several known characteristics of the BOLD signal has been demonstrated.

Simulation study of brain blood flow regulation by intra-cortical arterioles in an anatomically accurate large human vascular network: Part I: methodology and baseline flow

Hemodynamically based functional neuroimaging techniques, such as BOLD fMRI and PET, provide indirect measures of neuronal activity. The quantitative relationship between neuronal activity and the measured signals is not yet precisely known, with uncertainties remaining about the relative contribution by their metabolic and hemodynamic components. Empirical observations have demonstrated the importance of the latter component and suggested that micro-vascular anatomy has a potential influence. The recent development of a 3D computer-assisted method for micro-vascular cerebral network analysis has produced a large quantitative library on the microcirculation of the human cerebral cortex (Cassot et al., 2006), which can be used to investigate the hemodynamic component of brain activation through fluid dynamic modeling. For this purpose, we perform the first simulations of blood flow in an anatomically accurate large human intra-cortical vascular network (~10000 segments), using a 1D non-linear model taking account of the complex rheological properties of blood flow in microcirculation. This model predicts blood pressure, blood flow and hematocrit distributions, as well as volumes of functional vascular territories, and regional flow at voxel and network scales. First, the influence of the prescribed boundary conditions (BCs) on the baseline flow structure is investigated, highlighting relevant lower- and upper-bound BCs. Independent of these BCs, large heterogeneities of baseline flow from vessel to vessel and from voxel to voxel, are demonstrated. These heterogeneities are controlled by the architecture of the intra-cortical vascular network. In particular, a correlation between the blood flow and the proportion of vascular volume occupied by arterioles or venules, at voxel scale, is highlighted. Then, the extent of venous contamination downstream to the sites of neuronal activation is investigated, demonstrating a linear relationship between the catchment surface of the activated area and the diameter of the intra-cortical draining vein.

Changes in glucose uptake rather than lactate shuttle take center stage in subserving neuroenergetics: evidence from mathematical modeling

In this paper, we combined several mathematical models of cerebral metabolism and nutrient transport to investigate the energetic significance of metabolite trafficking within the brain parenchyma during a 360-secs activation. Glycolytic and oxidative cellular metabolism were homogeneously modeled between neurons and astrocytes, and the stimulation-induced neuronal versus astrocytic Na(+) inflow was set to 3:1. These assumptions resemble physiologic conditions and are supported by current literature. Simulations showed that glucose diffusion to the interstitium through basal lamina dominates the provision of the sugar to both neurons and astrocytes, whereas astrocytic endfeet transfer less than 4% of the total glucose supplied to the tissue. Neuronal access to paracellularly diffused glucose prevails even after halving (doubling) the ratio of neuronal versus astrocytic glycolytic (oxidative) metabolism, as well as after reducing the neuronal versus astrocytic Na(+) inflow to a nonphysiologic value of 1:1. Noticeably, displaced glucose equivalents as intercellularly shuttled lactate account for approximately 6% to 7% of total brain glucose uptake, an amount comparable with the concomitant drainage of the monocarboxylate by the bloodstream. Overall, our results suggest that the control of carbon recruitment for neurons and astrocytes is exerted at the level of glucose uptake rather than that of lactate shuttle.

A dynamic model of neurovascular coupling: implications for blood vessel dilation and constriction

Neurovascular coupling in response to stimulation of the rat barrel cortex was investigated using concurrent multichannel electrophysiology and laser Doppler flowmetry. The data were used to build a linear dynamic model relating neural activity to blood flow. Local field potential time series were subject to current source density analysis, and the time series of a layer IV sink of the barrel cortex was used as the input to the model. The model output was the time series of the changes in regional cerebral blood flow (CBF). We show that this model can provide excellent fit of the CBF responses for stimulus durations of up to 16 s. The structure of the model consisted of two coupled components representing vascular dilation and constriction. The complex temporal characteristics of the CBF time series were reproduced by the relatively simple balance of these two components. We show that the impulse response obtained under the 16-s duration stimulation condition generalised to provide a good prediction to the data from the shorter duration stimulation conditions. Furthermore, by optimising three out of the total of nine model parameters, the variability in the data can be well accounted for over a wide range of stimulus conditions. By establishing linearity, classic system analysis methods can be used to generate and explore a range of equivalent model structures (e.g., feed-forward or feedback) to guide the experimental investigation of the control of vascular dilation and constriction following stimulation.

A Kullback-Leibler methodology for HRF estimation in fMRI data

Hemodynamic Response Function (HRF) estimation in functional Magnetic Resonance Imaging (fMRI) experiments is an important issue in functional neuroimages analysis. Indeed, when modeling each brain region as a stationary linear system characterized by its impulse response, the HRF describes the temporal dynamic of the brain region response during activations. Using the mixed-effects model, a new algorithm for maximum likelihood HRF estimation is derived. 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 drift matrix. Estimations of the HRF and the hyperparameters are derived by alternating 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 relevance of proposed approach is demonstrated both on simulated and real data.

The Possible Role of CO(2) in Producing A Post-Stimulus CBF and BOLD Undershoot

Comprehending the underlying mechanisms of neurovascular coupling is important for understanding the pathogenesis of neurodegenerative diseases related to uncoupling. Moreover, it elucidates the casual relation between the neural signaling and the hemodynamic responses measured with various imaging modalities such as functional magnetic resonance imaging (fMRI). There are mainly two hypotheses concerning this mechanism: a metabolic hypothesis and a neurogenic hypothesis. We have modified recent models of neurovascular coupling adding the effects of both NO (nitric oxide) kinetics, which is a well-known neurogenic vasodilator, and CO₂ kinetics as a metabolic vasodilator. We have also added the Hodgkin–Huxley equations relating the membrane potentials to sodium influx through the membrane. Our results show that the dominant factor in the hemodynamic response is NO, however CO₂ is important in producing a brief post-stimulus undershoot in the blood flow response that in turn modifies the fMRI blood oxygenation level-dependent post-stimulus undershoot. Our results suggest that increased cerebral blood flow during stimulation causes CO₂ washout which then results in a post-stimulus hypocapnia induced vasoconstrictive effect.

A Dynamic Causal Model of the Coupling Between Pulse Stimulation and Neural Activity

We present a dynamic causal model that can explain context-dependent changes in neural responses, in the rat barrel cortex, to an electrical whisker stimulation at different frequencies. Neural responses were measured in terms of local field potentials. These were converted into current source density (CSD) data, and the time series of the CSD sink was extracted to provide a time series response train. The model structure consists of three layers (approximating the responses from the brain stem to the thalamus and then the barrel cortex), and the latter two layers contain nonlinearly coupled modules of linear second-order dynamic systems. The interaction of these modules forms a nonlinear regulatory system that determines the temporal structure of the neural response amplitude for the thalamic and cortical layers.

The model is based on the measured population dynamics of neurons rather than the dynamics of a single neuron and was evaluated against CSD data from experiments with varying stimulation frequency (1–40 Hz), random pulse trains, and awake and anesthetized animals. The model parameters obtained by optimization for different physiological conditions (anesthetized or awake) were significantly different.

Following Friston, Mechelli, Turner, and Price ( 2000 ), this work is part of a formal mathematical system currently being developed (Zheng et al., 2005 ) that links stimulation to the blood oxygen level dependent (BOLD) functional magnetic resonance imaging (fMRI) signal through neural activity and hemodynamic variables. The importance of the model described here is that it can be used to invert the hemodynamic measurements of changes in blood flow to estimate the underlying neural activity.

Bootstrap generation and evaluation of an fMRI simulation database

Computer simulations have played a critical role in functional magnetic resonance imaging (fMRI) research, notably in the validation of new data analysis methods. Many approaches have been used to generate fMRI simulations, but there is currently no generic framework to assess how realistic each one of these approaches may be. In this article, a statistical technique called parametric bootstrap was used to generate a simulation database that mimicked the parameters found in a real database, which comprised 40 subjects and five tasks. The simulations were evaluated by comparing the distributions of a battery of statistical measures between the real and simulated databases. Two popular simulation models were evaluated for the first time by applying the bootstrap framework. The first model was an additive mixture of multiple components and the second one implemented a non-linear motion process. In both models, the simulated components included the following brain dynamics: a baseline, physiological noise, neural activation and random noise. These models were found to successfully reproduce the relative variance of the components and the temporal autocorrelation of the fMRI time series. By contrast, the level of spatial autocorrelation was found to be drastically low using the additive model. Interestingly, the motion process in the second model intrisically generated some slow time drifts and increased the level of spatial autocorrelations. These experiments demonstrated that the bootstrap framework is a powerful new tool that can pinpoint the respective strengths and limitations of simulation models.

The in vivo neuron-to-astrocyte lactate shuttle in human brain: evidence from modeling of measured lactate levels during visual stimulation

Functional magnetic resonance spectroscopy (fMRS) allows the non-invasive measurement of metabolite concentrations in the human brain, including changes induced by variations in neurotransmission activity. However, the limited spatial and temporal resolution of fMRS does not allow specific measurements of metabolites in different cell types. Thus, the analysis of fMRS data in the context of compartmentalized metabolism requires the formulation and application of mathematical models. In the present study we utilized the mathematical model introduced by Simpson et al. (2007) to gain insights into compartmentalized metabolism in vivo from the fMRS data obtained in humans at ultra high magnetic field by Mangia et al. (2007a). This model simulates brain glucose and lactate levels in a theoretical cortical slice. Using experimentally determined concentrations and catalytic activities for the respective transporter proteins, we calculate inflow and export of glucose and lactate in endothelium, astrocytes, and neurons. We then vary neuronal and astrocytic glucose and lactate utilization capacities until close correspondence is observed between in vivo and simulated glucose and lactate levels. The results of the simulations indicate that, when literature values of glucose transport capacity are utilized, the fMRS data are consistent with export of lactate by neurons and import of lactate by astrocytes, a mechanism that can be referred to as a neuron-to-astrocyte lactate shuttle. A shuttle of lactate from astrocytes to neurons could be simulated, but this required the astrocytic glucose transport capacity to be increased by 12-fold, and required that neurons not respond to activation with increased glycolysis, two conditions that are not supported by current literature.

Origins of the BOLD post-stimulus undershoot

The interpretation of the blood-oxygenation level-dependent (BOLD) post-stimulus undershoot has been a topic of considerable interest, as the mechanisms behind this prominent BOLD transient may provide valuable clues on the neurovascular response process and energy supply routes of the brain. Biomechanical theories explain the origin of the BOLD undershoot through the passive ballooning of post-capillary vessels which leads to an increase in venous blood volume (CBV(v), comprising deoxygenated blood in capillary, venular and arteriolar compartments), resulting in susceptibility-induced signal decrease. While there has been substantial evidence supporting a role for venous ballooning, there have also been reports arguing for a prolonged post-stimulus elevation in cerebral oxygenation consumption (CMRo(2)) as the primary cause. Furthermore, a contribution of post-stimulus cerebral blood flow (CBF) undershoots has also been demonstrated. To clarify the role of the venous compartment in causing the BOLD undershoot, we performed in vivo fMRI measurements of the transient DeltaCBV(v), DeltaCBF and DeltaBOLD responses in healthy humans. We observed a slow post-stimulus return to baseline in venous CBV which supports the existence of a passive "balloon" effect, implying that previous observations of a quicker recovery of the total CBV response may be dominated by arterial CBV change. Our findings also support a significant contribution from the CBF undershoots, which, combined with a slow venous CBV response, would account for much of the BOLD undershoot.

Exploring neuro-vascular and neuro-metabolic coupling in rat somatosensory cortex

The existence of a coupling between changes in neuronal activity, cerebral blood flow and blood oxygenation is well known. The explicit relationship between these systems, however, is complex and remains a subject of intense research. Here, we use direct electrophysiological recordings to predict blood flow and oxygenation changes measured with optical methods during parametric stimulation applied to the somatosensory cortex in rat brain. Using a multimodal model of the cerebral functional unit, we estimate a neuro-vascular and a neuro-metabolic transfer function relating the experimentally measured neural responses with the inputs to a vascular model predicting hemodynamic and blood oxygenation changes. We show that our model can accurately predict experimentally measured parametric hemodynamic evoked responses by using a single linear transfer function relationship with a reduced number of state parameters to relate the level of neural activity to evoked cerebral blood flow and oxygen metabolism changes. At the same time, we characterize the metabolic and vascular neural response functions and interpret their physiological significance.

A model of brain circulation and metabolism: NIRS signal changes during physiological challenges

We construct a model of brain circulation and energy metabolism. The model is designed to explain experimental data and predict the response of the circulation and metabolism to a variety of stimuli, in particular, changes in arterial blood pressure, CO(2) levels, O(2) levels, and functional activation. Significant model outputs are predictions about blood flow, metabolic rate, and quantities measurable noninvasively using near-infrared spectroscopy (NIRS), including cerebral blood volume and oxygenation and the redox state of the Cu(A) centre in cytochrome c oxidase. These quantities are now frequently measured in clinical settings; however the relationship between the measurements and the underlying physiological events is in general complex. We anticipate that the model will play an important role in helping to understand the NIRS signals, in particular, the cytochrome signal, which has been hard to interpret. A range of model simulations are presented, and model outputs are compared to published data obtained from both in vivo and in vitro settings. The comparisons are encouraging, showing that the model is able to reproduce observed behaviour in response to various stimuli.

Multimodal functional neuroimaging: integrating functional MRI and EEG/MEG

Noninvasive functional neuroimaging, as an important tool for basic neuroscience research and clinical diagnosis, continues to face the need of improving the spatial and temporal resolution. While existing neuroimaging modalities might approach their limits in imaging capability mostly due to fundamental as well as technical reasons, it becomes increasingly attractive to integrate multiple complementary modalities in an attempt to significantly enhance the spatiotemporal resolution that cannot be achieved by any modality individually. Electrophysiological and hemodynamic/metabolic signals reflect distinct but closely coupled aspects of the underlying neural activity. Combining fMRI and EEG/MEG data allows us to study brain function from different perspectives. In this review, we start with an overview of the physiological origins of EEG/MEG and fMRI, as well as their fundamental biophysics and imaging principles, we proceed with a review of the major advances in the understanding and modeling of neurovascular coupling and in the methodologies for the fMRI-EEG/MEG simultaneous recording. Finally, we summarize important remaining issues and perspectives concerning multimodal functional neuroimaging, including brain connectivity imaging.

Increased glucose metabolism and ATP level in brain tissue of Huntington's disease transgenic mice

Huntington's disease (HD) is a progressive neurodegenerative disorder characterized by multifarious dysfunctional alterations including mitochondrial impairment. In the present study, the formation of inclusions caused by the mutation of huntingtin protein and its relationship with changes in energy metabolism and with pathological alterations were investigated both in transgenic and 3-nitropropionic acid-treated mouse models for HD. The HD and normal mice were characterized clinically; the affected brain regions were identified by immunohistochemistry and used for biochemical analysis of the ATP-producing systems in the cytosolic and the mitochondrial compartments. In both HD models, the activities of some glycolytic enzymes were somewhat higher. By contrast, the activity of glyceraldehyde-3-phosphate dehydrogenase was much lower in the affected region of the brain compared to that of the control. Paradoxically, at the system level, glucose conversion into lactate was enhanced in cytosolic extracts from the HD brain tissue, and the level of ATP was higher in the tissue itself. The paradox could be resolved by taking all the observed changes in glycolytic enzymes into account, ensuing an experiment-based detailed mathematical model of the glycolytic pathway. The mathematical modelling using the experimentally determined kinetic parameters of the individual enzymes and the well-established rate equations predicted the measured flux and concentrations in the case of the control. The same mathematical model with the experimentally determined altered V(max) values of the enzymes did account for an increase of glycolytic flux in the HD sample, although the extent of the increase was not predicted quantitatively. This suggested a somewhat altered regulation of this major metabolic pathway in HD tissue. We then used the mathematical model to develop a hypothesis for a new regulatory interaction that might account for the observed changes; in HD, glyceraldehyde-3-phosphate dehydrogenase may be in closer proximity (perhaps because of the binding of glyceraldehyde-3-phosphate dehydrogenase to huntingtin) with aldolase and engage in channelling for glyceraldehyde-3-phosphate. By contrast to most of the speculation in the literature, our results suggest that the neuronal damage in HD tissue may be associated with increased energy metabolism at the tissue level leading to modified levels of various intermediary metabolites with pathological consequences.

Mitochondrial Ca2+ uniporter blockers influence activation-induced CBF response in the rat somatosensory cortex

Effects of mitochondrial calcium signaling blockade on neural activation-induced CBF response were studied in urethane-anesthetized rats. Ruthenium red (RuR), a nonspecific inhibitor of the mitochondrial calcium uniporter (MCU), and Ru360, a highly specific inhibitor of the MCU, were delivered intravenously (i.v.) or intracerebroventricularly (i.c.v.). Baseline cerebral blood flow (CBF) and cerebral hyperemic response to whisker stimulation were measured through a thinned skull over the somatosensory cortex using laser Doppler imaging (LDI). Ruthenium red or Ru360 did not alter the baseline CBF at all doses used. However, the hyperemic response, defined as the activation area and amplitude of CBF increase in response to mechanical whisker stimulation, was significantly reduced in the presence of either RuR or Ru360 delivered i.c.v. The hyperemic response reduced significantly with a dose of 14.5 nmol RuR (i.c.v.), showing a further decrease with 29 nmol RuR (i.c.v.). A comparable decrease in the hyperemic response was observed during treatment with a relatively lower dose of 4.5 and 9 nmol Ru360 (i.c.v.). Delivered intravenously, Ru360 significantly diminished the cerebral hyperemic response at doses greater than 80 microg/kg i.v., up to a dose of 320 microg/kg i.v. However, RuR (i.v.) had an opposite effect with an enhancement in the cerebral hyperemic response at all doses studied. Ruthenium red or Ru360 had no significant effect on the cerebral reactivity to hypercapnia, indicating that altered cerebral hyperemic response to whisker stimulation was predominantly neural. We conclude that mitochondrial calcium signaling through the MCU mediates neural activation-induced CBF response in vivo.

Coupling between neuronal activity and microcirculation: implications for functional brain imaging

In the neocortex, neurons with similar response properties are often clustered together in column-like structures, giving rise to what has become known as functional architecture-the mapping of various stimulus feature dimensions onto the cortical sheet. At least partially, we owe this finding to the availability of several functional brain imaging techniques, both post-mortem and in-vivo, which have become available over the last two generations, revolutionizing neuroscience by yielding information about the spatial organization of active neurons in the brain. Here, we focus on how our understanding of such functional architecture is linked to the development of those functional imaging methodologies, especially to those that image neuronal activity indirectly, through metabolic or haemodynamic signals, rather than directly through measurement of electrical activity. Some of those approaches allow exploring functional architecture at higher spatial resolution than others. In particular, optical imaging of intrinsic signals reaches the striking detail of approximately 50 mum, and, together with other methodologies, it has allowed characterizing the metabolic and haemodynamic responses induced by sensory-evoked neuronal activity. Here, we review those findings about the spatio-temporal characteristics of neurovascular coupling and discuss their implications for functional brain imaging, including position emission tomography, and non-invasive neuroimaging techniques, such as funtional magnetic resonance imaging, applicable also to the human brain.

Reconstruction and flux analysis of coupling between metabolic pathways of astrocytes and neurons: application to cerebral hypoxia

BACKGROUND

It is a daunting task to identify all the metabolic pathways of brain energy metabolism and develop a dynamic simulation environment that will cover a time scale ranging from seconds to hours. To simplify this task and make it more practicable, we undertook stoichiometric modeling of brain energy metabolism with the major aim of including the main interacting pathways in and between astrocytes and neurons.

MODEL

The constructed model includes central metabolism (glycolysis, pentose phosphate pathway, TCA cycle), lipid metabolism, reactive oxygen species (ROS) detoxification, amino acid metabolism (synthesis and catabolism), the well-known glutamate-glutamine cycle, other coupling reactions between astrocytes and neurons, and neurotransmitter metabolism. This is, to our knowledge, the most comprehensive attempt at stoichiometric modeling of brain metabolism to date in terms of its coverage of a wide range of metabolic pathways. We then attempted to model the basal physiological behaviour and hypoxic behaviour of the brain cells where astrocytes and neurons are tightly coupled.

RESULTS

The reconstructed stoichiometric reaction model included 217 reactions (184 internal, 33 exchange) and 216 metabolites (183 internal, 33 external) distributed in and between astrocytes and neurons. Flux balance analysis (FBA) techniques were applied to the reconstructed model to elucidate the underlying cellular principles of neuron-astrocyte coupling. Simulation of resting conditions under the constraints of maximization of glutamate/glutamine/GABA cycle fluxes between the two cell types with subsequent minimization of Euclidean norm of fluxes resulted in a flux distribution in accordance with literature-based findings. As a further validation of our model, the effect of oxygen deprivation (hypoxia) on fluxes was simulated using an FBA-derivative approach, known as minimization of metabolic adjustment (MOMA). The results show the power of the constructed model to simulate disease behaviour on the flux level, and its potential to analyze cellular metabolic behaviour in silico.

CONCLUSION

The predictive power of the constructed model for the key flux distributions, especially central carbon metabolism and glutamate-glutamine cycle fluxes, and its application to hypoxia is promising. The resultant acceptable predictions strengthen the power of such stoichiometric models in the analysis of mammalian cell metabolism.

[Functional exploration of the brain by fMRI]

Functional magnetic resonance imaging (fMRI) permits to obtain physiological information about MRI signal, which is modulated by electrical, biochemical, and physiological properties of the cerebral tissue. It is possible to characterize the brain interactions from an fMRI signal. Particularly, the use of a spectral analysis at a given frequency allows access to the time series chronology, which occurs within various activated areas of the brain. Thus, spectral parameters such as coherency and phase shift may be calculated from presupposed stationary stochastic signals and of an estimate of the cross-spectral power density function. Coherency describes a correlation structure in frequency domain between signals and thus allows obtaining an accurate estimate of the phase relation (time delay), which connects the signals between them. We describe in the last part of the article a calculation method integrating spectral information obtained previously and which makes it possible to evaluate the intensity of the existing interaction between two distinct cerebral areas.

Modeling the Causes of Variation in Brain Tissue Oxygenation

BACKGROUND

Clinical markers of the adequacy of cerebral perfusion may be misleading. The effects of isolated changes in systemic blood pressure, Paco2, Pao2, and cerebral edema on cerebral blood flow and oxygenation are relatively well known, but the quantitative effects of interactions between these factors are not easily calculated. We aimed to investigate the relationship between these factors using a computational model.

METHODS

Using a validated, quantitative, computational model of cerebral blood flow, the simulated effects of changes in systemic blood pressure (50-180 mm Hg), Paco2 (33-55 mm Hg [4.3-7.3 kPa]), Sao2 (0.8-1.0), and cerebral edema (0%-10% increase in intercapillary distance) on middle cerebral artery flow velocity (MCAFV), brain tissue oxygenation (Pbo2), and jugular venous oxygen saturation (Sjo2) were recorded.

RESULTS

Individual markers of adequacy of cerebral perfusion (MCAFV, Sjo2, and Pbo2 behave in accordance with clinical data with single changes in the parameters studied: the lower limit of autoregulation for MCAFV and Sjo2 lies around 60 mm Hg mean arterial blood pressure. In our model, the upper limit of autoregulation lies around 170 mm Hg, but is much less distinct for Sjo2 and Pbo2 than for MCAFV. Significant cerebral ischemia appears unlikely to occur with isolated physiological changes according to our simulation. However, the combination of hypotension, hypoxia, and edema makes ischemia much more likely in this model. Edema increases the Sjo2:Pbo2 gradient, confirming that diffusion-limited oxygen delivery may make Sjo2 values falsely reassuring.

CONCLUSION

The simulated effects of pathophysiological changes on cerebral oxygenation and perfusion have been quantitatively described. Significant cerebral ischemia is predicted in the presence of two or more physiological derangements. Cerebral edema is associated with an increased gradient between Sjo2 and Pbo2.

Compartmentalization of brain energy metabolism between glia and neurons: insights from mathematical modeling

We review the contribution of mathematical modeling of metabolic pathways to the study of the compartmentalization of brain energy metabolism between neurons and glia. We especially focus on the role of lactate in the relationship between glia and neurons and the possible presence of an astrocyte-neuron lactate shuttle (ANLS). We first discuss models of glucose, pyruvate, and lactate kinetics, which are relevant to neuron-glia interactions. We then review models of compartmentalized energy metabolism, which deal with the concepts of 'red' and 'white' stimulations, and the ANLS hypothesis. We next show the contribution of a study of model robustness to the debate about the potential role of lactate in metabolic interactions between glia and neurons. Finally, we discuss the possible implications of modeling for further experimental studies.

Origins of blood volume change due to glutamatergic synaptic activity at astrocytes abutting on arteriolar smooth muscle cells

The cellular mechanisms that couple activity of glutamatergic synapses with changes in blood flow, measured by a variety of techniques including the BOLD signal, have not previously been modelled. Here we provide such a model, that successfully accounts for the main observed changes in blood flow in both visual cortex and somatosensory cortex following their stimulation by high-contrast drifting grating or by single whisker stimulation, respectively. Coupling from glutamatergic synapses to smooth muscle cells of arterioles is effected by astrocytes releasing epoxyeicosatrienoic acids (EETs) onto them, following glutamate stimulation of the astrocyte. Coupling of EETs to the smooth muscle of arterioles is by means of potassium channels in their membranes, leading to hyperpolarization, relaxation and hence an increase in blood flow. This model predicts a linear increase in blood flow with increasing numbers of activated astrocytes, but a non-linear increase with increasing glutamate release.

Comparing hemodynamic models with DCM

The classical model of blood oxygen level-dependent (BOLD) responses by Buxton et al. [Buxton, R.B., Wong, E.C., Frank, L.R., 1998. Dynamics of blood flow and oxygenation changes during brain activation: the Balloon model. Magn. Reson. Med. 39, 855-864] has been very important in providing a biophysically plausible framework for explaining different aspects of hemodynamic responses. It also plays an important role in the hemodynamic forward model for dynamic causal modeling (DCM) of fMRI data. A recent study by Obata et al. [Obata, T., Liu, T.T., Miller, K.L., Luh, W.M., Wong, E.C., Frank, L.R., Buxton, R.B., 2004. Discrepancies between BOLD and flow dynamics in primary and supplementary motor areas: application of the Balloon model to the interpretation of BOLD transients. NeuroImage 21, 144-153] linearized the BOLD signal equation and suggested a revised form for the model coefficients. In this paper, we show that the classical and revised models are special cases of a generalized model. The BOLD signal equation of this generalized model can be reduced to that of the classical Buxton model by simplifying the coefficients or can be linearized to give the Obata model. Given the importance of hemodynamic models for investigating BOLD responses and analyses of effective connectivity with DCM, the question arises which formulation is the best model for empirically measured BOLD responses. In this article, we address this question by embedding different variants of the BOLD signal equation in a well-established DCM of functional interactions among visual areas. This allows us to compare the ensuing models using Bayesian model selection. Our model comparison approach had a factorial structure, comparing eight different hemodynamic models based on (i) classical vs. revised forms for the coefficients, (ii) linear vs. non-linear output equations, and (iii) fixed vs. free parameters, epsilon, for region-specific ratios of intra- and extravascular signals. Using fMRI data from a group of twelve subjects, we demonstrate that the best model is a non-linear model with a revised form for the coefficients, in which epsilon is treated as a free parameter.

Abnormal cellular energy and phospholipid metabolism in the left dorsolateral prefrontal cortex of medication-free individuals with bipolar disorder: an in vivo 1H MRS study

OBJECTIVES

While the pathophysiology of bipolar disorder (BD) remains to be elucidated, postmortem and neuroimaging studies have suggested that abnormalities in the dorsolateral prefrontal cortex (DLPFC) are implicated. We compared the levels of specific brain chemicals of interest measured with proton magnetic resonance spectroscopy ((1)H MRS) in medication-free BD subjects and age- and gender-matched healthy controls. We hypothesized that BD subjects would present abnormal cellular metabolism within the DLPFC, as reflected by lower N-acetyl-aspartate (NAA) and creatine + phosphocreatine (Cr + PCr).

METHODS

Thirty-two medication-free BD subjects (33.8 +/- 10.2 years) and 32 matched controls (33.8 +/- 9.0 years) underwent a short echo-time (TE = 30 ms) (1)H MRS. An 8-cm(3) single voxel was placed in the left DLPFC, and individual concentrations of NAA, Cr + PCr, choline-containing compounds (GPC + PC), myo-inositol, and glutamate were obtained, using the water signal as an internal reference.

RESULTS

BD subjects had lower Cr + PCr [F((1,62)) = 5.85; p = 0.018; one-way analysis of variance (ANOVA)] and lower GPC + PC [F((1,62)) = 5.79; p = 0.019; one-way ANOVA] levels in the left DLPFC. No significant differences were observed for other brain metabolites.

CONCLUSIONS

These findings provide further evidence that the pathophysiology of BD involves impairment in the DLPFC. Our findings can be interpreted as evidence for reduced cellular energy and phospholipid metabolism, consistent with the hypothesis of mitochondrial dysfunction in BD.

Nonlinear local electrovascular coupling. II: From data to neuronal masses

In the companion article a local electrovascular coupling (LEVC) model was proposed to explain the continuous dynamics of electrical and vascular states within a cortical unit. These states produce certain mesoscopic reflections whose discrete time series can be reconstructed from electroencephalography (EEG) and functional magnetic resonance imaging (fMRI). In this article we develop a recursive optimization algorithm based on the local linearization (LL) filter and an innovation method to make statistical inferences about the LEVC model from both EEG and fMRI data, i.e., to estimate the unobserved states and the unknown parameters of the model. For a better understanding, the LL filter is described from a Bayesian point of view, providing the particulars for the case of hybrid data (e.g., EEG and fMRI), which could be sampled at different rates. The dynamics of the exogenous synaptic inputs going into the cortical unit are also estimated by introducing a set of Gaussian radial basis functions. In order to study the dynamics of the electrical and vascular states in the striate cortex of humans as well as their local interrelationships, we applied this algorithm to EEG and fMRI recordings obtained concurrently from two subjects while passively observing a radial checkerboard with a white/black pattern reversal. The EEG and fMRI data from the first subject was used to estimate the electrical/vascular states and parameters of the LEVC model in V1 for a 4.0 Hz reversion frequency. We used the EEG data from the second subject to investigate the changes in the dynamics of the electrical states when the frequency of reversion is varied from 0.5-4.0 Hz. Then we made use of the estimated electrical states to predict the effects on the vasculature that such variations produce.

Functional uncoupling of hemodynamic from neuronal response by inhibition of neuronal nitric oxide synthase

The cerebrovascular coupling under neuronal nitric oxide synthase (nNOS) inhibition was investigated in alpha-chloralose anesthetized rats. Cerebral blood flow (CBF), cerebral blood volume (CBV), and blood oxygenation level dependent (BOLD) responses to electrical stimulation of the forepaw were measured before and after an intraperitoneal bolus of 7-nitroindazole (7-NI), an in vivo inhibitor of the neuronal isoform of nitric oxide synthase. Neuronal activity was measured by recording somatosensory-evoked potentials (SEPs) via intracranial electrodes. 7-Nitroindazole produced a significant attenuation of the activation-elicited CBF (P<10(-6)), CBV (P<10(-6)), and BOLD responses (P<10(-6)), without affecting the baseline perfusion level. The average DeltaCBF was nulled, while DeltaBOLD and DeltaCBV decreased to approximately 30% of their respective amplitudes before 7-NI administration. The average SEP amplitude decreased (P<10(-5)) to approximately 60% of its pretreatment value. These data describe a pharmacologically induced uncoupling between neuronal and hemodynamic responses to functional activation, and provide further support for the critical role of neuronally produced NO in the cerebrovascular coupling.

A coherent neurobiological framework for functional neuroimaging provided by a model integrating compartmentalized energy metabolism

Functional neuroimaging has undergone spectacular developments in recent years. Paradoxically, its neurobiological bases have remained elusive, resulting in an intense debate around the cellular mechanisms taking place upon activation that could contribute to the signals measured. Taking advantage of a modeling approach, we propose here a coherent neurobiological framework that not only explains several in vitro and in vivo observations but also provides a physiological basis to interpret imaging signals. First, based on a model of compartmentalized energy metabolism, we show that complex kinetics of NADH changes observed in vitro can be accounted for by distinct metabolic responses in two cell populations reminiscent of neurons and astrocytes. Second, extended application of the model to an in vivo situation allowed us to reproduce the evolution of intraparenchymal oxygen levels upon activation as measured experimentally without substantially altering the initial parameter values. Finally, applying the same model to functional neuroimaging in humans, we were able to determine that the early negative component of the blood oxygenation level-dependent response recorded with functional MRI, known as the initial dip, critically depends on the oxidative response of neurons, whereas the late aspects of the signal correspond to a combination of responses from cell types with two distinct metabolic profiles that could be neurons and astrocytes. In summary, our results, obtained with such a modeling approach, support the concept that both neuronal and glial metabolic responses form essential components of neuroimaging signals.

Modelling the role of excitatory and inhibitory neuronal activity in the generation of the BOLD signal

A biophysical model of the coupling between neuronal activity and the BOLD signal that allows for explicitly evaluating the role of both excitatory and inhibitory activity is formulated in this paper. The model is based on several physiological assumptions. Firstly, in addition to glycolysis, the "glycogen shunt" is assumed for excitatory synapses as a mechanism for energy production in the astrocytes. As a result, oxygen-to-glucose index (OGI) is not constant but varies with excitatory neuronal activity. In contrast, a constant OGI=6 (glycolysis) is assumed for inhibitory synapses. Finally we assume that cerebral blood flow is not directly controlled by energy usage, but it is only related to excitatory activity. Simulations' results show that increases in excitatory activity amplify the oscillations associated with the transient BOLD response, by increasing the initial dip, the maximum, and the post-stimulus undershoot of the signal. In contrast, increasing the inhibitory activity evoked an overall decrease of the BOLD signal along the whole time interval of the response. Simultaneous increase of both types of activity is then expected to reinforce the initial dip and the post-stimulus undershoot, while respective effects on the maximum tend to counteract each other. Two mechanisms for negative BOLD response (NBS) generation were predicted by the model: (i) when inhibition was present alone or together with low activation levels and (ii) when deactivation occurred independently of the accompanying inhibition level. Interestingly, NBS was associated with negative oxygen consumption changes only for the case of mechanism (ii).

Exploring large-scale brain networks in functional MRI

Increasing emphasis has been recently put on large-scale network processing of brain functions. To explore these networks, many approaches have been proposed in functional magnetic resonance imaging (fMRI). Their objective is to answer the following two questions: (1) what brain regions are involved in the functional process under investigation? and (2) how do these regions interact? We review some of the key concepts and corresponding methods to cope with both issues.

Activity-dependent regulation of energy metabolism by astrocytes: An update

Astrocytes play a critical role in the regulation of brain metabolic responses to activity. One detailed mechanism proposed to describe the role of astrocytes in some of these responses has come to be known as the astrocyte-neuron lactate shuttle hypothesis (ANLSH). Although controversial, the original concept of a coupling mechanism between neuronal activity and glucose utilization that involves an activation of aerobic glycolysis in astrocytes and lactate consumption by neurons provides a heuristically valid framework for experimental studies. In this context, it is necessary to provide a survey of recent developments and data pertaining to this model. Thus, here, we review very recent experimental evidence as well as theoretical arguments strongly supporting the original model and in some cases extending it. Aspects revisited include the existence of glutamate-induced glycolysis in astrocytes in vitro, ex vivo, and in vivo, lactate as a preferential oxidative substrate for neurons, and the notion of net lactate transfer between astrocytes and neurons in vivo. Inclusion of a role for glycogen in the ANLSH is discussed in the light of a possible extension of the astrocyte-neuron lactate shuttle (ANLS) concept rather than as a competing hypothesis. New perspectives offered by the application of this concept include a better understanding of the basis of signals used in functional brain imaging, a role for neuron-glia metabolic interactions in glucose sensing and diabetes, as well as novel strategies to develop therapies against neurodegenerative diseases based upon improving astrocyte-neuron coupled energetics.

Cellular pathways of energy metabolism in the brain: Is glucose used by neurons or astrocytes?

Most techniques presently available to measure cerebral activity in humans and animals, i.e. positron emission tomography (PET), autoradiography, and functional magnetic resonance imaging, do not record the activity of neurons directly. Furthermore, they do not allow the investigator to discriminate which cell type is using glucose, the predominant fuel provided to the brain by the blood. Here, we review the experimental approaches aimed at determining the percentage of glucose that is taken up by neurons and by astrocytes. This review is integrated in an overview of the current concepts on compartmentation and substrate trafficking between astrocytes and neurons. In the brain in vivo, about half of the glucose leaving the capillaries crosses the extracellular space and directly enters neurons. The other half is taken up by astrocytes. Calculations suggest that neurons consume more energy than do astrocytes, implying that astrocytes transfer an intermediate substrate to neurons. Experimental approaches in vitro on the honeybee drone retina and on the isolated vagus nerve also point to a continuous transfer of intermediate metabolites from glial cells to neurons in these tissues. Solid direct evidence of such transfer in the mammalian brain in vivo is still lacking. PET using [(18)F]fluorodeoxyglucose reflects in part glucose uptake by astrocytes but does not indicate to which step the glucose taken up is metabolized within this cell type. Finally, the sequence of metabolic changes occurring during a transient increase of electrical activity in specific regions of the brain remains to be clarified.

Nonlinear local electrovascular coupling. I: A theoretical model

Here we present a detailed biophysical model of how brain electrical and vascular dynamics are generated within a basic cortical unit. The model was obtained from coupling a canonical neuronal mass and an expandable vasculature. In this proposal, we address several aspects related to electroencephalographic and functional magnetic resonance imaging data fusion: (1) the impact of the cerebral architecture (at different physical levels) on the observations; (2) the physiology involved in electrovascular coupling; and (3) energetic considerations to gain a better understanding of how the glucose budget is used during neuronal activity. The model has three components. The first is the canonical neural mass model of three subpopulations of neurons that respond to incoming excitatory synaptic inputs. The generation of the membrane potentials in the somas of these neurons and the electric currents flowing in the neuropil are modeled by this component. The second and third components model the electrovascular coupling and the dynamics of vascular states in an extended balloon approach, respectively. In the first part we describe, in some detail, the biophysical model and establish its face validity using simulations of visually evoked responses under different flickering frequencies and luminous contrasts. In a second part, a recursive optimization algorithm is developed and used to make statistical inferences about this forward/generative model from actual data.

LACTATE, NOT GLUCOSE, UP-REGULATES MITOCHONDRIAL OXYGEN CONSUMPTION BOTHIN SHAM AND LATERAL FLUID PERCUSSED RAT BRAINS

OBJECTIVE

Failure of energy metabolism after traumatic brain injury may be a major factor limiting outcome. Although glucose is the primary metabolic substrate in the healthy brain, the well documented surge in tissue lactate after traumatic brain injury suggests that lactate may provide an energy need that cannot be met by glucose. We hypothesized, therefore, that administration of lactate or the combination of lactate and supraphysiological oxygen may improve mitochondrial oxidative respiration in the brain after rat fluid percussion injury. We measured oxygen consumption (VO2) to determine what effects glucose, lactate, oxygen, and the combination of lactate and oxygen have on mitochondrial respiration in both injured and uninjured rat brain tissue.

METHODS

Anesthetized Sprague-Dawley rats were intubated and ventilated with either 0.21 or 1.0 fraction of inspired oxygen (FIO2). Brain tissue from acute sham animals was subjected in vitro to 1.1 mM, 12 mM and 100 mM concentrations of glucose and L-lactate. In another group, injury (fluid percussion injury of 2.5 +/- 0.02 atmospheres) was induced over the left hemisphere. The VO2 of mug amounts of brain tissues were measured in a microrespirometry system (Cartesian diver).

RESULTS

The VO2 was found to be independent of glucose concentrations, but dose-dependent for lactate. Moreover, the lactate dependent VO2s were all significantly higher than those generated by glucose. Injured rats on FIO2 0.21 had brain tissue VO2 rates that were significantly lower than those of shams or preinjury levels. In injured rats treated with FIO2 1.0, the reduction in VO2 levels was prevented. Injured rats that received an intravenous infusion of 100 mM lactate had VO2 rates that were significantly higher than those obtained with FIO2 1.0. Combined treatment further boosted the lactate generated VO2 rates by approximately 15%.

CONCLUSION

Glucose sustains mitochondrial respiration at a low level "fixed" rate because, despite increasing its concentration nearly 100-fold, it cannot up-regulate VO2 after fluid percussion injury. Lactate produces a dose-dependent VO2 response, possibly enabling mitochondria to meet the increased energy needs of the injured brain.

ON THE INTEGRATION OF PHYSIOLOGICAL MECHANISMS IN THE NERVOUS TISSUE USING THE MTIP: SYNAPTIC PLASTICITY DEPENDING ON NEURONS-ASTROCYTES-CAPILLARIES INTERACTIONS

The objective in this work is twofold: (i) to illustrate the use of the Mathematical Theory of Integrative Physiology (MTIP) [13], that is a general theory and practical method for the systematic and progressive mathematical integration of physiological mechanisms; (ii) to study a complex neurobiological system taken as an example, i.e., the synaptic plasticity depending on brain activity, on astrocytic and neuronal metabolism, and on brain hemodynamics. The functional organization of the nervous tissue is presented in the framework of the MTIP, the ultimate objective being the study of learning and memory by coupling the three networks of neurons, astrocytes and capillaries. Specifically in this paper, we study the influence of the variation of capillaries arterial oxygen on the induction of LTP/LTD by coupling validated mathematical models of AMPA, NMDA, VDCC channels, calcium current in the dendritic spine, vesicular glutamate dynamics in the presynaptic bouton derived from glycolysis and neuronal glucose, mitochondrial respiration, Ca/Na pumps, glycolysis, and calcium dynamics in the astrocytes, hemodynamics of the capillaries. The integration of all these models is discussed by claiming the advantages of using a common framework and a specific dedicated computing system, PhysioMatica.

Using nonlinear models in fMRI data analysis: model selection and activation detection

There is an increasing interest in using physiologically plausible models in fMRI analysis. These models do raise new mathematical problems in terms of parameter estimation and interpretation of the measured data. In this paper, we show how to use physiological models to map and analyze brain activity from fMRI data. We describe a maximum likelihood parameter estimation algorithm and a statistical test that allow the following two actions: selecting the most statistically significant hemodynamic model for the measured data and deriving activation maps based on such model. Furthermore, as parameter estimation may leave much incertitude on the exact values of parameters, model identifiability characterization is a particular focus of our work. We applied these methods to different variations of the Balloon Model (Buxton, R.B., Wang, E.C., and Frank, L.R. 1998. Dynamics of blood flow and oxygenation changes during brain activation: the balloon model. Magn. Reson. Med. 39: 855-864; Buxton, R.B., Uludağ, K., Dubowitz, D.J., and Liu, T.T. 2004. Modelling the hemodynamic response to brain activation. NeuroImage 23: 220-233; Friston, K. J., Mechelli, A., Turner, R., and Price, C. J. 2000. Nonlinear responses in fMRI: the balloon model, volterra kernels, and other hemodynamics. NeuroImage 12: 466-477) in a visual perception checkerboard experiment. Our model selection proved that hemodynamic models better explain the BOLD response than linear convolution, in particular because they are able to capture some features like poststimulus undershoot or nonlinear effects. On the other hand, nonlinear and linear models are comparable when signals get noisier, which explains that activation maps obtained in both frameworks are comparable. The tools we have developed prove that statistical inference methods used in the framework of the General Linear Model might be generalized to nonlinear models.

Are fMRI event-related response constant in time? A model selection answer

An accurate estimation of the hemodynamic response function (HRF) in functional magnetic resonance imaging (fMRI) is crucial for a precise spatial and temporal estimate of the underlying neuronal processes. Recent works have proposed non-parametric estimation of the HRF under the hypotheses of linearity and stationarity in time. Biological literature suggests, however, that response magnitude may vary with attention or ongoing activity. We therefore test a more flexible model that allows for the variation of the magnitude of the HRF with time in a maximum likelihood framework. Under this model, the magnitude of the HRF evoked by a single event may vary across occurrences of the same type of event. This model is tested against a simpler model with a fixed magnitude using information theory. We develop a standard EM algorithm to identify the event magnitudes and the HRF. We test this hypothesis on a series of 32 regions (4 ROIS on eight subjects) of interest and find that the more flexible model is better than the usual model in most cases. The important implications for the analysis of fMRI time series for event-related neuroimaging experiments are discussed.

Integration of EEG/MEG with MRI and fMRI

EEG and MEG are important functional neuroimaging modalities for studying the temporal dynamics of neural activities and interactions, but the accurate localization of neural activities still remains a challenging problem. Combining EEG/MEG with MRI or/and functional MRI (fMRI) holds promise to significantly increase the spatial resolution of electromagnetic source imaging, and at the same time, allows tracing the rapid neural processes and information pathways within the brain, which cannot be achieved using these modalities in isolation. In this paper, we review some recent progresses in multimodal neuroimaging, with special emphasis on the integration of EEG, MEG with MRI and fMRI. Some examples are shown to illustrate the importance of the combined source analysis in clinical and experimental studies.

fMRI MODELS OF DENDRITIC AND ASTROCYTIC NETWORKS

In order to elucidate the relationships between hierarchical structures within the neocortical neuropil and the information carried by an ensemble of neurons encompassing a single voxel, it is essential to predict through volume conductor modeling LFPs representing average extracellular potentials, which are expressed in terms of interstitial potentials of individual cells in networks of gap-junctionally connected astrocytes and synaptically connected neurons. These relationships have been provided and can then be used to investigate how the underlying neuronal population activity can be inferred from the measurement of the BOLD signal through electrovascular coupling mechanisms across the blood-brain barrier. The importance of both synaptic and extrasynaptic transmission as the basis of electrophysiological indices triggering vascular responses between dendritic and astrocytic networks, and sequential configurations of firing patterns in composite neural networks is emphasized. The purpose of this review is to show how fMRI data may be used to draw conclusions about the information transmitted by individual neurons in populations generating the BOLD signal.

About being BOLD

The last decade has seen an unprecedented increase in the use of functional magnetic resonance imaging (fMRI) to understand the neural basis of cognition and behavior. Being non-invasive and relatively easy to use, most studies relied on changes in the blood oxygenation level dependent (BOLD) contrast as an indirect marker of variations in brain activity. However, the fact that BOLD fMRI is dependent on the blood flow response that follows neural activity and does not measure neural activity per se is seen as an inherent cause for concern while interpreting data from these studies. In order to characterize the BOLD signal correctly, it is imperative that we have a better understanding of neural events that lead to the BOLD response. A review of recent studies that addressed several aspects of BOLD fMRI including events at the level of the synapse, the nature of the neurovascular coupling, and some parameters of the BOLD signal is provided. This is intended to serve as background information for the interpretation of fMRI data in normal subjects and in patients with compromised neurovascular coupling. One of the aims is also to encourage researchers to interpret the results of functional imaging studies in light of the dynamic interactions between different brain regions, something that often is neglected.