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.     

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.     

Mechanistic Mathematical Modeling Tests Hypotheses of the Neurovascular Coupling in fMRI

Functional magnetic resonance imaging (fMRI) measures brain activity by detecting the blood-oxygen-level dependent (BOLD) response to neural activity. The BOLD response depends on the neurovascular coupling, which connects cerebral blood flow, cerebral blood volume, and deoxyhemoglobin level to neuronal activity. The exact mechanisms behind this neurovascular coupling are not yet fully investigated. There are at least three different ways in which these mechanisms are being discussed. Firstly, mathematical models involving the so-called Balloon model describes the relation between oxygen metabolism, cerebral blood volume, and cerebral blood flow. However, the Balloon model does not describe cellular and biochemical mechanisms. Secondly, the metabolic feedback hypothesis, which is based on experimental findings on metabolism associated with brain activation, and thirdly, the neurotransmitter feed-forward hypothesis which describes intracellular pathways leading to vasoactive substance release. Both the metabolic feedback and the neurotransmitter feed-forward hypotheses have been extensively studied, but only experimentally. These two hypotheses have never been implemented as mathematical models. Here we investigate these two hypotheses by mechanistic mathematical modeling using a systems biology approach; these methods have been used in biological research for many years but never been applied to the BOLD response in fMRI. In the current work, model structures describing the metabolic feedback and the neurotransmitter feed-forward hypotheses were applied to measured BOLD responses in the visual cortex of 12 healthy volunteers. Evaluating each hypothesis separately shows that neither hypothesis alone can describe the data in a biologically plausible way. However, by adding metabolism to the neurotransmitter feed-forward model structure, we obtained a new model structure which is able to fit the estimation data and successfully predict new, independent validation data. These results open the door to a new type of fMRI analysis that more accurately reflects the true neuronal activity.     

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.     

Interictal functional connectivity of human epileptic networks assessed by intracerebral EEG and BOLD signal fluctuations

In this study, we aimed to demonstrate whether spontaneous fluctuations in the blood oxygen level dependent (BOLD) signal derived from resting state functional magnetic resonance imaging (fMRI) reflect spontaneous neuronal activity in pathological brain regions as well as in regions spared by epileptiform discharges. This is a crucial issue as coherent fluctuations of fMRI signals between remote brain areas are now widely used to define functional connectivity in physiology and in pathophysiology. We quantified functional connectivity using non-linear measures of cross-correlation between signals obtained from intracerebral EEG (iEEG) and resting-state functional MRI (fMRI) in 5 patients suffering from intractable temporal lobe epilepsy (TLE). Functional connectivity was quantified with both modalities in areas exhibiting different electrophysiological states (epileptic and non affected regions) during the interictal period. Functional connectivity as measured from the iEEG signal was higher in regions affected by electrical epileptiform abnormalities relative to non-affected areas, whereas an opposite pattern was found for functional connectivity measured from the BOLD signal. Significant negative correlations were found between the functional connectivities of iEEG and BOLD signal when considering all pairs of signals (theta, alpha, beta and broadband) and when considering pairs of signals in regions spared by epileptiform discharges (in broadband signal). This suggests differential effects of epileptic phenomena on electrophysiological and hemodynamic signals and/or an alteration of the neurovascular coupling secondary to pathological plasticity in TLE even in regions spared by epileptiform discharges. In addition, indices of directionality calculated from both modalities were consistent showing that the epileptogenic regions exert a significant influence onto the non epileptic areas during the interictal period. This study shows that functional connectivity measured by iEEG and BOLD signals give complementary but sometimes inconsistent information in TLE.     

Origins of the BOLD changes due to synaptic activity at astrocytes abutting arteriolar smooth muscle

We have recently provided a detailed model that links glutamatergic synaptic activity to volume and blood flow changes in nearby arterioles [Bennett, M.R., Farnell, L., Gibson, W.G., 2008. Origin of blood volume change due to glutamatergic synaptic activity at astrocytes abutting on arteriolar smooth muscle cells. J. Theor. Biol. 250, 172-185]. This neurovascular coupling model is used in the present work to predict changes in deoxyhemoglobin (Hbr) in capillaries, arterioles, venules and veins due to glutamatergic synaptic activity and hence the changes in the blood oxygen level dependent (BOLD) signals recorded by functional magnetic resonance imaging. The model provides a quantitative account of Hbr changes observed in each of the vascular compartments following stimulation of somatosensory cortex and visual cortex and of the BOLD signal following stimulation of motor and visual cortex.     

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.     

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.     

Purinergic mechanisms in gliovascular coupling

Regional elevations in cerebral blood flow (CBF) often occur in response to localized increases in cerebral neuronal activity. An ever expanding literature has linked this neurovascular coupling process to specific signaling pathways involving neuronal synapses, astrocytes and cerebral arteries and arterioles. Collectively, these structures are termed the "neurovascular unit" (NVU). Astrocytes are thought to be the cornerstone of the NVU. Thus, not only do astrocytes "detect" increased synaptic activity, they can transmit that information to proximal and remote astrocytic sites often through a Ca(2+)- and ATP-related signaling process. At the vascular end of the NVU, a Ca(2+)-dependent formation and release of vasodilators, or substances linked to vasodilation, can occur. The latter category includes ATP, which upon its appearance in the extracellular compartment, can be rapidly converted to the potent vasodilator, adenosine, via the action of ecto-nucleotidases. In the present review, we give consideration to experimental model-specific variations in purinergic influences on gliovascular signaling mechanisms, focusing on the cerebral cortex. In that discussion, we compare findings obtained using in vitro (rodent brain slice) models and multiple in vivo models (2-photon imaging; somatosensory stimulation-evoked cortical hyperemia; and sciatic nerve stimulation-evoked pial arteriolar dilation). Additional attention is given to the importance of upstream (remote) vasodilation; the key role played by extracellular ATP hydrolysis (via ecto-nucleotidases) in gliovascular coupling; and interactions among multiple signaling pathways.     

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

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

Role of astrocytes in cerebrovascular regulation.

Astrocytes send processes to synapses and blood vessels, communicate with other astrocytes through gap junctions and by release of ATP, and thus are an integral component of the neurovascular unit. Electrical field stimulations in brain slices demonstrate an increase in intracellular calcium in astrocyte cell bodies transmitted to perivascular end-feet, followed by a decrease in vascular smooth muscle calcium oscillations and arteriolar dilation. The increase in astrocyte calcium after neuronal activation is mediated, in part, by activation of metabotropic glutamate receptors. Calcium signaling in vitro can also be influenced by adenosine acting on A2B receptors and by epoxyeicosatrienoic acids (EETs) shown to be synthesized in astrocytes. Prostaglandins, EETs, arachidonic acid, and potassium ions are candidate mediators of communication between astrocyte end-feet and vascular smooth muscle. In vivo evidence supports a role for cyclooxygenase-2 metabolites, EETs, adenosine, and neuronally derived nitric oxide in the coupling of increased blood flow to increased neuronal activity. Combined inhibition of the EETs, nitric oxide, and adenosine pathways indicates that signaling is not by parallel, independent pathways. Indirect pharmacological results are consistent with astrocytes acting as intermediaries in neurovascular signaling within the neurovascular unit. For specific stimuli, astrocytes are also capable of transmitting signals to pial arterioles on the brain surface for ensuring adequate inflow pressure to parenchymal feeding arterioles. Therefore, evidence from brain slices and indirect evidence in vivo with pharmacological approaches suggest that astrocytes play a pivotal role in regulating the fundamental physiological response coupling dynamic changes in cerebral blood flow to neuronal synaptic activity. Future work using in vivo imaging and genetic manipulation will be required to provide more direct evidence for a role of astrocytes in neurovascular coupling.     

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.     

Time-dependent spatial specificity of high-resolution fMRI: insights into mesoscopic neurovascular coupling

High-resolution functional magnetic resonance imaging (fMRI) is becoming increasingly popular because of the growing availability of ultra-high magnetic fields which are capable of improving sensitivity and spatial resolution. However, it is debatable whether increased spatial resolutions for haemodynamic-based techniques, like fMRI, can accurately detect the true location of neuronal activity. We have addressed this issue in functional columns and layers of animals with haemoglobin-based optical imaging and different fMRI contrasts, such as blood oxygenation level-dependent, cerebral blood flow and cerebral blood volume fMRI. In this review, we describe empirical evidence primarily from our own studies on how well these fMRI signals are spatially specific to the neuronally active site and discuss insights into neurovascular coupling at the mesoscale.This article is part of the theme issue ‘Key relationships between non-invasive functional neuroimaging and the underlying neuronal activity’.     

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.     

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.     

A Computational Model of Neuro-Glio-Vascular Loop Interactions

We present a computational, biophysical model of neuron-astrocyte-vessel interaction. Unlike other cells, neurons convey “hunger” signals to the vascular network via an intervening layer of glial cells (astrocytes); vessels dilate and release glucose which fuels neuronal firing. Existing computational models focus on only parts of this loop (neuron→astrocyte→vessel→neuron), whereas the proposed model describes the entire loop. Neuronal firing causes release of a neurotransmitter like glutamate which triggers release of vasodilator by astrocytes via a cascade of biochemical events. Vasodilators released from astrocytic endfeet cause blood vessels to dilate and release glucose into the interstitium, part of which is taken up by the astrocyticendfeet. Glucose is converted into lactate in the astrocyte and transported into the neuron. Glucose from the interstitium and lactate (produced from glucose) influx from astrocyte are converted into ATP in the neuron. Neuronal ATP is used to drive the Na⁺/K⁺ATPase pumps, which maintain ionic gradients necessary for neuronal firing. When placed in the metabolic loop, the neuron exhibits sustained firing only when the stimulation current is more than a minimum threshold. For various combinations of initial neuronal [ATP] and external current, the neuron exhibits a variety of firing patterns including sustained firing, firing after an initial pause, burst firing etc. Neurovascular interactions under conditions of constricted vessels are also studied. Most models of cerebral circulation describe neurovascular interactions exclusively in the “forward” neuron→vessel direction. The proposed model indicates possibility of “reverse” influence also, with vasomotion rhythms influencing neural firing patterns. Another idea that emerges out of the proposed work is that brain''s computations may be more comprehensively understood in terms of neuro-glial-vascular dynamics and not in terms of neural firing alone.     

Oral glucose intake inhibits hypothalamic neuronal activity more effectively than glucose infusion

We previously showed that hypothalamic neuronal activity, as measured by the blood oxygen level-dependent (BOLD) functional MRI signal, declines in response to oral glucose intake. To further explore the mechanism driving changes in hypothalamic neuronal activity in response to an oral glucose load, we here compare hypothalamic BOLD signal changes subsequent to an oral vs. an intravenous (iv) glucose challenge in healthy humans. Seven healthy, normal-weight men received four interventions in random order after an overnight fast: 1) ingestion of glucose solution (75 g in 300 ml) or 2) water (300 ml), and 3) iv infusion of 40% glucose solution (0.5 g/kg body wt, maximum 35 g) or 4) infusion of saline (0.9% NaCl, equal volume). The BOLD signal was recorded as of 8 min prior to intervention (baseline) until 30 min after. Glucose infusion was associated with a modest and transient signal decline in the hypothalamus. In contrast, glucose ingestion was followed by a profound and persistent signal decrease despite the fact that plasma glucose levels were almost threefold lower than in response to iv administration. Accordingly, glucose ingestion tended to suppress hunger more than iv infusion (P < 0.1). We infer that neural and endocrine signals emanating from the gastrointestinal tract are critical for the hypothalamic response to nutrient ingestion.     

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).     

From Blood Oxygenation Level Dependent (BOLD) Signals to Brain Temperature Maps

A theoretical framework is presented for converting Blood Oxygenation Level Dependent (BOLD) images to brain temperature maps, based on the idea that disproportional local changes in cerebral blood flow (CBF) as compared with cerebral metabolic rate of oxygen consumption (CMRO ₂) during functional brain activity, lead to both brain temperature changes and the BOLD effect. Using an oxygen limitation model and a BOLD signal model, we obtain a transcendental equation relating CBF and CMRO ₂ changes with the corresponding BOLD signal, which is solved in terms of the Lambert W function. Inserting this result in the dynamic bioheat equation describing the rate of temperature changes in the brain, we obtain a nonautonomous ordinary differential equation that depends on the BOLD response, which is solved numerically for each brain voxel. Temperature maps obtained from a real BOLD dataset registered in an attention to visual motion experiment were calculated, obtaining temperature variations in the range: (−0.15, 0.1) which is consistent with experimental results. The statistical analysis revealed that significant temperature activations have a similar distribution pattern than BOLD activations. An interesting difference was the activation of the precuneus in temperature maps, a region involved in visuospatial processing, an effect that was not observed on BOLD maps. Furthermore, temperature maps were more localized to gray matter regions than the original BOLD maps, showing less activated voxels in white matter and cerebrospinal fluid.