Changes in cerebral arterial, tissue and venous oxygenation with evoked neural stimulation: implications for hemoglobin-based functional neuroimaging

Model of the transient neurovascular response based on prompt arterial dilation

Brief neural stimulation results in a stereotypical pattern of vascular and metabolic response that is the basis for popular brain-imaging methods such as functional magnetic resonance imagine. However, the mechanisms of transient oxygen transport and its coupling to cerebral blood flow (CBF) and oxygen metabolism (CMRO2) are poorly understood. Recent experiments show that brief stimulation produces prompt arterial vasodilation rather than venous vasodilation. This work provides a neurovascular response model for brief stimulation based on transient arterial effects using one-dimensional convection-diffusion transport. Hemoglobin oxygen dissociation is included to enable predictions of absolute oxygen concentrations. Arterial CBF response is modeled using a lumped linear flow model, and CMRO2 response is modeled using a gamma function. Using six parameters, the model successfully fit 161/166 measured extravascular oxygen time courses obtained for brief visual stimulation in cat cerebral cortex. Results show how CBF and CMRO2 responses compete to produce the observed features of the hemodynamic response: initial dip, hyperoxic peak, undershoot, and ringing. Predicted CBF and CMRO2 response amplitudes are consistent with experimental measurements. This model provides a powerful framework to quantitatively interpret oxygen transport in the brain; in particular, its intravascular oxygen concentration predictions provide a new model for fMRI responses.

Extra permeability is required to model dynamic oxygen measurements: evidence for functional recruitment?

Neural activation triggers a rapid, focal increase in blood flow and thus oxygen delivery. Local oxygen consumption also increases, although not to the same extent as oxygen delivery. This 'uncoupling' enables a number of widely-used functional neuroimaging techniques; however, the physiologic mechanisms that govern oxygen transport under these conditions remain unclear. Here, we explore this dynamic process using a new mathematical model. Motivated by experimental observations and previous modeling, we hypothesized that functional recruitment of capillaries has an important role during neural activation. Using conventional mechanisms alone, the model predictions were inconsistent with in vivo measurements of oxygen partial pressure. However, dynamically increasing net capillary permeability, a simple description of functional recruitment, led to predictions consistent with the data. Increasing permeability in all vessel types had the same effect, but two alternative mechanisms were unable to produce predictions consistent with the data. These results are further evidence that conventional models of oxygen transport are not sufficient to predict dynamic experimental data. The data and modeling suggest that it is necessary to include a mechanism that dynamically increases net vascular permeability. While the model cannot distinguish between the different possibilities, we speculate that functional recruitment could have this effect in vivo.

New developments in arterial spin labeling pulse sequences

Since it was introduced over 20 years ago, arterial spin labeling and related methods have steadily evolved over the years, and the field has seen not only improvements in technical specifications, such as signal-to-noise ratio and accuracy, but also the introduction of methods that allow for the collection of new information, such as maps of vascular territories and measurement of venous oxygenation. Some of these recent advances are reviewed here.

Neural and hemodynamic responses elicited by forelimb- and photo-stimulation in channelrhodopsin-2 mice: insights into the hemodynamic point spread function

Hemodynamic responses are commonly used to map brain activity; however, their spatial limits have remained unclear because of the lack of a well-defined and malleable spatial stimulus. To examine the properties of neural activity and hemodynamic responses, multiunit activity, local field potential, cerebral blood volume (CBV)-sensitive optical imaging, and laser Doppler flowmetry were measured from the somatosensory cortex of transgenic mice expressing Channelrhodopsin-2 in cortex Layer 5 pyramidal neurons. The magnitude and extent of neural and hemodynamic responses were modulated using different photo-stimulation parameters and compared with those induced by somatosensory stimulation. Photo-stimulation-evoked spiking activity across cortical layers was similar to forelimb stimulation, although their activity originated in different layers. Hemodynamic responses induced by forelimb- and photo-stimulation were similar in magnitude and shape, although the former were slightly larger in amplitude and wider in extent. Altogether, the neurovascular relationship differed between these 2 stimulation pathways, but photo-stimulation-evoked changes in neural and hemodynamic activities were linearly correlated. Hemodynamic point spread functions were estimated from the photo-stimulation data and its full-width at half-maximum ranged between 103 and 175 µm. Therefore, submillimeter functional structures separated by a few hundred micrometers may be resolved using hemodynamic methods, such as optical imaging and functional magnetic resonance imaging.

Sensitivity of BOLD response to increasing visual contrast: spin echo versus gradient echo EPI

Previous evidence showed that spin-echo (SE) BOLD signals offer an increased linearity and promptness with respect to gradient-echo (GE) acquisition, possibly providing a more accurate estimate of the amplitude of neuronal activity. However there is no evidence that the two sequences differ in representing different activation levels due to changes in stimulus intensity. In this study at 3T we compared GE and SE BOLD responses to visual stimuli at increasing contrast levels (5%, 20%, 60%, and 100%). Both sequences showed a monotonic increase of the BOLD response with stimulus contrast. While the larger sensitivity of GE yielded overall larger signal changes, step-wise increase in activation for GE was significant only when comparing 20% with 5% contrast, whereas for SE a significant increase was observed also when comparing 60% with 20% contrast. Moreover, BOLD responses normalized to the lowest contrast showed that relative increases of SE fMRI signal with increasing stimulus strength are larger with respect to the corresponding values of GE signal. This difference was observed also when excluding voxels attributed to large vessels, suggesting a non negligible role of the extravascular contribution to the modulation of SE fMRI signal with stimulus intensity. These results are shown to be in agreement with theoretical predictions that we derived from a recently proposed model of GE and SE functional signals. The present findings suggest that, despite the limited increase in functional localization accuracy at low field, SE fMRI might offer a potential advantage in distinguishing different levels of stimulus-evoked brain activity.

Measuring biexponential transverse relaxation of the ASL signal at 9.4 T to estimate arterial oxygen saturation and the time of exchange of labeled blood water into cortical brain tissue

The transverse decay of the arterial spin labeling (ASL) signal was measured at four inflow times in the rat brain cortex at 9.4 T. Biexponential T2 decay was observed that appears to derive from different T2 values associated with labeled water in the intravasculature (IV) and extravascular (EV) compartments. A two compartment biexponential model was used to assess the relative contribution of the IV and EV compartments to the ASL signal, without assuming a value for T2 of labeled blood water in the vessels. This novel methodology was applied to estimate the exchange time of blood water into EV tissue space and the oxygen saturation of blood on the arterial side of the vasculature. The mean exchange time of labeled blood water was estimated to be 370±40 ms. The oxygen saturation of the arterial side of the vasculature was significantly less than 100% (∼85%), which may have implications for quantitative functional magnetic resonance imaging studies where the arterial oxygen saturation is frequently assumed to be 100%.

Computational modeling of the transient hemodynamic response in cerebral cortex

Neural activity triggers a vascular response in the brain that leads to transient changes in oxygen transport, and this mechanism is the basis for popular and powerful functional imaging methods. However, there is limited understanding of oxygen delivery to cerebral cortex both in steady state and during transient perturbations. In this study, a computational model for oxygen transport in the brain was developed and used to fit polarographic oxygen measurements during transient stimulation in cerebral cortex. The hemodynamic response function (HRF) was modeled with convection-diffusion transport in a four-compartment system (erythrocyte, intravascular, extravascular, and intracellular) that includes oxygen dissociation from hemoglobin. This model explained the dynamics of oxygen transport in cortex after brief visual stimulation, successfully fitting ~90% of experimental measurements within a realistic range of parameters for steady-state flow speed and oxygen consumption, as well as flow and oxygen uptake perturbations.

Effects of the α₂-adrenergic receptor agonist dexmedetomidine on neural, vascular and BOLD fMRI responses in the somatosensory cortex

This article describes the effects of dexmedetomidine (DEX) - the active ingredient of medetomidine, which is the latest popular sedative for functional magnetic resonance imaging (fMRI) in rodents - on multiple unit activity, local field potential (LFP), cerebral blood flow (CBF), pial vessel diameter [indicative of cerebral blood volume (CBV)], and blood oxygenation level-dependent (BOLD) fMRI. These measurements were obtained from the rat somatosensory cortex during 10 s of forepaw stimulation. We found that the continuous intravascular systemic infusion of DEX (50 μg/kg/h, doses typically used in fMRI studies) caused epileptic activities, and that supplemental isoflurane (ISO) administration of ~0.3% helped to suppress the development of epileptic activities and maintained robust neuronal and hemodynamic responses for up to 3 h. Supplemental administration of N(2)O in addition to DEX nearly abolished hemodynamic responses even if neuronal activity remained. Under DEX + ISO anesthesia, spike firing rate and the delta power of LFP increased, whereas beta and gamma power decreased, as compared with ISO-only anesthesia. DEX administration caused pial arteries and veins to constrict nearly equally, resulting in decreases in baseline CBF and CBV. Evoked LFP and CBF responses to forepaw stimulation were largest at a frequency of 8-10 Hz, and a non-linear relationship was observed. Similarly, BOLD fMRI responses measured at 9.4 T were largest at a frequency of 10 Hz. Both pial arteries and veins dilated rapidly (artery, 32.2%; vein, 5.8%), and venous diameter returned to baseline slower than arterial diameter. These results will be useful for designing, conducting and interpreting fMRI experiments under DEX sedation.

Cerebral blood volume changes during brain activation

Cerebral blood volume (CBV) changes significantly with brain activation, whether measured using positron emission tomography, functional magnetic resonance imaging (fMRI), or optical microscopy. If cerebral vessels are considered to be impermeable, the contents of the skull incompressible, and the skull itself inextensible, task- and hypercapnia-related changes of CBV could produce intolerable changes of intracranial pressure. Because it is becoming clear that CBV may be useful as a well-localized marker of neural activity changes, a resolution of this apparent paradox is needed. We have explored the idea that much of the change in CBV is facilitated by exchange of water between capillaries and surrounding tissue. To this end, we developed a novel hemodynamic boundary-value model and found approximate solutions using a numerical algorithm. We also constructed a macroscopic experimental model of a single capillary to provide biophysical insight. Both experiment and theory model capillary membranes as elastic and permeable. For a realistic change of input pressure, a relative pipe volume change of 21±5% was observed when using the experimental setup, compared with the value of approximately 17±1% when this quantity was calculated from the mathematical model. Volume, axial flow, and pressure changes are in the expected range.

Biophysical and physiological origins of blood oxygenation level-dependent fMRI signals

After its discovery in 1990, blood oxygenation level-dependent (BOLD) contrast in functional magnetic resonance imaging (fMRI) has been widely used to map brain activation in humans and animals. Since fMRI relies on signal changes induced by neural activity, its signal source can be complex and is also dependent on imaging parameters and techniques. In this review, we identify and describe the origins of BOLD fMRI signals, including the topics of (1) effects of spin density, volume fraction, inflow, perfusion, and susceptibility as potential contributors to BOLD fMRI, (2) intravascular and extravascular contributions to conventional gradient-echo and spin-echo BOLD fMRI, (3) spatial specificity of hemodynamic-based fMRI related to vascular architecture and intrinsic hemodynamic responses, (4) BOLD signal contributions from functional changes in cerebral blood flow (CBF), cerebral blood volume (CBV), and cerebral metabolic rate of O(2) utilization (CMRO(2)), (5) dynamic responses of BOLD, CBF, CMRO(2), and arterial and venous CBV, (6) potential sources of initial BOLD dips, poststimulus BOLD undershoots, and prolonged negative BOLD fMRI signals, (7) dependence of stimulus-evoked BOLD signals on baseline physiology, and (8) basis of resting-state BOLD fluctuations. These discussions are highly relevant to interpreting BOLD fMRI signals as physiological means.

Contributions of dynamic venous blood volume versus oxygenation level changes to BOLD fMRI

Blood-oxygenation-level-dependent (BOLD) fMRI has contributions from venous oxygenation and venous cerebral blood volume (CBV) changes. To examine the relative contribution of venous CBV change (ΔCBV(v)) to BOLD fMRI, BOLD and arterial CBV changes (ΔCBV(a)) to a 40-s forepaw stimulation in six α-chloralose anesthetized rats were measured using a magnetization transfer-varied fMRI technique, while total CBV change (ΔCBV(t)) was measured with injection of iron oxide nanoparticles. ΔCBV(v) was obtained by subtracting ΔCBV(a) from ΔCBV(t). We observed a fast ΔCBV(a) response with a time constant of 2.9 ± 2.3s and a slower ΔCBV(v) response with a time constant of 13.5 ± 5.7s and an onset delay of 6.1 ± 3.3s. These results are consistent with earlier studies under different anesthesia and stimulus, supporting that fast CBV(a) and slow CBV(v) responses are generalizable. Assuming the observed post-stimulus BOLD undershoot is at least partly explained by the ΔCBV(v) contribution, the relative contribution of the ΔCBV(v)- and oxygenation-change-related components to the BOLD response was estimated. The relative ΔCBV(v) contribution increases with time during stimulation; whereby it is <0.14 during initial 10s and reaches a maximum possible value of ~0.45 relative to the oxygenation contribution during the 30-40s period after stimulus onset. Our data indicates that the contribution of venous oxygenation change to BOLD fMRI is dominant for short stimulations.

"Overshoot" of O₂ is required to maintain baseline tissue oxygenation at locations distal to blood vessels

In vivo imaging of cerebral tissue oxygenation is important in defining healthy physiology and pathological departures associated with cerebral disease. We used a recently developed two-photon microscopy method, based on a novel phosphorescent nanoprobe, to image tissue oxygenation in the rat primary sensory cortex in response to sensory stimulation. Our measurements showed that a stimulus-evoked increase in tissue pO₂ depended on the baseline pO₂ level. In particular, during sustained stimulation, the steady-state pO₂ at low-baseline locations remained at the baseline, despite large pO₂ increases elsewhere. In contrast to the steady state, where pO₂ never decreased below the baseline, transient decreases occurred during the "initial dip" and "poststimulus undershoot." These results suggest that the increase in blood oxygenation during the hemodynamic response, which has been perceived as a paradox, may serve to prevent a sustained oxygenation drop at tissue locations that are remote from the vascular feeding sources.

Measurements and modeling of transient blood flow perturbations induced by brief somatosensory stimulation

Proper interpretation of BOLD fMRI and other common functional imaging methods requires an understanding of neurovascular coupling. We used laser speckle-contrast optical imaging to measure blood-flow responses in rat somatosensory cortex elicited by brief (2 s) forepaw stimulation. Results show a large increase in local blood flow speed followed by an undershoot and possible late-time oscillations. The blood flow measurements were modeled using the impulse response of a simple linear network, a four-element windkessel. This model yielded excellent fits to the detailed time courses of activated regions. The four-element windkessel model thus provides a simple explanation and interpretation of the transient blood-flow response, both its initial peak and its late-time behavior.

Quantitative MRI of cerebral arterial blood volume

Baseline cerebral arterial blood volume (CBV_a) and its change are important for potential diagnosis of vascular dysfunctions, the determination of functional reactivity, and the interpretation of BOLD fMRI. To quantitative measure baseline CBV_a non-invasively, we developed arterial spin labeling methods with magnetization transfer (MT) or bipolar gradients by utilizing differential MT or diffusion properties of tissue vs. arteries. Cortical CBV_a of isoflurane-anesthetized rats was 0.6 – 1.4 ml/100 g. During 15-s forepaw stimulation, CBV_a change was dominant, while venous blood volume change was minimal. This indicates that the venous CBV increase may be ignored for BOLD quantification for a stimulation duration of less than 15 s. By incorporating BOLD fMRI with varied MT effects in a cat visual cortical layer model, the highest ΔCBV_a was observed at layer 4, while the highest BOLD signal was detected at the surface of the cortex, indicating that CBV_a change is highly specific to neural activity. The CBV_a MRI techniques provide quantified maps, thus, may be valuable tools for routine determination of vessel viability and function, as well as the identification of vascular dysfunction.

BOLD responses to different temporal frequency stimuli in the lateral geniculate nucleus and visual cortex: insights into the neural basis of fMRI

The neural basis of the blood oxygenation level dependent (BOLD) functional magnetic resonance imaging (fMRI) remains largely unknown after decades of research. To investigate this issue, the unique property of the temporal frequency tuning that could separate neural input and output in the primary visual cortex was used as a model. During moving grating stimuli of 1, 2, 10 and 20Hz temporal frequencies, we measured 9.4-T BOLD fMRI responses simultaneously in the primary visual cortex of area 17 (A17) and area 18 (A18), and the lateral geniculate nucleus (LGN) of isoflurane-anesthetized cat. Our results showed that preferred temporal frequencies of the BOLD responses for A17, A18 and LGN were 3.1Hz, 4.5Hz and 6.0Hz, respectively, which were comparable to the previously reported electrophysiological data. Additionally, the difference of BOLD response onset time between LGN and A17 was 0.5s, which is 18 times larger than the difference of neural activity onset time between these areas. We then compared the frequency-dependent BOLD fMRI response of A17 with tissue partial pressure of oxygen (pO(2)) and electrophysiological data of the same animal model reported by Viswanathan and Freeman (Nature Neuroscience, 2007). The BOLD tuning curve resembled the low frequency band (<12Hz) of local field potential (LFP) tuning curve rather than spiking activity, gamma band (25-90Hz) of LFP, and tissue pO(2) tuning curves, suggesting that the BOLD fMRI signal relates closer to low frequency LFP.

Temporal dynamics and spatial specificity of arterial and venous blood volume changes during visual stimulation: implication for BOLD quantification

Determination of compartment-specific cerebral blood volume (CBV) changes is important for understanding neurovascular physiology and quantifying blood oxygenation level-dependent (BOLD) functional magnetic resonance imaging (fMRI). In isoflurane-anesthetized cats, we measured the spatiotemporal responses of arterial CBV (CBV(a)) and total CBV (CBV(t)) induced by a 40-second visual stimulation, using magnetization transfer (MT)-varied BOLD and contrast-agent fMRI techniques at 9.4 T. To determine the venous CBV (CBV(v)) change, we calculated the difference between CBV(t) and CBV(a) changes. The dynamic response of CBV(a) was an order of magnitude faster than that of CBV(v), while the magnitude of change under steady-state conditions was similar between the two. Following stimulation offset, ΔCBV(a) showed small poststimulus undershoots, while ΔCBV(v) slowly returned to baseline. The largest CBV(a) and CBV(t) response occurred after 10 seconds of simulation in cortical layer 4, which we identified as the stripe of Gennari by T(1)-weighted MRI. The CBV(v) response, however, was not specific across the cortical layers during the entire stimulation period. Our data indicate that rapid, more-specific arterial vasodilation is followed by slow, less-specific venous dilation. Our finding implies that the contribution of CBV(v) changes to BOLD signals is significant for long, but not short, stimulation periods.

Microvascular oxygen tension and flow measurements in rodent cerebral cortex during baseline conditions and functional activation

Measuring cerebral oxygen delivery and metabolism microscopically is important for interpreting macroscopic functional magnetic resonance imaging (fMRI) data and identifying pathological changes associated with stroke, Alzheimer's disease, and brain injury. Here, we present simultaneous, microscopic measurements of cerebral blood flow (CBF) and oxygen partial pressure (pO(2)) in cortical microvessels of anesthetized rats under baseline conditions and during somatosensory stimulation. Using a custom-built imaging system, we measured CBF with Fourier-domain optical coherence tomography (OCT), and vascular pO(2) with confocal phosphorescence lifetime microscopy. Cerebral blood flow and pO(2) measurements displayed heterogeneity over distances irresolvable with fMRI and positron emission tomography. Baseline measurements indicate O(2) extraction from pial arterioles and homogeneity of ascending venule pO(2) despite large variation in microvessel flows. Oxygen extraction is linearly related to flow in ascending venules, suggesting that flow in ascending venules closely matches oxygen demand of the drained territory. Oxygen partial pressure and relative CBF transients during somatosensory stimulation further indicate arteriolar O(2) extraction and suggest that arterioles contribute to the fMRI blood oxygen level dependent response. Understanding O(2) supply on a microscopic level will yield better insight into brain function and the underlying mechanisms of various neuropathologies.

Spatiotemporal evolution of the functional magnetic resonance imaging response to ultrashort stimuli

The specificity of the hemodynamic response function (HRF) is determined spatially by the vascular architecture and temporally by the evolution of hemodynamic changes. The stimulus duration has additional influence on the spatiotemporal evolution of the HRF, as brief stimuli elicit responses that engage only the local vasculature, whereas long stimuli lead to the involvement of remote vascular supply and drainage. Here, we used functional magnetic resonance imaging to investigate the spatiotemporal evolution of the blood oxygenation level-dependent (BOLD), cerebral blood flow (CBF), and cerebral blood volume (CBV) HRF to ultrashort forelimb stimulation in an anesthetized rodent model. The HRFs to a single 333-μs-long stimulus were robustly detected and consisted of a rapid response in both CBF and CBV, with an onset time (OT) of 350 ms and a full width at half-maximum of 1 s. In contrast, longer stimuli elicited a dispersive transit of oxygenated blood across the cortical microvasculature that significantly prolonged the evolution of the CBV HRF, but not the CBF. The CBF and CBV OTs suggest that vasoactive messengers are synthesized, released, and effective within 350 ms. However, the difference between the BOLD and CBV OT (∼100 ms) was significantly smaller than the arteriolar-venular transit time (∼500 ms), indicating an arterial contribution to the BOLD HRF. Finally, the rapid rate of growth of the active region with stimulus elongation suggests that functional hyperemia is an integrative process that involves the entire functional cortical depth. These findings offer a new view into the spatiotemporal dynamics of functional hemodynamic regulation in the brain.

Improved fMRI calibration: precisely controlled hyperoxic versus hypercapnic stimuli

The calibration of functional magnetic resonance imaging (fMRI) for the estimation of neuronal activation-induced changes in cerebral metabolic rate of oxygen (CMRO(2)) has been achieved through hypercapnic-induced iso-metabolic increases in cerebral blood flow (CBF). Hypercapnia (HC) has been traditionally implemented through alterations in the fixed inspired fractional concentrations of carbon dioxide (F(I)CO(2)) without otherwise controlling end-tidal partial pressures of carbon dioxide (P(ET)CO(2)) or oxygen (P(ET)O(2)). There are several shortcomings to the use of this manual HC method that may be improved by using precise targeting of P(ET)CO(2) while maintaining iso-oxia. Similarly, precise control of blood gases can be used to induce isocapnic hyperoxia (HO) to reduce venous deoxyhaemoglobin (dHb) and thus increase BOLD signals, without appreciably altering CMRO(2) or CBF. The aim of our study was to use precise end-tidal targeting to compare the calibration of BOLD signals under an isocapnic hyperoxic protocol (HOP) (rises in P(ET)O(2) to 140, 240 and 340 mm Hg from baseline) to that of an iso-oxic hypercapnic protocol (HCP) (rises in P(ET)CO(2) of 3, 5, 7 and 9 mm Hg from baseline). Nine healthy volunteers were imaged at 3T while monitoring end-tidal gas concentrations and simultaneously measuring BOLD and CBF signals, via arterial spin labeling (ASL), during graded HCP and HOP, alternating with normocapnic states in a blocked experimental design. The variability of the calibration constant obtained under HOP (M(HOP)) was 0.3-0.5 that of the HCP one (M(HCP)). In addition, M-variances with precise gas targeting (M(HCP) and M(HOP)) were less than those reported in studies using traditional F(I)CO(2) and F(I)O(2) methods (M(HC) and M(HO), respectively). We conclude that precise controlled gas delivery markedly improves BOLD-calibration for fMRI studies of oxygen metabolism with both the HCP and the more precise HOP-alternative.

Cerebral oxygen delivery and consumption during evoked neural activity

Increases in neural activity evoke increases in the delivery and consumption of oxygen. Beyond observations of cerebral tissue and blood oxygen, the role and properties of cerebral oxygen delivery and consumption during changes in brain function are not well understood. This work overviews the current knowledge of functional oxygen delivery and consumption and introduces recent and preliminary findings to explore the mechanisms by which oxygen is delivered to tissue as well as the temporal dynamics of oxygen metabolism. Vascular oxygen tension measurements have shown that a relatively large amount of oxygen exits pial arterioles prior to capillaries. Additionally, increases in cerebral blood flow (CBF) induced by evoked neural activation are accompanied by arterial vasodilation and also by increases in arteriolar oxygenation. This increase contributes not only to the down-stream delivery of oxygen to tissue, but also to delivery of additional oxygen to extra-vascular spaces surrounding the arterioles. On the other hand, the changes in tissue oxygen tension due to functional increases in oxygen consumption have been investigated using a method to suppress the evoked CBF response. The functional decreases in tissue oxygen tension induced by increases in oxygen consumption are slow to evoked changes in CBF under control conditions. Preliminary findings obtained using flavoprotein autofluorescence imaging suggest cellular oxidative metabolism changes at a faster rate than the average changes in tissue oxygen. These issues are important in the determination of the dynamic changes in tissue oxygen metabolism from hemoglobin-based imaging techniques such as blood oxygenation-level dependent functional magnetic resonance imaging (fMRI).