Signal source separation in the analysis of neural activity in brain

Evaluation and Optimization of Methods for Generating High-Resolution Retinotopic Maps Using Visual Cortex Voltage-Sensitive Dye Imaging

The localization and measurement of neuronal activity magnitude at high spatial and temporal resolution are essential for mapping and better understanding neuronal systems and mechanisms. One such example is the generation of retinotopic maps, which correlates localized retinal stimulation with the corresponding specific visual cortex responses. Here we evaluated and compared seven different methods for extracting and localizing cortical responses from voltage-sensitive dye imaging recordings, elicited by visual stimuli projected directly on the rat retina by a customized projection system. The performance of these methods was evaluated both qualitatively and quantitatively by means of two cluster separation metrics, namely, the (adjusted) Silhouette Index (SI) and the (adjusted) Davies-Bouldin Index (DBI). These metrics were validated using simulated data, which showed that Temporally Structured Component Analysis (TSCA) outperformed all other analysis methods for localizing cortical responses and generating high-resolution retinotopic maps. The analysis methods, as well as the use of cluster separation metrics proposed here, can facilitate future research aiming to localize specific activity at high resolution in the visual cortex or other brain areas.

Modelling the emergence of whisker barrels

Brain development relies on an interplay between genetic specification and self-organization. Striking examples of this relationship can be found in the somatosensory brainstem, thalamus, and cortex of rats and mice, where the arrangement of the facial whiskers is preserved in the arrangement of cell aggregates to form precise somatotopic maps. We show in simulation how realistic whisker maps can self-organize, by assuming that information is exchanged between adjacent cells only, under the guidance of gene expression gradients. The resulting model provides a simple account of how patterns of gene expression can constrain spontaneous pattern formation to faithfully reproduce functional maps in subsequent brain structures.

Improving voltage-sensitive dye imaging: with a little help from computational approaches

Voltage-sensitive dye imaging (VSDI) is a key neurophysiological recording tool because it reaches brain scales that remain inaccessible to other techniques. The development of this technique from in vitro to the behaving nonhuman primate has only been made possible thanks to the long-lasting, visionary work of Amiram Grinvald. This work has opened new scientific perspectives to the great benefit to the neuroscience community. However, this unprecedented technique remains largely under-utilized, and many future possibilities await for VSDI to reveal new functional operations. One reason why this tool has not been used extensively is the inherent complexity of the signal. For instance, the signal reflects mainly the subthreshold neuronal population response and is not linked to spiking activity in a straightforward manner. Second, VSDI gives access to intracortical recurrent dynamics that are intrinsically complex and therefore nontrivial to process. Computational approaches are thus necessary to promote our understanding and optimal use of this powerful technique. Here, we review such approaches, from computational models to dissect the mechanisms and origin of the recorded signal, to advanced signal processing methods to unravel new neuronal interactions at mesoscopic scale. Only a stronger development of interdisciplinary approaches can bridge micro- to macroscales.

An automated workflow for the anatomo-functional mapping of the barrel cortex

BACKGROUND

The rodent barrel cortex is a widely used model to study the cortical processing of tactile sensory information. It is notable by the cytoarchitecture of its layer IV, which contains distinguishable structural units called barrels that can be considered as anatomical landmarks of the functional columnar organization of the cerebral cortex. To study sensory integration in the barrel cortex it is therefore essential to map recorded functional data onto the underlying barrel topography, which can be reconstructed from the post hoc alignment of tangential brain slices stained for cytochrome oxidase.

NEW METHOD

This article presents an automated workflow to perform the registration of histological slices of the barrel cortex followed by the 2-D reconstruction of the barrel map from the registered slices. The registration of two successive slices is obtained by computing a rigid transformation to align sets of detected blood vessel cross-sections. This is achieved by using a robust variant of the classical iterative closest point method. A single fused image of the barrel field is then generated by computing a nonlinear merging of the gradients from the registered images.

COMPARISON WITH EXISTING METHODS

This novel anatomo-functional mapping tool leads to a substantial gain in time and precision compared to conventional manual methods. It provides a flexible interface for the user with only a few parameters to tune.

CONCLUSIONS

We demonstrate here the usefulness of the method for voltage sensitive dye imaging of the mouse barrel cortex. The method could also benefit other experimental approaches and model species.

Vobi One: a data processing software package for functional optical imaging

Optical imaging is the only technique that allows to record the activity of a neuronal population at the mesoscopic scale. A large region of the cortex (10-20 mm diameter) is directly imaged with a CCD camera while the animal performs a behavioral task, producing spatio-temporal data with an unprecedented combination of spatial and temporal resolutions (respectively, tens of micrometers and milliseconds). However, researchers who have developed and used this technique have relied on heterogeneous software and methods to analyze their data. In this paper, we introduce Vobi One, a software package entirely dedicated to the processing of functional optical imaging data. It has been designed to facilitate the processing of data and the comparison of different analysis methods. Moreover, it should help bring good analysis practices to the community because it relies on a database and a standard format for data handling and it provides tools that allow producing reproducible research. Vobi One is an extension of the BrainVISA software platform, entirely written with the Python programming language, open source and freely available for download at https://trac.int.univ-amu.fr/vobi_one.

The effects of focal epileptic activity on regional sensory-evoked neurovascular coupling and postictal modulation of bilateral sensory processing

While it is known that cortical sensory dysfunction may occur in focal neocortical epilepsy, it is unknown whether sensory-evoked neurovascular coupling is also disrupted during epileptiform activity. Addressing this open question may help to elucidate both the effects of focal neocortical epilepsy on sensory responses and the neurovascular characteristics of epileptogenic regions in sensory cortex. We therefore examined bilateral sensory-evoked neurovascular responses before, during, and after 4-aminopyridine (4-AP, 15 mmol/L, 1 μL) induced focal neocortical seizures in right vibrissal cortex of the rat. Stimulation consisted of electrical pulse trains (16 seconds, 5 Hz, 1.2 mA) presented to the mystacial pad. Consequent current-source density neural responses and epileptic activity in both cortices and across laminae were recorded via two 16-channel microelectrodes bilaterally implanted in vibrissal cortices. Concurrent two-dimensional optical imaging spectroscopy was used to produce spatiotemporal maps of total, oxy-, and deoxy-hemoglobin concentration. Compared with control, sensory-evoked neurovascular coupling was altered during ictal activity, but conserved postictally in both ipsilateral and contralateral vibrissal cortices, despite neurovascular responses being significantly reduced in the former, and enhanced in the latter. Our results provide insights into sensory-evoked neurovascular dynamics and coupling in epilepsy, and may have implications for the localization of epileptogenic foci and neighboring eloquent cortex.

Spontaneous oscillations in intrinsic signals reveal the structure of cerebral vasculature

Functional imaging of intrinsic signals allows minimally invasive spatiotemporal mapping of stimulus representations in the cortex, but representations are often corrupted by stimulus-independent spatial artifacts, especially those originating from the blood vessels. In this paper, we present novel algorithms for unsupervised identification of cerebral vascularization, allowing blind separation of stimulus representations from noise. These algorithms commonly take advantage of the temporal fluctuations in global reflectance to extract anatomic information. More specifically, the phase of low-frequency oscillations relative to global fluctuations reveals local vascular identity. Arterioles can be reconstructed using their characteristically high power in those frequencies corresponding to respiration, heartbeat, and vasomotion signals. By treating the vasculature as a dynamic flow network, we finally demonstrate that direction of blood perfusion can be quantitatively visualized. Application of these methods for removal of stimulus-independent changes in reflectance permits isolation of stimulus-evoked representations even if the representation spatially overlaps with blood vessels. The algorithms can be expanded further to extract temporal information on blood flow, monitor revascularization following a focal stroke, and distinguish arterioles from venules and parenchyma.

Inter-trial variability in sensory-evoked cortical hemodynamic responses: the role of the magnitude of pre-stimulus fluctuations

Brain imaging techniques utilize hemodynamic changes that accompany brain activation. However, stimulus-evoked hemodynamic responses display considerable inter-trial variability and the sources of this variability are poorly understood. One of the sources of this response variation could be ongoing spontaneous hemodynamic fluctuations. We recently investigated this issue by measuring cortical hemodynamics in response to sensory stimuli in anesthetized rodents using 2-dimensional optical imaging spectroscopy. We suggested that sensory-evoked cortical hemodynamics displayed distinctive response characteristics and magnitudes depending on the phase of ongoing fluctuations at stimulus onset due to a linear superposition of evoked and ongoing hemodynamics (Saka et al., 2010). However, the previous analysis neglected to examine the possible influence of variability of the size of ongoing fluctuations. Consequently, data were further analyzed to examine whether the size of pre-stimulus hemodynamic fluctuations also influenced the magnitude of subsequent stimulus-evoked responses. Indeed, in the case of all individual trials, a moderate correlation between the size of the pre-stimulus fluctuations and the magnitudes of the subsequent sensory-evoked responses were observed. However, different correlations between the size of the pre-stimulus fluctuations and magnitudes of the subsequent sensory-evoked cortical hemodynamic responses could be observed depending on their phase at stimulus onset. These analyses suggest that both the size and phase of pre-stimulus fluctuations in cortical hemodynamics contribute to inter-trial variability in sensory-evoked responses.

Is optical imaging spectroscopy a viable measurement technique for the investigation of the negative BOLD phenomenon? A concurrent optical imaging spectroscopy and fMRI study at high field (7 T)

Traditionally functional magnetic resonance imaging (fMRI) has been used to map activity in the human brain by measuring increases in the Blood Oxygenation Level Dependent (BOLD) signal. Often accompanying positive BOLD fMRI signal changes are sustained negative signal changes. Previous studies investigating the neurovascular coupling mechanisms of the negative BOLD phenomenon have used concurrent 2D-optical imaging spectroscopy (2D-OIS) and electrophysiology (Boorman et al., 2010). These experiments suggested that the negative BOLD signal in response to whisker stimulation was a result of an increase in deoxy-haemoglobin and reduced multi-unit activity in the deep cortical layers. However, Boorman et al. (2010) did not measure the BOLD and haemodynamic response concurrently and so could not quantitatively compare either the spatial maps or the 2D-OIS and fMRI time series directly. Furthermore their study utilised a homogeneous tissue model in which is predominantly sensitive to haemodynamic changes in more superficial layers.

Here we test whether the 2D-OIS technique is appropriate for studies of negative BOLD. We used concurrent fMRI with 2D-OIS techniques for the investigation of the haemodynamics underlying the negative BOLD at 7 Tesla. We investigated whether optical methods could be used to accurately map and measure the negative BOLD phenomenon by using 2D-OIS haemodynamic data to derive predictions from a biophysical model of BOLD signal changes. We showed that despite the deep cortical origin of the negative BOLD response, if an appropriate heterogeneous tissue model is used in the spectroscopic analysis then 2D-OIS can be used to investigate the negative BOLD phenomenon.

Neurovascular coupling is brain region-dependent

Despite recent advances in alternative brain imaging technologies, functional magnetic resonance imaging (fMRI) remains the workhorse for both medical diagnosis and primary research. Indeed, the number of research articles that utilise fMRI have continued to rise unabated since its conception in 1991, despite the limitation that recorded signals originate from the cerebral vasculature rather than neural tissue. Consequently, understanding the relationship between brain activity and the resultant changes in metabolism and blood flow (neurovascular coupling) remains a vital area of research. In the past, technical constraints have restricted investigations of neurovascular coupling to cortical sites and have led to the assumption that coupling in non-cortical structures is the same as in the cortex, despite the lack of any evidence. The current study investigated neurovascular coupling in the rat using whole-brain blood oxygenation level-dependent (BOLD) fMRI and multi-channel electrophysiological recordings and measured the response to a sensory stimulus as it proceeded through brainstem, thalamic and cortical processing sites - the so-called whisker-to-barrel pathway. We found marked regional differences in the amplitude of BOLD activation in the pathway and non-linear neurovascular coupling relationships in non-cortical sites. The findings have important implications for studies that use functional brain imaging to investigate sub-cortical function and caution against the use of simple, linear mapping of imaging signals onto neural activity.

Linear superposition of sensory-evoked and ongoing cortical hemodynamics

Modern non-invasive brain imaging techniques utilize changes in cerebral blood flow, volume and oxygenation that accompany brain activation. However, stimulus-evoked hemodynamic responses display considerable inter-trial variability even when identical stimuli are presented and the sources of this variability are poorly understood. One of the sources of this response variation could be ongoing spontaneous hemodynamic fluctuations. To investigate this issue, 2-dimensional optical imaging spectroscopy was used to measure cortical hemodynamics in response to sensory stimuli in anesthetized rodents. Pre-stimulus cortical hemodynamics displayed spontaneous periodic fluctuations and as such, data from individual stimulus presentation trials were assigned to one of four groups depending on the phase angle of pre-stimulus hemodynamic fluctuations and averaged. This analysis revealed that sensory evoked cortical hemodynamics displayed distinctive response characteristics and magnitudes depending on the phase angle of ongoing fluctuations at stimulus onset. To investigate the origin of this phenomenon, "null-trials" were collected without stimulus presentation. Subtraction of phase averaged "null trials" from their phase averaged stimulus-evoked counterparts resulted in four similar time series that resembled the mean stimulus-evoked response. These analyses suggest that linear superposition of evoked and ongoing cortical hemodynamic changes may be a property of the structure of inter-trial variability.

Does neural input or processing play a greater role in the magnitude of neuroimaging signals?

An important constraint on how hemodynamic neuroimaging signals such as fMRI can be interpreted in terms of the underlying evoked activity is an understanding of neurovascular coupling mechanisms that actually generate hemodynamic responses. The predominant view at present is that the hemodynamic response is most correlated with synaptic input and subsequent neural processing rather than spiking output. It is still not clear whether input or processing is more important in the generation of hemodynamics responses. In order to investigate this we measured the hemodynamic and neural responses to electrical whisker pad stimuli in rat whisker barrel somatosensory cortex both before and after the local cortical injections of the GABA(A) agonist muscimol. Muscimol would not be expected to affect the thalamocortical input into the cortex but would inhibit subsequent intra-cortical processing. Pre-muscimol infusion whisker stimuli elicited the expected neural and accompanying hemodynamic responses to that reported previously. Following infusion of muscimol, although the temporal profile of neural responses to each pulse of the stimulus train was similar, the average response was reduced in magnitude by approximately 79% compared to that elicited pre-infusion. The whisker-evoked hemodynamic responses were reduced by a commensurate magnitude suggesting that, although the neurovascular coupling relationships were similar for synaptic input as well as for cortical processing, the magnitude of the overall response is dominated by processing rather than from that produced from the thalamocortical input alone.

Effects of urethane anaesthesia on sensory processing in the rat barrel cortex revealed by combined optical imaging and electrophysiology

The spatiotemporal dynamics of neuronal assemblies evoked by sensory stimuli have not yet been fully characterised, especially the extent to which they are modulated by prevailing brain states. In order to examine this issue, we induced different levels of anaesthesia, distinguished by specific electroencephalographic indices, and compared somatosensory-evoked potentials (SEPs) with voltage-sensitive dye imaging (VSDI) responses in the rat barrel cortex evoked by whisker deflection. At deeper levels of anaesthesia, all responses were reduced in amplitude but, surprisingly, only VSDI responses exhibited prolonged activation resulting in a delayed return to baseline. Further analysis of the optical signal demonstrated that the reduction in response amplitude was constant across the area of activation, resulting in a global down-scaling of the population response. The manner in which the optical signal relates to the various neuronal generators that produce the SEP signal is also discussed. These data provide information regarding the impact of anaesthetic agents on the brain, and show the value of combining spatial analyses from neuroimaging approaches with more traditional electrophysiological techniques.

OI and fMRI signal separation using both temporal and spatial autocorrelations

Separating brain imaging signals by maximizing their autocorrelations is an important component of blind source separation (BSS). Canonical correlation analysis (CCA), one of leading BSS techniques, has been widely used for analyzing optical imaging (OI) and functional magnetic resonance imaging (fMRI) data. However, because of the need to reduce dimensionality and ignore spatial autocorrelation, CCA is problematic for separating temporal signal sources. To solve the problems of CCA, "straightforward image projection" (SIP) has been incorporated into temporal BSS. This novel method, termed low-dimensional canonical correlation analysis (LD-CCA), relies on the spatial and temporal autocorrelations of all genuine signals of interest. Incorporating both spatial and temporal information, here we introduce a "generalized timecourse" technique in which data are artificially reorganized prior to separation. The quantity of spatial plus temporal autocorrelations can then be defined. By maximizing temporal and spatial autocorrelations in combination, LD-CCA is able to obtain expected "real" signal sources. Generalized timecourses are low-dimensional, eliminating the need for dimension reduction. This removes the risk of discarding useful information. The new method is compared with temporal CCA and temporal independent component analysis (tICA). Comparison of simulated data showed that LD-CCA was more effective for recovering signal sources. Comparisons using real intrinsic OI and fMRI data also supported the validity of LD-CCA.

Vascular Origins of BOLD and CBV fMRI Signals: Statistical Mapping and Histological Sections Compared

Comparison of 3T blood oxygenation level dependent (BOLD) and cerebral blood volume (CBV) activation maps to histological sections enables the spatial discrimination of functional magnetic resonance imaging (fMRI) signal changes into different vascular compartments. We use a standard gradient echo-echo planar imaging technique to measure BOLD signal changes in the somatosensory cortex in response to whisker stimulation. Corresponding changes in CBV were estimated following the infusion of a super-paramagnetic contrast agent. We imaged in a tangential imaging plane that covered the cortical surface. Images were associated with post mortem histological sections showing both the surface vasculature and cytochrome oxidase stained whisker barrel cortex. We found a significant BOLD signal change in the large draining veins which occurred in the absence of a corresponding CBV change. Results suggest that in the venous drainage system, ~3mm distant from the area of activity, there is a robust change in blood oxygen saturation with little or no volume change. CBV changes are localised over the somatosensory barrel cortex and overlying arterial supply, supporting the theory that CBV changes are greater in the arterial than in the venous vasculature. This work investigating BOLD signal and underlying hemodynamics provides more information on the vascular origins of these important neuroimaging signals.

Altered neurovascular coupling during information-processing states

Brain imaging techniques rely on changes in blood flow, volume and oxygenation to infer the loci and magnitude of changes in activity. Although progress has been made in understanding the link between stimulus-evoked neural activity and haemodynamics, the extent to which neurovascular-coupling relationships remain constant during different states of baseline cortical activity is poorly understood. Optical imaging spectroscopy, laser Doppler flowmetry and electrophysiology were used to measure haemodynamics and neural activity in the barrel cortex of anaesthetized rats. The responses to stimulation of the whisker pad were recorded during quiescence and cortical desynchronization produced by stimulation of the brainstem. Cortical desynchronization was accompanied by increases in baseline blood flow, volume and oxygenation. Haemodynamic responses to low-frequency whisker stimuli (1 Hz) were attenuated during arousal compared with that observed during quiescence. During arousal it was possible to increase stimulus-evoked haemodynamics by increasing the frequency of the stimulus. Neural responses to low-frequency stimuli were also attenuated but to a far lesser extent than the reduction in the accompanying haemodynamics. In contrast, neuronal activity evoked by high-frequency stimuli (40 Hz) was enhanced during arousal, but induced haemodynamic responses of a similar magnitude compared with that observed for the same high-frequency stimulus presented during quiescence. These data suggest that there may be differences in stimulus-evoked neural activity and accompanying haemodynamics during different information-processing states.

Fine detail of neurovascular coupling revealed by spatiotemporal analysis of the hemodynamic response to single whisker stimulation in rat barrel cortex

The spatial resolution of hemodynamic-based neuroimaging techniques, including functional magnetic resonance imaging, is limited by the degree to which neurons regulate their blood supply on a fine scale. Here we investigated the spatial detail of neurovascular events with a combination of high spatiotemporal resolution two-dimensional spectroscopic optical imaging, multichannel electrode recordings and cytochrome oxidase histology in the rodent whisker barrel field. After mechanical stimulation of a single whisker, we found two spatially distinct cortical hemodynamic responses: a transient response in the "upstream" branches of surface arteries and a later highly localized increase in blood volume centered on the activated cortical column. Although the spatial representation of this localized response exceeded that of a single "barrel," the spread of hemodynamic activity accurately reflected the neural response in neighboring columns rather than being due to a passive "overspill." These data confirm hemodynamics are capable of providing accurate "single-condition" maps of neural activity.

Functional optical signal analysis: a software tool for near-infrared spectroscopy data processing incorporating statistical parametric mapping

Optical topography (OT) relies on the near infrared spectroscopy (NIRS) technique to provide noninvasively a spatial map of functional brain activity. OT has advantages over conventional fMRI in terms of its simple approach to measuring the hemodynamic response, its ability to distinguish between changes in oxy- and deoxy-hemoglobin and the range of human participants that can be readily investigated. We offer a new software tool, functional optical signal analysis (fOSA), for analyzing the spatially resolved optical signals that provides statistical inference capabilities about the distribution of brain activity in space and time and by experimental condition. It does this by mapping the signal into a standard functional neuroimaging analysis software, statistical parametric mapping (SPM), and forms, in effect, a new SPM toolbox specifically designed for NIRS in an OT configuration. The validity of the program has been tested using synthetic data, and its applicability is demonstrated with experimental data.

Cocaine preferentially enhances sensory processing in the upper layers of the primary sensory cortex

Sensory systems are believed to play an important role in drug addiction, particularly in triggering craving and relapse, and it has been shown in previous studies that administration of cocaine can enhance evoked responses in the primary sensory cortex of experimental animals. Primary sensory cortex comprises a multi-layered structure to which a variety of roles have been assigned; an understanding of how cocaine affects evoked activity in these different layers may shed light on how drug-associated sensory cues gain control over behavior. The aim of the present study was to examine how cocaine affects whisker sensory responses in different layers of the primary sensory (barrel) cortex. Field potential and multi-unit activity were recorded from the cortex of anesthetized rats using 16 channel linear probes during repetitive (air puff) stimulation of the whiskers. In control conditions (under saline, i.v.), responses strongly adapted to the repeated sensory stimulation. Following an i.v. injection of cocaine (0.5 mg/kg, i.v.), this adaptation was strongly attenuated, giving each stimulus a more equal representation and weight. Attenuation of adaptation was more marked in the upper cortical layers in both field potential and multi-unit data. Indeed, in these layers, not only was adaptation attenuated but multi-unit response amplitudes under cocaine exceeded those under saline for stimuli occurring early in the train. The results extend our previous findings concerning the enhancement by cocaine of primary sensory responses. Insofar as enhanced neural responses equate to enhanced stimulus salience, the results indicate that cocaine may play a previously under-appreciated role in the formation of associations between drug and drug-related environmental cues by enhancing stimulus salience. The associative process itself may be assisted by a preferential action in the upper cortical layers, thought to be involved in learning and plasticity.

Simultaneous laser Doppler flowmetry and arterial spin labeling MRI for measurement of functional perfusion changes in the cortex

This study compares laser Doppler flowmetry (LDF) and arterial spin labeling (ASL) for the measurement of functional changes in cerebral blood flow (CBF). The two methods were applied concurrently in a paradigm of electrical whisker stimulation in the anaesthetised rat. Multi-channel LDF was used, with each channel corresponding to different fiber separation (and thus measurement depth). Continuous ASL was applied using separate imaging and labeling coils at 3 T. Careful experimental set up ensured that both techniques recorded from spatially concordant regions of the barrel cortex, where functional responses were maximal. Strong correlations were demonstrated between CBF changes measured by each LDF channel and ASL in terms of maximum response magnitude and response time-course within a 6-s-long temporal resolution imposed by ASL. Quantitatively, the measurements of the most superficial LDF channels agreed strongly with those of ASL, whereas the deeper LDF channels underestimated consistently the ASL measurement. It was thus confirmed that LDF quantifies CBF changes consistently at a superficial level, and for this case the two methods provided concordant measures of functional CBF changes, despite their essentially different physical principles and spatiotemporal characteristics.

Hemodynamic responses in cortex investigated with optical imaging methods. Implications for functional brain mapping

During the last 20 years, optical imaging methods - either alone or in combination with other recording techniques - has proven a fruitful approach to explore both the physiological and the functional aspects of activity-evoked hemodynamic responses in cortex. One of the main advantages of optical imaging consists in its high spatio-temporal resolution (in the order of few microns and milliseconds), allowing not only to unambiguously distinguish between activity patterns relating to the underlying functional architecture and those originating from the activation of medium/large blood vessels, but also to investigate the various activity-evoked hemodynamic processes at very fine detail. Here, we briefly review the principal findings obtained by optical imaging about the spatio-temporal properties of the various hemodynamic responses in cortex, i.e., changes in blood-oxygenation, blood-volume, and, to some extent, blood-flow. We also discuss the implications of those findings for non-invasive high-resolution functional brain imaging, in particular for fMRI. Finally, we underscore the importance of novel approaches for high-resolution blood-flow imaging, in the context of the need to gather information at fine spatial detail about the blood-flow response, necessary to constrain the multiple free parameters of hemodynamic response models.

Depth-resolved optical imaging and microscopy of vascular compartment dynamics during somatosensory stimulation

The cortical hemodynamic response to somatosensory stimulus is investigated at the level of individual vascular compartments using both depth-resolved optical imaging and in-vivo two-photon microscopy. We utilize a new imaging and spatiotemporal analysis approach that exploits the different characteristic dynamics of responding arteries, arterioles, capillaries and veins to isolate their three-dimensional spatial extent within the cortex. This spatial delineation is validated using vascular casts. Temporal delineation is supported by in-vivo two-photon microscopy of the temporal dynamics and vascular mechanisms of the arteriolar and venous responses. Using these techniques we have been able to characterize the roles of the different vascular compartments in generating and controlling the hemodynamic response to somatosensory stimulus. We find that changes in arteriolar total hemoglobin concentration agree well with arteriolar dilation dynamics, which in turn correspond closely with changes in venous blood flow. For 4-s stimuli, we see only small changes in venous hemoglobin concentration, and do not detect measurable dilation or ballooning in the veins. Instead, we see significant evidence of capillary hyperemia. We compare our findings to historical observations of the composite hemodynamic response from other modalities including functional magnetic resonance imaging. Implications of our results are discussed with respect to mathematical models of cortical hemodynamics, and to current theories on the mechanisms underlying neurovascular coupling. We also conclude that our spatiotemporal analysis approach is capable of isolating and localizing signals from the capillary bed local to neuronal activation, and holds promise for improving the specificity of other hemodynamic imaging modalities.

Investigating neural-hemodynamic coupling and the hemodynamic response function in the awake rat

An understanding of the relationship between changes in neural activity and the accompanying hemodynamic response is crucial for accurate interpretation of functional brain imaging data and in particular the blood oxygen level-dependent (BOLD) fMRI signal. Much physiological research investigating this topic uses anesthetized animal preparations, and yet, the effects of anesthesia upon the neural and hemodynamic responses measured in such studies are not well understood. In this study, we electrically stimulated the whisker pad of both awake and urethane anesthetized rats at frequencies of 1-40 Hz. Evoked field potential responses were recorded using electrodes implanted into the contralateral barrel cortex. Changes in hemoglobin oxygenation and concentration were measured using optical imaging spectroscopy, and cerebral blood flow changes were measured using laser Doppler flowmetry. A linear neural-hemodynamic coupling relationship was found in the awake but not the anesthetized animal preparation. Over the range of stimulation conditions studied, hemodynamic response magnitude increased monotonically with summed neural activity in awake, but not in anesthetized, animals. Additionally, the temporal structure of the hemodynamic response function was different in awake compared to anesthetized animals. The responses in each case were well approximated by gamma variates, but these were different in terms of mean latency (approximately 2 s awake; 4 s anesthetized) and width (approximately 0.6 s awake; 2.5 s anesthetized). These findings have important implications for research into the intrinsic signals that underpin BOLD fMRI and for biophysical models of cortical hemodynamics and neural-hemodynamic coupling.

Neurovascular coupling investigated with two-dimensional optical imaging spectroscopy in rat whisker barrel cortex

Optical imaging slit spectroscopy is a powerful method for estimating quantitative changes in cerebral haemodynamics, such as deoxyhaemoglobin, oxyhaemoglobin and blood volume (Hbr, HbO2 and Hbt, respectively). Its disadvantage is that there is a large loss of spatial data as one image dimension is used to encode spectral wavelength information. Single wavelength optical imaging, on the other hand, produces high-resolution spatiotemporal maps of brain activity, but yields only indirect measures of Hbr, HbO2 and Hbt. In this study we perform two-dimensional optical imaging spectroscopy (2D-OIS) in rat barrel cortex during contralateral whisker stimulation to obtain two-dimensional maps over time of Hbr, HbO2 and Hbt. The 2D-OIS was performed by illuminating the cortex with four wavelengths of light (575, 559, 495 and 587 nm), which were presented sequentially at a high frame rate (32 Hz). The contralateral whisker pad was stimulated using two different durations: 1 and 16 s (5 Hz, 1.2 mA). Control experiments used a hypercapnic (5% CO2) challenge to manipulate baseline blood flow and volume in the absence of corresponding neural activation. The 2D-OIS method allowed separation of artery, vein and parenchyma regions. The magnitude of the haemodynamic response elicited varied considerably between different vascular compartments; the largest responses in Hbt were in the arteries and the smallest in the veins. Phase lags in the HbO2 response between arteries and veins suggest that a process of upstream signalling maybe responsible for dilating the arteries. There was also a consistent increase in Hbr from arterial regions after whisker stimulation.

Concurrent fMRI and optical measures for the investigation of the hemodynamic response function

Functional magnetic resonance imaging (fMRI) signal variations are based on a combination of changes in cerebral blood flow (CBF) and volume (CBV), and blood oxygenation. We investigated the relationship between these hemodynamic parameters in the rodent barrel cortex by performing fMRI concurrently with laser Doppler flowmetry (LDF) or optical imaging spectroscopy (OIS), following whisker stimulation and hypercapnic challenge. A difference between the positions of the maximum blood oxygenation level-dependent (BOLD) and CBV changes was observed in coronal fMRI maps, with the BOLD region being more superficial. A 6.5% baseline blood volume fraction in this superficial region dropped to 4% in deeper cortical layers (corresponding to total hemoglobin baseline volumes Hbt0 = 110 microM and 67 microM, respectively), as inferred from maps of deltaR2*. Baseline volume profiles were used to parameterize the Monte Carlo simulations (MCS) to interpret the 2D OIS. From this it was found that the optical blood volume measurements (i.e., changes in total hemoglobin) equated with CBV-MRI measurements when the MRI data were taken from superficial cortical layers. Optical measures of activation showed a good spatial overlap with fMRI measurements taken in the same plane (covering the right hemisphere surface). Changes in CBV and CBF followed the scaling relationship CBV = CBF(alpha), with mean alpha = 0.38 +/- 0.06.

The effect of hypercapnia on the neural and hemodynamic responses to somatosensory stimulation

Modern non-invasive imaging techniques utilize the coupling between neural activity and changes in blood flow, volume and oxygenation to map the functional architecture of the human brain. An understanding of how the hemodynamic response is influenced by pre-stimulus baseline perfusion is important for the interpretation of imaging data. To address this issue, the present study measured hemodynamics with optical imaging spectroscopy and laser Doppler flowmetry, while multi-channel electrophysiology was used to record local field potentials (LFP) and multi-unit activity (MUA). The response to whisker stimulation in rodent barrel cortex was recorded during baseline (normocapnia) and elevated perfusion rates produced by two levels of hypercapnia (5 and 10%). With the exception of the 'washout' of deoxyhemoglobin, which was attenuated, all aspects of the neural and hemodynamic response to whisker stimulation were similar during 5% hypercapnia to those evoked during normocapnia. In contrast, 10% hypercapnia produced cortical arousal and a reduction in both the current sink and MUA elicited by stimulation. Blood flow and volume responses were reduced by a similar magnitude to that observed in the current sink. The deoxyhemoglobin 'washout', however, was attenuated to a greater degree than could be expected from the neural activity. These data suggest that imaging techniques based on perfusion or blood volume changes may be more robust to shifts in baseline than those based on the dilution of deoxyhemoglobin, such as conventional BOLD fMRI.

Long duration stimuli and nonlinearities in the neural-haemodynamic coupling

Recent studies have shown that the haemodynamic responses to brief (<2 secs) stimuli can be well characterised as a linear convolution of neural activity with a suitable haemodynamic impulse response. In this paper, we show that the linear convolution model cannot predict measurements of blood flow responses to stimuli of longer duration (>2 secs), regardless of the impulse response function chosen. Modifying the linear convolution scheme to a nonlinear convolution scheme was found to provide a good prediction of the observed data. Whereas several studies have found a nonlinear coupling between stimulus input and blood flow responses, the current modelling scheme uses neural activity as an input, and thus implies nonlinearity in the coupling between neural activity and blood flow responses. Neural activity was assessed by current source density analysis of depth-resolved evoked field potentials, while blood flow responses were measured using laser Doppler flowmetry. All measurements were made in rat whisker barrel cortex after electrical stimulation of the whisker pad for 1 to 16 secs at 5 Hz and 1.2 mA (individual pulse width 0.3 ms).

Further nonlinearities in neurovascular coupling in rodent barrel cortex

An essential prerequisite for the accurate interpretation of noninvasive functional brain imaging techniques, such as blood oxygen level dependent (BOLD) fMRI, is a thorough understanding of the coupling relationship between neural activity and the haemodynamic response. The current study investigates this relationship using rat barrel cortex as a model. Neural input was measured by applying current source density (CSD) analysis to multi-laminar field potentials to remove ambiguities regarding the origin of the signal inherent in single electrode recordings. Changes in cerebral blood flow (CBF) were recorded with a laser Doppler flowmetry probe. The magnitude of neural and CBF responses were modulated over a large range by altering both the intensity and frequency of electrical whisker pad stimulation. Consistent with previous findings [Devor, A., et al., 2003. Neuron 39, 353-359; Sheth, S.A., et al., 2004. Neuron 42, 347-355] a power law function well described the relationship between neural activity and haemodynamics. Despite the nonlinearity of the coupling over the whole data set, the relationship was very well approximated by a linear function over mid-range stimuli. Altering the frequency of stimulation at 1.2 mA shifted the neural activity and corresponding haemodynamic response along this linear region, reconciling recent reports of a nonlinear relationship [Devor, A., et al., 2003. Neuron 39, 353-359; Jones, M., et al., 2004. NeuroImage 22, 956-965; Sheth, S.A., et al., 2004. Neuron 42, 347-355] with previous work that found a linear coupling relationship when altering stimulation frequency [Martindale, J., et al., 2003. J. Cereb. Blood Flow Metab. 23, 546-555; Ngai, A.C., et al., 1999. Brain Res. 837, 221-228; Sheth, S., et al., 2003. NeuroImage 19, 884-894]. Using stimuli within this linear range in imaging studies would simplify the interpretation of findings.

Integration of neural responses originating from different regions of the cortical somatosensory map

The neural pathways responsible for detecting peripheral tactile stimuli are well known; however, the interactions between different somatosensory regions have been less well investigated. This study demonstrates how the contralateral sensory response of rat barrel cortex to whisker stimulation is affected by stimulation of contralateral forepaw and ipsilateral whisker and forepaw. The barrel cortex in the right hemisphere was located using optical imaging. A 16-channel multielectrode was used to measure field potentials evoked by contralateral electrical stimulation of the whisker pad. A standard response in the right barrel cortex to single pulse electrical stimulation of the contralateral whisker pad was modulated by applying conditioning stimulation to one of three other regions of the body (the ipsilateral whisker pad, the ipsilateral or contralateral forepaws). In conditions where the standard contralateral whisker stimulus preceded the conditioning pulse, the size of response was identical to when it was stimulated alone. However, when the ipsilateral whisker and contralateral forepaw conditioning stimuli preceded the contralateral whisker pad stimulation, up to a 35% reduction in the contralateral whisker response was observed. These results confirm and extend previous studies [Proc. Natl. Acad. Sci. U. S. A. 97 (2000) 11026-11031; J. Neurosci. 21 (2001) 5251-5261], which show bilateral integration of neural activity within the rat somatosensory system. Furthermore, the longer latency of the inhibition following stimulation of the contralateral forepaw suggests the possible involvement of extracortical circuitry.

Haemodynamic responses to sensory stimulation are enhanced following acute cocaine administration

Cocaine enhances neural activity in response to sensory stimulation, an effect that may play a role in the development of drug craving. However, cocaine-induced sensory enhancement may be difficult to study in humans using neuroimaging if the global increases in baseline haemodynamic parameters, which cocaine produces, interfere with the ability of enhanced sensory-related neural activity to lead to enhanced haemodynamic responses. To investigate the effect of cocaine-induced baseline haemodynamic changes on sensory-related haemodynamic (and electrophysiological) responses, field potential (FP) and haemodynamic responses (obtained using optical imaging spectroscopy and laser-Doppler flowmetry) in the barrel cortex of the anaesthetised rat were measured during mechanical whisker stimulation following cocaine (0.5 mg/kg) or saline administration. During cocaine infusion, the relationship between blood flow and volume transiently decoupled. Following this, cocaine caused large baseline increases in blood flow (133%) and volume (33%), which peaked after approximately 6 min and approached normal levels again after 25 min. During the peak baseline increases, FP responses to whisker stimulation were similar to saline whereas several haemodynamic response parameters were slightly reduced. After the peak, significant increases in FP responses were observed, accompanied by significantly enhanced haemodynamic responses, even though the haemodynamic baselines remained elevated. Hence, the haemodynamic response to sensory stimulation is transiently reduced in the presence of large increases in baseline but, after the baseline peak, enhanced neural responses are faithfully accompanied by enhanced haemodynamic responses. The findings suggest that any cocaine-induced enhancement of sensory-related neural activity in humans is likely to be detectable by neuroimaging.

Columnar resolution of blood volume and oximetry functional maps in the behaving monkey; implications for FMRI

The ultimate goal of high-resolution functional brain mapping is single-condition (stimulus versus no-stimulus maps) rather than differential imaging (comparing two "stimulus maps"), because the appropriate ("orthogonal") stimuli are rarely available. This requires some component(s) of activity-dependent hemodynamic signals to closely colocalize with electrical activity, like the early increase in deoxyhemoglobin, shown previously to yield high-quality functional single-condition maps. Conversely, nonlocal vascular responses dominate in cerebral blood volume (CBV)-based single-condition maps. Differential CBV maps are largely restricted to the parenchyma, implying that part of the CBV response does colocalize with electrical activity at fine spatial scale. By removing surface vascular activation from optical imaging data, we document the existence of a capillary CBV response component, regulated at fine spatial scale and yielding single-condition maps exhibiting approximately 100 microm resolution. Blood volume and -flow based single-condition functional mapping at columnar level should thus be feasible, provided that the capillary response component is selectively imaged.

Nonlinear coupling of neural activity and CBF in rodent barrel cortex

The relationship between neural activity and accompanying changes in cerebral blood flow (CBF) and oxygenation must be fully understood before data from brain imaging techniques can be correctly interpreted. Whether signals in fMRI reflect the neural input or output of an activated region is still unclear. Similarly, quantitative relationships between neural activity and changes in CBF are not well understood. The present study addresses these issues by using simultaneous laser Doppler flowmetry (LDF) to measure CBF and multichannel electrophysiology to record neural activity in the form of field potentials and multiunit spiking. We demonstrate that CBF-activation coupling is a nonlinear inverse sigmoid function. Comparing the data with previous work suggests that within a cortical model, CBF shows greatest spatial correlation with a current sink 500 microm below the surface corresponding to sensory input. These results show that care must be exercised when interpreting imaging data elicited by particularly strong or weak stimuli and that hemodynamic changes may better reflect the input to a region rather than its spiking output.

Shedding light on brain mapping: advances in human optical imaging

Several functional brain imaging techniques have been used to study human cortical organization. Optical imaging of intrinsic signals (OIS) offers perhaps the best combination of spatial coverage, resolution and speed for mapping the functional topography of human cortex. In this review, we discuss recent advances in optical imaging technology and methodology that have made human OIS easier to implement and more accessible, including improvements in detector characteristics and the development of sophisticated algorithms for reducing motion artifact. Moreover, we discuss how these advances have helped enhance our understanding of the functional organization of the human brain. We also review newly developed analyses for interpreting and validating optical signals, including refined signal analysis techniques and multimodality comparisons. Combined, these advances have enabled the study of not only primary sensory and motor cortices, but also higher cognitive processes such as language production and comprehension. Continued improvement and implementation of this technique promises to shed new light on the functional organization of human cortex.

The hemodynamic impulse response to a single neural event

This article investigates the relation between stimulus-evoked neural activity and cerebral hemodynamics. Specifically, the hypothesis is tested that hemodynamic responses can be modeled as a linear convolution of experimentally obtained measures of neural activity with a suitable hemodynamic impulse response function. To obtain a range of neural and hemodynamic responses, rat whisker pad was stimulated using brief (</=2 seconds) electrical stimuli consisting of single pulses (0.3 millisecond, 1.2 mA) combined both at different frequencies and in a paired-pulse design. Hemodynamic responses were measured using concurrent optical imaging spectroscopy and laser Doppler flowmetry, whereas neural responses were assessed through current source density analysis of multielectrode recordings from a single barrel. General linear modeling was used to deconvolve the hemodynamic impulse response to a single "neural event" from the hemodynamic and neural responses to stimulation. The model provided an excellent fit to the empirical data. The implications of these results for modeling schemes and for physiologic systems coupling neural and hemodynamic activity are discussed.

Optical imaging of intrinsic signals induced by peripheral nerve stimulation in the in vivo rat spinal cord

We examined neural response patterns evoked by peripheral nerve stimulation in in vivo rat spinal cords using an intrinsic optical imaging technique to monitor neural activity. Adult rats were anesthetized by urethane, and laminectomy was performed between C5 and Th1 to expose the dorsal surface of the cervical spinal cord. The median, ulnar, and radial nerves were dissected, and bipolar electrodes were implanted in the forelimb. Changes in optical reflectance were recorded from the dorsal cervical spinal cord in response to simultaneous stimulation of the median and ulnar nerves using a differential video acquisition system. In the region of the cervical spinal cord, intrinsic optical signals were detected between C5 and Th1 at wavelengths of 605, 630, 730, 750, and 850 nm: the image with the largest signal intensity and highest contrast was obtained at 605 nm. The signal intensity and response area expanded with an increase in the stimulation intensity and varied with the depth of the focal plane of the macroscope. The intrinsic optical response was mostly eliminated by Cd(2+), suggesting that the detected signals were mainly mediated by postsynaptic mechanisms activated by sensory nerve fibers. Furthermore, we succeeded in imaging neural activity evoked by individual peripheral nerve stimulation. We found that the response areas related to each peripheral nerve exhibited different spatial distribution patterns and that there were animal-to-animal variations in the evoked neural responses in the spinal cord. The results obtained in this study confirmed that intrinsic optical imaging is a very useful technique for acquiring fine functional maps of the in vivo spinal cord.

Optical imaging spectroscopy in the unanaesthetised rat

We describe a method for imaging the local cortical haemodynamic response to whisker stimulation in the rat without use of anaesthetic or paralytic agents. Female Hooded Lister rats were anaesthetised and a section of skull overlying somatosensory cortex thinned to translucency. A stainless steel chamber was then secured over the thin cranial window. Following recovery, animals were supported in a harness whilst the head was held by the implanted chamber using a pneumatically driven clamp. Optical imaging and optical imaging spectroscopy (OIS) of somatosensory cortex were performed whilst the contralateral whiskers were stimulated using a computer controlled air-puffer. Imaging sessions lasted approximately 15 min and data were collected for at least three consecutive days. Experiments were then repeated with the animals under urethane anaesthesia. Spectral analysis revealed qualitatively similar haemodynamic response functions across both anaesthetic states. However, our results indicate that the cortical haemodynamic response to somatosensory stimulation is larger by a factor of approximately 5 in the unanaesthetised rat compared with the anaesthetised rat. This preparation may make possible the investigation of the haemodynamic correlates of a broad range of neurological processes in the awake, behaving rodent.

A model of the hemodynamic response and oxygen delivery to brain

A recent nonlinear system by Friston et al. (2000. NeuroImage 12: 466-477) links the changes in BOLD response to changes in neural activity. The system consists of five subsystems, linking: (1) neural activity to flow changes; (2) flow changes to oxygen delivery to tissue; (3) flow changes to changes in blood volume and venous outflow; (4) changes in flow, volume, and oxygen extraction fraction to deoxyhemoglobin changes; and finally (5) volume and deoxyhemoglobin changes to the BOLD response. Friston et al. exploit, in subsystem 2, a model by Buxton and Frank coupling flow changes to changes in oxygen metabolism which assumes tissue oxygen concentration to be close to zero. We describe below a model of the coupling between flow and oxygen delivery which takes into account the modulatory effect of changes in tissue oxygen concentration. The major development has been to extend the original Buxton and Frank model for oxygen transport to a full dynamic capillary model making the model applicable to both transient and steady state conditions. Furthermore our modification enables us to determine the time series of CMRO(2) changes under different conditions, including CO(2) challenges. We compare the differences in the performance of the "Friston system" using the original model of Buxton and Frank and that of our model. We also compare the data predicted by our model (with appropriate parameters) to data from a series of OIS studies. The qualitative differences in the behaviour of the models are exposed by different experimental simulations and by comparison with the results of OIS data from brief and extended stimulation protocols and from experiments using hypercapnia.

Hemodynamic response in the unanesthetized rat: intrinsic optical imaging and spectroscopy of the barrel cortex

Optical imaging spectroscopy was used to measure the hemodynamic response of somatosensory cortex to stimulation of the whiskers. Responses to brief puffs of air were compared in anesthetized and unanesthetized rats. The hemodynamic response was approximately four times larger in the unanesthetized animal than the corresponding anesthetized animal. In unanesthetized animals, a short-latency (approximately 400 milliseconds) short-duration (approximately 300 milliseconds) hemodynamic startle response was observed. General linear model analysis was used to extract this component from the time series, and revealed an underlying short-latency increase in deoxygenated hemoglobin in response to somatosensory stimulation. It is proposed that anesthesia can have a marked affect on the relation between changes in blood volume and blood flow. This work represents a step in the development of an experimental model that can be used to investigate fundamental neurologic processes in the awake-behaving rodent.

Changes in blood flow, oxygenation, and volume following extended stimulation of rodent barrel cortex

Simultaneous optical imaging spectroscopy and laser-Doppler flowmetry were used in rodent barrel cortex to examine the hemodynamic response to extended electrical stimulation (20 s, 5 Hz) of the whisker pad. Stimulation results in a fast early increase in deoxyhemoglobin concentration (Hbr) followed by a later decrease to a "plateau" phase approximately 4 s after stimulation onset. There was no corresponding decrease in oxyhemoglobin (HbO(2)), which simply increased after stimulation, reaching a plateau at approximately 5 s. The time series of flow and volume had similar onset times and did not differ significantly throughout the presentation of the stimuli. Following stimulation cessation all aspects of the hemodynamic response returned to baseline with a long decay constant (>20 s), CBV doing so at a slower rate than CBF. The time courses of CBF, CBV, Hbr, and HbO(2) were very similar to that produced by a brief stimulus up to peak. The relationship between the flow and the volume changes is well approximated by the expression CBV = CBF(phi). We find phi to be slightly lower under stimulation (0.26 +/- 0.0152) than during hypercapnia (0.32 +/- 0.0172). Saturation and flow data were used to estimate changes in CMRO(2) for a range of baseline oxygen extraction fractions (OEF). In the case of hypercapnia CMRO(2) was biphasic, increasing after onset and sharply decreasing below baseline following cessation. If it is assumed that there is no "net" increase in CMRO(2) (i.e., SigmaDeltaCMRO(2) = 0) following the onset and offset of hypercapnia, then the corresponding estimate of baseline OEF is 0.45. Evidence for increased oxygen consumption was obtained for all stimulation intensities assuming a baseline OEF of 0.45.

Concurrent Optical Imaging Spectroscopy and Laser-Doppler Flowmetry: The Relationship between Blood Flow, Oxygenation, and Volume in Rodent Barrel Cortex

Functional magnetic resonance imaging (fMRI) is based on the coupling between neural activity and changes in the concentration of the endogenous paramagnetic contrast agent deoxygenated hemoglobin. Changes in the blood oxygen level-dependent (BOLD) signal result from a complex interplay of blood volume, flow, and oxygen consumption. Optical imaging spectroscopy (OIS) has been used to measure changes in blood volume and saturation in response to increased neural activity, while laser Doppler Flowmetry (LDF) can be used to measure flow changes and is now commonplace in neurovascular research. Here, we use concurrent OIS and LDF to examine the hemodynamic response in rodent barrel cortex using electrical stimulation of the whisker pad at varying intensities. Spectroscopic analysis showed that stimulation produced a biphasic early increase in deoxygenated hemoglobin (Hbr), followed by a decrease below baseline, reaching minima at approximately 3.7 s. There was no evidence for a corresponding early decrease in oxygenated hemoglobin (HbO(2)), which simply increased after stimulation, reaching maximum at approximately 3.2 s. The time courses of changes in blood volume (CBV) and blood flow (CBF) were similar. Both increased within a second of stimulation onset and peaked at approximately 2.7 s, after which CBV returned to baseline at a slower rate than CBF. The changes in Hbr, Hbt, and CBF were used to estimate changes in oxygen consumption (CMRO(2)), which increased within a second of stimulation and peaked approximately 2.2 s after stimulus onset. Analysis of the relative magnitudes of CBV and CBF indicates that the fractional changes of CBV could be simply scaled to match those of CBF. We found the relationship to be well approximated by CBV = CBF(0.29). A similar relationship was found using the response to elevated fraction of inspired carbon dioxide (FICO(2)).