Coupling between cerebral blood flow and cerebral blood volume: Contributions of different vascular compartments

A better understanding of the coupling between changes in cerebral blood flow (CBF) and cerebral blood volume (CBV) is vital for furthering our understanding of the BOLD response. The aim of this study was to measure CBF‐CBV coupling in different vascular compartments during neural activation. Three haemodynamic parameters were measured during a visual stimulus. Look‐Locker flow‐sensitive alternating inversion recovery was used to measure changes in CBF and arterial CBV (CBVa) using sequence parameters optimized for each contrast. Changes in total CBV (CBVtot) were measured using a gadolinium‐based contrast agent technique. Haemodynamic changes were extracted from a region of interest based on voxels that were activated in the CBF experiments. The CBF‐CBVtot coupling constant α tot was measured as 0.16 ± 0.14 and the CBF‐CBVa coupling constant α a was measured as 0.65 ± 0.24. Using a two‐compartment model of the vasculature (arterial and venous), the change in venous CBV (CBVv) was predicted for an assumed value of baseline arterial and venous blood volume. These results will enhance the accuracy and reliability of applications that rely on models of the BOLD response, such as calibrated BOLD.

coupling constant will overestimate changes in venous CBV (CBV v ). This led to measurements of a CBF-CBV v coupling constant using the CBV v sensitive venous refocusing for volume estimation (VERVE) technique. 9,10 Despite this, the coupling between CBF and CBV a is still poorly understood in humans, with the majority of research having been performed in rats. 6,7 Whilst changes in CBV a are typically invisible in the context of standard BOLD fMRI, they become significant in studies utilizing intravascular contrast agents 11 or hypoxic hypoxia, 12 where an arterial signal change occurs due to the presence of paramagnetic contrast agent or deoxyhaemoglobin, respectively, in the arterial blood volume, the latter having implications for the application of these methods in cerebrovascular disease, where patients may have a reduced arterial oxygen saturation.
One reason why there is only a small number of published studies examining the relationship between these parameters is the limited number of techniques for measuring CBV tot , CBV a and CBV v in humans. Fractional changes in CBV tot (ΔCBV tot ) during a stimulus have been measured via an infusion of a gadolinium-based contrast agent (GBCA). [13][14][15] Such experiments rely on measuring changes in the stimulus evoked BOLD response as a function of intravascular contrast agent concentration, which can either be increased using an extended infusion, or decreased by clearance of a bolus of contrast agent via the kidneys. 16 This is in contrast to dynamic susceptibility contrast based techniques that are not generally temporally resolved and are more commonly used to measure absolute resting CBV tot . Vascular space occupancy (VASO) has also been shown to provide a method for the assessment of total CBV. 17 However, it is not possible to measure ΔCBV tot using VASO without prior knowledge of the baseline CBV tot , thus making this technique unsuitable for the study of CBF-CBV tot coupling. Arterial spin labelling (ASL)-based approaches have emerged for the measurement of CBV a ; these include inflow-based VASO (iVASO) 18 and Look-Locker flow-sensitive alternating inversion recovery (LL-FAIR). 8 LL-FAIR combines the FAIR ASL technique with Look-Locker echo planar imaging (LL-EPI) sampling 19 to sensitize the signal to either CBF using vascular crushing 20 or CBV a , 8 depending on the sequence parameters. This technique is also presented in the literature as ITS-FAIR (inflow turbo-sampling EPI flow-sensitive alternating inversion recovery) 21 and QUASAR (quantitative signal targeting with alternating radio frequency labelling of arterial regions), 22 the latter requiring the subtraction of scans with and without vascular crushing to estimate CBV a . Since the LL-FAIR technique is also capable of measuring transit time of labelled blood, it is also able to account for changes in transit time that may occur during neuronal activation. LL-FAIR also has a higher signal to noise ratio (SNR) per unit time for measurement of perfusion than conventional FAIR. 21 CBV v measurements have been made using the VERVE technique 23 or hyperoxia BOLD contrast 24 methods. However, VERVE is hampered by assumptions regarding oxygenation changes during activation and hyperoxia BOLD contrast by relatively low SNR.
In this study, LL-FAIR-based measurements of CBF and CBV a are acquired alongside estimates of ΔCBV tot using a GBCA technique. The relationship between the resultant haemodynamic parameters is assessed using a power law relationship, building upon early studies of CBF-CBV coupling, 5 the calibrated BOLD method 1,2 and BOLD modelling studies. 3,4 This analysis yields CBF-CBV a and CBF-CBV tot coupling constants.
These measurements are also used to predict the change in CBV v for an assumed arterial and venous volume fraction.
2 | THEORY 2.1 | LL-FAIR for measurement of CBF LL-FAIR combines a FAIR ASL labelling scheme with LL-EPI sampling. The sequence can be sensitized to CBF by using an initial inversion delay (T I ) to allow inflowing blood to arrive at the imaging plane (T I = 600 ms) followed by low flip angle pulses (θ = 35°) for the EPI readouts with a time interval (T A = 350 ms) such that the perfusion signal is not fully suppressed and can be sampled multiple times Figure 1B). Vascular crushing is added to minimize any CBV a signal contribution from the macrovasculature. CBF is then quantified by iteratively modelling the signal due to multiple readout pulses using a kinetic model that takes into account the duration of the labelled blood arriving in the tissue, the effect of the readout pulse on both arterial blood magnetization and tissue magnetization, and incomplete blood magnetization recovery at short repetition times. This is performed by solving a three-compartment model, where Compartment 1 contains arterial blood located outside of the imaging volume, Compartment 2 contains arterial blood inside the imaging volume and Compartment 3 contains blood in the capillary bed, which is in exchange with the tissue. For a complete description see Reference 20.

| LL-FAIR for measurement of CBV a
Alternatively, the LL-FAIR scheme can be sensitized to CBV a . This is performed by using an LL-FAIR scheme with a short initial delay (T I = 150 ms) and closely spaced (T A = 100 ms) high flip angle pulses (θ = 50°) for the EPI readout, which are acquired at the shortest achievable echo time ( Figure 1C). This has the advantage of providing a large number of EPI readout time points of high SNR to well sample the arterial blood volume inflow curve for quantification of CBV a , 8 whilst suppressing any CBF contribution. 20 CBV a is quantified by iteratively modelling the signal across the readout pulses in the arterial blood compartment (Compartment 2 described above) using a kinetic model. 8

| Gadolinium infusion for measurement of CBV tot
By infusing a contrast agent during an fMRI paradigm whilst acquiring dual-echo BOLD weighted images for estimation of the transverse relaxation rate (R 2 *), the signal can be sensitized to changes in CBV tot . Quantification of this signal is achieved by comparing measurements of R 2 * at rest and during activation. [13][14][15] Under the assumption that stimulus evoked changes in R 2 * are constant across multiple trials, additional contributions to R 2 * across trials are expected to be solely due to the contrast agent in the blood. In addition, it is assumed that the effect of the contrast agent on the measured signal is predominantly extravascular in origin. Therefore, during rest the measured change in R 2 * due to contrast agent can be modelled as where κ is a constant representing physical properties of the experiment, V tot is the resting CBV tot , [CA] is the contrast agent concentration in the blood and χ CA is the molar magnetic susceptibility of the contrast agent. 11 During the active condition, the measured change in R 2 * due to contrast agent is where ΔV tot is the resultant change in CBV tot . Therefore, the fractional change in CBV tot (δCBV tot ) can be estimated by taking the ratio of Equation 1 and Equation 2.
In an idealized experiment the fMRI stimulus paradigm would be repeated twice, first in the absence of contrast agent and second during a steady state concentration of contrast. However, in practice this is not feasible in human subjects due to dosage limits of GBCAs and their rapid elimination. Therefore, here R 2 * measurements are made in the presence of a slowly changing contrast agent concentration provided by an infusion of a GBCA, with ΔR *rest 2 being extrapolated from periods of rest during activated time points. 15 3 | METHODS

| Imaging
This study was approved by the University of Nottingham Medical School Ethics Committee. Eight healthy volunteers aged 20 to 31 years (24 ± 3 years, mean ± standard deviation) gave written consent and were scanned as part of this study. A schematic diagram of the experimental protocol is given in Figure 1a. Subjects were cannulated prior to entering the scanner to provide access for the injection of contrast agent and ensure that any motion during the Gd injection in the CBV tot experiment was minimal.

FIGURE 1
A, overview of the experimental protocol including visual stimulus blocks (red lines), contrast agent injections (arrow Gd) and experimental details. B, example pulse sequence diagram of LL-FAIR scheme used for CBF quantification with FAIR labelling followed by five EPI readouts. The initial four flip angles have θ = 35°, with a final readout pulse of flip angle of 90°. The first readout pulse occurs following an initial inversion delay (T I = 600 ms) with subsequent readouts separated by a time interval (T A = 350 ms). Data are collected with vascular crushing (VENC = 7.8 mm/s). the sequence is then repeated with repetition time T R . C, CBV a quantification with FAIR labelling followed by 19 EPI readouts. The first 18 flip angles are θ = 50°, with a final readout pulse of flip angle of 90°. The first readout pulse occurs following an initial inversion delay (T I = 150 ms), with subsequent readouts separated by a time interval (T A = 100 ms). The sequence is then repeated with repetition time T R Data were acquired on a Philips Achieva 3 T system (Philips Healthcare, Best, The Netherlands), using a body transmit coil and eight-channel SENSE (sensitivity encoding) head receive coil. All three haemodynamic parameter measurements were acquired with a common spatial resolution of 3 × 3 × 5 mm 3 , matrix size of 64 × 64 and SENSE factor 2 and matched bandwidth. Measurements of CBF and CBV a were limited to a single slice acquisition at the time these experiments were performed. Therefore, an initial functional localizer scan was performed in order to select a single axial slice through the visual cortex with the largest region of BOLD activation. This slice prescription was then used throughout the rest of the experiment.
Visual stimulation was provided by red LED goggles flashing at 8 Hz. Lights were on for 19.2 s and off for the remainder of the 60 s cycle. The number of stimulus cycles varied reflecting the differing SNR of each method: eight cycles were collected for CBV a measurements, 12 cycles for CBF (which has a lower contrast to noise ratio) and 14 cycles for CBV tot .
An LL-FAIR acquisition was used to allow the assessment of both CBF and CBV a measurements accounting for transit time effects. The combination of a Look-Locker acquisition with a FAIR preparation enables the tagged bolus to be tracked through the macrovascular system and into the tissue sensitizing the signal to CBV a or CBF by using the appropriate combination of sequence parameters. In both cases the thickness of the

| Analysis
For each subject, CBF, CBV a and CBV tot data sets were first realigned within each data set and then across all data sets using SPM5 (5 mm FWHM Gaussian smoothing kernel and second degree B-spline interpolation). 25 Since the CBF and CBV a data were acquired for a single slice, motion correction was restricted to in-plane motion and rotation. In the case of the CBV tot measurement, the acquisition of three slices provided for the correction of small amounts of through-slice motion. For the CBF and CBV a data, the images from the final LL-FAIR readout pulse (90°flip angle and thus highest SNR) of each volume acquisition (T R period) were realigned, and this transformation matrix then applied to the images acquired from the other LL readout pulses within the corresponding T R period. The CBV tot datasets were realigned using the images acquired at the first echo, and this transformation matrix was then applied to the second echo data. Data for each echo time was then down-sampled to produce a complete time series with a 2.4 s temporal resolution (matching the CBF and CBV a datasets), and only a single slice co-registered to the CBF and CBV a datasets was retained.
For the CBF and CBV a data, difference images were first computed from the subtraction of consecutive label and control pairs to provide a time series of CBF-and CBV a -weighted images for each LL-readout pulse. Average CBF-and CBV a -weighted time series during the visual stimulus cycle were then formed by averaging across cycles, accounting for jittering in the data relative to the stimulus paradigm (thus generating a CBFweighted and CBV a -weighted time series of LL readouts for each time point per stimulus cycle). CBV a -weighted difference images were quantified to estimate arterial transit time and CBV a voxelwise using a two-parameter fit, as described in Reference 8, over an averaged stimulus cycle. CBFweighted difference images were initially analysed using a two-parameter fit for capillary transit time and CBF. 20 However, since the data had lower SNR than the CBV a data, a two-parameter fit for each time point within the stimulus cycle was found to increase the noise in the measurement of CBF. Therefore, a mean estimate of the transit time at baseline and on activation was computed and used in a one-parameter model fit to produce a voxelwise estimates of CBF at each time point over an averaged stimulus cycle.
For the CBV tot data, time series of R 2 * values were calculated for each voxel using the realigned, down-sampled, dual echo data. The fractional change in CBV tot (δCBV tot ) was calculated by considering the effect of the contrast agent on the R 2 * (transverse relaxation rate) changes that occur during the BOLD response, as shown previously by using an infusion to gradually increase the contrast agent concentration. 15 However, in this study two bolus injections of contrast agent were used to raise the initial blood contrast agent concentration, which gradually decreased due to washout through the kidneys. In the analysis, four stimulus cycles prior to the contrast agent injections provided a baseline.
Stimulus cycles following immediately after the injections were discarded to allow for recirculation of the contrast agent, leaving the final nine cycles for analysis. In all other aspects, this method is the same as in previous reports, and resulted in an estimate of ΔCBV tot over an averaged stimulus cycle. 11,15 Activated regions were generated for each subject using a correlation analysis of the stimulus delivery applied to the quantified CBF maps in order to be maximally sensitive to the site of activation. Each CBF region of interest (ROI CBF ) was defined based on the CBF statistical map threshold at p < 0.01 (uncorrected). In addition, a supplementary analysis was performed to examine the impact of a different ROI definition based on common activated voxels across the three measures of CBV a , CBF and δCBV tot . Statistical maps from each measure were thresholded at p < 0.01 (uncorrected) and voxels at the intersection retained to form a common ROI (ROI COMMON ).

| Estimation of CBF-CBV coupling
The coupling between CBF and CBV during neuronal activation was calculated assuming a power law relationship between CBF and CBV tot , where values of ζ and α tot have previously been measured in rhesus monkeys using a hyper/hypocapnia challenge as 0.80 and 0.38, respectively. 5 Given measurements of the fractional change (i.e. the absolute change in CBV divided by absolute baseline CBV) in CBV tot (δCBV tot ) and CBF (δCBF) in response to the visual stimulus, which is dimensionless, the CBF-CBV tot coupling constant α tot (Grubb's constant) can be estimated by rearranging Equation 4: Under the assumption that the relationship between CBF and CBV a can be described by the power law relationship given in Equation 4, a CBF-CBV a coupling constant α a can be defined. In this case δCBV a is the fractional change in CBV a , which is also dimensionless.
Using these equations, Grubb's constant, α tot , and the CBF-CBV a coupling constant, α a , were estimated on a per subject basis. Values for δCBF, δCBV tot and δCBV a were extracted from the quantified maps of each parameter and averaged over each of the ROIs. The time window for the active on condition was defined as between 9.6 s and 19.2 s from the start of the stimulus cycle, whilst the baseline off condition was defined to be between 40.8 s and 60 s. Estimates of α tot and α a were then computed using Equations 5 and 6, respectively.
In the absence of direct measurements of CBV v , we estimated the fractional change in venous CBV (δCBV v ) using a simple model of the vascular compartments. Changes in total blood volume were approximated as a volume-weighted sum of two compartments: arterial and venous,

FIGURE 3
Example time courses of the raw signal for each modality from a single subject averaged over the CBF-based region of interest. A, CBV a -weighted LL-FAIR difference data were acquired over eight stimulus cycles. B, CBF-weighted LL-FAIR difference data were acquired over 12 stimulus cycles. C, CBV tot -weighted gradient echo (GE) EPI data were acquired over a period of 16 min. Two single-dose boluses of a GBCA were injected at the beginning of minutes 4 and 5. The visual stimulus was presented for the remaining cycles where f a and f v are the volume fractions assigned to arterial and venous blood volume compartments ( f a = CBV a /CBV tot , f v = CBV v /CBV tot ), respectively, and here it is assumed that f a + f v = 1. The capillary volume is assumed to be distributed between the arterial and venous compartments. By rearranging Equation 7, δCBV v can be predicted as a function of arterial and venous volume fractions f a and f v : RESULTS   Figures 2 and 3 show examples of the raw data acquired in this study from a single subject. The former shows CBF-weighted (Figure 2A) and Estimates of the mean transit time for CBF-weighted (perfusion transit time) and CBV a -weighted (arterial transit time) data are presented in Table 1. These data were extracted from the CBF-based ROI of each subject. During activation the perfusion transit time was found to be significantly reduced (p < 0.05, paired two-tailed t-test), but the change in the arterial transit time was not significant (p = 0.11).  Table 1). Table 2 provides the fractional change measured for each haemodynamic parameter for ROI CBF , along with the predicted value of δCBV v estimated assuming a value of arterial volume fraction of f a = 0.3 ( f v = 0.7) (this choice of value is discussed below). The uncertainty in each parameter was estimated as the standard deviation of the voxels in the ROI for the measured parameters (baseline and changes in CBV a , CBF and CBV tot ) and propagated from these values for the calculated parameters (δCBV v , α tot and α a ). Measurements of δCBV tot and δCBV a were found to be statistically significantly different from zero across the group (one-sample t-test, p < 0.05), with estimates of α tot and α a provided in Table 2 for each subject and group means of 0.16 ± 0.14 and 0.65 ± 0.24, respectively. In contrast, the estimated value of δCBV v was not statistically significantly different from zero (p = 0.33), which would suggest a CBF-CBV v coupling constant, α v , of close to zero. Quantified baseline estimates of CBF and CBV a from the baseline time window are also presented inTable 2. Baseline CBV a was found to be inversely correlated with δCBV a (correlation coefficient, R = −0.68). Group means and standard deviations inTable 2 are weighted by the number of voxels in each subject's ROI. The number of voxels included in the ROI varied across subjects, probably due to the use of single-slice techniques, and in some subjects sub-optimal placement of the slice. It should be noted that, whilst measurements of δCBV tot have the lowest group standard deviation, when coupled with a low mean value of δCBV tot this technique has the highest relative standard deviation. This propagates through to greater uncertainty in the value of α tot compared with α a .
The results of the supplementary analysis using a common ROI are presented in the Supporting Information. Figure S1 parallels Figure 4, displaying the fractional changes in each of the haemodynamic measures for the common ROI. However, it should be noted that by producing the ROI COMMON as the intersection of changes in CBV a , CBF and CBV tot the number of included voxels is low across all subjects and zero for one subject (Table S1). Despite this, larger changes in all haemodynamic parameters were observed compared with the results from ROI CBF , and a significant increase in CBV v was detected (one-sample t-test, p < 0.05). This enabled α v to be estimated as 0.29 ± 0.15 across the group, alongside values of 0.45 ± 0.14 for α tot and 0.70 ± 0.29 for α a . These results can be found in Table S2. Details of how to access the data underpinning the results presented in this study can be found in the appendix.

| DISCUSSION
A good understanding of the relationship between changes in CBF and CBV is important for interpreting the physiological changes that underlie functional hyperaemia. However, how these changes translate to a measured BOLD response depends on how such changes are distributed across the different vascular compartments. The results of this study will help to improve models of the BOLD response. 11,26 In turn this will enhance the accuracy and reliability of applications that rely on a correct understanding of the BOLD response. For example, it has been shown that the accuracy of the calibrated BOLD method for quantifying stimulus evoked oxygen metabolism changes is critically dependent on accurate knowledge of CBF-CBV v coupling. 26,27 In this study, measurements of CBF, CBV a and CBV tot were combined to assess the coupling of CBF changes with changes in arterial, venous and total CBV, within two functionally defined ROIs. For the CBF derived ROI, the CBF-CBV tot coupling constant α tot was estimated to be 0.16 ± 0.14 and the CBF-CBV a coupling constant α a was estimated to be 0.65 ± 0.24 (mean ± standard deviation). The estimated change in CBV v within this ROI was not statistically significant. Supplementary analysis using a common ROI (ROI COMMON ) provided contrasting results, which are discussed later in this section.

| Comparison with the literature
The coupling between CBF and CBV tot has been the target of numerous studies. The power law relationship (Equation 1) was first introduced by   experiments using a perfluorocarbon contrast agent and continuous ASL (CASL) measured a value of α tot of 0.4 in rats. 6 However, in all of these cases measurements were made in the steady state. In this study, a relatively short stimulus duration of 19.2 s was used, which is more relevant for human imaging studies but may not be long enough to allow a steady state to be reached, and hence may explain the smaller value of α tot measured (0.16 ± 0.14) for ROI CBF . A larger value of α tot was measured (0.45 ± 0.14) for ROI COMMON , albeit for a much smaller active region of tissue.
The literature regarding the coupling of CBF with CBV a is more limited. Perfluorocarbon studies on rats measured the CBV a change due to steady state hypercapnia and the change in CBF using CASL. 6 Reviewing their data, we estimate α a = 0.84. A similar rat study performed by Kim et al 7 measured changes in CBF and CBV a in response to a 15 s somatosensory stimulus using the MOTIVE (MRI with modulation of tissue and vessel) technique, 31 and from these datasets we estimate α a = 1.73. The values for α a obtained in our study (0.65 ± 0.24 and 0.70 ± 0.29) are at the low end of this range, again perhaps suggesting that a steady state was not achieved using a short stimulus. However, further data are required to investigate the effects of stimulus, species and anaesthesia differences.
This experiment did not allow a direct measurement of CBV v changes. In addition, it was not possible to acquire absolute estimates of CBV tot . Therefore, the changes in CBV v could only be investigated based on assumptions regarding the partitioning of blood volume by a two-compartment model consisting of arterial and venous volume fractions. The arterial volume fraction f a has previously been measured as 0.27, 7 0.29, 32 and 0.3-0.37, 33 using a range of techniques, each of which is expected to include a small fraction of the post-arterial capillary blood volume, whilst the venous volume fraction f v has been measured as 0.77 using the quantitative BOLD technique. 34 This technique is specifically sensitive to blood vessels containing deoxygenated blood. Whilst this largely consists of blood within venous vessels, it is also expected to include deoxygenated blood within the capillaries. Therefore, the arterial and venous compartments defined in this study might more accurately be described as the oxygenated and deoxygenated compartments. Importantly, it is this deoxygenated blood volume that underlies the BOLD response and best reflects the BOLD specific CBF-CBV coupling. Therefore, based on the literature values above, f a was assumed to take a value of 0.3. Under this assumption, a non-significant change in CBV v was estimated for ROI CBF , whilst a significant change was recorded for ROI COMMON . This would suggest a CBF-CBV v coupling constant, α v , of around zero for the former and α v = 0.32 ± 0.14 for the latter. These values bracket the limited range of values of CBF-CBV v coupling constant given in the literature. In rats a value of α v of 0.20 was measured using a steady state hypercapnia stimulus, 6 whilst in humans α v was measured as 0.18 for a steady state hyper/hypocapnic stimulus, 10 and 0.18/0.31 for low/high intensity visual stimulation. 9 However, even in the latter visual stimulus experiments, the stimulus duration was 96 s and therefore significantly longer than that used in our study. In order to examine the effect of short stimuli we can consider recent work investigating the temporal dynamics of CBV v . 35 In this work CBV v was shown to be delayed with respect to changes in CBF and CBV a .
Given the short duration of our stimulus, it is likely that this would not produce an appreciable increase in CBV v , consistent with the results from ROI CBF .
Furthermore this is consistent with two photon microscopy measurements that demonstrated a minimal increase in CBV v for a 10 s stimulus, but a larger and delayed response for a 30 s stimulus. 36 Given these findings, the results from ROI COMMON appear to overestimate the change in CBV v .
The inconsistency between the two ROIs considered in this study results from the different voxel selection methods. In the case of ROI CBF , the use of a CBF localizer provides sensitivity to perfusion and hence to exchange at the capillary bed. CBF ROIs have previously been shown to be more robust than a BOLD-based localizer. 37 In contrast the CBV localizers used in combination with the CBF localizer to define the ROI COMMON are not specific to any particular vessel scale. Therefore, large vessels in the ROI are likely to be accompanied by small changes in CBV, whilst small vessels might see larger changes. Whilst the correlation between baseline CBV a and δCBV a is not statistically significant, this effect likely explains the intersubject variation in the δCBV a time courses (Figures 4 and S1). In addition, it has been observed that changes in CBV v during activation are spatially heterogenous with both increases and decreases. 24 Therefore, selecting for only positive changes in CBV has the potential to overestimate the fractional change during activation and may explain why a significant change in CBV v was observed for ROI COMMON .

| Limitations of the current study
In this work, ROIs were selected using the activated region defined by the CBF data. However, the use of such functionally defined ROIs can lead to statistical bias, resulting in an overestimation of changes in CBF. 38 Due to the importance of maintaining comfort in human volunteer studies, time within the scanner was limited. Therefore, it was not possible to acquire an additional CBF dataset to provide an independent definition of the ROI.
A pulsed ASL (PASL) preparation was employed in this study so that the same methodologies could be used for the quantification of both CBF and CBV a and the effects of transit time could be measured and accounted for. The use of a pseudocontinuous ASL (PCASL) approach to measure changes in CBF would likely improve the fidelity of such measurements. However, a PCASL preparation cannot be used for CBV a measurements due to SAR limitations. Therefore, in practice using a PASL preparation for both CBF and CBV a measurements is preferable to maintain the same labelling efficiency in both experiments.
Absolute quantification of CBV tot was not possible in this study, so we could not measure ΔCBV v . This might be measured by tracking the first bolus of contrast agent. 39 However, the resolution of the data acquired in this study was too coarse to yield an adequate arterial input function.
Absolute CBV tot is reported to be in the range of 3-5 mL/100 g, therefore the results of this study would predict an absolute change in CBV tot (ΔCBV tot ) between 0.18 and 0.3 mL/100 g.
Predictions of α v were based on a two-compartment model of the vasculature: arterial and venous. It was therefore assumed that the capillary compartment was distributed between these two compartments. However, it is likely that changes in capillary CBV will have their own characteristic coupling to CBF and may therefore contribute to an under/overestimation of CBV change in the arterial and venous compartments.
Finally, only steady state changes in haemodynamics were studied since the SNR was not sufficient to study dynamic changes. However, it has been shown that a post-stimulus undershoot in CBF may contribute to the BOLD post-stimulus undershoot 40 and that changes in CBV v are delayed with respect to changes in CBV a . 35 These dynamic variations are expected to add to the complexity of the temporal characteristics of the BOLD response. Repeating this work at higher field might allow the study of these dynamic characteristics, greater knowledge of which may enable the dynamics of changes in oxygen metabolism to be investigated using extensions to methods such as calibrated BOLD. 1,2

| CONCLUSION
In this study, measurements of CBF, CBV a and CBV tot were performed in individual subjects in a single experimental session to assess the coupling of haemodynamic responses. This information is valuable for furthering our understanding of the BOLD response and for enhancing the accuracy and reliability of applications that rely on models of the BOLD response, such as calibrated BOLD.