Cerebrovascular reactivity (CVR) mapping using MRI is increasingly used to assess the effects of cerebrovascular conditions such as atherosclerotic steno-occlusive disease (1, 2) and Moyamoya (3). CVR is conventionally mapped by administering CO2 mixed with air through an open oxygen face mask. In early measurements, this stimulus was applied in an interleaved fashion with blocks of air, while BOLD-weighted images and measurements of end-tidal PCO2 (PETCO2) are acquired (4, 5). This PETCO2 time-course is then regressed against the BOLD data on a pixel-by-pixel basis to create CVR maps showing the strength of the correlation (2, 6). The underlying assumption in generating maps in this way is that the CVR response occurs in all parts of the brain simultaneously. However, if the change in PCO2 carried by the blood arrived in various areas of the brain at different times, or if there were a delayed vascular response to this change in PCO2 in some brain regions, then the correlation between the BOLD signal and the PETCO2, and thus CVR, could be underestimated. Furthermore, variations in the arrival time of blood or response time of the vasculature, in different areas of the brain may provide useful diagnostic information.
The aim of this study is to improve upon the existing BOLD CVR methodology by acquiring potentially useful information about the regional delays in the BOLD CVR response while minimizing errors due to any regional delays. This is achieved by combining a sinusoidally varying carbon dioxide stimulus with Fourier analysis techniques. To apply an accurate sinusoidal stimulus, a computerized gas blender was used along with a model-based algorithm for prospective targeting and control of end-tidal PO2 (PETO2) and PCO2 (7). This algorithm allows more accurate and independent control of PETO2 and PETCO2 than that achieved by simply presenting CO2 mixed with air. This enables arbitrarily shaped changes in PETCO2 to be administered, such as the sinusoid used here. This stimulus delivery can then be coupled with Fourier analysis techniques, as used in retinotopic mapping (8). This analysis method was chosen as synchronization of the MRI, and PETCO2 data is not required, as it is the frequency of the signal that is detected, reducing confounding effects of inaccurate synchronization. In addition, the phase of the response at each tissue location will give temporal information about the spatial variability of the relative response time of the vasculature.
This study was approved by the institutional ethics committee. Six healthy subjects (three males) aged between 23 and 31 years of age (27 ± 3, mean ± standard deviation) were recruited and gave informed consent. MR imaging was performed on a Philips Achieva 7.0 T scanner equipped with a 16-channel SENSE (SENSitivity Encoding) receive coil and volume transmit coil (Nova Medical Inc., Wilmington, MA.). A multiple gradient echo EPI (Echo Planar Imaging) protocol was used for CVR mapping to maximize the BOLD contrast sensitivity by using a weighted summation of the echo signals (9) while keeping image distortion to a minimum by shortening the echo train length through parallel acceleration (10). Four gradient echoes were acquired with a SENSE acceleration factor of 4, flip angle 90°, and and echo times (TE) of 8, 22, 36, and 50 ms. Twenty-three 3-mm slices were acquired in a 2.5 s repetition time (TR), with a 104 × 76 matrix, and an in-plane resolution of 2 mm.
In addition, T1-weighted MPRAGE (Magnetization Prepared RApid Gradient Echo) images were acquired (150 slices, 384 × 384 matrix, 0.5 mm in-plane resolution, 1-mm slice thickness, TE/TR = 6.9/15 ms, and flip = 8°) for image registration and segmentation. A tailored FOCI inversion pulse was used to improve image homogeneity (11). T2*-weighted FFE images (TE/TR = 20/50 ms, EPI factor 3, bandwidth = 167 Hz) were acquired for localization of venous vessels (12).
The respiratory challenge was programmed into a computer-controlled gas blender (RespirAct™, Thornhill Research Inc., Toronto, Can.) that uses the prospective targeting algorithm of Slessarev et al. (7). The gas blender component of the device provided specific flows and concentrations of gases to an MR compatible sequential gas delivery breathing circuit (Thornhill Research Inc., Toronto, Can.) necessary to achieve the targeted end-tidal values (7, 13). The prospective nature of this method eliminates the requirement for a rapid feedback control mechanism allowing the gas blender, computer and source gases to be beyond the significant fringe field of the 7.0 T magnet. Gas flow to the sequential gas delivery circuit was provided through 12 m of flexible hosing extending from the gas blender (kept in the control room of the scanner), through a wave-guide in the wall of the shielded room of the scanner, to the gas inlet port of the sequential gas delivery circuit. Two 12-m and 1.2-mm O.D. sample lines drew gas samples and monitored pressure from inside the mask. Time courses of PCO2 and PO2 were generated by continuously monitoring exhaled gases with gas analyzers built into the gas blender. End-tidal PO2 and PCO2 values were manually selected from these time courses at points where the CO2 level plateaued at a high-level before the end of the subject's exhalation and the resulting drop in CO2. This manual method was required as the concentrations of PO2 and PCO2 supplied by the gas blender in this sinusoidal paradigm were continually changing, causing the automated methods of detecting end-tidal gases to fail. Long sampling tubes were necessary due to the extensive fringe field at 7.0 T but can lead to temporal smearing of the sampled gas concentrations. However, tests by the manufacturer of the RepirAct™ system have shown that this effect is small for breathing rates less than 20 min−1.
The stimulus consisted of a 1-min baseline period (PETCO2 = 40 mmHg) followed by 10, regularly spaced, sinusoidal cycles of PETCO2, with a mean of 40 mmHg, an amplitude of 10 mmHg and period of 1 min. PETO2 was targeted to be approximately 100 mmHg throughout the experiment. Breathing was cued at 15 min−1 using visual signals projected on a screen placed in front of the scanner. This was to avoid slow ventilatory rates and maintain a reasonable sampling rate for end-tidal gas concentrations.
Fourier analysis was used to analyze the time course of changes in the end-tidal gases. This enabled the identification of the component of variation due to the stimulus (with a frequency of 1/60 Hz) and measurement of the amplitude of the hypercapnic stimulus.
First the T2* of each voxel was calculated using linear least squares fitting to the averaged echo train from all the dynamics of the multi-echo EPI data set. Next, for each dynamic the images from all echoes were combined offline by weighted-summation of the echoes (9). Images were realigned using linear transformations (14) and nonbrain tissue was removed (15). MR time-courses were normalized to the mean signal and detrended by fitting a fourth-order polynomial series to the data. The resulting BOLD weighted signal is, henceforth, described as the CVR response.
A frequency analysis method, similar to that used in traveling wave retinotopic mapping (16), was then applied to the CVR response data. A Fast Fourier Transform (FFT) was applied to the modulus signal time-courses on a voxel-by-voxel basis. The amplitude of the CVR response to the sinusoidal CO2 stimulus was determined from the magnitude of the Fourier component at the frequency of the stimulus. The correlation coefficient, cc, between the stimulus and CVR response was calculated from:
where N is the number of frequency bins, af are the magnitudes in each of the frequency bins, and aF is the magnitude at the frequency of the applied stimulus. This definition of the correlation coefficient has been shown to be equivalent to the Pearson product moment correlation coefficient (8). To measure the SNR of the data in this spectral domain (sSNR)
an estimate of the noise level (σF) at the fundamental frequency is required. σF was taken as the mean magnitude of the Fourier components with frequencies (ƒ) greater than the stimulus frequency (F), assuming white noise and no artifactual high-frequency signals (17). The delay in the cerebrovascular response was calculated from the phase angle of the complex FFT data at the fundamental frequency of the stimulus, which was converted into a delay in seconds by dividing by 2πF. It has been shown that at high sSNR the standard deviation of the phase measurement, σϕ, can be approximated as (17):
Monte Carlo simulations of the experiment were performed to test the accuracy of Eq. 3 for the particular experimental protocol used here. Ten cycles of a sine wave with zero phase, a frequency of 1/60 Hz, an amplitude of 1, and sampled at 2.5-s temporal resolution were simulated. Gaussian random noise was added to the sine wave in the time domain, with a standard deviation ranging from 0.3 to 0.01. The generated time-course was then analyzed following the Fourier analysis procedures described above, allowing the phase of the signal to be estimated and the sSNR to be calculated using Eq. 2. A total of 10,000 repetitions were performed, and the mean spectral domain SNR, and mean and standard deviation of the measured phase were calculated.
Region of interest (ROI) analysis was performed on anatomically defined brain regions based on the probabilistic Montreal Neurological Institute (MNI) brain atlas (18). The brain atlas was transformed into the native space of each individual by linear registration via the MPRAGE images using linear image registration (14). Gray matter structures selected for analysis were the whole gray matter, frontal lobe, parietal lobe, occipital lobe, and temporal lobe. Each ROI was initially defined by the maximum probability estimate of the MNI atlas (thresholded at 0) to give relatively large ROIs, allowing for expected anatomical variation between subjects. To control for this variation, the ROIs were then masked using automatically segmented gray matter masks (19) generated from the MPRAGE data of each individual. For each ROI, the CVR delay was calculated for voxels with a sSNR greater than 10, as defined by Eq. 2. The absolute delay time of the cerebrovascular response in the brain is affected by a number of experimental factors including anatomical differences between subjects (transit time from lung to brain) and a delay caused by manual synchronization of the gas blender and scanner console. Therefore, the CVR delay for each ROI was calculated relative to the mean delay over the segmented gray matter mask.
The respiratory challenge proved to be reliable and accurate with peak-to-peak changes in PETCO2 showing good reproducibility across subjects with a standard deviation of 1 mmHg in the requested 10 mmHg increase. A high correlation (R2 = 0.97, mean across subjects) between the measured PETCO2 and the expected stimulus frequency was measured using the Fourier Analysis (Table 1). Figure 1 shows the end-tidal measurements of CO2 and O2, the corresponding MR signal time course of gray matter voxels showing a peak-to-peak signal amplitude change greater than 2%, and the frequency spectrum of this signal time-course for a single representative subject. The MR signal (Fig. 1c) closely followed the change in PETCO2 (Fig. 1a) and the frequency spectrum of the MR signal time-course was dominated by a peak at 1/60 Hz corresponding to the frequency of the CO2 stimulus (Fig. 1d). Following a 1-min baseline period, PETO2 remained reasonably constant (Fig 1b), despite the relatively large changes in PCO2 (Fig. 1a). Because of a technical problem, subject 6160 was only presented with nine cycles of the CO2 stimulus. For this subject, the MR data was converted to percentage signal change and the temporal mean subtracted, then zero-filled to the same number of volumes as the other datasets.
Table 1. End-Tidal Partial Pressure Changes During Respiratory Challenge (Mean ± Standard Deviation and Peak-to-Peak Change) and the Correlation (R2) of These Changes with a Sinusoid of Frequency 1/60 Hz
Subject 6160 was presented with only nine cycles due to a technical problem with the respiratory challenge.
The Monte Carlo simulations of the spectral SNR showed good agreement with the approximate theoretical value (17) (Eq. 2). The simulated standard deviation in the measured phase (indicative of CVR delay) was systematically slightly lower (up to 10%) than the approximate theoretical result (Fig. 2).
CVR amplitude and delay maps for all six subjects are displayed in Figure 3. All images are presented in their raw form without any processing to remove noisy or insignificant voxels and, therefore, the large CVR delays displayed by white matter voxels should be considered in light of the CVR delay error maps (see below). The Fourier analysis results for a single subject are shown in Figure 4. The CVR amplitude maps (which are reactivity maps if divided by the amplitude of the PETCO2 change) show the largest changes in gray matter, with particularly large changes around the large venous vessels such as the sagittal sinus (Fig. 4a). Highest correlation with the stimulus is also found in gray matter (Fig. 4b). To visualize regional variations in CVR delay, Figure 4c maps the CVR delay for each voxel relative to the mean gray matter CVR delay. Figure 4d shows that the error in the CVR delay (estimated from Eq. 3) is greater in the white matter. Figure 5 displays three slices close to the midline resliced in the sagittal plane for the same subject. Large venous vessels, notably the superior sagittal sinus and also the inferior sagittal sinus, can be seen as low-signal features on the T2*-weighted FFE images (Fig. 5a). These draining veins show large CVR amplitudes (Fig. 5b) and large CVR delays (Fig. 5c).
Table 2 lists the mean and standard deviation of the absolute CVR delay measured in regions defined from the MNI atlas (18). Figure 6 plots the median and inter-quartile range of the relative CVR delay, compared with mean gray matter CVR delay, for each brain region of all of the subjects. The frontal and parietal lobes tended to react earlier, whereas the occipital and temporal lobes tended to be delayed with respect to the whole head mean. There were significant differences between the regions (ANOVA < 0.0001) and post hoc comparison showed that the frontal (P < 0.001) and parietal (P = 0.004) lobes reacted earlier than the occipital lobe, and approached significance for the frontal lobe reacting earlier than the parietal lobe (P = 0.067).
Table 2. Absolute CVR Delay in Response to CO2 in Seconds (Mean ± Standard Deviation) for the Segmented Grey Matter Mask and for the Cortical Regions of Interest
12.0 ± 6.0
17.9 ± 4.6
15.9 ± 6.5
12.8 ± 4.9
17.7 ± 6.2
9.5 ± 4.7
14.3 ± 3.4
11.4 ± 6.0
17.6 ± 4.4
15.4 ± 6.1
11.9 ± 4.3
17.2 ± 5.8
9.0 ± 4.5
13.8 ± 3.5
11.9 ± 6.1
18.1 ± 4.3
16.0 ± 6.3
13.5 ± 4.5
17.8 ± 5.6
9.0 ± 3.8
14.4 ± 3.6
12.6 ± 4.5
19.6 ± 5.4
16.5 ± 6.5
14.1 ± 4.6
18.4 ± 5.4
10.2 ± 3.7
15.2 ± 3.6
12.4 ± 4.3
17.9 ± 4.3
15.3 ± 4.9
13.4 ± 4.5
16.9 ± 5.5
10.7 ± 4.9
14.4 ± 2.8
A histogram of the variation in CVR delay is presented in Figure 7a for all voxels with a BOLD amplitude change greater than 2%. This threshold was chosen to reduce the dependence of this mask on SNR variations across the image. The majority of voxels have a delay of less than 30 s and correspond to gray matter voxels, but all subjects also exhibit a small peak beyond 30 s suggesting that the signal in some voxels reacts in antiphase to the majority. Figure 7b highlights these voxels that are generally located within the ventricles and the subarachnoid space.
To test the linearity of the BOLD response to the CO2 stimulus, for each of the five subjects with complete data sets, the PETCO2 time-courses and BOLD signals were averaged across cycles. After manual temporal realignment, these data were plotted against each other (Fig. 8). Linear correlation as measured by the Pearson R2 coefficient had an intersubject mean value of 0.996, significant at P < 0.001. Similar observations were found when the same analysis was performed for the frontal, parietal, occipital, and temporal ROIs.
This study used a novel, sinusoidally modulated change in PETCO2, and a Fourier analysis approach to produce high-resolution maps of both the amplitude and the relative delay of the BOLD CVR response to a CO2 stimulus (CVR amplitude and CVR delay). The CVR delay provides information about the relative arrival times of blood to the cortex, assuming the rate of response of the blood vessels to changes in PCO2 does not differ between regions. The prospective targeting algorithm made it possible to administer a highly repeatable, measurable, sinusoidal PETCO2 stimulus while maintaining iso-oxia within a range that would not affect brain blood flow or the BOLD signal (20). The PETCO2 challenge used in our study was well tolerated by all subjects since the range of PETCO2 of 35 to 45 mmHg is well within the day-to-day experience of healthy people. When setting up the stimulus, it was assumed that the average resting PETCO2 was 40 mmHg. Therefore, each 1-min cycle consists of both hypercapnic (PETCO2 = 45 mmHg) and hypocapnic (PETCO2 = 35 mmHg) periods. Since the resting PETCO2 varies between subjects, the stimulus described here will be more, or less, hypercapnic on an individual basis.
A sinusoidal variation in the PETCO2 and BOLD signals allowed Fourier analysis to be used to generate maps of the CVR amplitude and relative CVR delay. By measuring CVR delay in the spectral domain, it is possible to measure changes that are shorter than the TR, although the minimum detectable change depends on the spectral SNR (sSNR). This was confirmed by simulation and compared with the approximation given in Eq. 3 (17). As the simulation and estimation of the error in measured CVR delay were not identical, it was found that Eq. 3 provided a good, conservative estimate of the error in the data. For the imaging parameters used here (TR = 2.5 s) and the measured gray matter sSNR of approximately 10, it is possible to measure a CVR delay with an error of less than 1 s. The much lower SNR levels measured in the white matter lead to an error in the CVR delay on the order of 10 s. The simulated sSNR was generated assuming that the spectral components at frequencies greater than the stimulus frequency reflected white noise and that the stimulus was the only other signal. In reality, the noise in the frequency domain has a 1/f distribution (pink noise) and contributions from other signals are present, such as aliased respiratory signals and other BOLD-like noise. Since the PETCO2 stimulus is presented at a low-frequency (0.0167 Hz), the pink noise contribution is likely to be greater than that estimated from higher frequencies. Measuring the noise in this way is likely to overestimate sSNR and, hence, somewhat underestimate the error in CVR.
This experiment benefited from the high-spatial resolution and SNR available at 7.0 T, but adequate data were acquired with fewer stimulus cycles (subject 6160) suggesting the technique would also be useful at lower field. Reducing the number of CO2 stimulus cycles would reduce the spectral resolution of the Fourier analysis, but the current spectral resolution is more than adequate to resolve the narrow bandwidth of frequencies represented by the sinusoidal stimulus (Fig. 1d). Our subjects were given visual cues to breathe at 15 min−1 to ensure that there were a sufficient number of breaths per cycle to give a smooth curve of PETCO2 within the cycle, which may also have caused some neuronal activation in the CVR maps (21). Ventilatory pacing, however, is not necessary when using the prospective targeting algorithm and this study could be run unpaced in subjects whose natural breathing frequency was 15 min−1 or greater (22).
There was a large intersubject variation in the apparent absolute mean gray matter CVR delay (Table 2). The apparent absolute CVR delay is the sum of the gas transit time from the exhaled gas to the gas analyzer through 12 m of sample tubing as well as the blood transit time from the lung to the brain. Delays due to tubing delays were minimized and along with the manual synchronization errors are quite constant between studies. This suggests that any remaining delay is due to physiological differences between subjects. Differences in the transit time of blood from the lung to the vascular beds of the gray matter should vary across subjects as this depends on the length of all the vessels involved and the velocity of the blood in those vessels. However, by subtracting the mean gray matter delay, it is possible to measure the relative delays between different brain regions and compare these values between subjects. If only the relative delays are of interest then using Fourier analysis means that temporal alignment of PCO2 and BOLD signal time-courses is not required, making this technique very simple to apply in the clinic.
Relative CVR delay maps were used to determine the differences in delay between brain regions. Gray matter reacted faster than white matter (Fig. 3b), the large draining veins reacted more slowly than the surrounding tissue (as shown in the sagittal sinus in Fig. 5c), and the frontal and parietal lobes and putamen reacted earlier than the occipital lobe (Fig. 6). This delay in response in the posterior circulation is probably due to the longer path for blood flowing from the heart via the posterior cerebral arteries to reach the cortex of the occipital lobe, compared with the more direct course of blood arriving at the parietal lobe via the internal carotid artery.
Bright et al. (21) also recently measured the BOLD CVR delay using ventilation coaching (Cued Deep Breathing, CDB) to induce hypocapnia and breath-holding to induce hypercapnia, and found broadly similar relative delays in the BOLD response across the brain. In the temporal lobe, they found hypocapnia caused a delayed response with respect to the mean, and hypercapnia caused an earlier response with respect to the mean, and this pattern was reversed for the parietal lobe. However, the extent of hypocapnia and hypercapnia caused by CDB or breath-holding could not be accurately controlled, and the changes in PETCO2 and PETO2 were unknown. Studies have shown that the changes in PCO2 during breath-holding are not linear with time, and breath-holding results in a reduction of PO2 of about 50 mmHg (23). The mental effort involved in the respiratory task could also have modulated the blood distribution by activating some brain areas (24, 25). Rostrup et al. (26) also studied the delay in the CVR response using a crude hypercapnic stimulus but found little variation in time of arrival across the cortex.
Regional differences in blood arrival time have also previously been measured using arterial spin labeling (ASL) techniques (27, 28), and the anatomic sequences of delays found with ASL were very similar to the sequence of delays found here with BOLD CVR (Fig. 6). The agreement between ASL and BOLD results suggest that the BOLD CVR delays are actually dominated by the time for the delivery of the CO2 to the tissue rather than variations in vascular reactivity time between different regions of the brain. Nonetheless, the ASL and BOLD CVR methods are fundamentally different; ASL directly measures the transit of blood through the arterial network, whereas BOLD CVR measures the change in venous blood oxygenation caused by a mismatch between blood flow and tissue metabolism. Furthermore, ASL generally studies the behavior of blood in vessels at rest, whereas, by definition, BOLD CVR studies are the vascular reaction to a CO2 stimulus. There may be a differing response across cortical areas, which arises from differences in dilation and oxygen uptake. Therefore, a direct comparison of the two techniques on a voxel-by-voxel basis would be interesting. It is possible that in pathological situations ASL and BOLD CVR techniques could give different and complimentary information about the vascular behavior.
Long CVR delays were observed in some voxels and corresponded to the signal change being in antiphase when compared with the average signal from the brain. These voxels were found to be located in the ventricles and the subarachnoid space. It has previously been shown that the volume of the lateral ventricles changes during the cardiac cycle, with a reduction in volume during peak arterial pressure (29). Similar changes are likely to occur on hypercapnia, driving CSF flow, and thus inflow artifacts that are correlated with the hypercapnic challenge. There will also be variable partial volume effects at the brain/CSF interface so that voxels bordering the CSF spaces would change from containing mainly CSF (higher signal) to containing mainly brain tissue (lower signal).
In contrast to the CVR delay maps, ROI analysis of the CVR amplitude maps showed very little variation between different regions of the brain in healthy volunteers, although large veins tended to show very large BOLD signal changes (Fig. 5). The signal change in large venous vessels is much larger than the change observed in standard fMRI experiments, probably because in standard fMRI, the CBF increases are local rather than global, and so surrounding areas of cortex continue to supply the draining veins with the resting level of deoxyhemoglobin, thus, limiting the BOLD signal change in large vessels. It is interesting to note (Fig. 8) that the change in BOLD signal is linear within the range of PETCO2 values experienced in this study. This linearity has also been observed using small stable PETCO2 steps over a similar range (12).
Maps of the CVR amplitude response have previously been shown to be useful for the diagnosis of cerebrovascular disease (3, 30). Information about the temporal sequence of the blood-flow response across the brain from the CVR delay data will also aid understanding of the underlying pathophysiology of cerebrovascular disease.
It has been shown that a sinusoidally varying PETCO2 stimulus can be used to produce high-resolution CVR maps. In addition, when combined with Fourier analysis this stimulus also enables the timing of blood arrival, or vascular response, in different regions of the brain to be determined.