Original Article
A novel approach to measure local cerebral haematocrit using MRI
Journal of Cerebral Blood Flow & Metabolism 2016, Vol. 36(4) 768–780 ! Author(s) 2015 Reprints and permissions: sagepub.co.uk/journalsPermissions.nav DOI: 10.1177/0271678X15606143 jcbfm.sagepub.com
Fernando Calamante1,2,3, Andre´ Ahlgren4, Matthias JP van Osch5 and Linda Knutsson4
Abstract The percentage blood volume occupied by red blood cells is known as haematocrit. While it is straightforward to measure haematocrit in large arteries, it is very challenging to do it in microvasculature (cerebral haematocrit). Currently, this can only be done using invasive methods (e.g. PET), but their use is very limited. Local variations in cerebral haematocrit have been reported in various brain abnormalities (e.g. stroke, tumours). We propose a new approach to image cerebral haematocrit using MRI, which relies on combining data from two measurements: one that provides haematocrit-weighted and other one haematocrit-independent values of the same parameter, thus providing an easily obtainable measurement of this important physiological parameter. Four different implementations are described, with one illustrated as proof-of-concept using data from healthy subjects. Cerebral haematocrit measurements were found to be in general agreement with literature values from invasive techniques (e.g. cerebral/arterial ratios of 0.88 and 0.86 for sub-cortical and cortical regions), and showed good test–retest reproducibility (e.g. coefficient-of-variation: 15% and 13% for those regions). The method was also able to detect statistically significant haematocrit gender differences in cortical regions (p < 0.01). The proposed MRI technique should have important applications in various neurological diseases, such as in stroke and brain tumours.
Keywords Haematocrit, perfusion MRI, arterial spin labelling, cerebral blood flow, cerebral blood volume Received 12 April 2015; Revised 14 August 2015; Accepted 14 August 2015
Introduction Red blood cells (or erythrocytes) carry oxygen from the lungs to the tissues and transport carbon dioxide back to the lungs. The percentage of the total blood volume occupied by red blood cells is known in physiology as the haematocrit (Hct). While it is straightforward to measure the haematocrit in large arteries (e.g. by centrifuging a blood sample), it is much more challenging to obtain it in the cerebral microvasculature. As shown by many studies,1–7 the cerebral haematocrit differs from the large vessel haematocrit (with a smaller value in the microvasculature, e.g. the ‘classical’ arterial/tissue haematocrit ratio value of 0.85),1,2,7 due to differences in velocity of blood plasma and the red blood cells residing in it (an effect known as the Fahraeus effect).2 Currently, only invasive methods have been proposed to measure the small vessel or cerebral haematocrit (Hctbrain or Hcttissue, i.e. haematocrit values of blood within small arterioles, venules and
capillaries of the brain). Available approaches are based upon positron emission tomography (PET), single photon emission computer tomography (SPECT), and autoradiography,1,2,8,9 but their use is very limited due to their invasive nature and the poor 1 The Florey Institute of Neuroscience and Mental Health, Melbourne, Australia 2 The Florey Department of Neuroscience and Mental Health, University of Melbourne, Melbourne, Australia 3 Department of Medicine, Austin Health and Northern Health, University of Melbourne, Australia 4 Department of Medical Radiation Physics, Lund University, Lund, Sweden 5 C.J. Gorter Center for high field MRI, Department of Radiology, LUMC, Leiden, Netherlands
Corresponding author: Fernando Calamante, Florey Institute of Neuroscience and Mental Health, Melbourne Brain Centre, 245 Burgundy Street, Heidelberg, Victoria 3084, Australia. Email: [email protected]
Calamante et al. availability of suitable radiotracers. The limited number of prior cerebral Hct mapping studies have, however, shown that the grey matter–white matter contrast is much lower than that seen in cerebral blood flow (CBF) and cerebral blood volume (CBV) maps,1,2,4,5,7 and there have been limited reports of higher Hcttissue values in basal ganglia5 and no right– left hemispheric asymmetry3–6 (although, one report2 did show lower Hcttissue values in the left hemisphere, in a sample of 10 healthy right-handed subjects). Cerebral haematocrit changes have been shown to directly influence the resistance of the microcirculation, and local variations have been reported in various brain abnormalities,3–7,10,11 such as increased values in acute stroke,3,6 decreased values in chronic arterial occlusion,4,5 decreased values in the contralateral cerebellar cortex in crossed cerebellar diaschisis,10 both increased and decreased values in brain tumours (likely due to the wide range of abnormal vasculature that can be found in different tumours),7 as well as reduced values during hypercarbia.2 Although haematocrit changes are known to affect rheological properties of blood and that rheological disorders within the microcirculation are known to play a significant role in various diseases, the clinical importance of these effects has not yet been fully established. This gap of knowledge can be directly attributed to the absence of easily applied measurement techniques, thereby limiting the clinical research on this topic. In addition to the clinical potential of a cerebral haematocrit imaging method, knowledge on small vessel haematocrit is also important for several perfusion imaging methods that aim to quantify cerebral blood flow (CBF).12,13 For example, assumptions on the cerebral haematocrit are necessary in cerebral perfusion measurements using MRI and computed tomography (CT), since the extracellular contrast agents that are applied in these techniques are transported within the blood plasma making these techniques sensitive to plasma flow rather than total blood flow. In practice, any technique that requires knowledge of local cerebral haematocrit levels, therefore, commonly relies on assuming a single uniform value (taken from published literature, such as Hct in capillaries ¼ 0.25)14 for the whole brain, regardless of the tissue type or particular patient; this can naturally lead to erroneous measurements. A more detailed characterisation of tissue haematocrit values could be used to better inform DSC-MRI and perfusion CT quantification (e.g. via the use of more detailed look-up tables rather than a uniform value for every voxel and every subject). In this study, we propose a novel approach to image local cerebral haematocrit levels using MRI. The proposed method relies on combining haemodynamic data
769 obtained from two MRI measurements: one that provides haematocrit-weighted values, and another one that provides haematocrit-independent values of the same parameter. By combining these two measurements, it is possible to isolate the local cerebral haematocrit information, thus providing an easily obtainable and minimally invasive measurement of this important physiological parameter.
Material and methods Because MRI offers many different approaches to probe cerebral perfusion, there are various ways to combine MRI measurements to measure cerebral haematocrit. We describe here a particular implementation for which we also demonstrate, as proof-ofconcept, in vivo results from a group of subjects; we refer to this implementation as Case 1 hereafter. Please refer to Appendix 1 for three further alternative implementations. Case 1 implementation is based on combining data from (i) a dynamic susceptibility contrast (DSC) MRI study in absolute units and (ii) an arterial spin labelling (ASL) study. It assumes that the DSC-MRI data can provide measurements in absolute units. This, for example, requires that the arterial input function (AIF) is measured in absolute units.15 This can be achieved, for example, by acquiring the DSC-MRI data using the method proposed by Kellner et al.,16 or by correcting the partial-volume-effect using postprocessing methods, such as those proposed by van Osch et al.17 and Knutsson et al.18 In this case, a deconvolution analysis14 of the DSCMRI data provides a Hct-weighted CBF (CBFHct) in absolute units, i.e. CBFDSC–MRI¼CBFHct, which can be explicitly written as14 CBFDSCMRI ¼ CBFHct ¼
CBF kHct
ð1Þ
where kHct ¼
Vplasma ½AIF 1 Hctart ¼ Vplasma ½tissue 1 Hcttissue
ð2Þ
and Vplasma[] is the relative plasma volume. It should be noted that, in most DSC-MRI studies, a given value for the proportionally constant kHct is assumed (either by assuming literature values for the Hct levels in the tissue and the artery, or simply by setting it to 1) and, therefore, the variations in Hct are most often disregarded in DSC-MRI studies. In fact, the Hct-weighting is usually considered a nuisance in DSC-MRI, but its presence is central to the method proposed here.
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From a complementary ASL measurement, which is known to provide absolute CBF measurements (i.e. CBFASL¼CBF), one can calculate kHct as the CBF ratio kHct ¼
CBFASL CBFHct
ð3Þ
Therefore, we get the local cerebral Hct as Hcttissue ¼ 1
1 Hctart CBFHct ¼1 kHct CBFASL
ð1 Hctart Þ
ð4Þ
where Hctart is the haematocrit measured in a large artery. In summary, from a DSC-MRI study in absolute units, combined with an ASL study and an arterial Hct value (such as that measured from a blood sample; or from an assumed literature value, if a blood sample is not available), the proposed method provides a means to calculate a map of local cerebral Hct (using equation (4)). Three alternative possible implementations of the Hct mapping method are described in Appendix 1, which are based on various types of CBV measurements – see Appendix 1 for theoretical formulas and details.
MRI experiments As illustration of the Case 1 implementation, cerebral haematocrit measurements were carried out in a group of healthy subjects. Furthermore, to investigate the reproducibility, the subjects were scanned on two occasions. Twenty healthy subjects (age range: 24–84, 10 females) were scanned twice each (with a time interval of 7–20 days between investigations) on a 3T MRI scanner (Philips Achieva, Philips Medical Systems, Best, The Netherlands); ASL and DSC-MRI data were acquired in each session. The project was approved by the Lund University regional ethical review board (following the ethical guidelines of the Helsinki Declaration of 1975 (and as revised in 1983)), and each subject gave written confirmed consent to participate in the study. All brain scans were considered normal by an experienced neurologist. Four ASL scans (from a total of 3 subjects) suffered from incomplete labelling of blood water (manifested as complete loss of ASL signal in a given vascular territory) and these studies were omitted from this proof-ofconcept study. Dynamic susceptibility contrast MRI. To obtain quantitative CBF measurements by DSC-MRI, the so-called
prebolus method was applied in which a separate injection of contrast agent allows for a quantitative measurement of the venous output function (VOF) by adjusting the MRI sequence parameters.18 For proper planning of this DSC-MRI pre-bolus experiment, a sagittal phase contrast angiography T1-FFE scan was performed (relevant parameters: 300 300 mm2 fieldof-view, 256 256 matrix, 50 mm slice thickness, 1.17 1.17 mm2 in plane resolution, 15 flip angle, TE/TR ¼ 5.68/20 ms, and two averages). In order to achieve similar planning for both experiments, the planning from the first experiment was saved and thereafter used for the planning of the second experiment. The planning of the actual DSC-MRI scan was performed using the Philips automatic planning tool SmartExam in order to minimise user interaction. A pre-bolus of contrast agent (Dotarem, Guerbet, Paris, France) was administered (0.02 mmol/kg, injection rate 5 ml/s) and a segmented echo planar imaging (EPI) was used to track the pre-bolus passage through the sagittal sinus in one single slice using a temporal resolution of 0.81 s. The imaging parameters were as follows: 220 220 mm2 field-of-view, 128 128 matrix, 5 mm slice thickness, 1.72 1.72 mm2 in-plane resolution, EPI factor 7, 22 flip angle, TE/TR ¼ 15/135 ms, acquisition time 98 s. In-plane PVE can be considered minimal given the much larger diameter of the sagittal sinus (mean diameter ranges from 4.3mm in the mid-anterior frontal region to 9.9mm in the midoccipital region)19; through-plane PVE was minimised by choosing the slice orientation approximately perpendicular to the sagittal sinus, in a section where this vein has a relatively large diameter. After the pre-bolus scan, a normal single dose of the contrast agent (0.1 mmol/ kg) was administered at an injection rate of 5 ml/s, and the actual DSC-MRI experiment was performed using a single-shot gradient-echo EPI with the following imaging parameters: 220 220 mm2 field-of-view, 128 128 matrix, 5 mm slice thickness, 1.72 1.72 mm2 in-plane resolution, 20 slices, 60 flip angle, TE/TR ¼ 29/1243 ms, acquisition time 91 s. Each bolus injection was followed by a 20 ml saline flush injected at the same rate as the contrast agent. Arterial spin labeling. ASL was carried out using a pseudo-continuous ASL (pCASL) sequence, which included a 1600 ms post-labelling delay to minimize sensitivity to transit time, and background suppression inversion pulses at 1710 and 2860 ms after a prelabelling saturation pulse to increase the signal-tonoise ratio in the perfusion weighted images. The image read-out was performed using single-shot EPI in combination with parallel imaging (96 96 matrix, 5 mm slice thickness, 1 mm slice gap, 2.29 2.29 mm2 reconstructed in-plane resolution, 16 slices, EPI factor
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37, 90 flip angle, TE/TR ¼ 14/4000 ms, 1650 ms label duration, 20 mm label gap, 30 repetitions, and SPIR fat suppression, total acquisition time 240 s). A reference scan for M0 calibration was performed using a sequence identical to the pCASL, except that labelling and background suppression were turned off, TR ¼ 10 s, and the number of repetitions was 4, total acquisition time 40 s.
where i is the fractional volume water content of compartment i, T2i is the effective transverse relaxation time of compartment i, and is the brain density in g/ml. Quantification was done using a model resembling the recommendations of the recent ASL consensus article23 M ¼ 2M0,a f T1a ð1 e=T1a Þew=T1a
Post-processing Dynamic susceptibility contrast MRI. The AIF was measured by using a semi-automatic method, as previously described in Knutsson et al.18 Absolute CBF was then obtained by scaling the measured AIF by the time integral of the VOF (the pre-bolus VOF area was multiplied by five, i.e. 0.1/0.02, to obtain the same VOF area as would have been observed for a normal dose), measured in the sagittal sinus during the pre-bolus experiment.18 Deconvolution was done using the block-circulant singular value decomposition method,20 to obtain a Hct-weighted CBF estimate in ml/100g/min14 R1 max RðtÞ 0 CðtÞdt R1 CBFHct ¼ 1 R 1R R ð t Þdt 0 0 Ca ðtÞdt
ð5Þ
where R(t) is the tissue residue function, and is the brain parenchyma mass density (set to 1.04 g/ml). Arterial spin labelling. The pCASL signal depends primarily on the CBF, the efficiency with which the inflowing blood is labelled, the rate at which the label decays, and the sensitivity of the scanner to the label. The labelling efficiency was estimated as the combined effects of inversion efficiency at the labelling site and the effective spoiling of labelled spins due to the background suppression pulses. This total labelling efficiency was assumed to be 70%.21 The arterial blood was assumed to have a longitudinal relaxation time (T1a ) of 1.65 s.22 The equilibrium blood magnetization (M0,a ) was estimated by using the intensity of white matter (WM) as a calibration standard. For each subject, a binary WM mask was automatically produced by thresholding the segmented WM tissue probability map at 95%, and the average intensity in the reference image within this region was calculated. This mean WM intensity was used as a measure of the equilibrium magnetization of WM, M0,WM . Correction for water content and transverse relaxation effects (compared to arterial blood) yield the M0,a estimation according to
M0,a ¼ M0,WM
a eTE=T2a TE=T 2WM WM e
ð6Þ
ð7Þ
where is the total labeling efficiency, f is perfusion, is the labeling duration, and w is the post-labelling delay. The post-labelling delay is unique for every slice according to w ¼ wps þ ðnslice 0:5Þ tro , where wps is the preset post-labelling delay, nslice is the slice number and tro is the slice read-out time. Perfusion values were estimated using the model stated above, and multiplied by a factor of 6000 to obtain values in ml/100g/min. Parameters , a , WM , T2a , and T2WM were taken from the literature as 1.04 g/ml,14 87%,24 73%,24 43.6 ms,25 and 44.7 ms,25 respectively. Hct mapping. Haematocrit-weighted CBF (from DSC-MRI) and Hct-independent CBF (from ASL) were calculated as described above. All CBF-maps were nonlinearly co-registered (spatially normalized) to the MNI152 template brain (ICBM, NIH P-20 project) using SPM8 (http://www.fil.ion.ucl.ac.uk/spm/ software/spm8/). Local cerebral haematocrit was estimated using Case 1, according to equation (4). Since no measurement of blood haematocrit was available, the arterial haematocrit was set to 0.45.26 Therefore, it should be noted that any results reported here of Hcttissue in absolute values have an underlying assumption on the arterial haematocrit (please refer to Discussion for details on the limitations of the current study). Furthermore, to investigate the sensitivity to the assumed Hctart values, the analysis was repeated for values ranging from 0.3 to 0.6. Finally, to investigate the gender differences in cerebral haematocrit, Hct ratio values were calculated for male and female subjects separately. Given the known gender differences in arterial haematocrit,26 the gender analysis was also repeated, but assuming Hctart ¼ 0.45 for the male subjects and 0.40 for females. To characterize the representative cerebral haematocrit values in normal healthy subjects, the normalized CBF maps were used to calculate the population average Hcttissue map. It should be noted, however, that artefacts in either DSC-MRI or pCASL will introduce unrealistic haematocrit values (e.g. negative or larger than 100%). In particular, both underestimation of white matter perfusion in ASL, overestimation of perfusion close to large vessels in DSC-MRI, and CSF areas were found to lead to severely underestimated haematocrit values (see Figure 1). The quantitative
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Figure 1. Single subject results. Top row: axial CBFHct maps calculated using DSC-MRI. Middle row: axial CBFASL maps calculated using ASL. Bottom row: axial cerebral Hct calculated using the method described in Case 1 implementation. A value of Hctart ¼ 0.45 was assumed for the arterial Hct. Arrows indicate example areas with severely underestimated Hct due to large vessel artefacts in DSC-MRI and underestimated white matter CBF in ASL, respectively.
analysis was therefore restricted to manually defined regions of interest in cortical matter and subcortical structures. Furthermore, voxels with negative Hcttissue values (for any Hctart case) were excluded from the analysis. The total number of voxels excluded from the analysis was 50% of the intracranial voxels (see Discussion section for possible ways to minimise this number by improved white matter measurements and reduced microvasculature contamination). To assess the test–retest reproducibility, the data from the two scans (for the 17 subjects with two successful ASL scans) were displayed in a Bland–Altman plot (difference values vs. mean values), characterised by its bias (mean difference) and limit-of-agreement (mean 1.96 standard deviation). Another commonly used and related measure, the repeatability coefficient (CR¼ˇ2 1.96 Sw, where Sw is the within-subject standard deviation), was also calculated as a measure of test-retest reliability. Finally, the coefficient of variation (CoV), defined as the standard deviation divided by the mean Hcttissue, was also computed.
Results Figure 1 shows the CBF maps calculated using DSCMRI and ASL on an illustrative subject. The figure also includes the computed Hcttissue maps using equation (4). Arrows in this figure illustrate regions with severely underestimated Hct values, corresponding to large vessel artifacts in the DSC-MRI map (top row), and areas with spuriously low CBF in the ASL map (middle row); both cases lead to very low Hct estimates
(bottom row). Figure 2 shows the corresponding population average results, including the average CBF maps (calculated using both DSC-MRI and ASL) and the average Hcttissue maps. Figure 2 shows the population average results, including the average CBF maps (calculated using both DSC-MRI and ASL) and the average Hcttissue maps. To get a more comprehensive visualization of the cerebral Hct results, Figure 3 shows the population average Hcttissue maps in MNI space, in three orthogonal projections. Supplementary Figure 1 shows the manually defined cortical and subcortical regions used for the quantitative analysis. The mean ( standard deviation) CBFDSC–MRI values were 72.6 21.5 and 76.8 13.0 ml/100g/min for the sub-cortical and cortical regions, respectively; the corresponding values for CBFASL were 65.7 16.8 and 69.3 11.1 ml/100g/min. Assuming a Hctart¼0.45, the mean ( standard deviation) cerebral Hct values were 0.395 0.060 and 0.387 0.040 for the sub-cortical and cortical regions, respectively (corresponding to mean Hcttissue/Hctart ratios of 0.88 and 0.86, respectively); this regional difference in Hct values did not, however, reach statistical significance. To characterise the dependency of the cerebral Hct on the assumed arterial Hct values, Figure 4 shows the cerebral-to-arterial Hct ratio in subcortical and cortical regions, as a function of Hctart . The figure also shows the overall variability (characterised by the standard deviation of the ratio, calculated over all 36 individual measurements) from both regions.
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Figure 2. Population average results. Top row: axial CBFHct maps calculated using DSC-MRI. Middle row: axial CBFASL maps calculated using ASL. Bottom row: axial cerebral Hct calculated using the method described in Case 1 implementation. A value of Hctart ¼ 0.45 was assumed for the arterial Hct.
Figure 3. Population average results for the cerebral Hct in MNI space, in axial (top), coronal (middle), and sagittal (bottom) projections. The maps are shown at 2 mm isotropic resolution. A value of Hctart ¼ 0.45 was assumed for the arterial Hct.
There was no statistical significant difference between the Hct measurements of the two scanning sessions (p > 0.2, paired two-sided Wilcoxon signed rank test). Figure 5 shows the results of the reproducibility analysis in form of Bland–Altman plots. Table 1 lists the bias (i.e. mean difference), the magnitude for the limits-of-agreement (i.e. 2 1.96 standard deviation), the CR, and the CoV values for the subcortical and cortical structures. This table also shows the corresponding values for the underlying perfusion MRI data used to calculate Hcttissue. Figure 6 shows the results for the gender differences for both cortical and subcortical regions in form of box-and-whisker plots, based on an assumed Hctart ¼ 0.45. The cerebral Hct ratio (relative
to Hctart) was higher in males. Based on a Mann– Whitney U-test, this gender difference was statistically significant in cortical regions (p < 0.01), but did not reach significance in subcortical structures. The corresponding results for the case of an assumed gender-dependent Hctart (0.45 for males and 0.40 for females)26 are shown in Supplementary Figure 2. Given the complexities of interpreting Hct ratio differences when using a non-uniform Hctart, Supplementary Figure 3 includes the Hcttissue results separately. For the ratio results, significant differences were detected in the cortex (p < 0.01), while significant Hcttissue differences were detected for both cortical (p < 0.0001) and subcortical (p < 0.05) regions.
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Figure 4. Cerebral-to-arterial haematocrit ratio as a function of Hctart for the subcortical region (grey line) and cortical region (black line). Triangles indicate the standard deviation of the ratio. The classical literature ratio value1,2,7 of 0.85 is shown as dashed line.
Discussion A new approach to image cerebral haematocrit using MRI was proposed. The method relies on combining MRI data from two separate measurements, one that provides Hct-weighted values and another that provides corresponding Hct-independent values. Various possible implementations of the method were described and, as proof-of-concept, in vivo data from a group of healthy subjects were presented for the particular implementation that relies on data from DSC-MRI and ASL (Case 1).
Comparison to literature
Figure 5. Reproducibility analysis shown by the Bland–Altman plot. The data from the subcortical region are shown by the blue circles, the data from the cortical region in red triangles. The solid lines indicate the bias, the dashed lines the limits of agreement.
The cerebral Hct maps are visually consistent with previously reported results using invasive methods in healthy subjects,1,2 including a much lower grey matter–white matter contrast than that seen in our CBF maps calculated from DSC-MRI and ASL. There was also a trend for an increased Hcttissue values in subcortical structures, consistent with a small increase detected in a previous report,5 although this did not reach significance in our data. As expected
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Table 1. Test–retest reproducibility. Subcortical region
Hcttissue CBFDSC-MRI CBFASL
Cortical region
Bias
LoA
CR
CoV
Bias
LoA
CR
CoV
0.007 6.7 6.3
0.230 44.6 32.2
0.112 25.3 19.9
15 16 12
0.018 0.9 2.9
0.204 58.6 41.1
0.105 28.5 20.7
13 19 15
LoA: limit-of-agreement; CR: repeatability coefficient; CoV: coefficient of variation (in %). The units for the bias, LoA and CR are in ml/100g/min for the CBF measurements, and are unitless for Hcttissue.
Figure 6. Characterisation of gender differences for Hcttissue/Hctart ratio for cortical (right) and subcortical (left) regions. A value of Hctart ¼ 0.45 was assumed for the arterial Hct. The line inside each box is the median, the edges of each box are the first and third quartiles, the whiskers stretch out to the most extreme values (excluding outliers), and the crosses shows automatically identified outliers. Significant gender differences were found in cortical regions, with the corresponding p-value indicated in the plot. F: female; M: male.
from theory (e.g. see equation (4)), the quantitative results for both Hcttissue and Hcttissue/Hctart are dependent on the assumed arterial Hct value (Note: for the current study, no blood samples were available). Nevertheless, the results from Figure 4 show that the cerebral-to-arterial Hct ratio is, in general, consistent with literature values, including with the ‘classical’ 0.85 haematocrit ratio value.1,2,7 Note, however, that there is no overall consensus regarding the exact value for this ratio, with some studies reporting lower ratios (mean values between 0.69 and 0.76)1,2,6,7 while other higher ratios (mean values between 0.88 and 0.93).4,5
Reproducibility The method was shown to have reasonably good test– retest reproducibility (CoV15%). Despite the method
relying on relatively noisy perfusion MRI measurements (for the Case 1 reported here), as well as the results shown here based on data not specifically optimised for Hct mapping, the Hct reproducibility was comparable to that of the underlying perfusion MRI data (CoV12–19%), suggesting that the proposed formalism does not lead to a major noise amplification. In fact, the CoV for Hct mapping was far better than that predicted solely from propagation of errors (see Appendix 1), where the CoVs from the two CBF methods would be expected to add up to lead to a larger CoV for Hct mapping. This, however, only accounts for the variance of the data associated with Gaussian random noise, and not of other sources of variance in the data. For example, if there are any global effects (e.g. some subjects in the group have much higher/ lower CBF values than the typical average values – not an uncommon situation), this would be reflected
776 both in the DSC-MRI and ASL CBF measurements (both CBF measurements can be considered, to some extent, correlated). While this would increase their variance, the situation is different for Hct mapping: this method is based on the CBF ratio (see equation (4)), and therefore this effect will tend to cancel out, thus decreasing the variance. The same situation applies to the other implementations (Cases 2–4), given that they are based on a CBV ratio. Taking together, all these findings suggest that Hcttissue measurements are actually much more stable than could have been initially expected purely from propagation of errors, and they have a precision similar to that of the input CBF or CBV maps.
Gender effects Gender differences in Hct ratio were found in cortical regions, which remain significant regardless of whether the Hctart values were assumed to be gender dependent (as suggested by literature)26 or uniform, suggesting that the Hcttissue gender difference was not due to the assumed Hctart values. Gender differences were also observed in subcortical structures, but these did only reach significance when measured as Hcttissue and assuming a gender-dependent Hctart value. This highlights that subject-specific Hctart measurements should be carried out, and that the current gender results should be taken with caution given the assumptions involved. While gender differences in arterial haematocrit are well documented,26 the differences within the brain are not well characterised. The techniques introduced here could open up the way to future studies to further our understanding of the regional, gender, and age variations in cerebral Hct. Given that decreased Hct are associated with increased CBF,27,28 non-invasive cerebral Hct mapping methods should prove valuable for clinical and neuroscience investigations.
Practical considerations A number of practical issues need to be taken in to account. First, the method relies on accurate registration between two MRI measurements, e.g. ASL and DSC-MRI data for Case 1. This not only includes rigid body registration but, ideally, it should include also matching for susceptibility-related distortions. Any mismatch between these data will lead to errors in Hct mapping. Therefore, the use of the same acquisition sequence or the use of distortion correction methods29 is preferable to avoid this source of error. In particular, the same bandwidth-per-pixel for all acquisitions (e.g. the same echo-train inter-echo spacing) should be selected in order to ensure the same level of
Journal of Cerebral Blood Flow & Metabolism 36(4) geometric distortion. Alternatively, one could consider the use of distortion correction based on, for example, the acquisition of a separate B0-map. Second, for a more robust quantification in cortical structures, the macrovascular contributions should be minimised. For DSC-MRI, this could be achieved by using a spin-echo based acquisition14 or by removing the macrovascular contribution during post-processing.30 Similarly, for ASL data, the macrovascular contribution can be minimised by using long post-labelling delays and/or using crusher gradients,14 or by postprocessing methods.31 Third, the other CBV-based implementations (see Appendix 1) are not affected by deconvolution-related errors (e.g. noise-sensitivity, errors associated with the regularization, bolus dispersion, sampling-related issues, etc). It could therefore be expected that using one of these other cases may provide more stable Hct measurements. Fourth, errors related to PVEs in the underlying MRI images will translate to PVE-related errors in the calculated Hcttissue maps. The degree of PVE will depend on the particular implementation used. For example, Case 1 can be subject to considerable PVEs, given that ASL is limited to a relatively coarse spatial resolution. In contrast, the implementation described in Case 4 (see Appendix 1) has the greatest potential to minimise PVE, given that it does not rely on dynamic measurements and it is, therefore, more amenable to higher resolution acquisition. The use of the same spatial resolution for all MRI data involved is also preferable, to avoid introducing a differential PVE effect between the various maps used for Hcttissue quantification. This was, however, a limitation of the current study, which was based on retrospective data, and not on a protocol specifically designed for haematocrit mapping. Partial volume contamination could be minimised, in principle, using post-processing methods. For example, various PVE correction methods have been proposed for ASL.32,33 However, similar PVE correction methods are yet to be developed for DSC-MRI. A further source of error in ASL is the coil sensitivity, which can introduce spatial intensity variations across the ASL results. This can be minimised by explicitly calculating the coil sensitivity profile, or by using a map as the calibration reference during quantitation.23 ASL can be also influenced by errors in the assumed parameters in the ASL quantification model (e.g. k, T1a, T2a ). It should be also noted that ASL quantification is not necessarily strictly Hct-independent, given the potential influence of Hcttissue on the assumed values for lambda and relaxation times. It should be emphasised that errors in the underlying MRI measurements could have important consequence
Calamante et al. for the accuracy of Hct mapping when studying certain patient groups. For example, ASL applications to stroke and severe vascular disease are known to be highly sensitive to artefacts due to prolonged transit delays.14 These errors will directly translate into errors on the cerebral Hct maps. For such clinical applications, the use of velocity-selective ASL34 may provide a better ASL variant for the implementation of Case 1, given its known reduced transit delay sensitivity. Similarly, DSC-MRI perfusion measurements in these patient groups can be subject to bolus dispersion errors35; the use of local AIF36 may provide a solution to minimise this source of error. A further example of possible errors relates to applications in tumours, where contrast leakage effects must be taken into account in DSC-MRI quantification.12 In the current study, we limited the quantitative analysis to grey matter structures. It should be noted that quantification of cerebral Hct in white matter is currently relatively unreliable. This is primarily due to the difficulties of quantifying CBF in white matter using ASL.21 One of the CBV-based methods (especially Case 4 with CBVT1) should allow a better prospect for measuring white matter Hct. In fact, the Case 4 implementation, when combined with a blood pool contrast agent (e.g. gadofosveset),37 may open up the possibility of mapping cerebral haematocrit with high spatial resolution and high signal-tonoise ratio. We also had to assume a value for the arterial Hct, since no blood samples were available. Individual arterial Hct measurements should be of great benefit to properly account for the inter-subject variability in this parameter. For example, different arterial Hct values are seen in neonates and young children, as well as in some patient groups (e.g. patients with sickle-cell disease).
Future studies A limitation of the current study is that data for only one of the implementations (Case 1) was available. Further work is required to compare the various implementations described here, and to determine their relative accuracy and precision, as well as their limitations. Further work is also required to optimise the acquisition protocols, particularly aimed at measuring cerebral Hct. A validation of the proposed method could be achieved by comparing the measurements from this MRI approach to those obtained using more traditional invasive methods, such as PET or SPECT measurements in humans subjects, or quantitative autoradiography in animal experiments. However, such a validation is beyond the scope of this study.
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Conclusion A novel non-invasive approach to measure cerebral haematocrit using MRI was proposed. The method relies on combining measurements from two MRI techniques, one that provides Hct-dependent and another one with Hct-independent values. As proof-of-concept, the method was illustrated using DSC-MRI and ASL data on a group of healthy subjects, and was shown to measure cerebral Hct in general agreement with literature values, with good test–retest reproducibility. The proposed MRI method could have important applications in various neurological diseases, such as stroke and tumours. Funding We are grateful to the National Health and Medical Research Council (NHMRC) of Australia, the Australian Research Council (ARC), the Victorian Government’s Operational Infrastructure Support Grant, and the Swedish Research Council [grant nos 13514 and 2010-4454] for their support.
Acknowledgements We also want to thank Emelie Lindgren, Dr Ylva Surova and Dr Danielle van Westen for assistance when acquiring the data.
Declaration of conflicting interests The author(s) declared the following potential conflicts of interest with respect to the research, authorship, and/or publication of this article: FC, MJPvO and LK: patent application of this methodology.
Authors’ contributions FC: study conception and design, data interpretation, drafting the article, critically revised draft for important intellectual content, and final approval of the version to be published. AA: data acquisition, analysis of data, interpretation of results, drafting the article, critically revised draft for important intellectual content, and final approval of the version to be published. MJPvO: study conception and design, data interpretation, drafting the article, critically revised draft for important intellectual content, and final approval of the version to be published. LK: study conception and design, data acquisition and interpretation, drafting the article, critically revised draft for important intellectual content, and final approval of the version to be published.
Supplementary Material Supplementary material for this paper can be found at http:// jcbfm.sagepub.com/content/by/supplemental-data.
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Appendix 1. Theoretical extensions Three alternative possible implementations of the Hct mapping method are described below.
Case 2: Implementation based on combining data from (i) a DSC-MRI study in absolute units and (ii) a ‘Bookend’-type study This implementation is similar to that in Case 1, but it is based on CBV measurements rather than CBF. It is based on combing a Hct-weighted CBV map (from DSC-MRI) and a Hct-independent CBV map (from a ‘Bookend’ type of acquisition,38 i.e. T1 measurements before and after the contrast agent injection). It assumes that DSC-MRI provides measurements in absolute units (see Case 1 for ways to achieve this). It further assumes that the DSC-MRI acquisition protocol included a ‘Bookend’ type of acquisition.38 Similar to the situation for Case 1, a DSC-MRI data set that can provide absolute units will give a Hctweighted CBV (CBVHct) in absolute units, i.e. CBVDSC14 MRI¼CBVHct, which can be explicitly written as
CBVDSCMRI
h i Þ AUC Rð2,tissue ðtÞ CBV h i ¼ CBVHct ¼ ¼ ðÞ kHct AUC R2,AIF ðtÞ ð8Þ
where AUC[] is the area under the curve.
From the T1 data of the ‘Bookend’ type acquisition,38 it is possible to calculate blood volume, CBVT1. Note that this CBV is in absolute units and not Hct-dependent, i.e. CBVT1¼CBV. This is because plasma and Hct are in fast exchange for T1 measurements,39 which makes CBV measurements from T1 Hct-independent. Therefore, combining equations (8) and (2) leads to
Hcttissue
1 Hctart CBVHct ¼1 ¼1 kHct CBVT1 ð1 Hctart Þ
ð9Þ
Note: In principle, it would be simpler and faster to use the steady-state from the DSC-MRI study (i.e. the contrast concentration plateau after the bolus passage) to calculate the extra required measurement of total CBV (cf. having to add the T1 measurements). However, T2 is not in fast exchange39 and, therefore, CBV measurements from T2 steady-state are Hct-dependent. In fact, this property is exploited in the approach described in Case 4 below.
Case 3: Implementation based on combining data from (i) a DSC-MRI study in absolute units and (ii) a contrast-agent calibrated vascular-space-occupancy (VASO) study The principles behind this implementation are exactly the same as Case 2, with the exception that the Hct-independent CBV measurement is not obtained from ‘Bookend’ data, but it is rather obtained from a contrast-agent calibrated VASO study.40 The latter was shown to provide absolute values of CBV, i.e. CBVVASO¼CBV. Therefore, similar to Case 2, we can measure local cerebral Hct as follows
Hcttissue ¼ 1
1 Hctart CBVHct ¼1 kHct CBVVASO
ð1 Hctart Þ
ð10Þ
Case 4: Implementation based on combining data from (i) a steady-state T2 -based study (ii) a contrast-agent calibrated VASO study This implementation is similar to Case 3, with the exception that the Hct-weighted CBV map is obtained from a steady-state T2 -based study (i.e. T2
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measurements before and after contrast injection). It assumes that the steady-state T2 -based study is carried with sufficient spatial resolution to make partial volume effect (PVE) in the arterial measurement negligible. In that case, and given that T2 is not in fast exchange,39 CBV measurement from these data is in absolute units, but Hct-dependent, i.e. CBVT2 ¼CBVHct. This method further assumes that there is also a measurement carried out using the contrast-agent calibrated VASO study (as done for Case 3), thus providing absolute values of CBV: CBVVASO¼CBV. Similar to equation (10) from Case 3, kHct can be calculated from the ratio of CBVVASO to CBVT2 Hcttissue ¼ 1
1 Hctart CBVT2 ¼1 kHct CBVVASO
ð1 Hctart Þ:
ð11Þ
CBF-based case. This corresponds to the Case 1. From equation (4), it follows that Hcttissue 2 1 Hcttissue 2 ¼ Hcttissue Hcttissue 2 3 CBFDSCMRI 2 CBFASL 2 þ 6 7 CBFASL 6 CBFDSCMRI 7 7 ð12Þ 6 2 2 6 7 4 5 Hctart Hctart þ Hctart 1 Hctart CBV-based cases. The expression here corresponds to Case 2–4 from the ‘‘Theoretical Extensions’’ section. Based on equations (9)–(11), one can write the more general equation for the CBV-based cases 1 Hctart CBVHct Hcttissue ¼ 1 ¼1 kHct CBVnonHct ð1 Hctart Þ
Note: As in Case 2 and Case 3, any other method that provides CBV in absolute units and Hctindependent, e.g. CBVT1 can be used instead of CBVVASO to calculate local cerebral Hct with an expression equivalent to equation (11).
Propagation of errors This section describes the formulas for propagation of errors. Note, however, that this only accounts for the variance of the data associated with Gaussian random noise (see Discussion for the effect of other sources of variance).
ð13Þ
where CBVHct is equal to CBVDSC-MRI for Cases 2 and 3, and equal to CBVT2 for Case 4, and CBVnon–Hct is equal to CBVT1 for Case 2, and equal to CBVVASO for Cases 3 and 4. It then follows that Hcttissue 2 1 Hcttissue 2 ¼ Hcttissue Hcttissue 2 2 3 CBVHct CBVnonHct 2 þ 6 7 CBVnonHct 6 CBVHct 7 7 6 2 2 7 ð14Þ 6 4 5 Hctart Hctart þ Hctart 1 Hctart
A novel approach to measure local cerebral haematocrit using MRI
Journal of Cerebral Blood Flow & Metabolism 2016, Vol. 36(4) 768–780 ! Author(s) 2015 Reprints and permissions: sagepub.co.uk/journalsPermissions.nav DOI: 10.1177/0271678X15606143 jcbfm.sagepub.com
Fernando Calamante1,2,3, Andre´ Ahlgren4, Matthias JP van Osch5 and Linda Knutsson4
Abstract The percentage blood volume occupied by red blood cells is known as haematocrit. While it is straightforward to measure haematocrit in large arteries, it is very challenging to do it in microvasculature (cerebral haematocrit). Currently, this can only be done using invasive methods (e.g. PET), but their use is very limited. Local variations in cerebral haematocrit have been reported in various brain abnormalities (e.g. stroke, tumours). We propose a new approach to image cerebral haematocrit using MRI, which relies on combining data from two measurements: one that provides haematocrit-weighted and other one haematocrit-independent values of the same parameter, thus providing an easily obtainable measurement of this important physiological parameter. Four different implementations are described, with one illustrated as proof-of-concept using data from healthy subjects. Cerebral haematocrit measurements were found to be in general agreement with literature values from invasive techniques (e.g. cerebral/arterial ratios of 0.88 and 0.86 for sub-cortical and cortical regions), and showed good test–retest reproducibility (e.g. coefficient-of-variation: 15% and 13% for those regions). The method was also able to detect statistically significant haematocrit gender differences in cortical regions (p < 0.01). The proposed MRI technique should have important applications in various neurological diseases, such as in stroke and brain tumours.
Keywords Haematocrit, perfusion MRI, arterial spin labelling, cerebral blood flow, cerebral blood volume Received 12 April 2015; Revised 14 August 2015; Accepted 14 August 2015
Introduction Red blood cells (or erythrocytes) carry oxygen from the lungs to the tissues and transport carbon dioxide back to the lungs. The percentage of the total blood volume occupied by red blood cells is known in physiology as the haematocrit (Hct). While it is straightforward to measure the haematocrit in large arteries (e.g. by centrifuging a blood sample), it is much more challenging to obtain it in the cerebral microvasculature. As shown by many studies,1–7 the cerebral haematocrit differs from the large vessel haematocrit (with a smaller value in the microvasculature, e.g. the ‘classical’ arterial/tissue haematocrit ratio value of 0.85),1,2,7 due to differences in velocity of blood plasma and the red blood cells residing in it (an effect known as the Fahraeus effect).2 Currently, only invasive methods have been proposed to measure the small vessel or cerebral haematocrit (Hctbrain or Hcttissue, i.e. haematocrit values of blood within small arterioles, venules and
capillaries of the brain). Available approaches are based upon positron emission tomography (PET), single photon emission computer tomography (SPECT), and autoradiography,1,2,8,9 but their use is very limited due to their invasive nature and the poor 1 The Florey Institute of Neuroscience and Mental Health, Melbourne, Australia 2 The Florey Department of Neuroscience and Mental Health, University of Melbourne, Melbourne, Australia 3 Department of Medicine, Austin Health and Northern Health, University of Melbourne, Australia 4 Department of Medical Radiation Physics, Lund University, Lund, Sweden 5 C.J. Gorter Center for high field MRI, Department of Radiology, LUMC, Leiden, Netherlands
Corresponding author: Fernando Calamante, Florey Institute of Neuroscience and Mental Health, Melbourne Brain Centre, 245 Burgundy Street, Heidelberg, Victoria 3084, Australia. Email: [email protected]
Calamante et al. availability of suitable radiotracers. The limited number of prior cerebral Hct mapping studies have, however, shown that the grey matter–white matter contrast is much lower than that seen in cerebral blood flow (CBF) and cerebral blood volume (CBV) maps,1,2,4,5,7 and there have been limited reports of higher Hcttissue values in basal ganglia5 and no right– left hemispheric asymmetry3–6 (although, one report2 did show lower Hcttissue values in the left hemisphere, in a sample of 10 healthy right-handed subjects). Cerebral haematocrit changes have been shown to directly influence the resistance of the microcirculation, and local variations have been reported in various brain abnormalities,3–7,10,11 such as increased values in acute stroke,3,6 decreased values in chronic arterial occlusion,4,5 decreased values in the contralateral cerebellar cortex in crossed cerebellar diaschisis,10 both increased and decreased values in brain tumours (likely due to the wide range of abnormal vasculature that can be found in different tumours),7 as well as reduced values during hypercarbia.2 Although haematocrit changes are known to affect rheological properties of blood and that rheological disorders within the microcirculation are known to play a significant role in various diseases, the clinical importance of these effects has not yet been fully established. This gap of knowledge can be directly attributed to the absence of easily applied measurement techniques, thereby limiting the clinical research on this topic. In addition to the clinical potential of a cerebral haematocrit imaging method, knowledge on small vessel haematocrit is also important for several perfusion imaging methods that aim to quantify cerebral blood flow (CBF).12,13 For example, assumptions on the cerebral haematocrit are necessary in cerebral perfusion measurements using MRI and computed tomography (CT), since the extracellular contrast agents that are applied in these techniques are transported within the blood plasma making these techniques sensitive to plasma flow rather than total blood flow. In practice, any technique that requires knowledge of local cerebral haematocrit levels, therefore, commonly relies on assuming a single uniform value (taken from published literature, such as Hct in capillaries ¼ 0.25)14 for the whole brain, regardless of the tissue type or particular patient; this can naturally lead to erroneous measurements. A more detailed characterisation of tissue haematocrit values could be used to better inform DSC-MRI and perfusion CT quantification (e.g. via the use of more detailed look-up tables rather than a uniform value for every voxel and every subject). In this study, we propose a novel approach to image local cerebral haematocrit levels using MRI. The proposed method relies on combining haemodynamic data
769 obtained from two MRI measurements: one that provides haematocrit-weighted values, and another one that provides haematocrit-independent values of the same parameter. By combining these two measurements, it is possible to isolate the local cerebral haematocrit information, thus providing an easily obtainable and minimally invasive measurement of this important physiological parameter.
Material and methods Because MRI offers many different approaches to probe cerebral perfusion, there are various ways to combine MRI measurements to measure cerebral haematocrit. We describe here a particular implementation for which we also demonstrate, as proof-ofconcept, in vivo results from a group of subjects; we refer to this implementation as Case 1 hereafter. Please refer to Appendix 1 for three further alternative implementations. Case 1 implementation is based on combining data from (i) a dynamic susceptibility contrast (DSC) MRI study in absolute units and (ii) an arterial spin labelling (ASL) study. It assumes that the DSC-MRI data can provide measurements in absolute units. This, for example, requires that the arterial input function (AIF) is measured in absolute units.15 This can be achieved, for example, by acquiring the DSC-MRI data using the method proposed by Kellner et al.,16 or by correcting the partial-volume-effect using postprocessing methods, such as those proposed by van Osch et al.17 and Knutsson et al.18 In this case, a deconvolution analysis14 of the DSCMRI data provides a Hct-weighted CBF (CBFHct) in absolute units, i.e. CBFDSC–MRI¼CBFHct, which can be explicitly written as14 CBFDSCMRI ¼ CBFHct ¼
CBF kHct
ð1Þ
where kHct ¼
Vplasma ½AIF 1 Hctart ¼ Vplasma ½tissue 1 Hcttissue
ð2Þ
and Vplasma[] is the relative plasma volume. It should be noted that, in most DSC-MRI studies, a given value for the proportionally constant kHct is assumed (either by assuming literature values for the Hct levels in the tissue and the artery, or simply by setting it to 1) and, therefore, the variations in Hct are most often disregarded in DSC-MRI studies. In fact, the Hct-weighting is usually considered a nuisance in DSC-MRI, but its presence is central to the method proposed here.
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From a complementary ASL measurement, which is known to provide absolute CBF measurements (i.e. CBFASL¼CBF), one can calculate kHct as the CBF ratio kHct ¼
CBFASL CBFHct
ð3Þ
Therefore, we get the local cerebral Hct as Hcttissue ¼ 1
1 Hctart CBFHct ¼1 kHct CBFASL
ð1 Hctart Þ
ð4Þ
where Hctart is the haematocrit measured in a large artery. In summary, from a DSC-MRI study in absolute units, combined with an ASL study and an arterial Hct value (such as that measured from a blood sample; or from an assumed literature value, if a blood sample is not available), the proposed method provides a means to calculate a map of local cerebral Hct (using equation (4)). Three alternative possible implementations of the Hct mapping method are described in Appendix 1, which are based on various types of CBV measurements – see Appendix 1 for theoretical formulas and details.
MRI experiments As illustration of the Case 1 implementation, cerebral haematocrit measurements were carried out in a group of healthy subjects. Furthermore, to investigate the reproducibility, the subjects were scanned on two occasions. Twenty healthy subjects (age range: 24–84, 10 females) were scanned twice each (with a time interval of 7–20 days between investigations) on a 3T MRI scanner (Philips Achieva, Philips Medical Systems, Best, The Netherlands); ASL and DSC-MRI data were acquired in each session. The project was approved by the Lund University regional ethical review board (following the ethical guidelines of the Helsinki Declaration of 1975 (and as revised in 1983)), and each subject gave written confirmed consent to participate in the study. All brain scans were considered normal by an experienced neurologist. Four ASL scans (from a total of 3 subjects) suffered from incomplete labelling of blood water (manifested as complete loss of ASL signal in a given vascular territory) and these studies were omitted from this proof-ofconcept study. Dynamic susceptibility contrast MRI. To obtain quantitative CBF measurements by DSC-MRI, the so-called
prebolus method was applied in which a separate injection of contrast agent allows for a quantitative measurement of the venous output function (VOF) by adjusting the MRI sequence parameters.18 For proper planning of this DSC-MRI pre-bolus experiment, a sagittal phase contrast angiography T1-FFE scan was performed (relevant parameters: 300 300 mm2 fieldof-view, 256 256 matrix, 50 mm slice thickness, 1.17 1.17 mm2 in plane resolution, 15 flip angle, TE/TR ¼ 5.68/20 ms, and two averages). In order to achieve similar planning for both experiments, the planning from the first experiment was saved and thereafter used for the planning of the second experiment. The planning of the actual DSC-MRI scan was performed using the Philips automatic planning tool SmartExam in order to minimise user interaction. A pre-bolus of contrast agent (Dotarem, Guerbet, Paris, France) was administered (0.02 mmol/kg, injection rate 5 ml/s) and a segmented echo planar imaging (EPI) was used to track the pre-bolus passage through the sagittal sinus in one single slice using a temporal resolution of 0.81 s. The imaging parameters were as follows: 220 220 mm2 field-of-view, 128 128 matrix, 5 mm slice thickness, 1.72 1.72 mm2 in-plane resolution, EPI factor 7, 22 flip angle, TE/TR ¼ 15/135 ms, acquisition time 98 s. In-plane PVE can be considered minimal given the much larger diameter of the sagittal sinus (mean diameter ranges from 4.3mm in the mid-anterior frontal region to 9.9mm in the midoccipital region)19; through-plane PVE was minimised by choosing the slice orientation approximately perpendicular to the sagittal sinus, in a section where this vein has a relatively large diameter. After the pre-bolus scan, a normal single dose of the contrast agent (0.1 mmol/ kg) was administered at an injection rate of 5 ml/s, and the actual DSC-MRI experiment was performed using a single-shot gradient-echo EPI with the following imaging parameters: 220 220 mm2 field-of-view, 128 128 matrix, 5 mm slice thickness, 1.72 1.72 mm2 in-plane resolution, 20 slices, 60 flip angle, TE/TR ¼ 29/1243 ms, acquisition time 91 s. Each bolus injection was followed by a 20 ml saline flush injected at the same rate as the contrast agent. Arterial spin labeling. ASL was carried out using a pseudo-continuous ASL (pCASL) sequence, which included a 1600 ms post-labelling delay to minimize sensitivity to transit time, and background suppression inversion pulses at 1710 and 2860 ms after a prelabelling saturation pulse to increase the signal-tonoise ratio in the perfusion weighted images. The image read-out was performed using single-shot EPI in combination with parallel imaging (96 96 matrix, 5 mm slice thickness, 1 mm slice gap, 2.29 2.29 mm2 reconstructed in-plane resolution, 16 slices, EPI factor
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37, 90 flip angle, TE/TR ¼ 14/4000 ms, 1650 ms label duration, 20 mm label gap, 30 repetitions, and SPIR fat suppression, total acquisition time 240 s). A reference scan for M0 calibration was performed using a sequence identical to the pCASL, except that labelling and background suppression were turned off, TR ¼ 10 s, and the number of repetitions was 4, total acquisition time 40 s.
where i is the fractional volume water content of compartment i, T2i is the effective transverse relaxation time of compartment i, and is the brain density in g/ml. Quantification was done using a model resembling the recommendations of the recent ASL consensus article23 M ¼ 2M0,a f T1a ð1 e=T1a Þew=T1a
Post-processing Dynamic susceptibility contrast MRI. The AIF was measured by using a semi-automatic method, as previously described in Knutsson et al.18 Absolute CBF was then obtained by scaling the measured AIF by the time integral of the VOF (the pre-bolus VOF area was multiplied by five, i.e. 0.1/0.02, to obtain the same VOF area as would have been observed for a normal dose), measured in the sagittal sinus during the pre-bolus experiment.18 Deconvolution was done using the block-circulant singular value decomposition method,20 to obtain a Hct-weighted CBF estimate in ml/100g/min14 R1 max RðtÞ 0 CðtÞdt R1 CBFHct ¼ 1 R 1R R ð t Þdt 0 0 Ca ðtÞdt
ð5Þ
where R(t) is the tissue residue function, and is the brain parenchyma mass density (set to 1.04 g/ml). Arterial spin labelling. The pCASL signal depends primarily on the CBF, the efficiency with which the inflowing blood is labelled, the rate at which the label decays, and the sensitivity of the scanner to the label. The labelling efficiency was estimated as the combined effects of inversion efficiency at the labelling site and the effective spoiling of labelled spins due to the background suppression pulses. This total labelling efficiency was assumed to be 70%.21 The arterial blood was assumed to have a longitudinal relaxation time (T1a ) of 1.65 s.22 The equilibrium blood magnetization (M0,a ) was estimated by using the intensity of white matter (WM) as a calibration standard. For each subject, a binary WM mask was automatically produced by thresholding the segmented WM tissue probability map at 95%, and the average intensity in the reference image within this region was calculated. This mean WM intensity was used as a measure of the equilibrium magnetization of WM, M0,WM . Correction for water content and transverse relaxation effects (compared to arterial blood) yield the M0,a estimation according to
M0,a ¼ M0,WM
a eTE=T2a TE=T 2WM WM e
ð6Þ
ð7Þ
where is the total labeling efficiency, f is perfusion, is the labeling duration, and w is the post-labelling delay. The post-labelling delay is unique for every slice according to w ¼ wps þ ðnslice 0:5Þ tro , where wps is the preset post-labelling delay, nslice is the slice number and tro is the slice read-out time. Perfusion values were estimated using the model stated above, and multiplied by a factor of 6000 to obtain values in ml/100g/min. Parameters , a , WM , T2a , and T2WM were taken from the literature as 1.04 g/ml,14 87%,24 73%,24 43.6 ms,25 and 44.7 ms,25 respectively. Hct mapping. Haematocrit-weighted CBF (from DSC-MRI) and Hct-independent CBF (from ASL) were calculated as described above. All CBF-maps were nonlinearly co-registered (spatially normalized) to the MNI152 template brain (ICBM, NIH P-20 project) using SPM8 (http://www.fil.ion.ucl.ac.uk/spm/ software/spm8/). Local cerebral haematocrit was estimated using Case 1, according to equation (4). Since no measurement of blood haematocrit was available, the arterial haematocrit was set to 0.45.26 Therefore, it should be noted that any results reported here of Hcttissue in absolute values have an underlying assumption on the arterial haematocrit (please refer to Discussion for details on the limitations of the current study). Furthermore, to investigate the sensitivity to the assumed Hctart values, the analysis was repeated for values ranging from 0.3 to 0.6. Finally, to investigate the gender differences in cerebral haematocrit, Hct ratio values were calculated for male and female subjects separately. Given the known gender differences in arterial haematocrit,26 the gender analysis was also repeated, but assuming Hctart ¼ 0.45 for the male subjects and 0.40 for females. To characterize the representative cerebral haematocrit values in normal healthy subjects, the normalized CBF maps were used to calculate the population average Hcttissue map. It should be noted, however, that artefacts in either DSC-MRI or pCASL will introduce unrealistic haematocrit values (e.g. negative or larger than 100%). In particular, both underestimation of white matter perfusion in ASL, overestimation of perfusion close to large vessels in DSC-MRI, and CSF areas were found to lead to severely underestimated haematocrit values (see Figure 1). The quantitative
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Figure 1. Single subject results. Top row: axial CBFHct maps calculated using DSC-MRI. Middle row: axial CBFASL maps calculated using ASL. Bottom row: axial cerebral Hct calculated using the method described in Case 1 implementation. A value of Hctart ¼ 0.45 was assumed for the arterial Hct. Arrows indicate example areas with severely underestimated Hct due to large vessel artefacts in DSC-MRI and underestimated white matter CBF in ASL, respectively.
analysis was therefore restricted to manually defined regions of interest in cortical matter and subcortical structures. Furthermore, voxels with negative Hcttissue values (for any Hctart case) were excluded from the analysis. The total number of voxels excluded from the analysis was 50% of the intracranial voxels (see Discussion section for possible ways to minimise this number by improved white matter measurements and reduced microvasculature contamination). To assess the test–retest reproducibility, the data from the two scans (for the 17 subjects with two successful ASL scans) were displayed in a Bland–Altman plot (difference values vs. mean values), characterised by its bias (mean difference) and limit-of-agreement (mean 1.96 standard deviation). Another commonly used and related measure, the repeatability coefficient (CR¼ˇ2 1.96 Sw, where Sw is the within-subject standard deviation), was also calculated as a measure of test-retest reliability. Finally, the coefficient of variation (CoV), defined as the standard deviation divided by the mean Hcttissue, was also computed.
Results Figure 1 shows the CBF maps calculated using DSCMRI and ASL on an illustrative subject. The figure also includes the computed Hcttissue maps using equation (4). Arrows in this figure illustrate regions with severely underestimated Hct values, corresponding to large vessel artifacts in the DSC-MRI map (top row), and areas with spuriously low CBF in the ASL map (middle row); both cases lead to very low Hct estimates
(bottom row). Figure 2 shows the corresponding population average results, including the average CBF maps (calculated using both DSC-MRI and ASL) and the average Hcttissue maps. Figure 2 shows the population average results, including the average CBF maps (calculated using both DSC-MRI and ASL) and the average Hcttissue maps. To get a more comprehensive visualization of the cerebral Hct results, Figure 3 shows the population average Hcttissue maps in MNI space, in three orthogonal projections. Supplementary Figure 1 shows the manually defined cortical and subcortical regions used for the quantitative analysis. The mean ( standard deviation) CBFDSC–MRI values were 72.6 21.5 and 76.8 13.0 ml/100g/min for the sub-cortical and cortical regions, respectively; the corresponding values for CBFASL were 65.7 16.8 and 69.3 11.1 ml/100g/min. Assuming a Hctart¼0.45, the mean ( standard deviation) cerebral Hct values were 0.395 0.060 and 0.387 0.040 for the sub-cortical and cortical regions, respectively (corresponding to mean Hcttissue/Hctart ratios of 0.88 and 0.86, respectively); this regional difference in Hct values did not, however, reach statistical significance. To characterise the dependency of the cerebral Hct on the assumed arterial Hct values, Figure 4 shows the cerebral-to-arterial Hct ratio in subcortical and cortical regions, as a function of Hctart . The figure also shows the overall variability (characterised by the standard deviation of the ratio, calculated over all 36 individual measurements) from both regions.
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Figure 2. Population average results. Top row: axial CBFHct maps calculated using DSC-MRI. Middle row: axial CBFASL maps calculated using ASL. Bottom row: axial cerebral Hct calculated using the method described in Case 1 implementation. A value of Hctart ¼ 0.45 was assumed for the arterial Hct.
Figure 3. Population average results for the cerebral Hct in MNI space, in axial (top), coronal (middle), and sagittal (bottom) projections. The maps are shown at 2 mm isotropic resolution. A value of Hctart ¼ 0.45 was assumed for the arterial Hct.
There was no statistical significant difference between the Hct measurements of the two scanning sessions (p > 0.2, paired two-sided Wilcoxon signed rank test). Figure 5 shows the results of the reproducibility analysis in form of Bland–Altman plots. Table 1 lists the bias (i.e. mean difference), the magnitude for the limits-of-agreement (i.e. 2 1.96 standard deviation), the CR, and the CoV values for the subcortical and cortical structures. This table also shows the corresponding values for the underlying perfusion MRI data used to calculate Hcttissue. Figure 6 shows the results for the gender differences for both cortical and subcortical regions in form of box-and-whisker plots, based on an assumed Hctart ¼ 0.45. The cerebral Hct ratio (relative
to Hctart) was higher in males. Based on a Mann– Whitney U-test, this gender difference was statistically significant in cortical regions (p < 0.01), but did not reach significance in subcortical structures. The corresponding results for the case of an assumed gender-dependent Hctart (0.45 for males and 0.40 for females)26 are shown in Supplementary Figure 2. Given the complexities of interpreting Hct ratio differences when using a non-uniform Hctart, Supplementary Figure 3 includes the Hcttissue results separately. For the ratio results, significant differences were detected in the cortex (p < 0.01), while significant Hcttissue differences were detected for both cortical (p < 0.0001) and subcortical (p < 0.05) regions.
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Figure 4. Cerebral-to-arterial haematocrit ratio as a function of Hctart for the subcortical region (grey line) and cortical region (black line). Triangles indicate the standard deviation of the ratio. The classical literature ratio value1,2,7 of 0.85 is shown as dashed line.
Discussion A new approach to image cerebral haematocrit using MRI was proposed. The method relies on combining MRI data from two separate measurements, one that provides Hct-weighted values and another that provides corresponding Hct-independent values. Various possible implementations of the method were described and, as proof-of-concept, in vivo data from a group of healthy subjects were presented for the particular implementation that relies on data from DSC-MRI and ASL (Case 1).
Comparison to literature
Figure 5. Reproducibility analysis shown by the Bland–Altman plot. The data from the subcortical region are shown by the blue circles, the data from the cortical region in red triangles. The solid lines indicate the bias, the dashed lines the limits of agreement.
The cerebral Hct maps are visually consistent with previously reported results using invasive methods in healthy subjects,1,2 including a much lower grey matter–white matter contrast than that seen in our CBF maps calculated from DSC-MRI and ASL. There was also a trend for an increased Hcttissue values in subcortical structures, consistent with a small increase detected in a previous report,5 although this did not reach significance in our data. As expected
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Table 1. Test–retest reproducibility. Subcortical region
Hcttissue CBFDSC-MRI CBFASL
Cortical region
Bias
LoA
CR
CoV
Bias
LoA
CR
CoV
0.007 6.7 6.3
0.230 44.6 32.2
0.112 25.3 19.9
15 16 12
0.018 0.9 2.9
0.204 58.6 41.1
0.105 28.5 20.7
13 19 15
LoA: limit-of-agreement; CR: repeatability coefficient; CoV: coefficient of variation (in %). The units for the bias, LoA and CR are in ml/100g/min for the CBF measurements, and are unitless for Hcttissue.
Figure 6. Characterisation of gender differences for Hcttissue/Hctart ratio for cortical (right) and subcortical (left) regions. A value of Hctart ¼ 0.45 was assumed for the arterial Hct. The line inside each box is the median, the edges of each box are the first and third quartiles, the whiskers stretch out to the most extreme values (excluding outliers), and the crosses shows automatically identified outliers. Significant gender differences were found in cortical regions, with the corresponding p-value indicated in the plot. F: female; M: male.
from theory (e.g. see equation (4)), the quantitative results for both Hcttissue and Hcttissue/Hctart are dependent on the assumed arterial Hct value (Note: for the current study, no blood samples were available). Nevertheless, the results from Figure 4 show that the cerebral-to-arterial Hct ratio is, in general, consistent with literature values, including with the ‘classical’ 0.85 haematocrit ratio value.1,2,7 Note, however, that there is no overall consensus regarding the exact value for this ratio, with some studies reporting lower ratios (mean values between 0.69 and 0.76)1,2,6,7 while other higher ratios (mean values between 0.88 and 0.93).4,5
Reproducibility The method was shown to have reasonably good test– retest reproducibility (CoV15%). Despite the method
relying on relatively noisy perfusion MRI measurements (for the Case 1 reported here), as well as the results shown here based on data not specifically optimised for Hct mapping, the Hct reproducibility was comparable to that of the underlying perfusion MRI data (CoV12–19%), suggesting that the proposed formalism does not lead to a major noise amplification. In fact, the CoV for Hct mapping was far better than that predicted solely from propagation of errors (see Appendix 1), where the CoVs from the two CBF methods would be expected to add up to lead to a larger CoV for Hct mapping. This, however, only accounts for the variance of the data associated with Gaussian random noise, and not of other sources of variance in the data. For example, if there are any global effects (e.g. some subjects in the group have much higher/ lower CBF values than the typical average values – not an uncommon situation), this would be reflected
776 both in the DSC-MRI and ASL CBF measurements (both CBF measurements can be considered, to some extent, correlated). While this would increase their variance, the situation is different for Hct mapping: this method is based on the CBF ratio (see equation (4)), and therefore this effect will tend to cancel out, thus decreasing the variance. The same situation applies to the other implementations (Cases 2–4), given that they are based on a CBV ratio. Taking together, all these findings suggest that Hcttissue measurements are actually much more stable than could have been initially expected purely from propagation of errors, and they have a precision similar to that of the input CBF or CBV maps.
Gender effects Gender differences in Hct ratio were found in cortical regions, which remain significant regardless of whether the Hctart values were assumed to be gender dependent (as suggested by literature)26 or uniform, suggesting that the Hcttissue gender difference was not due to the assumed Hctart values. Gender differences were also observed in subcortical structures, but these did only reach significance when measured as Hcttissue and assuming a gender-dependent Hctart value. This highlights that subject-specific Hctart measurements should be carried out, and that the current gender results should be taken with caution given the assumptions involved. While gender differences in arterial haematocrit are well documented,26 the differences within the brain are not well characterised. The techniques introduced here could open up the way to future studies to further our understanding of the regional, gender, and age variations in cerebral Hct. Given that decreased Hct are associated with increased CBF,27,28 non-invasive cerebral Hct mapping methods should prove valuable for clinical and neuroscience investigations.
Practical considerations A number of practical issues need to be taken in to account. First, the method relies on accurate registration between two MRI measurements, e.g. ASL and DSC-MRI data for Case 1. This not only includes rigid body registration but, ideally, it should include also matching for susceptibility-related distortions. Any mismatch between these data will lead to errors in Hct mapping. Therefore, the use of the same acquisition sequence or the use of distortion correction methods29 is preferable to avoid this source of error. In particular, the same bandwidth-per-pixel for all acquisitions (e.g. the same echo-train inter-echo spacing) should be selected in order to ensure the same level of
Journal of Cerebral Blood Flow & Metabolism 36(4) geometric distortion. Alternatively, one could consider the use of distortion correction based on, for example, the acquisition of a separate B0-map. Second, for a more robust quantification in cortical structures, the macrovascular contributions should be minimised. For DSC-MRI, this could be achieved by using a spin-echo based acquisition14 or by removing the macrovascular contribution during post-processing.30 Similarly, for ASL data, the macrovascular contribution can be minimised by using long post-labelling delays and/or using crusher gradients,14 or by postprocessing methods.31 Third, the other CBV-based implementations (see Appendix 1) are not affected by deconvolution-related errors (e.g. noise-sensitivity, errors associated with the regularization, bolus dispersion, sampling-related issues, etc). It could therefore be expected that using one of these other cases may provide more stable Hct measurements. Fourth, errors related to PVEs in the underlying MRI images will translate to PVE-related errors in the calculated Hcttissue maps. The degree of PVE will depend on the particular implementation used. For example, Case 1 can be subject to considerable PVEs, given that ASL is limited to a relatively coarse spatial resolution. In contrast, the implementation described in Case 4 (see Appendix 1) has the greatest potential to minimise PVE, given that it does not rely on dynamic measurements and it is, therefore, more amenable to higher resolution acquisition. The use of the same spatial resolution for all MRI data involved is also preferable, to avoid introducing a differential PVE effect between the various maps used for Hcttissue quantification. This was, however, a limitation of the current study, which was based on retrospective data, and not on a protocol specifically designed for haematocrit mapping. Partial volume contamination could be minimised, in principle, using post-processing methods. For example, various PVE correction methods have been proposed for ASL.32,33 However, similar PVE correction methods are yet to be developed for DSC-MRI. A further source of error in ASL is the coil sensitivity, which can introduce spatial intensity variations across the ASL results. This can be minimised by explicitly calculating the coil sensitivity profile, or by using a map as the calibration reference during quantitation.23 ASL can be also influenced by errors in the assumed parameters in the ASL quantification model (e.g. k, T1a, T2a ). It should be also noted that ASL quantification is not necessarily strictly Hct-independent, given the potential influence of Hcttissue on the assumed values for lambda and relaxation times. It should be emphasised that errors in the underlying MRI measurements could have important consequence
Calamante et al. for the accuracy of Hct mapping when studying certain patient groups. For example, ASL applications to stroke and severe vascular disease are known to be highly sensitive to artefacts due to prolonged transit delays.14 These errors will directly translate into errors on the cerebral Hct maps. For such clinical applications, the use of velocity-selective ASL34 may provide a better ASL variant for the implementation of Case 1, given its known reduced transit delay sensitivity. Similarly, DSC-MRI perfusion measurements in these patient groups can be subject to bolus dispersion errors35; the use of local AIF36 may provide a solution to minimise this source of error. A further example of possible errors relates to applications in tumours, where contrast leakage effects must be taken into account in DSC-MRI quantification.12 In the current study, we limited the quantitative analysis to grey matter structures. It should be noted that quantification of cerebral Hct in white matter is currently relatively unreliable. This is primarily due to the difficulties of quantifying CBF in white matter using ASL.21 One of the CBV-based methods (especially Case 4 with CBVT1) should allow a better prospect for measuring white matter Hct. In fact, the Case 4 implementation, when combined with a blood pool contrast agent (e.g. gadofosveset),37 may open up the possibility of mapping cerebral haematocrit with high spatial resolution and high signal-tonoise ratio. We also had to assume a value for the arterial Hct, since no blood samples were available. Individual arterial Hct measurements should be of great benefit to properly account for the inter-subject variability in this parameter. For example, different arterial Hct values are seen in neonates and young children, as well as in some patient groups (e.g. patients with sickle-cell disease).
Future studies A limitation of the current study is that data for only one of the implementations (Case 1) was available. Further work is required to compare the various implementations described here, and to determine their relative accuracy and precision, as well as their limitations. Further work is also required to optimise the acquisition protocols, particularly aimed at measuring cerebral Hct. A validation of the proposed method could be achieved by comparing the measurements from this MRI approach to those obtained using more traditional invasive methods, such as PET or SPECT measurements in humans subjects, or quantitative autoradiography in animal experiments. However, such a validation is beyond the scope of this study.
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Conclusion A novel non-invasive approach to measure cerebral haematocrit using MRI was proposed. The method relies on combining measurements from two MRI techniques, one that provides Hct-dependent and another one with Hct-independent values. As proof-of-concept, the method was illustrated using DSC-MRI and ASL data on a group of healthy subjects, and was shown to measure cerebral Hct in general agreement with literature values, with good test–retest reproducibility. The proposed MRI method could have important applications in various neurological diseases, such as stroke and tumours. Funding We are grateful to the National Health and Medical Research Council (NHMRC) of Australia, the Australian Research Council (ARC), the Victorian Government’s Operational Infrastructure Support Grant, and the Swedish Research Council [grant nos 13514 and 2010-4454] for their support.
Acknowledgements We also want to thank Emelie Lindgren, Dr Ylva Surova and Dr Danielle van Westen for assistance when acquiring the data.
Declaration of conflicting interests The author(s) declared the following potential conflicts of interest with respect to the research, authorship, and/or publication of this article: FC, MJPvO and LK: patent application of this methodology.
Authors’ contributions FC: study conception and design, data interpretation, drafting the article, critically revised draft for important intellectual content, and final approval of the version to be published. AA: data acquisition, analysis of data, interpretation of results, drafting the article, critically revised draft for important intellectual content, and final approval of the version to be published. MJPvO: study conception and design, data interpretation, drafting the article, critically revised draft for important intellectual content, and final approval of the version to be published. LK: study conception and design, data acquisition and interpretation, drafting the article, critically revised draft for important intellectual content, and final approval of the version to be published.
Supplementary Material Supplementary material for this paper can be found at http:// jcbfm.sagepub.com/content/by/supplemental-data.
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Appendix 1. Theoretical extensions Three alternative possible implementations of the Hct mapping method are described below.
Case 2: Implementation based on combining data from (i) a DSC-MRI study in absolute units and (ii) a ‘Bookend’-type study This implementation is similar to that in Case 1, but it is based on CBV measurements rather than CBF. It is based on combing a Hct-weighted CBV map (from DSC-MRI) and a Hct-independent CBV map (from a ‘Bookend’ type of acquisition,38 i.e. T1 measurements before and after the contrast agent injection). It assumes that DSC-MRI provides measurements in absolute units (see Case 1 for ways to achieve this). It further assumes that the DSC-MRI acquisition protocol included a ‘Bookend’ type of acquisition.38 Similar to the situation for Case 1, a DSC-MRI data set that can provide absolute units will give a Hctweighted CBV (CBVHct) in absolute units, i.e. CBVDSC14 MRI¼CBVHct, which can be explicitly written as
CBVDSCMRI
h i Þ AUC Rð2,tissue ðtÞ CBV h i ¼ CBVHct ¼ ¼ ðÞ kHct AUC R2,AIF ðtÞ ð8Þ
where AUC[] is the area under the curve.
From the T1 data of the ‘Bookend’ type acquisition,38 it is possible to calculate blood volume, CBVT1. Note that this CBV is in absolute units and not Hct-dependent, i.e. CBVT1¼CBV. This is because plasma and Hct are in fast exchange for T1 measurements,39 which makes CBV measurements from T1 Hct-independent. Therefore, combining equations (8) and (2) leads to
Hcttissue
1 Hctart CBVHct ¼1 ¼1 kHct CBVT1 ð1 Hctart Þ
ð9Þ
Note: In principle, it would be simpler and faster to use the steady-state from the DSC-MRI study (i.e. the contrast concentration plateau after the bolus passage) to calculate the extra required measurement of total CBV (cf. having to add the T1 measurements). However, T2 is not in fast exchange39 and, therefore, CBV measurements from T2 steady-state are Hct-dependent. In fact, this property is exploited in the approach described in Case 4 below.
Case 3: Implementation based on combining data from (i) a DSC-MRI study in absolute units and (ii) a contrast-agent calibrated vascular-space-occupancy (VASO) study The principles behind this implementation are exactly the same as Case 2, with the exception that the Hct-independent CBV measurement is not obtained from ‘Bookend’ data, but it is rather obtained from a contrast-agent calibrated VASO study.40 The latter was shown to provide absolute values of CBV, i.e. CBVVASO¼CBV. Therefore, similar to Case 2, we can measure local cerebral Hct as follows
Hcttissue ¼ 1
1 Hctart CBVHct ¼1 kHct CBVVASO
ð1 Hctart Þ
ð10Þ
Case 4: Implementation based on combining data from (i) a steady-state T2 -based study (ii) a contrast-agent calibrated VASO study This implementation is similar to Case 3, with the exception that the Hct-weighted CBV map is obtained from a steady-state T2 -based study (i.e. T2
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measurements before and after contrast injection). It assumes that the steady-state T2 -based study is carried with sufficient spatial resolution to make partial volume effect (PVE) in the arterial measurement negligible. In that case, and given that T2 is not in fast exchange,39 CBV measurement from these data is in absolute units, but Hct-dependent, i.e. CBVT2 ¼CBVHct. This method further assumes that there is also a measurement carried out using the contrast-agent calibrated VASO study (as done for Case 3), thus providing absolute values of CBV: CBVVASO¼CBV. Similar to equation (10) from Case 3, kHct can be calculated from the ratio of CBVVASO to CBVT2 Hcttissue ¼ 1
1 Hctart CBVT2 ¼1 kHct CBVVASO
ð1 Hctart Þ:
ð11Þ
CBF-based case. This corresponds to the Case 1. From equation (4), it follows that Hcttissue 2 1 Hcttissue 2 ¼ Hcttissue Hcttissue 2 3 CBFDSCMRI 2 CBFASL 2 þ 6 7 CBFASL 6 CBFDSCMRI 7 7 ð12Þ 6 2 2 6 7 4 5 Hctart Hctart þ Hctart 1 Hctart CBV-based cases. The expression here corresponds to Case 2–4 from the ‘‘Theoretical Extensions’’ section. Based on equations (9)–(11), one can write the more general equation for the CBV-based cases 1 Hctart CBVHct Hcttissue ¼ 1 ¼1 kHct CBVnonHct ð1 Hctart Þ
Note: As in Case 2 and Case 3, any other method that provides CBV in absolute units and Hctindependent, e.g. CBVT1 can be used instead of CBVVASO to calculate local cerebral Hct with an expression equivalent to equation (11).
Propagation of errors This section describes the formulas for propagation of errors. Note, however, that this only accounts for the variance of the data associated with Gaussian random noise (see Discussion for the effect of other sources of variance).
ð13Þ
where CBVHct is equal to CBVDSC-MRI for Cases 2 and 3, and equal to CBVT2 for Case 4, and CBVnon–Hct is equal to CBVT1 for Case 2, and equal to CBVVASO for Cases 3 and 4. It then follows that Hcttissue 2 1 Hcttissue 2 ¼ Hcttissue Hcttissue 2 2 3 CBVHct CBVnonHct 2 þ 6 7 CBVnonHct 6 CBVHct 7 7 6 2 2 7 ð14Þ 6 4 5 Hctart Hctart þ Hctart 1 Hctart
