In human brain studies, the capability of ASL to provide perfusion values which are consistent with those delivered by ^{15}O-H_{2}O PET can be considered established [10–12, 30]. The situation is less clear in small animal imaging, however. Despite the fact that there are many studies reporting on the use of ASL in pre-clinical imaging, there are only very few investigations regarding the quantitative accuracy of ASL-derived perfusion values [7, 8, 13, 14].

We have, therefore, conducted the present study with the aim of evaluating the quantitative accuracy of one common ASL technique, namely ASL-FAIR, for brain imaging in rats by a direct comparison with radioactive microspheres which are an accepted gold standard for perfusion quantification.

Our final results are presented in Figure 5 together with fits of two related models to the data. Although there is substantial scatter, we observe a clear monotonic relation between MS-derived brain perfusion *f* and ASL-derived unidirectional water uptake *K*
_{1}. Each data point results from averages over spatially registered transaxial brain slices with comparable thickness (1 mm in MRI, 3 mm in PET). The points can, therefore, be considered as representing the slice averages of the respective parameter (*f* and *K*
_{1}). It would have been desirable to compare *f* and *K*
_{1}also on a regional basis within the slices. However, the limited number of microspheres present in a single slice does not allow a reliable determination of perfusion values for different slice regions. The substantial dynamic range of the MS-derived flow (and the ASL-derived *K*
_{1}) values (ranging from about 0.2 to 1.9 mL/min/mL) might be surprising since no special measures were taken to achieve different flow levels in the different animals. The range can be explained by observing that the investigated animal group was heterogeneous with respect to age and weight and, more importantly, that the animal preparation (notably catheterisation and anaesthesia) does necessarily influence the individual animals differently.

The resulting large variability of the resting blood flow is actually advantageous in the present investigation since it made additional intervention (pharmacological or pacing) aiming at variation of blood flow unnecessary.

The observed correlation between *f* and *K*
_{1}is approximately linear as can be seen by comparison with the line of identity in the plots. At high flow values, however, there is some indication that the data deviate systematically from the line of identity as is to be expected if the permeability of water at the BBB is limited. At low flows, there is, moreover, a slight tendency of the ASL-*K*
_{1}values to overestimate the MS-derived perfusion.

The latter effect can easily be explained by observing that we had to fix two quantities, namely *V*
_{
d
} and *ρ*
_{
a
} in Equation 8 in order to derive *K*
_{1}. These values are not known precisely, and this uncertainty does introduce potential bias in the *K*
_{1}estimate. We account for this bias by modifying the standard Renkin-Crone formula through multiplication with a scale factor *N* whose adjustment in the fit can compensate for this bias. The resulting value, *N*=(1.25±0.17), can be interpreted as an indication that the chosen value of the product *V*
_{
d
}·*ρ*
_{
a
} is too high by about 25±17% which seems perfectly possible: reducing both *V*
_{
d
}and *ρ*
_{
a
} by about 10% would suffice to eliminate the observed bias.

A similar *K*
_{1}(*f*) dependency (*K*
_{1}slightly overestimating blood flow at low flow rates and increasingly underestimating it beyond *f*=1 mL/min/mL) has been also reported by Parkes and Tofts who used single compartment fits to simulated signal curves generated with a two-compartment model proposed by these authors (see Figure 4a in [31]). They, moreover, report a field strength dependency of the deviations from the line of identity which should decrease at decreasing field strength. All deviations, including the overestimate at low flows, are interpreted as a consequence of the one compartment model simplification. Although the simulations are not directly comparable to the present study (and the used one-compartment operational equation differs from ours), the qualitative agreement with our fitted *K*
_{1}(*f*) curve is remarkable.

Adopting our approach of including the additional model parameter *N* in the fit, we obtain *PS*=(1.53±0.46) mL/min/mL as our best estimate of the *PS*-product of water at the BBB of the rat. Although the statistical uncertainty of this result is large (30%), this result is comparable to the available information regarding this parameter.

In a PET study, Herscovitch and Raichle [32] reported a value of *PS*=(1.04±32) mL/g/min for water at the BBB of rhesus monkeys. Takagi and coworkers [33] performed ASL measurements at the rat brain and report 1.71 ± 0.86 mL/g/min. Parkes and Tofts [31] also referred to earlier publications where the values in whole human brain varied from 0.9 to 1.7 min^{−1} with a mean value of 1.2 min^{−1}
[34, 35]. We, therefore, consider the consistency of our result with the previously reported figures as indication that our description of the water kinetics with diffusion limited one-compartment model is adequate.

Consequently, we consider our results as proof that the ASL-FAIR technique is suitable to quantify brain perfusion in the rat at low, normal, and moderately increased flows (up to about 2 mL/min/mL). At higher flows, the limited permeability leads to increasingly reduced first-pass extraction of water across the BBB, and the measured *K*
_{1} becomes increasingly insensitive to further increases in blood flow. Below about 2 mL/min/mL, an extraction correction can be performed with the help of Equation 14 using the fitted values of *PS* and *N* (but note that *N* is directly proportional to the chosen value of *V*
_{
d
}·*ρ*
_{
a
}: if a different value were chosen for this product *N* would have to be adjusted accordingly). Although we consider our results as adequate proof of the quantitative capabilities of ASL-FAIR for perfusion measurements in the rat brain, it should be noted that our investigation has several obvious limitations.

The major concern which could be raised regards the fact that MS- and ASL-investigations might not probe the same physiologic state of the animal. MS-derived *f* reflects a snapshot of the blood flow level a few seconds after MS injection. ASL, on the other hand, required about 15 min measurement per slice (more than half an hour for both investigated slices) and was, moreover, performed sequentially with the MS-investigation (before or after MS, depending on radioactive label, see Figure 1). The ASL-measurements thus provide time-averages which are, moreover, measured at rather different time points than the MS-derived flow. Of course, much care was taken to ensure stable physiologic conditions as far as possible, but residual variability cannot be excluded. We presume that part of the scatter in Figure 5 can be attributed to this residual variability and does not reflect the inherent limit of achievable statistical accuracy either with MS or ASL. There is, however, no reason to expect a systematic change (increase or decrease) of the flow level between both measurements since stable physiological conditions were closely monitored in each animal. As a further check, we performed a separate MR experiment in a single (identically treated) animal, which underwent four repeated ASL measurements over a much longer time period (2 h, 20 min) which yielded a constant *K*
_{1} value of 1.2 mL/min/mL to within 8% (data not shown) which provides an estimate of the actually occurring perfusion changes in the given experimental setup. Moreover, PET and MR were performed in different order depending on the radioactive MS label used in the respective experiment without causing visible differences between both tracers in Figure 5. This is further evidence that no systematic flow change takes place between PET and MR measurement and that no sizable bias is present in the analysed *f* vs. *K*
_{1}correlation.

A further potential limitation of our study is the fact that we only compared slice averages of the target parameters (*f*,*K*
_{1}). While the slice thickness was comparable in MS and ASL (1 mm vs. 3 mm), the actual resolution mismatch implies a certain limitation of spatial correspondence. This, too, will contribute somewhat to the scatter in Figure 5. A spatially resolved comparison within the imaging planes was not performed since the combined image quality of MS and ASL was considered insufficient for such a comparison; also, regional differences were visible, notably in the ASL measurements. We believe that restriction to spatially averaged data does not adversely affect our accuracy: the MS-derived perfusion is simply related linearly to tracer uptake, and the slice averaged MS-associated radioactivity corresponds to the actual average perfusion in that region. The situation is markedly different for ASL. Therefore, the ASL data were quantified on a per-voxel basis and only averaged afterwards in order to obtain the correctly averaged uptake parameter *K*
_{1}.

Another restriction is the fact that the investigated flow range is limited to perfusion values below 1.9 mL/min/mL and that data above 1.0 mL/min/mL are scarce while exhibiting large fluctuations. Consequently, the derived *PS* value is not very precise, and validity of the Renkin-Crone assumption cannot be proven unambiguously. It, thus, would be desirable to perform further experiments targeting especially the high flow range.

A final important issue concerns the models applied for quantification of *f* and *K*
_{1}. While quantification of the MS data is completely straightforward and mathematically simple, quantification of the ASL data requires selection among quite a number of different modeling approaches [21–24, 36–38].

We essentially follow the approach described in [22] which leads to Equation 8. Since it is possible that the one-compartment Kety-Schmidt model leads to underestimation of perfusion at high flow values due to limited permeability of the BBB to water [9, 39], we do not postulate that the resulting parameter *K*
_{1}is identical to tissue perfusion *f*, but allow for a Renkin-Crone type relation between *K*
_{1} and *f*. The underlying assumption of this approach is that even in the presence of limited permeability, the kinetics is reasonably well described by a one-compartment model. We believe that this is reasonable at least as long as the *PS* product is higher than or comparable to the relevant flow levels. Treating the capillary as a separate identifiable kinetic compartment (see, e.g. [23, 24]) is of course possible, and different approximations and limiting cases have been investigated [31]. Given the limited statistical accuracy of the experimental data there is, in our view, no realistic possibility of identifying *f* and *PS* (plus the vascular fraction) simultaneously in the data (this assessment is in accord with [16]). The only really visible effect of limited *PS* is a reduction of tissue uptake *K*
_{1} relative to *f* at elevated flow levels.

By independently measuring *f* via the MS experiments, we were able to determine experimentally the relation between *f* and the effective *K*
_{1}. This relation, as presented in Figure 5, is reasonably described by a Renkin-Crone type formula (Equation 13 or 14) which supports the above conjecture that our one-compartment description is adequate. We note that the Renkin-Crone relation is not compatible with the two-compartment model which would yield a different expression for the flow dependent extraction (and a different numerical value for *PS*), namely *E*(*f*)=*PS*/(*f* + *PS*). We believe the Renkin-Crone model to be more reasonable since it accounts for the arterio-venous concentration gradient in the capillary (it can be considered as a simple variant of a distributed model) instead of making the rather strong assumption that the capillary reacts as a well-mixed compartment (which obviously is not really the case). The statistical accuracy of our data, however, is insufficient to decide between the two alternative expressions for the function *E*(*f*). Still, this question is irrelevant as long as the objective of the experiment is not to determine the *PS* product itself. We take the point of view that the one-compartment model combined with the Renkin-Crone formula regarding the flow dependence of the unidirectional uptake rate *K*
_{1} of the compartment model is phenomenologically sufficient for description of the data and for derivation of quantitative perfusion values from the ASL measurements.