The projections of midbrain serotonergic neurons are distributed throughout the brain, but the local serotonin transporter (SERT) concentration is quite diverse with a few areas of high concentration such as the midbrain, thalamus, and basal ganglia, with low to intermediate concentrations throughout the cortex (
Varnas et al 2004). As a variety of regions may be of interest in any given study, it is important to quantify high and low binding regions reliably. In fact, recent studies have implicated cortical and limbic SERT measured by [
11C]DASB in Parkinson’s disease and geriatric depression (
Kish et al 2010,
Smith et al 2008). However, quantification of regions with either high or low SERT density presents a challenge. In the case of low-density regions, the low specific binding signal may be difficult to distinguish from non-specific binding. For high-density regions, the tracer clearance is relatively slow which may be problematic for quantitative methods that assume some degree of equilibrium among compartments. TACs at all binding levels are generally well characterized when applying full compartmental modeling with a blood input function. However, it is particularly difficult to measure the input function for [
11C]DASB due to an atypical metabolite profile that likely reflects transient uptake in lung (
Parsey et al 2006b). That difficulty, along with the very low SERT binding in cerebellum, has further encouraged the use of reference tissue methods for quantifying [
11C]DASB PET studies (
Frankle et al 2006,
Ichise et al 2003).
An important distinction between the application of blood input and reference tissue methods is that quantification of specific binding with a blood input method is typically a two-step process, whereas application of a reference tissue method is typically a one-step process. For example, when applying a two-tissue compartmental model, the first step in the quantification of tracer binding is to estimate the non-specific volume of distribution (
VND) by modeling the cerebellar gray matter, which is nearly devoid of specific SERT binding and is thus considered to be a reference region (
Parsey et al 2006a). The second step is to model specific binding regions to measure
K1,
k3, BP
ND, with the assumption that
, where the ‘
r’ superscript denotes the reference region. Alternatively, the total volume of distribution (
VT) in a specific binding region can be measured with any suitable method, and then specific binding can be computed as BP
ND =
VT/
VND − 1. Note that since we have asserted that
is constant, it can be seen that
is constant. Therefore, setting
to be constant across regions is tantamount to setting
VND constant as is required in order to adhere to the assumption of uniform nonspecific binding. In addition to making the application of SRTM parsimonious with physiological assumptions, constraint of
adds stability to the analysis. Consider that for [
11C]DASB, it has been shown that with compartmental modeling, constraint of
VND either by fixing
K1/
k2 to a constant, or by coupling
K1/
k2 across TACs, gave better convergence and more consistent results than was obtained without constraint of
K1/
k2 (
Ginovart et al 2001). From the relation
, it is seen that setting
to a fixed value for SRTM is the kinetic equivalent of setting
K1/
k2 to a fixed value for the two-tissue compartmental model. Similarly, coupling of
across tissue regions is equivalent to coupling of
K1/
k2. Therefore, just as fixing or coupling of
K1/
k2 improves parameter estimation when using the two-tissue blood input model, fixing (SRTM2) or coupling (SRTMC) of
should improve parameter estimation when applying SRTM. Thus, it is not surprising that SRTM2 and SRTMC reduced the RMSE% of BP
ND estimates relative to SRTM, and also yielded better significance in the mock study. The linear method that was examined (Zhou) was also improved by constraint of
(Zhou2). In particular, Zhou2 had a smaller COV than the Zhou method, and tended to yield better significance, especially at high noise level. In the mock PET study, the Zhou2 method yielded
p-values that were quite comparable to those of SRTM2 and SRTMC, although Zhou2 did not perform as well in our clinical study.
It is instructive to examine the effects on estimation of other parameters, namely
R1 and
. The estimation of
R1 showed small Bias% (
<4%) and COV (
<3%) with SRTM-based methods () at all noise levels. As was the case for BP
ND estimation, for
R1 estimation SRTMC had a smaller COV than SRTM and SRTM2 as well as a somewhat larger bias. The Zhou and Zhou2 methods showed consistently larger COV and Bias% in
R1 than the SRTM methods. In particular, Zhou2 showed a much larger Bias% in
R1 at the highest noise level examined. For estimation of
, the Zhou method showed an extremely large Bias% that exceeded 100% even at low noise level (). That finding is consistent with the smaller, but still substantial bias in
R1 and
k2 that was found previously with application of the Zhou method to simulations of [
11C]Flumazenil (
Zhou et al 2003). It is important to note that for the Zhou method
is estimated from a ratio of parameters whereas BP
ND is estimated directly. That may account for why the Zhou method is able to achieve a rather good estimate of BP
ND despite yielding a rather poor estimate of
. In contrast, SRTM estimated
with much lower bias than Zhou2, while having similar COV. As compared with SRTM, SRTMC yielded even smaller COV for
especially at high noise level. However, SRTM showed a smaller Bias% in
(
<9%) relative to SRTMC (Bias% ~10–12%), but the Bias% and COV of
measured with SRTMC appeared to be insensitive to the noise level. In fact, in some cases the Bias% of BP
ND was slightly higher at medium noise level than at high noise level (), although COV increased as expected which suggests a noise/bias tradeoff in parameter estimates. In general, SRTMC gave larger Bias% and smaller COV than did SRTM for both
and BP
ND. That finding indicates that, at the cost of some bias, coupling of
via SRTMC does reduce variability associated with estimation of
, which translates to reduced variability in the estimation of BP
ND. Given the similarity in performance of SRTM2 and SRTMC when examining the RMSE% of control simulations () and the detection of differences in the mock patient study ( and ), it appears that either method of
constraint is suitable and definitely preferable to the standard SRTM approach for ROI analysis of [
11C]DASB PET studies.
The linear methods tested here (Zhou, Zhou2) performed about as good as the nonlinear methods at low noise level. As compared with the one-step method (Zhou), the two-step method (Zhou2) gave better discrimination between groups at high noise level ( and ), and showed less Bias% (). On average, Zhou2 gave somewhat less power for significant difference detection than SRTMC and SRTM2, although the overall performance of the Zhou2 method in the mock study simulations was quite comparable.
In the original publication of our [
11C]DASB study in HIV, SRTMC was selected for presentation because it yielded the highest significance. The present work provides some theoretical validation that SRTMC is indeed among the best current approaches for extracting a significant result given an underlying difference in BP
ND. It is important to note that although the mock patient simulations are useful for examining the relative performance of different quantitative methods, the simulations apply only to sets of parameters that are typical of [
11C]DASB PET studies. However, some inferences on the application of SRTMC to other tracers can be drawn from other work. For example, faster equilibrating tracers such as [
11C]carfentanil, [
11C]raclopride, and [
11C]flumazenil would probably not benefit as much from SRTMC as SRTM already obtains reliable estimates when the approach to equilibrium is relatively rapid (
Endres et al 2003). Similarly, in comparison of [
11C]PIB binding between healthy controls and Alzheimer’s patients, the statistical significance values obtained with SRTMC were about the same as those obtained using a simple Logan plot (
Zhou et al 2007). The SRTM2 results obtained here were generally consistent with those published previously for [
11C]DASB (
Ichise et al 2003). For example, it was found for SRTM2 that the bias of BP
ND was generally small as was the bias and variability of
R1, the latter of which showed subtle increases with noise. There were some differences, for example the work of Ichise showed that bias with SRTM2 increases with BP
ND at high noise levels which was not found here. A likely reason is that the present work targeted noise levels relevant to ROI analysis, whereas the Ichise paper included examination of voxel level noise. That work also presented a linear method known as the multilinear reference tissue model (MRTM), as well as a two-step procedure with constraint of
(MRTM2) (
Ichise et al 2003). In our experience, for parametric imaging of human brain studies with tracers such as [
11C]DASB and [
11C]PK11195, MRTM tends to show higher variability than the Zhou approach. However, there is apparently little distinction between the MRTM and Zhou methods at the lower ROI noise levels examined here. Consider that the Ichise study showed that BP
ND estimates obtained with MRTM2 had nearly identical variability to those obtained with SRTM2. The bias in BP
ND was also similar but was slightly higher for MRTM2. In this study, the BP
ND estimates obtained using Zhou2 were also similar to SRTM2 with Zhou2 showing somewhat smaller variance but also greater bias. The implication is that MRTM2 and Zhou2 give similar performance at ROI noise levels which is not surprising given that they are both linear methods based on different permutations of the same equation. Either SRTM2 (or MRTM2 or Zhou2) are applicable to voxelwise calculations, and should be implemented when constraint of
is desired for voxelwise analysis. SRTMC is not practical for voxelwise analysis due to the large number of parameters that would need to be included in a single regression equation.
The Zhou method was developed originally as a parametric imaging approach where tissue data were smoothed using a linear ridge regression penalty function (
Zhou et al 2003). Here, we are applying the method to region of interest TACs, where the tissue data are already quite smooth, and thus we did not further smooth the data. However, even in that case the limitation of the Zhou method when applied to a high binding region is apparent, and the performance of the method generally degrades at high noise levels. The poor performance of the Zhou method in that case is likely due to the increasing lack of equilibrium in regions of high SERT density. As compared with the Zhou method, Zhou2 gave a definite improvement in power in the mock study simulations. The control simulations showed that Zhou2 substantially reduced COV relative to Zhou, although RMSE% increased slightly for high BP
ND.
The publisher's final edited version of this article is available at 
) to a common value across regions were applied to the clinical and simulated data to compare measurement of the tracer binding potential (BPND). Compared with standard SRTM, either coupling of
across regions or constraining
to a first-pass estimate improved the sensitivity of SRTM to measuring a significant difference in BPND between patients and controls. Parameter coupling was particularly effective in reducing the variance of parameter estimates, which was less than 50% of the variance obtained with standard SRTM. A linear approach was also improved when constraining
to a first-pass estimate, although the SRTM-based methods yielded stronger significant differences when applied to the clinical study. This work shows that parameter coupling reduces the variance of parameter estimates and may better discriminate between-group differences in specific binding.
