PET Imaging of the Serotonin 1A Receptor in Major Depressive Disorder: Hierarchical Multivariate Analysis of [11C]WAY100635 Overcomes Outcome Measure Discrepancies

The serotonin 1A receptor has been linked to both the pathophysiology of major depressive disorder (MDD) and the antidepressant action of serotonin reuptake inhibitors. Most PET studies of the serotonin 1A receptor in MDD used the receptor antagonist radioligand, [carbonyl-11C]WAY100635; however the interpretation of the combined results has been contentious owing to reports of higher or lower binding in MDD with different outcome measures. The reasons for these divergent results originate from several sources, including properties of the radiotracer itself, which complicate its quantification and interpretation; as well as from previously reported differences between MDD and healthy volunteers in both reference tissue binding and plasma free fraction, which are typically assumed not to differ. Recently, we have developed two novel hierarchical multivariate methods which we validated for the quantification and analysis of [11C]WAY100635, which show better accuracy and inferential efficiency compared to standard analysis approaches. Importantly, these new methods should theoretically be more resilient to many of the factors thought to have caused the discrepancies observed in previous studies. We sought to apply these methods in the largest [11C]WAY100635 sample to date, consisting of 160 individuals, including 103 MDD patients, of whom 50 were not-recently-medicated and 53 were antidepressant-exposed, as well as 57 healthy volunteers. While the outcome measure discrepancies were substantial using conventional univariate analysis, our multivariate analysis techniques instead yielded highly consistent results across PET outcome measures and across pharmacokinetic models, with all approaches showing higher serotonin 1A autoreceptor binding potential in the raphe nuclei of not-recently-medicated MDD patients relative to both healthy volunteers and antidepressant-exposed MDD patients. Moreover, with the additional precision of estimates afforded by this approach, we can show that while binding is also higher in projection areas in this group, these group differences are approximately half of those in the raphe nuclei, which are statistically distinguishable from one another. These results are consistent with the biological role of the serotonin 1A autoreceptor in the raphe nuclei in regulating serotonin neuron firing and release, and with preclinical and clinical evidence of deficient serotonin activity in MDD due to over expression of autoreceptors resulting from genetic and/or epigenetic effects. These results are also consistent with downregulation of autoreceptors as a mechanism of action of selective serotonin reuptake inhibitors. In summary, the results using multivariate analysis approaches therefore demonstrate both face and convergent validity, and may serve to provide a resolution and consensus interpretation for the disparate results of previous studies examining the serotonin 1A receptor in MDD.

PET quantification involves fitting pharmacokinetic (PK) models to the time course of measured radioactivity concentrations in the brain, termed time activity curves (TACs).Using these models, PET allows for quantification of various binding potentials (BP), i.e. the equilibrium concentration of radioligand specifically bound to the target protein, normalized to a reference concentration.While in vitro studies can measure the concentration of the target protein available to bind the radioligand, B avail , this is not possible from a single in vivo PET examination.Rather, PET researchers make use of binding potential as a measure of specific binding, which is equal to B avail /K D , where K D represents the affinity of the target for the radioligand.Hence, as long as K D is unchanged, then BP should be proportional to B avail and can be used as an effective surrogate.However, in order to calculate binding potential, we do so using a suitable reference quantity.As such, there are several different types of binding potential which differ from one another as a function of which reference quantity is used for their calculation, i.e.BP X where X describes the reference quantity.
BP F represents the gold standard PET outcome measure which is, in the absence of active transport, equal to B avail /K D .The estimation of BP F , however, requires measurement both of the metabolite-corrected radioactivity in arterial plasma during the PET measurement, as well as the protein-free fraction of the radioligand in arterial plasma, f P (Innis et al., 2007;Parsey et al., 2010).Measurement of f P tends to be notoriously prone to measurement error due both to estimation inaccuracy, and especially so when f P values are low as is the case for [ 11 C]WAY100635.Moreover, measurement of f P tends to be sensitive to small experimental biases such as the temperature or pH of plasma samples, the latter of which can even vary as a result of storage time (Hinderling and Hartmann, 2005;Kochansky et al., 2008).Hence, even if data show a reasonably high degree of consistency within individuals, measured f P values could feasibly be impacted by unexpected experimental confounds over time.Measured values can therefore suffer from both variance and bias.On the other hand, BP P which is equal to f P B avail /K D , does not require the measurement of f P -however it is sensitive to differences in plasma protein binding between individuals.For this reason, group differences in f P values will yield biased inferences when analysing BP P .Finally, BP ND is one of the most common outcome measures in PET imaging, equal to f ND B avail /K D , where f ND represents the radioligand free fraction in the non-displaceable compartment.However, for this reason, group differences in f ND , will also yield biased inferences when analysing BP ND .These binding potential outcomes can be calculated directly from the rate constants of the PK model, which is known as direct estimation, however the reliability of these estimates has been found to be poor in many cases, particularly for BP ND (Slifstein and Laruelle, 2001).Alternatively, binding potential outcomes can be calculated relative to a reference region in the brain which is devoid of specific binding, when one is available, under the assumption that non-displaceable binding is equal throughout the brain.This is known as indirect estimation, and can greatly improve the reliability of binding potential estimates (Slifstein and Laruelle, 2001).Indirect estimation of BP ND is especially common as it does not require collection of arterial plasma samples, which is highly desirable as this procedure is costly, can be uncomfortable for research participants, and adds to the complexity of PET acquisition (Gunn et al., 2001).However, the improvements in reliability using indirect estimation come at a cost, since group differences in reference tissue binding will bias inferences.In summary, all binding potential outcomes are measures of specific binding relative to a reference concentration and should therefore be approximately proportional to one another in theory; however this is more complicated in practice as estimation inaccuracies or individual differences in f P , f ND or reference-region binding can introduce bias for inference.

Priors for the SiMBA 2TC models
For all priors, we use the same terminology used in Matheson and Ogden (2022).

Global Intercepts
Note that all priors are defined over the natural logarithms of the parameters, where the mean is shown first and the standard deviation second.
For the SiMBA BP F model, we used the following priors.
For the SiMBA BP P and BP ND models, we used the following priors.
Hence forth all priors for BP F , BP P and BP ND are all the same.Hence I will write simply BP X .

Individual deviations
Differences between individuals were defined by specifying the primary pharmacokinetic parameters in one variance-covariance matrix, and v B and σ on their own.

Regional deviations
For log BP X and log K 1 , regional differences were defined as unpooled effects using a dummy (indicator) variable defined with reference to the dorsolateral prefrontal cortex as covariates.For simplicity, all regional differences were defined for all other regions as zero-centred regularising priors with the same SD.
For the remaining parameters, regional differences were defined as partially-pooled variables, arising from a common distribution.

TAC deviations
Residual TAC effects were defined for the major four pharmacokinetic parameters, but were not included for v B or σ as these were not considered to be of central importance.
Covariates for PK Parameters For the effects of group on BP, we defined priors for each region and diagnosis separately in order to detect regionally-specific effects.
We also defined priors for age (per decade, centred) and sex as nuisance variables.

Measurement Error
For measurement error, σ , we used a combination of a global mean and partially pooled deviations across individuals and regions described above.We also made use of covariates for mean region size, injected radioactivity, and the duration of each frame, as well as a smooth function across the course of the PET measurement to accommodate any residual variability not accounted for by the covariates.The latter smooth term is expected to be more associated with the kinetics of the specific tracer after accounting for the influence of experimental factors.
All covariates are log-transformed and then centred.In this way, the global intercept is still interpretable as the geometric mean of the measurement error, and the covariates are related proportionally to the natural logarithm of the expectation of the measurement error.
The smooth basis function makes use of a penalised regression spline.The σ spline-coefficients term refers to the standard deviation of the spline coefficients, which penalises the wiggliness of the spline.The α spline-coefficients term refers to the fixed effects term, which describes the magnitude of the influence of the smooth term around the estimated mean value.For the half-Student-t distributions, the first parameter represents the degrees of freedom, ν, followed by the location, µ and scale, σ , parameters.

Priors for the PuMBA SRTM model
For all priors, we use the same terminology used in Matheson and Ogden (2023).
Global Intercepts Note that all priors are defined over the natural logarithms of the parameters, where the mean is shown first and the standard deviation second.

Individual deviations
Differences between individuals were defined by specifying the primary pharmacokinetic parameters in one variance-covariance matrix.

Regional deviations
For log BP ND and log R 1 , regional differences were defined as unpooled effects using a dummy (indicator) variable defined with reference to the dorsolateral prefrontal cortex as covariates.For simplicity, all regional differences were defined for all other regions as zero-centred regularising priors with the same SD.
For k ′ 2 , regional differences were defined as a partially-pooled variable, arising from a common distribution.

Covariates for PK Parameters
For the effects of group on BP ND , we defined priors for each region and diagnosis separately in order to detect regionally-specific effects.
We also defined priors for age (per decade, centred) and sex as nuisance variables.

Residual deviations
We defined residuals, ε, also as being correlated across the PK parameters in the same way as the individual and regional deviations.The residual variance hence corresponds to a combination of the TAC deviations described above for the SiMBA models, as well as inaccuracy in the estimation of these parameters.

Fixed Regional Effects Results
Below are shown the regional differences as shown in Figure 2. Below are shown the regional differences from the additional models fit with random slopes for regional differences in projection regions.And below are the comparisons between the raphe and projection region differences between groups, i.e. comparing whether the group differences were statistically differentiably larger in the raphe nuclei compared to the average group differences in projection regions.Here the differences are presented in the units of logBP.

Table S3 .
Summary of Regional Differences in Group Difference Estimates

10.4 Supplementary Materials S4: Binding Potential Values Figure
S1. Raphe nuclei binding potential values for all outcome measures 27/27