An abbreviated therapy-dosimetric equation for the companion diagnostic/therapeutic [64/67Cu]Cu-SARTATE

In a preclinical model of neuroblastoma, Dearling et al. recently demonstrated the potential interest for a theranostic approach of [64/67Cu]Cu-SARTATE for the detection and treatment of SSTR2-positive neuroblastoma lesions in pediatric patients whose widespread metastases survive initial therapy as minimal residual disease (MRD). MRD may be detected by [64Cu]Cu-SARTATE and subsequently treated by [67Cu]Cu-SARTATE. Since therapeutic dosimetry estimation of the latter agent from the uptake of the former one in the initial diagnostic scan was not addressed, the present theoretical commentary proposes the derivation of an abbreviated therapy-dosimetric equation for the companion diagnostic/therapeutic [64/67Cu]Cu-SARTATE that might be of interest for future clinical theranostic practice.


Background
Companion diagnostic/therapeutic radiopharmaceuticals (D-RP/T-RP) are the basis of the theranostic strategy that uses a molecule designed for a specific target, which is labeled with a suitable pair of radionuclides [1,2]. The strategy consists in a first diagnostic PET-imaging scan with D-RP that selects patients who can subsequently benefit from a therapy with T-RP. It therefore appears instrumental to predict cumulated activity ( Ã C ), and, hence, delivered radiation-dose of T-RP in tumors, from D-RP uptake in the initial diagnostic scan. In this connection, a model was previously proposed for comparing kinetic parameters and Ã C of the companion 64 Cu/ 177 Lucetuximab [2].

Derivation
Assuming irreversible trapping, when PET imaging is acquired at peak time of decay-uncorrected trappedtracer-activity concentration, it has been shown that [3]:

Open Access
*Correspondence: elaffon@u-bordeaux.fr 1 CHU de Bordeaux, 33000 Bordeaux, France Full list of author information is available at the end of the article where SUV Tumor and SUV Blood (g mL −1 ) are the mean standard-uptake-value in tumor and blood, respectively, K i (mL time −1 mL −1 ) is the tracer uptake-rate constant in tumor, λ (time −1 ) is the tracer physical-decayrate constant and F (mL mL −1 ) is the fraction of free tracer in blood and interstitial volume (i.e., Patlak-plot y-intercept).
Furthermore, the total number of disintegrations Ã C (i.e., cumulated activity; Bq s) occurring in tissue volume V (mL) after tracer injection can be estimated as [2,4]: where [Ã_IF] (Bq s mL −1 ) is the area under curve of the tracer decay-uncorrected IF.
Applying Eq. 1 to D-RP leads to: where λ T is the physical-decay-rate constant of [ 67 Cu]Cu-SARTATE, F T is its free fraction in blood and interstitial volume, and SUR D (t peak-uncorr ) is the tumor-to-blood SUV ratio (no unit) assessed at peak time of decay-uncorrected activity concentration of trapped D-RP [5].

Input function of [ 64 / 67 Cu]Cu-SARTATE and peak time
Mean blood-clearance data provided by Dearling et al. were used to fit the common IF of [ 64/67 Cu]Cu-SARTATE, after removing decay correction (Graph-Pad Prism 6 software) [1]: involving the above-reported mono-exponentially decaying IF [6]: Peak time could thus be graphically determined, and, when solving Eq. 5 for dC Trapped-D (t)/dt = 0, could be alternatively computed as t peak-uncorr = Log(α/ λ D )/(α − λ D ). Furthermore, SUR D (t peak-uncorr ) (= SUV Tumor-D (t peak-uncorr )/SUV Blood-D (t peak-uncorr )) in Eq. 4 was obtained by adding the term "F D × IF(t peak-uncorr )" to Eq. 5 right-hand side and by dividing the whole by IF(t peak-uncorr ), since the tumor-to-blood SUV ratio equals the tumor-to-blood activity-concentration ratio [6]. Figure 1 shows the decay-uncorrected activity concentration of trapped and tumor [ 64 Cu]Cu-SARTATE versus time (in arbitrary unit) that were obtained from Eq. 5. The trapped-tracer time-activity curve (TAC; in arbitrary unit) was drawn by setting an arbitrary K i-D value of 0.05 mL h −1 mL −1 , which does not play a role in determining its peak time (Eq. 5) [2,4,6]. The trapped-tracer-TAC peak time could thus be graphically assessed at 9 h post-injection, coherently with the computed outcome of t peak-uncorr = Log(α/λ D )/(α − λ D ) [2,6]. The t peak-uncorr computing emphasizes the [ 64/67 Cu]Cu-SARTATE IF time constant α, whose 95%-CI limits obtained from fitting Dearling et al. 's mean blood-clearance data yielded a 1.1%-relative change in the peak-time value (corresponding to a 6-min-absolute change). In comparison with the trapped-tracer TAC, the tumor TAC additionally involves free tracer in blood and interstitial volume, of which fraction F D was arbitrarily set to 0.1 mL mL −1 . Figure 1 also shows the corresponding SUR-versus-time curve. At t = 9 h post-injection, the SUR value is close to 1 (for the above K i-D and F D values), thus indicating that tumor-and blood-activity concentration are close, of about 27 × 10 3 Bq g −1 (for a mean [ 64 Cu]Cu-SARTATE IA of 3.61 × 10 6 Bq [1]). An ± 1-h uptake-time variability around peak time results in a + 19/− 17% increase/ decrease in SUR, respectively.

Results
Since the companion [ 64 / 67 Cu]Cu-SARTATE uses a "true" theranostic pair of radionuclides, resulting in chemically identical Cu-labeled SARTATE molecules, it is then assumed that k = 1 (i.e., K i-T = K i-D ) and F D = F T = F. As a consequence, an refined abbreviated equation of therapeutic [ 67 Cu]Cu-SARTATE Ã C , from [ 64 Cu]Cu-SARTATE uptake in a diagnostic scan achieved at t peak-uncorr = 9 h post-injection, is: where λ D /λ T = 4.87.

Discussion
In a pre-clinical intrahepatic model of NB metastatic disease representing MRD, Dearling et al. measured the biodistribution of [ 64 Cu]Cu-SARTATE and evaluated the potential of [ 67 Cu] Cu-SARTATE as a therapeutic agent [1]. In this framework, Eq. 6 allows computing of an estimate of [ 67 Cu]Cu-SARTATE Ã C , and, hence, of delivered radiation-dose, involving the SUR assessed in an initial [ 64 Cu]Cu-SARTATE diagnostic scan acquired at 9 h postinjection. The assumptions made for deriving Eq. 6 are justified since [ 64 / 67 Cu]Cu-SARTATE provides the opportunity of using a "true" theranostic pair of radionuclides for which (i) K i-T = K i-D (same irreversible trapping) (ii) F D = F T (same fraction of free tracer in blood and interstitial volume) and (iii) same IF.
The SUR increases with time ( Fig. 1), and, consequently, after/before peak time of 9 h post-injection, the SUR value involved in Eq. 6 is over/underestimated, respectively. A ± 1-h uptake-time variability around peak time results in a + 19/− 17% increase/decrease in SUR, and, hence, in an over/underestimation of [ 67 Cu] Cu-SARTATE Ã C , respectively. However, Hofheinz et al. have shown in human [ 18 F]-FDG PET imaging that correcting SUR for uptake time to an arbitrary value may lead to reduced test-retest variability in comparison with that of the SUV [7]. In this connection, we suggest that, potentially, correcting SUR for uptake time (to 9 h postinjection in the current mouse framework) might provide an [ 67 Cu]Cu-SARTATE Ã C value with reduced test-retest variability.
The accuracy of the blood-activity-concentration measurements plays a critical role in the measurement uncertainty of [ 67 Cu]Cu-SARTATE Ã C . Since t peakuncorr = Log(α/λ D )/(α − λ D ), inaccurate blood-activity-concentration measurements result in an inaccurate estimate of the time constant of the [ 64/67 Cu]Cu-SARTATE IF (i.e., of α), and, hence, in a biased estimate of the peak-time value, leading then to the above-addressed over/underestimation of [ 67 Cu]Cu-SARTATE Ã C . Furthermore, assuming t peak-uncorr is accurately known, an under/overestimation of [ 64 Cu]Cu-SARTATE blood-activity concentration in a mouse at peak time results in an increase/ decrease in SUR, and, hence, in an over/underestimation of [ 67 Cu]Cu-SARTATE Ã C , respectively. More precisely, the absolute change in [ 67 Cu]Cu-SARTATE Ã C may be assessed from Eq. 6, as: where f is the factor of either under-or overestimation of [ 64 Cu]Cu-SARTATE blood-activity concentration in a mouse at peak time. However, a convolutional neural network has been recently investigated in humans that can provide robust automatic image-based mean values of [ 18 F]-FDG SUV Blood over the aorta. We thus suggest that such a device might also be relevant in mouse [ 64 Cu] Cu-SARTATE PET imaging to reduce the measurement uncertainty of SUV Blood (t peak-uncorr ), and, hence, that of [ 64 Cu]Cu-SARTATE SUR(t peak-uncorr ) and of [ 67 Cu]Cu-SARTATE Ã C [8].
Equation 6 might be further simplified by using a mean value for F, obtained from experiments that remain to be performed. When F is considered negligible compared to SUR -64Cu (t = 9 h), an overestimate of Ã C-67Cu is provided, that is more acceptable than an underestimate for therapeutic purpose: the higher the [ 64 Cu]Cu-SARTATE uptake, the higher the peak-time SUR -64Cu and the less significant the overestimation.
The scope of Eq. 6 is limited to the pre-clinical intrahepatic model of NB metastatic disease representing MRD, since mouse data published by Dearling Cu-SARTATE IF involved in t peak-uncorr and in [Ã_IF -T ] , respectively, as well as that of the [ 64 Cu]Cu-SARTATE SUR possibly uptake-time corrected to t peak-uncorr .

Conclusions
The companion [ 64 / 67 Cu]Cu-SARTATE provides the opportunity of using a "true" theranostic pair of radionuclides, that allows deriving an abbreviated equation