 Commentary
 Open Access
 Published:
An abbreviated therapydosimetric equation for the companion diagnostic/therapeutic [^{64/67}Cu]CuSARTATE
EJNMMI Research volume 11, Article number: 75 (2021)
Abstract
In a preclinical model of neuroblastoma, Dearling et al. recently demonstrated the potential interest for a theranostic approach of [^{64}/^{67}Cu]CuSARTATE for the detection and treatment of SSTR2positive neuroblastoma lesions in pediatric patients whose widespread metastases survive initial therapy as minimal residual disease (MRD). MRD may be detected by [^{64}Cu]CuSARTATE and subsequently treated by [^{67}Cu]CuSARTATE. 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 therapydosimetric equation for the companion diagnostic/therapeutic [^{64}/^{67}Cu]CuSARTATE that might be of interest for future clinical theranostic practice.
Background
Companion diagnostic/therapeutic radiopharmaceuticals (DRP/TRP) 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 PETimaging scan with DRP that selects patients who can subsequently benefit from a therapy with TRP. It therefore appears instrumental to predict cumulated activity (\(\tilde{A}_{{\text{C}}}\)), and, hence, delivered radiationdose of TRP in tumors, from DRP uptake in the initial diagnostic scan. In this connection, a model was previously proposed for comparing kinetic parameters and \(\tilde{A}_{{\text{C}}}\) of the companion ^{64}Cu/^{177}Lucetuximab [2].
Recently, the [^{64}Cu]CuSARTATE biodistribution was assessed by Dearling et al. in a preclinical intrahepatic model of neuroblastoma (NB) metastatic disease, representing minimal residual disease (MRD), along with potential therapeutic effect of [^{67}Cu]CuSARTATE [1]. Unlike the companion ^{64}Cu/^{177}Lucetuximab, whose input function (IF, i.e., RPblood timeactivitycurve) was different for diagnosis/therapy (time constant of monoexponentially decaying IF of 0.0830 h^{−1} and 0.0224 h^{−1}, uncorrected for physical decay, respectively), the companion [^{64}/^{67}Cu]CuSARTATE provides the opportunity of using a “true” theranostic pair of radionuclides, resulting in identical DRP/TRP uptake features [1, 2].
The present theoretical commentary aims at deriving an abbreviated equation of therapeutic \(\tilde{A}_{{\text{C}}}\) with [^{67}Cu]CuSARTATE, from [^{64}Cu]CuSARTATE uptake assessed in a single initial diagnostic scan. In the preclinical framework of Dearling et al., this equation was refined by using the common mouse IF of [^{64/67}Cu]CuSARTATE and the physicaldecayrate constant of the ^{64/67}Cu radionuclides [1].
Methods
Derivation
Assuming irreversible trapping, when PET imaging is acquired at peak time of decayuncorrected trappedtraceractivity concentration, it has been shown that [3]:
where SUV_{Tumor} and SUV_{Blood} (g mL^{−1}) are the mean standarduptakevalue in tumor and blood, respectively, K_{i} (mL time^{−1} mL^{−1}) is the tracer uptakerate constant in tumor, λ (time^{−1}) is the tracer physicaldecayrate constant and F (mL mL^{−1}) is the fraction of free tracer in blood and interstitial volume (i.e., Patlakplot yintercept).
Furthermore, the total number of disintegrations \(\tilde{A}_{C}\) (i.e., cumulated activity; Bq s) occurring in tissue volume V (mL) after tracer injection can be estimated as [2, 4]:
where \([\tilde{A}\_{\text{IF}}]\) (Bq s mL^{−1}) is the area under curve of the tracer decayuncorrected IF.
Applying Eq. 1 to DRP leads to:
where k = K_{iT}/K_{iD}, λ_{D} is the physicaldecayrate constant of [^{64}Cu]CuSARTATE and F_{D} is its free fraction in blood and interstitial volume.
Incorporating Eq. 3 into Eq. 2 applied to TRP yields the general equation of its cumulated activity:
where λ_{T} is the physicaldecayrate constant of [^{67}Cu]CuSARTATE, F_{T} is its free fraction in blood and interstitial volume, and SUR_{D}(t_{peakuncorr}) is the tumortoblood SUV ratio (no unit) assessed at peak time of decayuncorrected activity concentration of trapped DRP [5].
Input function of [^{64}/^{67}Cu]CuSARTATE and peak time
Mean bloodclearance data provided by Dearling et al. were used to fit the common IF of [^{64/67}Cu]CuSARTATE, after removing decay correction (GraphPad Prism 6 software) [1]: IF(t) = Y_{0} × exp(−α × t) with Y_{0} = 4.11939 %IA/g (IA: injected activity in Bq) and α = 0.18934 h^{−1} (n = 4; R = 0.999; P < 0.01; 95%CI of 4.08542–4.15335 and of 0.18579–0.19289, respectively). As a result, \([\tilde{A}\_{\text{IF}}_{{\text{T}}} ]\) involving [^{67}Cu]CuSARTATE was 783 × IA mL^{−1} (= [Y_{0} × IA × 3600]/[100 × α]), assuming tissue density of 1 g mL^{−1}.
Peak time of decayuncorrected activity concentration of trapped [^{64}Cu]CuSARTATE was assessed from an analytical solution of the nonlinear Patlak’s equation, involving the abovereported monoexponentially decaying IF [6]:
Peak time could thus be graphically determined, and, when solving Eq. 5 for dC_{TrappedD}(t)/dt = 0, could be alternatively computed as t_{peakuncorr} = Log(α/λ_{D})/(α − λ_{D}). Furthermore, SUR_{D}(t_{peakuncorr}) (= SUV_{TumorD}(t_{peakuncorr})/SUV_{BloodD}(t_{peakuncorr})) in Eq. 4 was obtained by adding the term “F_{D} × IF(t_{peakuncorr})” to Eq. 5 righthand side and by dividing the whole by IF(t_{peakuncorr}), since the tumortoblood SUV ratio equals the tumortoblood activity–concentration ratio [6].
Results
Figure 1 shows the decayuncorrected activity concentration of trapped and tumor [^{64}Cu]CuSARTATE versus time (in arbitrary unit) that were obtained from Eq. 5. The trappedtracer timeactivity curve (TAC; in arbitrary unit) was drawn by setting an arbitrary K_{iD} 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 trappedtracerTAC peak time could thus be graphically assessed at 9 h postinjection, coherently with the computed outcome of t_{peakuncorr} = Log(α/λ_{D})/(α − λ_{D}) [2, 6]. The t_{peakuncorr} computing emphasizes the [^{64/67}Cu]CuSARTATE IF time constant α, whose 95%CI limits obtained from fitting Dearling et al.’s mean bloodclearance data yielded a 1.1%relative change in the peaktime value (corresponding to a 6minabsolute change). In comparison with the trappedtracer 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 SURversustime curve. At t = 9 h postinjection, the SUR value is close to 1 (for the above K_{iD} and F_{D} values), thus indicating that tumor and bloodactivity concentration are close, of about 27 × 10^{3} Bq g^{−1} (for a mean [^{64}Cu]CuSARTATE IA of 3.61 × 10^{6} Bq [1]). An ± 1h uptaketime variability around peak time results in a + 19/− 17% increase/decrease in SUR, respectively.
Since the companion [^{64}/^{67}Cu]CuSARTATE uses a “true” theranostic pair of radionuclides, resulting in chemically identical Culabeled SARTATE molecules, it is then assumed that k = 1 (i.e., K_{iT} = K_{iD}) and F_{D} = F_{T} = F. As a consequence, an refined abbreviated equation of therapeutic [^{67}Cu]CuSARTATE \(\tilde{A}_{C}\), from [^{64}Cu]CuSARTATE uptake in a diagnostic scan achieved at t_{peakuncorr} = 9 h postinjection, is:
where λ_{D}/λ_{T} = 4.87.
Discussion
In a preclinical intrahepatic model of NB metastatic disease representing MRD, Dearling et al. measured the biodistribution of [^{64}Cu]CuSARTATE and evaluated the potential of [^{67}Cu] CuSARTATE as a therapeutic agent [1]. In this framework, Eq. 6 allows computing of an estimate of [^{67}Cu]CuSARTATE \(\tilde{A}_{{\text{C}}}\), and, hence, of delivered radiationdose, involving the SUR assessed in an initial [^{64}Cu]CuSARTATE diagnostic scan acquired at 9 h postinjection. The assumptions made for deriving Eq. 6 are justified since [^{64}/^{67}Cu]CuSARTATE provides the opportunity of using a “true” theranostic pair of radionuclides for which (i) K_{iT} = K_{iD} (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 postinjection, the SUR value involved in Eq. 6 is over/underestimated, respectively. A ± 1h uptaketime variability around peak time results in a + 19/− 17% increase/decrease in SUR, and, hence, in an over/underestimation of [^{67}Cu]CuSARTATE \(\tilde{A}_{{\text{C}}}\), 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]CuSARTATE \(\tilde{A}_{{\text{C}}}\) value with reduced test–retest variability.
The accuracy of the bloodactivityconcentration measurements plays a critical role in the measurement uncertainty of [^{67}Cu]CuSARTATE \(\tilde{A}_{{\text{C}}}\). Since t_{peakuncorr} = Log(α/λ_{D})/(α − λ_{D}), inaccurate bloodactivityconcentration measurements result in an inaccurate estimate of the time constant of the [^{64/67}Cu]CuSARTATE IF (i.e., of α), and, hence, in a biased estimate of the peaktime value, leading then to the aboveaddressed over/underestimation of [^{67}Cu]CuSARTATE \(\tilde{A}_{{\text{C}}}\). Furthermore, assuming t_{peakuncorr} is accurately known, an under/overestimation of [^{64}Cu]CuSARTATE bloodactivity concentration in a mouse at peak time results in an increase/decrease in SUR, and, hence, in an over/underestimation of [^{67}Cu]CuSARTATE \(\tilde{A}_{{\text{C}}}\), respectively. More precisely, the absolute change in [^{67}Cu]CuSARTATE \(\tilde{A}_{{\text{C}}}\) may be assessed from Eq. 6, as:
where f is the factor of either under or overestimation of [^{64}Cu]CuSARTATE bloodactivity concentration in a mouse at peak time. However, a convolutional neural network has been recently investigated in humans that can provide robust automatic imagebased 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]CuSARTATE PET imaging to reduce the measurement uncertainty of SUV_{Blood}(t_{peakuncorr}), and, hence, that of [^{64}Cu]CuSARTATE SUR(t_{peakuncorr}) and of [^{67}Cu]CuSARTATE \(\tilde{A}_{{\text{C}}}\) [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 \(\tilde{A}_{{{\text{C}}67{\text{Cu}}}}\) is provided, that is more acceptable than an underestimate for therapeutic purpose: the higher the [^{64}Cu]CuSARTATE uptake, the higher the peaktime SUR_{64Cu} and the less significant the overestimation.
The scope of Eq. 6 is limited to the preclinical intrahepatic model of NB metastatic disease representing MRD, since mouse data published by Dearling et al. were used [1]. Therefore, the current theoretical commentary should be considered as a preclinical step for determining whether [^{64}Cu]CuSARTATE imaging might reliably predict dosimetry with [^{67}Cu]CuSARTATE and, hence, might predict therapeutic outcome of patients in future clinical theranostic practice. Indeed, clinical translation requires additional experiments in preclinical models, followed by experiments in humans to investigate the measurement uncertainty of the patientspecific [^{64/67}Cu]CuSARTATE IF involved in t_{peakuncorr} and in \([\tilde{A}\_{\text{IF}}_{{\text{T}}} ]\), respectively, as well as that of the [^{64}Cu]CuSARTATE SUR possibly uptaketime corrected to t_{peakuncorr}.
Conclusions
The companion [^{64}/^{67}Cu]CuSARTATE provides the opportunity of using a “true” theranostic pair of radionuclides, that allows deriving an abbreviated equation of therapeutic [^{67}Cu]CuSARTATE \(\tilde{A}_{{\text{C}}}\). This equation emphasizes the [^{64}Cu]CuSARTATE SUR assessed in a single diagnostic scan acquired at peak time of decayuncorrected activity concentration of trapped [^{64}Cu]CuSARTATE. We suggest that it might be of interest for future clinical theranostic practice.
Availability of data and materials
The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request.
Abbreviations
 \(\tilde{A}_{{\text{C}}}\) :

Cumulated activity
 \([\tilde{A}\_{\text{IF}}]\) :

Area under curve of the tracer decayuncorrected input function
 DRP/TRP:

Diagnostic/therapeutic radiopharmaceuticals
 F :

Fraction of free tracer in blood and interstitial volume
 IF:

Tracer input function
 Ki :

Tracer uptakerate constant in tumor
 λ :

Tracer physicaldecayrate constant
 MRD:

Minimal residual disease
 NB:

Neuroblastoma
 SUVBlood:

Mean standarduptakevalue in blood
 SUVTumor:

Mean standarduptakevalue in tumor
 SUR:

Tumortoblood SUV ratio
 TAC:

Time–activity curve
 tpeakuncorr:

Peak time of decayuncorrected trappedtracer activity concentration
 PET:

Positron emission tomography
References
 1.
Dearling JLJ, van Dam EM, Harris MJ, Packard AB. Detection and therapy of neuroblastoma minimal residual disease using [64/67Cu] CuSARTATE in a preclinical model of hepatic metastases. EJNMMI Res. 2021;11:20–33.
 2.
Laffon E, Thumerel M, Jougon J, Marthan R. Cumulated activity comparison of 64Cu/177Lulabeled antiepidermal growth factor receptor antibody in esophageal squamous cell carcinoma model. J Nucl Med. 2017;58:888–90.
 3.
Laffon E, Marthan R. Is there a relevant imaging time for optimal quantitative ^{89}ZrDFODaratumumab PET imaging? Radiology. 2021;299:E285.
 4.
Laffon E, Bardies M, Barbet J, Marthan R. Calculating an estimate of tissue integrated activity in 18FFDG PET imaging using one SUV value. EJNMMI Res. 2013;3:26–32.
 5.
van den Hoff J, Oehme L, Schramm G, et al. The PETderived tumortoblood standard uptake ratio (SUR) is superior to tumor SUV as a surrogate parameter of the metabolic rate of FDG. EJNMMI Res. 2013;3:77–85.
 6.
Laffon E, Calcagni ML, Galli G, Giordano A, Capotosti A, Marthan R, Indovina L. Comparison of threeparameter kinetic model analysis to standard Patlak’s analysis in ^{18}FFDG PET imaging of lung cancer patients. EJNMMI Res. 2018;8:24–32.
 7.
Hofheinz F, Apostolova I, Oehme L, Kotzerke J, Van den Hoff J. Test–retest variability in lesion SUV and lesion SUR in ^{18}FFDG PET: an analysis of data from two prospective multicenter trials. J Nucl Med. 2017;58:1770–5.
 8.
Nikulin P, Hofheinz F, Maus J, Li Y, Bütof R, Lange C, Furth C, Zschaeck S, Kreissl MC, Kotzerke J, van den Hoff J. A convolutional neural network for fully automated blood SUV determination to facilitate SUR computation in oncological FDGPET. Eur J Nucl Med Mol Imaging. 2021;48:995–1004.
Acknowledgements
Not applicable.
Funding
None.
Author information
Affiliations
Contributions
Study concept, EL; study design and manuscript writing, EL, HC, RM; guarantor of integrity of entire study, RM. All authors read and approved the final manuscript.
Corresponding author
Ethics declarations
Ethics approval and consent to participate
Not applicable.
Consent for publication
Not applicable.
Competing interests
The author(s) declare that they have no competing interests.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Laffon, E., de Clermont, H. & Marthan, R. An abbreviated therapydosimetric equation for the companion diagnostic/therapeutic [^{64/67}Cu]CuSARTATE. EJNMMI Res 11, 75 (2021). https://doi.org/10.1186/s13550021008146
Received:
Accepted:
Published:
Keywords
 Theranostics
 SARTATE
 Dosimetry
 Cumulated activity
 Neuroblastoma