## Abstract

This work aimed at estimating the kinetic parameters, and hence cumulated activity (A_{C}), of a diagnostic/therapeutic convergence radiopharmaceutical, namely ^{64}Cu-/^{177}Lu-labeled antibody (^{64}Cu-/^{177}Lu-cetuximab), that acts as anti–epidermal growth factor receptor. **Methods:** In mice bearing esophageal squamous cell carcinoma tumors, to estimate uptake (K), release rate constant (k_{R}), and hence A_{C}, a kinetic model analysis was applied to recently published biodistribution data of immuno-PET imaging with ^{64}Cu-cetuximab and of small-animal SPECT/CT imaging with ^{177}Lu-cetuximab, including blood and TE-8 tumor. **Results:** K, k_{R}, and A_{C} were estimated to be 0.0566/0.0593 g⋅h^{−1}⋅g^{−1}, 0.0150/0.0030 h^{−1}, and 2.3 × 10^{10}/4.1 × 10^{12} disintegrations (per gram of TE-8 tumor), with an injected activity of 3.70/12.95 MBq, for ^{64}Cu-/^{177}Lu-cetuximab, respectively. **Conclusion:** A model is available for comparing kinetic parameters and A_{C} of the companion diagnostic/therapeutic ^{64}Cu-/^{177}Lu-cetuximab that may be considered as a step for determining whether one can really use the former to predict dosimetry of the latter.

Theragnostics strategy relies on noninvasive quantitative immuno-PET to select patients eligible for radioimmunotherapy. In this framework, Song et al. recently investigated a companion diagnostic/therapeutic radiopharmaceutical acting as anti–epidermal growth factor receptor (EGFR) antibody that was prepared via identical chelator, 3,6,9,15-tetraazabicyclo[9.3.1]-pentadeca-1(15),11,13-trience-3,6,9,-triacetic acid (PCTA), labeled with ^{64}Cu or ^{177}Lu (^{64}Cu-/^{177}Lu-PCTA-cetuximab) (1). This compound was designed for assessing EGFR expression level in esophageal squamous cell carcinoma (ESCC) tumors as well as for subsequent radioimmunotherapy. Any advance in this field is of major interest because innovative therapeutic strategies are actually needed in ESCC patients. In ESCC tumor–bearing mice, the authors reported biodistribution data from immuno-PET imaging with ^{64}Cu-cetuximab and small-animal SPECT/CT imaging with ^{177}Lu-cetuximab, including blood (i.e., the tracer input function [IF]) and TE-8 tumor.

We suggest that further information can be derived from Song et al.’s results, which may prove of interest to comprehensively characterize this novel companion diagnostic/therapeutic radiopharmaceutical. Thus, the aim of this work was to estimate uptake (K), release rate constant (k_{R}), and hence cumulated activity (A_{C})—that is, the number of disintegrations per gram of TE-8 tissue that have occurred from the time of tracer administration (zero) to (theoretically) infinity, after administration of ^{64}Cu-cetuximab and ^{177}Lu-cetuximab for immuno-PET and small-animal SPECT/CT imaging, respectively. To this end, a simple model derived from a previously published kinetic model analysis was used (2,3). Furthermore, this study addresses the issue of determining whether ^{64}Cu-cetuximab imaging might predict ^{177}Lu-cetuximab A_{C}, and hence its dosimetry, in a real clinical situation.

## MATERIALS AND METHODS

A previously published formula was used for estimating A_{C} (expressed per gram of TE-8 tissue, in g^{−1}), including K and k_{R} (3):Eq. 1where AUC_{IF} is the area under the curve of the tracer IF (i.e., total number of disintegrations per gram of blood that have occurred from the time of tracer administration to infinity, in g^{−1}). A_{C} can be derived from mean blood data obtained by Song et al. in a TE-8 tumor model at 2, 24, 48, and 72 h after injection for ^{64}Cu-cetuximab: 20.5, 6.4, 4.4, and 2.5 %ID/g (percentage injected radioactivity dose per gram of tissue; Supplemental Table 1 in Song et al. (1)). For ^{177}Lu-cetuximab, mean blood data obtained in a TE-8 tumor model at 2, 24, 72, and 120 h after injection were used: 30.2, 12.1, 6.0, and 3.1 %ID/g (Supplemental Table 2 in Song et al. (1)). First, the decay correction of Song et al.’s data was removed—that is, the data were multiplied by exp(− λ t), where λ is the ^{64}Cu/^{177}Lu physical decay constant (i.e., Ln2/12.7 and Ln2/160 h^{−1}, respectively). Then, data were fitted with a monoexponential decreasing function (time constant α, in h^{−1}):Eq. 2where A_{b}(t = 0) is expressed in %ID/g. In Equation 1, AUC_{IF} is simply A_{b}(t = 0)/α.

The constant k_{R} (h^{−1}) appearing in Equation 1 can be estimated from the following formula that applies to both PET and SPECT tracer (2):Eq. 3where t_{max} is the uptake peak of the TE-8 tumor time–activity-curve, as published by Song et al. (i.e., involving decay correction): t_{max} = 48 and 120 h for ^{64}Cu-cetuximab and ^{77}Lu-cetuximab, respectively (1). Equation 3 can be solved for k_{R} using a solver (Excel; Microsoft).

The constant K (g. h^{−1}.g^{−1}) appearing in Equation 1 can be estimated from the following formula involving trapped tracer activity in TE-8 tumor, A_{Trap}(t) (2):Eq. 4Mean tissue data published by Song et al. for A_{Trap}(t) in a TE-8 tumor were used: 17.5 and 55.7 %ID/g at t = 48 and 120 h for ^{64}Cu-cetuximab and ^{177}Lu-cetuximab, respectively (Supplemental Tables 1 and 2 in Song et al. (1)). The decay correction of these data was removed—that is, they were multiplied by exp(−λ × t) where λ is the ^{64}Cu/^{177}Lu physical decay constant. Note that Equation 4 does not involve free tracer in blood and interstitial volume, because the part of free tracer becomes negligible in comparison to trapped tracer at late imaging. Indeed, the value of F × A_{b}(t) (with F < < 1; no unit) is much lower than that of A_{Trap}(t) at t = 48 and 120 h for ^{64}Cu-cetuximab and ^{177}Lu-cetuximab, respectively (Fig. 1) (2,3).

A_{C} can also be calculated from original data (after decay correction is removed) published by Song et al. for ^{64}Cu-cetuximab and ^{177}Lu-cetuximab in a TE-8 tumor model, respectively (Supplemental Tables 1 and 2 in Song et al. (1)). A crude estimate of A_{C} can be obtained by trapezoidal integration and assuming a simple radioactive decay after the last data point.

## RESULTS

From Song et al.’s data in a TE-8 model (Supplemental Tables 1 and 2 in Song et al. (1)), α (uncorrected for physical decay) was estimated to be 0.0830 h^{−1} for ^{64}Cu-cetuximab and 0.0224 h^{−1} for ^{177}Lu-cetuximab (Fig. 1, Eq. 2: *R* = 0.99–0.98; *P* < 0.01–0.02) (1). Numeric solving of Equation 3 provided the following estimate of k_{R}: 0.0150 and 0.0030 h^{−1} for ^{64}Cu- and ^{177}Lu-cetuximab, respectively. From Equation 4, K was estimated to be 0.0566/0.0593 g⋅h^{−1}⋅g^{−1} for ^{64}Cu-/^{177}Lu-cetuximab, respectively. Then, from Equation 1, A_{C} was estimated to be 2.3 × 10^{10} and 4.1 × 10^{12} disintegrations per gram of TE-8 tumor, with an injected activity of 3.70 and 12.95 MBq and K/(λ + k_{R}) ratio of 0.8 and 8.1, for ^{64}Cu-cetuximab and ^{177}Lu-cetuximab, respectively.

For comparison, A_{C} obtained by trapezoidal integration of Song et al.’s TE-8 tumor data and assuming a simple radioactive decay after the last data point was estimated to be 2.5 × 10^{10} and 5.3 × 10^{12} disintegrations per gram of TE-8 tumor, for ^{64}Cu-cetuximab and ^{177}Lu-cetuximab, respectively.

## DISCUSSION

This theoretic work aimed at providing further quantitative information, including A_{C}, regarding the companion diagnostic/therapeutic ^{64}Cu-/^{177}Lu-cetuximab from recently published biodistribution data in ESCC tumor–bearing mice. A simple model derived from a published kinetic model analysis was used, allowing us to obtain estimates of K, k_{R}, and hence A_{C} for ^{64}Cu-cetuximab and ^{177}Lu-cetuximab (2,3).

The uptake rate constants of ^{64}Cu-/^{177}Lu-cetuximab were found to be close: K = 0.0566/0.0593 g⋅h^{−1}⋅g^{−1}, respectively. In other words, labeling cetuximab with either ^{64}Cu or ^{177}Lu does not influence its trapping in TE-8 tumors. K actually represents the probability that a ^{64}Cu-/^{177}Lu-cetuximab molecule is trapped in the tissue of interest as the result of an antibody–antigen linking. It does not give any information about its further fate, such as internalization. The release rate constants of ^{64}Cu-/^{177}Lu-cetuximab were found to be low in comparison to K: k_{R} = 0.0150/0.0030 h^{−1}, respectively. k_{R} actually represents the probability that a ^{64}Cu-/^{177}Lu-cetuximab molecule trapped in the tissue of interest is released from its target and returns back to blood. This probability should, additionally, take into account a possible internalization of the antibody–antigen complex that lowers it. Furthermore, we suggest that the 5-fold difference in k_{R} reported for ^{64}Cu-cetuximab versus ^{177}Lu-cetuximab may be related to the fact that k_{R} was estimated using peak time values assessed with a 24- to 48-h time of resolution for ^{64}Cu-/^{177}Lu-cetuximab, respectively (Eq. 3). This large time of resolution very likely introduces some uncertainty measurement for k_{R}, especially because it is derived from a logarithmic equation (Eq. 3).

A_{C} for ^{177}Lu-cetuximab was found to be much greater than that for ^{64}Cu-cetuximab: 4.1 × 10^{12} versus 2.3 × 10^{10} disintegrations per gram of TE-8 tumor. This result is strengthened by the crude estimates for A_{C} provided by trapezoidal integration of Song et al.’s original data and assuming a simple radioactive decay after the last data point: A_{C} *=* 5.3 × 10^{12} versus 2.5 × 10^{10} disintegrations per gram of TE-8 tumor, for ^{177}Lu-cetuximab versus ^{64}Cu-cetuximab, respectively. Note that the injected activity was greater for ^{177}Lu-cetuximab than for ^{64}Cu-cetuximab: 12.95 versus 3.70 MBq. However, the difference in A_{C} may also be explained from Equation 1, showing that for close values of K and k_{R}, the lower the value of α and λ the greater that of A_{C}. It does emphasize the efficiency of radioimmunotherapy with ^{177}Lu-cetuximab investigated in ESCC tumor–bearing mice, and we suggest that the reliable IF fitting as a monoexponential decreasing function (Fig. 1B; *R* = 0.98; *P* < 0.02) is particularly relevant for assessing its dosimetry (Eq. 1). Furthermore, one may argue that Equation 1 does not take into account the part of free tracer in blood and interstitial volume (F) in the A_{C} calculation (3). However, we suggest that this part, and hence the related A_{C} underestimation, is negligible: F is indeed mandatorily much lower than 1, which has to be compared with the ratio K/(λ + k_{R}) whose value is 8.1 for ^{177}Lu-cetuximab.

Regarding the issue of determining whether ^{64}Cu-cetuximab imaging might predict^{177}Lu-cetuximab A_{C}, and hence its dosimetry, in real clinical situations, the current study showed that A_{C} for ^{64}Cu-cetuximab may be obtained from the computed value of k_{R} at uptake peak and the corresponding uptake value (Eqs. 1, 3, and 4). Thus, theoretically, if an average A_{C} ratio between ^{64}Cu-cetuximab and ^{177}Lu-cetuximab has been obtained from previous experiments (with arbitrary injected activities), an estimate for ^{177}Lu-cetuximab A_{C} may be obtained from a single quantitative imaging session with ^{64}Cu-cetuximab. However, a main concern about this line of argument must be underlined, which is related to performing PET imaging at uptake peak of ^{64}Cu-cetuximab (Eq. 3). Indeed, even if the ^{64}Cu-cetuximab IF is known in each individual (i.e., the value of α in Eq. 3), the relevant time delay between ^{64}Cu-cetuximab injection and PET acquisition cannot be predicted in each individual, because, precisely, k_{R} is unknown. Therefore, we suggest that additional experiments, involving lower times of resolution than those reported by Song et al., are required for knowledge of the k_{R} range in a large series of individuals that can also provide the range of the A_{C} ratio between ^{64}Cu-cetuximab and ^{177}Lu-cetuximab (for arbitrary injected activities). If k_{R} is found to vary within narrow limits for ^{64}Cu-cetuximab, the uptake-peak timing might be approximately predicted in each individual and, even, an average k_{R} value might be used for ^{64}Cu-cetuximab A_{C} calculation. Furthermore, the A_{C} ratio between ^{64}Cu-cetuximab and ^{177}Lu-cetuximab should also vary within narrow limits for deriving ^{177}Lu-cetuximab A_{C}. In other words, additional experiments are required to determine whether the measurement uncertainty of the ^{177}Lu-cetuximab A_{C} is acceptable or not. Finally, whatever results obtained in a preclinical model, some adjustment is required in humans.

## CONCLUSION

The study of Song et al. showed that the companion diagnostic/therapeutic radiopharmaceutical, namely ^{64}Cu-/^{177}Lu-cetuximab, may be useful as a diagnostic tool for patient selection as well as a potent radioimmunotherapy agent (1). As further evidence, although complexation and catabolism of copper and lutetium may be quite different, the current study showed that the uptake rate constants of ^{64}Cu-cetuximab and ^{177}Lu-cetuximab are close, and their release rate constants are low in comparison with the uptake rate constants. Moreover, because of a longer physical half-life of ^{177}Lu than ^{64}Cu, a longer IF life time of ^{177}Lu-cetuximab than ^{64}Cu-cetuximab, and a greater injected activity of ^{177}Lu-cetuximab than ^{64}Cu-cetuximab (12.95 vs. 3.70 MBq in Song et al.’s experiments), A_{C} of ^{177}Lu-cetuximab was found to be much greater (2 orders of magnitude in the current framework) than that of ^{64}Cu-cetuximab. However, the current study may be considered as a step for determining whether ^{64}Cu-cetuximab imaging might reliably predict dosimetry with ^{177}Lu-cetuximab in real clinical situations. This major issue requires additional experiments in preclinical models, of which results should be then tested in humans.

## DISCLOSURE

No potential conflict of interest relevant to this article was reported.

## Footnotes

Published online Jan. 12, 2017.

- © 2017 by the Society of Nuclear Medicine and Molecular Imaging.

- Received for publication July 1, 2016.
- Accepted for publication October 31, 2016.