64 Cu-/ 177 Lu-Cetuximab Theranostic Pair: May the Single 64 Cu-Cetuximab Diagnostic Scan Be Acquired at Any Time After Injection?

Arecently published study has proposed two independent equations for estimating ¹⁷⁷Lu-cetuximab cumulative activity from an initial positron emission tomography ⁶⁴Cu-cetuximab diagnostic scan, when acquired at peak time of decay-uncorrected or decay-corrected time–activity curve of trapped tracer (t _peak-uncorr or t _peak-corr), respectively. ^1,2 Applied to published TE-8 tumor-bearing mouse data, the ⁶⁴Cu-cetuximab standard uptake ratio (SUR_64Cu; a.u.), that is, the tumor-to-blood standard uptake value ratio, assessed at either t _peak-uncorr = 14 h or t _peak-corr = 59 h turned out to be a key metric. ^1,2

However, assessing SUR_64Cu at a mandatory acquisition time might be considered as a limitation of the proposed method, even if two options are possible, that is, 14 or 59 h postinjection for ⁶⁴Cu-cetuximab in TE-8 tumor-bearing mice. Therefore, in an attempt to overcome this limitation, the current note aims at theoretically investigating whether SUR_64Cu(t _peak-uncorr) and/or SUR_64Cu(t _peak-corr) could be derived from a single diagnostic scan acquired at time t (h) different from t _peak-uncorr and t _peak-corr.

The previously published study showed that: ^{1 –3}

where K_i-64Cu (mL × h⁻¹ × mL⁻¹) is the ⁶⁴Cu-cetuximab uptake rate constant in the tissue of interest. The ⁶⁴Cu-cetuximab release rate constant from the tissue of interest is k_R-64Cu (h⁻¹) that may involve both a release of the ⁶⁴Cu-cetuximab molecule from its target and a detached ⁶⁴Cu label. The ⁶⁴Cu physical decay rate constant is λ _64Cu ( = 0.05457 h⁻¹). The fraction of free ⁶⁴Cu-cetuximab in blood and interstitial volume is F_64Cu (mL × mL⁻¹), that is, sum of blood volume fraction and of constant ratio of concentrations between free compartment and blood. ³

Furthermore, K_i-64Cu can be expressed as (from previously published Eq. [10]): ^{1 –3}

where C_Tumor-64Cu(t) is total tissue activity concentration at time t (kBq × mL⁻¹), C_Blood-64Cu(t) is blood activity concentration at time t (kBq × mL⁻¹), which is equal to C_Blood-64Cu(t = 0) × exp(–α_64Cu × t) for a monoexponentially decaying input function, and f(t) is given by: ^1,2

Noteworthy, the ratio of the right-hand side of Eq. (3) cancels out the issue of applying or not ⁶⁴Cu physical decay correction to experimental data. Inserting Eq. (3) in Eqs. (1) and (2) then leads to:

In Eqs. (5) and (6), C_Tumor-64Cu(t) and C_Blood-64Cu(t) can be provided by the diagnostic scan. Table 1 compares SUR_64Cu(t _peak-uncorr) and SUR_64Cu(t _peak-corr) values obtained from Eqs. (1) and (2) with those obtained from Eqs. (5) and (6) that involve experimental values of C_Tumor-64Cu(t) and C_Blood-64Cu(t) reported by Song et al at t = 2–24–48–72 h postinjection ^1,2 A good agreement was found at t = 24 and 48 h unlike at t = 2 and 72 h. At t = 2 h, the role of the experimental measurement uncertainty of C_Blood-64Cu(t = 2h) is illustrated by comparing line 2 versus line 1 in Table 1 for both SUR_64Cu(t _peak-uncorr) and SUR_64Cu(t _peak-corr).

OPEN IN VIEWER

Table 1.

Comparison of Standard Uptake Ratio (SUR)_64cu(t _peak-uncorr) and SUR_64Cu(t _peak-corr) Involving Experimental Data

		From Eqs. (1) and (2) (gold standard)	From Eqs. (5) and (6) involving Song's experimental data
			t = 2 h	t = 24 h	t = 48 h	t = 72 h
SUR64Cu	1	0.94 a.u.	0.45 a.u.	0.97 a.u.	0.99 a.u.	0.64 a.u.
(t peak-uncorr = 14 h)	2		0.94 a.u.	0.94 a.u.	0.99 a.u.	0.64 a.u.
SUR64Cu	1	5.05 a.u.	1.60 a.u.	5.27 a.u.	5.38 a.u.	2.91 a.u.
(t peak-corr = 59 h)	2		5.05 a.u.	5.02 a.u.	5.38 a.u.	2.93 a.u.

SUR_64Cu(t _peak-uncorr = 14 h) and SUR_64Cu(t _peak-corr = 59 h) were computed from Eqs. (1) and (2), respectively, by using average values for K_i-64Cu, k_R-64Cu, and F_64Cu previously reported in Table 1 of Laffon and Marthan (from Song's data fitting). ¹ These gold-standard values were compared with values computed from Eqs. (5) and (6) that involved experimental data published by Song et al at t = 2–24–48–72 h postinjection: (1) both C_Tumor-64Cu(t) and C_Blood-64Cu(t) data were used; (2) C_Tumor-64Cu(t) data were only used and C_Blood-64Cu(t) was the average ⁶⁴Cu-cetuximab input function fitted by using Song's data. ^1,2 In lines 1 and 2, average values for k_R-64Cu and F_64Cu were used. ¹

SUR, standard uptake ratio.

Furthermore, Figure 1 shows that the experimental C_Blood-64Cu(t = 2 h) value is ∼25% greater than the fitted value. Figure 1 also shows that the experimental C_Tumor-64Cu(t = 72 h) value is ∼43% lower than the fitted value that may explain the discrepancy found at t = 72 h. Therefore, it was suggested that the diagnostic scan should not be performed too late, since the later the measurement, the greater the measurement uncertainty of C_Tumor-64Cu(t) and C_Blood-64Cu(t).

OPEN IN VIEWER

FIG. 1.

Blood and tumor activity concentration versus time. Fitting (dashed/solid) of Song's experimental data (rhomb/square; uncorrected for physical decay) for ⁶⁴Cu-cetuximab in TE-8 tumor, respectively.

Likewise, it should not be performed too early (1) so that the part of trapped tracer in C_Tumor-64Cu(t) should be greater than that of free tracer and (2) since the above proposed equations are valid for the period t > t* after ⁶⁴Cu-cetuximab injection, according to the reversible Patlak–Blasberg analysis. ^1,3 In other words, it was suggested that the diagnostic scan should be performed at any time around and between the two peak time values.

Regarding F_64Cu, using an average value seems reasonable, in particular for computing SUR_64Cu(t _peak-corr) from Eq. (6), because its part is reduced compared with K_i-64Cu/k_R-64Cu in Eq. (2) (∼5% from Song's data fitting in Table 1 of reference 1). ^1,2 Regarding k_R-64Cu, the lower its value in comparison with that of λ _64Cu ( = 0.05457 h⁻¹), the lower its part in Eq. (1), and, hence, in Eq. (5). When k_R-64Cu = 0, in other words, when ⁶⁴Cu-cetuximab is irreversibly trapped in the tissue of interest: (1) Eq. (5) is simplified and its measurement uncertainty is removed from that of SUR_64Cu(t _peak-uncorr) and (2) Eq. (6) is no more valid, that is, there is only one available peak time (t _peak-uncorr) and, hence, one available estimate of the ¹⁷⁷Lu-cetuximab cumulative activity.

Finally, f(t) has to be computed from Eq. (4), involving an average ⁶⁴Cu-cetuximab input function fitted by using Song's experimental data for ⁶⁴Cu-cetuximab in TE-8 tumor-bearing mouse: C_Blood-64Cu(t) = 17.39 × exp(−0.0830 × t). ^1,2 This feature stresses the relevance of developing systems for accurately measuring C_Blood-64Cu(t), or even better, for estimating the whole ⁶⁴Cu-cetuximab input function in preclinical situations and in forthcoming clinical theranostic practice. ⁴ In this connection, let us note that a multiexponentially decaying input function can be used in Eq. (4), which would not alter the current line of argument.

To conclude, Eqs. (5) and (6) show that it is theoretically possible to derive SUR_64Cu(t _peak-uncorr) and SUR_64Cu(t _peak-corr) from a single ⁶⁴Cu-cetuximab diagnostic scan acquired at time t different from t _peak-uncorr and t _peak-corr and, hence, to compute two estimates of ¹⁷⁷Lu-cetuximab cumulative activity (when ⁶⁴Cu-cetuximab trapping is reversible). ^1,2 Besides measurement of C_Tumor-64Cu(t) and C_Blood-64Cu(t) from this diagnostic scan, an average value of some parameters has to be used, including F_64Cu and k_R-64Cu, as well as an average ⁶⁴Cu-cetuximab input function. The proposed theoretical equations have to be probed in various preclinical situations, in particular, for assessing the additional measurement uncertainty introduced by this SUR normalization in estimating the ¹⁷⁷Lu-cetuximab cumulative activity.