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Review
. 2021 Jan:92:5-23.
doi: 10.1016/j.nucmedbio.2020.03.002. Epub 2020 Mar 12.

Concepts for design and analysis of receptor radiopharmaceuticals: The Receptor-Binding Radiotracers series of meetings provided the foundation

Kenneth A Krohn  1 , David R Vera  2
Affiliations
Review

Concepts for design and analysis of receptor radiopharmaceuticals: The Receptor-Binding Radiotracers series of meetings provided the foundation

Kenneth A Krohn et al. Nucl Med Biol. 2021 Jan.

Abstract

A symposium at George Washington University on Receptor-Binding Radiotracers in 1980 and three follow-up meetings held at University of California, San Diego provided a forum for debating the critical concepts involved in the new field of designing and evaluating radiotracers for imaging receptors and transporters. This review is intended to educate young investigators who may be relatively new to receptor radiopharmaceutical development. Our anticipated audience includes researchers in basic pharmacology, radiochemistry, imaging technology and kinetic data analysis and how these disciplines have worked together to build our understanding of the human biology of transporters and receptor signaling in health and disease. We have chosen to focus on radiochemical design of a useful imaging agent and how design is coupled to analysis of data collected from dynamic imaging with that agent. Some pharmacology may be required for designing the imaging agent and some imaging physics may be important in optimizing the quality of data that is collected. However, the key to a successful imaging agent is matching the radiotracer to the target receptor and to analysis of the time-course data that is used to parse delivery from specific binding and subsequent metabolism or degradation. Properly designed imaging agents are providing critical information about human biology in health and disease as well as pharmacodynamic response to drug interventions. The review emphasizes some of the ideas that were controversial at the 1980 conference and chronicles with literature examples how they have resolved over the four decades of using radiotracers to study transporters and receptors in human subjects. These examples show that there are situations where a very small KD, i.e. high affinity, has the potential to yield an image that reflects blood flow more than receptor density. The examples also show that by combining two studies, one with high specific activity and a second with low specific activity injections one can unravel the pseudo-first order rate B'max into the true second-order rate constant, k3, and the unoccupied receptor density. The final section describes how mathematical methods first presented to the receptor-imaging community in 1980 are now being used to provide confidence in the analysis of kinetic biodistribution studies. Our hope is that by bringing these concepts together in a single review, the next generation of scientists developing receptor imaging agents can be much more efficient than their pioneers in developing useful imaging methods.

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Figures

Fig. 1.
Fig. 1.
Receptor binding in vitro and in vivo. (A) The whole tissue section is exposed to a uniform level of ligand for sufficient time to achieve a steady state in the free and bound compartments. Then the medium is replaced by a ligand-free solution to wash away unbound or non-specifically bound ligand, leaving only Cbound, which can be measured by quantitative autoradiography. (B) The ligand is supplied in the vascular pool and requires transport across the capillary endothelium and a cell wall to enter the intracellular space where it then equilibrates between a bound and a free state. This is a dynamic process, so identifying a true steady-state condition is problematic.
Fig. 2.
Fig. 2.
Schematic of data collection and analysis for graphical analysis of a 11C-CGP-PET study. Note that the concentration axis is a logarithmic scale. Procedurally, a tracer dose D0* is injected at time T0 and imaged for sufficient time to accurately define the slope s0 of the plateau phase so that its intercept, C0*, can be estimated graphically. At approximately T30 a co-injection of labeled (D1*) and carrier CGP (D1) is administered and a new slope s1 is extrapolated to the time of the second injection to estimate C1*. If desired, a massive injection of carrier CGP with no added radioactivity can then be administered to displace bound radioactivity. The slope s2 is a measure of the unimolecular dissociation rate of the LR complex, koff or k4 in Fig. 1B.
Fig. 3.
Fig. 3.
Pharmacokinetic model used for analysis of TcNGA. Note similarities to Fig. 1, panel B. The physiochemical elements F, Ve, and Vh for the rate constants that determine the transfer of radiopharmaceutical in and out of the target organ plasma, and kon and [R] control the formation of the receptor-ligand complex C. If the amount of PR injected Lo is equal in magnitude to total amount of free receptor, the physiochemical element [R] will change in value during the imaging study. The model states, [L]e, [L]h, and [C] are in concentration units (mol/L). The initial conditions of the model assume an equilibrium between the [L]e and [L]h and conservation of mass between all compartments (model states) at the time that the plasma sampled as the fraction of the injected dose, f, at 2 min PI, which is the start of the simulation. Additionally, the koff is 9 orders of magnitude a smaller amount of than the kon and is not considered in the model. Additionally, metabolism of the complex is neglected. The observational data (Y1 & Y2) consists of a heart/lung and liver time-activity curves are coupled to the model states by the observational couplings (σ1, σ4 & σ3).
Fig. 4.
Fig. 4.
Sensitivity analysis shown as a percentage of change in SUV at different times after injection. This figure was helpful in evaluating different approaches to analysis of [11C]-acetate PET in brown adipose tissue activated by cold exposure in healthy elderly men. Models with only 2 or 3 tissue compartments and four model parameters provided the best compromise between quality of fit and stability/accuracy. Figure is reproduced from supplemental data for reference [60].
Fig. 5.
Fig. 5.
A sensitivity analysis of receptor quantity. This analysis used an in vitro measurement of receptor density from liver biopsy samples and the metric t90, which represents the rate of hepatic accumulation. The statistically significant correlation demonstrates kinetic sensitivity of TcNGA time-activity date to receptor quantity [62].
Fig. 6.
Fig. 6.
A sensitivity analysis of scaled molar dose. This analysis was performed in pigs using increasing molar doses of the radiopharmaceutical (RP). Measurements during the 20-minute dynamic study provided the calculation of F/Ve, the rate constant for RP delivery via hepatic plasma flow. Three different scaled molar doses (1.2, 12, & 110 nmol per kg of body weight) produced three time-activity curves with vastly different shapes, time-to-peak, and t90 values. Note the almost linear curve of the 110 nmol/kg dose- a hallmark of a second-order process.
Fig. 7.
Fig. 7.
Sensitivity analysis of the TcNGA system at “tracer” and “non-tracer” doses. (A) When the ratio of Lo to Ro is 0.01, the physiochemical element with the highest sensitivity is Ve. Hepatic flow, F, is higher than Ro/Vr, which is similar in magnitude as kon and Vh. The fact that the Ro/Vr and kon, curves have different shapes indicates good identifiability. Similar shapes to the Ro/Vr and F curves are an indication that an attempt to simultaneously estimate both parameters will yield high relative uncertainties. (B) When the ratio of Lo/Ro is 0.5, the parameter with the highest sensitivity is Ro/Vr. The sensitivity to F is significantly lower compared to the “tracer” dose scenario. The large difference in sensitivity predicts estimates of high precision for Ro/Vr and high uncertainty for F.
Fig. 8.
Fig. 8.
A graphical depiction of goodness-of-fit. Two contour plots of the Reduced Chi-Squared (RCS) space generated by changes in receptor concentration and hepatic plasma flow. The red lines represent the reduced Chi-square contours from curve-fits to a data set resulting from a “tracer” (Lo/Ro = 0.01) injection of TcNGA. The blue lines represent the reduced Chi-square contours for a data set resulting from a “non-tracer” (Lo/Ro = 0.5) injection of TcNGA. The numbers represent the RCS for each contour. The black dot at the center of the plot is the lowest Chi-square, where the curve-fitting algorithm will converge if it is properly controlled.
Fig. 9.
Fig. 9.
Local parameter identifiability analysis at “tracer” and “non-tracer” doses. Both panels provide the coefficient of variation (CV) for three model parameters: receptor concentration Ro/Vr, forward binding rate constant kon, and hepatic plasma flow F. (Panel A) At “tracer” doses it is not possible to simultaneously estimate kon & Ro/Vr; the orange and green curves in panel A do not fall below CVs of 40%. It is possible to estimate hepatic plasma flow F with uncertainties <25%. At both very low and very kon/Vr it is possible to estimate F to a relative uncertainty of <10%; at low and high affinities the blue line falls below CVs of <10%. (Panel B) At a “non-tracer” dose (Lo/Ro = 0.5), it will be possible to simultaneously estimate F, kon & Ro/Vr; this was predicted by the sensitivity analysis (Fig. 7B) where the “nontracer” dose produced F, kon & Ro/Vr curves of somewhat different shapes and vastly different magnitudes.
Fig. 10.
Fig. 10.
Analysis of diagnostic accuracy. Different combinations of model estimates provide different levels of diagnostic accuracy. The metric with the largest area-under curve (AUC) was kon{R]o{R]o/tbw (Az = 0.985 ± 0.011). The Ro/Vr metric produced an AUC (Az = 0.974 ± 0.018) that was not statistically different (P = 0.188) than kon{R]o{R]o/tbw. The ABT metric yielded a high AUC (Az = 0.939 ± 0.030). When the total amount of receptor Ro was tested, the AUC was 0.875 ± 0.042, which differed significantly (P < 0.005) from kon{R]o{R]o/tbw. We concluded from this analysis that intensive variables such as kon{R]o{R]o/tbw, [R]o, which equals Ro/Vr, provide the best diagnostic metrics. Such variables are independent of size. The extensive metric Ro yielded a poor AUC because it can change depending on the patient’s body weight and gender.
Fig. 11.
Fig. 11.
An ROC analysis of three hypoxia imaging metrics. Hypoxia can be distinguished from normoxia equally well with the maximum tumor-to-muscle ratio (T/M) or the hypoxic volume (HV) or even the SUVmax.
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