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Derivation of a Compartmental Model for Quantifying ⁶⁴Cu-DOTA-RGD Kinetics in Tumor-Bearing Mice

¹ Department of Molecular and Medical Pharmacology, David Geffen School of Medicine at UCLA, University of California, Los Angeles, California; ² Department of Nuclear Medicine, Medical University of Innsbruck, Innsbruck, Austria; ³ Division of Radiopharmacy, University of Tuebingen, Tuebingen, Germany; and ⁴ Department of Nuclear Medicine, University of Freiburg, Freiburg, Germany

View larger version (13K): [in this window] [in a new window]   FIGURE 1.  Compartmental model describing 64Cu-DOTA-RGD peptide kinetics in tumor. u(t) represents plasma-forcing function as measured from region corresponding to heart left ventricle in reconstructed PET/CT image, corrected for whole-blood/plasma differences and partial-volume effects (Eqs. 1 and 2). Compartment q1(t) represents free or unbound tracer within tumor interstitial space, and compartment q2(t) represents tracer bound to vβ3 integrin. Compartment q3(t) represents integrin bound tracer that has been internalized by tumor cell (20) and is assumed to be irreversible. K1 describes extravasation rate of tracer and has units of min–1. k2 represents tracer flux of free and nonspecifically bound tracer from tissue to plasma and has units of min–1. k3 and k4 are specific binding and dissociation rates (min–1), and kint is tracer internalization rate (min–1). Representative forcing or input function, u(t), is shown in inset. %ID/g = percentage injected dose per gram.

View larger version (25K): [in this window] [in a new window]   FIGURE 2.  Representative model fits to data from 60-min dynamic PET scans of mice bearing subcutaneous tumors expressing low (A431), intermediate (U373), or high (U87) levels of vβ3. Lower-right-hand panel shows representative model fit to data from mouse that received a coinjection of cold peptide (10 mg/kg) with hot tracer dose. Lines represent 2k, 3k, 4k, and 4kc models fitted to tumor time–activity curves from 4 selected 60-min dynamic scans (open circles). %ID/g = percentage injected dose per gram.

View larger version (23K): [in this window] [in a new window]   FIGURE 3.  AIC (Eq. 8) calculated for 2k, 3k, 4k, and 4kc models fitted to data from blocked (A) and nonblocked (B) dynamic PET studies. Lower AIC value indicates better fit of model to data. All tumors are located in mouse shoulder, and each PET scan is 60 min unless noted otherwise. *Tumor located in thigh of mouse. 90-min PET scan.

View larger version (21K): [in this window] [in a new window]   FIGURE 4.  Analysis of 20-h postinjection static PET scans. (A) Representative example of prediction of 20-h tracer concentration in tumor based on model fitted to 60-min dynamic scan data from blocked and nonblocked studies; that is, each model was fitted to dynamic scan data (inset) and extrapolated from to the 20-h data point for 2k, 3k, 4k, and 4kc models. (B) Representative example of 4kc model fitted to data from both 60-min dynamic and 20-h postinjection blocked and nonblocked PET scans (black curve); broken gray curve illustrates effect on simulation of setting estimated internalization rate (kint) to zero. Inset more clearly illustrates effect of kint on first 60 min after tracer injection. %ID/g = percentage injected dose per gram.

View larger version (19K): [in this window] [in a new window]   FIGURE 5.  Results based on 4kc model of 64Cu-DOTA-RGD kinetics. (A) 4kc model fits to dynamic scan data with and without 20-h postinjection data. Comparison of estimated parameters (mean ± SD) calculated by fitting model to 60-min dynamic scan data only (open gray circles; set to zero) and model fitted to both 60-min dynamic scan data and 20-h postinjection data ( adjustable), in which fits to blocked (black circles) and nonblocked (open black circles) data are shown. k4 is fixed to 0.00938 min–1 for all model fits. (B) Comparison of volumes of distribution (Eqs. 10 and 11) calculated for blocked (A431 and U87 tumors) and nonblocked (A431, U373, and U87 tumors) studies. All tumors were located in mouse shoulder, and each PET scan was 60 min unless noted otherwise. (C) Spearman correlation between ratio of tracer concentration in tumor at 60 min after injection () to tracer concentration in plasma at 10 min () and specific volume of distribution . Units for K1, k2, k3, k4, and kint are min–1; VND, VS, and VB are unitless. *Tumor located in thigh of mouse. 90-min PET scan. Results of 4k model fitted to dynamic 18F-galacto-RGD peptide PET scans from 19 patients with cancer (8).

View larger version (12K): [in this window] [in a new window]   FIGURE 6.  Model discrimination process by which 4kc model, compared with 2k, 3k, and 4k models, was determined to be most appropriate for describing in vivo 64Cu-DOTA-RGD kinetics in mouse models that carry vβ3-positive tumors.