Quantitative Modeling of 64Cu-DOTA-RGD Tumor Uptake

A linear compartmental model (Fig. 1) was used in this study, where u(t) represents plasma concentration of the tracer calculated by correcting PET-measured blood concentration for partial-volume effects and absence of uptake by blood cells. A recovery coefficient of 0.7 (18 (link)) and hematocrit of 50% (19 (link)) are assumed, resulting in a PET-measured whole-blood (WB_PET)–to–actual plasma (P_a) tracer concentration ratio of $$\frac{{\mathrm{C}}_{{\text{WB}}_{\text{PET}}}(\mathrm{t})}{{\mathrm{C}}_{{\mathrm{P}}_{\mathrm{a}}}(\mathrm{t})}\approx 0.7\times 0.5,$$ for the 60-min dynamic scans, and $$\frac{{\mathrm{C}}_{{\text{WB}}_{\text{PET}}}(\mathrm{t})}{{\mathrm{C}}_{{\mathrm{P}}_{\mathrm{a}}}(\mathrm{t})}\approx 0.5,$$ for the 20-h postinjection scans, where partial-volume effects are not an issue because of low plasma concentration of tracer and comparable activity in myocardium. Spillover from the myocardium may slightly increase apparent tracer concentration at 20 h after injection; here we assumed spillover error is negligible. Compartments q₁(t) and q₂(t) represent the amount of free or nonspecifically bound and specifically bound tracer within tumor extravascular space, respectively. Several model structures could be used to describe the 20-h postinjection data point; here we assumed internalization is a linear process mediated by binding of ligand to receptor, thus, compartment q₃(t) was added to represent tracer that has been irreversibly internalized by tumor cells (20 (link)). Model equations are written as $$\frac{\mathrm{d}{\mathrm{q}}_1(\mathrm{t})}{\text{dt}}={\mathrm{K}}_1\mathrm{u}(\mathrm{t})-({\mathrm{k}}_2+{\mathrm{k}}_3){\mathrm{q}}_1(\mathrm{t})+{\mathrm{k}}_4{\mathrm{q}}_2(\mathrm{t})$$ and $$\frac{\mathrm{d}{\mathrm{q}}_2(\mathrm{t})}{\text{dt}}={\mathrm{k}}_3{\mathrm{q}}_1(\mathrm{t})-({\mathrm{k}}_4+{\mathrm{k}}_{\text{int}}){\mathrm{q}}_2(\mathrm{t})$$ and $$\frac{\mathrm{d}{\mathrm{q}}_3(\mathrm{t})}{\text{dt}}={\mathrm{k}}_{\text{int}}{\mathrm{q}}_2(\mathrm{t}),$$ where, putatively, K₁ represents the tracer extravasation rate (min⁻¹), k₂ represents the rate of tissue efflux of free or nonspecifically bound tracer (min⁻¹), and k₃ represents the rate of specific binding (min⁻¹) of ⁶⁴Cu-DOTA-RGD to the extracellular portion of the α_vβ₃ integrin. k₄ and k_int represent rates of dissociation (min⁻¹) and internalization (min⁻¹) of specifically bound tracer, respectively. Note that k_int is assumed to represent internalization; however, all slow uptake mechanisms are lumped into this parameter. The measurement model is written as $$\mathrm{c}(\mathrm{t})={\mathrm{V}}_{\mathrm{B}}\times \mathrm{u}(\mathrm{t})+{\mathrm{q}}_1(\mathrm{t})+{\mathrm{q}}_2(\mathrm{t})+{\mathrm{q}}_3(\mathrm{t}),$$ where V_B is the fractional blood volume of the tumor (unitless) and c(t) is the tumor time–activity curve. Here we considered 4 structural perturbations of the model shown in Figure 1: a 2k model(k₃ = k₄ = 0) assumes PET data can be accurately described without explicitly accounting for the specific binding of ⁶⁴Cu-DOTA-RGD to the α_vβ₃ integrin; a 3k model (k₄ = 0) explicitly accounts for the specific binding of the tracer to integrin, which is assumed to be irreversible; a 4k model assumes reversible binding of tracer to integrin; and a 4k_c (k₄ = constant; k₄ > 0) model assumes that k₄ has approximately the same value across all datasets. Each of the 4 model variants is augmented with a compartment representing irreversible internalization of tracer by tumor cells (Eq. 5).