Correcting for targeted and control agent signal differences in paired-agent molecular imaging of cancer cell-surface receptors

Abstract

Paired-agent kinetic modeling protocols provide one means of estimating cancer cell-surface receptors with in vivo molecular imaging. The protocols employ the coadministration of a control imaging agent with one or more targeted imaging agent to account for the nonspecific uptake and retention of the targeted agent. These methods require the targeted and control agent data be converted to equivalent units of concentration, typically requiring specialized equipment and calibration, and/or complex algorithms that raise the barrier to adoption. This work evaluates a kinetic model capable of correcting for targeted and control agent signal differences. This approach was compared with an existing simplified paired-agent model (SPAM), and modified SPAM that accounts for signal differences by early time point normalization of targeted and control signals (SPAMPN). The scaling factor model (SPAMSF) outperformed both SPAM and SPAMPN in terms of accuracy and precision when the scale differences between targeted and imaging agent signals (α) were not equal to 1, and it matched the performance of SPAM for α = 1. This model could have wide-reaching implications for quantitative cancer receptor imaging using any imaging modalities, or combinations of imaging modalities, capable of concurrent detection of at least two distinct imaging agents (e.g., SPECT, optical, and PET/MR).

Keywords: kinetic modeling; optical tissue properties; paired-agent imaging.

Fig. 1

A schematic of subcutaneous mouse tumor model is shown. The targeted and control imaging agent compartmental models are shown on the left and right, respectively. $C_{p,T}(t)$ and $C_{p,C}(t)$ represent the blood plasma concentrations of targeted and control imaging agents, respectively, as a function of time, $t$; $C_{f,T}$ and $C_{f,C}$ represent the free (unbound) concentrations of the two imaging agents, $C_{b,T}$ represents the bound concentration of the targeted agent; $K_{1,T}$ and $K_{1,C}$ represent rate constants governing targeted and control imaging agent extravasation (transport from blood to extravascular extracellular space); $k_{2,T}$ and $k_{2,C}$ represent rate constants governing targeted and control agent tissue efflux (transport from extravascular extracellular space to blood); and $k_{3,T}$ and $k_{4,T}$ represent rate constants governing targeted agent binding and dissociation from the targeted biomolecule.

Fig. 2

Simulation results. Generated noisy targeted and control agent curves and model fits for (a) the linearized SPAM (b) the pixel-normalization SPAM (${\mathrm{SPAM}}_{\mathrm{PN}}$), and (c) the scaling factor SPAM (${\mathrm{SPAM}}_{\mathrm{SF}}$). The blue dots represent the targeted imaging agent signal intensity, ${\mathrm{ROI}}_T(t)$. The orange dots represent the control imaging agent signal intensity, ${\mathrm{ROI}}_C(t)$. Poisson noise was added to the data. The solid red, blue, and green lines represent SPAM, ${\mathrm{SPAM}}_{\mathrm{PN}}$, and ${\mathrm{SPAM}}_{\mathrm{SF}}$ fit results, respectively. The simulated values of kinetic parameters to create these simulated curves were: $K_1=0.013{\min }^{-1}$, $k_2=0.08{\min }^{-1}$, $k_3=0.2{\min }^{-1}$, $k_4=0.1{\min }^{-1}$, and $\alpha =1$, and simulated time was 60 min.

Fig. 3

Simulation results: BP estimation errors are presented for all three kinetic models tested in this study as a function of the ratios of correction factors, $\alpha$ (a), BP (b), the tissue-to-blood efflux rate constant, $k_2$ (c), and ratio of the targeted and control imaging agent blood-to-tissue extravasation rate constants, $R_1$ (d). The linearized SPAM results are presented in red, the pixel normalization SPAM (${\mathrm{SPAM}}_{\mathrm{PN}}$) results are presented in blue, and the scaling factor SPAM (${\mathrm{SPAM}}_{\mathrm{SF}}$) results are presented in green.

Fig. 4

Simulation results: (a) errors in BP estimation using the linearized pixel-normalization ${\mathrm{SPAM}}_{\mathrm{PN}}$ as a function of. Different colors correspond to sets of data created from different ratios of correction factors ($\alpha ={\eta }_T/{\eta }_C$). (b) Errors in BP estimation using ${\mathrm{SPAM}}_{\mathrm{PN}}$ and the SPAM scaling factor model (${\mathrm{SPAM}}_{\mathrm{SF}}$) as a function of time-spacing of imaging data ($t_e$) where $t_e$ also represents the first time point after agent administration with keeping $\alpha =1$. ${\mathrm{SPAM}}_{\mathrm{PN}}$ and ${\mathrm{SPAM}}_{\mathrm{SF}}$ results are presented in blue and green, respectively.

Fig. 5

In vivo experimental results: The linearized pixel-normalization simplified paired agent model ${\mathrm{SPAM}}_{\mathrm{PN}}$ in (a) targeted (IRDye 800CW-EGF) and control (IRDye 700DX) imaging agent signal curves measured with the Odyssey System in exposed subcutaneous human glioblastoma (U251) tumors grown in athymic mice, (b) targeted (IRDye 800CW-anti-EGFR-Affibody) and control (IRDye 700DX-negative-control-Affibody) imaging agent signal curves measured with the Pearl System in exposed subcutaneous U251 tumors and (c) targeted (IRDye 800CW-anti-EGFR-Affibody) and control (IRDye 700DX-negative-control-Affibody) imaging agent signal curves measured with an MRI–FMT system from a typical tumor region-of-interest, respectively. Corresponding model fits using the scaling factor SPAM (${\mathrm{SPAM}}_{\mathrm{SF}}$) are presented in (d)–(f), respectively. The blue dots represent the targeted imaging agent signal intensity, the orange dots represent the control imaging agent signal intensity before correcting for plasma input function differences, the black dots represent the control imaging agent signal intensity after correcting for plasma input function differences. The solid light blue line represents the ${\mathrm{SPAM}}_{\mathrm{PN}}$ fit and the solid green line represents the ${\mathrm{SPAM}}_{\mathrm{SF}}$ fit. In (g) and (h) a pixel-by-pixel correlation of ${\mathrm{SPAM}}_{\mathrm{SF}}$ and ${\mathrm{SPAM}}_{\mathrm{PN}}$ BP estimates in all regions of an image on the same mouse data presented in (a) and (b) are presented. The dashed line is the line-of-identity. A correlation between BP values estimated by ${\mathrm{SPAM}}_{\mathrm{SF}}$ and ${\mathrm{SPAM}}_{\mathrm{PN}}$ in Odyssey, Pearl and tomography imaging studies are presented in (i) for average tumor region-of-interest fits.

Fig. 6

In vivo experimental results: BP parametric maps of estimated epidermal growth factor receptor (EGFR) concentration are depicted as calculated by either the linearized pixel-normalization ${\mathrm{SPAM}}_{\mathrm{PN}}$ or the scaling factor SPAM (${\mathrm{SPAM}}_{\mathrm{SF}}$). Here, results of four mice are displayed: two from the group imaged on the Odyssey System (targeted agent = IRDye 800CW-EGF; control = IRDye 700DX), and two from the group imaged on the Pearl System (targeted agent = ABY-029; control = IRDye 700DX-negative-control-affibody). The left two columns show the two mice imaged on the Odyssey, and the right two columns show the two mice imaged on Pearl.