177Lu-PSMA-617 Transport in Solid Tumors via a 3D Image-based Spatio-temporal Model

Introduction: Radiopharmaceutical therapy (RPT) via the utilization of radioligands enables targeted delivery of radionuclides to cancer cells while keeping radiation exposure to untargeted cells low. An example application of tremendous value includes prostate-specific membrane antigen (PSMA) targeted RPTs of prostate cancer. Noninvasive magnetic resonance (MR) imaging has been widely used for pretreatment workup in patients with prostate cancer. We developed a 3D spatiotemporal drug delivery model based on patient MR imaging data to capture the essential pharmacokinetic interactions between PSMA radioligands and solid prostate tumors. This study is aimed to determine the effects of receptor density, recycling rate, and synthesis rate of PSMA receptors on the mean concentration of ¹⁷⁷Lu-PSMA-617 in the tumor.

Methods: Spatiotemporal distribution models (SDMs) are a category of computational models that are often utilized to investigate the influence of different biological features on drug delivery in the treatment of solid tumors. SDMs incorporate processes of convection, diffusion, and reaction, and have been extensively developed in other fields, which we extend to nuclear medicine. We first extract the geometry of the prostate tumor and surrounding tissue from a set of patient-specific MR images (Figure 1). Subsequently, governing equations of interstitial flow, drug transport in tissues, and receptor cycles are solved by incorporating realistic conditions and details, including association/dissociation with ligands, synthesis of PSMA receptors, receptor recycling, internalization of drugs, as well as degradation of receptors and drugs. Our simulations were performed using the commercial finite element software COMSOL Multiphysics 5.6 (COMSOL, Inc., Burlington, MA). We considered typical 90 nmol unlabeled and 10 nmol labeled ¹⁷⁷Lu-PSMA-617 (activity: 7.4 GBq). The model is studied for a range of values of receptor densities (10 to 100 nmol/L), recycle rates of receptors (10^-4 to 10^-1 min^-1), and constitutive receptor synthesis rates (10^-2 to 10¹ min^-1).

Results: Raising the receptor density from 10 to 100 nmol/L increases the mean concentration of labeled PSMA in tumors in a non-linear fashion; by up to 200% (Figure 2). The concentration is increased by 31.8% when the receptor recycling rate changes from 10^-4 to 10^-1 min^-1 (Figure 3), and 9.6% when the constitutive receptor synthesis rate is increased from 10^-2 to 10¹ min^-1 (Figure 4). As such, the tumor receptor density is identified as a key factor that strongly affects Lu-PSMA concentrations. However, concentrations are less sensitive to the recycling rate of receptors and constitutive receptor synthesis rates.

Conclusions: The presented spatiotemporal tumor transport model can analyze different physiological parameters that affect ¹⁷⁷Lu-PSMA transport and delivery. Furthermore, spatiotemporal modeling based on real images (e.g., MRI) reveals intriguing insights into drug bio-transport in RPTs, which can shed significant light on enhanced RPT deliveries.

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