Spatiotemporal modeling of radiopharmaceutical transport in solid tumors: Application to 177Lu-PSMA therapy of prostate cancer

Abstract

Background and objective: ¹⁷⁷Lu-labeled prostate-specific membrane antigen (PSMA) radiopharmaceutical therapy (RPT) represents a pivotal advancement in addressing prostate cancer. However, existing therapies, while promising, remain incompletely understood and optimized. Computational models offer potential insights into RPTs, aiding in clinical drug delivery enhancement. In this study, we investigate the impact of various physiological parameters on the delivery of ¹⁷⁷Lu-PSMA-617 RPT using the convection-diffusion-reaction (CDR) model.

Methods: Our investigation encompasses tumor geometry and surrounding tissue, characterized by well-defined boundaries and initial conditions. Utilizing the finite element method, we solve governing equations across a range of parameters: dissociation constant K_D (1, 0.1, 0.01 [nM]), internalization rate (0.01-0.0001 [min^-1]), diverse tumor shapes, and variable necrotic zone sizes. This model can provide an accurate analysis of radiopharmaceutical delivery from the injection site to the tumor cell, including drug transport in the vascular, interstitial, and intracellular spaces, and considering important parameters (e.g., drug extravasation from microvessels or to lymphatic vessels, the extracellular matrix, receptors, and intracellular space).

Results: Our findings reveal significant enhancements in tumor-absorbed doses as K_D decreases. This outcome can be attributed to the higher affinity of radiopharmaceuticals for PSMA receptors as K_D diminishes, facilitating a more efficient binding and retention of the therapeutic agent within the tumor microenvironment. Additionally, tumor-absorbed doses for K_D ∼ 1 [nM] show an upward trend with higher internalization rates. This observation can be rationalized by considering that a greater internalization rate would result in a higher proportion of radiopharmaceuticals being taken up by tumor cells after binding to receptors on the cell surface. Notably, tumor shape and necrotic zone size exhibit limited influence on tumor absorbed dose.

Conclusions: The present study employs the CDR model to explore the role of physiological parameters in shaping ¹⁷⁷Lu-PSMA-617 RPT delivery. These findings provide insights for improving prostate cancer therapy by understanding radiopharmaceutical transport dynamics. This computational approach contributes to advancing our understanding of radiopharmaceutical delivery mechanisms and has implications for enhancing treatment efficacy.

Keywords: (177)Lu-PSMA; Cancer; Convection-diffusion-reaction models; Radioligand therapy; Radiopharmaceutical therapy; Tumor microenvironment.