Investigation of Key Transport Parameters Impacting 177Lu-PSMA Therapy: Computational Modeling of Solid Tumors Integrating Microvasculature

Introduction: Computational modeling of targeted prostate cancer treatments, specifically ¹⁷⁷Lu-PSMA drug delivery, holds great promise for the optimization of therapies. This is particularly significant in the context of heterogeneous and drug-resistant prostate cancers. Given the intricacies involved in delivering ¹⁷⁷Lu-PSMA to solid tumors and the complexities of the tumor microenvironment, employing modeling based on partial differential equations proves to be an effective tool, towards identifying factors that hinder effective drug delivery and proposing enhancements. Unlike conventional compartmental modeling methods, such modeling comprehensively considers various parameters, including interstitial velocity, pressure, and tissue permeability, influencing the distribution of radiopharmaceuticals. Moreover, it can incorporate the heterogeneities inherent in the tumor microenvironment, encompassing intricate structures of the capillary network and transvascular fluid exchange. We aimed to investigate the impacts of binding affinity and release rate on concentrations of ¹⁷⁷Lu-PSMA within the vascularized tumor.

Methods: Our study employs a comprehensive spatiotemporal distribution model (SDM) to predict the distribution of ¹⁷⁷Lu-PSMA within a solid tumor precisely. Initially, a mathematical model of angiogenesis is utilized to generate the capillary network of a solid tumor and the surrounding normal tissues (Fig 1). The coupling mathematical method, which simultaneously addresses blood flow in the capillary network and fluid flow in the interstitium, calculates pressure and velocity distributions. Subsequently, numerical solutions for the convection-diffusion-reaction equations are obtained through the COMSOL Multiphysics software, enabling an investigation into the total concentration of ¹⁷⁷Lu-PSMA within the tumor. The model is examined across various values of binding affinity (1 to 0.01 [nmol/L]) and release rate (0.01 to 0.00001 [1/min]).

Results: For the dissociation constant (K_D= K_off/K_on), the decrease from 1 to 0.01 [nmol/L] implies a stronger binding affinity between ¹⁷⁷Lu-PSMA and its target receptors. This heightened affinity leads to a more prolonged interaction between the radiopharmaceutical and the tumor cells, resulting in an increased accumulation within the tumor. Increases in the release rate (K_rel) induce reductions in tumor concentration. As the rate K_rel escalates, the degradation kinetics of the drug accelerate, expediting its clearance from the tumor. The increase from 0.00001 to 0.0001 has a negligible impact on the total drug accumulation. However, the transition from 0.0001 to 0.001 in K_rel manifests a significant decline in the area under the concentration curve (AUC), suggesting a steep response. Following that, an ascent from 0.001 to 0.01 reveals a moderated slope, indicative of a mitigated influence of this parameter on the overall concentration of the radiopharmaceutical within the tumor microenvironment.

Conclusions: Our developed computational model elucidates the intricate relationship between tumor biology and ¹⁷⁷Lu-PSMA properties, focusing on binding affinity, and release rate. One of the innovations of the present model is the consideration of tumor heterogeneity, which is one of the challenges of treating malignant tumors. Results showed that a lower dissociation constant (K_D) enhances concentrations of ¹⁷⁷Lu-PSMA within the tumor. Furthermore, it was shown as the release rate increases the total concentration declines with different slopes. The fastest decreasing slope of concentration occurs in the transition from 0.0001 to 0.001. These findings underscore the significance of these properties in optimizing targeted radiopharmaceutical delivery for enhanced therapeutic efficacy, with ongoing validation efforts aimed at refining our model for real-world applications.

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