Abstract
In situ clinical measurement of receptor occupancy (RO) is challenging, particularly for solid tumors, necessitating the use of mathematical models that predict tumor receptor occupancy to guide dose decisions. A potency metric, average free tissue target to initial target ratio (AFTIR), was previously described based on a mechanistic compartmental model and is informative for near-saturating dose regimens. However, the metric fails at clinically relevant subsaturating antibody doses, as compartmental models cannot capture the spatial heterogeneity of distribution faced by some antibodies in solid tumors. Here we employ a partial differential equation (PDE) Krogh cylinder model to simulate spatiotemporal receptor occupancy and derive an analytical solution, a mechanistically weighted global AFTIR, that can better predict receptor occupancy regardless of dosing regimen. In addition to the four key parameters previously identified, a fifth key parameter, the absolute receptor density (targets/cell), is incorporated into the mechanistic AFTIR metric. Receptor density can influence equilibrium intratumoral drug concentration relative to whether the dose is saturating or not, thereby influencing the tumor penetration depth of the antibody. We derive mechanistic RO predictions based on distinct patterns of antibody tumor penetration, presented as a global AFTIR metric guided by a Thiele Modulus and a local saturation potential (drug equivalent of binding potential for positron emissions tomography imaging) and validate the results using rigorous global and local sensitivity analysis. This generalized AFTIR serves as a more accurate analytical metric to aid clinical dose decisions and rational design of antibody-based therapeutics without the need for extensive PDE simulations. SIGNIFICANCE STATEMENT: Determining antibody-receptor occupancy (RO) is critical for dosing decisions in pharmaceutical development, but direct clinical measurement of RO is often challenging and invasive, particularly for solid tumors. Significant efforts have been made to develop mathematical models and simplified analytical metrics of RO, but these often require complex computer simulations. Here we present a mathematically rigorous but simplified analytical model to accurately predict RO across a range of affinities, doses, drug, and tumor properties.