Mathematical modeling and sensitivity analysis of hypoxia-activated drugs

TL;DR

This work tackles the challenge of predicting hypoxia-activated drug behavior in solid tumors by developing a multiscale, mixed-dimensional framework that couples spatially resolved oxygen and drug transport (3D tissue with embedded 1D vasculature) to a surrogate 0D pharmacokinetics–pharmacodynamics model for Tirapazamine (TPZ). A one-way coupling reduces the computational burden while preserving the essential biology of TPZ activation under hypoxia, and a global sensitivity analysis (Morris elementary effects) identifies the most influential parameters, notably vascular TPZ input and oxygen-dependent metabolism. The 3D-1D-0D formulation enables efficient parametric studies and supports design guidance for hypoxia-targeted therapies, with results highlighting how intratumoral oxygen heterogeneity and metabolic rates govern drug activation and cell survival. The methodology lays groundwork for patient-specific extensions and digital twin frameworks to optimize hypoxia-targeted strategies in precision radiotherapy and chemotherapy.

Abstract

Hypoxia-activated prodrugs offer a promising strategy for targeting oxygen-deficient regions in solid tumors, which are often resistant to conventional therapies. However, modeling their behavior is challenging because of the complex interplay between oxygen availability, drug activation, and cell survival. In this work, we develop a multiscale and mixed-dimensional model that couples spatially resolved drug and oxygen transport with pharmacokinetics and pharmacodynamics to simulate the cellular response. The model integrates blood flow, oxygen diffusion and consumption, drug delivery, and metabolism. To reduce computational cost, we mitigate the global nonlinearity through a one-way coupling of the multiscale and mixed/dimensional models with a reduced 0D model for the drug metabolism. The global sensitivity analysis is then used to identify key parameters influencing drug activation and therapeutic outcome. This approach enables efficient simulation and supports the design of optimized hypoxia-targeted therapies.

Figures (15)

• Figure 1: Schematic of the full 3D-1D model. The vascular network (1D) supplies oxygen and drugs to the tissue (3D). Spatially resolved concentrations influence the cell survival model at each point in space and time (3D), which feeds back to modulate oxygen and TPZ consumption and reshape the microenvironment.
• Figure 2: Schematic of the 0D surrogate model. Vascular TPZ drives the tissue concentration $c_t^{tpz}$, which, together with the tissue oxygen $c_t^{ox}$, determines the surviving fraction $SF(t)$. This in turn modulates both TPZ and oxygen metabolism through the nonlinear terms $m^{tpz}$ and $m^{ox}$, capturing the feedback structure of the pharmacodynamics model described in equation \ref{['model_0D']}.
• Figure 3: Left panel: Comparison between the surviving fraction ($SF$) computed by the original 0D model and its sigmoid approximation. The remarkable correspondence underscores the adequacy of the sigmoid representation to capture the primary nonlinear transition observed in the 0D simulations. Right panel: Comparison of the computed metabolic rate $r(t)$ from the 0D model and its fitted rational approximation. The figure highlights both the successful capture of the general declining trend and areas where discrepancies remain, potentially indicating more complex underlying dynamics.
• Figure 4: Schematic representation of the multiscale 3D-1D-0D pharmacokinetics model architecture after implementing the one-way interaction with the 0D model. Tissue-level TPZ and oxygen concentrations are computed via the 3D transport equations, while the corresponding metabolic source terms are no longer evaluated through nested nonlinear functions. Instead, TPZ metabolism is modeled as a linear expression modulated by two surrogate functions derived offline from the 0D model: the surviving fraction $SF(t)$ and the effective metabolic coefficient $r(t)$. Oxygen metabolism is similarly represented via an exogenous effective function $m_{\mathrm{ox}}^{\text{eff}}(t)$. This reformulation reduces computational complexity while preserving the essential physiological feedback.
• Figure 5: Example of constrained Voronoi-based synthetic vascular network and visualization of radii distribution ($\mu m$). This is the vascular network that has been used consistently in all the numerical tests.