A Phenotype-Structured PDE Framework for Investigating the Role of Hypoxic Memory on Tumor Invasion under Cyclic Hypoxia

TL;DR

This paper introduces a mathematical model to study how hypoxic memory affects tumor invasion under cyclic hypoxia.

Contribution

The novel contribution is a phenotype-structured PDE framework that captures hypoxic memory effects on tumor dynamics.

Findings

Hypoxic memory significantly enhances tumor invasion without reducing tumor volume.

Shorter hypoxia cycles lead to more heterogeneous hypoxic memory profiles in the tumor population.

The induction rate of hypoxic memory strongly influences invasion, but not the dilution rate.

Abstract

Tumor growth and angiogenesis drive complex spatiotemporal variation in micro-environmental oxygen levels. Previous experimental studies have observed that cancer cells exposed to chronic hypoxia retained a phenotype characterized by enhanced migration and reduced proliferation, even after being shifted to normoxic conditions, a phenomenon which we refer to as hypoxic memory. However, because dynamic hypoxia and related hypoxic memory effects are challenging to measure experimentally, our understanding of their implications in tumor invasion is quite limited. Here, we propose a novel phenotype-structured partial differential equation modeling framework to elucidate the effects of hypoxic memory on tumor invasion along one spatial dimension in a cyclically varying hypoxic environment. We incorporated hypoxic memory by including time-dependent changes in hypoxic-to-normoxic phenotype transition rate upon continued exposure to hypoxic conditions. Our model simulations demonstrate that hypoxic memory significantly enhances tumor invasion without necessarily reducing tumor volume. This enhanced invasion was sensitive to the induction rate of hypoxic memory, but not the dilution rate. Further, shorter periods of cyclic hypoxia contributed to a more heterogeneous profile of hypoxic memory in the population, with the tumor front dominated by hypoxic cells that exhibited stronger memory. Overall, our model highlighted the complex interplay between hypoxic memory and cyclic hypoxia in shaping heterogeneous tumor invasion patterns.

The online version contains supplementary material available at 10.1007/s11538-025-01591-2.

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