A mathematical model of tumor growth driven by oxygen lactate exosome feedback

Solid tumors develop within a heterogeneous microenvironment shaped by coupled biochemical and metabolic processes. As a tumor grows, oxygen gradients develop from the periphery towards the core, giving rise to hypoxic regions. Hypoxia induces a metabolic shift from oxidative phosphorylation to glycolysis, leading to elevated lactate production. Experimental studies further indicate that increased lactate levels enhance the secretion of tumor-derived exosomes carrying proteins, mRNA, and lipids, which in turn promote tumor cell proliferation. Together, these interactions form a feedback loop linking oxygen availability, lactate accumulation, and exosome-mediated signaling. Despite growing experimental evidence for each component, the impact of this coupled oxygen lactate exosome axis on tumor growth dynamics has not yet been systematically explored from a mathematical perspective. It remains unclear how the oxygen lactate exosome axis affects tumor growth - impact of nonlocal effects. In this paper, we develop a mechanistic mathematical model to investigate how this feedback mechanisms affects tumor growth. We first consider an in vitro setting oxygen levels are spatially homogeneous and vary periodically in time between normoxic and hypoxic states, capturing key features of cyclic hypoxia observed in vivo. Numerical simulations reveal that exosome mediated feedback has a pronounced effect on tumor volume under chronic hypoxia. In addition, we observe that the tumor volume decreases as the period of cyclic hypoxia increases. We then extend the model to an in vivo framework by incorporating oxygen diffusion and consumption, allowing spatial heterogeneity to emerge. Simulations reveal that tumor cells in normoxic regions benefit indirectly from enhanced exosome secretion driven by lactate produced in hypoxic regions. Overall, the results show how spatially mediated metabolic signaling can amplify tumor growth and aggressiveness, and illustrate how mathematical modeling can increase understanding of non local feedback mechanisms within the tumor microenvironment.