Abstract
Being a hallmark of several solid tumors, hypoxia - a state of reduced level of tissue oxygen tension and a result of aberrant vasculature - leads to several alterations in the tumor microenvironment. Hypoxic regions of neoplasm are prone to be more resistant towards radiation therapy than compared to well oxygenated ones (A. L. Harris 2002). Furthermore, hypoxia and its mediators influence multiple signaling pathways and gene regulation to promote neovascularization, invasion, migration, adhesion, metastasis, and phenotypic switches (D. S. Widmer et al. 2013, A. Tameemi et al., 2019). Hence hypoxia is one of the leading factors which contributes towards intratumor heterogeneity and resistance against treatments, these two features being particularly important and common in many invasive tumors including melanoma (B. Bedogni et al. 2009, D'Aguanno et al. 2021). Estimation of accurate hypoxia profile would be key for better prognosis and design of more efficient treatment approaches. Mathematical modeling has been proven a useful tool to understand and predict such complex dynamics. Several computational and mathematical models have been proposed to describe tissue oxygenation, however the majority of them are restricted to synthetic data and qualitative results, lacking application to and connection with real tumor tissues and experimental results.We propose mechanistic modeling frameworks, which are driven by experimental data, to explain and mimic oxygen-hypoxia dynamics. The data is in the form of tissue scans of Patient Derived Xenograft (PDX) of breast, ovarian and pancreatic as well as human melanoma tumors. These scans of tumor tissue slices are immunohistochemical stained with CD31 -cluster of differentiation 31, marking the presence of endothelial cells- and CAIX- carbonic anhydrase IX, regulated by the hypoxia-inducible factor (HIF) 1, is an intrinsic marker of tumor hypoxia - markers. Keeping the data availability in mind, the distribution of oxygen is described by a reaction-diffusion partial differential equation with the source term incorporating the contribution from blood vessel density (obtained from CD31 staining) for the 2D model and from the vasculature architecture and the geometry of each blood vessel (reconstructed from several 2D tissue slices) for the 3D model. Next, hypoxia is modeled from the obtained oxygen distribution using an algebraic equation. The further steps include estimation of parameters and validation. The obtained parameters demonstrate biological relevance. 3D reconstruction, which is underway, is required for obtaining 3D profiles of oxygen and hypoxia. This requirement leads to another aspect of this work consisting in quantification of the error made when 2D models are used instead of more realistic 3D models. This is important since the 3D reconstruction is not always feasible, especially for patient tissue samples. A framework to quantify this approximation error would be essential for evaluating the hypoxia profile for clinical applications. Future work involves development of a general framework, applicable to most of the solid tumors, to estimate oxygen and hypoxia distribution based on the 3D reconstruction of blood vessels as well as for the 2D case with an error bound due to the approximation.