Hybrid model for tumor spheroids with intratumoral oxygen supply heterogeneity

Tumor growth involves numerous biochemical and biophysical processes related to the invasion of surrounding tissue and metastasis. Such phenomena occur at different scales of time and space. The desire to understand the interactions of these complex processes has given rise to various computational models allowing for multiple variable modeling using continuous, discrete and the most recent hybrid approaches. This paper presents a hybrid mathematical model of solid tumor invasion that incorporates both continuous macro-scale and discrete cell-level descriptions. Cell-based description reflects individual cell movement and state, while the continuous part formulates the nutrient supply of the tumor. In the presented model, apart from the usage of homogenous oxygen supply, intratumoral nutrient sources are introduced.