Mechanistic modeling of vascular tumor growth: an extension of Biot’s theory to hierarchical bi-compartment porous medium system

Existing continuum multiphase tumor growth models typically do not include microvasculature, or if present, this is modeled as non-deformable. Vasculature behavior and blood flow are usually non-coupled with the underlying tumor phenomenology from the mechanical viewpoint; hence, phenomena as vessel compression/occlusion modifying microcirculation and oxygen supply cannot be taken into account.The tumor tissue is here modeled as a reactive bi-compartment porous medium: the extracellular matrix constitutes the solid scaffold; blood is in the vascular porosity whereas the extra-vascular porous compartment is saturated by two cell phases and interstitial fluid (mixture of water and nutrient species). The pressure difference between blood and the extra-vascular overall pressure is sustained by vessel walls and drives shrinkage or dilatation of the vascular porosity. Model closure is achieved thanks to a consistent non-conventional definition of the Biot’s effective stress tensor.Angiogenesis is modeled by introducing a vascularization state variable, and accounting for tumor angiogenic factors and endothelial cells. Closure relationships and mass exchange terms related to vessel formation are detailed in a numerical example reproducing the principal features of angiogenesis. This example is preceded by a first pedagogical numerical study on one-dimensional bio-consolidation. Results are exquisite to realize that the bi-compartment poromechanical model is fully coupled (the external loads impact fluid flow in both porous compartments) and to envision further applications as for instance modeling of drugs delivery and tissue ulceration.

Growth pattern Learning for Unsupervised Extraction of Cancer Kinetics

Neoplastic processes are described by complex and heterogeneous dynamics. The interaction of neoplastic cells with their environment describes tumor growth and is critical for the initiation of cancer invasion. Despite the large spectrum of tumor growth models, there is no clear guidance on how to choose the most appropriate model for a particular cancer and how this will impact its subsequent use in therapy planning. Such models need parametrization that is dependent on tumor biology and hardly generalize to other tumor types and their variability. Moreover, the datasets are small in size due to the limited or expensive measurement methods. Alleviating the limitations that incomplete biological descriptions, the diversity of tumor types, and the small size of the data bring to mechanistic models, we introduce Growth pattern Learning for Unsupervised Extraction of Cancer Kinetics (GLUECK) a novel, data-driven model based on a neural network capable of unsupervised learning of cancer growth curves. Employing mechanisms of competition, cooperation, and correlation in neural networks, GLUECK learns the temporal evolution of the input data along with the underlying distribution of the input space. We demonstrate the superior accuracy of GLUECK, against four typically used tumor growth models, in extracting growth curves from a four clinical tumor datasets. Our experiments show that, without any modification, GLUECK can learn the underlying growth curves being versatile between and within tumor types.