Multiscale Modeling of Acid Mediated Cancer Invasion with Random Dynamics and Beyond

Beschreibung

This book is concerned with the mathematical study of various phenomena related to cancer growth and migration, with a focus on acid-mediated tumor invasion.
This book is concerned with the mathematical study of various phenomena related to cancer growth and migration, with a focus on acid-mediated tumor invasion. As cancer is a highly diversified disease we start with recalling the hallmark properties of cancer and present the functional role of acidity in the involved cellular processes and hence its impact on tumor progression. We then concentrate on a particular cellular pH regulator called the monocarboxylate transporter and present a mathematical model for the dynamics of protons induced by it. Subsequently we propose and investigate a multiscale model for the occurrence of gaps and infiltrative patterns during the advancement of a neoplasm. Based on the results obtained from the numerical simulations we discuss the significance of randomness and tissue heterogenieity on the type of invasion patterns that the cancer exhibits. In view of the substantial influence of randomness and of multiscality on the tumor dynamics we then aim at answering the question: how to deduce stochastic equations at the macroscopic level starting from a microscopic description of the biological phenomena affecting the evolution of the tumor? We motivate this question biologically and outline the fundamental reason for living systems -thus also of cancer- to diversify. Following this we present a novel mathematical framework to deduce stochastic macroscopic equations for a tumor cell population from the lower scale dynamics. As an exemplification of our approach we provide a stochastic fractional diffusion model for acid-mediated tumor invasion. Thereby, the use of the fractional Laplacian is motivated by the microscopic model of continuous time random walks on the individual cell level. Finally, we provide some concluding remarks and comments about further directions of research.

Autor*in

Sandesh Athni Hiremath
The author's current work mainly focuses on phenomenological modeling, via PDEs', SDEs', RODEs' and SPDEs', of certain hallmark features of cancer and thereby make predictions about the malignancy of cancer. Apart for this the author is also interested in system modelling, statistical estimation, probabilistic algorithms.

Themen in »Multiscale Modeling of Acid Mediated Cancer Invasion with Random Dynamics and Beyond«

Abstract Cauchy problem Semigroups Markov process Levy processes Cancer Acidity

Stimmen zu »Multiscale Modeling of Acid Mediated Cancer Invasion with Random Dynamics and Beyond«

Details

Link teilen