Slow and fast invasion waves in a model of acid-mediated tumour growth.
نویسندگان
چکیده
This work is concerned with a reaction-diffusion system that has been proposed as a model to describe acid-mediated cancer invasion. More precisely, we consider the properties of travelling waves that can be supported by such a system, and show that a rich variety of wave propagation dynamics, both fast and slow, is compatible with the model. In particular, asymptotic formulae for admissible wave profiles and bounds on their wave speeds are provided.
منابع مشابه
Tumour-stromal interactions in acid-mediated invasion: a mathematical model.
It is well established that the tumour microenvironment can both promote and suppress tumour growth and invasion, however, most mathematical models of invasion view the normal tissue as inhibiting tumour progression via immune modulation or spatial constraint. In particular, the production of acid by tumour cells and the subsequent creation of a low extracellular pH environment has been explore...
متن کاملA general reaction-diffusion model of acidity in cancer invasion.
We model the metabolism and behaviour of a developing cancer tumour in the context of its microenvironment, with the aim of elucidating the consequences of altered energy metabolism. Of particular interest is the Warburg Effect, a widespread preference in tumours for cytosolic glycolysis rather than oxidative phosphorylation for glucose breakdown, as yet incompletely understood. We examine a ca...
متن کاملAnatomical parameters of cardiopulmonary system, venous blood pCO2and pO2tensions and the development of ascites syndrome in two genetic line chickens that are differing in their growth rate
The present study was designed to examine the anatomical parameters of the cardiopulmonary system, the function of venous blood gas parameters and the development of ascites incidence in two genetic line chickens. Three hundred forty day-old chickens from two pure broiler breeder lines, which were different in their growth rate and susceptibility to ascites syndrome were obtained. The relative ...
متن کاملEffect of eight weeks of resistance training on the expression of klotho protein and insulin-like growth factor 1 genes in slow twitch and fast twitch skeletal muscles of aged Wistar rats
Background and Aims: Klotho protein is a substance effective in increasing life expectancy. Moreover, it prevents muscle atrophy, osteoporosis, and cardiovascular disease. Therefore, the present aimed to assess changes in the expression of klotho protein and insulin-like growth factor 1 (IGF-1) genes in the muscles of aged Wistar rats after eight weeks of resistance training. Materials and Met...
متن کاملFrequency-dependent electrophysiological properties of concealed slow pathway of isolated rabbit atrioventricular node preparation after fast pathway ablation in a functional model
Introduction: Intranodal pathways of atrioventricular (AV) node play a vital role in the delay of conduction time in response to various atrial inputs. The present study was aimed to determine the frequency-dependent electrophysiological properties of concealed slow pathway according to a functional model of isolated rabbit atrioventricular node preparation after fast pathway ablation. Meth...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Mathematical biosciences
دوره 220 1 شماره
صفحات -
تاریخ انتشار 2009