Avascular tumour growth models based on anomalous diffusion
نویسندگان
چکیده
منابع مشابه
Time Delays in Solid Avascular Tumour Growth
In the paper the model of early stage of tumour growth is described. Two main cellular processes are considered — proliferation and apoptosis. We focused on the effect of time delays in both processes. Mathematical analysis and computer simulations are presented. INTRODUCTION Many models which study different stages and effects of tumour growth were proposed and studied within last years, e.g. ...
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A system of nonlinear partial differential equations is proposed as a model for the growth of an avascular-tumour spheroid. The model assumes a continuum of cells in two states, living or dead, and, depending on the concentration of a generic nutrient, the live cells may reproduce (expanding the tumour) or die (causing contraction). These volume changes resulting from cell birth and death gener...
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Earlier mathematical models of the authors which describe avascular tumour growth are extended to incorporate the process of cell shedding, a feature known to affect the growth of rnulticell spheroids. A continuum of live cells is assumed within which. depending on the concentration of a generic nutrient, movement (described by a velocity field) occurs due to volume changes caused by cell birth...
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A mathematical model of infiltrative tumour growth taking into account cell proliferation, death and motility is considered. The model is formulated in terms of local cell density and nutrient (oxygen) concentration. In the model the rate of cell death depends on the local nutrient level. Thus heterogeneous nutrient distribution in tissue affects tumour structure and development. The existence ...
متن کاملA new mathematical model for avascular tumour growth.
The early development of solid tumours has been extensively studied, both experimentally via the multicellular spheroid assay, and theoretically using mathematical modelling. The vast majority of previous models apply specifically to multicell spheroids, which have a characteristic structure of a proliferating rim and a necrotic core, separated by a band of quiescent cells. Many previous models...
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ژورنال
عنوان ژورنال: Journal of Biological Physics
سال: 2020
ISSN: 0092-0606,1573-0689
DOI: 10.1007/s10867-020-09541-w