scholarly journals Lie Symmetries of Nonlinear Parabolic-Elliptic Systems and Their Application to a Tumour Growth Model

Symmetry ◽  
2018 ◽  
Vol 10 (5) ◽  
pp. 171 ◽  
Author(s):  
Roman Cherniha ◽  
Vasyl’ Davydovych ◽  
John King
Keyword(s):  
Growth Model ◽  
Tumour Growth ◽  
Elliptic Systems ◽  
Lie Symmetries ◽  
Nonlinear Parabolic ◽  
Tumour Growth Model

Assessment of a tumour growth model for virtual clinical trials of breast cancer screening

2021 ◽  
Author(s):  
Hanna Tomic ◽  
Anna Bejnö ◽  
Gustav O. Hellgren ◽  
Kristin Johnson ◽  
Daniel Förnvik ◽  
...  
Keyword(s):  
Breast Cancer ◽  
Clinical Trials ◽  
Cancer Screening ◽  
Breast Cancer Screening ◽  
Growth Model ◽  
Tumour Growth ◽  
Tumour Growth Model

scholarly journals Use of GPUs to boost the performance of a lattice-free tumour growth model

2014 ◽  
Vol 566 ◽  
pp. 012019
Author(s):  
Sabrina Stella ◽  
Roberto Chignola ◽  
Edoardo Milotti
Keyword(s):  
Growth Model ◽  
Tumour Growth ◽  
Tumour Growth Model

On the Williams-Bjerknes tumour growth model: II

1980 ◽  
Vol 88 (2) ◽  
pp. 339-357 ◽  
Author(s):  
Maury Bramson ◽  
David Griffeath
Keyword(s):  
Growth Model ◽  
Tumour Growth ◽  
Interacting Particle Systems ◽  
Dual Processes ◽  
Planar Lattice ◽  
Cellular Division ◽  
Asymptotic Shape ◽  
Regularity Properties ◽  
Abnormal Cells ◽  
Tumour Growth Model

AbstractWilliams and Bjerknes introduced in 1972 a stochastic model for the spread of cancer cells. Cells, normal and abnormal (cancerous), are situated on a planar lattice. With each cellular division, one daughter cell stays put, while the other usurps the position of a neighbour; abnormal cells reproduce at a faster rate than normal cells. We are interested in the long-term behaviour of this system. We showed in ‘On the Williams-Bjerknes Tumour Growth Model I’ (1) that, provided it lives forever, the tumour will eventually contain a ball of linearly expanding radius. Here it is shown that the rate of expansion is actually linear, and that the region of infection has an asymptotic shape which is given by some (unknown) norm. To demonstrate that the tumour contains a ball of linearly expanding radius, we applied in (1) certain techniques common to the field of interacting particle systems; in particular we made use of certain auxiliary Markov chains which are imbedded in the dual processes of our model. Here different techniques are applied. We show that the first infection times of different sites are almost subadditive, and we exhibit various regularity properties of the infection times such as bounds on their moments. These properties of the Williams-Bjerknes process allow one to follow the outline prescribed by Richardson in (7), where he showed that such a process does indeed exhibit a linear growth whose shape is prescribed by a norm.

scholarly journals Oxygen-Driven Tumour Growth Model: A Pathology-Relevant Mathematical Approach

2015 ◽  
Vol 11 (10) ◽  
pp. e1004550 ◽  
Author(s):  
Juan A. Delgado-SanMartin ◽  
Jennifer I. Hare ◽  
Alessandro P. S. de Moura ◽  
James W. T. Yates
Keyword(s):  
Growth Model ◽  
Tumour Growth ◽  
Mathematical Approach ◽  
Tumour Growth Model

On the global dynamics of one cancer tumour growth model

2014 ◽  
Vol 19 (5) ◽  
pp. 1486-1495 ◽  
Author(s):  
Konstantin E. Starkov ◽  
Alexander P. Krishchenko
Keyword(s):  
Growth Model ◽  
Tumour Growth ◽  
Global Dynamics ◽  
Tumour Growth Model
Sign in / Sign up

Export Citation Format

Share Document