A detailed numerical treatment of the boundary conditions imposed by the skull on a diffusion–reaction model of glioma tumor growth. Clinical validation aspects

2012 ◽  
Vol 218 (17) ◽  
pp. 8779-8799 ◽  
Author(s):  
Stavroula G. Giatili ◽  
Georgios S. Stamatakos
Keyword(s):  
Tumor Growth ◽  
Boundary Conditions ◽  
Reaction Model ◽  
Diffusion Reaction ◽  
Clinical Validation ◽  
Numerical Treatment ◽  
Glioma Tumor

scholarly journals A Numerical Handling of the Boundary Conditions Imposed by the Skull on an Inhomogeneous Diffusion-Reaction Model of Glioblastoma Invasion Into the Brain: Clinical Validation Aspects

2017 ◽  
Vol 16 ◽  
pp. 117693511668482
Author(s):  
Georgios S Stamatakos ◽  
Stavroula G Giatili
Keyword(s):  
Boundary Conditions ◽  
In Silico ◽  
Doubling Time ◽  
Neumann Boundary ◽  
Reaction Diffusion ◽  
Reaction Model ◽  
Diffusion Reaction ◽  
Clinical Validation ◽  
Imaging Data ◽  
Case Scenario

A novel explicit triscale reaction-diffusion numerical model of glioblastoma multiforme tumor growth is presented. The model incorporates the handling of Neumann boundary conditions imposed by the cranium and takes into account both the inhomogeneous nature of human brain and the complexity of the skull geometry. The finite-difference time-domain method is adopted. To demonstrate the workflow of a possible clinical validation procedure, a clinical case/scenario is addressed. A good agreement of the in silico calculated value of the doubling time (ie, the time for tumor volume to double) with the value of the same quantity based on tomographic imaging data has been observed. A theoretical exploration suggests that a rough but still quite informative value of the doubling time may be calculated based on a homogeneous brain model. The model could serve as the main component of a continuous mathematics-based glioblastoma oncosimulator aiming at supporting the clinician in the optimal patient-individualized design of treatment using the patient’s multiscale data and experimenting in silico (ie, on the computer).

Personalized image-based tumor growth prediction in a convection–diffusion–reaction model

2018 ◽  
Vol 120 (1) ◽  
pp. 49-57
Author(s):  
Nargess Meghdadi ◽  
M. Soltani ◽  
Hanieh Niroomand-Oscuii ◽  
Nooshin Yamani
Keyword(s):  
Tumor Growth ◽  
Reaction Model ◽  
Diffusion Reaction ◽  
Growth Prediction ◽  
Convection Diffusion

scholarly journals A permeation-diffusion-reaction model of gas transport in cellular tissue of plant materials

2006 ◽  
Vol 57 (15) ◽  
pp. 4215-4224 ◽  
Author(s):  
Q. T. Ho ◽  
B. E. Verlinden ◽  
P. Verboven ◽  
S. Vandewalle ◽  
B. M. Nicolai
Keyword(s):  
Gas Transport ◽  
Cellular Tissue ◽  
Reaction Model ◽  
Diffusion Reaction ◽  
Plant Materials

Diffusion-reaction model for ASR

2014 ◽  
pp. 639-648 ◽  
Author(s):  
J Liaudat ◽  
C López ◽  
I Carol
Keyword(s):  
Reaction Model ◽  
Diffusion Reaction

scholarly journals Fractal diffusion-reaction model for a porous electrode

2021 ◽  
pp. 26-26
Author(s):  
Ling Lin ◽  
Yun Qiao
Keyword(s):  
Surface Morphology ◽  
Porous Electrode ◽  
Enzymatic Reaction ◽  
Bright Light ◽  
Reaction Model ◽  
Solution Procedure ◽  
Diffusion Reaction ◽  
Fast Diffusion ◽  
Fractal Derivative ◽  
Intuitive Grasp

Fractal modifications of Fick?s laws are discussed by taking into account the electrode?s porous structure, and a fractal derivative model for diffusion-reaction process in a thin film of an amperometric enzymatic reaction is established. Particular attention is paid to giving an intuitive grasp for its fractal variational principle and its solution procedure. Extremely fast or extremely slow diffusion process can be achieved by suitable control of the electrode?s surface morphology, a sponge-like surface leads to an extremely fast diffusion, while a lotus-leaf-like uneven surface predicts an extremely slow process. This paper sheds a bright light on an optimal design of an electrode?s surface morphology.

Sign in / Sign up

Export Citation Format

Share Document