Stabilized second-order convex splitting schemes for Cahn-Hilliard models with application to diffuse-interface tumor-growth models

2013 ◽  
Vol 30 (2) ◽  
pp. 180-203 ◽  
Author(s):  
X. Wu ◽  
G. J. van Zwieten ◽  
K. G. van der Zee
Keyword(s):  
Tumor Growth ◽  
Growth Models ◽  
Second Order ◽  
Diffuse Interface ◽  
Splitting Schemes ◽  
Tumor Growth Models ◽  
Convex Splitting

GENERAL DIFFUSE-INTERFACE THEORIES AND AN APPROACH TO PREDICTIVE TUMOR GROWTH MODELING

2010 ◽  
Vol 20 (03) ◽  
pp. 477-517 ◽  
Author(s):  
J. TINSLEY ODEN ◽  
ANDREA HAWKINS ◽  
SERGE PRUDHOMME
Keyword(s):  
Tumor Growth ◽  
Uncertainty Quantification ◽  
Model Validation ◽  
Phase Field ◽  
Growth Models ◽  
Diffuse Interface ◽  
Calibration Model ◽  
Tumor Growth Models ◽  
Tumor Growth Modeling ◽  
Quantities Of Interest

While a large and growing literature exists on mathematical and computational models of tumor growth, to date tumor growth models are largely qualitative in nature, and fall far short of being able to provide predictive results important in life-and-death decisions. This is largely due to the enormous complexity of evolving biological and chemical processes in living tissue and the complex interactions of many cellular and vascular constituents in living organisms. Several new technologies have emerged, however, which could lead to significant progress in this important area: (i) the development of so-called phase-field, or diffuse-interface models, which can be developed using continuum mixture theory, and which provide a general framework for modeling the action of multiple interacting constituents. These are based on generalizations of the Cahn–Hilliard models for spinodal decomposition, and have been used recently in certain tumor growth theories; (ii) the emergence of predictive computational methods based on the use of statistical methods for calibration, model validation, and uncertainty quantification; (iii) advances in imaging, experimental cell biology, and other medical observational methodologies; and (iv) the advent of petascale computing that makes possible the resolution of features at scales and at speeds that were unattainable only a short time in the past. Here we develop a general phenomenological thermomechanical theory of mixtures that employs phase-field or diffuse interface models of surface energies and reactions and which provides a framework for generalizing existing theories of the types that are in use in tumor growth modeling. In principle, the framework provides for the effects of M solid constituents, which may undergo large deformations, and for the effect of N - M fluid constituents, which could include highly nonlinear, non-Newtonian fluids. We then describe several special cases which have the potential of providing acceptable models of tumor growth. We then describe the beginning steps of the development of Bayesian methods for statistical calibration, model validation, and uncertainty quantification, which, with further work, could produce a truly predictive tool for studying tumor growth. In particular, we outline the processes of statistical calibration and validation that can be employed to determine if tumor growth models, drawn from the broad class of models developed here, are valid for prediction of key quantities of interest critical to making decisions on various medical protocols. We also describe how uncertainties in such key quantities of interest can be quantified in ways that can be used to establish confidence in predicted outcomes.

Contour Instabilities in Early Tumor Growth Models

2011 ◽  
Vol 106 (14) ◽  
Author(s):  
M. Ben Amar ◽  
C. Chatelain ◽  
P. Ciarletta
Keyword(s):  
Tumor Growth ◽  
Growth Models ◽  
Tumor Growth Models ◽  
Early Tumor

Second order convex splitting schemes for periodic nonlocal Cahn–Hilliard and Allen–Cahn equations

2014 ◽  
Vol 277 ◽  
pp. 48-71 ◽  
Author(s):  
Zhen Guan ◽  
John S. Lowengrub ◽  
Cheng Wang ◽  
Steven M. Wise
Keyword(s):  
Second Order ◽  
Splitting Schemes ◽  
Convex Splitting

scholarly journals Controlled and Uncontrolled Stochastic Norton-Simon-Massagué Tumor Growth Models

2019 ◽  
Author(s):  
Zehor Belkhatir ◽  
Michele Pavon ◽  
James C. Mathews ◽  
Maryam Pouryahya ◽  
Joseph O. Deasy ◽  
...  
Keyword(s):  
Tumor Growth ◽  
Growth Models ◽  
Tumor Growth Models

scholarly journals Image Guided Personalization of Reaction-Diffusion Type Tumor Growth Models Using Modified Anisotropic Eikonal Equations

2010 ◽  
Vol 29 (1) ◽  
pp. 77-95 ◽  
Author(s):  
E. Konukoglu ◽  
O. Clatz ◽  
B.H. Menze ◽  
B. Stieltjes ◽  
M.-A. Weber ◽  
...  
Keyword(s):  
Tumor Growth ◽  
Growth Models ◽  
Reaction Diffusion ◽  
Diffusion Type ◽  
Eikonal Equations ◽  
Image Guided ◽  
Tumor Growth Models

scholarly journals An accurate front capturing scheme for tumor growth models with a free boundary limit

2018 ◽  
Vol 364 ◽  
pp. 73-94 ◽  
Author(s):  
Jian-Guo Liu ◽  
Min Tang ◽  
Li Wang ◽  
Zhennan Zhou
Keyword(s):  
Free Boundary ◽  
Tumor Growth ◽  
Growth Models ◽  
Boundary Limit ◽  
Tumor Growth Models

scholarly journals Fully Automatic Calibration of Tumor-Growth Models Using a Single mpMRI Scan

2021 ◽  
Vol 40 (1) ◽  
pp. 193-204
Author(s):  
Klaudius Scheufele ◽  
Shashank Subramanian ◽  
George Biros
Keyword(s):  
Tumor Growth ◽  
Growth Models ◽  
Automatic Calibration ◽  
Tumor Growth Models ◽  
Fully Automatic
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