A minimal model describing the effect of drug administration on tumor growth dynamics

2006 ◽  
Author(s):  
G. de Nicolao
Keyword(s):  
Tumor Growth ◽  
Drug Administration ◽  
Minimal Model ◽  
Growth Dynamics

scholarly journals Optimal control of stochastic phase-field models related to tumor growth

2020 ◽  
Vol 26 ◽  
pp. 104
Author(s):  
Carlo Orrieri ◽  
Elisabetta Rocca ◽  
Luca Scarpa
Keyword(s):  
Optimal Control ◽  
Tumor Growth ◽  
Phase Field ◽  
Phase Field Model ◽  
Growth Dynamics ◽  
Necessary Optimality Conditions ◽  
Reaction Diffusion ◽  
Adjoint System ◽  
Reaction Diffusion Equation ◽  
Cahn Hilliard Equation

We study a stochastic phase-field model for tumor growth dynamics coupling a stochastic Cahn-Hilliard equation for the tumor phase parameter with a stochastic reaction-diffusion equation governing the nutrient proportion. We prove strong well-posedness of the system in a general framework through monotonicity and stochastic compactness arguments. We introduce then suitable controls representing the concentration of cytotoxic drugs administered in medical treatment and we analyze a related optimal control problem. We derive existence of an optimal strategy and deduce first-order necessary optimality conditions by studying the corresponding linearized system and the backward adjoint system.

An Interdisciplinary Approach to Brain Tumor Growth Dynamics

2000 ◽  
Author(s):  
Salvatore Torquato ◽  
Thomas S. Deisboeck
Keyword(s):  
Brain Tumors ◽  
Tumor Growth ◽  
Computational Models ◽  
Growth Dynamics ◽  
Interdisciplinary Approach ◽  
Clinical Prognosis ◽  
Macroscopic Tumor ◽  
New Perspective ◽  
Clonal Composition

Abstract Intensive medical research over the last fifty years has left the prognosis for patients diagnosed with malignant brain tumors nearly unchanged. This suggests that a new perspective on the problem may offer important insight. We have undertaken an interdisciplinary research program, seeking to study brain tumors as complex systems. This research aims to develop computational models coupled with experimental assays to investigate the hypothesis of self-organizing behavior in tumor systems. Preliminary assays have revealed behavior consistent with this hypothesis. A cellular-automaton model to study the growth of the tumor core has been developed. This model has proven successful in reproducing macroscopic tumor growth from a limited parameter set. Further, it has been applied to investigate the importance of heterogeneity to determination of a clinical prognosis and has demonstrated the importance of understanding clonal composition in making an accurate prognosis.

scholarly journals P01.145 Tumor growth dynamics in serially-imaged low-grade glioma patients

2018 ◽  
Vol 20 (suppl_3) ◽  
pp. iii265-iii265
Author(s):  
J F Megyesi ◽  
C Gui ◽  
S Kosteniuk ◽  
J Lau
Keyword(s):  
Tumor Growth ◽  
Growth Dynamics ◽  
Low Grade Glioma ◽  
Low Grade

scholarly journals Using Ordinary Differential Equations to Explore Cancer-Immune Dynamics and Tumor Dormancy

2016 ◽  
Author(s):  
Kathleen P. Wilkie ◽  
Philip Hahnfeldt ◽  
Lynn Hlatky
Keyword(s):  
Mathematical Modeling ◽  
Immune Response ◽  
Differential Equations ◽  
Tumor Growth ◽  
Ordinary Differential Equations ◽  
Systemic Disease ◽  
Growth Dynamics ◽  
Tumor Dormancy ◽  
Cytotoxic Action ◽  
General Method

AbstractCancer is not solely a disease of the genome, but is a systemic disease that affects the host on many functional levels, including, and perhaps most notably, the function of the immune response, resulting in both tumor-promoting inflammation and tumor-inhibiting cytotoxic action. The dichotomous actions of the immune response induce significant variations in tumor growth dynamics that mathematical modeling can help to understand. Here we present a general method using ordinary differential equations (ODEs) to model and analyze cancer-immune interactions, and in particular, immune-induced tumor dormancy.

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