A bicompartmental dynamic tumor growth model

Abstract We introduce a simple nonlinear dynamic tumor growth model which distinguishes between a core and a peripherial compartment, and accounts for nutrient and congestion-dependent cell proliferation, necrosis and volume growth. The model synthesis procedure considers that later the model shall be extended with mechanisms describing angiogenesis and will be used in control based optimization of anti-angiogenic treatment procedures.

[1]  Nathan A. Berger,et al.  Impact of Sleep and Sleep Disturbances on Obesity and Cancer , 2014, Energy Balance and Cancer.

[2]  Levente Kovács,et al.  Comparison of mathematical tumor growth models , 2015, 2015 IEEE 13th International Symposium on Intelligent Systems and Informatics (SISY).

[3]  Eric Walter,et al.  On the identifiability and distinguishability of nonlinear parametric models , 1996 .

[4]  Arjan W. Griffioen,et al.  Tumour vascularization: sprouting angiogenesis and beyond , 2007, Cancer and Metastasis Reviews.

[5]  S. McDougall,et al.  Mathematical modeling of tumor-induced angiogenesis. , 2006, Annual review of biomedical engineering.

[6]  Jana L. Gevertz,et al.  Computational Modeling of Tumor Response to Vascular-Targeting Therapies—Part I: Validation , 2011, Comput. Math. Methods Medicine.

[7]  Lennart Ljung,et al.  On global identifiability for arbitrary model parametrizations , 1994, Autom..

[8]  J. Bauer,et al.  Chemical reaction network theory for in-silico biologists , 2003 .

[9]  Levente Kovács,et al.  Tumor Volume Estimation and Quasi-Continuous Administration for Most Effective Bevacizumab Therapy , 2015, PloS one.

[10]  Helen M. Byrne,et al.  A two-phase model of solid tumour growth , 2003, Appl. Math. Lett..

[11]  Z. Agur,et al.  A computer algorithm describing the process of vessel formation and maturation, and its use for predicting the effects of anti-angiogenic and anti-maturation therapy on vascular tumor growth , 2004, Angiogenesis.

[12]  M. Hendrix,et al.  Alternative vascularization mechanisms in cancer: Pathology and therapeutic implications. , 2007, The American journal of pathology.

[13]  Maria Pia Saccomani,et al.  DAISY: A new software tool to test global identifiability of biological and physiological systems , 2007, Comput. Methods Programs Biomed..

[14]  Yi Jiang,et al.  A cell-based model exhibiting branching and anastomosis during tumor-induced angiogenesis. , 2007, Biophysical journal.

[15]  Maria Pia Saccomani,et al.  Parameter identifiability of nonlinear systems: the role of initial conditions , 2003, Autom..

[16]  H. Yang,et al.  Mathematical modeling of solid cancer growth with angiogenesis , 2012, Theoretical Biology and Medical Modelling.

[17]  Eva Balsa-Canto,et al.  Parameter estimation and optimal experimental design. , 2008, Essays in biochemistry.

[18]  P. Hahnfeldt,et al.  Tumor development under angiogenic signaling: a dynamical theory of tumor growth, treatment response, and postvascular dormancy. , 1999, Cancer research.

[19]  Philip Hahnfeldt,et al.  Tumor morphological evolution: directed migration and gain and loss of the self-metastatic phenotype , 2010, Biology Direct.

[20]  Jelena Pjesivac-Grbovic,et al.  A multiscale model for avascular tumor growth. , 2005, Biophysical journal.

[21]  Alberto Gandolfi,et al.  Tumour eradication by antiangiogenic therapy: analysis and extensions of the model by Hahnfeldt et al. (1999). , 2004, Mathematical biosciences.