Multiphase and Multiscale Trends in Cancer Modelling

While drawing a link between the papers contained in this issue and those present in a previous one (Vol. 2, Issue 3), this introductory article aims at putting in evidence some trends and challenges on cancer modelling, especially related to the development of multiphase and multiscale models.

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[2]  H. Frieboes,et al.  Three-dimensional multispecies nonlinear tumor growth--I Model and numerical method. , 2008, Journal of theoretical biology.

[3]  B. Perthame,et al.  Kinetic Models for Chemotaxis and their Drift-Diffusion Limits , 2004 .

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[5]  Ignacio Ramis-Conde,et al.  Modeling the influence of the E-cadherin-beta-catenin pathway in cancer cell invasion: a multiscale approach. , 2008, Biophysical journal.

[6]  E Schöll,et al.  Comparing the growth kinetics of cell populations in two and three dimensions. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[7]  Ignacio Ramis-Conde,et al.  Multi-scale modelling of cancer cell intravasation: the role of cadherins in metastasis , 2009, Physical biology.

[8]  B Ribba,et al.  A multiscale mathematical model of avascular tumor growth to investigate the therapeutic benefit of anti-invasive agents. , 2006, Journal of theoretical biology.

[9]  K. Rejniak.  An immersed boundary framework for modelling the growth of individual cells: an application to the early tumour development. , 2007, Journal of theoretical biology.

[10]  V. Quaranta,et al.  Modelling of Cancer Growth, Evolution and Invasion: Bridging Scales and Models , 2007 .

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

[12]  A. Tosin,et al.  Mathematical model of tumour cord growth along the source of nutrient , 2007 .

[13]  K. Rejniak.  A single-cell approach in modeling the dynamics of tumor microregions. , 2005, Mathematical biosciences and engineering : MBE.

[14]  Luigi Preziosi,et al.  Mathematical modelling of the Warburg effect in tumour cords. , 2009, Journal of theoretical biology.

[15]  Helen M Byrne,et al.  A multiphase model describing vascular tumour growth , 2003, Bulletin of mathematical biology.

[16]  Jean Clairambault,et al.  Modelling Physiological and Pharmacological Control on Cell Proliferation to Optimise Cancer Treatments , 2009 .

[17]  K. Rejniak,et al.  Computational and Mathematical Methods in Medicine a Single Cell-based Model of the Ductal Tumour Microarchitecture a Single Cell-based Model of the Ductal Tumour Microarchitecture , 2022 .

[18]  Mirosław Lachowicz,et al.  FROM MICROSCOPIC TO MACROSCOPIC DESCRIPTION FOR GENERALIZED KINETIC MODELS , 2002 .

[19]  T. Hillen.  M5 mesoscopic and macroscopic models for mesenchymal motion , 2006, Journal of mathematical biology.

[20]  V. Cristini,et al.  Nonlinear simulation of tumor necrosis, neo-vascularization and tissue invasion via an adaptive finite-element/level-set method , 2005, Bulletin of mathematical biology.

[21]  A. Anderson,et al.  An evolutionary hybrid cellular automaton model of solid tumour growth. , 2007, Journal of theoretical biology.

[22]  Luigi Preziosi,et al.  Contact inhibition of growth described using a multiphase model and an individual cell based model , 2009, Appl. Math. Lett..

[23]  L. Preziosi,et al.  ON THE CLOSURE OF MASS BALANCE MODELS FOR TUMOR GROWTH , 2002 .

[24]  L. Preziosi,et al.  Cell adhesion mechanisms and stress relaxation in the mechanics of tumours , 2009, Biomechanics and modeling in mechanobiology.

[25]  Dirk Drasdo,et al.  Coarse Graining in Simulated Cell Populations , 2005, Adv. Complex Syst..

[26]  Alexander R. A. Anderson,et al.  Mathematical modelling of flow in 2D and 3D vascular networks: Applications to anti-angiogenic and chemotherapeutic drug strategies , 2005, Math. Comput. Model..

[27]  Nicola Bellomo,et al.  On the foundations of cancer modelling: Selected topics, speculations, and perspectives , 2008 .

[28]  Rebecca J Shipley,et al.  Multiscale Modeling of Fluid Transport in Tumors , 2008, Bulletin of mathematical biology.

[29]  P. Tracqui,et al.  Biophysical models of tumour growth , 2009 .

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

[31]  Michael A Henson,et al.  Incorporating energy metabolism into a growth model of multicellular tumor spheroids. , 2006, Journal of theoretical biology.

[32]  Fabien Crauste,et al.  Dynamics of Erythroid Progenitors and Erythroleukemia , 2009 .

[33]  J R King,et al.  Interactions between a uniformly proliferating tumour and its surroundings: uniform material properties. , 2003, Mathematical medicine and biology : a journal of the IMA.

[34]  J Malda,et al.  Design criteria for a printed tissue engineering construct: a mathematical homogenization approach. , 2009, Journal of theoretical biology.

[35]  Xiangrong Li,et al.  Nonlinear simulations of solid tumor growth using a mixture model: invasion and branching , 2009, Journal of mathematical biology.

[36]  N. Bellomo,et al.  MULTICELLULAR BIOLOGICAL GROWING SYSTEMS: HYPERBOLIC LIMITS TOWARDS MACROSCOPIC DESCRIPTION , 2007 .

[37]  Luigi Preziosi,et al.  Multiphase modelling of tumour growth and extracellular matrix interaction: mathematical tools and applications , 2009, Journal of mathematical biology.

[38]  S. McDougall,et al.  Multiscale modelling and nonlinear simulation of vascular tumour growth , 2009, Journal of mathematical biology.

[39]  D L S McElwain,et al.  A history of the study of solid tumour growth: The contribution of mathematical modelling , 2004, Bulletin of mathematical biology.

[40]  Helen M. Byrne,et al.  A Multiple Scale Model for Tumor Growth , 2005, Multiscale Model. Simul..

[41]  Alexander R. A. Anderson,et al.  Single-Cell-Based Models in Biology and Medicine , 2007 .

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[43]  D. Ambrosi,et al.  On the mechanics of a growing tumor , 2002 .

[44]  S. McDougall,et al.  Mathematical modelling of dynamic adaptive tumour-induced angiogenesis: clinical implications and therapeutic targeting strategies. , 2006, Journal of theoretical biology.

[45]  Marie Doumic.  Analysis of a Population Model Structured by the Cells Molecular Content , 2007 .

[46]  D. L. Sean McElwain,et al.  A Mixture Theory for the Genesis of Residual Stresses in Growing Tissues I: A General Formulation , 2005, SIAM J. Appl. Math..

[47]  M. Chaplain,et al.  Mathematical modelling of the loss of tissue compression responsiveness and its role in solid tumour development. , 2006, Mathematical medicine and biology : a journal of the IMA.

[48]  Antonio Fasano,et al.  ATP Production and Necrosis Formation in a Tumour Spheroid Model , 2007 .

[49]  Philip K Maini,et al.  Angiogenesis and vascular remodelling in normal and cancerous tissues , 2009, Journal of mathematical biology.

[50]  D. Drasdo,et al.  A single-cell-based model of tumor growth in vitro: monolayers and spheroids , 2005, Physical biology.

[51]  D. Drasdo,et al.  Individual-based approaches to birth and death in avascu1ar tumors , 2003 .

[52]  H. Othmer,et al.  A HYBRID MODEL FOR TUMOR SPHEROID GROWTH IN VITRO I: THEORETICAL DEVELOPMENT AND EARLY RESULTS , 2007 .

[53]  Dirk Drasdo,et al.  Individual-based and continuum models of growing cell populations: a comparison , 2009, Journal of mathematical biology.

[54]  A. Friedman,et al.  Free Boundary Problems Associated with Multiscale Tumor Models , 2009 .

[55]  A. Anderson,et al.  A hybrid cellular automaton model of clonal evolution in cancer: the emergence of the glycolytic phenotype. , 2008, Journal of theoretical biology.

[56]  M. Loeffler,et al.  Modeling the effect of deregulated proliferation and apoptosis on the growth dynamics of epithelial cell populations in vitro. , 2005, Biophysical journal.

[57]  D. L. Sean McElwain,et al.  A Mixture Theory for the Genesis of Residual Stresses in Growing Tissues II: Solutions to the Biphasic Equations for a Multicell Spheroid , 2005, SIAM J. Appl. Math..

[58]  D Ambrosi,et al.  The role of stress in the growth of a multicell spheroid , 2004, Journal of mathematical biology.

[59]  S. Schnell,et al.  A multiscale mathematical model of cancer, and its use in analyzing irradiation therapies , 2006, Theoretical Biology and Medical Modelling.

[60]  S. McDougall,et al.  Mathematical modelling of flow through vascular networks: Implications for tumour-induced angiogenesis and chemotherapy strategies , 2002, Bulletin of mathematical biology.

[61]  L Preziosi,et al.  An elasto-visco-plastic model of cell aggregates. , 2010, Journal of theoretical biology.