Study of Tumor Growth under Hyperthermia Condition

The new concept of keeping primary tumor under control in situ to suppress distant foci sheds light on the treatment of metastatic tumor. Hyperthermia is considered as one of the means for controlling tumor growth. To simulate the tumor growth, a continuum mathematical model has been introduced. The newest understanding of the Warburg effect on the cellular metabolism and diffusion of the nutrients in the tissue has been taken into consideration. The numerical results are compared with the in vivo experimental data by fitting the tumor cell doubling time/tumor cell growth rate under different thermal conditions. Both the tumor growth curve and corresponding average glucose concentration have been predicted. The numerical results have quantitatively illustrated the controlling effect on tumor growth under hyperthermia condition in the initial stage.

[1]  A. Anderson,et al.  A hybrid mathematical model of solid tumour invasion: the importance of cell adhesion. , 2005, Mathematical medicine and biology : a journal of the IMA.

[2]  M. Chaplain,et al.  A mathematical model for the growth and classification of a solid tumor: a new approach via nonlinear elasticity theory using strain-energy functions. , 1992, Mathematical biosciences.

[3]  Janusz Skowronek,et al.  Hyperthermia – description of a method and a review of clinical applications , 2007 .

[4]  D. Grecu MATHEMATICAL MODELLING OF TUMOR GROWTH , 2007 .

[5]  Burton Ac,et al.  Rate of growth of solid tumours as a problem of diffusion. , 1966, Growth.

[6]  H. Maeda,et al.  Tumor vascular permeability and the EPR effect in macromolecular therapeutics: a review. , 2000, Journal of controlled release : official journal of the Controlled Release Society.

[7]  G. Semenza,et al.  Oncogenic alterations of metabolism. , 1999, Trends in biochemical sciences.

[8]  Ping Liu,et al.  Immunologic response induced by synergistic effect of alternating cooling and heating of breast cancer , 2009, International journal of hyperthermia : the official journal of European Society for Hyperthermic Oncology, North American Hyperthermia Group.

[9]  Pamela F. Jones,et al.  Computational and Mathematical Methods in Medicine , 2011, Comput. Math. Methods Medicine.

[10]  J. Freyer,et al.  Regulation of growth saturation and development of necrosis in EMT6/Ro multicellular spheroids by the glucose and oxygen supply. , 1986, Cancer research.

[11]  J A Adam,et al.  Mathematical models of prevascular spheroid development and catastrophe-theoretic description of rapid metastatic growth/tumor remission. , 1996, Invasion & metastasis.

[12]  Albert Koong,et al.  Oxygen Consumption Can Regulate the Growth of Tumors, a New Perspective on the Warburg Effect , 2009, PloS one.

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

[14]  L. Tanoue Cancer Statistics, 2009 , 2010 .

[15]  C. Song Effect of local hyperthermia on blood flow and microenvironment: a review. , 1984, Cancer research.

[16]  M. Chaplain,et al.  A new mathematical model for avascular tumour growth , 2001, Journal of mathematical biology.

[17]  S. V. Sotirchos,et al.  Glucose diffusivity in multicellular tumor spheroids. , 1988, Cancer research.

[18]  Tutut Herawan,et al.  Computational and mathematical methods in medicine. , 2006, Computational and mathematical methods in medicine.

[19]  R. Collins,et al.  Effects of radiotherapy and of differences in the extent of surgery for early breast cancer on local recurrence and 15-year survival: an overview of the randomised trials , 2005, The Lancet.

[20]  C. Graham,et al.  Oxygen-mediated Regulation of Tumor Cell Invasiveness , 2002, The Journal of Biological Chemistry.

[21]  R. Deberardinis,et al.  The biology of cancer: metabolic reprogramming fuels cell growth and proliferation. , 2008, Cell metabolism.

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

[23]  Daniel A Beard,et al.  The Role of Theoretical Modeling in Microcirculation Research , 2008, Microcirculation.

[24]  N Gunduz,et al.  Influence of the interval between primary tumor removal and chemotherapy on kinetics and growth of metastases. , 1983, Cancer research.

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

[26]  K. Camphausen,et al.  Radiation therapy to a primary tumor accelerates metastatic growth in mice. , 2001, Cancer research.

[27]  J. Pouysségur,et al.  Oxygen, a source of life and stress , 2007, FEBS letters.

[28]  N. Komarova Mathematical modeling of tumorigenesis: mission possible , 2005, Current opinion in oncology.

[29]  H M Byrne,et al.  Growth of nonnecrotic tumors in the presence and absence of inhibitors. , 1995, Mathematical biosciences.

[30]  Aili Zhang,et al.  Mechanical Study on Tumor Microvessel Damage Induced by Alternate Cooling and Heating Treatment , 2009 .

[31]  J. King,et al.  Mathematical modelling of avascular-tumour growth. , 1997, IMA journal of mathematics applied in medicine and biology.

[32]  Adam Ja Mathematical models of prevascular spheroid development and catastrophe-theoretic description of rapid metastatic growth/tumor remission. , 1996 .

[33]  O. Warburg [Origin of cancer cells]. , 1956, Oncologia.

[34]  J. Lepock,et al.  Cellular effects of hyperthermia: relevance to the minimum dose for thermal damage , 2003, International journal of hyperthermia : the official journal of European Society for Hyperthermic Oncology, North American Hyperthermia Group.

[35]  Laird Ak DYNAMICS OF TUMOR GROWTH. , 1964 .

[36]  Liu Ping,et al.  Thermal environmental effect on breast tumor growth. , 2009 .

[37]  S. V. Sotirchos,et al.  Mathematical modelling of microenvironment and growth in EMT6/Ro multicellular tumour spheroids , 1992, Cell proliferation.

[38]  S. Jonathan Chapman,et al.  Mathematical Models of Avascular Tumor Growth , 2007, SIAM Rev..

[39]  Marissa J Carter,et al.  Chronic cellular hypoxia as the prime cause of cancer: what is the de-oxygenating role of adulterated and improper ratios of polyunsaturated fatty acids when incorporated into cell membranes? , 2008, Medical hypotheses.

[40]  A C Burton,et al.  Rate of growth of solid tumours as a problem of diffusion. , 1966, Growth.

[41]  M. Chaplain,et al.  Continuous and discrete mathematical models of tumor-induced angiogenesis , 1998, Bulletin of mathematical biology.

[42]  H. Greenspan Models for the Growth of a Solid Tumor by Diffusion , 1972 .

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

[44]  L. Cantley,et al.  Understanding the Warburg Effect: The Metabolic Requirements of Cell Proliferation , 2009, Science.

[45]  H. Kampinga,et al.  Nuclear matrix as a target for hyperthermic killing of cancer cells. , 1998, Cell stress & chaperones.

[46]  J R Oleson,et al.  Tumor temperature distributions predict hyperthermia effect. , 1989, International journal of radiation oncology, biology, physics.

[47]  Johan Bussink,et al.  Tumor hypoxia at the micro-regional level: clinical relevance and predictive value of exogenous and endogenous hypoxic cell markers. , 2003, Radiotherapy and oncology : journal of the European Society for Therapeutic Radiology and Oncology.

[48]  D. Connolly,et al.  Tumor vascular permeability factor stimulates endothelial cell growth and angiogenesis. , 1989, The Journal of clinical investigation.

[49]  J. Rhee,et al.  Implication of Blood Flow in Hyperthermic Treatment of Tumors , 1984, IEEE Transactions on Biomedical Engineering.

[50]  J. King,et al.  Mathematical modelling of avascular-tumour growth. II: Modelling growth saturation. , 1999, IMA journal of mathematics applied in medicine and biology.

[51]  D. Sabatini,et al.  Cancer Cell Metabolism: Warburg and Beyond , 2008, Cell.

[52]  M. Chaplain Avascular growth, angiogenesis and vascular growth in solid tumours: The mathematical modelling of the stages of tumour development , 1996 .

[53]  P R Stauffer,et al.  Introduction: Thermal ablation therapy , 2004, International journal of hyperthermia : the official journal of European Society for Hyperthermic Oncology, North American Hyperthermia Group.

[54]  Emma Saavedra,et al.  Energy metabolism in tumor cells , 2007, The FEBS journal.

[55]  The Prime Cause and Prevention of Cancer by with two prefaces on prevention , 2008 .

[56]  W Cramer,et al.  On the Origin of Cancer* , 1938, British medical journal.

[57]  R. Gillies,et al.  Why do cancers have high aerobic glycolysis? , 2004, Nature Reviews Cancer.

[58]  Avner Friedman,et al.  Interaction of Tumor with Its Micro-environment: A Mathematical Model , 2010, Bulletin of mathematical biology.

[59]  Michael Berens,et al.  A mathematical model of glioblastoma tumor spheroid invasion in a three-dimensional in vitro experiment. , 2007, Biophysical journal.

[60]  X. Ruan,et al.  A simple cellular automaton model for tumor-immunity system , 2003, IEEE International Conference on Robotics, Intelligent Systems and Signal Processing, 2003. Proceedings. 2003.