Mathematical modelling of tumour acidity.

[1]  J. Shirlaw.  THE METABOLISM OF TUMOURS , 1931 .

[2]  E. Boyland.  Metabolism of Tumours , 1940, Nature.

[3]  L. H. Gray,et al.  The Histological Structure of Some Human Lung Cancers and the Possible Implications for Radiotherapy , 1955, British Journal of Cancer.

[4]  E. Hill.  Journal of Theoretical Biology , 1961, Nature.

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

[6]  S. V. Sotirchos,et al.  Variations in tumor cell growth rates and metabolism with oxygen concentration, glucose concentration, and extracellular pH , 1992, Journal of cellular physiology.

[7]  R K Jain,et al.  Noninvasive measurement of interstitial pH profiles in normal and neoplastic tissue using fluorescence ratio imaging microscopy. , 1994, Cancer research.

[8]  S. Cross,et al.  Fractal geometric analysis of colorectal polyps , 1994, The Journal of pathology.

[9]  E. T. Gawlinski,et al.  A reaction-diffusion model of cancer invasion. , 1996, Cancer research.

[10]  Gaston H. Gonnet,et al.  On the LambertW function , 1996, Adv. Comput. Math..

[11]  M. Dewhirst,et al.  Fourier analysis of fluctuations of oxygen tension and blood flow in R3230Ac tumors and muscle in rats. , 1999, American journal of physiology. Heart and circulatory physiology.

[12]  W. Godwin.  Article in Press , 2000 .

[13]  E. T. Gawlinski,et al.  A cellular automaton model of early tumor growth and invasion. , 2001, Journal of theoretical biology.

[14]  E. T. Gawlinski,et al.  A Cellular Automaton Model of Early Tumor Growth and Invasion: The Effects of Native Tissue Vascularity and Increased Anaerobic Tumor Metabolism , 2001 .

[15]  Gregory S Karczmar,et al.  MRI of the tumor microenvironment , 2002, Journal of magnetic resonance imaging : JMRI.

[16]  R. Rickert,et al.  Hypoxia-Inducible Factor 1 (cid:2) Is Essential for Cell Cycle Arrest during Hypoxia , 2002 .

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

[18]  Benoit Macq,et al.  Physiological noise in murine solid tumours using T2*-weighted gradient-echo imaging: a marker of tumour acute hypoxia? , 2004, Physics in medicine and biology.

[19]  M. Loda,et al.  Hypoxia regulation of the cell cycle in malignant melanoma: putative role for the cyclin‐dependent kinase inhibitor p27Kip1 , 2004, Journal of cutaneous pathology.

[20]  P. Maini,et al.  The role of acidity in solid tumour growth and invasion. , 2005, Journal of theoretical biology.

[21]  哲史 小池,et al.  Hypoxia inducible factorにより誘導される癌細胞の接着分子 , 2005 .

[22]  J. Brady,et al.  Quiescence as a mechanism for cyclical hypoxia and acidosis , 2007, Journal of mathematical biology.

[23]  P. Maini,et al.  Metabolic changes during carcinogenesis: potential impact on invasiveness. , 2007, Journal of theoretical biology.

[24]  D. Peet,et al.  Hypoxia Inducible Factor , 2007 .