Avascular growth, angiogenesis and vascular growth in solid tumours: The mathematical modelling of the stages of tumour development

[1]  S. Timoshenko,et al.  Theory of elasticity , 1975 .

[2]  W. Cliff.  Observations on healing tissue: A combined light and electron microscopic investigation , 1963, Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences.

[3]  G. Schoefl,et al.  STUDIES ON INFLAMMATION. III. GROWING CAPILLARIES: THEIR STRUCTURE AND PERMEABILITY. , 1963, Virchows Archiv fur pathologische Anatomie und Physiologie und fur klinische Medizin.

[4]  P. Shubik,et al.  The growth of the blood supply to melanoma transplants in the hamster cheek pouch. , 1966, Laboratory investigation; a journal of technical methods and pathology.

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

[6]  E. Laurence,et al.  Extraction, purification and preliminary characterisation of the epidermal chalone: A tissue specific mitotic inhibitor obtained from vertebrate skin. , 1968, European journal of biochemistry.

[7]  Inch Wr,et al.  Growth of nodular carcinomas in rodents compared with multi-cell spheroids in tissue culture. , 1970 .

[8]  The pattern of tumour growth. , 1971 .

[9]  R. Sutherland,et al.  Growth of multicell spheroids in tissue culture as a model of nodular carcinomas. , 1971, Journal of the National Cancer Institute.

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

[11]  Howard I. Maibach,et al.  Epidermal wound healing , 1972 .

[12]  J. Folkman,et al.  SELF-REGULATION OF GROWTH IN THREE DIMENSIONS , 1973, The Journal of experimental medicine.

[13]  F. Marks.  A tissue-specific factor inhibiting DNA synthesis in mouse epidermis. , 1973, National Cancer Institute monograph.

[14]  Greenspan Hp,et al.  On the self-inhibited growth of cell cultures. , 1974 .

[15]  J. Folkman,et al.  Tumor growth and neovascularization: an experimental model using the rabbit cornea. , 1974, Journal of the National Cancer Institute.

[16]  G. Brugal,et al.  EXISTENCE OF TWO CHALONE‐LIKE SUBSTANCES IN INTESTINAL EXTRACT FROM THE ADULT NEWT, INHIBITING EMBRYONIC INTESTINAL CELL PROLIFERATION , 1975, Cell and tissue kinetics.

[17]  J. Folkman.  The vascularization of tumors. , 1976, Scientific American.

[18]  Shymko Rm,et al.  Cellular and geometric control of tissue growth and mitotic instability. , 1976 .

[19]  R E Durand,et al.  CELL CYCLE KINETICS IN AN IN VITRO TUMOR MODEL , 1976, Cell and tissue kinetics.

[20]  H. Greenspan.  On the growth and stability of cell cultures and solid tumors. , 1976, Journal of theoretical biology.

[21]  J. Folkman,et al.  Migration and proliferation of endothelial cells in preformed and newly formed blood vessels during tumor angiogenesis. , 1977, Microvascular research.

[22]  G M Saidel,et al.  Diffusion model of tumor vascularization and growth , 1977, Bulletin of mathematical biology.

[23]  R. Cotran,et al.  Cellular migration and replication in endothelial regeneration: a study using irradiated endothelial cultures. , 1977, Laboratory investigation; a journal of technical methods and pathology.

[24]  P. J. Ponzo,et al.  A model for the growth of a solid tumor with non-uniform oxygen consumption , 1977 .

[25]  Epidermal chalones and squamous cell carcinomas , 1978, Virchows Archiv B Cell Pathology.

[26]  Epidermal chalones and squamous cell carcinomas. The growth inhibitory effects of aqueous epidermal extracts (G1 and G2 chalones) on the epidermis and on a transplantable keratinizing carcinoman in nude mice. , 1978 .

[27]  B. Goodwin,et al.  A field description of the cleavage process in embryogenesis. , 1980, Journal of theoretical biology.

[28]  L I Krishtalik,et al.  Catalytic acceleration of reactions by enzymes. Effect of screening of a polar medium by a protein globule. , 1980, Journal of theoretical biology.

[29]  A. Hunding.  Dissipative structures in reaction-diffusion systems: Numerical determination of bifurcations in the sphere , 1980 .

[30]  R. Baserga,et al.  Tissue Growth Factors , 1981, Handbook of Experimental Pharmacology.

[31]  P. Vaupel,et al.  Heterogeneous oxygen partial pressure and pH distribution in C3H mouse mammary adenocarcinoma. , 1981, Cancer research.

[32]  W. Loewenstein,et al.  Junctional intercellular communication: the cell-to-cell membrane channel. , 1981, Physiological reviews.

[33]  R. Ma,et al.  Endothelial regeneration. III. Time course of intimal changes after small defined injury to rat aortic endothelium. , 1981 .

[34]  O. Kaalhus,et al.  Cell Kinetic Characteristics In Different Parts of Multicellular Spheroids of Human Origin , 1981, Cell and tissue kinetics.

[35]  R. Auerbach,et al.  Tumor-induced neovascularization in the mouse eye. , 1982, Journal of the National Cancer Institute.

[36]  J P Freyer,et al.  A model for the growth of multicellular spheroids , 1982, Cell and tissue kinetics.

[37]  J. Murray,et al.  Parameter space for turing instability in reaction diffusion mechanisms: a comparison of models. , 1982, Journal of theoretical biology.

[38]  J. Freyer,et al.  Determination of diffusion constants for metabolites in multicell tumor spheroids. , 1983, Advances in experimental medicine and biology.

[39]  J P Freyer,et al.  In situ oxygen consumption rates of cells in V‐79 multicellular spheroids during growth , 1984, Journal of cellular physiology.

[40]  A. Hunding.  Bifurcations of nonlinear reaction-diffusion systems in oblate spheroids , 1983, Journal of mathematical biology.

[41]  Ferguson Gp,et al.  Mechanisms of neovascularization. Vascular sprouting can occur without proliferation of endothelial cells. , 1984 .

[42]  G. Chatelain,et al.  Density‐dependent inhibition of growth: Inhibitorydiffusible factors from 3T3‐ and rous sarcoma virus (RSV)‐transformed 3T3 cells , 1984, Journal of cellular physiology.

[43]  R. Sutherland,et al.  Growth and cellular characteristics of multicell spheroids. , 1984, Recent results in cancer research. Fortschritte der Krebsforschung. Progres dans les recherches sur le cancer.

[44]  M. Brattain,et al.  Identification of a tumor inhibitory factor in rat ascites fluid. , 1984, Biochemical and biophysical research communications.

[45]  D. Balding,et al.  A mathematical model of tumour-induced capillary growth. , 1985, Journal of theoretical biology.

[46]  W. Young,et al.  Extracellular matrix modulation of endothelial cell shape and motility following injury in vitro. , 1985, Journal of cell science.

[47]  P. Gullino,et al.  Cooperation between fibronectin and heparin in the mobilization of capillary endothelium. , 1985, Invasion & metastasis.

[48]  O. Iversen.  What is new in endogenous growth stimulators and inhibitors (chalones). , 1985, Pathology, research and practice.

[49]  V. Terranova,et al.  Human endothelial cells are chemotactic to endothelial cell growth factor and heparin , 1985, The Journal of cell biology.

[50]  J P Freyer,et al.  Proliferative and clonogenic heterogeneity of cells from EMT6/Ro multicellular spheroids induced by the glucose and oxygen supply. , 1986, Cancer research.

[51]  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.

[52]  P. Gullino,et al.  Interaction of gangliosides with fibronectin in the mobilization of capillary endothelium. Possible influence on the growth of metastasis. , 1986, Invasion & metastasis.

[53]  J. Adam.  A simplified mathematical model of tumor growth , 1986 .

[54]  Paul F. McDonagh.  Microvascular perfusion and transport in health and disease , 1987 .

[55]  J. Adam.  A mathematical model of tumor growth. III. comparison with experiment , 1987 .

[56]  J. Adam.  A mathematical model of tumor growth. II. effects of geometry and spatial nonuniformity on stability , 1987 .

[57]  R. Sutherland.  Cell and environment interactions in tumor microregions: the multicell spheroid model. , 1988, Science.

[58]  R. Sutherland,et al.  Mathematical modelling of oxygen supply and oxygenation in tumor tissues: prognostic, therapeutic, and experimental implications. , 1988, International journal of radiation oncology, biology, physics.

[59]  H. Moses,et al.  Transforming growth factors in the regulation of malignant cell growth and invasion. , 1988, Cancer investigation.

[60]  N Paweletz,et al.  Tumor-related angiogenesis. , 1989, Critical reviews in oncology/hematology.

[61]  R K Jain,et al.  Transport of fluid and macromolecules in tumors. I. Role of interstitial pressure and convection. , 1989, Microvascular research.

[62]  A. Balmain,et al.  Chalones revisited--a possible role for transforming growth factor beta in tumour promotion. , 1990, Carcinogenesis.

[63]  M. Chaplain,et al.  A mathematical model for the production and secretion of tumour angiogenesis factor in tumours. , 1990, IMA journal of mathematics applied in medicine and biology.

[64]  Jonathan A. Sherratt,et al.  Models of epidermal wound healing , 1990, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[65]  R. Durand.  Invited review Multicell spheroids as a model for cell kinetic studies , 1990, Cell and tissue kinetics.

[66]  M A Rupnick,et al.  Chemotaxis of human microvessel endothelial cells in response to acidic fibroblast growth factor. , 1990, Laboratory investigation; a journal of technical methods and pathology.

[67]  G. S. H. Lock,et al.  The effects of tilt, skew and roll on natural convection in a slender, laterally-heated cavity , 1990 .

[68]  R K Jain,et al.  Transport of fluid and macromolecules in tumors. II. Role of heterogeneous perfusion and lymphatics. , 1990, Microvascular research.

[69]  J. Leith,et al.  Autocrine and paracrine growth factors in tumor growth: a mathematical model. , 1991, Bulletin of mathematical biology.

[70]  O. Iversen,et al.  The hunt for endogenous growth-inhibitory and/or tumor suppression factors: their role in physiological and pathological growth regulation. , 1991, Advances in cancer research.

[71]  Lowell A. Goldsmith,et al.  Biochemistry and physiology of the skin , 1991 .

[72]  K. Groebe,et al.  Biological response of multicellular emt6 spheroids to exogenous lactate , 1991, International journal of cancer.

[73]  R K Jain,et al.  Transport of fluid and macromolecules in tumors. IV. A microscopic model of the perivascular distribution. , 1991, Microvascular research.

[74]  M. Chaplain,et al.  A mathematical model for the diffusion of tumour angiogenesis factor into the surrounding host tissue. , 1991, IMA journal of mathematics applied in medicine and biology.

[75]  D A Lauffenburger,et al.  Analysis of the roles of microvessel endothelial cell random motility and chemotaxis in angiogenesis. , 1991, Journal of theoretical biology.

[76]  S. Paku,et al.  First steps of tumor-related angiogenesis. , 1991, Laboratory investigation; a journal of technical methods and pathology.

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

[78]  C. Gerharz,et al.  Rhabdomyosarcoma spheroids with central proliferation and differentiation. , 1992, Cancer research.

[79]  S. Walenta,et al.  Proliferation‐associated oxygen consumption and morphology of tumor cells in monolayer and spheroid culture , 1992, Journal of cellular physiology.

[80]  G W Swan.  The diffusion of an inhibitor in a spherical tumor. , 1992, Mathematical biosciences.

[81]  N F Britton,et al.  On the concentration profile of a growth inhibitory factor in multicell spheroids. , 1993, Mathematical biosciences.

[82]  M. Chaplain,et al.  Modelling the growth of solid tumours and incorporating a method for their classification using nonlinear elasticity theory , 1993, Journal of mathematical biology.

[83]  N F Britton,et al.  A qualitative analysis of some models of tissue growth. , 1993, Mathematical biosciences.

[84]  Sophia Maggelakis,et al.  Mathematical model of prevascular growth of a spherical carcinoma-part II , 1993 .

[85]  M. Apuzzo,et al.  Differential effects of tumor necrosis factor-alpha on proliferation, cell surface antigen expression, and cytokine interactions in malignant gliomas. , 1993, Neurosurgery.

[86]  M. Chaplain,et al.  A model mechanism for the chemotactic response of endothelial cells to tumour angiogenesis factor. , 1993, IMA journal of mathematics applied in medicine and biology.

[87]  Mark A. J. Chaplain,et al.  The Development of a Spatial Pattern in a Model for Cancer Growth , 1993 .

[88]  Philip K. Maini,et al.  Experimental and Theoretical Advances in Biological Pattern Formation , 1993, NATO ASI Series.

[89]  Robert C. Bast,et al.  Tumor Necrosis Factor α as an Autocrine and Paracrine Growth Factor for Ovarian Cancer: Monokine Induction of Tumor Cell Proliferation and Tumor Necrosis Factor α Expression , 1993 .

[90]  P K Maini,et al.  Nonlinear diffusion of a growth inhibitory factor in multicell spheroids. , 1994, Mathematical biosciences.

[91]  R K Jain,et al.  Barriers to drug delivery in solid tumors. , 1994, Scientific American.

[92]  Robert Dillon,et al.  Pattern formation in generalized Turing systems , 1994 .

[93]  Hiroshi Yamamoto,et al.  Tumor Necrosis Factor-α (TNF-α) Stimulates Proliferation of Mouse Primordial Germ Cells in Culture , 1994 .

[94]  A. Giaccia,et al.  Tumour hypoxia: the picture has changed in the 1990s. , 1994, International journal of radiation biology.

[95]  T. Jacks,et al.  The cell cycle and cancer. , 1997, Proceedings of the National Academy of Sciences of the United States of America.