A history of the study of solid tumour growth: The contribution of mathematical modelling

[1]  Y. C. Fung,et al.  What are the residual stresses doing in our blood vessels? , 2006, Annals of Biomedical Engineering.

[2]  Miljenko Marušić,et al.  Mathematical models of tumor growth , 2006 .

[3]  S. Orrenius,et al.  Apoptosis: a basic biological phenomenon with wide‐ranging implications in human disease , 2005, Journal of internal medicine.

[4]  D. L. Sean McElwain,et al.  The nature of the stresses induced during tissue growth , 2005, Appl. Math. Lett..

[5]  L. C. Barr,et al.  The encapsulation of tumours , 1989, Clinical & Experimental Metastasis.

[6]  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..

[7]  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..

[8]  D L S McElwain,et al.  New insights into vascular collapse and growth dynamics in solid tumors. , 2004, Journal of theoretical biology.

[9]  D. McElwain,et al.  A linear-elastic model of anisotropic tumour growth , 2004, European Journal of Applied Mathematics.

[10]  Ben D MacArthur,et al.  Residual stress generation and necrosis formation in multi-cell tumour spheroids , 2004, Journal of mathematical biology.

[11]  J. Olson,et al.  Bathsheba’s Breast: Women, Cancer and History , 2004, Nursing History Review.

[12]  L. Weiss The Morphologic Documentation of Clinical Progression, Invasion Metastasis - Staging , 2000, Cancer and Metastasis Reviews.

[13]  J. Sherratt,et al.  Alterations in proteolytic activity at low pH and its association with invasion: A theoretical model , 1999, Clinical & Experimental Metastasis.

[14]  Christine E. Canman,et al.  P53, cell cycle control and apoptosis: Implications for cancer , 1995, Cancer and Metastasis Reviews.

[15]  Rakesh K. Jain,et al.  Transport of molecules across tumor vasculature , 2004, Cancer and Metastasis Reviews.

[16]  E. T. Gawlinski,et al.  The glycolytic phenotype in carcinogenesis and tumor invasion: insights through mathematical models. , 2003, Cancer research.

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

[18]  H. M. Byrne,et al.  Modelling the early growth of ductal carcinoma in situ of the breast , 2003, Journal of mathematical biology.

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

[20]  V. Cristini,et al.  Nonlinear simulation of tumor growth , 2003, Journal of mathematical biology.

[21]  J. King,et al.  Mathematical modelling of drug transport in tumour multicell spheroids and monolayer cultures. , 2003, Mathematical biosciences.

[22]  P. Maini,et al.  Mathematical oncology: Cancer summed up , 2003, Nature.

[23]  L. Preziosi,et al.  Modelling Solid Tumor Growth Using the Theory of Mixtures , 2001, Mathematical medicine and biology : a journal of the IMA.

[24]  Numerical simulation of the growth of a multicellular spheroid , 2003 .

[25]  Robyn P. Araujo,et al.  An anisotropic model of vascular tumour growth: implications for vascular collapse , 2003 .

[26]  Sean McElwain,et al.  The Genesis of Residual Stresses and Vascular Collapse in Solid Tumours , 2003 .

[27]  D. Blakey,et al.  ZD6126: a novel vascular-targeting agent that causes selective destruction of tumor vasculature. , 2002, Cancer research.

[28]  Lawrence M Wein,et al.  A mathematical model of the impact of infused targeted cytotoxic agents on brain tumours: implications for detection, design and delivery , 2002, Cell proliferation.

[29]  Vlado A. Lubarda,et al.  On the mechanics of solids with a growing mass , 2002 .

[30]  H. Byrne,et al.  The role of cell-cell interactions in a two-phase model for avascular tumour growth , 2002, Journal of mathematical biology.

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

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

[33]  C. Lewis,et al.  Fibrinogen E fragment selectively disrupts the vasculature and inhibits the growth of tumours in a syngeneic murine model , 2002, British Journal of Cancer.

[34]  C. Please,et al.  Multiphase flow in a roll press nip , 2002, European Journal of Applied Mathematics.

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

[36]  Shangbin Cui,et al.  Analysis of a mathematical model for the growth of tumors under the action of external inhibitors , 2002, Journal of mathematical biology.

[37]  Antonio Fasano,et al.  Cell kinetics in tumour cords studied by a model with variable cell cycle length. , 2002, Mathematical biosciences.

[38]  L. Preziosi,et al.  On Darcy's law for growing porous media , 2002 .

[39]  T. Jackson,et al.  Multiphase mechanics of capsule formation in tumors. , 2002, Journal of biomechanical engineering.

[40]  Trachette L. Jackson,et al.  Vascular tumor growth and treatment: Consequences of polyclonality, competition and dynamic vascular support , 2002, Journal of mathematical biology.

[41]  E. Ruoslahti Specialization of tumour vasculature , 2002, Nature Reviews Cancer.

[42]  Paola Pisani,et al.  Estimates of the world‐wide prevalence of cancer for 25 sites in the adult population , 2002, International journal of cancer.

[43]  J. Sherratt,et al.  Travelling wave solutions to a haptotaxis-dominated model of malignant invasion , 2001 .

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

[45]  H M Byrne,et al.  The influence of growth-induced stress from the surrounding medium on the development of multicell spheroids , 2001, Journal of mathematical biology.

[46]  C. Please,et al.  Tumour dynamics and necrosis: surface tension and stability. , 2001, IMA journal of mathematics applied in medicine and biology.

[47]  D J Mooney,et al.  Up-Regulation of Bcl-2 in microvascular endothelial cells enhances intratumoral angiogenesis and accelerates tumor growth. , 2001, Cancer research.

[48]  G. J. Pettet,et al.  The migration of cells in multicell tumor spheroids , 2001, Bulletin of mathematical biology.

[49]  D. Chadwick,et al.  The Tumour Microenvironment: Causes and Consequences of Hypoxia and Acidity , 2001 .

[50]  Helen M. Byrne,et al.  USING MATHEMATICS TO STUDY SOLID TUMOUR GROWTH , 2001 .

[51]  E. T. Gawlinski,et al.  Mathematical models of tumour invasion mediated by transformation-induced alteration of microenvironmental pH. , 2001, Novartis Foundation symposium.

[52]  W. Mueller‐Klieser Tumor biology and experimental therapeutics. , 2000, Critical reviews in oncology/hematology.

[53]  Jonathan A. Sherratt,et al.  Wavefront propagation in a competition equation with a new motility term modelling contact inhibition between cell populations , 2000, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[54]  R. Jain,et al.  Absence of functional lymphatics within a murine sarcoma: a molecular and functional evaluation. , 2000, Cancer research.

[55]  R. Jain,et al.  Oncotic pressure in solid tumors is elevated. , 2000, Cancer research.

[56]  Renato Perucchio,et al.  Modeling Heart Development , 2000 .

[57]  A. Bertuzzi,et al.  Cell kinetics in a tumour cord. , 2000, Journal of theoretical biology.

[58]  A. Hoger,et al.  Constitutive Functions of Elastic Materials in Finite Growth and Deformation , 2000 .

[59]  H M Byrne,et al.  A mathematical model of the stress induced during avascular tumour growth , 2000, Journal of mathematical biology.

[60]  L. Preziosi,et al.  ADVECTION-DIFFUSION MODELS FOR SOLID TUMOUR EVOLUTION IN VIVO AND RELATED FREE BOUNDARY PROBLEM , 2000 .

[61]  R K Jain,et al.  Openings between defective endothelial cells explain tumor vessel leakiness. , 2000, The American journal of pathology.

[62]  A. Friedman,et al.  Analysis of a mathematical model of the effect of inhibitors on the growth of tumors. , 2000, Mathematical biosciences.

[63]  H M Byrne,et al.  A mathematical model to study the effects of drug resistance and vasculature on the response of solid tumors to chemotherapy. , 2000, Mathematical biosciences.

[64]  A. J. Perumpanani,et al.  Traveling Shock Waves Arising in a Model of Malignant Invasion , 1999, SIAM J. Appl. Math..

[65]  J Norbury,et al.  Lotka-Volterra equations with chemotaxis: walls, barriers and travelling waves. , 2000, IMA journal of mathematics applied in medicine and biology.

[66]  J. King,et al.  Modelling The Effect of Cell Shedding on Avascular Tumour Growth , 2000 .

[67]  A. Perumpanani,et al.  Numerical interactions of random and directed motility during cancer invasion , 1999 .

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

[69]  H. Byrne,et al.  Extracellular matrix concentration exerts selection pressure on invasive cells. , 1999, European journal of cancer.

[70]  R K Jain,et al.  Taxane-induced apoptosis decompresses blood vessels and lowers interstitial fluid pressure in solid tumors: clinical implications. , 1999, Cancer research.

[71]  Helen M. Byrne,et al.  A weakly nonlinear analysis of a model of avascular solid tumour growth , 1999, Journal of mathematical biology.

[72]  H. Byrne,et al.  Modelling the internalization of labelled cells in tumour spheroids , 1999, Bulletin of mathematical biology.

[73]  Graeme J. Pettet,et al.  AVASCULAR TUMOUR DYNAMICS AND NECROSIS , 1999 .

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

[75]  J. Sherratt,et al.  A two parameter family of travelling waves with a singular barrier arising from the modelling of extracellular matrix mediated cellular invasion , 1999 .

[76]  J. Sherratt,et al.  Mathematical modelling of tumour acidity: regulation of intracellular pH. , 1999, Journal of theoretical biology.

[77]  John R. King,et al.  Mathematical Modelling of the Effects of Mitotic Inhibitors on Avascular Tumour Growth , 1999 .

[78]  J. Millán,et al.  Epidemiology of Usher Syndrome in Valencia and Spain , 1999, Public Health Genomics.

[79]  Arun R. Srinivasa,et al.  Mechanics of the inelastic behavior of materials—part 1, theoretical underpinnings , 1998 .

[80]  D. Drew,et al.  Theory of Multicomponent Fluids , 1998 .

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

[82]  D P Pioletti,et al.  Viscoelastic constitutive law in large deformations: application to human knee ligaments and tendons. , 1998, Journal of biomechanics.

[83]  Graeme J. Pettet,et al.  A new approach to modelling the formation of necrotic regions in tumours , 1998 .

[84]  B. Sleeman,et al.  Fluid transport in vascularized tumours and metastasis. , 1998, IMA journal of mathematics applied in medicine and biology.

[85]  R. Knuechel,et al.  Multicellular spheroids: a three‐dimensional in vitro culture system to study tumour biology , 1998, International journal of experimental pathology.

[86]  Robert A. Gatenby,et al.  Mathematical models of tumor-host interactions , 1998 .

[87]  H. M. Byrne,et al.  Necrosis and Apoptosis: Distinct Cell Loss Mechanisms in a Mathematical Model of Avascular Tumour Growth , 1998 .

[88]  R. Porter,et al.  The Greatest Benefit to Mankind: A Medical History of Humanity from Antiquity to the Present , 1997 .

[89]  M. Chaplain,et al.  Free boundary value problems associated with the growth and development of multicellular spheroids , 1997, European Journal of Applied Mathematics.

[90]  H M Byrne,et al.  The importance of intercellular adhesion in the development of carcinomas. , 1997, IMA journal of mathematics applied in medicine and biology.

[91]  Andrew C. Fowler,et al.  Mathematical Models in the Applied Sciences , 1997 .

[92]  H M Byrne,et al.  The effect of time delays on the dynamics of avascular tumor growth. , 1997, Mathematical biosciences.

[93]  Helen M. Byrne,et al.  The role of growth factors in avascular tumour growth , 1997 .

[94]  Paolo A. Netti,et al.  Solid stress inhibits the growth of multicellular tumor spheroids , 1997, Nature Biotechnology.

[95]  Jd Jan Janssen,et al.  Quadriphasic mechanics of swelling incompressible porous media , 1997 .

[96]  R. Skalak,et al.  Macro- and Microscopic Fluid Transport in Living Tissues: Application to Solid Tumors , 1997 .

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

[98]  M. Chaplain,et al.  Modelling the role of cell-cell adhesion in the growth and development of carcinomas , 1996 .

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

[100]  Nicola Bellomo,et al.  A Survey of Models for Tumor-Immune System Dynamics , 1996 .

[101]  R. Mansel,et al.  Progress in anti-invasion and anti-metastasis research and treatment. , 1996, International Journal of Oncology.

[102]  R K Jain,et al.  Tumor angiogenesis and interstitial hypertension. , 1996, Cancer research.

[103]  E. Ruoslahti How cancer spreads. , 1996, Scientific American.

[104]  A. Ruifrok,et al.  Accelerated repopulation during fractionated irradiation of a murine ovarian carcinoma: downregulation of apoptosis as a possible mechanism. , 1996, International journal of radiation oncology, biology, physics.

[105]  L A Taber,et al.  Theoretical study of stress-modulated growth in the aorta. , 1996, Journal of theoretical biology.

[106]  Mark A. J. Chaplain,et al.  A mathematical model of vascular tumour growth and invasion , 1996 .

[107]  S C Cowin,et al.  Strain or deformation rate dependent finite growth in soft tissues. , 1996, Journal of biomechanics.

[108]  R. Gatenby,et al.  Application of competition theory to tumour growth: implications for tumour biology and treatment. , 1996, European journal of cancer.

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

[110]  Altered glucose metabolism and the invasive tumor phenotype. , 1996, International journal of oncology.

[111]  R. Jain,et al.  Effect of radiation on interstitial fluid pressure and oxygenation in a human tumor xenograft. , 1996, Cancer research.

[112]  R. Jain,et al.  Pharmacokinetic analysis of the microscopic distribution of enzyme-conjugated antibodies and prodrugs: comparison with experimental data. , 1996, British Journal of Cancer.

[113]  H M Byrne,et al.  Growth of necrotic tumors in the presence and absence of inhibitors. , 1996, Mathematical biosciences.

[114]  B. Adelmann-Grill,et al.  Differentiation stage and cell cycle position determine the chemotactic response of fibroblasts. , 1996, Folia histochemica et cytobiologica.

[115]  J. Sherratt,et al.  Biological inferences from a mathematical model for malignant invasion. , 1996, Invasion & metastasis.

[116]  R K Jain,et al.  Compatibility and the genesis of residual stress by volumetric growth , 1996, Journal of mathematical biology.

[117]  R. Hoffman,et al.  Liver colonization competence governs colon cancer metastasis. , 1995, Proceedings of the National Academy of Sciences of the United States of America.

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

[119]  R. Skalak,et al.  Time-dependent behavior of interstitial fluid pressure in solid tumors: implications for drug delivery. , 1995, Cancer research.

[120]  R. Gatenby,et al.  Models of tumor-host interaction as competing populations: implications for tumor biology and treatment. , 1995, Journal of theoretical biology.

[121]  Kumbakonam R. Rajagopal,et al.  Mechanics of Mixtures , 1995 .

[122]  John A. Adam,et al.  A simple mathematical model and alternative paradigm for certain chemotherapeutic regimens , 1995 .

[123]  J. Hendry,et al.  Apoptosis, intrinsic radiosensitivity and prediction of radiotherapy response in cervical carcinoma. , 1995, Radiotherapy and oncology : journal of the European Society for Therapeutic Radiology and Oncology.

[124]  R. Gatenby,et al.  The potential role of transformation-induced metabolic changes in tumor-host interaction. , 1995, Cancer research.

[125]  L. Taber Biomechanics of Growth, Remodeling, and Morphogenesis , 1995 .

[126]  John A. Adam,et al.  A mathematical model of cycle-specific chemotherapy , 1995 .

[127]  G. Storme,et al.  Patterns of Axillary Lymph Node Metastasis in Breast Cancer , 1995, American journal of clinical oncology.

[128]  Z. Darżynkiewicz Apoptosis in anititumor strategies: Modulation of cell cycle or differentiation , 1995, Journal of cellular biochemistry.

[129]  M. Miyasaka Cancer metastasis and adhesion molecules. , 1995, Clinical orthopaedics and related research.

[130]  J. Murray,et al.  A mathematical model of glioma growth: the effect of chemotherapy on spatio‐temporal growth , 1995, Cell proliferation.

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

[132]  C. Potten,et al.  Apoptosis and cancer chemotherapy. , 1994, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

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

[134]  A. McCulloch,et al.  Stress-dependent finite growth in soft elastic tissues. , 1994, Journal of biomechanics.

[135]  R. Nagle,et al.  Adhesion molecules, extracellular matrix, and proteases in prostate carcinoma. , 1994, Journal of cellular biochemistry. Supplement.

[136]  Jonathan A. Sherratt,et al.  Cellular Growth Control and Travelling Waves of Cancer , 1993, SIAM J. Appl. Math..

[137]  W M Lai,et al.  Constitutive modeling of articular cartilage and biomacromolecular solutions. , 1993, Journal of biomechanical engineering.

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

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

[140]  G J Pettet,et al.  Cell migration in multicell spheroids: swimming against the tide. , 1993, Bulletin of mathematical biology.

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

[142]  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.

[143]  J. Adam,et al.  Equilibrium model of a vascularized spherical carcinoma with central necrosis — Some properties of the solution , 1993, Journal of mathematical biology.

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

[145]  L. Liotta,et al.  Tumor cell interactions with the extracellular matrix during invasion and metastasis. , 1993, Annual review of cell biology.

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

[147]  R. Jain,et al.  Angiogenesis, microvascular architecture, microhemodynamics, and interstitial fluid pressure during early growth of human adenocarcinoma LS174T in SCID mice. , 1992, Cancer research.

[148]  R K Jain,et al.  Microvascular pressure is the principal driving force for interstitial hypertension in solid tumors: implications for vascular collapse. , 1992, Cancer research.

[149]  M. Raff,et al.  Social controls on cell survival and cell death , 1992, Nature.

[150]  K Messmer,et al.  Interstitial hypertension in head and neck tumors in patients: correlation with tumor size. , 1992, Cancer research.

[151]  M. Hendrix,et al.  Role of the alpha v beta 3 integrin in human melanoma cell invasion. , 1992, Proceedings of the National Academy of Sciences of the United States of America.

[152]  JD Jan Janssen,et al.  A mixture approach to the mechanics of the human intervertebral disc , 1992 .

[153]  T. Karalis Mechanics of Swelling , 1992, NATO ASI Series.

[154]  R K Jain,et al.  Interstitial hypertension in superficial metastatic melanomas in humans. , 1991, Cancer research.

[155]  W M Lai,et al.  A triphasic theory for the swelling and deformation behaviors of articular cartilage. , 1991, Journal of biomechanical engineering.

[156]  D. Hirst,et al.  Changes in tumour morphology with alterations in oxygen availability: further evidence for oxygen as a limiting substrate. , 1991, British Journal of Cancer.

[157]  R. Gatenby,et al.  Population ecology issues in tumor growth. , 1991, Cancer research.

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

[159]  C. McCulloch,et al.  Quantification of chemotactic response of quiescent and proliferating fibroblasts in Boyden chambers by computer-assisted image analysis. , 1991, The journal of histochemistry and cytochemistry : official journal of the Histochemistry Society.

[160]  R K Jain,et al.  Transport of fluid and macromolecules in tumors. III. Role of binding and metabolism. , 1991 .

[161]  R. Clarke,et al.  The process of malignant progression in human breast cancer. , 1990, Annals of oncology : official journal of the European Society for Medical Oncology.

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

[163]  G. Mazzini,et al.  Cell cycle-related proteins and flow cytometry. , 1990, Haematologica.

[164]  L. Liotta,et al.  Signal transduction for chemotaxis and haptotaxis by matrix molecules in tumor cells , 1990, The Journal of cell biology.

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

[166]  V. C. Mow,et al.  Biphasic and Quasilinear Viscoelastic Theories for Hydrated Soft Tissues , 1990 .

[167]  J A Adam,et al.  Diffusion regulated growth characteristics of a spherical prevascular carcinoma. , 1990, Bulletin of mathematical biology.

[168]  Savio Lau-Yuen Woo,et al.  Biomechanics of diarthrodial joints , 1990 .

[169]  J. Adam,et al.  Mathematical models of tumor growth. IV. Effects of a necrotic core. , 1989, Mathematical biosciences.

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

[171]  J. Adam A mathematical model of tumor growth by diffusion , 1988 .

[172]  R K Jain,et al.  Mechanisms of heterogeneous distribution of monoclonal antibodies and other macromolecules in tumors: significance of elevated interstitial pressure. , 1988, Cancer research.

[173]  J. Volpe Genetic instability of cancer. Why a metastatic tumor is unstable and a benign tumor is stable. , 1988, Cancer genetics and cytogenetics.

[174]  R. Carter,et al.  ENCAPSULATION OF TUMOURS AS A MODIFIED WOUND HEALING RESPONSE , 1988, The Lancet.

[175]  Partial purification of a protein growth inhibitor from multicellular spheroids. , 1988, Biochemical and biophysical research communications.

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

[177]  Athanasios I. Liapis,et al.  Oxygen tension profiles in tumors predicted by a diffusion with absorption model involving a moving free boundary , 1988 .

[178]  R. Gatenby,et al.  AN ANALYSIS OF SYSTEMIC TUMOR OXYGENATION USING MULTI-REGION MODELS , 1988 .

[179]  P. Pelcé Dynamics of curved fronts , 1988 .

[180]  A. Kolmogoroff,et al.  Study of the Diffusion Equation with Growth of the Quantity of Matter and its Application to a Biology Problem , 1988 .

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

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

[183]  W. King,et al.  On the analysis of oxygen diffusion and reaction in biological systems , 1987 .

[184]  van Dh Dick Campen,et al.  A mixture approach to the mechanics of skin. , 1987, Journal of biomechanics.

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

[186]  R F Kallman,et al.  Effect of cytochalasin B, nocodazole and irradiation on migration and internalization of cells and microspheres in tumor cell spheroids. , 1986, Experimental cell research.

[187]  R. Gatenby,et al.  Multi-region models for describing oxygen tension profiles in human tumors , 1986 .

[188]  M. Sato [Mechanical properties of living tissues]. , 1986, Iyo denshi to seitai kogaku. Japanese journal of medical electronics and biological engineering.

[189]  L. Gerschenson,et al.  Evidence for soluble factors regulating cell death and cell proliferation in primary cultures of rabbit endometrial cells grown on collagen. , 1986, Proceedings of the National Academy of Sciences of the United States of America.

[190]  G. Todaro,et al.  Isolation of tumor cell growth-inhibiting factors from a human rhabdomyosarcoma cell line. , 1985, Cancer research.

[191]  J. Moore,et al.  Tumour cords in 52 human bronchial and cervical squamous cell carcinomas: inferences for their cellular kinetics and radiobiology. , 1985, British Journal of Cancer.

[192]  W. Au,et al.  Normal sister chromatid exchange frequencies during growth of a transplantable murine myeloid leukemia. , 1985, Cancer genetics and cytogenetics.

[193]  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.

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

[195]  S. L. Passman,et al.  A Theory of Multiphase Mixtures , 1984 .

[196]  W. Looney,et al.  Tumour-cord parameters in two rat hepatomas that differ in their radiobiological oxygenation status , 1984, Radiation and environmental biophysics.

[197]  S. Levin Lectu re Notes in Biomathematics , 1983 .

[198]  W. Looney,et al.  Response of cell populations in tumor cords to a single dose of cyclophosphamide or radiation. , 1983, European journal of cancer & clinical oncology.

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

[200]  R F Kallman,et al.  Migration and internalization of cells and polystyrene microsphere in tumor cell spheroids. , 1982, Experimental cell research.

[201]  D. Hirst,et al.  Proliferation kinetics of endothelial and tumour cells in three mouse mammary carcinomas , 1982, Cell and tissue kinetics.

[202]  E Otten,et al.  Analytical description of growth. , 1982, Journal of theoretical biology.

[203]  R. Sutherland,et al.  A move for the better. , 1994, Environmental health perspectives.

[204]  A. Liapis,et al.  A model of oxygen diffusion in absorbing tissue , 1982 .

[205]  Vinay G. Vaidya,et al.  Evaluation of some mathematical models for tumor growth. , 1982, International journal of bio-medical computing.

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

[207]  Y. Fung,et al.  Biomechanics: Mechanical Properties of Living Tissues , 1981 .

[208]  J P Freyer,et al.  Shedding of mitotic cells from the surface of multicell spheroids during growth , 1981, Journal of cellular physiology.

[209]  Richard Skalak,et al.  Growth as A Finite Displacement Field , 1981 .

[210]  R. M. Bowen,et al.  Incompressible porous media models by use of the theory of mixtures , 1980 .

[211]  D L McElwain,et al.  A model of vascular compression in solid tumours. , 1979, Journal of theoretical biology.

[212]  D. Hirst,et al.  TUMOUR CELL PROLIFERATION IN RELATION TO THE VASCULATURE , 1979, Cell and tissue kinetics.

[213]  J. Yuhas,et al.  Multicellular tumor spheroid formation by breast cancer cells isolated from different sites. , 1978, Cancer research.

[214]  J. Yuhas,et al.  Growth fraction as the major determinant of multicellular tumor spheroid growth rates. , 1978, Cancer research.

[215]  D. McElwain,et al.  Apoptosis as a volume loss mechanism in mathematical models of solid tumor growth , 1978 .

[216]  J. Carlsson,et al.  Proliferation and viability in cellular spheroids of human origin. , 1978, Cancer research.

[217]  D L McElwain,et al.  A re-examination of oxygen diffusion in a spherical cell with Michaelis-Menten oxygen uptake kinetics. , 1978, Journal of theoretical biology.

[218]  Method for quantitating tumor cell removal and tumor cell-invasive capacity in experimental metastases. , 1977, Cancer research.

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

[220]  Morton E. Gurtin,et al.  On the diffusion of biological populations , 1977 .

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

[222]  S. Garattini,et al.  Cancer invasion and metastasis : biologic mechanisms and therapy , 1977 .

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

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

[225]  G M Saidel,et al.  Stochastic model of metastases formation. , 1976, Biometrics.

[226]  S. H. Lin,et al.  Oxygen diffusion in a spherical cell with nonlinear oxygen uptake kinetics. , 1976, Journal of theoretical biology.

[227]  Donald A. Drew,et al.  Two-phase flows: Constitutive equations for lift and Brownian motion and some basic flows , 1976 .

[228]  L. Liotta,et al.  The significance of hematogenous tumor cell clumps in the metastatic process. , 1976, Cancer research.

[229]  G M Saidel,et al.  System dynamics of metastatic process from an implanted tumor. , 1976, Journal of theoretical biology.

[230]  R. M. Bowen Part I – Theory of Mixtures , 1976 .

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

[232]  Deakin As,et al.  Model for the growth of a solid in vitro tumor. , 1975 .

[233]  A S Deakin,et al.  Model for the growth of a solid in vitro tumor. , 1975, Growth.

[234]  I. N. Katz,et al.  Stochastic processes for solid tumor kinetics II. Diffusion-regulated growth , 1974 .

[235]  J. Folkman,et al.  Proceedings: Tumor angiogenesis factor. , 1974, Cancer research.

[236]  L. Liotta,et al.  Quantitative relationships of intravascular tumor cells, tumor vessels, and pulmonary metastases following tumor implantation. , 1974, Cancer research.

[237]  I. N. Katz,et al.  Stochastic processes for solid tumor kinetics I. surface-regulated growth☆ , 1974 .

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

[239]  S. Robbins,et al.  Pathologic basis of disease , 1974 .

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

[241]  I. Tannock,et al.  The response of viable tumor cords to a single dose of radiation. , 1973, Radiation research.

[242]  M. Gurtin,et al.  Letter: A system of equations for age-dependent population diffusion. , 1973, Journal of theoretical biology.

[243]  L. Glass Instability and Mitotic Patterns in Tissue Growth , 1973 .

[244]  G. Casarett,et al.  Development of the vascular system in the hamster malignant neurilemmoma. , 1973, Microvascular research.

[245]  R. Sutherland,et al.  Hypoxic cells in an in vitro tumour model. , 1973, International journal of radiation biology and related studies in physics, chemistry, and medicine.

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

[247]  A. Wyllie,et al.  Apoptosis: A Basic Biological Phenomenon with Wide-ranging Implications in Tissue Kinetics , 1972, British Journal of Cancer.

[248]  Lee A. Segel,et al.  Averaged Equations for Two-Phase Flows , 1971 .

[249]  J F Kerr,et al.  Shrinkage necrosis: A distinct mode of cellular death , 1971, The Journal of pathology.

[250]  Donald A. Drew,et al.  Averaged Field Equations for Two‐Phase Media , 1971 .

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

[252]  W. Bullough,et al.  The pattern of tumour growth. , 1971, Symposia of the Society for Experimental Biology.

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

[254]  R. M. Bowen,et al.  Diffusion in Mixtures of Elastic Materials. , 1969 .

[255]  J. Folkman,et al.  Preservation of Vascular Integrity in Organs perfused in vitro with a Platelet-rich Medium , 1969, Nature.

[256]  D. Lal,et al.  Chemical Composition of Nuclei of Z > 22 in Cosmic Rays using Meteoritic Minerals as Detectors , 1969, Nature.

[257]  I. Tannock The relation between cell proliferation and the vascular system in a transplanted mouse mammary tumour. , 1968, British journal of cancer.

[258]  M Takahashi,et al.  Theoretical basis for cell cycle analysis: II. Further studies on labelled mitosis wave method. , 1968, Journal of theoretical biology.

[259]  J. Meixner,et al.  S. Flügge, Herausgeber: Handbuch der Physik, Band III/3: Die nicht‐linearen Feldtheorien der Mechanik. Von C. Truesdell und W. Noll. Springer‐Verlag, Berlin/Heidelberg/New York 1965. VIII/602 Seiten. Preis: 198,‐ DM , 1967, Berichte der Bunsengesellschaft für physikalische Chemie.

[260]  J. Griffiths,et al.  Circulating cancer cells , 1965 .

[261]  Manabu Takahashi,et al.  Theoretical basis for cell cycle analysis I. Labelled mitosis wave method , 1966 .

[262]  J. Folkman,et al.  Tumor Behavior in Isolated Perfused Organs: In Vitro Growth and Metastases of Biopsy Material in Rabbit Thyroid and Canine Intestinal Segment , 1966, Annals of surgery.

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

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

[265]  C. Truesdell,et al.  The Non-Linear Field Theories Of Mechanics , 1992 .

[266]  W. Bullough Mitotic and functional homeostasis: a speculative review. , 1965, Cancer research.

[267]  Tyler Sa,et al.  Dynamics of normal growth. , 1965 .

[268]  A. K. Laird,et al.  Dynamics of relative growth. , 1965, Growth.

[269]  A. D. Barton,et al.  Dynamics of normal growth. , 1965, Growth.

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

[271]  A. K. Laird Dynamics of Tumour Growth , 1964, British Journal of Cancer.

[272]  A. Koike Mechanism of blood‐borne metastases. I. Some factors affecting lodgment and growth of tumor cells in the lungs , 1964, Cancer.

[273]  A. Otis,et al.  BLOOD FLOW, BLOOD OXYGEN TENSION, OXYGEN UPTAKE, AND OXYGEN TRANSPORT IN SKELETAL MUSCLE. , 1964, The American journal of physiology.

[274]  B. Sylvén,et al.  On the Access of Blood-Borne Dyes to Various Tumour Regions , 1962, British Journal of Cancer.

[275]  G. Froese,et al.  The respiration of ascites tumour cells at low oxygen concentrations. , 1962, Biochimica et biophysica acta.

[276]  E. M. Renkin,et al.  Autoregulation of blood flow in resting skeletal muscle , 1961 .

[277]  W. Nowinski Fundamental Aspects of Normal and Malignant Growth , 1961 .

[278]  O. Bodansky Fundamental Aspects of Normal and Malignant Growth , 1960 .

[279]  C. Truesdell,et al.  The Classical Field Theories , 1960 .

[280]  B. Chance Cellular oxygen requirements. , 1957, Federation proceedings.

[281]  M. De Handbuch der Physik , 1957 .

[282]  E E OSGOOD,et al.  A unifying concept of the etiology of the leukemias, lymphomas, and cancers. , 1957, Journal of the National Cancer Institute.

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

[284]  L. H. Gray,et al.  The concentration of oxygen dissolved in tissues at the time of irradiation as a factor in radiotherapy. , 1953, The British journal of radiology.

[285]  W. Cramer [Prevention of cancer]. , 1934, Prakticky lekar.

[286]  David G. Kendall,et al.  ON THE ROLE OF VARIABLE GENERATION TIME IN THE DEVELOPMENT OF A STOCHASTIC BIRTH PROCESS , 1948 .

[287]  L. Walford,et al.  Bioenergetics and Growth , 1947 .

[288]  H. Greene HETEROLOGOUS TRANSPLANTATION OF MAMMALIAN TUMORS I. THE TRANSFER OF RABBIT TUMORS TO ALIEN SPECIES , 1941 .

[289]  H. Greene HETEROLOGOUS TRANSPLANTATION OF MAMMALIAN TUMORS , 1941, The Journal of experimental medicine.

[290]  A. Haddow The biological characters of spontaneous tumours of the mouse, with special reference to rate of growth , 1938 .

[291]  R. Fisher THE WAVE OF ADVANCE OF ADVANTAGEOUS GENES , 1937 .

[292]  J. C. Mottram,et al.  A Factor of Importance in the Radio Sensitivity of Tumours , 1936 .

[293]  W. V. Mayneord On a Law of Growth of Jensen's Rat Sarcoma , 1932 .

[294]  J. Huxley Problems of relative growth , 1932 .

[295]  C. Winsor,et al.  The Gompertz Curve as a Growth Curve. , 1932, Proceedings of the National Academy of Sciences of the United States of America.

[296]  Otto Warburn,et al.  THE METABOLISM OF TUMORS , 1931 .

[297]  Archibald Vivian Hill,et al.  The Diffusion of Oxygen and Lactic Acid through Tissues , 1928 .

[298]  T. Brailsford Robertson,et al.  The chemical basis of growth and senscence , 1923 .

[299]  R. Lomer Zur Frage der Heilbarkeit des Carcinoms , 1903 .

[300]  J. Cruveilhier Anatomie pathologique du corps humain , 2022 .

[301]  Benjamin Gompertz,et al.  XXIV. On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies. In a letter to Francis Baily, Esq. F. R. S. &c , 1825, Philosophical Transactions of the Royal Society of London.

[302]  Benjamin Gompertz,et al.  On the Nature of the Function Expressive of the Law of Human Mortality , 1815 .

[303]  R. A. ANDERSONa,et al.  Mathematical Modelling of Tumour Invasion and Metastasis , 2022 .