Tumor Immune System Interactions: The Kinetic Cellular Theory

The growth of a tumor and its relationships with the host environment are complex events that kinetically mutate during tumor progression. Several aspects of these interactions and their dynamical evolution can be modeled through equations that take into account a few key variables related to microscopic interacting populations: tumor, host, immune cells, cytokine signals.

[1]  J. Adam.  Effects of vascularization on lymphocyte/tumor cell dynamics: Qualitative features , 1996 .

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

[3]  I. Stewart.  On the coagulation-fragmentation equation , 1990 .

[4]  G. Webb,et al.  A nonlinear structured population model of tumor growth with quiescence , 1990, Journal of mathematical biology.

[5]  W. Linehan,et al.  Experience with the Use of High‐Dose Interleukin‐2 in the Treatment of 652 Cancer Patients , 1989, Annals of surgery.

[6]  P Hogeweg,et al.  Interactions between macrophages and T-lymphocytes: tumor sneaking through intrinsic to helper T cell dynamics. , 1986, Journal of theoretical biology.

[7]  G. Forni,et al.  Role of neutrophils and CD4+ T lymphocytes in the primary and memory response to nonimmunogenic murine mammary adenocarcinoma made immunogenic by IL-2 gene. , 1992, Journal of immunology.

[8]  Lee A. Segel,et al.  On the distribution of dominance in populations of social organisms , 1992 .

[9]  N Bellomo,et al.  Lecture Notes on Mathematical Theory of the Boltzmann Equation , 1995 .

[10]  R T Prehn,et al.  Stimulatory effects of immune reactions upon the growths of untransplanted tumors. , 1994, Cancer research.

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

[12]  J Urbain,et al.  On the kinetics and optimal specificity of cytotoxic reactions mediated by T-lymphocyte clones , 1992, Bulletin of mathematical biology.

[13]  P. Comoglio,et al.  Growth of Syngeneic Tumours in Unimmunized Newborn and Adult Hosts , 1973, British Journal of Cancer.

[14]  A. Abbas,et al.  Cellular and Molecular Immunology , 1991 .

[15]  Edward J. Beltrami,et al.  Mathematics for Dynamic Modeling , 1987 .

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

[17]  Miljenko Marušić,et al.  PREDICTION POWER OF MATHEMATICAL MODELS FOR TUMOR GROWTH , 1993 .

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

[19]  A. Albert,et al.  Tumors and the immune system: the effects of a tumor growth modulator☆ , 1980 .

[20]  G. Forni,et al.  Low doses of IL-4 injected perilymphatically in tumor-bearing mice inhibit the growth of poorly and apparently nonimmunogenic tumors and induce a tumor-specific immune memory. , 1990, Journal of immunology.

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

[22]  Nicola Bellomo,et al.  Solution of a new class of nonlinear kinetic models of population dynamics , 1996 .

[23]  M. Rasetti.  FUNDAMENTALS OF MAXWELL KINETIC-THEORY OF A SIMPLE MONOATOMIC GAS - TRUESDELL,C, MUNCASTER,RG , 1982 .

[24]  A. Perelson,et al.  Delivery of lethal hits by cytotoxic T lymphocytes in multicellular conjugates occurs sequentially but at random times. , 1982, Journal of immunology.

[25]  R. Ash,et al.  Topics in stochastic processes , 1975 .

[26]  P. Musiani,et al.  Inhibition of tumor growth and enhancement of metastasis after transfection of the γ‐interferon gene , 1993 .

[27]  G. Nossal.  Life, death and the immune system. , 1993, Scientific American.

[28]  Nicola Bellomo,et al.  Population dynamics with stochastic interaction , 1995 .

[29]  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.

[30]  M. Lo Schiavo,et al.  DISCRETE KINETIC CELLULAR MODELS OF TUMORS IMMUNE SYSTEM INTERACTIONS , 1996 .

[31]  S. Maggelakis.  Type α and type β transforming growth factors as regulators of cancer cellular growth: a mathematical model , 1993 .

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

[33]  I. Stewart.  Density conservation for a coagulation equation , 1991 .

[34]  G Taubes,et al.  Do immunologists dream of electric mice? , 1994, Science.

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

[36]  A Yu Yakovlev,et al.  Stochastic Models of Tumor Latency and Their Biostatistical Applications , 1996 .

[37]  M. Smoluchowski.  Versuch einer mathematischen Theorie der Koagulationskinetik kolloider Lösungen , 1918 .

[38]  James P. Freyer,et al.  Tumor growthin vivo and as multicellular spheroids compared by mathematical models , 1994, Bulletin of mathematical biology.

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

[40]  A. Perelson,et al.  Nonlinear dynamics of immunogenic tumors: parameter estimation and global bifurcation analysis. , 1994, Bulletin of mathematical biology.

[41]  J. Leith,et al.  Growth factors and growth control of heterogeneous cell populations. , 1993, Bulletin of mathematical biology.

[42]  B. Fitzpatrick,et al.  APPROXIMATION AND PARAMETER ESTIMATION PROBLEMS FOR ALGAL AGGREGATION MODELS , 1994 .

[43]  A. Perelson,et al.  Kinetics of cell-mediated cytotoxicity: Stochastic and deterministic multistage models☆ , 1984 .

[44]  Z. Grossman,et al.  Tumor escape from immune elimination. , 1980, Journal of theoretical biology.

[45]  P Hogeweg,et al.  Tumor escape from immune elimination: simplified precursor bound cytotoxicity models. , 1985, Journal of theoretical biology.

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

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

[48]  Nicola Bellomo,et al.  Dynamics of tumor interaction with the host immune system , 1994 .

[49]  P. Lollini,et al.  Immunizing and Curative Potential of Replicating and Nonreplicating Murine Mammary Adenocarcinoma Cells Engineered with Interleukin (IL)-2, IL-4, IL-6, IL-7, IL-10, Tumor Necrosis Factor α, Granulocyte-Macrophage Colony-stimulating Factor, and γ-Interferon Gene or Admixed with Conventional Adjuvants , 1994 .

[50]  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.

[51]  Simon A. Levin,et al.  Frontiers in Mathematical Biology , 1995 .

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

[53]  Z Bajzer,et al.  Modeling autostimulation of growth in multicellular tumor spheroids. , 1991, International journal of bio-medical computing.

[54]  I. W. Stewart,et al.  A global existence theorem for the general coagulation-fragmentation equation with unbounded kernels , 1989 .

[55]  Stanley N Cohen,et al.  Mechanisms of tumor immunity , 1977 .

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

[57]  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.

[58]  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.

[59]  S. Rosenberg,et al.  Adoptive immunotherapy of established pulmonary metastases with LAK cells and recombinant interleukin-2. , 1984, Science.

[60]  W. Bodmer,et al.  Failure of programmed cell death and differentiation as causes of tumors: some simple mathematical models. , 1995, Proceedings of the National Academy of Sciences of the United States of America.

[61]  P. Coulie,et al.  From defined human tumor antigens to effective immunization? , 1995, Immunology today.

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

[63]  G. Forni,et al.  Interleukin 2 activated tumor inhibition in vivo depends on the systemic involvement of host immunoreactivity. , 1987, Journal of immunology.

[64]  S. Markovitch.  The particular role of cell loss in tumor growth , 1993 .

[65]  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.