Tumor Heterogeneity and Growth Control

Tumor growth control is described especially as it pertains to tumor heterogeneity. Four facets heterogeneity are reviewed; statistical or distributional heterogeneity, epigenetic or environmental heterogeneity, emergence of intrinsic or clonal heterogeneity, and the development of clonal subpopulations in a heterogeneous micro-environment. A model of tumor growth and its control is developed. Growth control is defined for a heterogeneous tumor composed of a cycling, proliferative compartment and a non-cycling, quiescent one. The paradigm for this form of heterogeneity is hypoxia in a solid tumor. It is used to establish a linkage between the carrying capacity of a tumor-bearing host for its tumor burden. The model is then applied to three disparate tumor growth phenomena. Each study is accompanied by an exploration of what we know (the experimental and clinical literature describing the phenomenon), what we think we know (a summary of the underlying growth processes we surmise accounts for the phenomenon), what we wish we know (areas which are still unexplored in the laboratory or clinic), and a description of the experiment and its analysis (a means of gathering and analyzing the missing information to complete a picture of the phenomenon in question).

[1]  J. Leith,et al.  Tumor radiocurability: relationship to intrinsic tumor heterogeneity and to the tumor bed effect. , 1990, Invasion & metastasis.

[2]  Roger S. Day,et al.  A branching-process model for heterogeneous cell populations , 1986 .

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

[4]  S. Michelson Comparison of Stochastic Models for Tumor Escape , 1986 .

[5]  J. Leith,et al.  Growth properties of artificial heterogeneous human colon tumors. , 1987, Cancer research.

[6]  T Kuczek,et al.  Mathematical modeling for tumor resistance. , 1988, Journal of the National Cancer Institute.

[7]  L. Révész,et al.  Analysis of the growth of tumor cell populations , 1974 .

[8]  B. Fisher,et al.  Experimental studies of factors influencing hepatic metastases. I. The effect of number of tumor cells injected and time of growth , 1959, Cancer.

[9]  Elliott W. Montroll,et al.  Nonlinear Population Dynamics. (Book Reviews: On the Volterra and Other Nonlinear Models of Interacting Populations) , 1971 .

[10]  A theoretical explanation of "concomitant resistance". , 1995, Bulletin of mathematical biology.

[11]  J. Rubin,et al.  A broad-spectrum human lung fibroblast-derived mitogen is a variant of hepatocyte growth factor. , 1991, Proceedings of the National Academy of Sciences of the United States of America.

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

[13]  J. Leith,et al.  Tumor micro-ecology and competitive interactions. , 1987, Journal of theoretical biology.

[14]  M. Brattain,et al.  Heterogeneity of malignant cells from a human colonic carcinoma. , 1981, Cancer research.

[15]  J. Leith,et al.  Tumor bed expression in xenografted artificial heterogeneous colon tumors. , 1988, International journal of radiation oncology, biology, physics.

[16]  I. Fidler,et al.  Interactions among clonal subpopulations affect stability of the metastatic phenotype in polyclonal populations of B16 melanoma cells. , 1981, Proceedings of the National Academy of Sciences of the United States of America.

[17]  R. Taub,et al.  The gene encoding rat insulinlike growth factor-binding protein 1 is rapidly and highly induced in regenerating liver , 1991, Molecular and cellular biology.

[18]  A SIMPLE MODEL OF A STEADY STATE DIFFERENTIATING CELL SYSTEM , 1969, The Journal of cell biology.

[19]  B. Stoll Spontaneous regression of cancer: New insights , 1992, Biotherapy.

[20]  J. Leith,et al.  Modification of the growth rates and hypoxic fractions of xenografted A431 tumors by sialoadenectomy or exogenously supplied epidermal growth factor. , 1991, Cancer research.

[21]  G. F. Webb,et al.  A NONLINEAR CELL POPULATION MODEL OF PERIODIC CHEMOTHERAPY TREATMENT , 1992 .

[22]  James H. Goldie,et al.  The effect of cellular differentiation on the development of permanent drug resistance , 1985 .

[23]  K. Ito,et al.  Stochastic models for subpopulation emergence in heterogeneous tumors , 1989 .

[24]  A. Cantarow,et al.  Tumor growth in partially hepatectomized rats. , 1955, Cancer research.

[25]  M. Sporn,et al.  Type beta transforming growth factor: a bifunctional regulator of cellular growth. , 1985, Proceedings of the National Academy of Sciences of the United States of America.

[26]  F. Miller,et al.  Tumor subpopulation interactions in neoplasms. , 1983, Biochimica et biophysica acta.

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

[28]  I. Fidler,et al.  Development of biological diversity and susceptibility to chemotherapy in murine cancer metastases. , 1984, Cancer research.

[29]  P. Nowell Mechanisms of tumor progression. , 1986, Cancer research.

[30]  E. Trucco,et al.  Mathematical models for cellular systems. The von foerster equation. Part II , 1965 .

[31]  M Gyllenberg,et al.  Quiescence as an explanation of Gompertzian tumor growth. , 1989, Growth, development, and aging : GDA.

[32]  G. Papa,et al.  Modification of the volumetric growth responses and steady-state hypoxic fractions of xenografted DLD-2 human colon carcinomas by administration of basic fibroblast growth factor or suramin. , 1992, British Journal of Cancer.

[33]  W. Kendal,et al.  Gompertzian growth as a consequence of tumor heterogeneity , 1985 .

[34]  B. Fisher,et al.  Experimental studies of factors influencing hepatic metastases. II. Effect of partial hepatectomy , 1959, Cancer.

[35]  R T Schimke,et al.  Gene amplification in cultured cells. , 1988, The Journal of biological chemistry.

[36]  S. Michelson A system for Monte Carlo simulation of heterogeneous tumor cell populations , 1990 .

[37]  P. Månsson,et al.  Heparin-binding growth factor type 1 (acidic fibroblast growth factor): a potential biphasic autocrine and paracrine regulator of hepatocyte regeneration. , 1989, Proceedings of the National Academy of Sciences of the United States of America.

[38]  R T Prehn,et al.  The inhibition of tumor growth by tumor mass. , 1991, Cancer research.

[39]  R T Schimke,et al.  Gene amplification, drug resistance, and cancer. , 1984, Cancer research.

[40]  Environmental stress induced by the tumor bed effect leads to subpopulation exclusion within heterogeneous neoplasms: modeling studies. , 1988, Radiation research.

[41]  G. Minuk,et al.  Effects of partial hepatectomy on hepatic insulinlike growth factor binding protein‐1 expression , 1992, Hepatology.

[42]  B. V. Bronk,et al.  The stochastic theory of cell proliferation. , 1968, Biophysical journal.

[43]  Goldie Jh,et al.  Rationale for the use of alternating non-cross-resistant chemotherapy. , 1982 .

[44]  B. Fisher,et al.  Experimental Studies of Factors Influencing Hepatic Metastases: III. Effect of Surgical Trauma with Special Reference to Liver Injury , 1959, Annals of surgery.

[45]  R. Ruggiero,et al.  "Concomitant immunity" in murine tumours of non-detectable immunogenicity. , 1985, British Journal of Cancer.

[46]  J H Goldie,et al.  The genetic origin of drug resistance in neoplasms: implications for systemic therapy. , 1984, Cancer research.

[47]  B. Fisher,et al.  Experimental Studies of Factors Influencing Hepatic Metastases: IX. The Pituitary Gland , 1961, Annals of surgery.

[48]  Goldie Jh,et al.  A mathematic model for relating the drug sensitivity of tumors to their spontaneous mutation rate. , 1979 .

[49]  J. Mead,et al.  Transforming growth factor alpha may be a physiological regulator of liver regeneration by means of an autocrine mechanism. , 1989, Proceedings of the National Academy of Sciences of the United States of America.

[50]  S. Rockwell Effect of host age on the transplantation, growth, and radiation response of EMT6 tumors. , 1981, Cancer research.

[51]  J. Leith,et al.  Effects of differential cell kill on the dynamic composition of heterogeneous tumors , 1990 .

[52]  J. Leith,et al.  Interlocking triads of growth control in tumors. , 1995, Bulletin of mathematical biology.

[53]  S. I. Rubinow,et al.  A maturity-time representation for cell populations. , 1968, Biophysical journal.

[54]  K. Matsumoto,et al.  Hepatocyte growth factor: molecular structure, roles in liver regeneration, and other biological functions. , 1992, Critical reviews in oncogenesis.

[55]  Z Bajzer,et al.  Analysis of growth of multicellular tumour spheroids by mathematical models , 1994, Cell proliferation.

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

[57]  R. Ruggiero,et al.  Correlation between seric antitumor activity and concomitant resistance in mice bearing nonimmunogenic tumors. , 1990, Cancer research.

[58]  I. Győri,et al.  Time-dependent subpopulation induction in heterogeneous tumors. , 1988, Bulletin of mathematical biology.

[59]  E. Gorelik Concomitant tumor immunity and the resistance to a second tumor challenge. , 1983, Advances in cancer research.

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

[61]  N. Fausto Growth factors in liver development, regeneration and carcinogenesis. , 1991, Progress in growth factor research.

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

[63]  J. Leith,et al.  Dormancy, regression, and recurrence: towards a unifying theory of tumor growth control. , 1994, Journal of theoretical biology.

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

[65]  R. Prehn Two competing influences that may explain concomitant tumor resistance. , 1993, Cancer research.

[66]  J. Leith,et al.  Compositional stability of artificial heterogeneous tumors in vivo: use of mitomycin C as a cytotoxic probe. , 1988, Cancer research.

[67]  K. Kurokawa,et al.  Stimulation of liver growth by exogenous human hepatocyte growth factor in normal and partially hepatectomized rats , 1993, Hepatology.

[68]  G. Poste,et al.  Interactions between tumor cell subpopulations in malignant tumors. , 1983, Symposium on Fundamental Cancer Research.

[69]  J. Leith,et al.  Effects of partial hepatectomy on the growth characteristics and hypoxic fractions of xenografted DLD-2 human colon cancers. , 1992, Radiation research.

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

[71]  C. Cornelisse,et al.  A prolactin-dependent, metastasising rat mammary carcinoma as a model for endocrine-related tumour dormancy. , 1991, British Journal of Cancer.

[72]  J. Goldie,et al.  A model for the resistance of tumor cells to cancer chemotherapeutic agents , 1983 .

[73]  Lars Holmgren,et al.  Angiostatin: A novel angiogenesis inhibitor that mediates the suppression of metastases by a lewis lung carcinoma , 1994, Cell.

[74]  B. Nordlinger,et al.  Dormant liver metastases: an experimental study , 1992, The British journal of surgery.

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

[76]  L Kates,et al.  Multi‐Type Galton‐Watson Process As A Model For Proliferating Human Tumour Cell Populations Derived From Stem Cells: Estimation of Stem Cell Self‐Renewal Probabilities In Human Ovarian Carcinomas , 1986, Cell and tissue kinetics.

[77]  S. Watson,et al.  Co-stimulation of gastrointestinal tumour cell growth by gastrin, transforming growth factor alpha and insulin like growth factor-I. , 1991, British Journal of Cancer.