Tumor growth instability and its implications for chemotherapy.

Optimal delivery of chemotherapy intensity is dependent on host- and tumor-specific characteristics. In this article, the chemotherapy late intensity schedule is revised to account for tumor growth instability, where a small tumor cell fraction emerges that exhibits a higher proliferation rate than the parent strain. Modeling this instability as simplified two-population dynamics, we find that: (a) if this instability precedes the onset of treatment, the slope of the linear increase of the drug concentration for the standard "Norton-Simon late intensity schedule" changes and the initial value of the dose strongly depends on the ratio of the two tumor cell populations and on their distinct growth rates; and (b) if the instability trails the initial treatment, the effective chemotherapeutic drug concentration changes as well. Both cases point toward testable potential refinements of the Norton-Simon late intensity schedule.

[1]  P. Castorina,et al.  Classification scheme for phenomenological universalities in growth problems in physics and other sciences. , 2006, Physical review letters.

[2]  Marcin Molski.  On the Classification Scheme for Phenomenological Universalities in Growth Problems in Physics and Other Sciences , 2007 .

[3]  Larry Norton,et al.  Phase I study of a novel capecitabine schedule based on the Norton-Simon mathematical model in patients with metastatic breast cancer. , 2008, Journal of clinical oncology : official journal of the American Society of Clinical Oncology.

[4]  A. Luini,et al.  Expression of ER, PgR, HER1, HER2, and response: a study of preoperative chemotherapy. , 2008, Annals of oncology : official journal of the European Society for Medical Oncology.

[5]  J. M. Murray,et al.  Optimal control for a stochastic model of cancer chemotherapy. , 2000, Mathematical biosciences.

[6]  James H Brown,et al.  Allometric scaling of metabolic rate from molecules and mitochondria to cells and mammals , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[7]  James H. Brown,et al.  A general model for ontogenetic growth , 2001, Nature.

[8]  M. Delbrück,et al.  Mutations of Bacteria from Virus Sensitivity to Virus Resistance. , 1943, Genetics.

[9]  M. Retsky,et al.  A stochastic numerical model of breast cancer growth that simulates clinical data. , 1984, Cancer research.

[10]  Pier Paolo Delsanto,et al.  Does tumor growth follow a "universal law"? , 2003, Journal of theoretical biology.

[11]  P. Castorina,et al.  Growth Laws in Cancer: Implications for Radiotherapy , 2006, Radiation research.

[12]  J. Goldie,et al.  Quantitative model for multiple levels of drug resistance in clinical tumors. , 1983, Cancer treatment reports.

[13]  Larry Norton,et al.  Dose-dense adjuvant chemotherapy for primary breast cancer , 2005, Breast Cancer Research.

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

[15]  M. Retsky,et al.  Is Gompertzian or exponential kinetics a valid description of individual human cancer growth? , 1990, Medical hypotheses.

[16]  Skipper He.  Laboratory models: some historical perspective. , 1986 .

[17]  Larry Norton,et al.  Conceptual and practical implications of breast tissue geometry: toward a more effective, less toxic therapy. , 2005, The oncologist.

[18]  Goldie Jh,et al.  Quantitative model for multiple levels of drug resistance in clinical tumors. , 1983 .

[19]  A. Howell,et al.  Dissociation between steroid receptor expression and cell proliferation in the human breast. , 1997, Cancer research.

[20]  Eamonn A Gaffney,et al.  Modelling chemotherapy resistance in palliation and failed cure. , 2009, Journal of theoretical biology.

[21]  L. Norton,et al.  The Norton-Simon hypothesis revisited. , 1986, Cancer treatment reports.

[22]  Lurias,et al.  MUTATIONS OF BACTERIA FROM VIRUS SENSITIVITY TO VIRUS RESISTANCE’-’ , 2003 .

[23]  Goldie Jh,et al.  Application of theoretical models to chemotherapy protocol design. , 1986 .

[24]  Shea N Gardner,et al.  Modeling multi-drug chemotherapy: tailoring treatment to individuals. , 2002, Journal of theoretical biology.

[25]  P. Neven,et al.  Prognostic and predictive value of centrally reviewed expression of estrogen and progesterone receptors in a randomized trial comparing letrozole and tamoxifen adjuvant therapy for postmenopausal early breast cancer: BIG 1-98. , 2007, Journal of clinical oncology : official journal of the American Society of Clinical Oncology.

[26]  L. Norton,et al.  The Norton–Simon hypothesis: designing more effective and less toxic chemotherapeutic regimens , 2006, Nature Clinical Practice Oncology.