Abstract
Over the past 25 years stepwise improvement in the cure of disseminated cancers has been good, fair or very poor depending on the particular cancer one is discussing. “Cancer chemotherapy provides variably effective treatment for the majority of forms of human cancer and curative treatment for some 12 categories.” We have been slow to gain and learn how to apply quantitative information on the biologic phenomena that underlie the responsiveness, or lack of responsiveness, of many different cancers to single drugs and combinations of drugs delivered in different ways. I am of the opinion that continuing development and integration of rational biomathematical models based on principles already identified, and testing them for compatibility with much already available experimental and clinical data, will lead to models that will help in planning more effective treatment regimens for cancers now classified as moderately refractory or very refractory to chemotherapy. Some of the critical variables are considered briefly. My advice, for what it is worth, is “try to be sure that the biologic concepts that you use in modeling are almost as good as the arithmetic.”
Article PDF
Similar content being viewed by others
Literature
Frei, E. III. 1985. “Curative Cancer Chemotherapy.”Cancer Res. 45, 6523–6537.
— and E. J. Freireich. 1965. “Progress and Perspectives in the Chemotherapy of Acute Leukemia.” InAdvances in Chemotherapy, A. Goldin, F. Hawking and R. J. Schnitzer (Eds), Vol. 2, pp. 269–298. New York: Academic Press.
Goldie, J. H. and A. J. Coldman. 1979. “A mathematic Model for Relating the Drug Sensitivity of Tumors to Their Spontaneous Mutation Rate.”Cancer Treat. Rep. 63, 1727–1733.
— and —. 1983. “Quantitative Model for Multiple Levels of Drug Resistance in Clinical Tumors.”Cancer Treat. Rep. 67, 923–931.
—— and G. A. Gudauskas. 1982. “Rationale for the Use of Alternating Noncross-resistant Chemotherapy.”Cancer Treat. Rep. 62, 439–449.
Holland, J. 1981. “Chemotherapy of Gigacytomas: the Treatment and Curability of ‘Solid’ Tumors With Drugs.” InCancer Achievements, Challenges and Prospects for the 1980’s, J. H. Burchenal and H. R. Oettgen (Eds), Vol. 2, pp. 563–583. New York: Grune & Stratton.
Hryniuk, W. and H. Bush. 1984. “The Importance of Dose Intensity in Chemotherapy of Metastatic Breast Cancer.”J. clin. Oncol. 2, 1281–1288.
Schabel, F. M. Jr., H. E. Skipper, M. W. Trader, W. R. Laster, Jr., T. H. Corbett and D. P. Griswold, Jr. 1980. “Concepts for Controlling Drug-resistant Tumor Cells.” InBreast Cancer Experimental and Clinical Aspects, H. T. Mourisden and T. Palshof (Eds), pp. 129–211. Oxford: Pergamon Press.
Schmid, F. A., D. J. Hutchinson, G. M. Otter and C. Stock. 1976. “Development of Resistance to Combinations of Six Antimetabolites in Mice With L1210 Leukemia.Cancer Treat. Rep. 60, 23–27.
Skipper, H. E. 1980. “Some Thoughts on a Recent Publication by Goldie and Coldman Entitled ‘A Mathematic Model for Relating the Drug Sensitivity of Tumors to Their Spontaneous Mutation Rate‘.” Southern Research Institute, Birmingham, AL, Booklet 9.
Skipper, H. E. 1981–1985. Booklets 9–22, 1981; Booklets 4, 6, 7, 13, 14, 20 and 21, 1982; Booklets 2–14, 1983; Booklets 3, 10–15 and 19, 1984; Booklets 5–7, 1985. Southern Research Institute, Birmingham, AL.
—. 1983. “The Forty-year-old Mutation Theory of Luria and Delbrück and Its Pertinence to Cancer Chemotherapy.” InAdvances in Cancer Research, G. Klein and S. Weinhouse (Eds.), Vol. 40, pp. 331–363. New York: Academic Press.
—. 1985a. “Experimental Adjuvant Chemotherapy: An Overview.” InRecent Results in Cancer Research, Ragaz, Band and J. H. Goldie (Eds), Vol. 103,Preoperative (Neoadjuvant) Chemotherapy, pp. 6–29. Heidelberg: Springer-Verlag.
—. 1985b. “A Review of Extensive Data on the Response of Different Experimental Neoplasms at Different Stages of Advancement to Varying Dose Intensities, Schedules and durations of Treatment with Ara-C and a Slow-release Form of Ara-C.” Southern Research Institute, Birningham, AL, Booklet 9.
—. 1985c. “A Review of Extensive Data on the Response of Different Experimental Neoplasms at Different Stages of Advancement to Varying Dose Intensities, Schedules, and Durations of Treatment with Cyclophosphamide (CPA).” Southern Research Institute, Birmingham, AL, Booklet 10.
Neoplasms. 1986. “Critical Variables in the Design of Combination Chemotherapy Regimens to be Used Alone or in an Adjuvant Setting.”Proc. First Int. Congress on Neo-Adjuvant Chemotherapy, Paris, November 1985. to be published by John Libbey Eurotext, Montrouge, France as a co-edition with INSERM.
— and F. M. Schabel, Jr. 1984. “Tumor Stem Cell Heterogeneity: Implications With Respect to Classification of Cancers by Chemotherapeutic Effect.”Cancer Treat. Rep. 68, 43–61.
— and L. Simpson-Herren. 1985. “Relationship between Tumor Stem Cell Heterogeneity and Responsiveness to Chemotherapy.” InImportant Advances in Oncology 1985, V. T. DeVita, Jr., S. Hellman and S. A. Rosenberg (Eds), pp. 63–77. Philadelphia: J. B. Lippincott.
—, F. M. Schabel, Jr. and W. S. Wilcox. 1964. “Experimental Evaluation of Potential Anticancer Agents. XIII. On the Criteria and Kinetics Associated with ‘Curability’ of Experimental Leukemia.”Cancer Chemother. Rep. 35, 1–111.
Wilcox, W. S. 1966. “The Last Surviving Cancer Cell: the Chances of Killing It.”Cancer Chemother. Rep. 50, 541–542.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Skipper, H.E. On mathematical modeling of critical variables in cancer treatment (goals: Better understanding of the past and better planning in the future). Bltn Mathcal Biology 48, 253–278 (1986). https://doi.org/10.1007/BF02459681
Issue Date:
DOI: https://doi.org/10.1007/BF02459681