Skip to main content
PMC home page
Biophysical Journal logoLink to Biophysical Journal
. 1976 Nov;16(11):1257–1271. doi: 10.1016/S0006-3495(76)85772-4

A mathematical model of the chemotherapeutic treatment of acute myeloblastic leukemia.

S I Rubinow, J L Lebowitz
PMCID: PMC1334956  PMID: 1067874

Abstract

Based on our previous mathematical model of the acute myeloblastic leukemic (AML) state in man, we superimpose a chemotherapeutic drug treatment regimen. Our calculations suggest that small changes in the protocol can have significant effects on the result of treatment. Thus, the optimal period between drug doses is the S-phase interval of the leukemic cells--about 20h--and the greater the number of doses administered in a given course treatment, the longer the rest interval should be before the next course is administered. For a patient with a "slow" growing AML cell population, remission can be achieved with one or two courses of treatment, and further suppression of the leukemic population can be achieved with continued courses of treatment. However, for patients with a "fast" growing AML cell population, a similar aggressive treatment regimen succeeds in achieving remission status only at the cost of very great toxic effects on the normal neutrophil population and its precursors.

Full text

PDF
1269

Selected References

These references are in PubMed. This may not be the complete list of references from this article.

  1. Bradley T. R., Metcalf D., Robinson W. Stimulation by leukaemic sera of colony formation in solid agar cultures by proliferation of mouse bone marrow cells. Nature. 1967 Mar 4;213(5079):926–927. doi: 10.1038/213926a0. [DOI] [PubMed] [Google Scholar]
  2. Bullough W. S. Mitotic control in adult mammalian tissues. Biol Rev Camb Philos Soc. 1975 Feb;50(1):99–127. doi: 10.1111/j.1469-185x.1975.tb00990.x. [DOI] [PubMed] [Google Scholar]
  3. Chan S. H., Metcalf D. Inhibition of bone marrow colony formation by normal and leukaemic human serum. Nature. 1970 Aug 22;227(5260):845–846. doi: 10.1038/227845a0. [DOI] [PubMed] [Google Scholar]
  4. Clarkson B. D. Acute myelocytic leukemia in adults. Cancer. 1972 Dec;30(6):1572–1582. doi: 10.1002/1097-0142(197212)30:6<1572::aid-cncr2820300624>3.0.co;2-m. [DOI] [PubMed] [Google Scholar]
  5. Clarkson B. D., Dowling M. D., Gee T. S., Cunningham I. B., Burchenal J. H. Treatment of acute leukemia in adults. Cancer. 1975 Aug;36(2):775–795. doi: 10.1002/1097-0142(197508)36:2+<775::aid-cncr2820360824>3.0.co;2-v. [DOI] [PubMed] [Google Scholar]
  6. Clarkson B. D., Dowling M. D., Jr, Gee T. S., Burchenal J. H. Treatment of acute myeloblastic leukemia. Bibl Haematol. 1973;39:1098–1114. doi: 10.1159/000427816. [DOI] [PubMed] [Google Scholar]
  7. Clarkson B. D., Fried J. Changing concepts of treatment in acute leukemia. Med Clin North Am. 1971 May;55(3):561–600. doi: 10.1016/s0025-7125(16)32504-4. [DOI] [PubMed] [Google Scholar]
  8. Gee T. S., Haghbin M., Dowling M. D., Cunningham I., Middleman M. P., Clarkson B. D. Acute lymphoblastic leukemia in adults and children. Differences in response with similar therapeutic regimens. Cancer. 1976 Mar;37(3):1256–1264. doi: 10.1002/1097-0142(197603)37:3<1256::aid-cncr2820370305>3.0.co;2-r. [DOI] [PubMed] [Google Scholar]
  9. Gee T. S., Yu K. P., Clarkson B. D. Treatment of adult acute leukemia with arabinosylcytosine and thioguanine. Cancer. 1969 May;23(5):1019–1032. doi: 10.1002/1097-0142(196905)23:5<1019::aid-cncr2820230506>3.0.co;2-n. [DOI] [PubMed] [Google Scholar]
  10. Haghbin M., Tan C. C., Clarkson B. D., Miké V., Burchenal J. H., Murphy M. L. Intensive chemotherapy in children with acute lymphoblastic leukemia (L-2 protocol). Cancer. 1974 Jun;33(6):1491–1498. doi: 10.1002/1097-0142(197406)33:6<1491::aid-cncr2820330604>3.0.co;2-#. [DOI] [PubMed] [Google Scholar]
  11. Haghbin M., Tan C. T., Clarkson B. D., Miké V., Burchenal J. H., Murphy M. L. Treatment of acute lymphoblastic leukemia in childreq with "prophylactic" intrathecal methotrexate and intensive systemic chemotherapy. Cancer Res. 1975 Mar;35(3):807–811. [PubMed] [Google Scholar]
  12. Metcalf D. The nature of leukaemia: neoplasm or disorder of haemopoietic regulation? Med J Aust. 1971 Oct 9;2(15):739–746. [PubMed] [Google Scholar]
  13. Rubinow S. I., Lebowitz J. L. A mathematical model of the acute myeloblastic leukemic state in man. Biophys J. 1976 Aug;16(8):897–910. doi: 10.1016/S0006-3495(76)85740-2. [DOI] [PMC free article] [PubMed] [Google Scholar]
  14. Shackney S. E. A computer model for tumor growth and chemotherapy, and its application to L1210 leukemia treated with cytosine arabinoside (NSC-63878). Cancer Chemother Rep. 1970 Dec;54(6):399–429. [PubMed] [Google Scholar]
  15. Skipper H. E., Schabel F. M., Jr, Wilcox W. S. Experimental evaluation of potential anticancer agents. XXI. Scheduling of arabinosylcytosine to take advantage of its S-phase specificity against leukemia cells. Cancer Chemother Rep. 1967 Jun;51(3):125–165. [PubMed] [Google Scholar]
  16. Steward P. G., Hahn G. M. The application of age response functions to the optimization of treatment schedules. Cell Tissue Kinet. 1971 May;4(3):279–291. doi: 10.1111/j.1365-2184.1971.tb01539.x. [DOI] [PubMed] [Google Scholar]

Articles from Biophysical Journal are provided here courtesy of The Biophysical Society

RESOURCES