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Sequencing Surgery, Radiotherapy and Chemotherapy: Insights from a Mathematical Analysis

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Abstract

We present results from a mathematical analysis that is aimed at finding the best way to sequence the three traditional cancer treatments: surgery (S), chemotherapy (C), and radiotherapy (R). The mathematical model tracks the temporal evolution of the primary tumor and its associated metastases, and incorporates the primary tumor's effect on the dormancy and growth of the metastases. We show that the SCR schedule (i.e., surgery followed by chemotherapy followed by radiotherapy) achieves a higher cure probability than SRC if the primary tumor is sufficiently large or if the metastatic population is sufficiently large relative to the primary tumor. We also show that a novel schedule, SRCR, which splits the radiotherapy regimen into two disjoint portions, is optimal among all schedules, provided that the patient's dormant metastatic tumors do not become vascularized within about 40 days after surgery.

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References

  1. Recht A, Come SE, Henderson IC, Gelman RS, Silver B, Hayes DF, Shulman LN, Harris JR: The sequencing of chemo-therapy and radiation therapy after conservative surgery for early-stage breast cancer. N Engl J Med 334: 1356–1361, 1996

    Google Scholar 

  2. Bonadonna G: Current and future trends in the multidisciplin-ary approach for high-risk breast cancer. The experience of the Milan Cancer Institute. Eur J Cancer 32A: 209–214, 1996

    Google Scholar 

  3. Weidner N, Semple JP, Welch WR, Folkman J: Tumor an-giogenesis and metastasis - correlation in invasive breast carcinoma. N Engl J Med 324: 1–8, 1991

    Google Scholar 

  4. Chambers AF, MacDonald IC, Schmidt EE, Koop S, Morris VL, Khokha R, Groom AC: Steps in tumor metastasis: new concepts from intravital videomicroscopy. Cancer Metast Rev 14: 279–301, 1995

    Google Scholar 

  5. Luzzi KJ, MacDonald IC, Schmidt EE, Kerkvliet N, Morris VL, Chambers AF, Groom AC: Multistep nature of metastatic inefficiency: dormancy of solitary cells after successful extravasation and limited survival of early micrometastases. Amer J Pathol 153: 865–873, 1998

    Google Scholar 

  6. O'Reilly MS, Holmgren L, Shing Y, Chen C, Rosenthal RA, Moses M, Lane WS, Cao Y, Sage EH, Folkman J: Angiostatin: a novel angiogenesis inhibitor that mediates the suppression of metastases by a Lewis lung carcinoma. Cell 79: 315–328, 1994

    Google Scholar 

  7. Holmgren L, O'Reilly MS, Folkman J: Dormancy of micro-metastases: balanced proliferation and apoptosis in the presence of angiogenesis suppression. Nature Med 1: 149–153, 1995

    Google Scholar 

  8. Browder T, Butterfield CE, Kräling BM, Shi B, Marshall B, O'Reilly MS, Folkman J: Antiangiogenic scheduling of chemotherapy improves efficacy against experimental drug-resistant cancer. Cancer Res 60: 1878–1886, 2000

    Google Scholar 

  9. Beil DR, Wein LM: Analysis and comparison of multimodal cancer treatments. To appear in IMA Journal of Mathematics Applied in Medicine and Biology, 2002

  10. Skipper HE, Schabel Jr FM, Wilcox WS: Experimental evaluation of potential anticancer agents. XIII. On the criteria and kinetics associated with ‘curability’ of experimental leukemia. Cancer Chemotherap Rep 35: 1–111, 1964

    Google Scholar 

  11. Fowler JF: The linear-quadratic formula and progress in fractionated radiotherapy. Br J Radiol 62: 679–694, 1989

    Google Scholar 

  12. Folkman J: Clinical applications of research on angiogenesis. In: Flier JS, Underhill LH (eds) Seminars in Medicine of the Beth Israel Hospital, Boston. N Engl J Med 333: 1757–1763, 1995

  13. Landry J, Freyer JP, Sutherland RM: A model for the growth of multicellular spheroids. Cell Tissue Kinet 15: 585–594, 1982

    Google Scholar 

  14. Camphausen K, Moses MA, Beecken WD, Khan MK, Folkman J, O'Reilly MS: Radiation therapy to a primary tumor accelerates metastatic growth in mice. Cancer Res 61: 2207–2211, 2001

    Google Scholar 

  15. Tucker SL, Taylor JMG: Improved models of tumor cure. Int J Radiat Biol 70: 539–553, 1996

    Google Scholar 

  16. Hanahan D, Folkman J: Patterns and emerging mechanisms of the angiogenic switch during tumorigenesis. Cell 86: 353–364, 1996

    Google Scholar 

  17. Demicheli R, Terenziani M, Bonadonna G: Estimate of tumor growth time for breast cancer local recurrences: rapid growth after wake-up. Breast Cancer Res Treat 51: 133–137, 1998

    Google Scholar 

  18. Tubiana M, Koscielny S: Natural history of human breast cancer: recent data and clinical implications. Breast Cancer Res Treat 18: 125–140, 1991

    Google Scholar 

  19. Lewis AM, Su M, Doty J, Chen Y, Pardo FS: Relationship between intrinsic radiation sensitivity and metastatic potential. Int J Radiat Oncol Biol Phys 34: 103–110, 1996

    Google Scholar 

  20. Koscielny S, Tubiana M, Lê MG, Valleron AJ, Mouriesse H, Contesso G, Sarrazin D: Breast cancer: relationship between the size of the primary tumour and the probability of metastatic dissemination. Br J Cancer 49: 709–715, 1984

    Google Scholar 

  21. Koscielny S, Tubiana M: The link between local recurrence and distant metastases in human breast cancer. Int J Rad Oncol Biol Phys 43: 11–24, 1999

    Google Scholar 

  22. Bonadonna G, Valagussa P, Brambilla C, Ferrari L, Moliterni A, Tereziani M, Zambetti M: Primary chemotherapy in operable breast cancer: eight-year experience at the Milan Cancer Institute. J Clin Oncol, 16: 93–100, 1998

    Google Scholar 

  23. Tubiana M, Arriagada R, Cosset J-M: Sequencing of drugs and radiation: the integrated alternating regimen. Cancer 55: 2131–2139, 1985

    Google Scholar 

  24. Graeber TG, Osmanian C, Jacks T, Housman DE, Koch CJ, Lowe SW, Giaccia AJ: Hypoxia-mediated selection of cells with diminished apoptotic potential in solid tumors. Nature, 397: 88–91, 1996

    Google Scholar 

  25. Coldman AJ, Goldie JH: A model for the resistance of tumor cells to cancer chemotherapeutic agents. Math Biosci 65: 291–307, 1983

    Google Scholar 

  26. The Ludwig Breast Cancer Study Group: Combination adjuvant chemotherapy for node-positive breast cancer: inadequacy of a single perioperative cycle. N Engl J Med 319: 677–683, 1988

    Google Scholar 

  27. Sertoli MR, Bruzzi P, Pronzato P, Queirolo P, Amoroso D, Delmastro L, Venturini M, Vigani A, Bertelli G, Campora E, Boccardo F, Monzeglio C, Paganini E, Pastorino G, Canavese G, Catturich A, Cafiero F, Vecchio C, Miccoli P, Rubagotti A, Rosso R: Randomized cooperative study of perioperative chemotherapy in breast cancer. J Clin Oncol 13: 2712–2721, 1995

    Google Scholar 

  28. Hall EJ: Radiobiology for the Radiologist. 4th edn, Lippincott, Philadelphia, 1994

    Google Scholar 

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Authors and Affiliations

  1. Operations Research Center, Massachusetts Institute of Technology, Cambridge, MA, USA

    Damian R. Beil

  2. Sloan School of Management, Massachusetts Institute of Technology, Cambridge, MA, USA

    Lawrence M. Wein

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  1. Damian R. Beil
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  2. Lawrence M. Wein
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Beil, D.R., Wein, L.M. Sequencing Surgery, Radiotherapy and Chemotherapy: Insights from a Mathematical Analysis. Breast Cancer Res Treat 74, 279–286 (2002). https://doi.org/10.1023/A:1016357311845

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