Dynamic optimization of a linear-quadratic model with incomplete repair and volume-dependent sensitivity and repopulation

International Journal of Radiation Oncology Biology Physics

Volumn 47, Issue 4, 2000, Pages 1073-1083

  Wein, Lawrence M ^a   Cohen, Jonathan E ^b   Wu, Joseph T ^b  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^b MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Dynamic optimization; Linear quadratic; Reoxygenation; Repair; Repopulation

Indexed keywords

ANGIOGENESIS; ARTICLE; CELL DENSITY; CELL REGENERATION; FRACTIONATION; HYPOXIA; MATHEMATICAL MODEL; PRIORITY JOURNAL; RADIOSENSITIVITY; REOXYGENATION; TUMOR MODEL;

ALGORITHMS; CELL DIVISION; CELL HYPOXIA; DNA REPAIR; DOSE FRACTIONATION; DOSE-RESPONSE RELATIONSHIP, RADIATION; LINEAR MODELS; MODELS, BIOLOGICAL; OXYGEN CONSUMPTION; RADIATION TOLERANCE; RADIOBIOLOGY; RADIOTHERAPY, COMPUTER-ASSISTED; RELATIVE BIOLOGICAL EFFECTIVENESS; SPHEROIDS, CELLULAR;

EID: 0034237241     PISSN: 03603016     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0360-3016(00)00534-4     Document Type: Article

References (70)

1. Fowler J.F. The linear-quadratic formula and progress in fractionated radiotherapy. Br J Radiol. 62:1989;679-694.
2. Thames H.D., Hendry J.H. Fractionation in radiotherapy. 1987;Taylor & Francis, London.
3. Orton C.G., Brenner D.J., Dale R.G., et al. Radiobiology. Nag S. High dose rate brachytherapy A textbook . 1994;11-25 Futura, Armonk, NY.
4. Withers H.R. Biological basis of radiation therapy for cancer. Lancet. 339:1992;156-159.
5. Thames H.D. An 'incomplete repair' model for survival after fractionated and continuous irradiations. Int J Radiat Oncol Biol Phys. 47:1985;319-339.
6. Travis E.L., Tucker S.L. Iso-effect models and fractionated radiation therapy. Int J Radiat Oncol Biol Phys. 13:1987;283-287.
7. Chen P.-L., Brenner D.J., Sachs R.K. Ionizing radiation damage to cells Effects of cell cycle redistribution . Math Biosc. 126:1995;147-170.
8. Hahnfeldt P., Hlatky L. Resensitization due to redistribution of cells in the phases of the cell cycle during arbitrary radiation protocols. Radiat Res. 145:1996;134-143.
9. King C.R., Nath R., Rockwell S. Effects of continuous low dose-rate irradiation Computer simulations . Cell Tissue Kinet. 21:1998;339-351.
10. Yakovlev AY, Zorin AV. Computer simulation in cell radiobiology. In: Lecture notes in biomathematics. Vol. 74. Berlin: Springer-Verlag; 1988.
11. 2 block, and cell division. Radiat Res. 124:1990;201-207.
12. Zaider M., Wuu C.S., Minerbo G.N. The combined effects of sublethal damage repair, cellular repopulation and redistribution in the mitotic cycle. I. Survival probabilities after exposure to radiation. Radiat Res. 145:1996;457-466.
13. Steel G.G. Cell synchronization unfortunately may not benefit cancer therapy. Radiother Oncol. 32:1994;96-97.
14. Wouters B.G., Brown J.M. Cells at intermediate oxygen levels can be more important than the "hypoxic fraction" in determining tumor response to fractionated radiotherapy. Radiat Res. 147:1997;541-550.
15. Jones B., Dale R.G. Cell loss factors and the linear-quadratic model. Radiother Oncol. 37:1995;136-139.
16. Hlatky L.R., Hahnfeldt P., Sachs R.K. Influence of time-dependent, stochastic heterogeneity on the radiation response of a cell population. Math Biosci. 122:1994;201-220.
17. Brenner D.J., Hlatky L.R., Hahnfeldt P.J., et al. A convenient extension of the linear-quadratic model to include redistribution and reoxygenation. Int J Radiat Oncol Biol Phys. 32:1995;379-390.
18. Withers H.R., Peters L.J. Biologic aspects of radiation therapy. Gilbert G.H. Textbook of radiotherapy. 1980;103-180 Lea and Feibiger, Philadelphia.
19. Withers H.R., Peters L.J., Thames H.D., et al. Hyperfractionation. Int J Radiat Oncol Biol Phys. 8:1982;1807-1809.
20. Fowler J.F. How worthwhile are short schedules? A series of exploratory calculations . Radiother Oncol. 18:1990;165-181.
21. Jones B., Tan L.T., Dale R.G. Derivation of the optimum dose per fraction from the linear quadratic model. Br J Radiol. 68:1995;894-902.
22. Brenner D.J., Hall E.J., Huang Y., et al. Optimizing the time course of brachytherapy and other accelerated radiotherapeutic proptocols. Int J Radiat Oncol Biol Phys. 29:1994;893-901.
23. Gray L.H., Conger A.D., Ebert M., et al. The concentration of oxygen dissolved in tissues at the time of irradiation as a factor in radiotherapy. Br J Radiol. 26:1953;638-648.
24. Powers W.E., Tolmach L.J. A multicomponent x-ray survival curve for mouse lymphosarcoma cells irradiated in vivo. Nature. 197:1963;710-711.
25. Thomlinson R.H., Craddock E.A. The gross response of an experimental tumour to single doses of X-rays. Br J Cancer. 21:1967;108-123.
26. Fowler J.F. The phantom of tumor treatment - Continually rapid proliferation unmasked. Radiother Oncol. 22:1991;156-158.
27. Sham E., Durand R.E. Cell kinetics and repopulation during multifraction irradiation of spheroids. Radiother Oncol. 46:1998;201-207.
28. Duchting W., Ulmer W., Ginsberg T. Cancer A challenge for control theory and computer modeling . Eur J Cancer. 32A:1996;1283-1292.
29. O'Donoghue J.A. The response of tumours with Gompertzian growth characteristics to fractionated radiotherapy. Int J Radiat Oncol Biol Phys. 72:1997;325-339.
30. Sutherland R.M., McCredie J.A., Inch W.R. Growth of multicell spheroids in tissue culture as a model of nodular carcinoma. J Natl Cancer Inst. 46:1971;113-120.
31. Thomlinson R.H., Gray L.H. The histological structure of some human lung cancers and the possible implications for radiotherapy. Br J Cancer. 9:1955;539-549.
32. Conger A.D., Ziskin M.C. Growth of mammalian multicellular tumor spheroids. Cancer Res. 43:1983;556-560.
33. Tannock I.F. The relation between cell proliferation and the vascular system in a transplanted mouse mammary tumor. Br J Cancer. 22:1968;258-273.
34. Hall E.J. Radiobiology for the radiologist. 4th ed. 1994;Lippincott, Philadelphia.
35. Tannock I.F. Oxygen diffusion and the distribution of cellular radiosensitivity in tumors. Br J Radiol. 45:1972;515-524.
36. Alper T., Howard-Flanders P. The role of oxygen in modifying the radiosensitivity of E. coli B. Nature. 178:1956;978-979.
37. Froese G. The respiration of ascites tumor cells at low oxygen concentrations. Biochem Biophys Acta. 57:1962;509-519.
38. Schultheiss T.E., Zagars G.K., Peters L.J. An explanatory hypothesis for early- and late-effect parameter values in the LQ model. Radiother Oncol. 9:1987;241-248.
39. Sachs R.K., Hahnfeld P., Brenner D.J. The link between low-LET dose-response relations and the underlying kinetics of damage production/repair/misrepair. Int J Radiat Oncol Biol Phys. 72:1997;351-374.
40. Byrne H.M., Chaplain M.A.J. Growth of necrotic tumours in the presence and absence of inhibitors. Math Biosci. 135:1996;187-216.
41. Barendsen G.W. Dose fractionation, dose rate and iso-effect relationships for normal tissue responses. Int J Radiat Oncol Biol Phys. 8:1982;1981-1997.
42. Tucker S.L., Taylor J.M.G. Improved models of tumour cure. Int J Radiat Oncol Biol Phys. 70:1996;539-553.
43. Turesson I., Thames H.D. Repair capacity and kinetics of human skin during fractionated radiotherapy Erythema, desquamation, and telangiectasia after 3 and 5 year's follow-up . Radiother Oncol. 15:1989;169-188.
44. Harrison J.M. Brownian motion and stochastic flow systems. 1985;John Wiley and Sons, New York.
45. Pontryagin L.S., Boltyanskii V.G., Gamkrelidze R.V., et al. The mathematical theory of optimal processes. 1962;Interscience, New York.
46. Athans M., Falb P.L. Optimal control. 1966;McGraw-Hill, New York.
47. Luus R. On the application of iterative dynamic programming to singular optimal control problems. IEEE Trans Automatic Control. 37:1992;1802-1806.
48. Folkman J. The vascularization of tumors. Sci Am. 234:1976;58-73.
49. O'Donoghue J.A., Bardies M., Wheldon T.E. Relationships between tumor size and curability for uniformly targeted therapy with beta-emitting radionuclides. J Nucl Med. 36:1995;1902-1909.
50. Fowler J.F. Potential for increasing the differential response between tumors and normal tissues Can proliferation rate be used? Int J Radiat Oncol Biol Phys. 12:1986;641-645.
51. Thames H.D., Bentzen S.M., Turesson I., et al. Time-dose factors in radiotherapy A review of human data . Radiother Oncol. 19:1990;219-235.
52. Hethcote H., Waltman P. Theoretical determination of optimal treatment schedules for radiation therapy. Radiat Res. 56:1973;150-161.
53. Almquist K.J., Banks H.T. A theoretical and computational method for determining optimal treatment schedules in fractionated radiation therapy. Math Biosci. 29:1976;159-179.
54. Norton L., Simon R. Tumor size, sensitivity to therapy, and design of treatment schedules. Cancer Treat Rep. 61:1977;1307-1317.
55. Norton L., Simon R. The Norton-Simon hypothesis revisited. Cancer Treat Rep. 70:1986;163-169.
56. Skipper H.E., Schabel F.M. Jr, Wilcox W.S. Experimental evaluation of potential anticancer agents. XIII. On the criteria and kinetics associated with "curability" of experimental leukemia. Cancer Chemother Rep. 35:1964;1-111.
57. Laird A.K. Dynamics of tumor growth. Br J Cancer. 18:1964;490-502.
58. Burton A.C. Rate of growth of solid tumors as a problem of diffusion. Growth. 30:1966;157-176.
59. Ang K.K., Peters L.J., Weber R.S., et al. Concomitant boost radiotherapy schedules in the treatment of carcinoma of the oropharynx andnasopharynx. Int J Radiat Oncol Biol Phys. 19:1990;1339-1345.
60. Peters L.J., Withers H.R., Thames H.D. Radiobiological bases for multiple daily fractionation. Karcher K.H., Kogelnik H.D., Reinartz G. Progress in radio-oncology II. 1982;317-323 Raven Press, New York.
61. Knee R., Fields R.S., Peters L.J. Concomitant boost radiotherapy for advanced squamous cell carcinoma of the head and neck. Radiother Oncol. 4:1985;1-7.
62. Peters L.J. Accelerated fractionation using concomitant boost A contribution of radiobiology to radiotherapy . Br J Radiat. 24:(Suppl.):1992;200-203.
63. Schwade J., Markoe A., Abitbol A., et al. Accelerating hyperfractionation for carcinoma of the head and neck. Semin Radiat Oncol. 2:1992;51-53.
64. Maciejewski B., Zajusz A., Pilecki B., et al. Escalated hyperfractionation and stimulation of acute mucosal reaction in radiotherapy for cancer of the oral cavity an oropharynx. Semin Radiat Oncol. 2:1992;54-57.
65. Harari P.M. Adding dose escalation to accelerated hyperfractionation for head and neck cancer. Semin Radiat Oncol. 2:1992;58-61.
66. Brown J.M., Giaccia A.J. The unique physiology of solid tumors Opportunities (and problems) for cancer therapy . Cancer Res. 58:1998;1408-1416.
67. Langer R., Conn H., Vacanti J., et al. Control of tumour growth in animals by infusion of an angiogenesis inhibitor. Proc Natl Acad Sci USA. 77:1980;4331.
68. Thompson W.D., Shiach K.J., Fraser R.A., et al. Tumors acquire their vasculature by vessel incorporation, not vessel ingrowth. J Pathol. 151:1987;323-332.
69. Khalil A.A., Horsman M.R., Overgaard J. The importance of determining necrotic fraction when studying the effect of tumor volume on tissue oxygenation. Acta Oncol. 34:1995;297-300.
70. Stadler P., Feldmann H.J., Creighton C., et al. Changes in tumor oxygenation during combined treatment with split-course radiotherapy and chemotherapy in patients with head and neck cancer. Radiother Oncol. 48:1998;157-164.