title: A partial differential equation model and its reduction to an ordinary differential equation model for prostate tumor growth under intermittent hormone therapy.
abstract: Hormonal therapy with androgen suppression is a common treatment for advanced prostate tumors. The emergence of androgen-independent cells, however, leads to a tumor relapse under a condition of long-term androgen deprivation. Clinical trials suggest that intermittent androgen suppression (IAS) with alternating on- and off-treatment periods can delay the relapse when compared with continuous androgen suppression (CAS). In this paper, we propose a mathematical model for prostate tumor growth under IAS therapy. The model elucidates initial hormone sensitivity, an eventual relapse of a tumor under CAS therapy, and a delay of a relapse under IAS therapy, which are due to the coexistence of androgen-dependent cells, androgen-independent cells resulting from reversible changes by adaptation, and androgen-independent cells resulting from irreversible changes by genetic mutations. The model is formulated as a free boundary problem of partial differential equations that describe the evolution of populations of the abovementioned three types of cells during on-treatment periods and off-treatment periods. Moreover, the model can be transformed into a piecewise linear ordinary differential equation model by introducing three new volume variables, and the study of the resulting model may help to devise optimal IAS schedules.
authors: Department of Applied Mathematics, Dong Hua University, Shanghai , 200051, People's Republic of China, taoys@dhu.edu.cn.
authors: Youshan
authors: Y
authors: Tao
authors: Qian
authors: Q
authors: Guo
authors: Kazuyuki
authors: K
authors: Aihara
mesh_terms: D006727:Hormone Antagonists / Q000008:administration & dosage / Q000494:pharmacology* / Q000627:therapeutic use; D006801:Humans; D008297:Male; D018448:Models, Immunological; D009364:Neoplasm Recurrence, Local / Q000517:prevention & control; D009376:Neoplasms, Hormone-Dependent / Q000188:drug therapy* / Q000276:immunology; D009716:Numerical Analysis, Computer-Assisted; D017430:Prostate-Specific Antigen / Q000097:blood; D011471:Prostatic Neoplasms / Q000188:drug therapy* / Q000276:immunology
chemical_list: D006727:Hormone Antagonists; D017430:Prostate-Specific Antigen
references: Int J Cancer. 1996 Sep 17;67(6):785-90
references: 8824549
references: Math Biosci Eng. 2013 Feb;10(1):263-78
references: 23311372
references: Eur Urol. 2010 Jan;57(1):49-59
references: 19683858
references: Math Biosci. 2003 Feb;181(2):177-207
references: 12445761
references: Cancer Res. 1990 Apr 15;50(8):2275-82
references: 2317815
references: Mol Urol. 2000 Fall;4(3):191-9;discussion 201
references: 11062374
references: Philos Trans A Math Phys Eng Sci. 2006 Jun 15;364(1843):1563-78
references: 16766361
references: Chaos. 2010 Dec;20(4):045125
references: 21198137
references: J Math Biol. 2003 Nov;47(5):391-423
references: 14605856
references: Nat Rev Cancer. 2001 Oct;1(1):34-45
references: 11900250
references: Philos Trans A Math Phys Eng Sci. 2010 Nov 13;368(1930):5045-59
references: 20921011
references: J Theor Biol. 2010 May 21;264(2):517-27
references: 20176032
references: Cancer. 2007 Mar 1;109(5):858-67
references: 17265527
references: Philos Trans A Math Phys Eng Sci. 2010 Nov 13;368(1930):5029-44
references: 20921010
references: J Steroid Biochem Mol Biol. 1990 Dec 20;37(6):843-7
references: 2126735
references: Neoplasia. 2004 Nov-Dec;6(6):697-704
references: 15720795
references: Cancer. 1993 May 1;71(9):2782-90
references: 7682149
references: Cancer. 2006 Jul 15;107(2):389-95
references: 16783817