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Mathematical modelling of prostate cancer growth and its application to hormone therapy. (English) Zbl 1211.37118

Summary: Hormone therapy in the form of androgen deprivation is a major treatment for advanced prostate cancer. However, if such therapy is overly prolonged, tumour cells may become resistant to this treatment and result in recurrent fatal disease. Long-term hormone deprivation also is associated with side effects poorly tolerated by patients. In contrast, intermittent hormone therapy with alternating on- and off-treatment periods is a possible clinical strategy to delay progression to hormone-refractory disease with the advantage of reduced side effects during the off-treatment periods. In this paper, we first overview previous studies on mathematical modelling of prostate tumour growth under intermittent hormone therapy. The model is categorized into a hybrid dynamical system because switching between on-treatment and off-treatment intervals is treated in addition to continuous dynamics of tumour growth. Next, we present an extended model of stochastic differential equations and examine how well the model is able to capture the characteristics of authentic serum prostate-specific antigen (PSA) data. We also highlight recent advances in time-series analysis and prediction of changes in serum PSA concentrations. Finally, we discuss practical issues to be considered towards establishment of mathematical model-based tailor-made medicine, which defines how to realize personalized hormone therapy for individual patients based on monitored serum PSA levels.

MSC:

37N25 Dynamical systems in biology
92C50 Medical applications (general)
37M10 Time series analysis of dynamical systems
60H30 Applications of stochastic analysis (to PDEs, etc.)
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[1] European urology 57 pp 10– (2010)
[2] 71 pp 2782– (1993)
[3] Berges, Clinical Cancer Research 1 (5) pp 473– (1995)
[4] Bhandari, Journal of Clinical Oncology 23 (32) pp 8212– (2005) · doi:10.1200/JCO.2005.03.2557
[5] Bladou, International journal of cancer. Journal international du cancer 67 (6) pp 785– (1996) · doi:10.1002/(SICI)1097-0215(19960917)67:6<785::AID-IJC6>3.0.CO;2-N
[6] 8 pp 35– (2006)
[7] Bruchovsky, Cancer Research 50 (8) pp 2275– (1990)
[8] Bruchovsky, Molecular urology 4 (3) pp 191– (2000)
[9] 107 pp 389– (2006)
[10] 109 pp 858– (2007)
[11] 7 pp 13– (2005)
[12] Chuu, Cancer Research 65 (6) pp 2082– (2005) · doi:10.1158/0008-5472.CAN-04-3992
[13] Dehm, Expert review of anticancer therapy 5 (1) pp 63– (2005) · doi:10.1586/14737140.5.1.63
[14] Edwards, BJU international 95 (9) pp 1320– (2005) · doi:10.1111/j.1464-410X.2005.05526.x
[15] Feldman, Nature reviews. Cancer 1 (1) pp 34– (2001) · doi:10.1038/35094009
[16] PROSTATE CANCER PROSTATE DIS 1 pp 289– (1998)
[17] Goldenberg, Urology 45 (5) pp 839– (1995) · doi:10.1016/S0090-4295(99)80092-2
[18] 18 pp 3789– (2008)
[19] Hirata, Journal of Theoretical Biology 264 (2) pp 517– (2010) · doi:10.1016/j.jtbi.2010.02.027
[20] Huggins, Cancer Research 1 (4) pp 293– (1941)
[21] Hurtado-Coll, Urology 60 (3 Suppl 1) pp 52– (2002)
[22] J NONLINEAR SCI 18 pp 593– (2008)
[23] Jackson, Neoplasia (New York, N.Y.) 6 (6) pp 697– (2004) · doi:10.1593/neo.04259
[24] DISC CONT DYN SYST B 4 pp 187– (2004)
[25] Kokontis, Cancer Research 54 (6) pp 1566– (1994)
[26] Kokontis, Molecular Endocrinology 12 (7) pp 941– (1998) · doi:10.1210/me.12.7.941
[27] Kokontis, The Prostate 65 (4) pp 287– (2005) · doi:10.1002/pros.20285
[28] Ochiai, The Journal of urology 177 (3) pp 903– (2007) · doi:10.1016/j.juro.2006.10.072
[29] Pether, BJU international 93 (3) pp 258– (2004) · doi:10.1111/j.1464-410X.2004.04597.x
[30] Rao, BJU international 101 (1) pp 5– (2008) · doi:10.1111/j.1464-410X.2007.07488.x
[31] Rashid, The Oncologist 9 (3) pp 295– (2004) · doi:10.1634/theoncologist.9-3-295
[32] Rennie, The Journal of steroid biochemistry and molecular biology 37 (6) pp 843– (1990) · doi:10.1016/0960-0760(90)90430-S
[33] Sato, The Journal of steroid biochemistry and molecular biology 58 (2) pp 139– (1996) · doi:10.1016/0960-0760(96)00018-0
[34] Scher, Endocrine-Related Cancer 11 (3) pp 459– (2004) · doi:10.1677/erc.1.00525
[35] Shaw, BJU international 99 (5) pp 1056– (2007) · doi:10.1111/j.1464-410X.2007.06770.x
[36] Shimada, Mathematical biosciences 214 (1-2) pp 134– (2008) · Zbl 1143.92023 · doi:10.1016/j.mbs.2008.03.001
[37] PHIL TRANS R SOC A 368 pp 5045– (2010) · Zbl 1211.93069 · doi:10.1098/rsta.2010.0220
[38] Physica. D 237 pp 2616– (2008)
[39] PHYS. LETT. A 373 pp 3134– (2009)
[40] MATH MOD METH APPL SCI 19 pp 2177– (2009)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.