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Volumn 69, Issue 4, 2014, Pages 817-838

A partial differential equation model and its reduction to an ordinary differential equation model for prostate tumor growth under intermittent hormone therapy

Author keywords

Androgen independence; Free boundary problem; Hybrid system; Intermittent androgen suppression; Partial differential equations; Prostate cancer

Indexed keywords


EID: 84882518867     PISSN: 03036812     EISSN: 14321416     Source Type: Journal    
DOI: 10.1007/s00285-013-0718-y     Document Type: Article
Times cited : (21)

References (30)
  • 1
    • 70449523110 scopus 로고    scopus 로고
    • Potential benefits of intermittent androgen suppression therapy in the treatment of prostate cancer: A systematic review of the literature
    • Abrahamsson PA (2010) Potential benefits of intermittent androgen suppression therapy in the treatment of prostate cancer: a systematic review of the literature. Eur Urol 57:49–59
    • (2010) Eur Urol , vol.57 , pp. 49-59
    • Abrahamsson, P.A.1
  • 2
    • 0022799748 scopus 로고    scopus 로고
    • A simplified mathematical model of tumor growth
    • Adam JA (1996) A simplified mathematical model of tumor growth. Math Biosci 81:224–229
    • (1996) Math Biosci , vol.81 , pp. 224-229
    • Adam, J.A.1
  • 3
    • 0027416692 scopus 로고
    • Effects of intermittent androgen suppression on androgen-dependent tumors: Apoptosis and serum prostate-specific antigen
    • Akakura K, Bruchovsky N, Goldenbeg SL, Rennie PS, Buckley AR, Sullivan LD (1993) Effects of intermittent androgen suppression on androgen-dependent tumors: apoptosis and serum prostate-specific antigen. Cancer 71:2782–2790
    • (1993) Cancer , vol.71 , pp. 2782-2790
    • Akakura, K.1    Bruchovsky, N.2    Goldenbeg, S.L.3    Rennie, P.S.4    Buckley, A.R.5    Sullivan, L.D.6
  • 4
    • 44349107599 scopus 로고    scopus 로고
    • On the foundations of cancer modelling: Selected topics, speculations and perspective
    • Bellomo N, Li NK, Maini PK (2008) On the foundations of cancer modelling: selected topics, speculations and perspective. Math Mod Meth Appl Sci 18:593–646
    • (2008) Math Mod Meth Appl Sci , vol.18 , pp. 593-646
    • Bellomo, N.1    Li, N.K.2    Maini, P.K.3
  • 5
    • 0029956738 scopus 로고    scopus 로고
    • Cell proliferation and apoptosis during prostatic tumor xenograft involution and regrowth after castration
    • Bladou F, Vessella RL, Buhler KR, Ells WJ, True LD, Lange PH (1996) Cell proliferation and apoptosis during prostatic tumor xenograft involution and regrowth after castration. Int. J. Cancer 7:785–790
    • (1996) Int. J. Cancer , vol.7 , pp. 785-790
    • Bladou, F.1    Vessella, R.L.2    Buhler, K.R.3    Ells, W.J.4    True, L.D.5    Lange, P.H.6
  • 8
    • 33745813551 scopus 로고    scopus 로고
    • Final results of the Canadian prospective phase II trial of intermittent androgen suppression for men in biochemical recurrence after radiotherapy for locally advanced prostate cancer: Clinical parameters
    • Bruchovsky N, Klotz L, Crook J, Malone S, Ludgte C, Morris WJ, Gleave ME, Goldenberg SL (2006) Final results of the Canadian prospective phase II trial of intermittent androgen suppression for men in biochemical recurrence after radiotherapy for locally advanced prostate cancer: clinical parameters. Cancer 107:389–395
    • (2006) Cancer , vol.107 , pp. 389-395
    • Bruchovsky, N.1    Klotz, L.2    Crook, J.3    Malone, S.4    Ludgte, C.5    Morris, W.J.6    Gleave, M.E.7    Goldenberg, S.L.8
  • 9
    • 33847384225 scopus 로고    scopus 로고
    • Locally advanced prostate cancer – biochemical results from a prospective phase II study of intermittent androgen suppression for men with evidence of prostate-specific antigen recurrence after radiotherapy
    • Bruchovsky N, Klotz L, Crook J, Larry S, Goldenberg SL (2007) Locally advanced prostate cancer – biochemical results from a prospective phase II study of intermittent androgen suppression for men with evidence of prostate-specific antigen recurrence after radiotherapy. Cancer 109:858–867
    • (2007) Cancer , vol.109 , pp. 858-867
    • Bruchovsky, N.1    Klotz, L.2    Crook, J.3    Larry, S.4    Goldenberg, S.L.5
  • 11
    • 0035496220 scopus 로고    scopus 로고
    • The development of androgen-independent prostate cancer
    • Feldman BJ, Feldman D (2001) The development of androgen-independent prostate cancer. Nat Rev Cancer 1:34–45
    • (2001) Nat Rev Cancer , vol.1 , pp. 34-45
    • Feldman, B.J.1    Feldman, D.2
  • 12
    • 35348819870 scopus 로고    scopus 로고
    • Mathematical analysis and challenges arising from models of tumor growth
    • Friedman A (2007) Mathematical analysis and challenges arising from models of tumor growth. Math Mod Meth Appl Sci 17:1751–1772
    • (2007) Math Mod Meth Appl Sci , vol.17 , pp. 1751-1772
    • Friedman, A.1
  • 13
    • 85130332650 scopus 로고    scopus 로고
    • Bifurcation from stability to instability for a free boundary problem arising in a tumor model
    • Friedman A, Hu B (2006) Bifurcation from stability to instability for a free boundary problem arising in a tumor model. Arch Ration Mech Anal 180:293–330
    • (2006) Arch Ration Mech Anal , vol.180 , pp. 293-330
    • Friedman, A.1    Hu, B.2
  • 14
    • 1342310604 scopus 로고    scopus 로고
    • Analysis of a model of a virus that replicates selectively in tumor cells
    • Friedman A, Tao Y (2003) Analysis of a model of a virus that replicates selectively in tumor cells. J Math Biol 47:391–423
    • (2003) J Math Biol , vol.47 , pp. 391-423
    • Friedman, A.1    Tao, Y.2
  • 15
    • 0000128125 scopus 로고
    • Models for the growth of a solid tumor by diffusion
    • Greenspan H (1972) Models for the growth of a solid tumor by diffusion. Stud Appl Math 52:317–340
    • (1972) Stud Appl Math , vol.52 , pp. 317-340
    • Greenspan, H.1
  • 16
    • 60749116929 scopus 로고    scopus 로고
    • Mathematical modeling of prostate tumor growth under intermittent androgen suppression with partial differential equations
    • Guo Q, Tao Y, Aihara K (2008) Mathematical modeling of prostate tumor growth under intermittent androgen suppression with partial differential equations. Int J Bifurcat Chaos 18:3789–3797
    • (2008) Int J Bifurcat Chaos , vol.18 , pp. 3789-3797
    • Guo, Q.1    Tao, Y.2    Aihara, K.3
  • 17
    • 77951652729 scopus 로고    scopus 로고
    • Development of a mathematical model that predicts the outcome of hormone therapy for prostate cancer
    • Hirata Y, Bruchovsky N, Aihara K (2010a) Development of a mathematical model that predicts the outcome of hormone therapy for prostate cancer. J Theor Biol 264:517–527
    • (2010) J Theor Biol , vol.264 , pp. 517-527
    • Hirata, Y.1    Bruchovsky, N.2    Aihara, K.3
  • 18
    • 78650691811 scopus 로고    scopus 로고
    • Hybrid optimal scheduling for intermittent androgen suppression of prostate cancer
    • Hirata Y, di Bernardo M, Bruchovsky N, Aihara K (2010b) Hybrid optimal scheduling for intermittent androgen suppression of prostate cancer. Chaos 20:045125
    • (2010) Chaos , vol.20 , pp. 045125
    • Hirata, Y.1    di Bernardo, M.2    Bruchovsky, N.3    Aihara, K.4
  • 19
    • 84867969197 scopus 로고    scopus 로고
    • A mathematical model of intermittent androgen suppression for prostate cancer
    • Ideta AM, Tanaka G, Takeuchi T, Aihara K (2008) A mathematical model of intermittent androgen suppression for prostate cancer. J Nonlinear Sci 18:593–614
    • (2008) J Nonlinear Sci , vol.18 , pp. 593-614
    • Ideta, A.M.1    Tanaka, G.2    Takeuchi, T.3    Aihara, K.4
  • 20
    • 1042279438 scopus 로고    scopus 로고
    • A mathematical model of prostate tumor growth and androgen-independent relapse
    • Jackson TL (2004a) A mathematical model of prostate tumor growth and androgen-independent relapse. Discrete Contin Dyn Syst B 4:187–201
    • (2004) Discrete Contin Dyn Syst B , vol.4 , pp. 187-201
    • Jackson, T.L.1
  • 21
    • 11144352221 scopus 로고    scopus 로고
    • A mathematical investigation of multiple pathways to recurrent prostate cancer: Comparsion with experiment data
    • Jackson TL (2004b) A mathematical investigation of multiple pathways to recurrent prostate cancer: comparsion with experiment data. Neoplasia 6:697–704
    • (2004) Neoplasia , vol.6 , pp. 697-704
    • Jackson, T.L.1
  • 22
    • 0025684708 scopus 로고
    • Loss of androgen dependence is associated with an increase in tumorigenic stem cells and resistance to cell-death genes
    • Rennie PS, Bruchovsky N, Coldman AJ (1990) Loss of androgen dependence is associated with an increase in tumorigenic stem cells and resistance to cell-death genes. J Steroid Biochem Mol Biol 37:843–847
    • (1990) J Steroid Biochem Mol Biol , vol.37 , pp. 843-847
    • Rennie, P.S.1    Bruchovsky, N.2    Coldman, A.J.3
  • 23
    • 77951652457 scopus 로고    scopus 로고
    • Hormones and Cancer
    • Tannock IF, Hill RP, Bristow RG, Harrington L, (eds), McGraw-Hill, New York
    • Rennie P, Read J, Murphy L (2005) Hormones and Cancer. In: Tannock IF, Hill RP, Bristow RG, Harrington L (eds) The basic science of oncology. McGraw-Hill, New York, pp 400–430
    • (2005) The basic science of oncology , pp. 400-430
    • Rennie, P.1    Read, J.2    Murphy, L.3
  • 24
    • 78649366933 scopus 로고    scopus 로고
    • Piecewise affine systems modelling for optimizing hormone therapy of prostate cancer
    • Suzuki T, Bruchovsky N, Aihara K (2010) Piecewise affine systems modelling for optimizing hormone therapy of prostate cancer. Phil Trans R Soc A 368:5045–5059
    • (2010) Phil Trans R Soc A , vol.368 , pp. 5045-5059
    • Suzuki, T.1    Bruchovsky, N.2    Aihara, K.3
  • 25
    • 78649369807 scopus 로고    scopus 로고
    • Mathematical modelling of prostate cancer growth and its application to hormone therapy
    • Tanaka G, Hirata Y, Goldenberg SL, Bruchovsky N, Aihara K (2010a) Mathematical modelling of prostate cancer growth and its application to hormone therapy. Phil Trans R Soc 368:5029–5044
    • (2010) Phil Trans R Soc , vol.368 , pp. 5029-5044
    • Tanaka, G.1    Hirata, Y.2    Goldenberg, S.L.3    Bruchovsky, N.4    Aihara, K.5
  • 26
    • 30644465735 scopus 로고    scopus 로고
    • An elliptic-hyperbolic free boundary problem modelling cancer therapy
    • Tao Y, Chen M (2006) An elliptic-hyperbolic free boundary problem modelling cancer therapy. Nonlinearity 19:419–440
    • (2006) Nonlinearity , vol.19 , pp. 419-440
    • Tao, Y.1    Chen, M.2
  • 27
    • 75649115406 scopus 로고    scopus 로고
    • A model at the macroscopic scale of prostate tumor growth under intermittent androgen suppression
    • Tao Y, Guo Q, Aihara K (2009) A model at the macroscopic scale of prostate tumor growth under intermittent androgen suppression. Math Mod Meth Appl Sci 19:2177–2201
    • (2009) Math Mod Meth Appl Sci , vol.19 , pp. 2177-2201
    • Tao, Y.1    Guo, Q.2    Aihara, K.3
  • 28
    • 77953325145 scopus 로고    scopus 로고
    • A mathematical model of prostate tumor growth under hormone therapy with mutation inhibitor
    • Tao Y, Guo Q, Aihara K (2010b) A mathematical model of prostate tumor growth under hormone therapy with mutation inhibitor. J Nonlinear Sci 20:219–240
    • (2010) J Nonlinear Sci , vol.20 , pp. 219-240
    • Tao, Y.1    Guo, Q.2    Aihara, K.3
  • 29
    • 84874741533 scopus 로고    scopus 로고
    • On a mathematical model of tumor growth based on cancer stem cells
    • Tello JI (2013) On a mathematical model of tumor growth based on cancer stem cells. Math Biosci Eng 10:263–278
    • (2013) Math Biosci Eng , vol.10 , pp. 263-278
    • Tello, J.I.1
  • 30
    • 0037299744 scopus 로고    scopus 로고
    • Mathematical modelling of drug transport in tumour multicell spheroids and monolayer cultures
    • Ward JP, King JR (2003) Mathematical modelling of drug transport in tumour multicell spheroids and monolayer cultures. Math Biosci 181:177–207
    • (2003) Math Biosci , vol.181 , pp. 177-207
    • Ward, J.P.1    King, J.R.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.