June  2013, 18(4): 945-967. doi: 10.3934/dcdsb.2013.18.945

Modeling prostate cancer response to continuous versus intermittent androgen ablation therapy

1. 

Department of Mathematics, Florida State University, Tallahassee, FL 32306, United States

2. 

The Ohio State University, Department of Mathematics, Columbus, OH 43210

Received  March 2012 Revised  April 2012 Published  February 2013

Due to its dependence on androgens, metastatic prostate cancer is typically treated with continuous androgen ablation. However, such therapy eventually fails due to the emergence of castration-resistance cells. It has been hypothesized that intermittent androgen ablation can delay the onset of this resistance. In this paper, we present a biochemically-motivated ordinary differential equation model of prostate cancer response to anti-androgen therapy, with the aim of predicting optimal treatment protocols based on individual patient characteristics. Conditions under which intermittent scheduling is preferable over continuous therapy are derived analytically for a variety of castration-resistant cell phenotypes. The model predicts that while a cure is not possible for androgen-independent castration-resistant cells, continuous therapy results in longer disease-free survival periods. However, for androgen-repressed castration-resistant cells, intermittent therapy can significantly delay the emergence of resistance, and in some cases induce tumor regression. Numerical simulations of the model lead to two interesting cases, where even though continuous therapy may be non-viable, an optimally chosen intermittent schedule leads to tumor regression, and where a sub-optimally chosen intermittent schedule can initially appear to result in a cure, it eventually leads to resistance emergence. These results demonstrate the model's potential impact in a clinical setting.
Citation: Harsh Vardhan Jain, Avner Friedman. Modeling prostate cancer response to continuous versus intermittent androgen ablation therapy. Discrete & Continuous Dynamical Systems - B, 2013, 18 (4) : 945-967. doi: 10.3934/dcdsb.2013.18.945
References:
[1]

D. B. Agus, C. Cordon-Cardo, W. Fox, M. Drobnjak, A. Koff, D. W. Golde and H. I. Scher, Prostate cancer cell cycle regulators: Response to androgen withdrawal and development of androgen independence,, J. Natl. Cancer. Inst., 91 (1999), 1869.  doi: 10.1093/jnci/91.21.1869.  Google Scholar

[2]

G. L. Andriole, E. D. Crawford, R. L. Grubb III, S. S. Buys, D. Chia, T. R. Church, M. N. Fouad, E. P. Gelmann, P. A. Kvale, D. J. Reding, J. L. Weissfeld, L. A. Yokochi, B. O'Brien, J. D. Clapp, J. M. Rathmell, T. L. Riley, R. B. Hayes, B. S. Kramer, G. Izmirlian, A. B. Miller, P. F. Pinsky, P. C. Prorok, J. K. Gohagan and C. D. Berg, Mortality results from a randomized prostate-cancer screening trial,, N. Engl. J. Med., 360 (2009), 1310.  doi: 10.1056/NEJMoa0810696.  Google Scholar

[3]

R. R. Berges, J. Vukanovic, J. I. Epstein, M. CarMichel, L. Cisek, D. E. Johnson, R. W. Veltri, P. C. Walsh and J. T. Isaacs, Implication of cell kinetic changes during the progression of human prostatic cancer,, Clin. Cancer Res., 1 (1995), 473.   Google Scholar

[4]

G. Birkenmeier, F. Struck and R. Gebhardt, Clearance mechanism of prostate specific antigen and its complexes with alpha2-macroglobulin and alpha1-antichymotrypsin,, J. Urol., 162 (1999), 897.  doi: 10.1097/00005392-199909010-00086.  Google Scholar

[5]

M. L. Cher, G. S. Bova, D. H. Moore, E. J. Small, P. R. Carroll, S. S. Pin, J. I. Epstein, W. B. Isaacs and R. H. Jensen, Genetic alterations in untreated metastases and androgen-independent prostate cancer detected by comparative genomic hybridization and allelotyping,, Cancer Res., 56 (1996), 3091.   Google Scholar

[6]

M. W. Dunn and M. W. Kazer, Prostate cancer overview,, Semin. Oncol. Nurs., 27 (2011), 241.  doi: 10.1016/j.soncn.2011.07.002.  Google Scholar

[7]

S. E. Eikenberry, J. D. Nagy and Y. Kuang, The evolutionary impact of androgen levels on prostate cancer in a multi-scale mathematical model,, Biol. Direct, 5 (2010), 24.  doi: 10.1186/1745-6150-5-24.  Google Scholar

[8]

B. J. Feldman and D. Feldman, The development of androgen-independent prostate cancer,, Nat. Rev. Cancer, 1 (2001), 34.  doi: 10.1038/35094009.  Google Scholar

[9]

D. Gillatt, Antiandrogen treatments in locally advanced prostate cancer: are they all the same?,, J. Cancer Res. Clin. Oncol., 132 (2006).  doi: 10.1007/s00432-006-0133-5.  Google Scholar

[10]

R. F. Gittes, Carcinoma of the prostate,, N. Engl. J. Med., 324 (1991), 236.  doi: 10.1056/NEJM199101243240406.  Google Scholar

[11]

M. Gleave, S. L. Goldenberg, N. Bruchovsky and P. Rennie, Intermittent androgen suppression for prostate cancer: Rationale and clinical experience,, Prostate Cancer Prostatic Dis., 1 (1998), 289.  doi: 10.1038/sj.pcan.4500260.  Google Scholar

[12]

S. L. Goldenberg, N. Bruchovsky, M. E. Gleave, L. D. Sullivan and K. Akakura, Intermittent androgen suppression in the treatment of prostate cancer: A preliminary report,, Urology, 45 (1995), 839.  doi: 10.1016/S0090-4295(99)80092-2.  Google Scholar

[13]

C. W. Gregory, R. T. Johnson, J. L. Mohler Jr, F. S. French and E. M. Wilson, Androgen receptor stabilization in recurrent prostate cancer is associated with hypersensitivity to low androgen,, Urology, 61 (2001), 2892.   Google Scholar

[14]

M. A. Haider, T. H. van der Kwast, J. Tanguay, A. J. Evans, A. Hashmi, G. Lockwood and J. Trachtenberg, Combined T2-weighted and diffusion-weighted MRI for localization of prostate cancer,, AJR Am J Roentgenol., 189 (2007), 323.  doi: 10.2214/AJR.07.2211.  Google Scholar

[15]

C. A. Heinlein and C. Chang, Androgen receptor in prostate cancer,, Endocr. Rev., 25 (2004), 276.  doi: 10.1210/er.2002-0032.  Google Scholar

[16]

Y. Hirata, N. Bruchovsky and K. Aihara, Development of a mathematical model that predicts the outcome of hormone therapy for prostate cancer,, J. Theor. Biol., 264 (2010), 517.  doi: 10.1016/j.jtbi.2010.02.027.  Google Scholar

[17]

A. M. Ideta, G. Tanaka, T. Takeuchi and K. Aihara, A mathematical model of intermittent androgen suppression for prostate cancer,, J. Nonlinear Sci., 18 (2008), 593.  doi: 10.1007/s00332-008-9031-0.  Google Scholar

[18]

T. L. Jackson, A mathematical model of prostate tumor growth and androgen-independent relapse,, Discrete Cont. Dyn.-B, 4 (2004), 187.  doi: 10.3934/dcdsb.2004.4.187.  Google Scholar

[19]

T. L. Jackson, A mathematical investigation of the multiple pathways to recurrent prostate cancer: Comparison with experimental data,, Neoplasia, 6 (2004), 697.  doi: 10.1593/neo.04259.  Google Scholar

[20]

H. V. Jain, S. K. Clinton, A. Bhinder and A. Friedman, Mathematical modeling of prostate cancer progression in response to androgen ablation therapy,, Proc. Natl. Acad. Sci. U. S. A., 108 (2011), 19701.  doi: 10.1073/pnas.1115750108.  Google Scholar

[21]

M. Marcelli, W. D. Tilley, C. M. Wilson, J. E. Griffin, J. D. Wilson and M. J. McPhaul, Definition of the human androgen receptor gene structure permits the identification of mutations that cause androgen resistance: premature termination of the receptor protein at amino acid residue 588 causes complete androgen resistance,, Mol. Endocrinol., 4 (1990), 1105.  doi: 10.1210/mend-4-8-1105.  Google Scholar

[22]

H. C. Monro and E. A Gaffney, Modelling chemotherapy resistance in palliation and failed cure,, J. Theor. Biol., 257 (2009), 292.  doi: 10.1016/j.jtbi.2008.12.006.  Google Scholar

[23]

W. D. Nes, Y. O. Lukyanenko, Z. H. Jia, S. Quideau, W. N. Howald, T. K. Pratum, R. R. West and J. C. Hutson, Identification of the lipophilic factor produced by macrophages that stimulates steroidogenesis,, Endocrinology, 141 (2000), 953.  doi: 10.1210/en.141.3.953.  Google Scholar

[24]

T. Portz, Y. Kuang and J. D. Nagy, A clinical data validated mathematical model of prostate cancer growth under intermittent androgen suppression therapy,, AIP Advances, 2 (2012).  doi: 10.1063/1.3697848.  Google Scholar

[25]

L. K. Potter, M. G. Zager and H. A. Barton, Mathematical model for the androgenic regulation of the prostate in intact and castrated adult male rats,, Am. J. Physiol. Endocrinol. Metab., 291 (2006).  doi: 10.1152/ajpendo.00545.2005.  Google Scholar

[26]

E. M Wilson and F. S. French, Binding properties of androgen receptors. Evidence for identical receptors in rat testis, epididymis, and prostate,, J. Biol. Chem., 51 (1976), 5620.   Google Scholar

[27]

A. S. Wright, L. N. Thomas, R. C. Douglas, C. B. Lazier and R. S. Rittmaster, Relative potency of testosterone and dihydrotestosterone in preventing atrophy and apoptosis in the prostate of the castrated rat,, J. Clin. Invest., 98 (1996), 255.  doi: 10.1172/JCI119074.  Google Scholar

[28]

C. Y-F. Young, B. T. Montgomery, P. E. Andrews, S. Qiu, D. L. Bilhartz and D. J. Tindall, Hormonal regulation of prostate-specific antigen messenger RNA in human prostatic adenocarcinoma cell line LNCaP,, Cancer Res., 51 (1991), 3748.   Google Scholar

[29]

K. Yörükoglu, S Aktas, C Güler, M. Sade and Z. Kirkali, Volume-weighted mean nuclear volume in renal cell carcinoma,, Urology, 52 (1998), 44.   Google Scholar

[30]

H. Y. E. Zhau, S. Chang, B. Chen, Y. Wang, H. Zhang, C. Kao, Q. A. Sang, S. J. Pathak and L. W. K. Chung, Androgen-repressed phenotype in human prostate cancer,, Proc. Natl. Acad. Sci. U. S. A., 93 (1996), 15152.  doi: 10.1073/pnas.93.26.15152.  Google Scholar

show all references

References:
[1]

D. B. Agus, C. Cordon-Cardo, W. Fox, M. Drobnjak, A. Koff, D. W. Golde and H. I. Scher, Prostate cancer cell cycle regulators: Response to androgen withdrawal and development of androgen independence,, J. Natl. Cancer. Inst., 91 (1999), 1869.  doi: 10.1093/jnci/91.21.1869.  Google Scholar

[2]

G. L. Andriole, E. D. Crawford, R. L. Grubb III, S. S. Buys, D. Chia, T. R. Church, M. N. Fouad, E. P. Gelmann, P. A. Kvale, D. J. Reding, J. L. Weissfeld, L. A. Yokochi, B. O'Brien, J. D. Clapp, J. M. Rathmell, T. L. Riley, R. B. Hayes, B. S. Kramer, G. Izmirlian, A. B. Miller, P. F. Pinsky, P. C. Prorok, J. K. Gohagan and C. D. Berg, Mortality results from a randomized prostate-cancer screening trial,, N. Engl. J. Med., 360 (2009), 1310.  doi: 10.1056/NEJMoa0810696.  Google Scholar

[3]

R. R. Berges, J. Vukanovic, J. I. Epstein, M. CarMichel, L. Cisek, D. E. Johnson, R. W. Veltri, P. C. Walsh and J. T. Isaacs, Implication of cell kinetic changes during the progression of human prostatic cancer,, Clin. Cancer Res., 1 (1995), 473.   Google Scholar

[4]

G. Birkenmeier, F. Struck and R. Gebhardt, Clearance mechanism of prostate specific antigen and its complexes with alpha2-macroglobulin and alpha1-antichymotrypsin,, J. Urol., 162 (1999), 897.  doi: 10.1097/00005392-199909010-00086.  Google Scholar

[5]

M. L. Cher, G. S. Bova, D. H. Moore, E. J. Small, P. R. Carroll, S. S. Pin, J. I. Epstein, W. B. Isaacs and R. H. Jensen, Genetic alterations in untreated metastases and androgen-independent prostate cancer detected by comparative genomic hybridization and allelotyping,, Cancer Res., 56 (1996), 3091.   Google Scholar

[6]

M. W. Dunn and M. W. Kazer, Prostate cancer overview,, Semin. Oncol. Nurs., 27 (2011), 241.  doi: 10.1016/j.soncn.2011.07.002.  Google Scholar

[7]

S. E. Eikenberry, J. D. Nagy and Y. Kuang, The evolutionary impact of androgen levels on prostate cancer in a multi-scale mathematical model,, Biol. Direct, 5 (2010), 24.  doi: 10.1186/1745-6150-5-24.  Google Scholar

[8]

B. J. Feldman and D. Feldman, The development of androgen-independent prostate cancer,, Nat. Rev. Cancer, 1 (2001), 34.  doi: 10.1038/35094009.  Google Scholar

[9]

D. Gillatt, Antiandrogen treatments in locally advanced prostate cancer: are they all the same?,, J. Cancer Res. Clin. Oncol., 132 (2006).  doi: 10.1007/s00432-006-0133-5.  Google Scholar

[10]

R. F. Gittes, Carcinoma of the prostate,, N. Engl. J. Med., 324 (1991), 236.  doi: 10.1056/NEJM199101243240406.  Google Scholar

[11]

M. Gleave, S. L. Goldenberg, N. Bruchovsky and P. Rennie, Intermittent androgen suppression for prostate cancer: Rationale and clinical experience,, Prostate Cancer Prostatic Dis., 1 (1998), 289.  doi: 10.1038/sj.pcan.4500260.  Google Scholar

[12]

S. L. Goldenberg, N. Bruchovsky, M. E. Gleave, L. D. Sullivan and K. Akakura, Intermittent androgen suppression in the treatment of prostate cancer: A preliminary report,, Urology, 45 (1995), 839.  doi: 10.1016/S0090-4295(99)80092-2.  Google Scholar

[13]

C. W. Gregory, R. T. Johnson, J. L. Mohler Jr, F. S. French and E. M. Wilson, Androgen receptor stabilization in recurrent prostate cancer is associated with hypersensitivity to low androgen,, Urology, 61 (2001), 2892.   Google Scholar

[14]

M. A. Haider, T. H. van der Kwast, J. Tanguay, A. J. Evans, A. Hashmi, G. Lockwood and J. Trachtenberg, Combined T2-weighted and diffusion-weighted MRI for localization of prostate cancer,, AJR Am J Roentgenol., 189 (2007), 323.  doi: 10.2214/AJR.07.2211.  Google Scholar

[15]

C. A. Heinlein and C. Chang, Androgen receptor in prostate cancer,, Endocr. Rev., 25 (2004), 276.  doi: 10.1210/er.2002-0032.  Google Scholar

[16]

Y. Hirata, N. Bruchovsky and K. Aihara, Development of a mathematical model that predicts the outcome of hormone therapy for prostate cancer,, J. Theor. Biol., 264 (2010), 517.  doi: 10.1016/j.jtbi.2010.02.027.  Google Scholar

[17]

A. M. Ideta, G. Tanaka, T. Takeuchi and K. Aihara, A mathematical model of intermittent androgen suppression for prostate cancer,, J. Nonlinear Sci., 18 (2008), 593.  doi: 10.1007/s00332-008-9031-0.  Google Scholar

[18]

T. L. Jackson, A mathematical model of prostate tumor growth and androgen-independent relapse,, Discrete Cont. Dyn.-B, 4 (2004), 187.  doi: 10.3934/dcdsb.2004.4.187.  Google Scholar

[19]

T. L. Jackson, A mathematical investigation of the multiple pathways to recurrent prostate cancer: Comparison with experimental data,, Neoplasia, 6 (2004), 697.  doi: 10.1593/neo.04259.  Google Scholar

[20]

H. V. Jain, S. K. Clinton, A. Bhinder and A. Friedman, Mathematical modeling of prostate cancer progression in response to androgen ablation therapy,, Proc. Natl. Acad. Sci. U. S. A., 108 (2011), 19701.  doi: 10.1073/pnas.1115750108.  Google Scholar

[21]

M. Marcelli, W. D. Tilley, C. M. Wilson, J. E. Griffin, J. D. Wilson and M. J. McPhaul, Definition of the human androgen receptor gene structure permits the identification of mutations that cause androgen resistance: premature termination of the receptor protein at amino acid residue 588 causes complete androgen resistance,, Mol. Endocrinol., 4 (1990), 1105.  doi: 10.1210/mend-4-8-1105.  Google Scholar

[22]

H. C. Monro and E. A Gaffney, Modelling chemotherapy resistance in palliation and failed cure,, J. Theor. Biol., 257 (2009), 292.  doi: 10.1016/j.jtbi.2008.12.006.  Google Scholar

[23]

W. D. Nes, Y. O. Lukyanenko, Z. H. Jia, S. Quideau, W. N. Howald, T. K. Pratum, R. R. West and J. C. Hutson, Identification of the lipophilic factor produced by macrophages that stimulates steroidogenesis,, Endocrinology, 141 (2000), 953.  doi: 10.1210/en.141.3.953.  Google Scholar

[24]

T. Portz, Y. Kuang and J. D. Nagy, A clinical data validated mathematical model of prostate cancer growth under intermittent androgen suppression therapy,, AIP Advances, 2 (2012).  doi: 10.1063/1.3697848.  Google Scholar

[25]

L. K. Potter, M. G. Zager and H. A. Barton, Mathematical model for the androgenic regulation of the prostate in intact and castrated adult male rats,, Am. J. Physiol. Endocrinol. Metab., 291 (2006).  doi: 10.1152/ajpendo.00545.2005.  Google Scholar

[26]

E. M Wilson and F. S. French, Binding properties of androgen receptors. Evidence for identical receptors in rat testis, epididymis, and prostate,, J. Biol. Chem., 51 (1976), 5620.   Google Scholar

[27]

A. S. Wright, L. N. Thomas, R. C. Douglas, C. B. Lazier and R. S. Rittmaster, Relative potency of testosterone and dihydrotestosterone in preventing atrophy and apoptosis in the prostate of the castrated rat,, J. Clin. Invest., 98 (1996), 255.  doi: 10.1172/JCI119074.  Google Scholar

[28]

C. Y-F. Young, B. T. Montgomery, P. E. Andrews, S. Qiu, D. L. Bilhartz and D. J. Tindall, Hormonal regulation of prostate-specific antigen messenger RNA in human prostatic adenocarcinoma cell line LNCaP,, Cancer Res., 51 (1991), 3748.   Google Scholar

[29]

K. Yörükoglu, S Aktas, C Güler, M. Sade and Z. Kirkali, Volume-weighted mean nuclear volume in renal cell carcinoma,, Urology, 52 (1998), 44.   Google Scholar

[30]

H. Y. E. Zhau, S. Chang, B. Chen, Y. Wang, H. Zhang, C. Kao, Q. A. Sang, S. J. Pathak and L. W. K. Chung, Androgen-repressed phenotype in human prostate cancer,, Proc. Natl. Acad. Sci. U. S. A., 93 (1996), 15152.  doi: 10.1073/pnas.93.26.15152.  Google Scholar

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