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.

[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.

[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.

[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.

[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.

[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.

[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.

[8]

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

[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.

[10]

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

[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.

[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.

[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.

[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.

[15]

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

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

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.

[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.

[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.

[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.

[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.

[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.

[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.

[8]

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

[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.

[10]

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

[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.

[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.

[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.

[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.

[15]

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

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[1]

T.L. Jackson. A mathematical model of prostate tumor growth and androgen-independent relapse. Discrete & Continuous Dynamical Systems - B, 2004, 4 (1) : 187-201. doi: 10.3934/dcdsb.2004.4.187

[2]

Alacia M. Voth, John G. Alford, Edward W. Swim. Mathematical modeling of continuous and intermittent androgen suppression for the treatment of advanced prostate cancer. Mathematical Biosciences & Engineering, 2017, 14 (3) : 777-804. doi: 10.3934/mbe.2017043

[3]

Ami B. Shah, Katarzyna A. Rejniak, Jana L. Gevertz. Limiting the development of anti-cancer drug resistance in a spatial model of micrometastases. Mathematical Biosciences & Engineering, 2016, 13 (6) : 1185-1206. doi: 10.3934/mbe.2016038

[4]

Erica M. Rutter, Yang Kuang. Global dynamics of a model of joint hormone treatment with dendritic cell vaccine for prostate cancer. Discrete & Continuous Dynamical Systems - B, 2017, 22 (3) : 1001-1021. doi: 10.3934/dcdsb.2017050

[5]

Hsiu-Chuan Wei. Mathematical and numerical analysis of a mathematical model of mixed immunotherapy and chemotherapy of cancer. Discrete & Continuous Dynamical Systems - B, 2016, 21 (4) : 1279-1295. doi: 10.3934/dcdsb.2016.21.1279

[6]

Urszula Ledzewicz, Heinz Schättler. Drug resistance in cancer chemotherapy as an optimal control problem. Discrete & Continuous Dynamical Systems - B, 2006, 6 (1) : 129-150. doi: 10.3934/dcdsb.2006.6.129

[7]

Cristian Tomasetti, Doron Levy. An elementary approach to modeling drug resistance in cancer. Mathematical Biosciences & Engineering, 2010, 7 (4) : 905-918. doi: 10.3934/mbe.2010.7.905

[8]

J. Ignacio Tello. On a mathematical model of tumor growth based on cancer stem cells. Mathematical Biosciences & Engineering, 2013, 10 (1) : 263-278. doi: 10.3934/mbe.2013.10.263

[9]

Marcello Delitala, Tommaso Lorenzi. Recognition and learning in a mathematical model for immune response against cancer. Discrete & Continuous Dynamical Systems - B, 2013, 18 (4) : 891-914. doi: 10.3934/dcdsb.2013.18.891

[10]

Shuo Wang, Heinz Schättler. Optimal control of a mathematical model for cancer chemotherapy under tumor heterogeneity. Mathematical Biosciences & Engineering, 2016, 13 (6) : 1223-1240. doi: 10.3934/mbe.2016040

[11]

Avner Friedman. A hierarchy of cancer models and their mathematical challenges. Discrete & Continuous Dynamical Systems - B, 2004, 4 (1) : 147-159. doi: 10.3934/dcdsb.2004.4.147

[12]

Alexander S. Bratus, Svetlana Yu. Kovalenko, Elena Fimmel. On viable therapy strategy for a mathematical spatial cancer model describing the dynamics of malignant and healthy cells. Mathematical Biosciences & Engineering, 2015, 12 (1) : 163-183. doi: 10.3934/mbe.2015.12.163

[13]

Urszula Ledzewicz, Shuo Wang, Heinz Schättler, Nicolas André, Marie Amélie Heng, Eddy Pasquier. On drug resistance and metronomic chemotherapy: A mathematical modeling and optimal control approach. Mathematical Biosciences & Engineering, 2017, 14 (1) : 217-235. doi: 10.3934/mbe.2017014

[14]

Avner Friedman, Najat Ziyadi, Khalid Boushaba. A model of drug resistance with infection by health care workers. Mathematical Biosciences & Engineering, 2010, 7 (4) : 779-792. doi: 10.3934/mbe.2010.7.779

[15]

Svetlana Bunimovich-Mendrazitsky, Yakov Goltser. Use of quasi-normal form to examine stability of tumor-free equilibrium in a mathematical model of bcg treatment of bladder cancer. Mathematical Biosciences & Engineering, 2011, 8 (2) : 529-547. doi: 10.3934/mbe.2011.8.529

[16]

Yangjin Kim, Avner Friedman, Eugene Kashdan, Urszula Ledzewicz, Chae-Ok Yun. Application of ecological and mathematical theory to cancer: New challenges. Mathematical Biosciences & Engineering, 2015, 12 (6) : i-iv. doi: 10.3934/mbe.2015.12.6i

[17]

M.A.J Chaplain, G. Lolas. Mathematical modelling of cancer invasion of tissue: dynamic heterogeneity. Networks & Heterogeneous Media, 2006, 1 (3) : 399-439. doi: 10.3934/nhm.2006.1.399

[18]

Christoph Sadée, Eugene Kashdan. A model of thermotherapy treatment for bladder cancer. Mathematical Biosciences & Engineering, 2016, 13 (6) : 1169-1183. doi: 10.3934/mbe.2016037

[19]

Hengki Tasman, Edy Soewono, Kuntjoro Adji Sidarto, Din Syafruddin, William Oscar Rogers. A model for transmission of partial resistance to anti-malarial drugs. Mathematical Biosciences & Engineering, 2009, 6 (3) : 649-661. doi: 10.3934/mbe.2009.6.649

[20]

Michela Eleuteri, Luca Lussardi, Ulisse Stefanelli. A rate-independent model for permanent inelastic effects in shape memory materials. Networks & Heterogeneous Media, 2011, 6 (1) : 145-165. doi: 10.3934/nhm.2011.6.145

2017 Impact Factor: 0.972

Metrics

  • PDF downloads (10)
  • HTML views (0)
  • Cited by (9)

Other articles
by authors

[Back to Top]