Skip to main content

Advertisement

SpringerLink
Log in

BCG immunotherapy optimization on an isoperimetric optimal control problem for the treatment of superficial bladder cancer

  • Published:
International Journal of Dynamics and Control Aims and scope Submit manuscript

Abstract

The Bacillus Calmette-Guerin immunotherapy (BCG) is a clinical procedure used as the treatment by success for superficial bladder cancer. However, the toxicity of BCG, its maintenance schedule, optimal amount of dosage sufficient for the destruction of cancerous cells and its efficiency remain all unclear due to the lack of published data. We serve in this paper the optimization of BCG treatment by seeking the optimal dose we inject in the bladder during the intravesical therapy for a hypothetical patient. We outline the different steps of resolution of an optimal control problem resolved using the Pontryagin’s maximum principle. The theoretical approach lead us to use the forward-backward sweep method and the secant-method as the appropriate numerical technique to solve a two-point boundary value problem with an isoperimetric constraint on the control process function representing the optimal concentration suggested to use in each instillation of BCG.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  1. Pearl R (1929) Cancer and tuberculosis. Am J Hyg 9:97

    Google Scholar 

  2. Mathé G, Amiel JL, Schwarzenberg L, Schneider M, Cattan A, Schlumberger JR, Hayat M, De Vassal F (1969) Active immunotherapy for acute lymphoblastic leukaemia. Lancet 293(7597):697–699

  3. Zbar B, Rapp HJ (1974) Immunotherapy of guinea pig cancer with BCG. Cancer 34(8):1532–1540

    Article  Google Scholar 

  4. Bloomberg SD, Brosmn SA, Hausman MS, Cohen A, Battenberg JD (1975) The effect of BCG on the dog bladder. Invest Urol 12:423–427

    Google Scholar 

  5. Dekernion JB, Golub SH, Gupta RK, Silverstein M, Morton DL (1975) Successful transurethral intralesional BCG therapy of a bladder melanoma. Cancer 36(5):1662–1667

    Article  Google Scholar 

  6. Morales A, Eidinger D, Bruce AW (1976) Intracavitary Bacillus Calmette-Guerin in the treatment of superficial bladder tumors. J Urol 116(2):180–183

    Google Scholar 

  7. Martinez-Pineiro JA, Muntanola P (1977) Nonspecific immunotherapy with BCG vaccine in bladder tumors: a preliminary report. Eur Urol 3:11–22

  8. Chopin D, Saint F, Gattegno B (2001) Immunothérapie endovésicale: le bacille de Calmette-Guerin. Progrès en Urol 11(5):1065–1115

  9. Neuzillet Y, Rouprêt M, Wallerand H, Pignot G, Larré S, Irani J, Pfister C (2012) Diagnostic et prise en charge des évènements indésirables survenant au décours des instillations endovésicales de BCG pour le traitement des tumeurs de vessie n’infiltrant pas le muscle (TVNIM): revue du comité de cancérologie de l’Association française d’urologie. Progrès en Urol 22(16):989–998

  10. Wallerand H (2009) Instillations endovésicales et cancer de la vessie. Progrès en Urol 19(12):868–871

  11. Saint F (2008) Immunothérapie par Bacille de Calmette-Guérin: quel protocole? Progrès en Urol 18:S99–S104

  12. Cheng CW, Ng MT, Chan SY, Sun WH (2004) Low dose BCG as adjuvant therapy for superficial bladder cancer and literature review. ANZ J Surg 74(7):569–572

    Article  Google Scholar 

  13. Nanda S, Moore H, Lenhart S (2007) Optimal control of treatment in a mathematical model of chronic myelogenous leukemia. Math Biosci 210:143–156

    Article  MathSciNet  MATH  Google Scholar 

  14. De Pillis LG, Gu W, Fister KR, Head T, Maples K, Neal T, Murugan A, Yoshida K (2007) Chemotherapy for tumors: an analysis of the dynamics and a study of quadratic and linear optimal controls. Math Biosci 209:292–315

    Article  MathSciNet  MATH  Google Scholar 

  15. Bunimovich-Mendrazitsky S, Shochat E, Stone L (2007) Mathematical model of BCG immunotherapy in superficial bladder cancer. Bull Math Biol 69:1847–1870

  16. Archuleta J, Mullens P, Primm TP (2002) The relationship of temperature to desiccation and starvation tolerance of the Mycobacterium avium complex. Arch Microbiol 178:311–314

    Article  Google Scholar 

  17. Kuznetsov VA, Makalkin IA, Taylor MA, Perelson AS (1994) Nonlinear dynamics of immunogenic tumours: parameter estimation and global bifurcation analysis. Bull Math Biol 56:295– 321

  18. Wigginton J, Kirschner D (2001) A model to predict cell-mediated immune regulatory mechanisms during human infection with mycobacterium tuberculosis. J Immunol 166:1951–1967

    Article  Google Scholar 

  19. Lämmle M, Beer A, Settles M, Hanning C, Schwaibold H, Drews C (2002) Reliability of MR imaging-based virtual cystoscopy in the diagnosis of cancer of the urinary bladder. Am J Roentgenol 178:1483–1488

    Article  Google Scholar 

  20. Spratt JA, Von Fournier D, Spratt JS, Weber EE (1993) Decelerating growth and human breast cancer. Cancer 71(6):2013–2019

    Article  Google Scholar 

  21. Garira W, Musekwa SD, Shiri T (2005) Optimal control of combined therapy in a single strain HIV-1 Model. Electron J Differ Equ 52:1–22

    MathSciNet  MATH  Google Scholar 

  22. Kamien MI, Schwartz NL (1991) Dynamic optimization: the calculus of variations and optimal control in economics and management, 2nd edn. Elsevier Science, New York

    MATH  Google Scholar 

  23. Pagano F, Bassi P, Piazza N, Abatangelo G, Drago Ferrante GL, Milani C (1991) Improving the efficacy of BCG immunotherapy by dose reduction. Eur Urol 27:19–22

    Google Scholar 

  24. Takashi M, Wakai K, Ohno Y, Murase T, Miyake K (1995) Evaluation of a low-dose intravesical bacillus Calmette-Guerin (Tokyo strain) therapy for superficial bladder cancer. Int Urol Nephrol 27:723–733

  25. Mack D, Frick J (1995) Low-dose bacilli Calmette-Guerin (BCG) therapy in superficial high-risk bladder cancer: a phase II study with the BCG strain Connaught Canada. Br J Urol 75: 1857

  26. Hurle R, Losa A, Ranieri A, Graziotti P, Lembo A (1996) Low dose Pasteur bacillus Calmette-Guerin regimen in stage T1, Grade 3 bladder cancer therapy. J Urol 156:1602–1605

  27. Losa A, Hurle R, Lembo A (2000) Low dose bacillus Calmette-Guerin for carcinoma in situ of the bladder: long-term results. J Urol 163:68–71

    Article  Google Scholar 

  28. Boltyanskii VG, Gamkrelidze RV, Pontryagin LS (1956) Towards a theory of optimal processes, (Russian), Reports. Acad Sci USSR 110(1)

  29. Fister KR, Panetta JC (2003) Optimal control applied to competing chemotherapeutic cell-kill strategies. SIAM J Appl Math 63:1954

  30. Lenhart S, Workman J (2007) Optimal control applied to biological models. Chapman Hall/CRC, Boca Raton

    MATH  Google Scholar 

  31. Gumel AB, Lenhart S (2010) Modeling paradigms and analysis of disease transmission models, vol 75. American Mathematical Society, Providence

Download references

Acknowledgments

The authors would like to thank the anonymous referees for their valuable comments and suggestions to improve the content of this paper.

Author information

Authors and Affiliations

  1. Department of mathematics and computer sciences, Faculty of sciences Ben M’Sik-Casablanca, Hassan II University Mohammedia-Casablanca Morocco, Avenue Commandant Driss ELHARTI, B.P: 7955-Ben M’Sik, 20800 , Casablanca, Morocco

    Ilias Elmouki & Smahane Saadi

Authors
  1. Ilias Elmouki
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Smahane Saadi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ilias Elmouki.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Elmouki, I., Saadi, S. BCG immunotherapy optimization on an isoperimetric optimal control problem for the treatment of superficial bladder cancer. Int. J. Dynam. Control 4, 339–345 (2016). https://doi.org/10.1007/s40435-014-0106-5

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40435-014-0106-5

Keywords

Search

Navigation