Skip to main content

Advertisement

SpringerLink
Log in

Optimization of Virotherapy for Cancer

  • Original Article
  • Published:
Bulletin of Mathematical Biology Aims and scope Submit manuscript

Abstract

Several viruses preferentially infect and replicate in cancer cells by usurping pathways that are defective in the tumor cell population. Such viruses have a potential as oncolytic agents. The aim of tumor virotherapy is that after injection of the replicating virus, it propagates in the tumor cell population with amplification. As a result, the oncolytic virus spreads to eradicate the tumor. The outcome of tumor virotherapy is determined by population dynamics and different from standard cancer therapy. Several models have been developed that provided considerable insights on the potential therapeutic scenarios. However, virotherapy is potentially risky since large amounts of a replicating virus are injected in the host with a risk of adverse effects. Therefore, the optimal dose, number of doses, and timing are expected to play an important role on the outcome both for the tumor and the host. In the current work, we combine a model of the dynamics of tumor virotherapy that was validated with experimental data with optimization theory to illustrate how we can improve the outcome of tumor therapy. In this first report, we demonstrate that (i) in most circumstances, anything more than two administrations of a vector is not helpful, (ii) correctly timed delivery of the virus provides superior results compared to regularly scheduled therapy or continuous infusion, (iii) a second dose of virus that is not properly timed leads to a worse outcome compared to a single dose of virus, and (iv) it is less costly to treat larger tumors.

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

Similar content being viewed by others

References

  • Anderson, B.D., Nakamura, T., Russel, S.J., Peng, K.W., 2004. High cd46 receptor density determines preferential killing of tumor cells by oncolytic measles virus. Cancer Res. 64(14), 4919–4926.

    Article  Google Scholar 

  • Bajzer, Ž., Marušić, M., Vuk-Pavlović, S., 1996. Conceptual frameworks for mathematical modeling of tumor growth dynamics. Math. Comput. Model. 23, 31–46.

    Article  MATH  Google Scholar 

  • Bajzer, Ž., Vuk-Pavlović, S., Huzak, M., 1997. Mathematical modeling of tumor growth kinetics. In: Adam, J., Bellomo, N. (Eds.), A Survey of Models for Tumor-immune System Dynamics, pp. 89–133. Birkhäuser, New York. Chapter 3.

    Google Scholar 

  • Bajzer, Ž., Carr, T., Josic, K., Russel, S.J., Dingli, D., 2008. Modelling of cancer virotherapy with recombinant measles virus. J. Theor. Biol. 252, 109–122.

    Article  Google Scholar 

  • Byrne, H.M., 2003. Modelling avascular tumor growth. In: Preziosi, L. (Ed.), Cancer Modelling and Simulation, pp. 75–120. CRC Press, Boca Raton. Chapter 4.

    Google Scholar 

  • Cappuccio, A., Castiglione, F., Piccoli, B., 2007. Determination of the optimal therapeutic protocol in cancer immunotherapy. Math. Biosci. 209, 1–13.

    Article  MATH  MathSciNet  Google Scholar 

  • Castiglione, F., Piccoli, B., 2007. Cancer immunotherapy, mathematical modelling, and optimal control. J. Theor. Biol. 247, 713–732.

    Article  MathSciNet  Google Scholar 

  • de Pillis, L.G., Radunskaya, A.E., 2003. The dynamics of an optimally controlled tumor model: A case study. Math. Comput. Model. 37(11), 1221–1244.

    Article  MATH  Google Scholar 

  • Dingli, D., Peng, K.W., Harvey, M.E., Greipp, P.R., O’Connor, M.K., Cattaneo, R., Morris, J.C., Russell, S.J., 2004. Image-guided radiovirotherapy for multiple myeloma using a recombinant measles virus expressing the thyroidal sodium iodide symporter. Blood 103, 1641–1646.

    Article  Google Scholar 

  • Dingli, D., Cascino, M.D., Josić, K., Russell, S.J., Bajzer, Ž., 2006. Mathematical modeling of cancer radiovirotherapy. Math. Biosci. 199(1), 55–78.

    Article  MATH  MathSciNet  Google Scholar 

  • Dingli, D., Pacheco, J.M., Dispenzieri, A., Hayman, S.R., Kumar, S.K., Lacy, M.Q., Gastineau, D.A., Gertz, M.A., 2007. Serum m-spike and transplant outcome in patients with multiple myeloma. Cancer Sci. 98(7), 1035–1040.

    Article  Google Scholar 

  • Fister, K.R., Panetta, J.C., 2000. Optimally control applied to cell-cycle specific cancer chemotherapy. SIAM J. Appl. Math. 60, 1059–1072.

    Article  MATH  MathSciNet  Google Scholar 

  • Friedman, A., Tian, J., Fulci, G., Chiocca, E., Wang, J., 2006. Glioma virotherapy: Effects of innate immune supression and increased viral replication capacity. Cancer Res. 66, 2314–2319.

    Article  Google Scholar 

  • Galanis, E., Carlson, S.K., Foster, N.R., Lowe, V., Quevedo, F., McWilliams, R.R., Grothey, A., Jatoi, A., Alberts, S.R., Rubin, J., 2008. Phase 1 trial of a pathotropic retroviral vector expressing a cytocidal cyclin g1 construct (rexin-g) in patients with advanced pancreatic cancer. Mol. Ther. 16(5), 979–984.

    Article  Google Scholar 

  • Grote, D., Russell, S.J., Cornu, T.I., Cattaneo, R., Vile, R., Poland, G.A., Fielding, A.K., 2001. Live attenuated measles virus induces regression of human lymphoma xenografts in immunodeficient mice. Blood 97(12), 3746–3754.

    Article  Google Scholar 

  • Hirasawa, K., Nishikawa, S.G., Normal, K.L., Coffey, M.C., Thompson, B.G., Yoon, C.S., Waisman, D.M., Lee, P.W., 2003. Systemic reovirus therapy of metastaic cancer in immune-competent mice. Cancer Res. 63(2), 348–353.

    Google Scholar 

  • Kirn, D., Martuza, R.L., Zwiebel, J., 2001. Replication-selective virotherapy for cancer: Biological principles, risk management and future directions. Nat. Med. 7(7), 781–877.

    Article  Google Scholar 

  • Liu, Y., Teo, K.L., Jennings, L.S., Wang, S., 1998. On a class of optimal control problems with state jumps. J. Optim. Theory Appl. 98(1), 65–82.

    Article  MATH  MathSciNet  Google Scholar 

  • Martin, R., Teo, K.L., 1994. Optimal Drug Administration in Cancer Chemotherapy. Singapore.

  • Mukhopadhyay, B., Bhattacharyya, R., 2008. Analysis of a virus-immune system model with two distinct delays. Nonlinear Stud. 15(1), 37–50.

    MATH  MathSciNet  Google Scholar 

  • Myers, R., Greiner, S., Harvey, M., Soeffker, D., Frenzke, M., Abraham, K., Shaw, A., Rozenblatt, S., Federspiel, M.J., Russell, S.J., Peng, K.W., 2005. Oncolytic activities of approved mumps and measles vaccines for therapy of ovarian cancer. Cancer Gene Ther. 12(7), 593–599.

    Article  Google Scholar 

  • Nemunaitis, J., Khuri, F., Ganly, I., Arseneau, J., Posner, M., Vokes, E., Kuhn, J., McCarty, T., Landers, S., Blackburn, A., Romel, L., Randlev, B., Kaye, S., Kirn, D., 2001. Phase ii trial of intratumoral administration of onyx-015, a replication-selective adenovirus, in patients with refractory head and neck cancer. J. Clin. Oncol. 19(2), 289–298.

    Google Scholar 

  • Ong, H.T., Timm, M.M., Greipp, P.R., Witzig, T.E., Dispenzieri, A., Russell, S.J., Peng, K.W., 2006. Oncolytic measles virus targets high cd46 expression on multiple myeloma cells. Exp. Hematol. 34(6), 713–720.

    Article  Google Scholar 

  • Paiva, L.T., Binny, C., Ferreira, S.C., Martins, M.L., 2009. A multiscale mathematical model for oncolytic virotherapy. Cancer Res. 69(3), 1205–1211.

    Article  Google Scholar 

  • Pecora, A.L., Rizvi, N., Cohen, G.I., Meropol, N.J., Sterman, D., Marshall, J.L., Goldberg, S., Gross, P., O’Neil, J.D., Groene, W.S., Roberts, M.S., Rabin, H., Bamat, M.K., Lorence, R.M., 2002. Phase i trial of intravenous administration of pv701, an oncolytic virus, in patients with advanced solid cancers. J. Clin. Oncol. 20(9), 2251–2266.

    Article  Google Scholar 

  • Peng, K.W., Ahmann, G.J., Pham, L., Greipp, P.R., Cattaneo, R., Russell, S.J., 2001. Systemic therapy of myeloma xenografts by an attenuated measles virus. Blood 98(7), 2002–2007.

    Article  Google Scholar 

  • Peng, K.W., Facteau, S., Wegman, T., O’Kane, D., Russell, S.J., 2002. Non-invasive in vivo monitoring of trackable viruses expressing soluble marker peptides. Nat. Med. 8(5), 527–531.

    Article  Google Scholar 

  • Peng, K.W., Hadac, E.M., Anderson, B.D., Myers, R., Harvey, M., Greiner, S.M., Soeffker, D., Federspiel, M.J., Russell, S.J., 2006. Pharmacokinetics of oncolytic measles virotherapy: Eventual equilibrium between virus and tumor in an ovarian cancer xenograft model 13(8), 732–738

  • Peng, K.W., TenEyck, C.J., Galanis, E., Kalli, K.R., Hartmann, L.C., Russell, S.J., 2002. Intraperitoneal therapy of ovarian cancer using an engineered measles virus. Cancer Res. 62(16), 4656–4662.

    Google Scholar 

  • Phuong, L.K., Allen, C., Peng, K.W., Giannini, C., Greiner, S., TenEyck, C.J., Mishra, P.K., Macura, S.I., Russell, S.J., Galanis, E.C., 2003. Use of a vaccine strain of measles virus genetically engineered to produce carcinoembryonic antigen as a novel therapeutic agent against glioblastoma multiforme. Cancer Res. 63(10), 2462–2469.

    Google Scholar 

  • Pratt, G., Goodyear, O., Moss, P., 2007. Immunodeficiency and immunotherapy in multiple myeloma. Br. J. Haematol. 138(5), 563–579.

    Article  Google Scholar 

  • Reid, T., Galanis, E., Abbruzzese, J., Sze, D., Andrews, J., Hatfield, M., Romel, L., Rubin, J., Kirn, D., 2001. Intra-arterial administration of a replication-selective adenovirus (dl1520) in patients with colorectal carcinoma metastatic to the liver: A phase i trial. Gene Ther. 8(21), 1618–1626.

    Article  Google Scholar 

  • Reid, T., Galanis, E., Abbruzzese, J., Sze, D., Wein, L.M., Andrews, J., Randlev, B., Heise, C., Uprichard, M., Hatfield, M., Rome, L., Rubin, J., Kirn, D., 2002. Hepatic arterial infusion of a replication-selective oncolytic adenovirus (dl1520): phase ii viral, immunologic, and clinical endpoints. Cancer Res. 62(21), 6070–6079.

    Google Scholar 

  • Russell, S.J., 2002. RNA viruses as virotherapy agents. Cancer Gene Ther. 9(12), 961–966.

    Article  Google Scholar 

  • Schneider, U., von Messling, V., Devaux, P., Cattaneo, R., 2002. Efficiency of measles virus entry and dissemination through different receptors. J. Virol. 76(15), 7460–7467.

    Article  Google Scholar 

  • Spratt, J.A., von Fournier, D., Spratt, J.S., Weber, E.E., 1993. Decelerating growth and human breast cancer. Cancer 71(6), 2013–2019.

    Google Scholar 

  • Tao, Y., Guo, Q., 2005. The competitive dynamics between tumor cells, a replication-competent virus and an immune response. J. Math. Biol. 51(1), 37–74.

    Article  MATH  MathSciNet  Google Scholar 

  • Todo, T., Rabkin, S.D., Sundaresan, P., Wu, A., Meehan, K.R., Herscowitz, H.B., Martuza, R.L., 1999. Systemic antitumor immunity in experimental brain tumor therapy using a multimutated, replication-competent herpes simplex virus. Hum. Gene Ther. 10(17), 2741–2755.

    Article  Google Scholar 

  • Venkataraman, P., 2001. Applied Optimization with Matlab Programming. Wiley Interscience, New York.

    Google Scholar 

  • Walter, W., 1998. Ordinary Differential Equations. Springer, New York.

    MATH  Google Scholar 

  • Wodarz, D., 2001. Viruses as antitumor weapons: Defining conditions for tumor remission. Cancer Res. 61, 3501–3507.

    Google Scholar 

  • Wodarz, D., 2003. Gene therapy for killing p53-negative cancer cells: use of replicating versus nonreplicating agents. Hum. Gene Ther. 14(2), 153–159.

    Article  Google Scholar 

  • Wu, J.T., Byrne, H.M., Kirn, D.H., Wein, L.M., 2001. Modeling and analysis of a virus that replicates selectively in tumor cells. Bull. Math. Biol. 63(4), 731–768.

    Article  Google Scholar 

  • Wu, J.T., Kirn, D.H., Wein, L.M., 2004. Analysis of a three-way race between tumor growth, a replication-competent virus and an immune response. Bull. Math. Biol. 66(4), 605–625.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, South Dakota State University, Brookings, SD, 57007, USA

    Matt Biesecker & Jung-Han Kimn

  2. Department of Engineering Technology and Management, South Dakota State University, Brookings, SD, 57007, USA

    Huitian Lu

  3. Department of Molecular Medicine, Mayo Clinic, Rochester, MN, 55905, USA

    David Dingli

  4. Biomathematics Resource Core, Department of Biochemistry and Molecular Biology, Mayo Clinic, Rochester, MN, 55905, USA

    Željko Bajzer

Authors
  1. Matt Biesecker
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jung-Han Kimn
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Huitian Lu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. David Dingli
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Željko Bajzer
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Željko Bajzer.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Biesecker, M., Kimn, JH., Lu, H. et al. Optimization of Virotherapy for Cancer. Bull. Math. Biol. 72, 469–489 (2010). https://doi.org/10.1007/s11538-009-9456-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11538-009-9456-0

Keywords

Search

Navigation