(764f) Equilibrium Conditions In Tumors Undergoing Virotherapy

Oncolytic viruses selectively infect and replicate inside tumor cells, which demonstrate their great potential in cancer treatment [1][2][3]. However, there are several factors that diminish the effectiveness of virotherapy. Among these factors is the development of undesirable immune responses that attacks the virus inside the tumor [4]. Therefore, immune suppression drugs, like cyclophosphamide (CPA), have been used in conjunction with oncolytic viruses in order to maintain the effectiveness of virotherapy during treatment [5]. Nevertheless, the use of such drugs weakens the immune system, which promotes the development of infections in treated patients [6].

This work determines the minimum amount of CPA necessary to halt tumor growth under virotherapy. Such a limited amount provides the highest immune system levels that could be made available while cancer progress is hampered. Such a circumstance is referred as equilibrium or static condition.  Two spatial virotherapy dynamic models are considered in this work for the calculation of such equilibrium conditions. The first model developed by Friedman et. al [4] and analyzed by Wang and Tian [7] considers a convective radial migration of immune system cells along the solid tumor. This model is based on the assumption that immune cells are large enough to be considered part of the tumor mass. A second model developed by Tao and Guo [8] considers the immune cells to penetrate and migrate by diffusion inside the tumor mass.

In these two models the tumor growth is based on the tumor cell velocity evaluated at the tumor surface, U(R), where R represents the tumor radius. A positive velocity at the boundary indicates tumor enlargement. In general, the tumor radius and the velocity are related by dR/dt=U(R). This relation is used to define the equilibrium or static line (SL) for tumor growth, in which dR/dt=0. This SL is a function of the CPA drug delivery and can determine the minimum dose to prevent the tumor enlargement after few hours of virotherapy. Higher doses than the ones specified by SL will make the cancer to shrink, while doses below the ones suggested by SL will make the tumor to grow. Because fast tumor shrinking might be achieved at the expense of weakening the immune system, only CPA doses  slightly above the one suggested by the SL are considered desirable for treatment.

References

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[2] M. Vaha-Koskela, J. E. Heikkila, A. E. Hinkkanen, Oncolytic viruses in cancer therapy, Cancer Letters 254 (2007).

[3] L. M. Wein, J. T. Wu, D. H. Kirn, Validation and analysis of a mathematical model of a replication-competent oncolytic virus for cancer treatment: implications for virus design and delivery, Cancer Research 63 (2003).

[4] A. Friedman, J. P. Tian, G. Fulci, E. A. Chiocca, J. Wang, Glioma virotherapy: Effects of innate immune suppression and increase viral replication capacity, Cancer Research 66 (4) (2006).

[5] H. Wakimoto, G. Fulci, E. Tyminski, E. A. Chiocca, Altered expression of antiviral cytokine mrnas associated with cyclophosphamide's enhancement of viral oncolysis, Gene Therapy 11 (2004).

[6] H. Vladar, J. Gonzalez, Dynamic response of cancer under the influence of immunological activity and therapy, Journal of Theoretical Biology 227 (2004).

[7] J. Wang, J. Tian, Numerical study for a model of tumor virotherapy, Applied Mathematics and Computation 196 (2008).

[8] Y. Tao, Q. Guo, The competitive dynamics between tumor cells, a replication-competent virus and an immune response, Journal of Mathematical Biology 51 (2005).