Skip to main content

Mathematical Modelling of the Interaction Between Cancer Cells and an Oncolytic Virus: Insights into the Effects of Treatment Protocols

Abstract

Oncolytic virotherapy is an experimental cancer treatment that uses genetically engineered viruses to target and kill cancer cells. One major limitation of this treatment is that virus particles are rapidly cleared by the immune system, preventing them from arriving at the tumour site. To improve virus survival and infectivity Kim et al. (Biomaterials 32(9):2314–2326, 2011) modified virus particles with the polymer polyethylene glycol (PEG) and the monoclonal antibody herceptin. Whilst PEG modification appeared to improve plasma retention and initial infectivity, it also increased the virus particle arrival time. We derive a mathematical model that describes the interaction between tumour cells and an oncolytic virus. We tune our model to represent the experimental data by Kim et al. (2011) and obtain optimised parameters. Our model provides a platform from which predictions may be made about the response of cancer growth to other treatment protocols beyond those in the experiments. Through model simulations, we find that the treatment protocol affects the outcome dramatically. We quantify the effects of dosage strategy as a function of tumour cell replication and tumour carrying capacity on the outcome of oncolytic virotherapy as a treatment. The relative significance of the modification of the virus and the crucial role it plays in optimising treatment efficacy are explored.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Notes

  1. Nude mice have non-functioning immune systems.

References

  • Aghi M, Martuza RL (2005) Oncolytic viral therapies-the clinical experience. Oncogene 24(52):7802–7816

    Article  Google Scholar 

  • Chen Y, DeWeese T, Dilley J, Zhang Y, Li Y, Ramesh N, Lee J, Pennathur-Das R, Radzyminski J, Wypych J et al (2001) Cv706, a prostate cancer-specific adenovirus variant, in combination with radiotherapy produces synergistic antitumor efficacy without increasing toxicity. Cancer Res 61(14):5453–5460

    Google Scholar 

  • Jebar AH, Errington-Mais F, Vile RG, Selby PJ, Melcher AA, Griffin S (2015) Progress in clinical oncolytic virus-based therapy for hepatocellular carcinoma. J Gen Virol 96(7):1533–1550

    Article  Google Scholar 

  • Kelly E, Russell SJ (2007) History of oncolytic viruses: genesis to genetic engineering. Mol Ther 15(4):651–659

    Article  Google Scholar 

  • Kim PH, Sohn JH, Choi JW, Jung Y, Kim SW, Haam S, Yun CO (2011) Active targeting and safety profile of PEG-modified adenovirus conjugated with herceptin. Biomaterials 32(9):2314–2326

    Article  Google Scholar 

  • Laird AK (1964) Dynamics of tumour growth. Br J Cancer 18(3):490

    Article  Google Scholar 

  • Mok H, Palmer DJ, Ng P, Barry MA (2005) Evaluation of polyethylene glycol modification of first-generation and helper-dependent adenoviral vectors to reduce innate immune responses. Mol Ther 11(1):66–79

    Article  Google Scholar 

  • Slamon DJ, Clark GM, Wong SG, Levin WJ, Ullrich A, McGuire WL (1987) Human breast cancer: correlation of relapse and survival with amplification of the HER-2/neu oncogene. Science 235(4785):177–182

    Article  Google Scholar 

  • Wang YG, Huang PP, Zhang R, Ma BY, Zhou XM, Sun YF (2016) Targeting adeno-associated virus and adenoviral gene therapy for hepatocellular carcinoma. World J Gastroenterol 22(1):326

    Article  Google Scholar 

  • Wares JR, Crivelli JJ, Yun CO, Choi IK, Gevertz JL, Kim PS (2015) Treatment strategies for combining immunostimulatory oncolytic virus therapeutics with dendritic cell injections. Math Biosci Eng MBE 12(6):1237–1256

    MathSciNet  Article  MATH  Google Scholar 

Download references

Acknowledgements

The authors received support through an Australian Postgraduate Award (ALJ) and Australian Research Council Discovery Project DP180101512 (PSK and ACFC).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Adelle C. F. Coster.

Appendix

Appendix

Table 3 Parameter values and fit statistics for the optimisation of the individual mouse-specific data in Fig. 2

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Jenner, A.L., Yun, CO., Kim, P.S. et al. Mathematical Modelling of the Interaction Between Cancer Cells and an Oncolytic Virus: Insights into the Effects of Treatment Protocols. Bull Math Biol 80, 1615–1629 (2018). https://doi.org/10.1007/s11538-018-0424-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11538-018-0424-4

Keywords

  • Oncolytic virus
  • Optimisation
  • Mathematical modelling
  • Ordinary differential equations