In vivo delivery of gene therapy to tumours L. R. Band, R. J. S. Booth, L. J. Cummings, R. J. Dyson, K. D. Fisher, I. M. Griffiths, J. P. Moles & S. L. Waters August 11, 2006 Abstract In gene therapy, tumour growth is inhibited by viruses which are delivered to the tumour via the blood stream. This therapy utilises the leakiness of the tumour capillaries, which enables virus particles to pass through gaps between the endothelial cells. Our models assess the key influences on the number of virus particles which enter the tumour. We model on both the macroscale, where we represent the tumour as a porous medium, and on the cellular scale, where we consider a single virus particle entering a single gap. In both models, a proportion of the virus particles are found to enter the tumour. Several types of virus particle can be used for the therapy, and the size and physical characteristics of the virus particle will affect its interactions with the blood flow. In particular, the fluid stresses on an encapsulated virus particle cause the particle to deform. These deformations influence the virus particle’s position within the capillary which in turn is likely to affect the number of virus particles that enter the tumour. 1 Introduction Cancer-specific viruses are able to replicate inside tumour cells and destroy them [9]. In early clinical trials viruses have been injected straight into a single tumour nodule; these trials exhibit encouraging anti-cancer activity and regression of the tumour. However, the virus is unable to spread between the disseminated tumour masses, therefore this technique is limited to isolated tumours. Unfortunately, most common cancer types present with multiple metastatic tumours and it is often impractical to inject viruses into each tumour nodule. Virus particles are generally not compatible with intravenous administration because they are rapidly cleared by the immune system. The group led by Dr Len Seymour in the Department of Clinical Pharmacology at Oxford, has devised a novel way of treating virus particles with polymers to ensure the particles are less susceptible to attack by the host immune system [3]. These polymer- coated vectors are able to circulate in the blood stream for sufficient time to reach distant tumours [5]. Functional capillaries exist in the proliferating zone toward the edge of the tumour. The leaky vasculature associated with tumour structure lends itself to accumulation of virus particles delivered via the blood stream. Unlike the continuous endothelium of most normal tissues, the endothelial cells of tumour capillaries are discontinuous, with large 1 Report on a problem studied at the UK Mathematics-in-Medicine Study Group Oxford 2005 < http://www.maths-in-medicine.org/uk/2005/gene-therapy/ >