The paper is exploring glioma virotherapy, which uses synthetic viral capsules to target cancer cells and kill them, while not harming the surrounding normal cells. These viruses are known as ontolytic viruses and while they may originate from harmful strains they've had almost all of their own DNA knocked out, turning them into little balls of protein designed to target cancer cells only. This approach has several problems associated with it, but one of the main ones is that the human body generally doesn't like having virus's inside it. Any injected cancer-targeting virus capsids are in danger or being effectively destroyed by the bodies immune system.
One solution to this is to use immunosuppressants, which naturally comes with problems of its own, including the question of dosage. How much immunosuppressant do you give the patient, depending on the corresponding number of viruses used, and the size of the cancer. In order to explore this without having to kill huge numbers of rats, Friedman and colleagues developed a model to explore the effects of differing virus and immunosuppressant concentrations.
First, they needed to specify the parameters they were using:
Number of tumour cells infected with virus = y
Number of tumour cells uninfected = x
Necrotic (dying) cells = n
Immune cells (destroying the viruses) = z
Free virus particles = v
Then some rates to take into account:
Proliferation of non-infected cells = λ
Infection rate of tumour cells = B
Diffusion coefficient of virus particles = D
Adding this all together with some mathematical magic (and a function to include immunosuppressant levels) leads to what is to me a totally incomprehensible series of mathematical squiggles (anyone whose desperate to read them can find them in the appendix of the reference paper below). But somewhere along the line the magic works, as seen when they compare it to experimental data:
The table above (from the reference) isn't remarkably clear, suffice to say that the blue bars are the actual experiment results (carried out in rats) while the red bars are the results of the model simulation. Graph A shows infected tumour cells (after 6 and 72 hours), graph B shows immune cells (after 6 hours 72 hours and just before the rat dies) while graph C shows the immune cells after addition of the immunosuppressant (after 6 hours, 72 hours, and just before the rat dies). The x-axis shows the percentage of cells.
Having got a model that shows a reasonable degree of accuracy, the experimenters can then play around with the parameters without any more rats having too be involved. For example they can explore the effects of adding more viruses. More viruses in the system increase the immune cell response, even in suppressed patients (although obviously the response is lessened). However as the numbers of viruses decrease, the immune cells start to leave the area, allowing any viruses that have survived to quickly recover the population and the immune cells rush back in again. This leads to a feedback loop which, with my knowledge of the effects of the immune system, can't be all that good for the patient.
The results below from the model show the effect of adding varying amounts of virus on the number of infected tumour cells.
The cyclical pattern can be clearly seen, especially for the larger numbers of viruses (the blue, red and green lines represent increasing numbers of virus's injected into the system - as the colours are rather faint the blue line is the mostly straight one, the red line is the bumpy one and the green 'line' is a series of peaks). The model was also used to explore different concentrations of immunosuppressant and different dosage schedules (one a week, twice a week etc.) for treatment.
There are limitations to the model, it only considers injections into the centre of spherical tumours, for example, and does nothing to model any potential problems caused by metastasis (bits of the tumour breaking off and moving away). However is does provide the framework of a system to explore different options for bench experimentation, to ensure that any work that is done on animals will be the useful and relevant for the development of this system into a working treatment for human cancers.
Friedman, A. (2006). Glioma Virotherapy: Effects of Innate Immune Suppression and Increased Viral Replication Capacity Cancer Research, 66 (4), 2314-2319 DOI: 10.1158/0008-5472.CAN-05-2661