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If both responses coexist, then the size of the tumor is given by x + y = cv/ct■ Thus, a strong tumor-specific response, ct, reduces tumor load. On the other hand, a strong virus-specific response, cv, increases tumor load. The reason is that a strong virus-specific response results in low virus load and therefore in low stimulatory signals promoting the induction of tumor-specific immunity. Note that this last statement only applies to the parameter region where both types of CTL responses co-exist.

12.5 Treatment strategies

The above discussion has shown that the outcome of therapy depends on a complex balance between host and viral parameters. An important variable is the death rate of infected tumor cells. In order to achieve maximum reduction of the tumor, the death rate of the infected cells must be around its optimum, defined by the mathematical models. If the death rate of infected cells lies around its optimum, a fast replication rate of the virus and a slow growth rate of the tumor increase the chances of tumor eradication. The death rate of infected tumor cells can be influenced by a variety of factors: (i) Viral cytotoxicity alone kills tumor cells, (ii) A CTL response against the virus contributes to killing infected tumor cells. (Hi) The virus helps eliciting a tumor-specific CTL response following the release of immuno-stimulatory signals.

The most straightforward way to use viruses as anti-cancer weapons is in the absence of immunity. If the cytotoxicity of the virus is around its optimum value, minimum tumor size is achieved. It is important to note that the highest rate of virus induced tumor cell killing does not necessarily contribute to the elimination of the tumor. The reason is that a very high rate of virus-induced cell death compromises the overall spread of the infection through the tumor. If a virus specific CTL response is induced, the best strategy would be to use a fast replicating and weakly cytotoxic virus. This is because the CTL will increase the death rate of infected cells. If the overall death rate of infected cells is too high, this is detrimental to the patient, since virus spread is prevented. In addition, a weakly cytotoxic and fast replicating virus may provide the strongest stimulatory signals for the establishment of tumor-specific immunity.

Because the model suggests that a fast growth rate of the tumor decreases the efficacy of treatment, success of therapy could be promoted by using a combination of virus therapy and conventional chemo- or radiotherapy. These suggestions are supported by recent experimental data [Freytag et al. (1998); Heise et al. (1997); Rogulski et al. (2000); You et al. (2000)]. A combination of treatment with the adenovirus ONYX-O15 and chemotherapy or radiotherapy has been shown to be significantly more effective than treatment with either agent alone.

The principles of the mathematical modeling approaches presented here can help to improve treatment and to attain higher levels of success. In order to achieve this, however, more work is needed. Basic parameters of viruses and virus mutants need to be measured as a first step. Because the optimal death rate of infected tumor cells is crucial, it will be important to precisely measure the rate at which different viruses kill the tumor cells. Equally important is the quantification of the viral replication kinetics. Once such basic parameters have been measured, it is important to re-consider some model assumptions. The models discussed in this chapter are only a first approach to use computational methods for the analysis of oncolytic virus therapy, and the models will probably need to be revised and improved. For example, it is unclear whether and how the replication rate of the virus correlates with the rate of virus-induced cell killing. Many possibilities exist, and this is similar to the relationship between pathogen spread and "virulence" in an epidemiological context. Such more detailed information, based on experimental measurements, will be important to incorporate into the models in order to make more solid and reliable predictions.

12.6 Evaluating viruses in culture

A central result derived from the mathematical models is that success is promoted by using a virus which induces an optimal death rate of infected cells. Too high a rate of virus-induced cell death is detrimental and leads to the persistence of both tumor and virus, because overall virus spread is impaired. This gives rise to important insights for the methods used to evaluate potential viruses in culture [Wodarz (2003)].

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Time (arbitrary units)

Strongly cytopathic virus Weakly cytopathic virus

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Time (arbitrary units)

Fig. 12.8 Simulation showing the evaluation of potential replicating viruses in culture. A weakly and a strongly cytopathic virus are compared. Introduction of the virus is indicated by an arrow, (a) High multiplicity of infection, (b) Low multiplicity of infection. Parameters were chosen as follows: r=0.5; s=0; k=10; ¡3=1.5; d=0.01; k=0.1; u=l. For the strongly cytopathic virus, a = 0.4. For the weakly cytopathic virus, a = 0.04. Virus inoculum was y = 10 for high MOI and y = 0.01 for low MOI.

In vitro experiments can be used to evaluate the potential efficiency with which the virus can eradicate a tumor. This is done by infecting a population of cancer cells with virus in a dish and monitoring the number of cancer cell over time. The models suggest that a low multiplicity of infection (MOI, i.e. the initial abundance of the virus relative to the tumor cells) is required to evaluate the virus. The reason is that in vivo, the replicating virus has to spread through the cancer cell population, and this has to be mimicked in culture. Using a high MOI can lead to misleading evaluations. These notions are illustrated in Figure 12.8 with computer simulations. This figure depicts the dynamics in culture for strongly and weakly cytopathic viruses, using different MOIs. Figure 12.6a shows the dynamics for a high MOI. In this simulation, the strongly cytopathic virus results in quick elimination of the tumor cells, while the weakly cytopathic virus is much less effective. Thus, if viruses are evaluated using a high MOI, the virus with the strongest degree of tumor cell killing receives the highest grades. Importantly, this is the virus which is predicted to be least efficient at reducing tumor load in vivo. The situation is different when viruses are evaluated in culture using a low MOI (Figure 12.6b). The less cytopathic virus results in elimination of tumor cells in culture, while the more cytopathic virus fails to eliminate tumor cells in culture. Therefore, the less cytopathic virus gets the better marks, and this is also the virus which is predicted to be more efficient at reducing tumor load in vivo.

Appendix A

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