Mathematical modelling of tumor growth in mice following electrotherapy and bleomycin treatment

In treatment of subcutaneous solid tumors in mice locally applied electrotherapy by direct current and i.v. administered bleomycin were combined. The study showed the interaction of both treatments in a way, that the antitumour effect of both was more than additive when compared to single treatments. The electrotherapy by means of 0.6 mA of one hour duration, as single treatment significantly delayed tumour growth in comparison to control group (growth delay GD = 6.7 ± 1.2 days), whereas therapy by 250 μg bleomycin i.v. injection had only moderate effect on tumour growth (GD = 0.5 ± 0.2 days). When both treatments were combined the tumour growth delay observed was 10.8±1.9 days. A model was developed in which the pharmacokinetic model of bleomycin was extended and transformed to the level of macroscopic biologically detectable effect i.e. tumour growth retardation. The data on tumor growth in control group was used to determine parameters of the Gompertz model (V0, αv0 and β). For modelling of both single treatments the extended Gompertz equation was used. In the case of electrotherapy a two component effect had to be introduced in order to obtain satisfactory fit. The effect of bleomycin on tumour growth was obtained by introducing the influential parameter which transferred the bleomycin concentration in tumour tissue obtained from pharmacokinetic model to the effect on tumour growth.