Modeling of Tumor Growth Inhibition in Mice Following Electrochemotherapy

Assessment of a tumor response to electrochemotherapy is still limited to the observation of long-term outcomes. Monitoring tumor volume changes can provide additional information required for a more detailed analysis of the tumor response. In this paper, we present a new mathematical model of tumor growth inhibition in mice following electrochemotherapy. The model is based on a single ordinary differential equation describing tumor growth and shrinkage. The growth curve is represented by a function describing initial exponential growth followed by a gradual transition to a linear growth. The opposite process, tumor shrinkage, is modeled by a shifted Gaussian function. Free parameters of the model were estimated using nonlinear least squares fitting. Average value of linear growth rate obtained from the control group was used by fitting the tumor volumes of treated animals. Results show that the model is flexible enough to fit partial as well as complete responses. Additionally, three parameters reflecting the treatment effect were used to calculate the tumor growth delay according to the formula derived from the model. An excellent agreement with observed growth delays confirms that proposed model can serve as a basis for a quantitative assessment of tumor response to electrochemotherapy.