Adjoint sensitivity analysis of a tumor growth model and its application to spatiotemporal radiotherapy optimization

We investigate a spatial model of growth of a tumor and its sensitivity to radiotherapy. It is assumed that the radiation dose may vary in time and space, like in intensity modulated radiotherapy (IMRT). The change of the final state of the tumor depends on local differences in the radiation dose and varies with the time and the place of these local changes. This leads to the concept of a tumor's spatiotemporal sensitivity to radiation, which is a function of time and space. We show how adjoint sensitivity analysis may be applied to calculate the spatiotemporal sensitivity of the finite difference scheme resulting from the partial differential equation describing the tumor growth. We demonstrate results of this approach to the tumor proliferation, invasion and response to radiotherapy (PIRT) model and we compare the accuracy and the computational effort of the method to the simple forward finite difference sensitivity analysis. Furthermore, we use the spatiotemporal sensitivity during the gradient-based optimization of the spatiotemporal radiation protocol and present results for different parameters of the model.