Data-based modeling of breast cancer and optimal therapy

Excessive accumulation of β-catenin proteins is a vital driver in the development of breast cancer. Many clinical assessments incorporating immunotherapy with targeted mRNA of β-catenin are costly endeavor. This paper develops novel mathematical models for different treatments by invoking available clinical data to calibrate models, along with the selection and evaluation of therapy strategies in a faster manner with lower cost. Firstly, in order to explore the interactions between cancer cells and the immune system within the tumor microenvironment, we construct different types of breast cancer treatment models based on RNA interference technique and immune checkpoint inhibitors, which have been proved to be an effective combined therapy in pre-clinical trials associated with the inhibition of β-catenin proteins to enhance intrinsic anti-tumor immune response. Secondly, various techniques including MCMC are adopted to estimate multiple parameters and thus simulations in agreement with experimental results sustain the validity of our models. Furthermore, the gradient descent method and particle swarm algorithm are designed to optimize therapy schemes to inhibit the growth of tumor and lower the treatment cost. Considering the mechanisms of drug resistance in vivo, simulations exhibit that therapies are ineffective resulting in cancer relapse in the prolonged time. For this reason, parametric sensitivity analysis sheds light on the choice of new treatments which indicate that, in addition to inhibiting β-catenin proteins and improving self-immunity, the injection of dendritic cells promoting immunity may provide a novel vision for the future of cancer treatment. Overall, our study provides witness of principle from a mathematical perspective to guide clinical trials and the selection of treatment regimens.