Mathematical Models About Radioactive Iodine-Refractory Differentiated Thyroid Cancer

Clinical and pathological evidence suggests that the progression of Differentiated Thyroid Carcinomas to a poorly differentiated stage, or even an anaplasic cancer, is a natural process in the development of malignancy. The immune regulatory molecule PD-L1, Programmed Death-Ligand 1, blocks the immune response of activated T cells by binding to the PD-1 receptor, an immune checkpoint expressed in T cells and others, to modulate their activation or inhibition. In addition to the traditional 131-I radioiodine treatment, other therapeutic options for DTC are needed when cells lose their ability to capture and concentrate iodine. Two examples of drugs used due to the evolution of DTC to a progressive state in the loss of sensitivity to RAI correspond to Lenvatinib, which is a target therapy with the function of inhibiting multiple tyrosine kinases, and thus reducing tumor cell proliferation; and Pembrolizumab, a monoclonal antibody of human immunoglobulin G4 that aims to prevent the binding of PD-1 to PD-L1, and thus restore the anti-tumor immune response of anti-tumor T cells. We propose two mathematical models of ordinary differential equations in order to evaluate two modes of treatment for patients with DTC refractory to RAI. In the first model, considering the variables concentration of Lenvatinib, number of malignant cells and NK cells, we evaluated the effectiveness of the target therapy in the treatment. The second model includes the addition of the variable concentration of Pembrolizumab, and T cells in the group of NK immune cells, and for this reason, we simulate in this case the effectiveness of the therapeutic combination with patients. As a result, we obtained that both drugs were able to generate responses such as stable disease or partial response, however, greater control of the tumor was observed from the combination of the proposed therapies.