A NONLINEAR MATHEMATICAL MODEL OF AN IMMUNOTHERAPY TREATMENT OF PARATHYROID CARCINOMA

A mathematical model has been developed that describes the competitive binding process present in an immunotherapy treatment for parathyroid carcinoma. Compartmental analysis was employed to relate the flow and interaction of parathyroid hormone (PTH) and antibodies during the treatment. The model indicates a mechanism of how the antibody response effectively reduces the levels of free PTH. The results suggest that a maximum immune response occurs at approximately 13 weeks after the initial treatment. The immunotherapy treatment used injections of PTH hormone to induce an immune response; it was found that these injections had no negative effect on the PTH levels in the system. Additionally, the model allowed several conclusions to be drawn relating to optimal parameter choices with respect to treatment. For antibody binding the optimal level of effect was around 109s–1, this is within the published in vivo range of 108-1010s–1. It was also established that the concentrations of parathyroid receptors are crucial in determining the pharmacodynamic effects of the treatment.