Mathematical Models
in Medicine

These models have the potential to specifically improve the timing and dosage of medication for the patient, but are only rarely used clinically. In order to calibrate the developed model on a patient-specific basis, a mathematical model for the disease in question and longitudinal patient data from key markers are required. The model can then be used to predict and develop optimal and adaptive control algorithms to determine the optimal timing and dose of medication that would bring the patient closer to a pre-defined target state. This method can be used, for example, to correctly adjust hormones. For example, when adjusting thyroid hormones, which play a central role in metabolism, control algorithms can be used to optimally adjust hormone release to a desired euthyroid state. Another example is the transplantation of organs, where the lifelong immunosuppression required must be adjusted so that the transplant is not rejected and protection against viral infections such as CMV is guaranteed. Adaptive control algorithms based on mathematical models can optimize the dose of immunosuppression between these two poles, depending on measured patient data. More generally, adaptive control algorithms could be used in medicine wherever a measurable parameter that well characterizes the patient's state of health is to be kept within a certain target range by medication. We plan to establish this method in clinical medicine with the help of pilot projects. As an application example, we will optimize vaccination responses between the poles of successful generation of neutralizing antibodies and the development of autoimmunity.


Prof. Dr. Michael Meyer-Hermann, HZI


Prof. Dr. Matthias Müller, L3S