On probabilistic certification of combined cancer therapies using strongly uncertain models

• A general framework for the use of the concept of probabilistic certification is proposed for combined therapy of cancer.
• It is shown that this concept is more suited when a high number of uncertain parameters are involved in the definition of the dynamic model of the cancer.
• While the proposed framework is general, and may apply to a wide class of model and control design, it is illustrated through the particular case of combined therapy of cancer involving immunotherapy and chemotherapy.
• Two design frameworks with probabilistic certification frameworks are proposed for two different criteria to be optimized, namely, the quantity of drugs being used or the total duration of the hospitalization.

This paper proposes a general framework for probabilistic certification of cancer therapies. The certification is defined in terms of two key issues which are the tumor contraction and the lower admissible bound on the circulating lymphocytes which is viewed as indicator of the patient health. The certification is viewed as the ability to guarantee with a predefined high probability the success of the therapy over a finite horizon despite of the unavoidable high uncertainties affecting the dynamic model that is used to compute the optimal scheduling of drugs injection. The certification paradigm can be viewed as a tool for tuning the treatment parameters and protocols as well as for getting a rational use of limited or expensive drugs. The proposed framework is illustrated using the specific problem of combined immunotherapy/chemotherapy of cancer.