System Identification of Thermal Transfers Inside the Lungs Using Fractional Models

Abstract This paper is about fractional system identification of thermal transfers in the lungs. Usually, during open-heart surgery, an extracorporeal circulation (ECC) is carried out on the patient. In order to plug the artificial heart/lung machine on the blood stream, the lungs are disconnected from the circulatory system. No longer receiving blood, pulmonary cells die which, for the patient, may result in postoperative respiratory complications. A method to protect the lungs has been developed by surgeons and anesthetists. It is called: bronchial hypothermia. The aim is to cool the organ in order to slow down its deterioration. Unfortunately the thermal properties of the lungs are not well-known yet. Mathematical models are useful and needed in order to improve the knowledge of these organs. As proved by several previous works, fractional models are very appropriate to model thermal systems (model compactness, accuracy) and the dynamic of fractal systems. Thus, this paper studies the comparison between two fractional models, a classical one and another one using the Havriliak-Negami function.

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