Lung Thermal Transfer System Identification With Fractional Models

System identification through fractional models is proposed for modeling thermal transfers in the lungs. In general, during open-heart surgery, an extracorporeal circulation is carried out on the patient. First, the lungs are disconnected from the circulatory system so that an artificial heart/lung machine can be plugged on the bloodstream. Pulmonary cells die when they are no more supplied with fresh blood, which may result in postoperative respiratory complications for the patient. Also, bronchial hypothermia is carried out to protect the lungs. Indeed, cooling the lung organ helps slowing down its deterioration. Unfortunately, the lung thermal properties are not well known yet; therefore, mathematical models are useful and needed in order to improve the knowledge of these organs. As proved by several previous works, fractional models are well suited to model the dynamics of fractal systems and to model thermal systems, thanks to its model parameter compactness but also thanks to the solving of the heat equation whose analytical result reveals a fractional differentiation operator of order 0.5. System identification results are provided on real data measured on sheep lungs. Thus, this paper studies the comparison between a rational model and two kinds of fractional models, a classic one and another one using the Havriliak-Negami function. Time-domain and frequency-domain analysis are provided, showing the efficiency of fractional models, but more precisely of Havriliak-Negami transfer functions.