Patients suffering from chronic respiratory failure can no longer ensure a correct oxigenation and remove carbon dioxide of their blood and present shortness of breath, rapid breathing, air hunger and diurn sleepiness. To overcome such a weakness, patient need breathing support provided by a ventilator. In the early 20th century, devices worked in a noninvasive way by applying a negative pressure on the thorax (the patient was thus immersed in large pressurized cage, the so-called "iron lung" as shown in Fig. 1) : a negative pressure was applied during inspiration for inflating the lung, the pressure return to the atmospheric pressure during expiration.
Today, noninvasive mechanical ventilation uses a positive pressure - here designated as the high pressure (between 10 and 30 cmH2O) - applied during inspiration through a nasal or facial mask ; during expiration a low positive pressure (from 4 to 8 cmH2) is applied to drain the ventilation circuit (the tube between the ventilator and the mask) from the carbon dioxide rejected by patient’s expiration. The challenge in noninvasive ventilation is therefore to synchronize the pressure cycle delivered by the device to patient’s breathing cycle. From the dynamical system point of view, the aim is to obtain phase synchronization between these two cycles, high (low) pressure arising during inspiration (expiration). In what seems to be the optimal ventilation mode (named pressure support ventilation), the ventilator is driven by patient’s inspiratory demand : the device must detect patient’s inspiratory demand to deliver the high pressure up to muscle ventilatory relaxation (expiration) during which the device must deliver a low pressure. Unfortunately, there are commonly asynchrony events - breathing cycles during which there is a lack of phase synchronization - resulting from leakage in the ventilation circuit (mostly at the interface between the mask and the facial skin) and/or a too large high pressure delivered during inspiration .
 L. Vignaux, F. Vargas, J. Roeseler, D. Tassaux, A. W. Thille, M. P. Kossowsky, L. Brochard & P. Jolliet, Patient-ventilator asynchrony during non-invasive ventilation for acute respiratory failure : a multicenter study, Intensive Care Medicine, 35 (5), 840-846, 2009.