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The aim of this study was to develop a lung model which adapted its active simulation of spontaneous breathing to the ventilatory assistance it received--an "aa" or "a-squared" lung model. The active element required was the waveform of negative pressure (pmus), which is equivalent to respiratory muscle activity. This had been determined previously in 12 healthy volunteers and comprised a contraction phase, relaxation phase and expiratory pause. Ventilatory assistance had shortened the contraction and relaxation phases without changing their shape, and lengthened the pause phase to compensate. In this study, the contraction and relaxation phases could be adequately represented by two quadratic equations, in addition to a third to provide a smooth transition. Therefore, the adaptive element required was the prediction of the duration of the contraction phase. The best predictive variables were flow at the end of contraction or peak mouth pressure. Determination of either of these allowed adjustment of the "standard" waveform to the level of assistance produced by an "average" ventilator, in a manner that matched the mean response of 12 healthy conscious subjects.