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A nonlinear dynamic morphometric model of breathing mechanics during artificial ventilation is described. On the basis of the Weibel symmetrical representation of the tracheo-bronchial tree, the model accurately accounts for the geometrical and mechanical characteristics of the conductive zone and packs the respiratory zone into a viscoelastic Voigt body. The model also accounts for the main mechanisms limiting expiratory flow (wave speed limitation and viscous flow limitation), in order to reproduce satisfactorily, under dynamic conditions, the expiratory flow limitation phenomenon occurring in normal subjects when the difference between alveolar pressure and tracheal pressure (driving pressure) is high. Several expirations characterized by different levels of driving pressure are simulated and expiratory flow limitation is detected by plotting the isovolume pressure-flow curves. The model is used to study the time course of resistance and total cross-sectional area as well as the ratio of fluid velocity to wave speed (speed index), in conductive airway generations. The results highlight that the coupling between dissipative pressure losses and airway compliance leads to onset of expiratory flow limitation in normal lungs when driving pressure is increased significantly by applying a subatmospheric pressure to the outlet of the ventilator expiratory channel; wave speed limitation becomes predominant at still higher driving pressures.

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A new one-step computational procedure is presented for estimating the parameters of the nonlinear three-element windkessel model of the arterial system incorporating a pressure-dependent compliance. The data required are pulsatile aortic pressure and flow. The basic assumptions are a steady-state periodic regime and a purely elastic compliant element. By stating two conditions, zero mean flow and zero mean power in the compliant element, peripheral and characteristic resistances are determined through simple closed form formulas as functions of mean values of the square of aortic pressure, the square of aortic flow, and the product of aortic pressure with aortic flow. The pressure across as well as the flow through the compliant element can be then obtained so allowing the calculation of volume variation and compliance as functions of pressure. The feasibility of this method is studied by applying it to both simulated and experimental data relative to different circulatory conditions and comparing the results with those obtained by an iterative parameter optimization algorithm and with the actual values when available. The conclusion is that the proposed method appears to be effective in identifying the three-element windkessel even in the case of nonlinear compliance.

A physiologically based simulation model of breathing mechanics was considered in an attempt to interpret and explain the time course of input respiratory resistance during the breathing cycle, observed in recent studies on ventilated patients. The model assumes a flow-dependent Rohrer resistance for the upper extrathoracic airways and volume-dependent resistance and elastance for the intermediate airways. A volume-dependent resistance describes the dissipative pressure loss in the lower airways, and two constant elastances represent lung and chest wall elasticity. Simulated mouth flow and pressure signals obtained in a variety of well-controlled conditions were used to analyze total respiratory resistance and elastance estimated by an on-line algorithm based on a time-varying parameter model. These estimates were compared with those provided by classical estimation algorithms based on time-invariant models with two, three, and four parameters. The results show that the four-parameter model is difficult to identify, while the three-parameter one offers no substantial advantage for estimating input resistance with respect to the more simple two-parameter model. In contrast, the time-varying approach provides good on-line estimates of the simulated end-expiration and end-inspiration resistances. These values provide further information of potential clinical utility, with respect to time-invariant models. For example, the results show that the difference between the end-expiration and end-inspiration resistance increases when obstructions shift from the upper to the lower airways. The similarity of the results obtained with measured and simulated data indicates that, in spite of its simplicity, the simulation model describes important physiological mechanisms underlying changes in respiratory input resistance, specifically the mechanical properties of intermediate airways.