A NONLINEAR MATHEMATICAL-MODEL OF PRESSURE PRESET VENTILATION - DESCRIPTION AND LIMITING VALUES FOR KEY OUTCOME VARIABLES

In recent years, several new forms of pressure preset mechanical venti lation (PPV) have been introduced to clinical practice. Although these modes are widely employed in patient care, clinical decision making r emains a largely empirical ''trial and error'' process. Existing predi ctive equations for ventilation are questionably accurate, in part bec ause most attempts to model ventilation have assumed constant values f or inspiratory and expiratory resistance, even though the pressure-flo w relationship is clearly nonlinear in biological systems. In this pap er, we present and analyze a nonlinear mathematical model of PPV which accounts for the interactive behavior of inspiratory and expiratory h alf cycles. It comprises a set of nonlinear differential equations whi ch incorporate a variably nonlinear relationship between the resistive component of the applied pressure and flow rate. This model is compar ed to our previously described biphasic (linear) exponential model of PPV (J. Appl. Physiol. 67 (1989) 1081-0192) which serves to link the c linical ''input'' variables of pressure level, frequency, inspiratory time fraction, and impedance with the key ''outcome'' variables of cli nical interest: tidal volume, minute ventilation, power, airway pressu re, mean alveolar pressure, and expiratory alveolar pressure. Predicti ve differences arise between linear and nonlinear formulations. Althou gh general closed-form solutions for several of the outcome variables could not be obtained, implicit expressions are derived. Explicit deri vations are also presented for selected flow exponents of interest. Fu rthermore, we found that the limiting values for each outcome variable as a function of cycling frequency could be derived explicitly, once the exponent for flow is uniquely specified.