Dynamic models and solutions for evaluating ventilation, perfusion, and mass transfer in the lung--Part II: Analog solutions

Modelling mixing within the dead space of the lung improves predictions of functional residual capacity

Routine estimation of functional residual capacity (FRC) in ventilated patients has been a long held goal, with many methods previously proposed, but none have been used in routine clinical practice. This paper proposes three models for determining FRC using the nitrous oxide concentration from the entire expired breath in order to improve the precision of the estimate. Of the three models proposed, a dead space with two mixing compartments provided the best results, reducing the mean limits of agreement with the FRC measured by whole body plethysmography by up to 41%. This moves away from traditional lung models, which do not account for mixing within the dead space. Compared to literature values for FRC, the results are similar to those obtained using helium dilution and better than the LUFU device (Dräger Medical, Lubeck, Germany), with significantly better limits of agreement compared to plethysmography.

Estimation of pulmonary blood flow from sinusoidal gas exchange during anaesthesia: a theoretical study

We simulated the use of simultaneous sinusoidal changes of inspired O2 and N2O (Williams et al., J Appl Physiol, 1994; 76: 2130-9) at fractional concentrations up to 0.3 and 0.7, respectively, to estimate FRC and pulmonary blood flow (PBF) during anaesthesia, using O2 as an insoluble indicator. Hahn's approximate equations, which neglect the effect of pulmonary uptake and excretion on expiratory flow, estimate dead space and alveolar volume (VA) with systematic errors less than 10%, but yield systematic errors in PBF which are approximately proportional to FIN2O in magnitude. A correction factor (1 - P)-1 for Hahn's equations for PBF (where P is the mean partial pressure of the soluble indicator) reduces the dependence of PBF estimates of FIN2O, and the solution of equations describing the simultaneous mass balance of both indicators yields accurate results for a wide range of mean FIN2O. However, PBF estimates are sensitive to measurement errors and a third gas must be present to ensure that the indicator gases behave independently.

A tidal breathing model of the forced inspired inert gas sinewave technique

We have shown previously that it is possible to assess the cardio-respiratory function using sinusoidally oscillating inert gas forcing signals of nitrous oxide and argon (Hahn et al., 1993). This method uses an extension of a mathematical model of respiratory gas exchange introduced by Zwart et al. (1976), which assumed continuous ventilation. We investigate the effects of this assumption by developing a mathematical model using a single alveolar compartment and incorporating tidal ventilation, which must be solved using numerical methods. We compare simulated results from the tidal model with those from the continuous model, as the governing ventilatory and cardiac parameters are varied. The mathematical model is designed to be the basis of an on-line, non-invasive, cardio-respiratory measurement method, and will only be useful if the associated parameter recovery techniques are both reliable and robust. We demonstrate, in the presence of simulated measurement errors, that: (a) accurate recovery of the ventilatory parameters end-tidal volume, VA, and airways series dead-space, VD, are possible using the tidal breathing model; and (b) that a robust technique for recovery of pulmonary blood flow, QP, can be obtained using the more familiar continuous ventilation model.

A mathematical evaluation of the alveolar amplitude response technique

The underlying mathematical model of the forcing sinewave alveolar amplitude response technique (AART) for measuring lung volume and perfusion is investigated. Making use of numerical techniques, we are able to to evaluate the effects of several assumptions which are implicit in the original technique introduced by Zwart et al., J. Appl. Physiol. 41: 419-429, 1976, and development by several other workers. In particular we are able to show that AART is appropriate for gases of a wider range of solubilities than originally suggested, allowing it to be used with agents, such as nitrous oxide, which are more clinically acceptable. In addition, we are able to show that the effects of recirculation times are likely to be very small using figures for standard man. A least squares parameter recovery technique proves to be very robust to simulated measurement errors and is used to quantify the effects of the modelling assumptions.