British Journal of Anaesthesia 97 (5): 718–31 (2006) doi:10.1093/bja/ael216 Advance Access publication August 21, 2006 RESPIRATION AND THE AIRWAY A tidally breathing model of ventilation, perfusion and volume in normal and diseased lungs† J. S. Yem1, M. J. Turner1*, A. B. Baker1, I. H. Young2 and A. B. H. Crawford3 1Department of Anaesthetics, and 2Department of Respiratory Medicine, The University of Sydney, Royal Prince Alfred Hospital, Missenden Road, Camperdown, NSW 2050, Australia. 3Department of Respiratory Medicine, Westmead Hospital, Westmead, NSW 2145, Australia *Corresponding author: Department of Anaesthetics, University of Sydney, Royal Prince Alfred Hospital, Building 89 Level 4, Missenden Road, Camperdown, NSW 2050, Australia. E-mail: [email protected] Background. To simulate the short-term dynamics of soluble gas exchange (e.g. CO2 rebreath- _ ing), model structure, ventilation–perfusion (V_ A/Q) and ventilation–volume (V_ A/VA) parameters _ must be selected correctly. Some diseases affect mainly the V_ A/Q distribution while others _ affect both V_ A/Q and V_ A/VA distributions. Results from the multiple inert gas elimination technique (MIGET) and multiple breath nitrogen washout (MBNW) can be used to select _ _ V_ A/Q and V_ A/VA parameters, but no method exists for combining V_ A/Q and V_ A/VA parameters in a multicompartment lung model. Methods. We define a tidally breathing lung model containing shunt and up to eight alveolar compartments. Quantitative and qualitative understanding of the diseases is used to reduce the number of model compartments to achieve a unique solution. The reduced model is _ fitted simultaneously to inert gas retentions calculated from published V_ A/Q distributions and normalized MBNWs obtained from similar subjects. Normal lungs and representative cases of emphysema and embolism are studied. Results. The normal, emphysematous and embolism models simplify to one, three and two alveolar compartments, respectively. Conclusions. The models reproduce their respective MIGET and MBNW patient results well, and predict disease-specific steady-state and dynamic soluble and insoluble gas responses. Br J Anaesth 2006; 97: 718–31 Keywords: modelling, ventilation/perfusion distribution, ventilation inhomogeneity Accepted for publication: May 19, 2006 Simulation of respiratory exchange of soluble gases in strongly on the distribution of V_ A/Q_ ratios but is indepen- diseased lungs under dynamic conditions requires that dent of alveolar volumes. Exchange of soluble gases during the model structure and parameters associated with the transients, however, depends on the distributions of both distributions of both ventilation–perfusion (V_ A/Q_ ) and V_ A/Q_ and V_ A/VA ratios. Some diseases, e.g. pulmonary ventilation–volume (V_ A/VA) ratios are selected correctly. embolism, affect mainly the V_ A/Q_ distribution while others, For example, the simulation of cardiac output measurement e.g. emphysema, affect both V_ A/Q_ and V_ A/VA distributions. 1 by short respiratory manoeuvres such as CO2 rebreathing, To simulate the transport and storage of soluble gases which is increasingly used in anaesthesia and intensive during dynamic manoeuvres in subjects with both V_ A/Q_ 23 care for measurement and monitoring of cardiac output, and V_ A/VA heterogeneity, the parameters associated with requires models that predict well short-term changes in the V_ A/Q_ and V_ A/VA distributions should be selected in a transfer and storage of such a soluble gas. Steady-state exchange of soluble gases in diseased lungs depends †This article is accompanied by the Editorial. Ó The Board of Management and Trustees of the British Journal of Anaesthesia 2006. All rights reserved. For Permissions, please e-mail: [email protected] A tidal model of diseased lungs rational manner. Parameters of simple models are often The subject breathes air before the procedure. At the selected arbitrarily to produce outputs that match clinical start of the MBNW, the inspired gas is switched to a observations qualitatively.4–8 In more complex models arbi- mixture containing no nitrogen, and end-tidal nitrogen trary selection of parameters may lead to invalid or extreme concentration is monitored over a washout period that predictions, particularly during dynamic changes in is typically 7 min. ventilation or perfusion. Numerous studies have shown that the information in a At present there is no systematic approach for selecting washout curve is sufficient to describe only two or at most mutually consistent sets of parameters for respiratory mod- three compartments.22 24 25 Lewis and colleagues22 des- els that incorporate both V_ A/Q_ and V_ A/VA heterogeneity. In cribed a technique for recovering a continuous distribution this study, we describe procedures for selecting alveolar of ventilation from a MBNW. This technique uses a compartment ventilation, volume and perfusion parameters smoothed least-squares fitting procedure similar to that used 13 for a tidally breathing respiratory model, based on multiple in the MIGET to recover distributions of V_ A/Q_ ratios. inert gas elimination technique (MIGET) and multiple breath Both normal and more complex distributions recovered nitrogen washout (MBNW) measurements. These models are from nitrogen washouts were shown to be reproducible developed for the purposes of simulating the exchange of within an individual.22 Therefore, significant changes in soluble and insoluble gases during dynamic respiratory the shape of the distribution can be attributed to changes manoeuvres such as full, or partial rebreathing which is to the subject’s lungs.22 Wagner21 examined the variability now commonly used in anaesthesia and intensive care. among compatible ventilation distributions, and found that in general, the achievable resolution depends on the specific underlying distribution, and physiologically significant Materials and methods features of the distribution can usually be specified, although the more complex a distribution is, the less resolution is Background possible. Other studies to assess the effects of experimental error on the resolution of the MBNW confirm that the Ventilation–perfusion ratio heterogeneity information present in a MBNW is insufficient to allow 910 The MIGET has long been used for investigating the confident resolution of more than two ventilation modes matching of ventilation and perfusion in the lungs. Small and an estimate of dead-space.25 26 Thus, a model based quantities of six inert gases are dissolved in saline and i.v. on MBNW measurements may contain lung compartments infused until the mixed venous blood content of each inert with only two different V_ A/VA ratios. gas is constant or changing at a slow uniform rate. The V_ A/Q_ distributions are constructed from measurements of the Ventilation, perfusion and volume heterogeneity steady-state concentrations of the inert gases in mixed We propose a subset of the three dimensional alveolar struc- venous blood, mixed arterial blood and mixed expired ture suggested by Whiteley and colleagues,27 in a tidally O CO gas. Arterial and mixed expired P 2 and P 2 calculated breathing model, to simulate simultaneous ventilation, using the derived V_ A/Q_ distribution compare well with 11–13 perfusion and volume heterogeneity. The eight alveolar corresponding measured values. compartments and shunt (Fig. 1) allow this model to exhibit _ _ The shapes of MIGET-derived V A/Q distributions steady-state gas exchange behaviour consistent with any for many respiratory conditions are known, and in many cases distinct patterns can be associated with specific res- 14–17 2 _ _ V Q different V piratory conditions. As the A/ distribution is a · · · · Q Q Q Q steady-state property of the lungs, predictions made by a s · 1a · 2a · 3a · · respiratory model derived only from MIGET measurements V1a V2a V3a V4a Va 15 V1a V2a V3a V4a Va are likely to be incorrect in non-steady-state conditions. · A Shunt /V The V_ A/Q_ distributions recovered by MIGET have been · · · A 9111318–20 Q Q Q Compartments shown to contain a limited amount of information. · 1b · 2b · 3b · · While the lungs contain a great number of gas exchange V1b V2b V3b V4b Vb units, the MIGET has been shown to be able to discriminate V1b V2b V3b V4b Vb _ _ only three distinct V A/Q modes, or two modes in addition ·· ·· ·· 911 Shunt(V /Q ) (V /Q ) (V /Q ) Dead-space to shunt, and dead-space. Hence, in general, a model · A · 1 A · 2 A· 3 · Q Q Q Q VAlv, DS based on MIGET measurements needs to contain only s ·1 ·2 ·3 V V V three different V_ A/Q_ lung compartments in addition to 1 2 3 shunt and dead-space. ·· 3 different VA/Q compartments Ventilation–volume ratio heterogeneity Fig 1 Alveolar compartment structure containing pure shunt, two The MBNW technique is commonly used for alveolar dead-space compartments and six ventilated and perfused investigating indices of ventilation inhomogeneity.21–23 alveolar compartments. 719 Yem et al. measured V_ /Q_ distribution and dynamic characteristics implemented using Matlab and Simulink (Mathworks, Nat- consistent with any measured N2 washout. ick, MA, USA). Alveolar volume and the spread of the V_ A/VA distribution have been shown to have negligible effect on V_ A/Q_ distri- butions recovered using the MIGET5 if the retention ratios Parameter estimation are averaged over a complete respiratory cycle. Although Measured MIGET and MBNW data obtained in subjects nitrogen has a low solubility, we anticipate that the N2 who are representative of adults with normal lungs, emphys- washout and hence the measured V_ A/Q_ distribution may ema and pulmonary embolism were selected from the be affected by the V_ A/Q_ distribution by three mechanisms. literature. All model parameters other than compartmental _ First, the rate at which N2 dissolved in body tissues is VA, V_ A and Q were obtained from the respective articles 22 eliminated in expired gas may be affected by V_ /Q_ ratios from which individual V_ A/Q_ or V_ A/VA data were obtained of low V_ /Q_ compartments.