Gas exchange modelling: no more gills, please

Abstract

Concepts of continuous ventilation and perfusion havefounded mathematical models of lung gas mixing and cardiopulmonary blood±gas exchange, whether for anaesthetic vapour uptake or for cardiorespiratory measurement, for several decades now. 20 28 37 42 The beauty of continuousventilation and perfusion models is that they allow mathematical expressions that are readily soluble, and they describe body processes in a linear and intuitive way. Hlastala and Robertson 21 describe the success of these conventional approaches,`For the lung, perhaps more than any other organ, simple models have proven exceptionally fruitful in the process of investigation. Our textbooks are ®lled with analogies of springs and dashpots, sluices and waterfalls, gravitational gradients, and bubbles. When the simplest analogies failed to precisely represent observed properties, the inclusion of two or three compartments with different parameters usually suf®ced to smooth over discrepancies between predictions and observations.'These simple mathematical models are attractive yet beguiling. They can mislead because they divert our gaze from the reality that ventilation is not continuous but tidal in nature. Unfortunately, mathematical models that involve discontinuities in inspired and expired gas¯ow, and therefore in lung volume, produce equations that do not have simple analytical solutions. There is a reluctance to consider, let alone teach from, such`tidal' models in clinical practice because they appear complex and are intuitively opaque.Here we can see the application of the philosophical concept of Occam's razor. Named after the 14th century logician and Franciscan friar, William of Occam, the principle states:`Frustra ®t per plura quod potest ®eri per pauciora', which very roughly paraphrased means`when you have two competing theories which make exactly the same predictions, the one that is simpler is the better'. This philosophy is a form of logical positivism in which any

Assessment of lung function using a non-invasive oscillating gas-forcing technique

“…Also, such models do not lend themselves readily to physiological interpretation. This is why simple one-alveolar lung compartment models have survived the succeeding decades after they were first proposed (Hahn and Farmery, 2003). Our techniques are likely to be valid in exercise testing in subjects or patients without overt lung disease, and could be applied to the field of human exercise physiology, as pioneered by Luijendijk et al (Luijendijk et al, 1981) for the forced inspired sine wave technique.…”

“…We employ a “balloon-on-a-straw” tidal ventilation model (Hahn and Farmery, 2003), shown in Fig. 1(b).…”

“…Compared with the rigid volume of the continuous ventilation model, the lung volume (the balloon) in the “balloon-on-a-straw” model reflects the reality of breathing, where the lung expands during inspiration and empties during expiration. A detailed description of the “balloon-on-a-straw” tidal ventilation model can be found in Hahn and Farmery (2003).…”

Simulating hypoxia and modelling the airway

“…there is no discrete boundary between what we used to consider to be alveolar and upper airway dead space compartments [5]. The relevance of this kind of modelling is that we can apply it to real clinical situations to get answers or predictions that match reality.…”

“…Models can be divided into 'forward' and 'inverse' [5]. The simpler forward models create a mathematical model based on physical laws, such as in the falling ball example given above, but in physiology, the model might be based on the conservation of mass, Fick's law of diffusion, the gas laws etc.…”