Gas exchange modelling: no more gills, please.

Concepts of continuous ventilation and perfusion have founded mathematical models of lung gas mixing and cardiopulmonary blood±gas exchange, whether for anaesthetic vapour uptake or for cardiorespiratory measurement, for several decades now. 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 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 element of theory that cannot be perceived (or experimentally observed) is cut out with Occam's razor, leaving a simpler more heuristic model. It can work well in philosophy or particle physics, but less often so in meteorology or biology, for example, where things usually turn out to be more complicated than ever expected. In the study of gas exchange, Occam's razor has been wielded indiscriminately. It has been used not to eliminate elements of theory that cannot be measured, but rather to cut out elements which can be measured but which we don't like the look of. For example, conventional gas-exchange models appear to have some glaring omissions. Neither lung volume nor the inspiratory:expiratory (I:E) time ratio play any part in the conventional mathematical equations that govern gas exchange in the lung. Yet clinical experience would tell us otherwise. Conventional models also assume steady-state conditions, and this is seldom the reality even in normal physiology, let alone in the disease state. More fatally, conventional models are linear. Godin and Buchman remind us that non-linear behaviour is the rule rather than the exception in medicine. They state, `the selection of linear mathematical models to describe non-linear phenomena was until recently a matter of sheer necessity. Nonlinear models are intractable without the aid of modern high-speed computers.' In the case of a speci®c form of non-linear behaviour, namely `chaos', such models can be intractable even with the aid of supercomputers. Godin and Buchman argue that the in ̄uence of the linear approximation on the interpretation of natural phenomena is pervasive. They hypothesize that non-linear interpretations of human physiology could suggest alternative explanations for human pathophysiology. The constant danger for us is that when we attempt to match physiological data to analytical expressions for continuous ventilation and then ponder the inevitable mismatch, our instinct is to think that we must have made British Journal of Anaesthesia 91 (1): 2±15 (2003) DOI: 10.1093/bja/aeg142