KISS, the well-known acronym for keep it simple, stupid, is often taken to be good advice for life in general. Not always, though, because simplicity can be very alluring but wrong. A recent editorial1 on septic shock (a complex, not simple subject), in another journal, had the title For every complex problem, there is a solution that is simple ... and wrong. This writer wishes that he had thought of that clever one-liner.
Suspicion of simplicity could also apply to the whole subject-matter of developing mathematical models and clinically useful indices to describe pulmonary oxygen transfer in the lung. This particular subject has exercised the minds of clinicians and physiologists for decades and forms an essential chapter in textbooks on respiratory physiology, anaesthesia and intensive care medicine. Moreover, for the trainee there is a galaxy of advice, opinions and controversies to be digested.27 The experts offer differing advice. The Holy Grail has always seemed to be a simple index that will quantify the degree of pulmonary oxygen transfer occurring in a given patient, and which can then be used to chart the progress of the patient as lung function improves or deteriorates.
The problem of reconciling theory and clinical practice in blood-gas exchange has long been recognized. A group of (mainly European) specialists from various medical fields was brought together a decade ago to bridge this gap between theory and practice and to discuss and argue about the oxygen status of arterial blood. The proceedings were published as a book, The Oxygen Status of Arterial Blood in 1991.8 A cursory glance at it reveals the real difficulties and complexities involved not only in the measurement of blood oxygen status and the subsequent clinical, therapeutic and diagnostic application of this knowledge, but also in the terminology used to define this status. Over 50 definitions are contained within the appendix! More recently, Siggaard-Andersen and Gothgen9 considered more than 40 different quantities involved in the complete pH and blood-gas analysis of arterial and mixed venous blood. Out of these they selected 16, including patient temperature, and proceeded to discuss the relevance of these various quantities in clinical practice. Arterial oxygen tension (PaO2), of course, figured prominently in their thinking. Hypoxaemia was suggested to be synonymous with a decreased PaO2 and arterial haemoglobin oxygen saturation was described as primarily an indirect measure of PaO2. Thus PaO2, not oxygen saturation, was their benchmark.
Correspondingly, because both PaO2 and the patients inspired oxygen concentration, FIO2, can be easily measured and, moreover, FIO2 varies at will, it is temptingly simple to relate the lungs pulmonary oxygen output signal (the PaO2) to its input signal (the FIO2) and then compare them. Consequently, these oxygen output and input values have been arranged by many workers to devise indices of hypoxaemia, such as the alveolararterial oxygen tension difference, P(Aa)O2; the arterial/alveolar ratio, PAO2/PaO2; the respiratory index, P(Aa)O2/PaO2; and the PaO2/FIO2 ratio.5 Each of these indices relates the arterial oxygen tension to the driving force for oxygen transfer in the lung, expressed either as the FIO2 or the alveolar oxygen tension, PAO2.
The other index of pulmonary oxygen transfer insufficiency, commonly referred to as physiological shunt, pulmonary shunt, right-to-left shunt (QS/QT), or venous admixture (QVA/QT),10 is based on measurements of the oxygen content of alveolar air, arterial and mixed venous blood. This is described by the well-known shunt10 or Berggren11 equation, although the actual contents are often calculated from algorithms incorporated into blood-gas analysers rather than measured directly.
Siggaard-Andersen and Gothgen compared physiological shunt to the indices mentioned above, and concluded that physiological shunt was a better indicator of pulmonary function than any of the oxygen tension indices based on PaO2 and FIO2.9 Perhaps it has always been naïve to expect such simple linear indices to describe adequately a system in which the non-linearity of the oxyhaemoglobin dissociation curve is fundamental.
In this issue of the BJA, Nirmalan and colleagues12 have revisited the subject of pulmonary oxygen transfer indices and have come to the same conclusion as Siggaard-Andersen and Gothgen, but from a different approach. They have taken a published ventilationdistribution (V/Q) curve describing an acute respiratory distress syndrome (ARDS) patient, and have checked its predictions against arterial blood obtained from real patients and then used this model to test three of the indices of pulmonary oxygen transfer (namely, QS/QT, P(Aa)O2 and PaO2/FIO2) together with the alveolararterial oxygen content difference, when FIO2 was varied between 0.21 and 1.0. As they admit, various other assumptions had to be made for the sake of simplicity, in order to test the effects of changes in the arterialmixed venous content difference on their model predictions. Thus, they are by necessity caught in the vortex of applying more simplifications to already simple mathematical models of pulmonary oxygen transfer in the dysfunctioning lung.
The conclusion of the studies of Nirmalan and colleagues is that the popularity of indices based on oxygen tension can be traced to their simplicity and not to their validity. They conclude that QS/QT is the best available measure of pulmonary oxygen transfer. They suggest that the PaO2/FIO2 index, in particular, has gained widespread acceptance for clinical and research purposes because of its simplicity alone. Their bottom line is that there is still no reliable substitute for QS/QT and that the inclusion of PaO2/FIO2 in the American European Consensus Conference recommendations without qualification may lead to its inappropriate use.12
This is, no doubt, a reasonable conclusion based on the evidence currently available and on the aetiology of the models themselves. Perhaps this is where the problem really lies. In our rush towards simplicity, have we not fallen into the all-too-common trap of equating simplicity with truth? Is it not time to acknowledge that, just as septic shock and the multiple organ dysfunction syndrome are complex,1 13 so oxygen transfer in the lung, especially in the sick lung, is extremely complex and cannot be described adequately by simple models. The respiratory system is itself amazingly complex, with as many as 23 generations in the respiratory tree, terminating with at least 108 alveoli, and breathing is also a dynamic process. Yet we continue to view the human lung as a continuous ventilation process in the steady state. We simply alter FIO2 to produce yet another steady state. A cursory glance at a textbook of comparative physiology14 will reveal that our models of pulmonary oxygen transfer are based on the fish gill model of gas exchange.15 John Nunn10 and John West16 17 developed this model to great effect in their classic teaching books on human respiratory physiology and gas exchange. We certainly owe these two authors an immense debt of gratitude for the clarity of their teaching and for the simple mathematical models they devised and handed down to generations of physiologists and clinicians.
However, this editorial writer has an uneasy feeling that we have remained static in our thoughts and ideas for far too long and have not followed the example of some of our physician colleagues, who have realized for a long time now that disease is a dynamic process. Their models of dynamic disease may be mathematically complex, but if the development of a disease process is complex, then so must be the mathematical model. One illustration of this approach is the book Dynamic Disease: Mathematical Analysis of Human Ilness,18 which gives diverse examples such as non-linear modelling of the immune response, phase-space analysis of dynamic parathyroid hormone secretion, the dynamic structure of tremor in tardive dyskinesia, phase-locking and other non-linear dynamic phenomena in slow insulin and glucose oscillations, self-organizing dynamics in the brain, among others.
Compared with this, our own approach to gas exchange, based on 1960s models, looks very dated now. On the positive side, Hlastala and Robertson, in their recent book Complexity in Structure and Function of the Lung,19 are perhaps pushing us into the 21st century and are persuading us that new models need to be devised whenever the old paradigms fail in clinical practice.
So where do we go to from here? Nirmalan and colleagues have joined a growing group of authors who have challenged the use of clinical indices of pulmonary oxygen transfer that are attractive solely because of their mathematical simplicity. Although they advocate the use of QS/QT, this index is not without its own problems and has, itself, been shown to vary with FIO2, sometimes upwards, sometimes downwards and sometimes not at all (the so-called isoshunt phenomenon).3 10 We also need to remember that the shunt equation is itself built upon the premises of steady-state alveolar gas and continuous blood flow.10 Others have questioned recently whether the concept of a steady-state pulmonary shunt is adequate to describe the ARDS lung.20
Thus, it is not easy at the moment to answer the question Where do we go from here? There are no realistic, comprehensive but still clinically useful mathematical models available. Surely what we need to do is to follow the example of the physicians and to develop realistic dynamic models of gas exchange in the failing lung, even if such models may not provide simple analytical formulae that can be derived and quoted in a textbook? The availability of powerful modern desktop computers and associated software and the growing interest of mathematicians in clinical medicine will surely produce new models of gas exchange that can be used in clinical practice. The advent of the Human Physiome Project21 (with a concurrent, and necessary, resurgence in systems physiology), with the aim of mathematically modelling all the bodys major organs during this new century, will eventually provide accurate models for the anaesthetist and the intensivist. The Human Physiome Project is, however, in its infancy at the moment and the announcement of a comprehensive mathematical model of the pulmonary system is still on the distant horizon.
So, in the meantime, we are left with the classical steady-state and continuous blood and gas flow indices with which we currently work. Some efforts are now being made to introduce tidal ventilation relationships into gas exchange models.22 23 But even these are based on the balloon-on-a-straw description of the respiratory system, and this is hardly an accurate description of the lung! Still, this model might be better that the fish gill model of pulmonary gas exchange that we work with at present.15 It is now time for the new generation of anaesthetists not only to challenge the current status quo, as Nirmalan and colleagues have done in this issue,12 but also to devise new and better mathematical relationships to describe pulmonary oxygen transfer in the ARDS patient. The challenge is there. Who will take it up?
Clive E. W. Hahn
Nuffield Department of Anaesthetics
University of Oxford
Radcliffe Infirmary
Woodstock Road
Oxford OX2 6HE
UK
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