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Gas exchange modelling: no more gills, please

2003; Elsevier BV; Volume: 91; Issue: 1 Linguagem: Inglês

10.1093/bja/aeg142

1471-6771

C.E.W. Hahn, Andrew D. Farmery,

Renal function and acid-base balance

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.20Hlastala MP Berger AJ Physiology of Respiration. Oxford University Press, Oxford1996Google Scholar 28Nunn JF Applied Respiratory Physiology. 4th Edn. Butterworth-Heinemann, Oxford1993Google Scholar 37Salanitre E The role of physiological factors in exchange of anesthetic gas.in: Mushin WW Severinghaus JW Teingo M Gorini S Physiological Basis of Anaesthesiology. Theory and Practice. Piccin Medical Books, Padua1975: 149-164Google Scholar 42Tobin MJ Principles and Practice of Intensive Care Monitoring. McGraw Hill Inc., New York1998Google Scholar The beauty of continuous-ventilation 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 Robertson21Hlastala MP Robertson HT Complexity in Structure and Function of the Lung. Marcel Dekker Inc., New York1998Google Scholar 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 filled 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 sufficed 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 flow, 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 fit per plura quod potest fieri 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 Buchman15Godin PJ Buchman TG Uncoupling of biological oscillators: A complementary hypothesis concerning the pathogenesis of multiple organ dysfunction syndrome.Crit Care Med. 1996; 24: 1107-1116Crossref PubMed Scopus (313) Google Scholar 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. Non-linear models are intractable without the aid of modern high-speed computers.’15Godin PJ Buchman TG Uncoupling of biological oscillators: A complementary hypothesis concerning the pathogenesis of multiple organ dysfunction syndrome.Crit Care Med. 1996; 24: 1107-1116Crossref PubMed Scopus (313) Google Scholar In the case of a specific form of non-linear behaviour, namely ‘chaos’, such models can be intractable even with the aid of supercomputers. Godin and Buchman15Godin PJ Buchman TG Uncoupling of biological oscillators: A complementary hypothesis concerning the pathogenesis of multiple organ dysfunction syndrome.Crit Care Med. 1996; 24: 1107-1116Crossref PubMed Scopus (313) Google Scholar argue that the influence 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 a mistake with our measurement technique. Seldom do we consider re-thinking the theory, with the exception of a minor modification such as adding yet another compartment, because we are reluctant to face the fact that our simplified formulae might be wrong. Glenny and Robertson14Glenny RW Robertson HT Regional differences in the lung.in: Hlastala MP Robertson HT Complexity in Structure and Function of the Lung. Marcel Dekker Inc., New York1998Google Scholar summed this up in their re-examination of models of regional differences in blood-flow distribution in the lung, and have reminded us of Thomas Kuhn's essay24Kuhn TS The structure of scientific revolutions.in: Neurath International Encyclopedia of Unified Science. The University of Chicago Press, Chicago1970Google Scholar on the process by which major shifts in scientific models take place: ‘observations are expected to be interpreted in the context of the accepted paradigm – and thus restricting the peripheral vision of the researchers, since they reject the observations if they do not fit the model’.14Glenny RW Robertson HT Regional differences in the lung.in: Hlastala MP Robertson HT Complexity in Structure and Function of the Lung. Marcel Dekker Inc., New York1998Google Scholar Well-established paradigms are therefore resistant to change, even when new evidence is readily available. Almost inevitably the status quo remains, as it has done for models of respiratory gas exchange and for mathematical indices of hypoxaemia over the past decades. What is the balance then between the laws of parsimony and comprehensiveness in the modelling of gas exchange? Einstein has perhaps summed up this balance in the statement: ‘Everything should be made as simple as possible, but not simpler.’ Before we consider the mathematical models of gas exchange in detail, we need to ask why they are useful. Broadly speaking, mathematical models have been used in medicine to teach, predict and quantify. We shall take the teaching function of biomathematical models as axiomatic, but the other two aspects need further brief consideration under the headings of the forwards process and the backwards (or inverse) process. This process can be explained by reference to Figure 1 and is the means by which both teaching and predicting can be extracted from the model. The mathematical model is developed as a set of equations and the investigator puts into the model as many theoretical ‘inputs’ (such as inspired gases, gas and blood flow etc.) as the model can allow. The model then generates ‘outputs’ such as expired gases, blood gases, V˙/Q˙ relationships and so on. The model therefore predicts the outcomes, and on the basis of these the investigator can proceed to change any combination of the inputs to generate a whole new series of output predictions. In the clinical setting, these can be used to say ‘if I did this to a patient, then that would be the predicted outcome’. This forwards process is the most common way that biomathematical models have been used in medicine and this is the way that many textbook diagrams of gas exchange have been developed. This is perhaps the ‘holy grail’ for mathematical modellers, and is a decidedly difficult tool to develop. Figure 2 explains the general principles applied to respiration. Here, the inputs to the biomathematical gas-exchange model are actual physiological signals (such as gas flow, expired gases, blood gases etc.) taken from instruments connected to a patient. In the backwards (or inverse) process, the model equations are inverted, or solved, to provide ‘guesses’ of the physiological phenomena (such as cardiac output, dead space, lung volume and so on) that created the patient's signals that had been input into the model. This may work very successfully for imaging techniques that build up pictures of the body's anatomy from input signals from ultrasound or magnetic imaging transducers, although the model outputs in these instances are not really guesses. On the other hand, respiratory signals are never constant and always contain measurement uncertainty and ‘noise’. Respiratory model ‘guesses’ are therefore not robust and can even be bizarre at times! So far, not much mathematical and computing effort has been placed on the inverse process in respiratory gas-exchange analysis, apart from the multiple inert gas elimination technique (MIGET), which is discussed later.45West JB Wagner PD Pulmonary gas exchange.in: West JB Bioengineering Aspects of the Lung. Dekker, New York1977: 361-457Google Scholar 46Whiteley JP Gavaghan DJ Hahn CEW A tidal breathing model for the multiple inert gas elimination technique.J Appl Physiol. 1999; 87: 161-169PubMed Google Scholar In this particular instance, the input signals are not ‘real-time’ measurements and the inverse process does not produce anatomical data but guesses the distribution between pulmonary blood flow and alveolar ventilation in a given patient. In light of the current impossibility to invert complex respiratory equations in real time, and in the absence of excellent error-free respiratory measurement signals, this article will concentrate on the forwards (or predictive) process for respiratory gas-exchange models. Conventional lung models are based on the intertwined hypotheses of: (i) continuous gas and blood flow, and (ii) the ‘steady state’. The implications and limitations of these two hypotheses need to be considered separately. The aetiology of these two hypotheses can be traced to the fish-gill model of gas exchange by referring to any standard textbook on comparative mammalian physiology. Weibel,44Weibel ER The Pathway for Oxygen: Structure and Function in the Mammalian Respiratory System. Harvard University Press, Cambridge, USA1984Google Scholar in his seminal text The Pathway for Oxygen: Structure and Function in the Mammalian Respiratory System elegantly describes the evolution of oxygen transport systems from the insect, tadpole, frog, the fish's gill and the bird, through to the human. The fish gill, with its continuous flow of water over the filaments and the continuous flow of blood through the laminae mounted on them, is the obvious archetypal model for continuous-flow respiration (Fig. 3). This has been approximated to the human lung by the simple expedient of replacing the water flow by gas flow, and the filaments by a bubble. The human blood–gas interface is, however, far from the mathematically elegant counter-current blood–water interface of the gill, but a complex cul-de-sac arrangement whereby gas is shunted in and out of a heterogeneous matrix of bubbles via a heterogeneous system of common and personal conduits. Here, structure cannot be sketched as a ‘thumbnail’, but more resembles a fractal. Likewise the mathematics are not linear, but non-linear, and changes in variables within this structure do not have an easily predictable output. As Weibel succinctly put the case in 1984, ‘Function is the domain of the physiologist, structure that of the morphologist, and they operate with often vastly disparate concepts and approaches. To put it drastically, the physiologist will interpret his measurements of vital functions on the basis of models which get rid of as many structural complications as possible; it will often be ‘good enough’ to consider the lungs simply as an air bubble in contact with blood; as long as we can measure how much air flows into the bubble, how much blood passes along it, and how much O2 is exchanged, we need not worry about how the two are brought into contact. Problems arise when such simple models, amenable to simple mathematical manipulations, are taken to be reality, for they are clearly artificial contraptions that ignore a lot of pertinent features of the system.’44Weibel ER The Pathway for Oxygen: Structure and Function in the Mammalian Respiratory System. Harvard University Press, Cambridge, USA1984Google Scholar The details of the physical and mathematical basis of this ‘conventional’ gas-exchange model derived from the fish gill are given in Appendix A. Only the important premises are summarized below. Figure 4 illustrates the important features of the classic continuous gas flow–continuous blood flow model, with a single alveolar compartment of fixed volume, a parallel dead-space gas flow and a parallel shunt blood flow. Since alveolar gas flow is constant in this model, there is no I:E ventilation ratio, and no change in alveolar volume or respiratory rate – all these are constants. Consequently, the lung's ‘output signals’ – the arterial blood gas tensions – have constant values (once the steady state has been achieved) and the pulmonary blood flow shunt fraction is constant. This is the classic model still used to teach gas exchange and blood gas physiology today.20Hlastala MP Berger AJ Physiology of Respiration. Oxford University Press, Oxford1996Google Scholar 28Nunn JF Applied Respiratory Physiology. 4th Edn. Butterworth-Heinemann, Oxford1993Google Scholar The application of the steady-state condition to equation A1 is simple in its execution but profound in its consequences. Under these circumstances, the left-hand side of equation A1 is zero, since the steady state dictates that there is no change in alveolar gas concentration with time, and the equation reduces to the following: 0= V˙A (FI-FA)+Q˙P (Ca-Cv¯)(1) In this expression, all of the terms are treated as ‘parameters’ (i.e. constants in the mathematical sense, although each can vary between individuals or between measurements) rather than as ‘variables’. This relationship is used as the basis of conventional indices of the efficiency of the gas exchange.10Folgering H Smolders FDJ Kreuzer F Respiratory oscillations of arterial PO2 and their effects on the ventilatory controlling system in the cat.Pflugers Arch. 1978; 375: 1-7Crossref PubMed Scopus (20) Google Scholar, 11Fretschner R Deusch H Weitnauer A et al.A simple method to estimate functional residual capacity in mechanically ventilated patients.Intensive Care Med. 1993; 19: 372-376Crossref PubMed Scopus (30) Google Scholar, 12Gan K Nishi I Slutsky AS Estimation of ventilation-perfusion ratio distribution in the lung by respiratory gas analysis.Ann Int Conf IEEE Eng Med Biol Soc. 1991; 13: 2270-2271Google Scholar Because for inert soluble gases there is a linear relationship between blood concentration (C) and partial pressure (P), equation 1 can be simplified by relating C to P (via C=λP, where λ is the blood–gas partition coefficient), and by replacing F with P throughout the relationship to give the classic form: V˙A(PI-PA)=λQ˙P(Pa-Pv¯)(2) An important and far-reaching consequence of the imposition of steady-sate conditions on equation A1 is that alveolar lung volume is eliminated from the expression, since it is only included on the left-hand side of the equation. So lung volume, no matter how large or small, appears to play no part in human physiology, or in any measurement technique based on this equation. This applies equally to oxygen, carbon dioxide and inert gas mass balance. All that remains are the gas and blood gas concentrations, the alveolar ventilation and pulmonary blood flow. Equation 2 is one of the most important expressions in modern-day respiratory theory, since it links ventilation directly to perfusion via the gas and blood gas tensions. This equation has been rearranged in many ways by many authors. One way is to force Pi to be zero (i.e. the trace gas is not inspired by the subject). If this condition is imposed, and it is also assumed that Pa=Pa, then Equation 2 can be rearranged to give: PaPv¯=λλ+V˙A/Q˙P(3) This was the expression published by Farhi7Farhi LE Elimination of inert gas by the lung.Respir Physiol. 1967; 3: 1-11Crossref PubMed Scopus (116) Google Scholar, 8Farhi LE Plews JL Inert gas exchange.in: West JB Pulmonary Gas Exchange, Volume II. Organism and Environment. Academic Press, New York1980: 1-31Google Scholar, 9Farhi LE Yokoyama T Effects of ventilation-perfusion inequality on elimination of inert gases.Respir Physiol. 1967; 3: 12-20Crossref PubMed Scopus (37) Google Scholar and then developed by West and Wagner45West JB Wagner PD Pulmonary gas exchange.in: West JB Bioengineering Aspects of the Lung. Dekker, New York1977: 361-457Google Scholar to describe the MIGET, where several tracer gases are dissolved in saline, infused via a peripheral vein and elimination is measured at the mouth. None is present in the inspired gas (i.e. Pi=0). In MIGET, a large number of ventilated and perfused lung compartments are considered using Equation 3, each one possessing its own mass balance relationship described by the equation. The application of MIGET to the sick lung has featured extensively in research over the past three decades, and the technique has attracted some controversy. All information derived from MIGET depends on the mathematical inversion of Equation 3 in a multi-compartment (usually 50) computer model of the lung. However, it must be remembered that the model itself is founded not on tidal-ventilation principles, but on continuous V˙/Q˙ equations, which are more appropriate to the fish gill38Scheid P Piiper J Intrapulmonary gas mixing and stratification.in: West JB Pulmonary Gas Exchange, Volume I. Ventilation, Blood Flow and Diffusion. Academic Press, New York1980: 87-130Crossref Google Scholar than to tidally breathing mammals. It must also be noted that in this technique there is no consideration of inspired V˙/Q˙ ratio in the mathematical formulation since the tracer gases are not present in the inspired air (apart from those rebreathed). MIGET therefore only calculates the expired V˙/Q˙ ratio. It is now accepted that the lung in acute respiratory distress syndrome (ARDS) can partially collapse and then partially reopen during the ventilatory cycle,48Whiteley JP Farmery AD Gavaghan DJ Hahn CEW A tidal ventilation model for oxygenation in respiratory failure.Respir PhysiolNeurobiol. 2003; (in press)Google Scholar and therefore the inspired V˙/Q˙ ratio will be variable. It will be this inspired V˙/Q˙ ratio that determines blood gas exchange in the sick lung during inspiration, and not solely the expired V˙/Q˙ ratio. Recently, Peyton and colleagues31Peyton PJ Robinson GJB Thompson B Effect of ventilation-perfusion inhomogeneity and N2O on oxygenation: physiological modelling of gas exchange.J Appl Physiol. 2001; 91: 17-25PubMed Google Scholar, 32Peyton PJ Robinson GJB Thompson B Ventilation-perfusion inhomogeneity gas uptake in anesthesia: computer modelling of gas exchange.J Appl Physiol. 2001; 91: 10-16PubMed Google Scholar, 33Peyton PJ Robinson GJB Thompson B Ventilation-perfusion inhomogeneity gas uptake: theoretical modelling of gas exchange.J Appl Physiol. 2001; 91: 3-9PubMed Google Scholar have re-emphasized that inspired and expired ventilation give quantitatively different results for PaO2. They argue that inspired V˙/Q˙ models relate better to mechanically ventilated patients in the intensive care unit (ICU), whereas expired V˙/Q˙ models relate more closely to spontaneous ventilation where the subject regulates the degree of expansion of the thorax in response to the natural ventilatory requirement.33Peyton PJ Robinson GJB Thompson B Ventilation-perfusion inhomogeneity gas uptake: theoretical modelling of gas exchange.J Appl Physiol. 2001; 91: 3-9PubMed Google Scholar Unfortunately, the inspired V˙/Q˙ ratio cannot be determined by MIGET. This important equation relates oxygen and carbon dioxide production and consumption to the other physiological parameters, and follows logically from Equation 1. Note that the far right-hand term in Equation 1 is ‘pulmonary uptake’ (V˙o2 or V˙co2). If this is written simultaneously for oxygen and carbon dioxide, and inspired Pco2=0, we obtain: PAO2=PIO2-PaCO2V˙O2/V˙CO2(4) Since the respiratory quotient, R, is defined by R=V˙co2/V˙o2 then Equation 4 becomes: PAO2=PIO2-PaCO2R(5) This is another assumption of steady-state conditions, since R (defined as the ratio of metabolic oxygen consumption and carbon dioxide production) only equals oxygen uptake and carbon dioxide evolution at the lung in the steady state. Equation 5 has been modified extensively to correct for differences in the inspired and expired gas flows.28Nunn JF Applied Respiratory Physiology. 4th Edn. Butterworth-Heinemann, Oxford1993Google Scholar However, no matter how complicated the resulting ideal gas formulae become, they are still based on the continuous-ventilation steady-state hypothesis. (1), (2), (3), (4), (5) have been used for decades now. It is true that they mimic physiological processes qualitatively but perhaps that is where their use should end because they fail to agree numerically with known human physiological input data when put to the test. Perhaps more importantly, their indiscriminate use blinds our peripheral vision (to quote Thomas Kuhn24Kuhn TS The structure of scientific revolutions.in: Neurath International Encyclopedia of Unified Science. The University of Chicago Press, Chicago1970Google Scholar) and can prevent us from discovering what is happening in physiological reality. It is easy to test the hypothesis of the continuous-ventilation equation by collecting experimental tidal data from a known ‘gold-standard’ source (the truth), and then inputting this data into the appropriate continuous-ventilation equation. By solving the equation mathematically, lung variables can be calculated and their values compared with ‘the truth’. One way to do this is to ventilate a mechanical bench lung of known geometrical resting volume (i.e. functional residual capacity) that can expand with each inspiration and be ventilated with a known tidal volume and respiratory rate through a geometrically known series dead space. This bench lung will eliminate all physical problems of blood flow and blood gas exchange, and will enable us to test the simplest form of equation A1 – that is, equation A4. If equation A4 fails the acid test in the case of a single-compartment well-mixed homogeneous mechanical lung, then how can Equation 1 possibly succeed when the complications of blood flow and multiple lung compartments are added to it? When tested this way, equation A4 fails – no matter what inspired gas forcing function is applied. Sainsbury and colleagues36Sainsbury MC Lorenzi A Williams EM et al.A reconciliation of continuous and tidal ventilation gas exchange models.Respir Physiol. 1997; 108: 89-99Crossref PubMed Scopus (5) Google Scholar applied both tidal inert-gas wash in/wash out, and inspired forced sinewaves to such a mechanical lung and solved equation A4 to calculate the lung volume from the tidal inspired/expired gas data. The calculated volume always over-estimated the true geometrical lung volume, depending on the respiratory rate, the dead space volume and the tidal volume. The physical reason for this discrepancy is that gas mixing takes place in the mechanical lung only when it is expanding from its resting volume, Va, to its fully expanded volume Va+Vt. At the end of the inspiratory phase the mechanical lung ‘alveolar’ gas concentration remains constant at its end-inspired value throughout the expiratory phase. Thus, gas mixing takes place only during the inspiratory phase. The prevailing dead-space volume must also be accounted for in the calculations. The authors calculated that the continuous-ventilation formulae over-estimated the true lung volume by an amount given by ½(Vd+Vt), irrespective of the inspired-gas forcing function mode.20Hlastala MP Berger AJ Physiology of Respiration. Oxford University Press, Oxford1996Google Scholar Thus, the continuous-ventilation formula in its very simplest form fails the acid test. What confidence do we have that calculations of dead-space volume and pulmonary blood flow, based on the same continuous-ventilation hypotheses, are any better than those of lung volume? We have no grounds for any such confidence. In fact the evidence, whether theoretical36Sainsbury MC Lorenzi A Williams EM et al.A reconciliation of continuous and tidal ventilation gas exchange models.Respir Physiol. 1997; 108: 89-99Crossref PubMed Scopus (5) Google Scholar or experimental,36Sainsbury MC Lorenzi A Williams EM et al.A reconciliation of continuous and tidal ventilation gas exchange models.Respir Physiol. 1997; 108: 89-99Crossref PubMed Scopus (5) Google Scholar 51Williams EM Sainsbury MC Sutton L et al.Pulmonary blood flow measured by inspiratory inert gas concentration forcing oscillations.Respir Physiol. 1998; 113: 47-56Crossref PubMed Scopus (14) Google Scholar all points the other way. This hypothesis, with the corollaries that neither lung volume nor I:E ratio play any part in the calculation of alveolar or arterial oxygen and carbon dioxide tensions, has formed the foundation for many of our physiological beliefs for decades. Neither lung volume nor I:E ratio play any part in the currently accepted mathematical indices for hypoxaemia,5Cane RD Shapiro BA Templin R et al.Unreliability of oxygen tension-based indices in reflecting intrapulmonary shunting in critically ill patients.Crit Care Med. 1998; 16: 1243-1245Crossref Scopus (53) Google Scholar 17Gould MK Ruoss SJ Rizk NW et al.Indices of hypoxemia in patients with acute respiratory distress syndrome: Reliability, validity, and clinical usefulness.Crit Care Med. 1997; 25: 6-8Crossref PubMed Scopus (26) Google Scholar 18Gowda MS Klocke RA Variability of indices of hypoxemia in adult respiratory distress syndrome.Crit Care Med. 1997; 25: 41-45Crossref PubMed Scopus (124) Google Scholar 28Nunn JF Applied Respiratory Physiology. 4th Edn. Butterworth-Heinemann, Oxford1993Google Scholar 35Quan SF Kronberg GM Schlobohm RM et al.Changes in venous admixture with alterations of inspired oxygen concentration.Anesthesiology. 1980; 52: 477-482Crossref PubMed Scopus (26) Google Scholar 54Zetterstrom H Assessment of the efficiency of pulmonary oxygenation. The choice of oxygenation index.Acta Anaesthesiol Scand. 1998; 32: 579-584Crossref Scopus (54) Google Scholar or in the practice and interpretation of inert-gas techniques such as MIGET. It is as if both the magnitude of lung volume and the I:E ratio are irrelevant. However, we know that lung volume must play an important part in blood–gas exchange, otherwise we would not strive to open the lung of the ICU patient and to keep it open.25Lachman B Open up the lung and keep the lung open.Intensive Care Med. 1992; 18: 319-321Crossref PubMed Scopus (874) Google Scholar Similarly, the design of ventilators would not include a variable I:E ratio, nor would inverse I:E be employed in clinical practice, if this ratio did not alter blood–gas exchange in any way. Thus, it is already clear that we know that a ‘steady state’ does not occur when the ICU patient is ventilated, as expressed in Equation 1 and its succeeding corollaries. Furthermore, Whiteley and colleagues47Whiteley JP Gavaghan DJ Hahn CEW A tidal breathing model of the inert gas sinewave technique for inhomogeneous lungs.Respir Physiol. 2000; 124: 65-83Crossref Scopus (14) Google Scholar have tested the accuracy of the steady-state hypothesis by developing a tidal-ventilation mathematical model of inert gas exchange; they then used this model to generate data sets which were fed back as ‘input data’ into appropriate steady-state continuous-ventilation gas-exchange equations. These were, in turn, solved to calculate the physical lung parameters such as lung volume and dead space that were originally incorporated into the tidal model. The steady-state equations failed to reproduce these values. So, if steady-state equations cannot calculate lung parameters accurately on a computer simulation with noise-free data, their use in clinical practice should be used with great caution. On the other hand, if tidal models can be developed to examine the effects of changing such variables as lung volume, airway dead-space volume, respiratory rate, I:E ratio, FIO2 and FICO2 etc. on the lung outputs of expired, arterial and mixed-venous partial pressures, then a major advance will have been made. If the effects of these variables on the calculated model output values (for example oxyhaemoglobin saturation, blood gas concentrations and blood gas tensions) prove to be pronounced, then the steady-state hypothesis is untenable