British Journal of Anaesthesia, 2003, Vol. 91, No. 1 2-15
© 2003 The Board of Management and Trustees of the British Journal of Anaesthesia
Review Article |
Gas exchange modelling: no more gills, please
Nuffield Department of Anaesthetics, University of Oxford, Radcliffe Infirmary, Woodstock Road, Oxford, OX2 6HE, UK
Corresponding author. E-mail: clive.hahn@nda.ox.ac.uk
Keywords: model, lung; ventilation, continuous; ventilation, steady-state hypothesis; ventilation, tidal
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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.20 28 37 42 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 Robertson21 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
The usefulness of mathematical models
The forwards process
The backwards (or inverse) process
Conventional hypotheses
Continuous gas and blood flow
The steady-state condition
The ideal alveolar equation
Failure of the continuous-ventilation and steady-state theories in practice
Continuous ventilation
The steady-state hypothesis
A simple tidal-ventilation model
Advantages of the tidal-ventilation model
Output parameters
The trumpet model
The human physiome lung model
Do tidal-ventilation models have implications on the interpretation of clinical data?
The trumpet model
The human physiome lung model
The balloon-on-a-straw model
Inert gases
Oxygen
Conclusions
Appendix A: the continuous-ventilation model
Mass balance
Dead space
Blood flow shunt fraction
Insoluble inert gases
Forcing
Appendix B: a tidal-ventilation model
Inspiration
Expiration
The body mass balance relationship
Airway dead space
Shunt fraction
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