Computational Biology Group - Respiratory System Modelling

This aim of this research is to develop non-invasive monitoring techniques for estimating cardio-respiratory parameters, especially techniques that may be used in intensive care units and for spontaneously breathing patients in chest clinics. It is in collaboration with clinical groups at the Nuffield Department of Anaesthetics at the University of Oxford and the Department of Anaesthesia at the University of Sydney. We have investigated several aspects of the respiratory system with the aim of: (i) explaining clinical observations; and (ii) developing robust mathematical models that are sufficiently tractable to be used as part of a clinical measurement technique.

Our original models simple conservation of mass models, and most of the research effort went into devising robust recovery techniques to give estimates of the parameters which were embedded in a complex system of ordinary differential equations. Dissatisfaction with the results of this work led us to investigate and evaluate mathematically a whole class of inert gas methods introduced by other researchers, and has allowed us to show that the information content of such techniques is very limited for patients with cardiorespiratory disorders.

Our more recent work focuses on modelling individual components of the respiratory system accurately using a variety of numerical and analytical techniques. This allows us to investigate the effects of these individual components on current techniques for assessing cardio-respiratory function. This work promises to provide a much better understanding of how the gas-exchange processes (and hence the workings of the cardio-respiratory system) are affected by a variety of lung disorders, and has allowed us to assess the likely validity of a range of commonly-used clinical indices. The areas of the respiratory system that we have modelled are:

• Gas transport in the respiratory tree
• Gas transport from alveolar sacs across the alveolar membrane into pulmonary blood
• Cardio-respiratory control
• Gas transport to tissue

People involved

• David Gavaghan
• Jonathan Whiteley

Related publications

1. E.M. Williams, D.J. Gavaghan, P.A. Oakley, M.C. Sainsbury, L. Xiong, A.M.S. Black and C.E.W Hahn. Measurement of dead-space in a lung model using an inspired argon signal. Acta Anaesthesiol. Scand. 38, 126-129, 1994.
2. D.J. Gavaghan and C.E.W. Hahn. A mathematical evaluation of the alveolar amplitude response technique. Respiration Physiology, 102, 105-120, 1995.
3. D.J. Gavaghan and C.E.W. Hahn. A tidal breathing model of the forced inspired inert gas sinewave technique. Respiration Physiology, 106, 209-221, 1996.
4. E.M. Williams, M.C. Sainsbury, L. Sutton, L. Xiong, A.M.S. Black, J.P. Whiteley, D.J. Gavaghan and C.E.W. Hahn. Pulmonary blood flow measured by inspiratory inert gas concentration forcing oscillations. Respiration Physiology, 113, 47-56, 1998.
5. J.P. Whiteley, D.J. Gavaghan and C.E.W. Hahn. A mathematical evaluation of the multiple breath nitrogen washout technique and the multiple inert gas elimination technique. Journal of Theoretical Biology, 194, 517-539, 1998.
6. J.P. Whiteley, D.J. Gavaghan and C.E.W. Hahn. A tidal breathing model for the multiple inert gas elimination technique. Journal of Applied Physiology, 87, 161-169, 1999.
7. J.P. Whiteley, D.J. Gavaghan and C.E.W. Hahn. The effect of the width of the distribution of volume, ventilation and perfusion on arterial blood oxygen content. Journal of Theoretical Biology, 201, 271-279, 1999.
8. J.P. Whiteley, D.J. Gavaghan and C.E.W. Hahn. The effect of inspired oxygen concentration on the ventilation--perfusion distribution in inhomogeneous lungs. Journal of Theoretical Biology, 204, 575-585, 2000.
9. J.P. Whiteley, D.J. Gavaghan and C.E.W. Hahn. A tidal breathing model of the inert gas sinewave technique for inhomogeneous lungs. Respiration Physiology, 124: 65-83, 2000.
10. J.P. Whiteley, D.J. Gavaghan and C.E.W. Hahn. Modelling inert gas exchange in tissue and mixed--venous blood return to the lungs. Journal of Theoretical Biology, 209, 431-443, 2001.
11. A.D. Farmery and J.P. Whiteley. A mathematical model of electron transfer within the mitochondrial respiratory cytochromes. Journal of Theoretical Biology, 213, 197-207, 2001.
12. J.P. Whiteley, D.J. Gavaghan and C.E.W. Hahn. Some factors affecting oxygen uptake by red blood cells in the pulmonary capillaries. Mathematical Biosciences, 169, 153-172, 2001.
13. J.P. Whiteley, D.J. Gavaghan and C.E.W. Hahn. Variation of venous admixture, SF6 shunt, PaO2 and the PaO2/FIO2 ratio with FIO2. British Journal of Anaesthesia 88, 771-778, 2002.
14. J.P. Whiteley, M.J. Turner, A.B. Baker, D.J. Gavaghan and C.E.W. Hahn. The effects of ventilation pattern on carbon dioxide transfer in three computer models of the airways. Respiration Physiology & Neurobiology, 131, 269-284, 2002.
15. J.P. Whiteley, D.J. Gavaghan and C.E.W. Hahn. Mathematical modelling of oxygen transport to tissue. Journal of Mathematical Biology, 44, 503-522, 2002.
16. J.P. Whiteley, D.J. Gavaghan and C.E.W. Hahn. The effect of diffusion in the respiratory tree on the Alveolar Amplitude Response Technique (AART). Respiration Physiology & Neurobiology, 137, 81-96, 2003.
17. J.P. Whiteley, A.D. Farmery, D.J. Gavaghan and C.E.W. Hahn. A tidal ventilation model for oxygenation in acute respiratory failure. Respiration Physiology & Neurobiology, 136, 77-88, 2003.
18. J.P. Whiteley and D.J. Gavaghan. Efficient computations of gas transport in the respiratory tree. Mathematical Medicine & Biology, 20, 91-104, 2003.
19. J.P. Whiteley, D.J. Gavaghan and C.E.W. Hahn. Mathematical modelling of pulmonary gas transport. Journal of Mathematical Biology, 47, 79-99, 2003.
20. J.P. Whiteley, D.J. Gavaghan and C.E.W. Hahn. Periodic breathing induced by arterial oxygen partial pressure oscillations. Mathematical Medicine & Biology, 20, 205-224, 2003.
21. J.P. Whiteley, D.J. Gavaghan and C.E.W. Hahn. Oxygen transport to muscle tissue where regions of low oxygen tension exist. Mathematical and Computer Modelling, to appear.

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