Use of Adair Four-Step Kinetics in Mathematical Simulation of Oxygen Transport in the Microcirculation
The Adair four-step kinetic model for the reactions of haemoglobin and oxygen recognizes five haemoglobin species, corresponding to deoxyhaemoglobin and one species for each level of oxygenation of the four haem groups. Thus, an oxygen transport problem involves a system of five simultaneous non-linear partial differential equations for diffusion with chemical reaction. This mathematical complexity has impeded application of the Adair model despite its theoretical advantages over the one-step model often used in practice.
The Adair kinetic model has been incorporated into a simulation of microcirculatory oxygen transport. The results show that the usual one-step kinetic model is inaccurate in comparison with the Adair model. However, an empirical modification can be made to the one-step model to ensure compatibility with the equilibrium curve. This modified one-step kinetic model (the VRC model) is much more tractable mathematically than the Adair model. In the physiological range of fluxes, the VRC kinetic model appears to be of sufficient accuracy for most purposes, and the mathematical complexity of the Adair model is not required.
KeywordsKinetic Model Nusselt Number Oxygen Transport Mathematical Simulation Haem Group
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- Adair, G.S. (1925). The hemoglobin system: VI. The oxygen dissociation curve of hemoglobin. J. Biol. Chem. 63, 529–545.Google Scholar
- Baxley, P. and Hellums, J.D. (1983). Simulation of oxygen transport in the microcirculation. Ann. Biomed. Eng. 11, 401–416.Google Scholar
- Clark, A., Federspiel, W.J., Clark, P.A.A. and Cokelet, G.R. (1985). Oxygen delivery from red cells. Biophys. J. 47, 171–181.Google Scholar
- Gibson, Q.H. (1970). The reaction of oxygen with hemoglobin and the kinetic basis of the effect of salt on binding of oxygen. J. Biol. Chem. 245, 3285–3288.Google Scholar
- Madsen, N.K. and Sincovec, R.F. (1976). PDECOLD: General collocation software for partial differential equations. ACM Trans. Math. Software.Google Scholar
- Moll, W. (1969). The influence of hemoglobin diffusion on oxygen uptake and release by red cells. Respir. Physiol. 65 1–15.Google Scholar
- Yap, E.W.H. (1985). Mathematical modelling of oxygen transport in the microcirculation. M.S. Thesis, Rice Univ., Houston, Texas, U.S.A.Google Scholar