@article{M2AN_2013__47_4_935_0, author = {Martin, S\'ebastien and Maury, Bertrand}, title = {Modeling of the oxygen transfer in the respiratory process}, journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique}, publisher = {EDP-Sciences}, volume = {47}, number = {4}, year = {2013}, pages = {935-960}, doi = {10.1051/m2an/2012052}, zbl = {06198325}, mrnumber = {3082284}, language = {en}, url = {http://www.numdam.org/item/M2AN_2013__47_4_935_0} }

Martin, Sébastien; Maury, Bertrand. Modeling of the oxygen transfer in the respiratory process. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 47 (2013) no. 4, pp. 935-960. doi : 10.1051/m2an/2012052. http://www.numdam.org/item/M2AN_2013__47_4_935_0/

[1] Static behavior of the respiratory system, in Handbook of physiology, edited by S.R. Geiger, 2nd edition. American Physiological Society, Bethesda (1986) 113-130.

and ,[2] Variations in the pulmonary capillary blood volume and membrane diffusion component in health and disease. J. Clin. Invest. 39 (1960) 1401-1412.

, , and ,[3] Flow and age dependence of airway closure and dynamic compliance. J. Appl. Physiol. 38 (1975) 199-207.

, , and ,[4] Simplified models for gas exchange in the human lungs. J. Theor. Biol. 238 (2006) 474-495.

,[5] A simulation model of the oxygen alveolo-capillary exchange in normal and pathological conditions. Physiol. Meas. 24 (2003) 261-275.

, and ,[6] Noninvasive ventilation for acute exacerbations of chronic obstructive pulmonary disease. N. Engl. J. Med. 333 (1995) 817-822.

, , , , , , , , , , and ,[7] Lung function: Physiology, Measurement and Application in Medicine, 6th edition. Blackwell Publishing Ltd. (2006).

, and ,[8] Standardization of the measurement of transfer factor (diffusing capacity). Eur. Respir. J. suppl 16 (1993) 41-52.

, , , and ,[9] Effect of time-varying blood flow on oxygen uptake in the pulmonary capillaries. Appl. Physiol. 23 (1967) 944-953.

and ,[10] The lung: Scientific Foundations, edited by R.G. Crystal, J.B. West, E.R. Weibel and P.J. Barnes, 2nd edition. Lippincott-Raven Press, Philadelphia 2 (1997).

[11] Is cooperative oxygen binding by hemoglobin really understood?. Nat. Struct. Biol. 6 (1999) 351-358.

, , and ,[12] Diffusional screening in the human pulmonary acinus. J. Appl. Physiol. 94 (2003) 2010-2016.

, and ,[13] Renormalized random walk study of oxygen absorption in the human lung. Phys. Rev. Lett. 92 (2004) 068101.

, and ,[14] Diffusional screening in real 3D human acini - a theoretical study. Respir. Physiol. Neurobiol. 145 (2005) 279-293.

, , , and ,[15] The stationary flow in a heterogeneous compliant vessel network. J. Phys. Conf. Ser. 319 (2011) 012008.

and ,[16] Dynamique du transport et du transfert de l'oxygène au sein de l'acinus pulmonaire humain. Ph.D. thesis, École Polytechnique (2010).

,[17] The normal human lung: ultrastructure and morphometric estimation of diffusion capacity. Respir. Physiol. 32 (1978) 121-140.

, and ,[18] Textbook of medical physiology, 9th edition. W.B. Saunders Co, Philadelphia (1996).

and ,[19] Physiology of Respiration, 2nd edition. Oxford University Press, Oxford (2001).

and ,[20] Gas diffusion through the fractal landscape of the lung: How deep does oxygen enter the alveolar system? in Fractals in Biology and Medicine, edited by G.A. Losa, D. Merlini, T.F. Nonnenmacher, E.R. Weibel. Basel: Birkhäuser IV (2005) 17-30.

, , , and ,[21] Pulmonary gas exchange. in Lung Function Testing, edited by R. Gosselink and H. Stam. European Respiratory Monograph 10 (2005) 106-126.

,[22] Mathematical Physiology. Interdisciplinary Applied Mathematics. Springer (1998). | MR 1673204 | Zbl 1273.92017

and ,[23] Digital computer subroutine for the conversion of oxygen tension into saturation. J. Appl. Physiol. 21 (1966) 1375-1376.

,[24] Medical Physiology, The Big Picture. McGraw Hill (2009).

and ,[25] Airway mechanics, gas exchange, and blood flow in a nonlinear model of the normal human lung. J. Appl Physiol. 84 (1998) 1447-1469.

, , , , and ,[26] Impact of respiratory mechanics model parameter on gas exchange efficiency. ESAIM Proc. 23 (2008) 30-47. | MR 2509204 | Zbl 1156.92310

, , and ,[27] Influence of variability on the optimal shape of a dichotomous airway tree branching asymmetrically. Phys. Biol. 7 (2010) 016007.

and ,[28] Interplay between flow distribution and geometry in an airway tree. Phys. Rev. Lett. 90 (2003) 14.

, , and ,[29] An optimal bronchial tree may be dangerous. Nature 427 (2004) 633-636.

, , , and ,[30] Optimal Poiseuille flow in a finite elastic dyadic tree. ESAIM: M2AN 42 (2008) 507-534. | Numdam | MR 2437772 | Zbl 1203.74033

and ,[31] Model analysis of gas distribution within human lung acinus. J. Appl. Physiol. 56 (1984) 418-425.

and ,[32] Respiration: alveolar gas exchange. Annu. Rev. Physiol. 33 (1971) 131-154.

and ,[33] Relative importance of diffusion and chemical reaction rates in determining rate of exchange of gases in the human lung, with special reference to true diffusing capacity of pulmonary membrane and volume of blood in the lung capillaries. J. Appl. Physiol. 11 (1957) 290-302.

and ,[34] Role of diffusion screening in pulmonary diseases. Adv. Exp. Med. Biol. 605 (2008) 173-178.

and ,[35] Smaller is better − but not too small: a physical scale for the design of the mammalian pulmonary acinus. Proc. Natl. Acad. Sci. USA 99 (2002) 10411.

, and ,[36] Two-compartment modelling of respiratory system mechanics at low frequencies: gas redistribution or tissue rheology? Eur. Respir. J. 4 (1991) 353-358.

and ,[37] A statistical description of the human tracheobronchial tree geometry. Respir. Physiol. 37 (1979) 161-72.

, , and ,[38] Evidence for minimal oxygen heterogeneity in the healthy human pulmonary acinus. J. Appl. Physiol. 110 (2011) 528-537.

and ,[39] Convective gas transport in the pulmonary acinus: comparing roles of convective and diffusive lengths. J. Biomech. 42 (2009) 789-792.

,[40] The best peak expiratory flow is flow-limited and effort-independent in normal subjects. Am. J. Respir. Crit. Care Med. 165 (2002) 1304-1308.

, , , , and ,[41] Characterising respiratory airway gas mixing using a lumped parameter model of the pulmonary acinus. Respir. Physiol. 127 (2001) 241-248.

and ,[42] Morphometry of the human lung, Springer Verlag and Academic Press, Berlin, New York (1963).

,[43] The pathway for oxygen, Harvard University Press (1984).

,[44] Design and morphometry of the pulmonary gas exchanger, in The lung: scientific foundations, 2nd edition, edited by R.G. Crystal, J.B. West, E.R. Weibel, P.J. Barnes. Lippincott-Raven Press, Philadelphia 1 (1997) 1147-1157.

,[45] Design of peripheral airways for efficient gas exchange. Resp. Phys. Neur. 148 (2005) 3-21.

, and ,[46] How does lung structure affect gas exchange? Chest 83 (1983) 657-665.

,[47] Respiratory physiology: the essentials, Baltimore: Williams and Wilkins (1974).

,[48] Some factors affecting oxygen uptake by red blood cells in the pulmonary capillaries. Math. Biosci. 169 (2001) 153-172. | MR 1818484 | Zbl 0977.92006

, and ,