Two-dimensional mathematical model of the dynamic for the fluid and gases (CO2 and O2 ) concentrations in the pulmonary alveolar sacs

Authors

  • Luis Caucha . Mathematics, Universidad Nacional de Tumbes, Peru.
  • Obidio Rubio . Universidad Nacional de Trujillo.
  • Alexis Rodriguez . Universidad Nacional de Trujillo.

DOI:

https://doi.org/10.17268/sel.mat.2017.02.09

Keywords:

Alveolar gas dynamic, Arbitrary Lagrangian-Eulerian, Navier-Stokes equation

Abstract

We simulated the dynamics of CO2 transport in the alveolar sacs of the human lung. Using Arbitrary Lagrangian Eulerian (ALE) framework, we control the movement domain for a normal and fast maneuver. The fluid of room air inspired and CO2 concentrations were approximated by Navier-Stokes and convection diffusion equations; the stress-stretch in the wall for different volumes were quantified in equal time of respiration. The expansion for a normal and forced maneuver were represented as 9 and 90% to the initial geometry. The difference of the CO2 was 73x10

References

L. J. Caucha, J. C. Cruz, L. A. Rueda, Modeling a co2 expirogram obtained with a forced expiratory maneuver., FASEB J. 24 (2010)1063.5.

P. W. Scherer, L. H. Shendalman, N. M. Green, Simultaneous diffusion and convection in single breath lung washout, Bull. Math Biophys. 34 (1972) 393–412.

E. R. Weibel, Morphometry of the human lung, Berlin:Springer, 1963.

L. Engel, Gas mixing within the acinus of the lung., J. Appl. Physiol. 54 (1983) 609–618.

M. Paiva, L. Engel, Model analysis of intra-acinar gas exchange., Respiration Physiology 62 (1985) 257–272.

D. A. Scrimshire, P. J. Tomlin, R. A. Ethridge, Computer simulation of gas exchange in human lungs, J. Appl. Physiol. 34(5) (1973)687–696.

M. Felici, M. Filoche, B. Sapoval, Diffusional screening in the human pulmonary acinus, J. Appl. Physiol. 94 (2003) 2010–2016.

A. J. Swan, M. H. Tawhai, Evidence for minimal oxygen heterogeneity in the healthy human pulmonary acinus, J. Appl. Physiol. 110(2011) 528–537.

W. J. Federspiel, J. J. Fredberg, Axial dispersion in respiratory bronchioles and alveolar ducts, J. Appl. Physiol. 64(6) (1988) 2614–2621.

J. Donéa, P. Fasoli-Stella, S. Giuliani, Lagrangian and eulerian finite element techniques for transient fluid-structure interaction problems, in: Structural mechanics in reactor technology, 1977.

T. Hughes,W. Liu, T. Zimmermann, Lagrangian-Eulerian finite element formulation for incompressible viscous flows, Comput. Methods Appl. Mech. Engrg. 29 (1981) 329–349.

X. Flores, J. Cruz, Single-breath, room-air method for measuring closing volume (phase iv) in the normal human lung., Chest 102 (1992)438–443.

R. Sikand, P. Cerretelli, L. E. Farhi, Effects of va and va/q distribution and of time on the alveolar plateau, J. Appl. Physiol. 21 (1966)1331–1337.

J. Milic-Emili, J. A. M. Henderson, M. B. Dolovich, D. Trop, K. Kaneko, Regional distribution of inspired gas in the lung., J. Appl. Physiol. 21 (3) (1966) 749–759.

L. J. Caucha, J. C. Cruz, J. M. Melendrez, Modeling exhaled gases after a tidal breath of air to remark the difference between the inhaled oxygen and the exhaled carbon dioxide., Am. J. Respir. Crit. Care Med. 183 (2011) A5180.

M. Braack, P. B. Mucha, Directional do-nothing condition for the navier-stokes equations., Journal of Computational Mathematics 35(5)(2014) 507–521.

R. Becker, Mesh adaptation for dirichlet flow control via nitsche’s method., Commun. Numer. Meth. Engng. 18 (2002) 669–680.

G. P. Galdi, R. Rannacher, Fundamental Trends in Fluid Structure Interaction, World Scientific Publishing Co., 2010.

R. Dziri, J. P. Zolesio, Eulerian derivative fof non-cylindrical functionals., Shape optimization and optimal design 216 (2001) 87–108.

C. Grandmont, Existence for a three-dimensional steady state fluid-structure interaction problem, J. Math. fluid mech. 4 (2002) 76–94.

R. Temam, Navier-stokes equation and nonlinear functional analysis., CBMS-NSF Regional Conference Series in Applied Mathematics 66 SIAM, Philadelphia.

Q. Du, M. D. Gunzburger, L. S. Hou, J. Lee, Analysis of a linear fluid-structure interaction problem., Discrete and continuous dynamical systems. 9(3) (2003) 633–650.

R. S. Adams, Sobolev Space, Academic Press, New York, 1975.

H. Brezis, Funtional Analysis, Sobolev Space and Partial Differential Equations, Springer New York, London, Rutgers University, 2010.

P. A. Kvale, J. Davis, R. Schrotter, Effect of gas density and ventilatory pattern on steady-state co uptake by the lung, Respiration Physiology 24 (1975) 385–398.

J. Sznitman, Effect of gas density and ventilatory patter on steady-state co uptake by the lung, Journal of Biomechanics 46 (2013)284–298.

R. Becker, M. Braack, D. Meidner, T. Richter, B. Vexler, The finite element toolkit GASCOIGNE 3D, HTTP://WWW.GASCOIGNE.UNIHD.DE.

Published

2017-12-15

How to Cite

., L. C., ., O. R., & ., A. R. (2017). Two-dimensional mathematical model of the dynamic for the fluid and gases (CO2 and O2 ) concentrations in the pulmonary alveolar sacs. Selecciones Matemáticas, 4(02), 220-229. https://doi.org/10.17268/sel.mat.2017.02.09