Modelo matemático de la dinámica bidimensional del flujo y concentraciones de gases (O2 y CO2 ) en los sacos alveolares pulmonares

Luis Caucha ., Obidio Rubio ., Alexis Rodriguez .

Resumen


En este artículo simulamos la dinámica del transporte de CO2 en los sacos alveolares pulmonares. Usando el método Euleriano-Lagrangiano arbitrario, se pudo controlar el movimiento del dominio para una respiración normal y forzada. El fluido de gas de ambiente inhalado y las concentraciones de CO2 fueron aproximadas por las ecuaciones de Navier-stokes y la ecuación de convección difusión, el stress paras diferentes maniobras fueron calculadas en tiempos iguales. La expansión para la maniobra normal y forzadas fueron representadas como el 9
y 90% de la geometría inicial. Las diferencias de la cantidad de CO2 fue 73x10


Palabras clave


Dinámica del gas Alveolar; Arbitrary Lagrangian-Eulerian; Navier-Stokes equation

Texto completo:

PDF

Referencias


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.

-----------------------------------------------------------

Received: Ap. 04, 2017.

Accepted: Aug. 31, 2017.

Corresponding author: ljcaucham@untumbes.edu.pe

------------------------------------------------------------




DOI: http://dx.doi.org/10.17268/sel.mat.2017.02.09

Enlaces refback

  • No hay ningún enlace refback.


Short Title: Sel. mat.

-------------------------------------------------------------------------------------

 ISSN:  2411-1783  Versión Electrónica.                      

-------------------------------------------------------------------------------------

Derechos reservados © 2014 Departamento de Matemáticas.

                  E-mail: selecmat@unitru.edu.pe

 

Licencia de Creative Commons 

Selecciones Matemáticas es una revista de la Universidad Nacional de Trujillo publica sus contenidos bajo licencia Creative Commons Reconocimiento-NoComercial 3.0.