Contemporary Materials I−1 (2010)
Contemporary Materials, I–1 (2010) Page 51 - 60
CHARACTERISTICS OF BIOLOGICAL MEMBRANES AND COMPUTER MODELING
M. Kojić,1,2,3,4, I. Vlastelica,5,6 B. Stojanović,3,7 V. Ranković,3 A. Tsuda1
Abstract
Mechanical characteristics of biological membranes are very important in functioning of some human organs. A typical example is lung microstructure which represents an alveolated system where the gas exchange occurs at the surface of biological membranes. The overall area of the membrane surface is huge and it significantly changes during inspiration-expiration breathing cycles. The membranes are covered by a surfactant, a surface-active lipoprotein complex, vitally important for the normal lung function.
In this paper we first describe membrane tissue material characteristics obtained by experimental investigations and then briefly summarize computational procedures employed for computer modeling of the biological membrane mechanical response experiencing large deformations over cycling loading. These procedures are implemented to a simple model of biaxial cycling stretching of a biological membrane covered by surfactant, and with elliptical hole and a ring at the hole rim.
Keywords: Soft tissue hardening characteristics, hysteresis of tissue and surfactant, computer modeling, finite element method, stress integration.
References
[1] M. Kojić, N. Filipović, B. Stojanović, N. Kojić, Computer Modeling in Bioengineering – Theoretical Background, Examples and Software, J. Wiley and Sons, 2008.
[2] C. G. Lee, F. G. Jr Hoppin (1972). Lung elasticity. In: Biomechanics-Its Foundations and Objectives. edited by Fung YC, Perrone N, Anliker M, 317-335, Prentice-Hall, Inc., Englewood Cliffs, N.J.
[3] E.H. Oldmixon, F. G. Jr Hoppin (1989). Distribution of elastin and collagen in canine lung alveolar parenchyma, J. Appl. Physiol., 67(5), 1941-1949.
PMid:2600027
[4] R. Kowe, R. C. Schroter, F. L. Matthews, D. Hitchings (1986). Analysis of elastic and surface tension effects in the lung alveolus using finite element methods. J. Biomechanics 19 (7): 541-549.
[5] E. Denny, R. C. Schroter (2000). Viscolelastic behavior of a lung alveolar duct model, J. Biomech. Engrg. Trans. ASME, 122, 143-151.
PMid:10834154
[6] H. Fukaya, C. J. Martin, A. C. Young, S. Katsura (1968). Mechanical properties of alveolar walls, J. Appl. Physiol., 25(6), 689-695. PMid:5727194
[7] J. Hildebrandt, H. Fukaya, C.J. Martin (1969). Stress-strain relations of tissue sheets under-going uniform two-dimensional stretch, J. Appl. Physiol., 27(5), 758-762. PMid:5360461
[8] M. S. Sacks (2000). Biaxial mechanical evaluation of planar biological materials, J. Elasticity, 61, 194-246.
[9] H. Sasaki, F. G. Jr Hoppin (1979). Hysteresis of contracted airway smooth muscle, J. Appl. Physiol: Respirat. Environ. Excercise Physiol., 47(6), 1251-1262.
[10] S. M. Mijailovic (1991). Elasticity and Energy Dissipation in Lung Connective Tissue. Ph. D. Thesis, MIT, Cambridge, MA.
[11] S. M. Mijailovic, D. Stamenovic, J. J. Fredberg (1993). Toward a kinetic theory of connective tissue micromechanics, J. Appl. Physiol., 74(2), 665-681. PMid:8458781
[12] S. M. Mijailovic, D. Stamenovic, R. Brown, D.E. Leith, J.J. Fredberg (1994). Dynamic moduli of rabit lung tissue and pigeon ligamentum propatagiale undergoing uniaxial cyclic loading, J. Appl. Physiol., 76(2), 773-782. PMid:8175588
[13] M. Kojic, S. Mijailovic, N. Zdravkovic (1998). A numerical algorithm for stress integration of a fiber-fiber kinetics model with Coulomb friction for connective tissue, Comp. Mech., 21(2), 189-198.
[14] M. Kojic, N. Zdravkovic, S Mijailovic (2003). A numerical stress calculation procedure for a fiber-fiber kinetics model with Coulomb and viscous friction of connective tissue, Comp. Mech., 30, 185-195.
[15] T. A. Wilson (1982) Surface tension-surface area curves calculated from pressure-volume loops, J. Appl. Physiol: Respirat. Environ. Excercise Physiol., 53(6), 1512-1520.
[16] E. P. Ingenito, L. Mark, J. Morris, F. F. Espinosa, R.D. Kamm, M. Johnson (1999). Biophysical chracterization and modeling of lung sur-factant components, J. Appl. Physiol., 86(5), 1702-1714. PMid:10233138
[17] H. P. Bachofen, H. Schurch (2001). Alveolar surface forces and lung architecture, Comp. Biochem. Physiol. Part A, 129, 183-193.
[18] Miloš Kojić and Klaus-Jürgen Bathe, Inelastic Analysis of Solids and Structures, Berlin-Heidelberg, 2005.
[19] M. Kojić, R. Slavković, M. Živković, N. Grujović, (1998), Finite Element Method I – Linear analysis, Mechanical Engineering Faculty, University of Kragujevac, Serbia.
[20] M. Kojic, I. Vlastelica, B. Stojanovic, V. Rankovic, A. Tsuda (2006). Stress integration procedures for a biaxial isotropic material model of biological membranes and for hysteretic models of muscle fibers and surfactant, Int. J. Num. Meth. Engrg., 68, 893-909.
[21] J. Gil, H. Bachofen, P. Gehr and E.R. Weibel. Alveolar volume-surface area relation in air- and saline-filled lungs fixed by vascular perfusion. J. Appl. Physiol: Respirat. Environ. Excercise Physiol. 47(5): 990-1001, 1979.
[22] M. Kojic, J. P. Butler, I. Vlastelica, B. Stojanovic, V. Rankovic, A. Tsuda, Geometric hysteresis of alveolated ductal architecture, to be submitted.