Contemporary Materials I−1 (2010)

Contemporary Materials, I–1 (2010)     Page 51 - 60

UDK 616–001:004.4


M. Kojić,1,2,3,4, I. Vlastelica,5,6 B. Stojanović,3,7 V. Ranković,3 A. Tsuda1

Harvard School of Public Health Harvard University, 677 Huntington Avenue, MA 02115, Boston, USA
Department of Nanomedicine and Biomedical Engineering, University of Texas Medical Center at Houston, Houston, USA
Research and Development Center for Bioengineering, Sretenjskog ustava 27, 34000 Kragujevac, Serbia
University of Kragujevac, Kragujevac, Serbia
High School, Čačak, Serbia
Metropolitan University, Belgrade, Serbia
Faculty of Science, University of Kragujevac, Kragujevac, Serbia


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.



[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.
[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.

[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.