Damarların Mekanik Davranışları için Şekil Değiştirme Enerjisi Fonksiyonuna Yeni Bir Yaklaşım

Abstract

Bu çalışmada, damarların lineer olmayan, anizotropik davranışını karakterize eden yeni bir bünye denklemi önerilmiştir. Damar çapı ile iç basıncı arasındaki ilişkiyi belirlemek genel kan akışı probleminin önemli bir parçasıdır. Bu ilişki insan torakik aortunda incelenmiştir. Literatürden elde edilen klinik veriler sadece iç basınç-çap ilişkisini sağlamaktadır. Bu veriler kullanılarak lineer olmayan regresyon analizi ile bünye denkleminin parametreleri belirlenmiştir

Keywords

• insan, damarlar, bünye denklemleri

A New Approach on the Strain Energy Function for the Mechanical Behavior of Arteries

Abstract

In this study, a new constitutive equation that includes the characteristic nonlinear anisotropic response of arteries is proposed. The measurement of the relationship between arterial diameter and arterial pressure is important part of the general problem of blood flow measurements. This relationship was examined in the human thoracic aorta. The clinical data that obtained from literature provide only a pressurediameter relationship. To determine the parameters of the constitutive formulations, nonlinear regression analysis was used on these data

Keywords

• human, arteries, constitutive equations

References

1. [1] M.E. Hansen, E.K. Yucel, J. Megerman, G.J.L. Italien, W.M. Abbott, A.C. Waltman, In vivo determination of human arterial compliance: preliminary investigation of a new technique. CardioVascular and Interventional Radiology. 17 (1994), 22–26.
2. [2] T. Sugahara, Noninvasive method for measurement of elasticity in aortic wall using cineradiography. Angiology 39, (1988), 572–576.
3. [3] C. Stefanadis, C. Stratos, C. Vlachopoulos, S. Marakas, H. Boudoulas, I. Kallikazaros, E. Tsiamis, K. Toutouzas, L. Sioros, P. Toutouzas, Pressure-diameter relation of the human aorta. A new method of determination by the application of a special ultrasonic dimension catheter. Circulation Research 92, (1995), 2210– 2219.
4. [4] H.W. Weizsäcker, H. Lambert, K. Pascale, Analysis of the passive mechanical properties of rat carotid arteries. Journal of Biomechanics 16, (1983), 703–715.
5. [5] H.W. Weizsäcker, J.G. Pinto, Isotropy and anisotropy of the arterial wall. Journal of Biomechanics 21 (1988), 477–487.
6. [6] R.N. Vaishnav, J.T. Young and D.J. Patel, Distribution of stresses and of strainenergy density through the wall thickness in a canine aortic segment. Circulation Research. 32, (1973), 577–583.
7. [7] Y.C. Fung, K. Fronek, P. Patitucci, Pseudoelasticity of arteries and the choice of its mathematical expression. American Journal of Physiology. 237 (1979), H620– 631.
8. [8] K. Takamizawa, K. Hayashi, Strain energy density function and uniform strain hypothesis for arterial mechanics. Journal of Biomechanics 20, (1987), 7–17.

9. [9] H. Demiray, A layered cylindrical shell model for an aorta. International Journal of Engineering Science . 29,(1991), 47–54.
10. [10] G.A. Holzapfel, R. Eberlein, P. Wriggers, H.W. Weizsacker, A new axisymmetrical membrane element for anisotropic, finite strain analysis of arteries. Communications in Numerical Methods in Engineering 12 (1996), 507–517.
11. [11] A. Delfino, N. Stergiopulos, J.E. Moore Jr., J.J. Meister, Residual strain effects on the stress field in a thick wall finite element model of the human carotid bifurcation. Journal of Biomechanics 30 (1997), 777–786.
12. [12] T.E. Carew, R.N. Vaishnav and D.J. Patel, Compressibility of the arterial wall. Circulation Research. 23, (1968), 61–68.
13. [13] Y. Lanir and Y.C. Fung, Two-dimensional mechanical properties of rabbit skin-I. Experimental system. Journal of Biomechanics 7,(1974), 29–34.
14. [14] H. Demiray, A quasi-linear constitutive relation for arterial wall materials. Journal of Biomechanics 29, (1996), 1011-1014.
15. [15] G.A. Holzapfel and T.C. Gasser, A viscoelastic model for fiber-reinforced composites at finite strains: Continuum basis, computational aspects and applications. Computer Methods in Applied Mechanics and Engineering 190, (2001), 4379-4403.
16. [16] G. Pontrelli, A mathematical model of flow in a liquid-filled visco-elastic tube. Medical and Biological Engineering and Computing.40, (2002), 550-556.
17. [17] G.A. Holzapfel, T.C. Gasser, M. Stadler, A structural model for the viscoelastic behavior of arterial walls: Continuum formulation and finite element analysis. European Journal of Mechanics 21, (2002), 441-463.
18. [18] W.-W. Von Maltzahn, D. Besdo and W. Wiemer, Elastic properties of arteries: A nonlinear two-layer cylindrical model. Journal of Biomechanics 14, (1981), 389– 397.
19. [19] G.A. Holzapfel, T.C. Gasser, R.W. Ogden,. A new constitutive framework for arterial wall mechanics and a comparative study of material models. Journal Elasticity 61, (2000), 1–48.
20. [20] M. S. Bazaraa, D. Sherali, C. M. Shetty, Nonlinear Programming: Theory and Algorithms, 3rd Edition,Willey, New Jersey (2006).
21. [21] C.J. Chuong and Y.C. Fung, Three-dimensional stress distribution in arteries. Journal of Biomechanical Engineering. 105, (1983), 268–274.-