Abstract
Intracranial aneurysms (ICA) are abnormal dilations of the cerebral arteries, most commonly located at the apices of bifurcations. The ability of the arterial wall, particularly the endothelial cells forming the inner lining of the wall, to respond appropriately to hemodynamic stresses is critical to arterial health. ICA initiation is believed to be caused by a breakdown in this homeostatic mechanism leading to wall degradation. Due to the complex nature of this process, there is a need for both controlled in vitro and in vivo studies. Chung et al. developed an in vitro chamber for analyzing the response of biological cells to the hemodynamic wall shear stress fields generated by the impinging flows found at arterial bifurcations [7, 6]. Here, we build on this work and design an in vitro flow chamber that can be used to reproduce specific magnitudes of wall shear stress (WSS) and gradients of wall shear stress. Particular attention is given to reproducing spatial distributions of these functions that have been shown to induce pre-aneurysmal changes in vivo [38]. We introduce a measure of the gradient of the wall shear stress vector (WSSVG) which is appropriate for complex 3D flows and reduces to expected measures in simple 2D flows. The WSSVG is a scalar invariant and is therefore appropriate for use in constitutive equations for vessel remodeling in response to hemodynamic loads [34, 35].
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References
Anderson, E., Falls, T., Sorkin, A., Tate, M.: The imperative for controlled mechanical stresses in unraveling cellular mechanisms of mechanotransduction. BioMed. Eng. OnLine 5, 27 (2006) doi: 10.1186/1475-925X-5-27
Barbee, K., Davies, P., Lal, R.: Shear stress-induced reorganization of the surface topography of living endothelial cells imaged by atomic force microscopy. Circ. Res. 74(1), 163–171 (1994)
Bathe, K.: Finite Element Procedures. Prentice Hall, Prentice (1996)
Berger, S.A., Lou, L.D.: Flows in stenotic vessels. Annu. Rev. Fluid Mech. 32, 347–382 (2000)
Buchanan, J.R., Kleinstreuer, C., Truskey, G.A., Lei, M.: Relation between non-uniform hemodynamics and sites of altered permeability and lesion growth at the rabbit aorto-celiac junction. Atherosclerosis 143(1), 27–40 (1999)
Chung, B.J.: The study of blood flow in arterial bifurcations: the influence of hemodynamics on endothelial cell response to vessel wall mechanics. Ph.D. thesis, University of Pittsburgh (2004)
Chung, B.J., Robertson, A.M.: A novel flow chamber to evaluate endothelial cell response to flow at arterial bifurcations. In: Annual meeting of the Biomedical Engineering Society (BMES), p. 6P5.113. Nashville, Tennessee (2003)
Chung, B.J., Robertson, A.M., Peters, D.G.: The numerical design of a parallel plate flow chamber for investigation of endothelial cell response to shear stress. Comput. Struct. 81, 535–546 (2003). doi:10.1016/S0045-7949(02)00416-9
Davies, P.F., Shi, C., Depaola, N., Helmke, B.P., Polacek, D.C.: Hemodynamics and the focal origin of atherosclerosis: A spatial approach to endothelial structure, gene expression, and function. Ann. N.Y. Acad. Sci. 947, 7–16; discussion 16–17 (2001)
DePaola, N., Gimbrone, M., Davies, P.F., Dewey, C.: Vascular endothelium responds to fluid shear stress gradients. [erratum appears in Arterioscler Thromb 1993 Mar;13(3):465]. Arterio. Thromb. 12(11), 1254–1257 (1992)
Foutrakis, G.N., Yonas, H., Sclabassi, R.J.: Saccular aneurysm formation in curved and bifurcating arteries. Am. J. Neuroradiol. 20(7), 1309–1317 (1999)
Frangos, J.A., McIntire, L., Eskin, S.G.: Shear stress induced stimulation of mammalian cell metabolism. Biotechnol. Bioeng. 32, 1053–1060 (1988)
Galdi, G.P.: Mathematical problems in classical and non-newtonian fluid mechanics. In: G.P. Galdi, R. Rannacher, A.M. Robertson, S. Turek (eds.) Hemodynamical Flows: Modeling, Analysis and Simulation, Oberwolfach Seminars, vol. 37. Birkhäuser, Cambridge (2008)
Gao, L., Hoi, Y., Swartz, D.D., Kolega, J., Siddiqui, A., Meng, H.: Nascent aneurysm formation at the basilar terminus induced by hemodynamics. Stroke J. Cereb. Circ. 39(7), 2085–2090 (2008)
Glagov, S., Zarins, C., Giddens, D., Ku, D.N.: Hemodynamics and atherosclerosis: insights and perspectives gained from studies of human arteries. Arch. Pathol. Lab. Med. 112, 1018–1031 (1988)
Goode, T., Davies, P., Reidy, M., Bowyer, D.: Aortic endothelial cell morphology observed in situ by scanning electron microscopy during atherogenesis in the rabbit. Atherosclerosis 27(2), 235–51 (1977)
Gresho, P.M.: Some current CFD issues relevant to the incompressible Navier-Stokes equations. Comput. Methods Appl. 87, 201–252 (1991)
Haljasmaa, I., Robertson, A.M., Galdi, G.P.: On the effect of apex geomery on wall shear stress and pressure in two-dimensional models of arterial bifurcations. Math. Models Methods Appl. S. 11(3), 499–520 (2001)
Hashimoto, N., Handa, H., Nagata, I., Hazama, F.: Experimentally induced cerebral aneurysms in rats: Part V. Relation of hemodynamics in the circle of Willis to formation of aneurysms. Surg. Neurol. 13(1), 41–45 (1980)
Hassler, O.: Experimental carotid ligation followed by aneurysmal formation and other morphological changes in the circle of Willis. J. Neurosurg. 20, 1–7 (1963)
Heywood, J.G., Rannacher, R., Turek, S.: Artificial boundaries and flux and pressure conditions for the incompressible Navier-Stokes equations. Int. J. Numer. Methods Fluids 22, 325–352 (1996)
Huo, Y., Guo, X., Kassab, G.S.: The flow field along the entire length of mouse aorta and primary branches. Ann. Biomed. Eng. 36(5), 685–699 (2008)
Kamiya, A., Togawa, T.: Adaptive regulation of wall shear stress to flow change in the canine carotid artery. Am. J. Physiol. 239, H14–H21 (1980)
Kayembe, K., Sasahara, M., Hazama, F.: Cerebral aneurysms and variations in the circle of Willis. Stroke 15, 846–850 (1984)
Keynton, R.S., Evancho, M.M., Sims, R.L., Rodway, N.V., Gobin, A., Rittgers, S.E.: Intimal hyperplasia and wall shear in arterial bypass graft distal anastomoses: An in vivo model study. J. Biomech. Eng. 123(5), 464–473 (2001)
Kleinstreuer, C., Hyun, S., Buchanan, J.R., J, Longest, P.W., Archie J.P., J, Truskey, G.A.: Hemodynamic parameters and early intimal thickening in branching blood vessels. Crit. Rev. Biomed. Eng. 29(1), 1–64 (2001)
Ku, D.N.: Blood flow in arteries. Annu. Rev. Fluid Mech. 29(1), 399–434 (1997)
Kučera, P., Skalák, Z.: Local solutions to the Navier-Stokes equations with mixed boundary conditions. Acta Appl. Math. 54(3), 275–288 (1998) 10.1023/A:1006185601807
LaMack, J.A., Himburg, H.A., Li, X.M., Friedman, M.H.: Interaction of wall shear stress magnitude and gradient in the prediction of arterial macromolecular permeability. Ann. Biomed. Eng. 33(4), 457–464 (2005)
Langille, B.L.: Arterial remodeling: relation to hemodynamics. Can. J. Physiol. Pharmacol. 74(7), 834–841 (1996)
Larkin, J., Barrow, J., Durka, M., Remic, D., Zeng, Z., Robertson, A.M.: Design of a flow chamber to explore the initiation and development of cerebral aneurysms. In: Annual Fall Meeting of the Biomedical Engineering Society (BMES). Los Angeles, CA (2007)
Lei, M., Archie, J.P., Kleinstreuer, C.: Computational design of a bypass graft that minimizes wall shear stress gradients in the region of the distal anastomosis. J. Vasc. Surg. 25(4), 637–646 (1997)
Leone, J.M., Gresho, P.M.: Finite element simulations of steady, two-dimensional, viscous incompressible flow over a step. J. Comput. Phys. 41(1), 167–191 (1981) doi: 10.1016/0021-9991(81)90086-3
Li, D., Robertson, A.M.: A structural multi-mechanism damage model for cerebral arterial tissue and its finite element implementation. Proceedings of the ASME 2008 Summer Bioengineering Conference (SBC-2008) (2008)
Li, D., Robertson, A.M.: A structural multi-mechanism damage model for cerebral arterial tissue. J. Biomech. Eng. 131(10), 101013 (2009), doi:10.1115/1-3202559.
Malek, A.M., Izumo, S.: Mechanism of endothelial cell shape change and cytoskeletal remodeling in response to fluid shear stress. J. Cell Sci. 109, 713–726 (1996)
McCann, J., Peterson, S., Plesniak, M., Webster, T., Haberstroh, K.: Non-uniform flow behavior in a parallel plate flow chamber alters endothelial cell responses. Ann. Biomed. Eng. 33(3), 328–336 (2005) 10.1007/s10439-005-1735-9
Meng, H., Swartz, D.D., Wang, Z., Hoi, Y., Kolega, J., Metaxa, E.M., Szymanski, M.P., Yamamoto, J., Sauvageau, E., Levy, E.I.: A model system for mapping vascular responses to complex hemodynamics at arterial bifurcations in vivo. Neurosurgery 59(5), 1094–1100; discussion 1100–1101 (2006)
Meng, H., Wang, Z., Hoi, Y., Gao, L., Metaxa, E., Swartz, D.D., Kolega, J.: Complex hemodynamics at the apex of an arterial bifurcation induces vascular remodeling resembling cerebral aneurysm initiation. Stroke 38(6), 1924–1931 (2007)
Murray, C.D.: The physiological principle of minimum work. Proc. Natl. Acad. Sci. USA 12(3), 207–214 (1926)
Nagel, T., Resnick, N., Dewey, C., Forbes, J., Gimbrone Michael, A., Jr.: Vascular endothelial cells respond to spatial gradients in fluid shear stress by enhanced activation of transcription factors. Arterio. Thromb. Vasc. Biol. 19(8), 1825–1834 (1999)
Robertson, A.M., Sequeira, A., Kameneva, M.: Hemorheology. In: G.P. Galdi, R. Rannacher, A.M. Robertson, S. Turek (eds.) Hemodynamical Flows: Modeling, Analysis and Simulation, Oberwolfach Seminars, vol. 37. Birkhäuser, Cambridge (2008)
Sakamoto, N., Ohashi, T., Sato, M.: High shear stress induces production of matrix metalloproteinase in endothelial cells. In: Proceedings of the ASME 2008 Summer Bioengineering Conference (SBC2008). Marco Island, Florida (2008)
Sasaki, T., Kodama, N., Itokawa, H.: Aneurysm formation and rupture at the site of anastomosis following bypass surgery. J. Neurosurg. 85, 500–502 (1996)
Sekhar, L.N., Heros, R.C.: Origin, growth, and rupture of saccular aneurysms: A review. Neurosurgery 8, 248–260 (1981)
Szymanski, M.: Endothelial cell layer subjected to flow mimickng the apex of an arterial bifurcation. Ph.d., State University of New York at Buffalo (2007)
Szymanski, M., Metaxa, E., Meng, H., Kolega, J.: Endothelial cell layer subjected to impinging flow mimicking the apex of an arterial bifurcation. Ann. Biomed. Eng. 36(10), 1681–1689 (2008)
Truesdell, C., Noll, W.: Non-linear field theories of mechanics. In: S. Flugge (ed.) Handbuch der Physik, vol. III/3. Springer-Verlag, Berlin (1965)
Zakaria, H., Robertson, A.M., Kerber, C.: A parametric model for studies of flow in arterial bifurcations. Ann. Biomed. Eng. 36(9), 1515–1530 (2008)
Zamir, M.: Optimality principles in arterial branching. J. Theor. Biol. 62(1), 227–251 (1976)
Zheng, L., Yang, W.: Biofluid dynamics at arterial bifurcations. Crit. Rev. Biomed. Eng. 19, 455–493 (1992)
Acknowledgments
The authors would like to thank Andy Holmes of the Swanson Center for Product Innovation at the University of Pittsburgh for his valuable suggestions on the design and manufacture of the T-chamber. A number of graduates from the Department of Mechanical Engineering and Materials Science at the University of Pittsburgh have worked on an earlier version of the T-chamber as part of their senior design project and as undergraduate researchers. In particular, the authors would like to acknowledge John Barrow, Jason Larkin and David Remic [31]. A.M. Robertson would like to thank the Aachen Institute for Advanced Study in Computational Engineering Science (AICES) of the University of Aachen for a visiting professorship which she held during the period this paper was written.
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Zeng, Z., Chung, B.J., Durka, M., Robertson, A.M. (2010). An In Vitro Device for Evaluation of Cellular Response to Flows Found at the Apex of Arterial Bifurcations. In: Rannacher, R., Sequeira, A. (eds) Advances in Mathematical Fluid Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04068-9_35
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