Hostname: page-component-77c89778f8-swr86 Total loading time: 0 Render date: 2024-07-16T13:27:34.080Z Has data issue: false hasContentIssue false
  • English
  • Français

Inverse problems in the mechanical characterization of elastic arteries

Published online by Cambridge University Press:  01 April 2015

Claire Morin  and
Stéphane Avril
Claire Morin
Affiliation:
École Nationale Supérieure des Mines, Saint-Etienne, France; claire.morin@mines-stetienne.fr
Stéphane Avril
Affiliation:
École Nationale Supérieure des Mines, Saint-Etienne, France; stephane.avril@mines-stetienne.fr
Get access

Abstract

This article presents an overview of various material models used to represent the mechanical behavior of arteries and the inverse problems posed by the identification of their constitutive parameters. After briefly defining inverse problems and describing the general features of arteries, this article addresses three main queries involving inverse problems and arterial wall characterization: (1) macroscopic identification of the parameters of sophisticated constitutive models from traditional uniaxial and biaxial experiments; (2) mesoscopic identification of regional variations in the material parameters of arteries, tracking the effects of functional adaptation or lesions; and (3) how constitutive models and inverse problems allow information to be obtained on the arterial microstructure and how the structural constituents interact in the mechanical response. Finally, the article shows that while significant effort has been made to relate the complex mechanical behavior of arteries to their microstructure, a new class of inverse problems has recently appeared related to the identification of mechanobiological parameters, which are involved in the numerical models of growth and remodeling.

Keywords

Stress/strain relationshipfiberbiologicaltissuemicrostructure
Type
Research Article
Information
MRS Bulletin , Volume 40 , Issue 4: Multiscale mechanics of biological, bioinspired, and biomedical materials , April 2015 , pp. 317 - 323
Copyright
Copyright © Materials Research Society 2015 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Avril, S., Bonnet, M., Bretelle, A.S., Grédiac, M., Hild, F., Ienny, P., Latourte, F., Lemosse, D., Pagano, S., Pagnacco, E., Pierron, F., Exp. Mech. 48, 381 (2008).Google Scholar
Riveros, F., Chandra, S., Finol, E.A., Gasser, T.C., Rodriguez, J.F., Ann. Biomed. Eng. 41, 694 (2013).Google Scholar
Criscione, J., J. Elast. 77, 57 (2004).Google Scholar
Avril, S., Badel, P., Duprey, A., J. Biomech. 43, 2978 (2010).Google Scholar
Grediac, M., Pierron, F., Avril, S., Toussaint, E., Strain 42, 233 (2006).Google Scholar
Barbone, P., Gokhale, N., Inverse Probl. 20, 283 (2004).Google Scholar
Tikhonov, A., Arsenin, V., Solutions of Ill-Posed Problems (Wiley, Washington, DC, 1977).Google Scholar
Fillinger, M., Marra, S., Raghavan, M., Kennedy, F., J. Vasc. Surg. 37, 724 (2003).Google Scholar
Li, Z., Howarth, S., Tang, T., Gillard, J., Stroke 37, 1195 (2006).Google Scholar
Nishimura, R., Edwards, W.D., Warnes, C.A., Reeder, G.S., Holmes, D.R. Jr., Tajik, A.J., Yock, P.G., J. Am. Coll. Cardiol. 16, 145 (1990).Google Scholar
Gussenhoven, E.J., Essed, C.E., Lancée, C.T., Mastik, F., Frietman, P., van Egmond, F.C., Reiber, J., Bosch, H., van Urk, H., Roelandt, J., J. Am. Coll. Cardiol. 14, 947 (1989).CrossRefGoogle Scholar
Tobis, J.M., Mallery, J., Mahon, D., Lehmann, K., Zalesky, P., Griffith, J., Gessert, J., Moriuchi, M., McRae, M., Dwyer, M.L., Circulation 83, 913 (1991).Google Scholar
Woodrum, D., Romano, A.J., Lerman, A., Pandya, U.H., Brosh, D., Rossman, P.J., Lerman, L.O., Ehman, R.L., Magn. Reson. Med. 56, 593 (2006).CrossRefGoogle Scholar
Yabushita, H., Bouma, B.E., Houser, S.L., Aretz, H.T., Jang, I.K., Schlendorf, K.H., Kauffman, C.R., Shishkov, M., Kang, D.H., Halpern, E.F., Tearney, G.J., Circulation 106, 1640 (2002).Google Scholar
Badel, P., Avril, S., Lessner, S., Sutton, M., Comput. Methods Biomech. Biomed. Eng. 15, 37 (2012).CrossRefGoogle Scholar
Chuong, C., Fung, Y., J. Biomech. 17, 35 (1984).Google Scholar
Duprey, A., Khanafer, K., Schlicht, M., Avril, S., Williams, D., Berguer, R., Eur. J. Vasc. Endovasc. Surg. 39, 700 (2010).Google Scholar
Eskandari, H., Salcudean, S., Rohling, R., Ohayon, J., Phys. Med. Biol. 53, 6569 (2008).Google Scholar
Ferruzzi, J., Vorp, D.A., Humphrey, J.D., J. R. Soc. Interface 8, 435 (2011).Google Scholar
Fonck, E., Prod'hom, G., Roy, S., Augsburger, L., Rüfenacht, D.A., Stergiopulos, N., Am. J. Physiol. Heart Circ. Physiol. 292, 2754 (2007).Google Scholar
Fung, Y.C., Fronek, K., Patitucci, P., Am. J. Physiol. Heart Circ. Physiol. 237, H620 (1979).Google Scholar
Gasser, T., Ogden, R., Holzapfel, G., J. R. Soc. Interface 3, 15 (2006).Google Scholar
Holzapfel, G., Weizsäcker, H., Comput. Biol. Med. 28, 377 (1998).Google Scholar
Holzapfel, G., J. Theor. Biol. 238, 290 (2006).Google Scholar
Kalita, P., Schaefer, R., Arch. Comput. Methods Eng. 15, 1 (2008).Google Scholar
Kauer, M., Vuskovic, V., Dual, J., Szekely, G., Bajka, M., Med. Image Anal. 6, 275 (2002).CrossRefGoogle Scholar
Kroon, M., Holzapfel, G., Comput. Methods Appl. Mech. Eng. 198, 3622 (2009).Google Scholar
Masson, I., Boutouyrie, P., Laurent, S., Humphrey, J., Zidi, M., J. Biomech. 41, 2618 (2008).Google Scholar
Pandit, A., Lu, X., Wang, C., Kassab, G.S., Am. J. Physiol. Heart Circ. Physiol. 288, H2581 (2005).Google Scholar
Stalhand, J., Klarbring, A., Karlsson, M., Biomech. Model. Mechanobiol. 2, 169 (2004).CrossRefGoogle Scholar
Wan, W., Dixon, J.B., Gleason, R.L. Jr., Biophys. J. 102, 2916 (2012).Google Scholar
Zulliger, M., Fridez, P., Hayashi, K., Stergiopulos, N., J. Biomech. 37, 989 (2004).Google Scholar
Fung, Y.C., Biomechanics: Mechanical Properties of Living Tissues (Springer-Verlag, New York, NY, 1993).Google Scholar
Humphrey, J., Cardiovascular Solid Mechanics: Cells, Tissues, and Organs (Springer, New York, NY, 2002).Google Scholar
Dobrin, P., Physiol. Rev. 58, 397 (1978).Google Scholar
Doyle, J., Dobrin, P., Microvasc. Res. 3, 400 (1971).Google Scholar
Van Loon, P., Klip, W., Bradley, E., Biorheology 14, 181 (1977).Google Scholar
Holzapfel, G., Gasser, T., Stadler, M., Eur. J. Mech. A Solids 21, 441 (2002).Google Scholar
Holzapfel, G.A., Gasser, T.C., Ogden, R.W., J. Elast. 61, 1 (2000).Google Scholar
Zeller, P., Skalak, T., J. Vasc. Res. 35, 8 (1995).Google Scholar
Saini, A., Berry, C., Greenwald, S., J. Vasc. Res. 32, 398 (1995).Google Scholar
Bergel, D., thesis, Queen Mary University of London, UK (1960).Google Scholar
Chuong, C.J., Fung, Y.C., J. Biomech. Eng. 108, 189 (1986).Google Scholar
Takamizawa, K., Hayashi, K., J. Biomech. 20, 7 (1987).Google Scholar
Badel, P., Genovese, K., Avril, S., Strain 48, 528 (2012).CrossRefGoogle Scholar
Zeinali-Davarani, S., Choi, J., Baek, S., J. Biomech. 42, 524 (2009).Google Scholar
Auricchio, F., Conti, M., Ferrara, A., Arch. Comput. Methods Eng. 21, 273 (2014).Google Scholar
Volokh, K., J. Biomech. 41, 447 (2008).Google Scholar
Pena, E., Doblare, M., Mech. Res. Commun. 36, 784 (2009).Google Scholar
Gasser, T., Auer, M., Labruto, F., Swedenborg, J., Roy, J., Eur. J. Vasc. Endovasc. 40, 176 (2010).Google Scholar
Balzani, D., Schröder, J., Gross, D., Acta Biomater. 2, 609 (2006).Google Scholar
Le Floc’h, S., Ohayon, J., Tracqui, P., Finet, G., Gharib, A.M., Maurice, R.L., Cloutier, G., Pettigrew, R.I., IEEE Trans. Med. Imaging 28, 1126 (2009).Google Scholar
Chai, C., Speelman, L., Oomens, C., Baaijens, F., J. Biomech. 47, 784 (2014). .Google Scholar
Boudou, T., Ohayon, J., Arntz, Y., Finet, G., Picart, C., Tracqui, P., J. Biomech. 39, 1677 (2006).Google Scholar
Holzapfel, G.A., Sommer, G., Gasser, C.T., Regitnig, P., Am. J. Physiol. Heart Circ. Physiol. 289, 2048 (2005).Google Scholar
Lu, J., Zhou, X., Raghavan, M., Biomech. Model. Mechanobiol. 7, 477 (2008).Google Scholar
Khalil, A., Bouma, B., Kaazempur Mofrad, M., Cardiovasc. Eng. 6, 93 (2006).Google Scholar
Seshaiyer, P., Humphrey, J.D., J. Biomech. Eng. 125, 363 (2003).Google Scholar
Romo, A., Badel, P., Duprey, A., Favre, J., Avril, S., J. Biomech. 47, 607 (2014).Google Scholar
Roy, S., Boss, C., Rezakhaniha, R., Stergiopulos, N., J. Biorheol. 24, 84 (2010).Google Scholar
Wolinsky, H., Glagov, S., Circ. Res. 14, 400 (1964).Google Scholar
Schrauwen, J.T.C., Villanova, A., Rezakhaniha, R., Stergiopulos, N., van de Vosse, F.N., Bovendeerd, P.H.M., J. Struct. Biol. 180, 335 (2012).CrossRefGoogle Scholar
Humphrey, J., J. Mech. Med. Biol. 9, 243 (2009).Google Scholar
Lanir, Y., J. Biomech. 16, 1 (1983).Google Scholar
Kim, J., Avril, S., Duprey, A., Favre, J., Biomech. Model. Mechanobiol. 11, 841 (2012).Google Scholar
Bank, A., Wang, H., Holte, J.E., Mullen, K., Shammas, R., Kubo, S.H., Circulation 94, 3263 (1996).Google Scholar
Cox, R.H., Am. J. Physiol. 234, 542 (1978).CrossRefGoogle Scholar
O’Connell, M., Murthy, S., Phan, S., Xu, C., Buchanan, J., Spilker, R., Dalman, R.L., Zarins, C.K., Denk, W., Taylor, C.A., Matrix Biol. 27, 171 (2008).Google Scholar
Zulliger, M., Stergiopulos, N., J. Biomech. 40, 3061 (2007).Google Scholar
Anidjar, S., Salzmann, J.L., Gentric, D., Lagneau, P., Camilleri, J.P., Michel, J.B., Circulation 82, 973 (1990).Google Scholar
Aaron, B.B., Gosline, J.M., Biopolymers 20, 1247 (1981).Google Scholar
Ferruzzi, J., Collins, M., Yeh, A., Humphrey, J., Cardiovasc. Res. 92, 287 (2011).Google Scholar
Zeinali-Davarani, S., Chow, M., Turcotte, R., Zhang, Y., Ann. Biomed. Eng. 41, 1528 (2013).Google Scholar
Samila, Z., Carter, S., Can. J. Physiol. Pharmacol. 59, 1050 (1981).Google Scholar
Campa, J., Greenhalgh, R., Powell, J.T., Atherosclerosis 65, 13 (1987).Google Scholar
Scott, S., Ferguson, G., Roach, M., Can. J. Physiol. Pharmacol. 50, 328 (1972).Google Scholar
Bellini, C., Ferruzzi, J., Roccabianca, S., Martino, E.S.D., Humphrey, J.D., Ann. Biomed. Eng. 42, 488 (2014).CrossRefGoogle Scholar
Cyron, C., Humphrey, J., Int. J. Eng. Sci. 85, 203 (2014).Google Scholar
Wilson, J., Humphrey, J., J. Biomech. 47, 2995 (2014).Google Scholar
Azeloglu, E., Albro, M., Thimmappa, V., Ateshian, G., Costa, K., Am. J. Physiol. Heart Circ. Physiol. 294, H1197 (2008).Google Scholar