Abstract
The aim of the present study was to develop and validate a method based on medical imaging to identify the parameters of a hyper-viscoelastic model suitable for describing the mechanical behavior of vascular tissues, focusing on the aorta. The method uses an inflation-extension test, and the model comprises one hyperelastic element in parallel with one or more Maxwell elements. Cylindrical samples of elastomeric silicone materials with a mechanical behavior similar to vascular tissues were placed in a circuit simulating hemodynamic flow through adequate controlled-pressure variation. Ultrasound B-mode image sequences were analyzed to measure the cyclic circumferential and longitudinal elongations. Precautions were taken a posteriori to resynchronize pressure and deformation signals, and thus minimize errors in the viscosity parameters estimated. The hyper-viscoelastic parameters of the samples were identified with reasonable accuracy as compared with the values obtained via standard measurements, namely tensile tests and dynamic mechanical analysis. However, the estimates of the viscosity parameters can be hampered in the case of stiffer samples. This limitation is bound to a restricted range of frequencies analyzed by the test, which mainly depends on the image acquisition rate. The use of the present method in the clinical environment for in vivo experiments can be foreseen provided that the local pressure measurements are available.
References
Long A, Rouet L, Bissery A, Rossignol P, Mouradian D, Sapoval M (2005) Compliance of abdominal aortic aneurysms evaluated by tissue Doppler imaging: correlation with aneurysm size. J Vasc Surg 42(1):18–26. doi:10.1016/j.jvs.2005.03.037
Riley WA, Barnes RW, Evans GW, Burke GL (1992) Ultrasonic measurement of the elastic modulus of the common carotid artery. The atherosclerosis risk in communities (ARIC) study. Stroke 23(7):952–956. doi:10.1161/01.str.23.7.952
Astrand H, Stalhand J, Karlsson J, Karlsson M, Sonesson B, Lanne T (2011) In vivo estimation of the contribution of elastin and collagen to the mechanical properties in the human abdominal aorta: effect of age and sex. J Appl Physiol 110(1):176–187
Wilson KA, Lindholt JS, Hoskins PR, Heickendorff L, Vammen S, Bradbury AW (2001) The relationship between abdominal aortic aneurysm distensibility and serum markers of elastin and collagen metabolism. Eur J Vasc Endovasc Surg 21(2):175–178
Konig G, McAllister TN, Dusserre N, Garrido SA, Iyican C, Marini A, Fiorillo A, Avila H, Wystrychowski W, Zagalski K, Maruszewski M, Jones AL, Cierpka L, de la Fuente LM, L’Heureux N (2009) Mechanical properties of completely autologous human tissue engineered blood vessels compared to human saphenous vein and mammary artery. Biomaterials 30(8):1542–1550. doi:10.1016/j.biomaterials.2008.11.011
Corbett TJ, Doyle BJ, Callanan A, Walsh MT, McGloughlin TM (2010) Engineering silicone rubbers for in vitro studies: creating AAA models and ILT analogues with physiological properties. J Biomech Eng 132(1):011008. doi:10.1115/1.4000156
Shimamura J, Kubota H, Endo H, Tsuchiya H, Kawashima N, Sudo K (2012) Three-dimensional replica of a life-sized model of aortic arch aneurysm for preoperative assessments. Ann Thorac Surg 93(5):1699–1702. doi:10.1016/j.athoracsur.2012.01.072
Sulaiman A, Boussel L, Taconnet F, Serfaty JM, Alsaid H, Attia C, Huet L, Douek P (2008) In vitro non-rigid life-size model of aortic arch aneurysm for endovascular prosthesis assessment. Eur J Cardio-Thoracic Surg: Off J Eur Assoc Cardio-Thoracic Surg 33(1):53–57. doi:10.1016/j.ejcts.2007.10.016
van’t Veer M, Buth J, Merkx M, Tonino P, van den Bosch H, Pijls N, van de Vosse F (2008) Biomechanical properties of abdominal aortic aneurysms assessed by simultaneously measured pressure and volume changes in humans. J Vasc Surg 48(6):1401–1407. doi:10.1016/j.jvs.2008.06.060
Molacek J, Baxa J, Houdek K, Treska V, Ferda J (2011) Assessment of abdominal aortic aneurysm wall distensibility with electrocardiography-gated computed tomography. Ann Vasc Surg 25(8):1036–1042
Astrand H, Ryden-Ahlgren A, Sandgren T, Lanne T (2005) Age-related increase in wall stress of the human abdominal aorta: an in vivo study. J Vasc Surg 42(5):926–931. doi:10.1016/j.jvs.2005.07.010
Redheuil A, Yu WC, Wu CO, Mousseaux E, de Cesare A, Yan R, Kachenoura N, Bluemke D, Lima JA (2010) Reduced ascending aortic strain and distensibility: earliest manifestations of vascular aging in humans. Hypertension 55(2):319–326. doi:10.1161/hypertensionaha.109.141275
Li L, Qian X, Yan S, Hua L, Zhang H, Liu Z (2012) Determination of the material parameters of four-fibre family model based on uniaxial extension data of arterial walls. Comp Methods Biomech Biomed Eng. doi:10.1080/10255842.2012.714374
Holzapfel G, Gasser T, Ogden R (2000) A new constitutive framework for arterial wall mechanics and a comparative study of material models. J Elast 61(1):1–48
Holzapfel GA, Gasser TC, Stadler M (2002) A structural model for the viscoelastic behavior of arterial walls: continuum formulation and finite element analysis. Eur J Mech A/Solids 21(3):441–463
Valdez-Jasso D, Bia D, Haider MA, Zocalo Y, Armentano RL, Olufsen MS (2010) Linear and nonlinear viscoelastic modeling of ovine aortic biomechanical properties under in vivo and ex vivo conditions. Conf Proc: Annu Int Conf IEEE Eng Med Biol Soc IEEE Eng Med Biol Soc Conf 2010:2634–2637. doi:10.1109/iembs.2010.5626563
Zhang W, Liu Y, Kassab GS (2007) Viscoelasticity reduces the dynamic stresses and strains in the vessel wall: implications for vessel fatigue. Am J Physiol Heart Circ Physiol 293(4):H2355–H2360. doi:10.1152/ajpheart.00423.2007
van Dam EA, Dams SD, Peters GW, Rutten MC, Schurink GW, Buth J, van de Vosse FN (2008) Non-linear viscoelastic behavior of abdominal aortic aneurysm thrombus. Biomech Model Mechanobiol 7(2):127–137. doi:10.1007/s10237-007-0080-3
Bell V, Mitchell WA, Sigurðsson S, Westenberg JJM, Gotal JD, Torjesen AA, Aspelund T, Launer LJ, de Roos A, Gudnason V, Harris TB, Mitchell GF (2014) Longitudinal and circumferential strain of the proximal aorta. J Am Heart Assoc 3 (6). doi:10.1161/jaha.114.001536
Chong CK, How TV, Harris PL (2005) Flow visualization in a model of a bifurcated stent-graft. J Endovasc Ther 12(4):435–445. doi:10.1583/04-1465.1
Gulan U, Luthi B, Holzner M, Liberzon A, Tsinober A, Kinzelbach W (2014) Experimental investigation of the influence of the aortic stiffness on hemodynamics in the ascending aorta. IEEE J Biomed Health Inf. doi:10.1109/jbhi.2014.2322934
Anssari-Benam A, Korakianitis T (2013) An experimental model to simulate arterial pulsatile flow: in vitro pressure and pressure gradient wave study. Exp Mech 53(4):649–660. doi:10.1007/s11340-012-9675-4
Holzapfel GA, Gasser TC (2001) A viscoelastic model for fiber-reinforced composites at finite strains: continuum basis, computational aspects and applications. Comput Methods Appl Mech Eng 190(34):4379–4403
Nierenberger M (2013) Multiscale mechanics of vascular walls: Experiments, imaging, modeling. Mécanique des matériaux, Université de Strasbourg
Balocco S, Basset O, Courbebaisse G, Boni E, Frangi AF, Tortoli P, Cachard C (2010) Estimation of the viscoelastic properties of vessel walls using a computational model and Doppler ultrasound. Phys Med Biol 55(12):3557–3575. doi:10.1088/0031-9155/55/12/019
Courtial E-J (2015) Elaboration of silicone materials with a mechanical behavior tailored for manufacturing patient-specific aortic phantom. University of Claude Bernard Lyon 1
Holzapfel GA (2000) Nonlinear solid mechanics: A continuum approach for engineering. Wiley edn
Yeoh OH (1993) Some forms of the strain energy function for rubber. Rubber Chem Technol 66(5):754–771. doi:10.5254/1.3538343
Vassal J-P, Avril S, Genovese K (2009) Caractérisation des propriétés mécaniques d’un tronçon d’aorte par une méthode inverse basée sur des mesures ex-vivo du champ de déformations. Paper presented at the 19ème congrès de mécanique, Marseilles
Friedrich C, Honerkamp J, Weese J (1996) New ill-posed problems in rheology. Rheol Acta 35(2):186–193. doi:10.1007/BF00396045
Benkahla J, Baranger TN, Issartel J (2012) Experimental and numerical simulation of elastomeric outsole bending. Exp Mech 52(9):1461–1473. doi:10.1007/s11340-012-9606-4
Mullins L (1969) Softening of rubber by deformation. Rubber Chem Technol 42(1):339–362. doi:10.5254/1.3539210
Sorensen D (1982) Newton’s method with a model trust region modification. SIAM J Numer Anal 19(2):409–426. doi:10.1137/0719026
Dong Y, Lin RJT, Bhattacharyya D (2005) Determination of critical material parameters for numerical simulation of acrylic sheet forming. J Mater Sci 40(2):399–410. doi:10.1007/s10853-005-6096-0
Idel’cik IE (1969) Mémento des pertes de charge, coefficients de pertes de charge singulières et de pertes de charge par frottement, vol 13. vol Collection du Centre de recherches et d’essais de Chatou. Eyrolles
Dávila Serrano EE, Guigues L, Roux JP, Cervenansky F, Camarasu-Pop S, Riveros Reyes JG, Flórez Valencia L, Hernández Hoyos M, Orkisz M (2012) CreaTools: applications and development framework for medical image-processing software. Paper presented at the ISBI Workshop on Open Source Medical Image Analysis Software, Barcelona, Spain, 05/2012
Zahnd G, Orkisz M, Serusclat A, Moulin P, Vray D (2013) Evaluation of a Kalman-based block matching method to assess the bi-dimensional motion of the carotid artery wall in B-mode ultrasound sequences. Med Image Anal 17(5):573–585. doi:10.1016/j.media.2013.03.006
Zahnd G, Orkisz M, Serusclat A, Moulin P, Vray D (2013) Simultaneous extraction of carotid artery intima-media interfaces in ultrasound images: assessment of wall thickness temporal variation during the cardiac cycle. Int J Comput Assist Radiol Surg. doi:10.1007/s11548-013-0945-0
Fazeli N, Kim C-S, Rashedi M, Chappell A, Wang S, MacArthur R, McMurtry MS, Finegan B, Hahn J-O (2014) Subject-specific estimation of central aortic blood pressure via system identification: preliminary in-human experimental study. Med Biol Eng Comput 52(10):895–904. doi:10.1007/s11517-014-1185-3
Acknowledgments
This study was conducted within the CARDIO project co-funded by Segula Matra Technologies and the French Ministry of National Education and Technological Research, and of the LABEX PRIMES (ANR-11-LABX-0063). Our thanks are extended to Maël ROY, an engineering student at INSA Lyon (department of mechanical engineering and development) and Adeline BERNARD, an engineer assistant at CREATIS laboratory (Lyon, France) for their technical support.
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Courtial, EJ., Orkisz, M., Douek, P.C. et al. Identifying Hyper-Viscoelastic Model Parameters from an Inflation-Extension Test and Ultrasound Images. Exp Mech 55, 1353–1366 (2015). https://doi.org/10.1007/s11340-015-0042-0
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DOI: https://doi.org/10.1007/s11340-015-0042-0