River Rapids Conference Proceedings of the Society for Experimental Mechanics Series Mechanics of Biological Systems and Materials, Volume 2 Tom Proulx Proceedings of the 2011 Annual Conference on Experimental and Applied Mechanics River Publishers
Conference Proceedings of the Society for Experimental Mechanics Series
River Publishers Tom Proulx Editor Mechanics of Biological Systems and Materials, Volume 2 Proceedings of the 2011 Annual Conference on Experimental and Applied Mechanics
Published, sold and distributed by: River Publishers Broagervej 10 9260 Gistrup Denmark www.riverpublishers.com ISBN 978-87-7004-854-5 (eBook) Conference Proceedings of the Society for Experimental Mechanics An imprint of River Publishers © The Society for Experimental Mechanics, Inc. 2011 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, or reproduction in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Preface Mechanics of Biological Systems and Materials—The 1st International Symposium on the Mechanics of Biological Systems and Materials—represents one of eight volumes of technical papers presented at the Society for Experimental Mechanics Annual Conference & Exposition on Experimental and Applied Mechanics, held at Uncasville, Connecticut, June 13-16, 2011. The full set of proceedings also includes volumes on Dynamic Behavior of Materials, Mechanics of Time-Dependent Materials and Processes in Conventional and Multifunctional Materials, MEMS and Nanotechnology; Optical Measurements, Modeling and, Metrology; Experimental and Applied Mechanics, Thermomechanics and Infra-Red Imaging, and Engineering Applications of Residual Stress. Each collection presents early findings from experimental and computational investigations on an important area within Experimental Mechanics. The 1st International Symposium on the Mechanics of Biological Systems and Materials was organized by: Bart Prorok, Auburn University; Francois Barthelat, McGill University; Chad Korach, State University of New York (SUNY) at Stony Brook; K. Jane Grande-Allen, Rice University; Elizabeth Lipke, Auburn University. This symposium was organized to providing a forum to foster the exchange of ideas and information among scientists and engineers involved in the research and analysis of how mechanical loads interact with the structure, properties and function of living organisms and their tissues. The scope includes experimental, imaging, numerical and mathematical techniques and tools spanning various length and time scales. Establishing this symposium at the Annual Meeting of the Society for Experimental Mechanics provides a venue where state-of-the-art experimental methods can be leveraged in the study of biomechanics. A major goal of the symposium is for participants to collaborate in the asking of fundamental questions and the development of new techniques to address bio-inspired problems in society, human health, and the natural world. The current volume on The 1st International Symposium on the Mechanics of Biological Systems and Materials includes studies on: Simulation and Modeling in Biomechanics Mechanics of Tissue Damage Cell Mechanics Mechanics of Cardiovascular Tissues
Advanced Imaging Methods Applied to Biomechanics Mechanics of Hydro Gels and Soft Materials Mechanics of Hard Tissues Mechanics of Biocomposites Nanomechanics in Nature Indentation Methods for Biological and Soft Materials The Biological Systems and Materials TD would like to thank the presenters, authors and session chairs for their participation. The opinions expressed herein are those of the individual authors and not necessarily those of the Society for Experimental Mechanics, Inc. Bethel, Connecticut Dr. Thomas Proulx Society for Experimental Mechanics, Inc vi
Contents 1 Analysis and Simulation of PTMA Device Deployment Into the Coronary Sinus: Impact of Stent Strut Thickness 1 T.M. Pham, University of Connecticut; M. DeHerrera, Advanced Technology Group; W. Sun, University of Connecticut 2 Mechanical Identification of Hyperelastic Anisotropic Properties of Mouse Carotid Arteries University of South Carolina 3 An Inverse Method to Determine Material Properties of Soft Tissues L. Ruggiero, H. Sol, H. Sahli, S. Adriaenssens, N. Adriaenssens, Vrije Universiteit Brussel 4 Estimation of the 3D Residual Strain Field in the Arterial Wall of a Bovine Aorta Using Optical Full-field Measurements and Finite Element Reconstruction K. Genovese, Università degli Studi della Basilicata; P. Badel, S. Avril, Ecole des Mines, France 5 Estimating Hydraulic Conductivity in Vivo Using Magnetic Resonance Elastography A.J. Pattison, P.R. Perrinez, M.D.J. McGarry, Dartmouth College; J.B. Weaver, Dartmouth-Hitchcock Medical Center; K.D. Paulsen, Dartmouth College/Dartmouth-Hitchcock Medical Center 6 Comparison of Iterative and Direct Inversion MR Elastography Algorithms M.D.J. McGarry, Dartmouth College; E.E.W. van Houten, University of Canterbury; A.J. Pattison, Dartmouth College; J.B. Weaver, Dartmouth-Hitchcock Medical Center; K.D. Paulsen, Dartmouth College/Dartmouth-Hitchcock Medical Center 7 Brain Response to Extracranial Pressure Excitation Imaged in vivo by MR Elastography E.H. Clayton, P.V. Bayly, Washington University in St. Louis 8 Mechanical Properties of Abnormal Human Aortic and Mitral Valves K. Paranjothi, U. Saravanan, R. KrishnaKumar, Indian Institute of Technology Madras; K.R. Balakrishnan, Malar Hospitals 9 Bio-prosthetic Heart Valve Stress Analysis: Impacts of Leaflet Properties and Stent Tip Deflection C. Martin, W. Sun, University of Connecticut 11 19 33 41 49 57 65 73 P. Badel, S. Avril, Ecole des Mines de Saint Etienne; S. Lessner, M. Sutton,
10 Mechanical Properties of Human Saphenous Vein K. Paranjothi, U. Saravanan, R. KrishnaKumar, Indian Institute of Technology Madras; K.R. Balakrishnan, Malar Hospitals 11 The Scleral Inflation Response of Mouse Eyes to Increases in Pressure K.M. Myers, Columbia University; F. Cone, H.A. Quigley, T.D. Nguyen, Johns Hopkins Medical Institute 12 Microstructure and Mechanical Properties of Dungeness Crab Exoskeletons J. Lian, J. Wang, University of Washington 13 The Mechanical Properties of Tendril of Climbing Plant N.-S. Liou, G.-W. Ruan, Southern Taiwan University 14 A Multiscale Triphasic Biomechanical Model for Tumors Classification K. Barber, C.S. Drapaca, Pennsylvania State University 15 Developing Hyper-viscoelastic Constitutive Models of Porcine Meniscus From Unconfined Compression Test Data N.-S. Liou, Southern Taiwan University; Y.-R. Jeng, National Chung Cheng University; S.-F. Chen, G.-W. Ruan, Southern Taiwan University; K.-T. Wu, National Chung Cheng University 16 The Mechanical Performance of Teleost Fish Scales D. Zhu, McGill University; F. Vernerey, University of Colorado; F. Barthelat, McGill University 17 Effects of Processing Conditions on Chitosan-hydroxyapatite Biocomposite Mechanical Properties C.S. Korach, G. Halada, H. Mubarez, State University of New York at Stony Brook 18 Mechanical Properties of a Nanostructured Poly (KAMPS)/Aragonite Composite C.S. Korach, State University of New York at Stony Brook; R. Krishna Pai, Brookhaven National Laboratory 19 Nanoscale Fracture Resistance Measurement of a Composite Bone Cement M. Khandaker, S. Tarantini, University of Central Oklahoma 20 Impact Resistance of Antibiotic-impregnated Orthopedic Bone Cement S. Choopani, A. Hashemi, AmirKabir University of Technology 21 Use of Nanoindentation for Investigating the Nanostructure of Dentin Tissue B.-H. Wu, C.-J. Chung, C.-H. Han, T.Y.-F. Chen, S.-F. Chuang, W.-L. Li, J.-F. Lin, National Cheng Kung University 22 Epinephrine Upregulates Sickle Trait Erythrocyte Adhesion to Laminin and Integrins J.L. Maciaszek, University of Connecticut; B. Andemariam, University of Connecticut Health Center; G. Lykotrafitis, University of Connecticut 23 Organ Culture Modeling of Distraction Osteogenesis M.M. Saunders, The University of Akron; J. Van Sickels, B. Heil, K. Gurley, University of Kentucky viii 79 87 93 101 105 111 117 125 131 137 145 153 159 163
24 Mechanical Properties of Tooth Enamel: Microstructural Modeling and Characterization T. Nakamura, C. Lu, C.S. Korach, State University of New York at Stony Brook 25 A Novel Biomimetic Material Duplicating the Structure and Mechanics of Natural Nacre D. Zhu, F. Barthelat, McGill University 26 Z. Zhang, J.F. Diaz, N. Olgac, University of Connecticut 27 Design of a Mechatronic Positioner for Holographic Otoscope System I. Dobrev, Worcester Polytechnic Institute; C. Furlong, Worcester Polytechnic Institute/ 28 Characterization of Shape and Deformation of Tympanic Membranes by Dual-wavelength Lensless Digital Holography W. Lu, Worcester Polytechnic Institute; C. Furlong, Worcester Polytechnic Institute/ Massachusetts Eye and Ear Infirmary; J.J. Rosowski, Massachusetts Eye and Ear Infirmary/ MIT-Harvard Division of Health Sciences and Technology; J.T. Cheng, Massachusetts Eaton-Peabody Laboratory, Massachusetts Eye and Ear Infirmary 29 Investigating Mechanical Properties of Porcine Articular Cartilage by Flat Plate Compression Tests S.-F. Chen, Southern Taiwan University; K.-T. Wu, National Chung Cheng University 30 Characterization of Tendon Mechanics Following Subfailure Damage S.E. Duenwald-Kuehl, J. Kondratko, R. Vanderby, Jr., R. Lakes, University of Wisconsin-Madison 31 Modeling Sickle Hemoglobin Fibers as one Chain of Coarse-grained Particles ix 171 181 189 193 199 209 213 219 Adaptive Hybrid Control for Low Resolution Feedback Systems With Application on a Novel Microinjector: Ros-drill Massachusetts Eye and Ear Infirmary; J.J. Rosowski, Massachusetts Eye and Ear Infirmary N.-S. Liou, Southern Taiwan University; Y.-R. Jeng, National Chung Cheng University; S.-H. Yen, H. Li, H. Vi, G. Lykotrafitis, University of Connecticut
for Experimental Mechanics Series 9999, DOI 10.1007/978-1-4614-0219-0_1, © The Society for Experimental Mechanics, Inc. 2011 1 T. Proulx (ed.), Mechanics of Biological Systems and Materials, Volume 2, Conference Proceedings of the Society Analysis and Simulation of PTMA Device Deployment into the Coronary Sinus: Impact of Stent Strut Thickness Thuy M Pham1, Milton DeHerrera2, Wei Sun1 1Tissue Mechanics Lab Biomedical Engineering & Department of Mechanical Engineering, University of Connecticut, Storrs, CT 06269 2Advanced Technology Group, Edwards Lifesciences, Irvine, CA, 92614 ABSTRACT Surgical repair and replacement of mitral valve for functional mitral regurgitation (MR) are often limited due to high operative mortality. Recently, a new non-surgical intervention, percutaneous transvenous mitral annuloplasty (PTMA), is being investigated as an endovascular alternative to invasive open-heart surgery. Excellent short-term results have been reported in animal and several human clinical trials, proving the device is feasible. However, device fracture was observed. It is postulated that PTMA device failure is associated with its design (e.g., material, structural geometry) and interactive coupling effects between the device and hosting tissues. In this study, we developed a computational model to investigate the impact of PTMA design on its performance and fatigue life by simulating the deployment of a variety of anchor stents into human coronary sinus (CS) vessel. Peak stresses, strains, interaction forces (shear, normal) of CS wall and stent, as well as device fatigue life and safety factor, were examined, offering insights for a better PTMA design. Results showed that a stiffer Nitinol stent induced high stresses on the vessel wall. Consequently, using a stiffer stent should be coupled with an alternation of stent geometry (e.g. strut thickness) in order to reduce vessel stress as well as radial structural stiffness. INTRODUCTION Surgical repair and replacement of mitral valve for functional mitral regurgitation (MR) are often limited due to high operative mortality [1, 2]. Recently, a new non-surgical intervention, percutaneous transvenous mitral annuloplasty (PTMA), utilizing the trans-coronary sinus (CS) vein approach, is being investigated as an endovascular alternative to invasive openheart surgery. A PTMA device, as illustrated in Fig. 1, is consisted of three parts - the proximal and distal anchors and the “spring-like” bridge elements. The anchors are made of self-expanding Nitinol material that is now frequently used for stent grafts [3]. The proximal and distal anchors are deployed into the CS ostium and the great cardiac vein (GCV), respectively. The bridge element is also a Nitinol material and intertwined with a biodegradable suture, which dissolves over a period of 1 month. Once the suture completely absorbs, the bridge element will shorten and induce tension, drawing the proximal and distal anchors together, hence the septo-lateral mitral annulus distance can be reduced. The initial human clinical study of the first generation of PTMA device was reported by Webb et al [4]. Four of the five patients received the implants successfully, and an acute reduction in MR (35 ± 1 mm vs. 36 ± 3 mm at baseline) was observed in three out of these four patients. However, a reduction in contraction force of the device following bridge separation occurred in all three patients several weeks implantation, leading to the recurrence of MR. Currently, another study of 72 patients reported results of a second generation PTMA device with a reduction in MR by ≥ 1 grade in 50% of 22 implanted patients and 85.7% of 7 severe MR patients [5]. The device was modified with a non-biodegradable suture to reinforce the bridge element. No bridge separation but fractures in the proximal anchor in 4 cases were observed. We postulate that the device fracture is associated with the design (e.g., material and structural geometry) and the interactive coupling effects between the device and the hosting tissues. Numerous computational studies of stent (both self-expandable and balloon expansion) deployment into the arterial vessels, including stenotic coronary arteries [6, 7], carotid arteries [8, 9], iliac arteries [10, 11], and other arteries [12-14], have shown that stent induces mechanical stress on the vessel wall [7, 14] and reversely undergoes stress itself during the pulsatile constriction of the vessel resulted from the cardiac cycle [15].
2 Therefore, it is necessary to be able to predict the behavior (e.g. reaction forces and changes in the mechanical factors such as stress and strain fields) of both the device and the host tissue prior to the procedure, to minimize the negative outcomes and reduce the procedural cost. Currently, biomechanics involved in the PMTA procedure has not been well studied. In our previous work [16, 17], we have studied the deployment of proximal anchor of the PTMA device using computational models to predict the interaction between the human/porcine derived material CS vessel models and the stent. We observed that stiffer stent material tends to have a better safety factor when deployed in a relatively softer tissue (porcine). Although human tissue offered an adequate radial forces, another concern arises that is high stresses on the vessel wall may induce a vascular injury. In this study, we attempted to alter the stent design to reduce radial interactive forces. The approach includes maintain the same material properties of the stent and varying the design parameters, e.g. the strut thickness. Two stents models with different strut thickness values were developed. The results from these models include peak stresses and strains, interaction forces (shear and normal) of the CS wall and the stent, as well as the device fatigue life and safety factor were compared to the original design, and differences between these design can provide insights into the stent designs that may help to reduce future device failure in the PTMA intervention. Figure 1 Illustration of a Monarch™ PTMA being deployed into the CS vessel, which is adjacent to the posterior mitral annulus. ANT - anterior mitral leaflet. PML - posterior mitral leaflet. GCV - great cardiac vein. METHODS/MATERIALS Stent models. Typical mechanical properties of superelastic Nitinol material are illustrated in Fig. 2a, and the material parameters used in this study are listed in Table 1. Three stent designs were developed, 1) the original design with a stent strut thickness of 0.30 mm, 2) modified stents with a thickness of 0.23 mm and 3) thickness of 0.18 mm, denoted as, Original, Mod1 and Mod2, respectively. Fig. 3 illustrates the stent in the undeformed and deformed configurations. Details of design parameters of these stent models are listed in Table 2. The original PTMA device is composed of two and twelve strut cells in the axial and circumferential directions, respectively.
3 Figure 2 a) A stress-strain curve for Nitinol material, and b) a mean human CS stress-stretch response from inflation experiment fitted with the Ogden model Table 1 The material parameters of the CS vessels and stents µ 1 (GPa) a 1 µ 2 (GPa) a 2 µ 2 (GPa) a 2 Human 127.653 5.928 -63.082 11.851 4.674 19.317 E A (MPa) ν A /ν M E M (MPa) ε L σ S L σ E L σ S U σ E U σ S CL T Nitin 70,000 0.3 47,800 0.063 600 670 288 254 900 37 Details of the proximal anchor design in 2D drawings and 3D crimped geometry were reported previously [18]. All stents are consisted of brick elements (ABAQUS element type C3D8R, the 8-node linear brick, reduced integration with hourglass control element). One end of the anchor is attached to the bridge-to-anchor connector, see Fig. 3. Two unit cells are joined together by a strut bridge, and two adjacent cells share a strut bar. Other FE models for the simulation system include the expanding and crimping sleeves. The expanding sleeve was used in the expansion-annealing process and the crimping sleeve acted as a restraining sheath which is removed to release the stent into contact with the CS wall. Both the expanding and crimping sleeves are consisted of 2,231 4-node quadrilateral membrane elements. Characterization of tissue model. The CS material parameters were obtained from fitting the experimental pressureinflation data collected from four cadaver CS vessels to the nonlinear hyperelastic Ogden model [19]. Briefly, the CS vessels were subjected to the pressure inflation test while they were intact (i.e. CS was not dissected out from its surrounding myocardium) and submerged in the small tank of phosphate buffered saline (PBS) solution at room temperature. After 10 preconditioning cycles, vessels were incrementally dilated up to 80 mmHg of pressure, the dilated CS diameters were measured to obtain the CS pressure-radius curve. The hoop/axial stress-stretch relation were calculated [20]. We chose the Ogden constitutive model [21] to characterize the mean experimental data, = µ = λ +λ +λ − ∑ i i i N a a a i 1 2 3 2 i 1 i 2 W ( 3) a (1) where μi and ai are material constants and λi are the principal stretches. The goodness of the fit was determined using the Rsquare value based on the Levenberg-Marquardt nonlinear regression algorithm using SYSTAT 10 (Systat Software Inc., Chicago, IL). The Ogden model curve fitting results are illustrated in Fig. 3, with the parameters listed in Table 2 below. For simplicity the geometry of the CS, at the section that is in contact with the proximal anchor stent, is assumed to be a cylindrical tube with an ID of 12 mm and a thickness of 0.74 mm for the CS vessel. A total of 43,200 brick elements were used to model the CS.
4 Figure 3 Stent designs in the undeformed (top) and deformed configurations: top – undeformed original, bottom – deformed original and Mod1 after released to come in contact with the vessel wall Table 2 Values of undeformed design parameters of different stents No. of strut Length Thickness Circ. Axial No. of elements Original 26 0.30 12 2 114,000 Mod1 26 0.23 12 2 91,370 Mod2 26 0.18 12 2 68,532 Finite Element (FE) modeling of stent expansion and crimping. Prior to the deployment, each stent model underwent the expansion and annealing process to reach a targeted 15.50 mm ID. This is achieved by applying a series of displacement-controlled expansion of the sleeve, allowing it to contact and expand radially the inner surface of the stent. Afterwards, stents were crimped to a final ID of 11.98 mm, which is slightly less than the CS’s ID of 12 mm. Crimping was performed by radially displaced the crimping sleeve inward. PTMA implantation FE modeling. The PTMA procedure consists of a series of steps including stent crimping, stent release, interaction with the vessel wall, contraction of the bridge element, and displacement of the mitral annulus. This study focuses on the tissue-stent interaction (TSI). The simulation is divided into a three-step loading procedure: Step 1 – Release of the stent anchor. The initial contact between the stent and the CS wall is accomplished by removing the crimping sleeve to release the proximal anchor into contact with the CS inner wall. Step 2 – Contraction force at the connector end of the anchor. An axial load with a magnitude of 2.45 N in the axial direction is applied to the connector elements to simulate the pulling force generated by the contraction of the bridge section. Step 3 – Simulation of the pressure in the vessel wall. The incremental pressure, from 0 to 10 mmHg, is imposed directly on the luminal surface of the CS wall to mimic internal blood pressure. The coefficient of friction between the CS inner wall and the stent for the Step-1 and -2 is 0.1. For Step-3, the contact definition is set as a rough surface (no slipping) condition (an ABAQUS option: ROUGH) to imitate the condition
5 that is equivalent to tissue in-growth over time resulting in the attachment between the stent and the CS wall. The analysis was run with ABAQUS/Explicit release 6.9 on a Linux cluster using typically 12 2.8GHz CPUs. FE analysis of the tissue-stent interaction (TSI). Each step in the TSI simulation after crimping was analyzed, and the following output variables were obtained: 1) Stress and strain. Distribution of von Mises stress and maximum values were investigated, which can provide insight into the potential injury induced by stents on the vessel wall. Stent strain measurements were analyzed with the maximum tensile strains (SDV24). Stent strain is zero at the initial un-crimped configuration and is at the maximum after crimping. When release to the vessel, stent will undergo unloading deformation or expanding to its pre-set shape or approaching its zero strain. The maximum principal strains (LE) were used for the CS wall strains. 2) Contact forces. Contact forces between the outer stent and inner CS wall were measured. This is an important measure because elevated contact forces in the vicinity of stent struts may lead to injury of the CS wall, which may increase neo-intimal hyperplasia formation, or ultimately causes tears of the posterior CS wall. Conversely, insufficient radial contact forces will prevent proper device anchoring; hence the stent may migrate and lost its annulus cinching function. The contact forces have normal and shear components, denoted by CNF and CSF, respectively, and are expressed as: , 1 , 1 , c c n n post n n n post n CNF NF CSF SF = = = = ∑ ∑ . (2) where nc is the total number of nodes of the stent cell that are in contact with the CS inner wall, and NFi,post and SFi,post are the normal contact force and shear contact forces, respectively, at each node after deployment. 3) Stent fatigue analysis and safety factor [22]. Quantitative studies of metal fatigue often make use of the wellestablished Goodman-Haigh diagram [23], which is recommended by the FDA for stent fatigue analysis [24]. In Goodman diagrams, a pair of the mean stress or strain and its amplitude (or half-amplitude) at a particular point is plotted and compared with constant life curves [24] for that particular material. The mean tensile strain, εmean, and the half-amplitude oscillating strain, Δε, at a given node are calculated by: max min max min ( )/2 ( )/2 mean ε ε ε ε ε ε = + ∆ = − , (3) where εmax and εmin are the maximal and minimal strains, upon the application of 10 mmHg at a node on the PTMA stent after deployment. For a Nitinol material, the constant life curves from Pelton et al. 2008 [15, 25, 26] were used. Using the 0.4% strain amplitude delineated by the constant life line [15], the stent fatigue safety factor can be predicted using the equation: safety factor = 0.4%/half-amplitude strain. RESULTS Stress and strain analysis. It can be seen in Fig. 4 that the stent strut was twisted after expansion and annealing. The stent outer surface is not smooth. Thus, it is necessary to perform the expansion and annealing procedure to obtain accurate per-deployment stent geometries. Table 3 lists all the maximum Von mises stresses and strains of the vessel wall, as well as three stent models. Both Mod1 and Mod2 stents are softer than the original stent model, resulted in higher maximum strains on the stent after releasing the stents. Stresses on the stent increased as strains increased.
6 Fig. 4 The illustration of a twisted strut after expansion Table 3 Maximum von Mises stresses and strains of CS wall and stent models STRESS (MPa) STRAIN Steps Original Mod1 Mod2 Original Mod1 Mod2 CS WALL 1 3.47E-02 3.44E-02 3.30E-02 0.23 0.23 0.23 2 3.66E-02 3.55E-02 3.52E-02 0.26 0.23 0.28 3 3.58E-02 3.55E-02 3.46E-02 0.27 0.25 0.25 STENT 1 1001.00 955.00 947.40 2.49E-02 2.40E-02 2.38E-02 2 358.60 380.00 371.60 4.96E-03 5.40E-03 5.32E-03 3 444.70 480.30 525.90 6.37E-03 6.88E-03 7.54E-03 After releasing the stent, stresses induced by the stents on the CS wall were similar. However, stresses on the CS wall were lowest when interacted with the Mod2 stent compared to the other two stents. Fig. 5 illustrates the stress distribution on the CS wall induced by each stent. By reducing the strut thickness, stresses were lower at the region of contact in both Mod1 and Mod2 stents.
7 Figure 5 – Stress distributions on CS walls induced by the three stent models in 3 steps. Normal and shear forces. Because stiffer stent generated a higher normal force, Mod1 and Mod2 stents exerted less forces compared to the original stent, as shown in Fig. 6a. There is a slight difference in forces between the stent models in steps 1 and 2 but no difference was observed in step 3. No device slippage was observed in step 2. Shear forces, illustrated in Fig. 6b, increased in step 3demonstrating the tissue in-growth over time.
8 Fig. 6 a) Normal and b) shear forces of the original, Mod1 and Mod2 stents in 3-step TSI simulation Stent fatigue analysis. The strain amplitude of the original model is 8.43E-2% and the safety factor is 4.75. Decreasing in strain amplitudes of Mod1 and Mod2 (6.61E-2% and 6.68E-2%) resulted in higher safety factors of 6.05 and 5.98, respectively. Changing stent thickness does not reduce the fatigue life of the stent in the PTMA intervention. As shown in Fig. 7, strain points on the Goodman diagram of Mod1 and Mod2 are similar to the strain points of the original design, and all are condensed and below 0.1% strain amplitude and 1% mean strain. Figure 7 – Goodman diagrams of the stent models. DISCUSSION/CONCLUSION The evaluation of PTMA device performance was performed based on two criteria: 1) inducing a minimal vessel injury and 2) enabling stent mechanical function (i.e., anchoring and fatigue life). The mechanical stress on the vessel wall
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Mechanical identification of hyperelastic anisotropic properties of mouse carotid arteries Badel Pierre(a), PhD, Avril Stéphane(a), Pr, Lessner Susan(b), PhD, Sutton Michael(c), Pr (a) Center for Health Engineering – Ecole des Mines de Saint Etienne – 158, cours Fauriel – 42023 Saint Etienne – France (b) Department of Cell Biology and Anatomy - University of South Carolina School of Medicine - Columbia, South Carolina 29208, USA (c) Department of Mechanical Engineering - University of South Carolina - Columbia, South Carolina 29208, USA ABSTRACT The role of mechanics is known to be of primary order in many arterial diseases; however determining mechanical properties of arteries remains a challenge. This paper discusses the identifiability of a Holzapfel-type material model for a mouse carotid artery, using an inverse method based on a finite element model and 3D digital image correlation measurements of the surface strain during an inflation/extension test. Layer-specific mean fiber angles are successfully determined using a five parameter constitutive model, demonstrating good robustness of the identification procedure. Importantly, we show that a model based on a single thick layer is unable to render the biaxial mechanical response of the artery tested here. On the contrary, difficulties related to the identification of a seven parameter constitutive model are evidenced; such a model leads to multiple solutions. Nevertheless, it is shown that an additional mechanical test, different in nature with the previous one, solves this problem. 1. Introduction Identification of mechanical and structural properties of the arteries is a major topic in cardiovascular research. Many arterial disorders involve significant changes in vascular mechanical properties. Not only do the structure and mechanical response of arteries vary according to many factors such as the location in the vasculature and age, but also their properties may alter under various physiological conditions and during the development of diseases [1,2]. Accurate mechanical identification of the arteries can therefore provide helpful information for clinical diagnoses and treatments. To improve the contribution of solid mechanics, a lot of effort has been undertaken to develop constitutive models of the arterial wall as well as experimental and numerical methods to identify these models. T. Proulx (ed.), Mechanics of Biological Systems and Materials, Volume 2, Conference Proceedings of the Society for Experimental Mechanics Series 9999, DOI 10.1007/978-1-4614-0219-0_2, © The Society for Experimental Mechanics, Inc. 2011 11
Several constitutive models intended to describe the mechanical response of arterial tissues at finite strains have been developed, see [3] for an extensive review of these models. Most of anisotropic non-linear models considering the passive response of arteries are hyperelastic. Fung [1] first introduced a phenomenological exponential strain energy function. More recently, structurally-motivated models including fiber reinforcements have been developed. Bischoff [4] suggested representing the nonlinear orthotropic material response of the arterial wall, with a homogeneous orthotropic model. This model has proven adequate to capture the nonlinear orthotropic response of vascular tissues although the physical meaning of its parameters is not clear [5]. Holzapfel [6] introduced a two-fiber family model to account for the helically-oriented distribution of collagen fibers within the arterial wall. To ideally describe the arterial wall from the mechanical point of view, two separate layers of this material are required for medial and adventitial layers. Originally, Holzapfel [6] grounded the choice of two symmetrically- and helically-oriented fiber families per layer on histological observations. Since the compositions of medial and adventitial layers (elastin, collagen and cell contents) are different [2], two separate layers must be distinguished. Note also that some authors introduced the active response of the arterial wall due to smooth muscle activity [7], which is not the concern of this paper. Correct identification of the parameters of the constitutive model is a key issue in considering the reliability of interpretation for medical purposes or subsequent utilization in numerical models, for instance. The process of identification requires experimental data obtained from mechanical testing. Most of the previous biomechanical studies on mouse carotid arteries have been conducted using global or average data such as pressure-diameter and/or force-length measurements [8,9]. In addition, the identification of layer-specific parameters of the Holzapfel model has been performed, at this time, only from dissected layers on large arteries [10]. The data which are used in this study are collected with a 3D-DIC stereo-microscopy system on a mouse carotid artery, which is, to our knowledge, unique at this time. See [11] for a description of this previous experimental work. From experimental data, the identification of constitutive models relies, most of the time, on inverse approaches because establishing response curves from the model may involve complex non-linear relations between the parameters. Classical inverse approaches are based on updating methods [5, 7, 10, 12] using optimization algorithms such as the LevenbergMarquardt algorithm to find the best-fit parameters in a least-square sense with respect to a given cost function. In these approaches, previous authors have most often used analytical developments to derive their modeled data from the given constitutive equations, which presupposed multiple assumptions. Among these, note the widely-accepted assumption of axisymmetry and that of a single homogeneous layer. The latter may be relevant when experimental data is global or averaged over the arterial wall, though two separate layers would be closer to reality and would emphasize the distinction between the layer properties. In addition, for the study of mouse carotid arteries, Gleason [12] performed analytical developments within the frame of thin-tube elasticity theory. This may be a strong assumption in cases of thick arteries like mouse carotid arteries where the ratio of thickness to inner radius was reported to be about 0.6 [8, 12]. Finite element (FE) simulations have rarely been used to recover those modeled data and perform inverse identification. Yet, this kind of approach allows using experimental tests capable of providing richer or otherwise unavailable data and modeling complex problems. Regarding non-linear anisotropic vascular properties, the study of Ning [5] was focused on stress and strain distributions within the arterial wall and how they are influenced by axial pre-stretch. Using the same data as the present study, they identified the parameters of the constitutive model of Bischoff [4], thereby not considering heterogeneity between media and adventitia, which would likely affect these distributions. From our point of view, the advantage of using finite element based identification approaches is to model complex mechanical tests and/or complex structures (see, for instance, [13]), like a thick multi-layer artery presented in this paper. The question of whether an identification method is relevant with respect to the problem to be treated is seldom addressed. Introducing multiple assumptions and parameters may lead to improper identification or multiple solutions. The objective of the present paper is to address the feasibility of the simultaneous inverse identification of mean fiber angles in both medial and adventitial layers using DIC surface strain measurements. 2. Methods 2.1. Experimental considerations The experimental data referenced to in this study were described in deep details in [12] where three-dimensional digital image correlation (3D-DIC) is used to obtain full-field surface strain measurements on mouse carotid arteries at the microscale during an inflation/extension test (Fig. 1). The mechanical test performed here allows both pressurization loading and 12
extension loading at the same time (see the schematic principle of the setup in Fig. 1). This test is relevant as it provides biaxial loading conditions close to physiological conditions. To briefly describe the experimental setup, both ends of a freshly-dissected carotid artery are cannulated with Luer stubs. For image processing and local deformation measurements, a high contrast speckle pattern is incorporated into the vessel structure thanks to ethidium bromide nuclear staining. The experiments are performed with one end of the artery attached to the pressure controller and pressure source, while the other capped end is free in the axial direction, thereby allowing axial translation. The artery is pressurized from 5 to 150 mmHg in steps of 9 mmHg with a flow rate of 0.2 ml/min and an average pressurization rate of 1.8 mmHg/s. After each pressurization step, synchronized images are acquired from two cameras and analyzed using existing commercial software, VIC-3D. The region of interest being small (about 200 by 140 μm²), due to the depth of field of the system, and displaying very little heterogeneity, only the strains averaged over this region are considered in the analysis. Note that usual 2DDIC is not suitable for this problem due to the non planar nature of the specimen and possible out-of-plane deformation. More details about the experimental setup and procedure can be found in (Sutton et. al. 2008). 2.2. Numerical and constitutive model The development of the FE model of the inflation/extension test in Abaqus® is based on the experimental considerations and measurements described in Sutton et al. (2008). The geometry of the artery is assumed to be perfectly cylindrical with one end of the artery being capped. Due to axial symmetry, only one quarter of the geometry is meshed with 4280 8-node brick elements resulting in 22070 degrees of freedom. The element type chosen here, called C3D8RH in Abaqus® (hybrid formulation with constant pressure), is recommended for nearly incompressible constitutive models. The open end of the cylinder is blocked in the axial direction whereas symmetry boundary conditions are applied on the surfaces of the quarter cylinder. Pressure is applied onto the inner surface of the artery, with values ranging up to 140 mmHg. The constitutive model used in this study is implemented in Abaqus® and based on the developments of Holzapfel [6]. This hyperelastic incompressible model was developed to describe the passive mechanical response of arterial tissues at finite strains. The material considered is a collagen-fiber-reinforced material with two fiber directions being symmetrically arranged with respect to the axis of the artery. This theoretical basis provides a strong physical meaning to the constitutive parameters involved in the model. The simplest form of its isochoric strain energy function consists of two terms (note that incompressibility of the tissue is a well-known characteristic). The first term represents the isotropic response of the medium, related to the ground substance and elastin content, and the other two terms represent the response of the collagenous fiber network, each fiber direction having its own contribution: ( ) ( ) ( ) ( ) ( ) 2 2 1 1 1 2 4 2 6 2 2 3 exp 1 1 exp -1 1 2 2 2 ψ = − + − − + − ª º ª º ¬ ¼ ¬ ¼ k k C I k I k I k k (1) where C is the parameter of the isotropic neo-Hookean term, k1 and k2 are the parameters for the exponential response of the collagen fiber networks. The structural anisotropy induced by the fiber network arises from both I4 and I6. These terms are pseudo-invariants of the right Cauchy Green tensor C and the fiber directions f1 and f2. Therefore they are driven by ȕ, the mean fiber angle, in the medium, with respect to the circumferential direction. I4 and I6 give the squares of stretch for the two fiber families. Figure 1. Schematic of the inflation/extension test of the mouse carotid artery showing one fixed end (on the left) linked to the pressure controller and one end (on the right) free to translate axially. Dashed lines represent the schematic shape of the deformed segment. 13
Due to histological differences between media and adventitia, two separate strain energy functions are assigned to each of these mechanically-relevant layers of an artery, the contribution of the intima being commonly considered negligible. Thus, two sets of parameters are to be identified for each layer, yielding eight material parameters. In this study, two variants of this model are considered: a simplified five parameter model and a seven parameter model. The simplified five parameter model includes the assumption that media and adventitia have identical exponential parameters. In addition, it is assumed that the value of C is the same in both layers. Hence, it features the following five parameters: C for the Neo-Hookean isotropic term (elastin and ground substance), two parameters k1 and k2 for the exponential response of collagen fibers, and two parameters ȕmedia and ȕadventitia for the fiber angles in media and adventitia. However, a full two-layer Holzapfel-type model considers that the exponential terms used in medial and adventitial layers are different [6], necessitating two additional parameters. Therefore, the seven parameter model releases the constraint on exponential parameters, making them different in each arterial layer. 2.3. Identification procedure Given a set of experimental pressure and surface strain measurements, the principle of the present identification method is to minimize the following cost function: ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 2 sim exp sim exp 11 11 22 22 1 2 χ = − + − ª º « » ¬ ¼ ¦ G i i i i i J E p E p E p E p (2) where χ G is the vector of parameters to be identified (ie. the constitutive parameters), pi is the pressure applied during the inflation test, with index i ranging over the available experimental data points., E11 and E22 are Green Lagrange circumferential and axial strain components on the surface of the artery, superscripts ‘sim’ and ‘exp’ standing respectively for the simulated and experimental data. In this study, synthetic data generated by a FE calculation are also used in order to avoid noise issues when identifying the seven parameter model. This cost function is minimized using an in-house Levenberg-Marquardt algorithm with bounds handling. To asses the robustness of the identification method, multiple identification runs with random starting points are performed in order to compare the obtained results. However in the case of the seven parameter model, since noise in data is a major source of identification errors, especially when identifying a lot of parameters, we choose to use noise-free data which are obtained by finite element simulation with an arbitrary set of parameters. Here the set of parameters obtained with the first identification run is used. 3. Results Using the five parameter model, convergence of the optimization algorithm is obtained after 46 iterations. We report in Table 1 the results of this first identification run. The pressure/strain curves are shown in Fig. 2. To further test the identification method, a second set of experimental data obtained by performing a second identical test with the same arterial segment is also used, the aim being to compare the results. We also report in Table 1 the results of this identification run (curves are not shown here). Note that they are very close to those obtained with the first set of data. In the following developments, only the first set of data is used. In addition to these results, the robustness of the identification method is assessed with the method mentioned in section 2.3. The range of spanned starting points is chosen according to values found in the literature for this type of artery [12]. The range of the obtained results is reported in Table 1. Note that C shows quite a large standard deviation because these multiple runs showed that there exist two close minima in the space of parameters, the influence on the response being negligible. 14
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