1
|
Biomechanics of Hollow Organs: Experimental Testing and Computational Modeling. Bioengineering (Basel) 2023; 10:bioengineering10020175. [PMID: 36829669 PMCID: PMC9952441 DOI: 10.3390/bioengineering10020175] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/23/2022] [Accepted: 01/24/2023] [Indexed: 01/31/2023] Open
Abstract
Hollow organs are visceral organs that are hollow tubes or pouches (such as the intestine or the stomach, respectively) or that include a cavity (such as the heart) and which subserve a vital function [...].
Collapse
|
2
|
Sánchez-Molina D, García-Vilana S, Llumà J, Galtés I, Velázquez-Ameijide J, Rebollo-Soria MC, Arregui-Dalmases C. Mechanical Behavior of Blood Vessels: Elastic and Viscoelastic Contributions. BIOLOGY 2021; 10:831. [PMID: 34571709 PMCID: PMC8472519 DOI: 10.3390/biology10090831] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 07/14/2021] [Revised: 08/19/2021] [Accepted: 08/23/2021] [Indexed: 11/16/2022]
Abstract
The mechanical properties of the cerebral bridging veins (CBVs) were studied using advanced microtensile equipment. Detailed high-quality curves were obtained at different strain rates, showing a clearly nonlinear stress-strain response. In addition, the tissue of the CBVs exhibits stress relaxation and a preconditioning effect under cyclic loading, unequivocal indications of viscoelastic behavior. Interestingly, most previous literature that conducts uniaxial tensile tests had not found significant viscoelastic effects in CBVs, but the use of more sensitive tests allowed to observe the viscoelastic effects. For that reason, a careful mathematical analysis is presented, clarifying why in uniaxial tests with moderate strain rates, it is difficult to observe any viscoelastic effect. The analysis provides a theoretical explanation as to why many recent studies that investigated mechanical properties did not find a significant viscoelastic effect, even though in other circumstances, the CBV tissue would clearly exhibit viscoelastic behavior. Finally, this study provides reference values for the usual mechanical properties, as well as calculations of constitutive parameters for nonlinear elastic and viscoelastic models that would allow more accurate numerical simulation of CBVs in Finite Element-based computational models in future works.
Collapse
Affiliation(s)
- David Sánchez-Molina
- Escola d’Enginyeria de Barcelona Est, Universitat Politècnica de Catalunya, Av. Eduard Maristany, 16, 08019 Barcelona, Spain; (S.G.-V.); (J.L.); (J.V.-A.)
| | - Silvia García-Vilana
- Escola d’Enginyeria de Barcelona Est, Universitat Politècnica de Catalunya, Av. Eduard Maristany, 16, 08019 Barcelona, Spain; (S.G.-V.); (J.L.); (J.V.-A.)
| | - Jordi Llumà
- Escola d’Enginyeria de Barcelona Est, Universitat Politècnica de Catalunya, Av. Eduard Maristany, 16, 08019 Barcelona, Spain; (S.G.-V.); (J.L.); (J.V.-A.)
| | - Ignasi Galtés
- Institut de Medicina Legal i Ciències Forenses de Catalunya, G.V. Corts Catalanes, 111, 08014 Barcelona, Spain;
- Departament de Psiquiatria i de Medicina Legal, Universitat Autònoma de Barcelona, Cerdanyola del Vallès, 08193 Barcelona, Spain
| | - Juan Velázquez-Ameijide
- Escola d’Enginyeria de Barcelona Est, Universitat Politècnica de Catalunya, Av. Eduard Maristany, 16, 08019 Barcelona, Spain; (S.G.-V.); (J.L.); (J.V.-A.)
| | | | | |
Collapse
|
3
|
Bhattarai A, Kowalczyk W, Tran TN. A literature review on large intestinal hyperelastic constitutive modeling. Clin Biomech (Bristol, Avon) 2021; 88:105445. [PMID: 34416632 DOI: 10.1016/j.clinbiomech.2021.105445] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 12/03/2020] [Revised: 06/29/2021] [Accepted: 07/29/2021] [Indexed: 02/07/2023]
Abstract
Impacts, traumas and strokes are spontaneously life-threatening, but chronic symptoms strangle patient every day. Colorectal tissue mechanics in such chronic situations not only regulates the physio-psychological well-being of the patient, but also confirms the level of comfort and post-operative clinical outcomes. Numerous uniaxial and multiaxial tensile experiments on healthy and affected samples have evidenced significant differences in tissue mechanical behavior and strong colorectal anisotropy across each layer in thickness direction and along the length. Furthermore, this study reviewed various forms of passive constitutive models for the highly fibrous colorectal tissue ranging from the simplest linearly elastic and the conventional isotropic hyperelastic to the most sophisticated second harmonic generation image based anisotropic mathematical formulation. Under large deformation, the isotropic description of tissue mechanics is unequivocally ineffective which demands a microstructural based tissue definition. Therefore, the information collected in this review paper would present the current state-of-the-art in colorectal biomechanics and profoundly serve as updated computational resources to develop a sophisticated characterization of colorectal tissues.
Collapse
Affiliation(s)
- Aroj Bhattarai
- Department of Orthopaedic Surgery, University of Saarland, Germany
| | | | - Thanh Ngoc Tran
- Department of Orthopaedic Surgery, University of Saarland, Germany.
| |
Collapse
|
4
|
Pybus HJ, Tatler AL, Edgar LT, O'Dea RD, Brook BS. Reduced biomechanical models for precision-cut lung-slice stretching experiments. J Math Biol 2021; 82:35. [PMID: 33721103 PMCID: PMC7960642 DOI: 10.1007/s00285-021-01578-2] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/25/2020] [Revised: 08/25/2020] [Accepted: 02/14/2021] [Indexed: 01/25/2023]
Abstract
Precision-cut lung-slices (PCLS), in which viable airways embedded within lung parenchyma are stretched or induced to contract, are a widely used ex vivo assay to investigate bronchoconstriction and, more recently, mechanical activation of pro-remodelling cytokines in asthmatic airways. We develop a nonlinear fibre-reinforced biomechanical model accounting for smooth muscle contraction and extracellular matrix strain-stiffening. Through numerical simulation, we describe the stresses and contractile responses of an airway within a PCLS of finite thickness, exposing the importance of smooth muscle contraction on the local stress state within the airway. We then consider two simplifying limits of the model (a membrane representation and an asymptotic reduction in the thin-PCLS-limit), that permit analytical progress. Comparison against numerical solution of the full problem shows that the asymptotic reduction successfully captures the key elements of the full model behaviour. The more tractable reduced model that we develop is suitable to be employed in investigations to elucidate the time-dependent feedback mechanisms linking airway mechanics and cytokine activation in asthma.
Collapse
Affiliation(s)
- Hannah J Pybus
- School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, UK.
| | - Amanda L Tatler
- Respiratory Medicine, NIHR Biomedical Research Centre, University of Nottingham, Nottingham, UK
| | - Lowell T Edgar
- Usher Institute of Population Health Sciences and Informatics, University of Edinburgh, Edinburgh, UK
| | - Reuben D O'Dea
- School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, UK
| | - Bindi S Brook
- School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, UK
| |
Collapse
|
5
|
Roy R, Warren E, Xu Y, Yow C, Madhurapantula RS, Orgel JPRO, Lister K. Functional Grading of a Transversely Isotropic Hyperelastic Model with Applications in Modeling Tricuspid and Mitral Valve Transition Regions. Int J Mol Sci 2020; 21:ijms21186503. [PMID: 32899559 PMCID: PMC7554844 DOI: 10.3390/ijms21186503] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/12/2020] [Revised: 08/27/2020] [Accepted: 09/02/2020] [Indexed: 01/20/2023] Open
Abstract
Surgical simulators and injury-prediction human models require a combination of representative tissue geometry and accurate tissue material properties to predict realistic tool-tissue interaction forces and injury mechanisms, respectively. While biological tissues have been individually characterized, the transition regions between tissues have received limited research attention, potentially resulting in inaccuracies within simulations. In this work, an approach to characterize the transition regions in transversely isotropic (TI) soft tissues using functionally graded material (FGM) modeling is presented. The effect of nonlinearities and multi-regime nature of the TI model on the functional grading process is discussed. The proposed approach has been implemented to characterize the transition regions in the leaflet (LL), chordae tendinae (CT) and the papillary muscle (PM) of porcine tricuspid valve (TV) and mitral valve (MV). The FGM model is informed using high resolution morphological measurements of the collagen fiber orientation and tissue composition in the transition regions, and deformation characteristics predicted by the FGM model are numerically validated to experimental data using X-ray diffraction imaging. The results indicate feasibility of using the FGM approach in modeling soft-tissue transitions and has implications in improving physical representation of tissue deformation throughout the body using a scalable version of the proposed approach.
Collapse
Affiliation(s)
- Rajarshi Roy
- Corvid Technologies, Mooresville, NC 28117, USA; (Y.X.); (C.Y.); (K.L.)
- Correspondence: ; Tel.: +1-704-799-6944
| | | | - Yaoyao Xu
- Corvid Technologies, Mooresville, NC 28117, USA; (Y.X.); (C.Y.); (K.L.)
| | - Caleb Yow
- Corvid Technologies, Mooresville, NC 28117, USA; (Y.X.); (C.Y.); (K.L.)
| | - Rama S. Madhurapantula
- Department of Biology, Illinois Institute of Technology, Chicago, IL 60616, USA; (R.S.M.); (J.P.R.O.O.)
- Pritzker Institute of Biomedical Science and Engineering, Illinois Institute of Technology, Chicago, IL 60616, USA
| | - Joseph P. R. O. Orgel
- Department of Biology, Illinois Institute of Technology, Chicago, IL 60616, USA; (R.S.M.); (J.P.R.O.O.)
- Pritzker Institute of Biomedical Science and Engineering, Illinois Institute of Technology, Chicago, IL 60616, USA
- Department of Biomedical Engineering, Illinois Institute of Technology, Chicago, IL 60616, USA
| | - Kevin Lister
- Corvid Technologies, Mooresville, NC 28117, USA; (Y.X.); (C.Y.); (K.L.)
| |
Collapse
|
6
|
Ross CJ, Laurence DW, Richardson J, Babu AR, Evans LE, Beyer EG, Childers RC, Wu Y, Towner RA, Fung KM, Mir A, Burkhart HM, Holzapfel GA, Lee CH. An investigation of the glycosaminoglycan contribution to biaxial mechanical behaviours of porcine atrioventricular heart valve leaflets. J R Soc Interface 2019; 16:20190069. [PMID: 31266416 PMCID: PMC6685018 DOI: 10.1098/rsif.2019.0069] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/03/2019] [Accepted: 06/03/2019] [Indexed: 01/06/2023] Open
Abstract
The atrioventricular heart valve (AHV) leaflets have a complex microstructure composed of four distinct layers: atrialis, ventricularis, fibrosa and spongiosa. Specifically, the spongiosa layer is primarily proteoglycans and glycosaminoglycans (GAGs). Quantification of the GAGs' mechanical contribution to the overall leaflet function has been of recent focus for aortic valve leaflets, but this characterization has not been reported for the AHV leaflets. This study seeks to expand current GAG literature through novel mechanical characterizations of GAGs in AHV leaflets. For this characterization, mitral and tricuspid valve anterior leaflets (MVAL and TVAL, respectively) were: (i) tested by biaxial mechanical loading at varying loading ratios and by stress-relaxation procedures, (ii) enzymatically treated for removal of the GAGs and (iii) biaxially mechanically tested again under the same protocols as in step (i). Removal of the GAG contents from the leaflet was conducted using a 100 min enzyme treatment to achieve approximate 74.87% and 61.24% reductions of all GAGs from the MVAL and TVAL, respectively. Our main findings demonstrated that biaxial mechanical testing yielded a statistically significant difference in tissue extensibility after GAG removal and that stress-relaxation testing revealed a statistically significant smaller stress decay of the enzyme-treated tissue than untreated tissues. These novel findings illustrate the importance of GAGs in AHV leaflet behaviour, which can be employed to better inform heart valve therapeutics and computational models.
Collapse
Affiliation(s)
- Colton J. Ross
- Biomechanics and Biomaterials Design Laboratory, School of Aerospace and Mechanical Engineering, The University of Oklahoma, Norman, OK, USA
| | - Devin W. Laurence
- Biomechanics and Biomaterials Design Laboratory, School of Aerospace and Mechanical Engineering, The University of Oklahoma, Norman, OK, USA
| | - Jacob Richardson
- Biomechanics and Biomaterials Design Laboratory, School of Aerospace and Mechanical Engineering, The University of Oklahoma, Norman, OK, USA
| | - Anju R. Babu
- Biomechanics and Biomaterials Design Laboratory, School of Aerospace and Mechanical Engineering, The University of Oklahoma, Norman, OK, USA
| | - Lauren E. Evans
- Biomechanics and Biomaterials Design Laboratory, School of Aerospace and Mechanical Engineering, The University of Oklahoma, Norman, OK, USA
| | - Ean G. Beyer
- Biomechanics and Biomaterials Design Laboratory, School of Aerospace and Mechanical Engineering, The University of Oklahoma, Norman, OK, USA
| | - Rachel C. Childers
- Stephenson School of Biomedical Engineering, The University of Oklahoma, Norman, OK, USA
| | - Yi Wu
- Biomechanics and Biomaterials Design Laboratory, School of Aerospace and Mechanical Engineering, The University of Oklahoma, Norman, OK, USA
| | - Rheal A. Towner
- Advanced Magnetic Resonance Center, MS 60, Oklahoma Medical Research Foundation, Oklahoma City, OK, USA
| | - Kar-Ming Fung
- Department of Pathology, The University of Oklahoma Health Sciences Center, Oklahoma City, OK, USA
- Stephenson Cancer Center, The University of Oklahoma Health Sciences Center, Oklahoma City, OK, USA
| | - Arshid Mir
- Division of Pediatric Cardiology, Department of Pediatrics, The University of Oklahoma Health Sciences Center, Oklahoma City, OK, USA
| | - Harold M. Burkhart
- Division of Cardiothoracic Surgery, Department of Surgery, The University of Oklahoma Health Sciences Center, Oklahoma City, OK, USA
| | - Gerhard A. Holzapfel
- Institute of Biomechanics, Graz University of Technology, Graz, Austria
- Department of Structural Engineering, Norwegian University of Science and Technology (NTNU), Trondheim, Norway
| | - Chung-Hao Lee
- Biomechanics and Biomaterials Design Laboratory, School of Aerospace and Mechanical Engineering, The University of Oklahoma, Norman, OK, USA
- Institute for Biomedical Engineering, Science and Technology, The University of Oklahoma, Norman, OK, USA
| |
Collapse
|
7
|
Hoffman AH, Teng Z, Zheng J, Wu Z, Woodard PK, Billiar KL, Wang L, Tang D. Stiffness Properties of Adventitia, Media, and Full Thickness Human Atherosclerotic Carotid Arteries in the Axial and Circumferential Directions. J Biomech Eng 2018; 139:2653366. [PMID: 28857112 DOI: 10.1115/1.4037794] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/19/2017] [Indexed: 11/08/2022]
Abstract
Arteries can be considered as layered composite material. Experimental data on the stiffness of human atherosclerotic carotid arteries and their media and adventitia layers are very limited. This study used uniaxial tests to determine the stiffness (tangent modulus) of human carotid artery sections containing American Heart Association type II and III lesions. Axial and circumferential oriented adventitia, media, and full thickness specimens were prepared from six human carotid arteries (total tissue strips: 71). Each artery yielded 12 specimens with two specimens in each of the following six categories; axial full thickness, axial adventitia (AA), axial media (AM), circumferential full thickness, circumferential adventitia (CA), and circumferential media (CM). Uniaxial testing was performed using Inspec 2200 controlled by software developed using labview. The mean stiffness of the adventitia was 3570 ± 667 and 2960 ± 331 kPa in the axial and circumferential directions, respectively, while the corresponding values for the media were 1070 ± 186 and 1800 ± 384 kPa. The adventitia was significantly stiffer than the media in both the axial (p = 0.003) and circumferential (p = 0.010) directions. The stiffness of the full thickness specimens was nearly identical in the axial (1540 ± 186) and circumferential (1530 ± 389 kPa) directions. The differences in axial and circumferential stiffness of media and adventitia were not statistically significant.
Collapse
Affiliation(s)
- Allen H Hoffman
- Mechanical Engineering Department, Worcester Polytechnic Institute, Worcester, MA 01609
| | - Zhongzhao Teng
- Mathematical Sciences Department, Worcester Polytechnic Institute, Worcester, MA 01609.,Department of Radiology, University of Cambridge, Cambridge CB2 0QQ, UK
| | - Jie Zheng
- Mallinckrodt Institute of Radiology, Washington University, St. Louis, MO 63110
| | - Zheyang Wu
- Mathematical Sciences Department, Worcester Polytechnic Institute, Worcester, MA 01609
| | - Pamela K Woodard
- Mallinckrodt Institute of Radiology, Washington University, St. Louis, MO 63110
| | - Kristen L Billiar
- Biomedical Engineering Department, Worcester Polytechnic Institute, Worcester, MA 01609
| | - Liang Wang
- School of Biological Science and Medical Engineering, Southeast University, Nanjing 210096, China
| | - Dalin Tang
- School of Biological Science and Medical Engineering, Southeast University, Nanjing 210096, China.,Mathematical Sciences Department, Worcester Polytechnic Institute, Worcester, MA 01609 e-mail:
| |
Collapse
|
8
|
Suki B, Hu Y, Murata N, Imsirovic J, Mondoñedo JR, de Oliveira CLN, Schaible N, Allen PG, Krishnan R, Bartolák-Suki E. A microfluidic chamber-based approach to map the shear moduli of vascular cells and other soft materials. Sci Rep 2017; 7:2305. [PMID: 28536424 PMCID: PMC5442161 DOI: 10.1038/s41598-017-02659-3] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/05/2016] [Accepted: 04/18/2017] [Indexed: 11/09/2022] Open
Abstract
There is growing interest in quantifying vascular cell and tissue stiffness. Most measurement approaches, however, are incapable of assessing stiffness in the presence of physiological flows. We developed a microfluidic approach which allows measurement of shear modulus (G) during flow. The design included a chamber with glass windows allowing imaging with upright or inverted microscopes. Flow was controlled gravitationally to push culture media through the chamber. Fluorescent beads were conjugated to the sample surface and imaged before and during flow. Bead displacements were calculated from images and G was computed as the ratio of imposed shear stress to measured shear strain. Fluid-structure simulations showed that shear stress on the surface did not depend on sample stiffness. Our approach was verified by measuring the moduli of polyacrylamide gels of known stiffness. In human pulmonary microvascular endothelial cells, G was 20.4 ± 12 Pa and decreased by 20% and 22% with increasing shear stress and inhibition of non-muscle myosin II motors, respectively. The G showed a larger intra- than inter-cellular variability and it was mostly determined by the cytosol. Our shear modulus microscopy can thus map the spatial distribution of G of soft materials including gels, cells and tissues while allowing the visualization of microscopic structures such as the cytoskeleleton.
Collapse
Affiliation(s)
- Béla Suki
- Department of Biomedical Engineering, Boston University, Boston, MA, 02215, USA.
| | - Yingying Hu
- Department of Biomedical Engineering, Boston University, Boston, MA, 02215, USA
| | - Naohiko Murata
- Department of Biomedical Engineering, Boston University, Boston, MA, 02215, USA
| | - Jasmin Imsirovic
- Department of Biomedical Engineering, Boston University, Boston, MA, 02215, USA
| | - Jarred R Mondoñedo
- Department of Biomedical Engineering, Boston University, Boston, MA, 02215, USA
| | | | - Niccole Schaible
- Center for Vascular Biology Research, Beth Israel Deaconess Medical Center, Harvard Medical School, Boston, MA, 02215, USA
| | - Philip G Allen
- Department of Biomedical Engineering, Boston University, Boston, MA, 02215, USA
| | - Ramaswamy Krishnan
- Center for Vascular Biology Research, Beth Israel Deaconess Medical Center, Harvard Medical School, Boston, MA, 02215, USA
| | | |
Collapse
|
9
|
A functionally graded material model for the transmural stress distribution of the aortic valve leaflet. J Biomech 2017; 54:88-95. [PMID: 28256242 DOI: 10.1016/j.jbiomech.2017.01.039] [Citation(s) in RCA: 36] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/21/2016] [Revised: 12/02/2016] [Accepted: 01/28/2017] [Indexed: 11/22/2022]
Abstract
Heterogeneities in structure and stress within heart valve leaflets are of significant concern to their functional physiology, as they affect how the tissue constituents remodel in response to pathological and non-pathological (e.g. exercise, pregnancy) alterations in cardiac function. Indeed, valve interstitial cells (VICs) are known to synthesize and degrade leaflet extracellular matrix (ECM) components in a manner specific to their local micromechanical environment. Quantifying local variations in ECM structure and stress is thus necessary to understand homeostatic valve maintenance as well as to develop predictive models of disease progression and post-surgical outcomes. In the aortic valve (AV), transmural variations in stress have previously been investigated by modeling the leaflet as a composite of contiguous but mechanically distinct layers. Based on previous findings about the bonded nature of these layers (Buchanan and Sacks, BMMB, 2014), we developed a more generalized structural constitutive model by treating the leaflet as a functionally graded material (FGM), whose properties vary continuously over the thickness. We informed the FGM model using high-resolution morphological measurements, which demonstrated that the composition and fiber structure change gradually over the thickness of the AV leaflet. For validation, we fit the model against an extensive database of whole-leaflet and individual-layer mechanical responses. The FGM model predicted large stress variations both between and within the leaflet layers at end-diastole, with low-collagen regions bearing significant radial stress. These novel results suggest that the continually varying structure of the AV leaflet has an important purpose with regard to valve function and tissue homeostasis.
Collapse
|
10
|
Oskui IZ, Hashemi A, Jafarzadeh H. Biomechanical behavior of bovine periodontal ligament: Experimental tests and constitutive model. J Mech Behav Biomed Mater 2016; 62:599-606. [DOI: 10.1016/j.jmbbm.2016.05.036] [Citation(s) in RCA: 24] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/07/2016] [Revised: 05/17/2016] [Accepted: 05/30/2016] [Indexed: 11/29/2022]
|
11
|
Chen H, Kassab GS. Microstructure-based biomechanics of coronary arteries in health and disease. J Biomech 2016; 49:2548-59. [PMID: 27086118 PMCID: PMC5028318 DOI: 10.1016/j.jbiomech.2016.03.023] [Citation(s) in RCA: 39] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/11/2016] [Accepted: 03/16/2016] [Indexed: 12/27/2022]
Abstract
Coronary atherosclerosis is the major cause of mortality and disability in developed nations. A deeper understanding of mechanical properties of coronary arteries and hence their mechanical response to stress is significant for clinical prevention and treatment. Microstructure-based models of blood vessels can provide predictions of arterial mechanical response at the macro- and micro-mechanical level for each constituent structure. Such models must be based on quantitative data of structural parameters (constituent content, orientation angle and dimension) and mechanical properties of individual adventitia and media layers of normal arteries as well as change of structural and mechanical properties of atherosclerotic arteries. The microstructural constitutive models of healthy coronary arteries consist of three major mechanical components: collagen, elastin, and smooth muscle cells, while the models of atherosclerotic arteries should account for additional constituents including intima, fibrous plaque, lipid, calcification, etc. This review surveys the literature on morphology, mechanical properties, and microstructural constitutive models of normal and atherosclerotic coronary arteries. It also provides an overview of current gaps in knowledge that must be filed in order to advance this important area of research for understanding initiation, progression and clinical treatment of vascular disease. Patient-specific structural models are highlighted to provide diagnosis, virtual planning of therapy and prognosis when realistic patient-specific geometries and material properties of diseased vessels can be acquired by advanced imaging techniques.
Collapse
Affiliation(s)
- Huan Chen
- California Medical Innovations Institute, Inc., San Diego, CA 92121, United States
| | - Ghassan S Kassab
- California Medical Innovations Institute, Inc., San Diego, CA 92121, United States.
| |
Collapse
|
12
|
Ge L. A Characteristic-Based Constitutive Law for Dispersed Fibers. J Biomech Eng 2016; 138:2520869. [PMID: 27138358 DOI: 10.1115/1.4033517] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/03/2015] [Indexed: 11/08/2022]
Abstract
Biological tissues are typically constituted of dispersed fibers. Modeling the constitutive laws of such tissues remains a challenge. Direct integration over all fibers is considered to be accurate but requires very expensive numerical integration. A general structure tensor (GST) model was previously developed to bypass this costly numerical integration step, but there are concerns about the model's accuracy. Here we estimate the approximation error of the GST model. We further reveal that the GST model ignores strain energy induced by shearing motions. Subsequently, we propose a new characteristic-based constitutive law to better approximate the direct integration model. The new model is very cost-effective and closely approximates the "true" strain energy as calculated by the direct integration when stress-strain nonlinearity or fiber dispersion angle is small.
Collapse
|
13
|
Chen H, Guo X, Luo T, Kassab GS. A validated 3D microstructure-based constitutive model of coronary artery adventitia. J Appl Physiol (1985) 2016; 121:333-42. [PMID: 27174925 PMCID: PMC4967241 DOI: 10.1152/japplphysiol.00937.2015] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/03/2015] [Accepted: 05/05/2016] [Indexed: 11/22/2022] Open
Abstract
A structure-based model that accurately predicts micro- or macromechanical behavior of blood vessels is necessary to understand vascular physiology. Based on recently measured microstructural data, we propose a three-dimensional microstructural model of coronary adventitia that incorporates the elastin and collagen distributions throughout the wall. The role of ground substance was found to be negligible under physiological axial stretch λz = 1.3, based on enzyme degradation of glycosaminoglycans in swine coronary adventitia (n = 5). The thick collagen bundles of outer adventitia (n = 4) were found to be undulated and unengaged at physiological loads, whereas the inner adventitia consisted of multiple sublayers of entangled fibers that bear the majority of load at higher pressures. The microstructural model was validated against biaxial (inflation and extension) experiments of coronary adventitia (n = 5). The model accurately predicted the nonlinear responses of the adventitia, even at high axial force (axial stretch ratio λz = 1.5). The model also enabled a reliable estimation of material parameters of individual fibers that were physically reasonable. A sensitivity analysis was performed to assess the effect of using mean values of the distributions for fiber orientation and waviness as opposed to the full distributions. The simplified mean analysis affects the fiber stress-strain relation, resulting in incorrect estimation of mechanical parameters, which underscores the need for measurements of fiber distribution for a rigorous analysis of fiber mechanics. The validated structure-based model of coronary adventitia provides a deeper understanding of vascular mechanics in health and can be extended to disease conditions.
Collapse
Affiliation(s)
- Huan Chen
- California Medical Innovations Institute, Incorporated, San Diego, California
| | - Xiaomei Guo
- California Medical Innovations Institute, Incorporated, San Diego, California
| | - Tong Luo
- California Medical Innovations Institute, Incorporated, San Diego, California
| | - Ghassan S Kassab
- California Medical Innovations Institute, Incorporated, San Diego, California
| |
Collapse
|
14
|
Chen H, Zhao X, Berwick ZC, Krieger JF, Chambers S, Kassab GS. Microstructure and Mechanical Property of Glutaraldehyde-Treated Porcine Pulmonary Ligament. J Biomech Eng 2016; 138:061003. [PMID: 27040732 DOI: 10.1115/1.4033300] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/22/2015] [Indexed: 01/15/2023]
Abstract
There is a significant need for fixed biological tissues with desired structural and material constituents for tissue engineering applications. Here, we introduce the lung ligament as a fixed biological material that may have clinical utility for tissue engineering. To characterize the lung tissue for potential clinical applications, we studied glutaraldehyde-treated porcine pulmonary ligament (n = 11) with multiphoton microscopy (MPM) and conducted biaxial planar experiments to characterize the mechanical property of the tissue. The MPM imaging revealed that there are generally two families of collagen fibers distributed in two distinct layers: The first family largely aligns along the longitudinal direction with a mean angle of θ = 10.7 ± 9.3 deg, while the second one exhibits a random distribution with a mean θ = 36.6 ± 27.4. Elastin fibers appear in some intermediate sublayers with a random orientation distribution with a mean θ = 39.6 ± 23 deg. Based on the microstructural observation, a microstructure-based constitutive law was proposed to model the elastic property of the tissue. The material parameters were identified by fitting the model to the biaxial stress-strain data of specimens, and good fitting quality was achieved. The parameter e0 (which denotes the strain beyond which the collagen can withstand tension) of glutaraldehyde-treated tissues demonstrated low variability implying a relatively consistent collagen undulation in different samples, while the stiffness parameters for elastin and collagen fibers showed relatively greater variability. The fixed tissues presented a smaller e0 than that of fresh specimen, confirming that glutaraldehyde crosslinking increases the mechanical strength of collagen-based biomaterials. The present study sheds light on the biomechanics of glutaraldehyde-treated porcine pulmonary ligament that may be a candidate for tissue engineering.
Collapse
|
15
|
Holzapfel GA, Niestrawska JA, Ogden RW, Reinisch AJ, Schriefl AJ. Modelling non-symmetric collagen fibre dispersion in arterial walls. J R Soc Interface 2016; 12:rsif.2015.0188. [PMID: 25878125 DOI: 10.1098/rsif.2015.0188] [Citation(s) in RCA: 119] [Impact Index Per Article: 14.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/16/2023] Open
Abstract
New experimental results on collagen fibre dispersion in human arterial layers have shown that the dispersion in the tangential plane is more significant than that out of plane. A rotationally symmetric dispersion model is not able to capture this distinction. For this reason, we introduce a new non-symmetric dispersion model, based on the bivariate von Mises distribution, which is used to construct a new structure tensor. The latter is incorporated in a strain-energy function that accommodates both the mechanical and structural features of the material, extending our rotationally symmetric dispersion model (Gasser et al. 2006 J. R. Soc. Interface 3, 15-35. (doi:10.1098/rsif.2005.0073)). We provide specific ranges for the dispersion parameters and show how previous models can be deduced as special cases. We also provide explicit expressions for the stress and elasticity tensors in the Lagrangian description that are needed for a finite-element implementation. Material and structural parameters were obtained by fitting predictions of the model to experimental data obtained from human abdominal aortic adventitia. In a finite-element example, we analyse the influence of the fibre dispersion on the homogeneous biaxial mechanical response of aortic strips, and in a final example the non-homogeneous stress distribution is obtained for circumferential and axial strips under fixed extension. It has recently become apparent that this more general model is needed for describing the mechanical behaviour of a variety of fibrous tissues.
Collapse
Affiliation(s)
- Gerhard A Holzapfel
- Institute of Biomechanics, Graz University of Technology, Kronesgasse 5-I, 8010 Graz, Austria
| | - Justyna A Niestrawska
- Institute of Biomechanics, Graz University of Technology, Kronesgasse 5-I, 8010 Graz, Austria
| | - Ray W Ogden
- School of Mathematics and Statistics, University of Glasgow, University Gardens, Glasgow G12 8QW, UK
| | - Andreas J Reinisch
- Institute of Biomechanics, Graz University of Technology, Kronesgasse 5-I, 8010 Graz, Austria
| | - Andreas J Schriefl
- Institute of Biomechanics, Graz University of Technology, Kronesgasse 5-I, 8010 Graz, Austria
| |
Collapse
|
16
|
Witzenburg CM, Dhume RY, Lake SP, Barocas VH. Automatic Segmentation of Mechanically Inhomogeneous Tissues Based on Deformation Gradient Jump. IEEE TRANSACTIONS ON MEDICAL IMAGING 2016; 35:29-41. [PMID: 26168433 PMCID: PMC4739827 DOI: 10.1109/tmi.2015.2453316] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
Variations in properties, active behavior, injury, scarring, and/or disease can all cause a tissue's mechanical behavior to be heterogeneous. Advances in imaging technology allow for accurate full-field displacement tracking of both in vitro and in vivo deformation from an applied load. While detailed strain fields provide some insight into tissue behavior, material properties are usually determined by fitting stress-strain behavior with a constitutive equation. However, the determination of the mechanical behavior of heterogeneous soft tissue requires a spatially varying constitutive equation (i.e., one in which the material parameters vary with position). We present an approach that computationally dissects the sample domain into many homogeneous subdomains, wherein subdomain boundaries are formed by applying a betweenness based graphical analysis to the deformation gradient field to identify locations with large discontinuities. This novel partitioning technique successfully determined the shape, size and location of regions with locally similar material properties for: (1) a series of simulated soft tissue samples prescribed with both abrupt and gradual changes in anisotropy strength, prescribed fiber alignment, stiffness, and nonlinearity, (2) tissue analogs (PDMS and collagen gels) which were tested biaxially and speckle tracked (3) and soft tissues which exhibited a natural variation in properties (cadaveric supraspinatus tendon), a pathologic variation in properties (thoracic aorta containing transmural plaque), and active behavior (contracting cardiac sheet). The routine enables the dissection of samples computationally rather than physically, allowing for the study of small tissues specimens with unknown and irregular inhomogeneity.
Collapse
Affiliation(s)
- Colleen M. Witzenburg
- University of Minnesota, Minneapolis, MN 55455 USA and is now with the University of Virginia, Charlottesville, VA 22908 USA
| | | | - Spencer P. Lake
- University of Minnesota, Minneapolis, MN 55455 USA as is now with Washington University, St. Louis, MO 63130 USA
| | | |
Collapse
|
17
|
Wijeratne PA, Vavourakis V, Hipwell JH, Voutouri C, Papageorgis P, Stylianopoulos T, Evans A, Hawkes DJ. Multiscale modelling of solid tumour growth: the effect of collagen micromechanics. Biomech Model Mechanobiol 2015; 15:1079-90. [PMID: 26564173 DOI: 10.1007/s10237-015-0745-2] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/12/2015] [Accepted: 11/02/2015] [Indexed: 01/16/2023]
Abstract
Here we introduce a model of solid tumour growth coupled with a multiscale biomechanical description of the tumour microenvironment, which facilitates the explicit simulation of fibre-fibre and tumour-fibre interactions. We hypothesise that such a model, which provides a purely mechanical description of tumour-host interactions, can be used to explain experimental observations of the effect of collagen micromechanics on solid tumour growth. The model was specified to mouse tumour data, and numerical simulations were performed. The multiscale model produced lower stresses than an equivalent continuum-like approach, due to a more realistic remodelling of the collagen microstructure. Furthermore, solid tumour growth was found to cause a passive mechanical realignment of fibres at the tumour boundary from a random to a circumferential orientation. This is in accordance with experimental observations, thus demonstrating that such a response can be explained as purely mechanical. Finally, peritumoural fibre network anisotropy was found to produce anisotropic tumour morphology. The dependency of tumour morphology on the peritumoural microstructure was reduced by adding a load-bearing non-collagenous component to the fibre network constitutive equation.
Collapse
Affiliation(s)
- Peter A Wijeratne
- Department of Medical Physics and Bioengineering, Centre for Medical Image Computing, University College London, Engineering Front Building, Malet Place, London, WC1E 6BT, UK.
| | - Vasileios Vavourakis
- Department of Medical Physics and Bioengineering, Centre for Medical Image Computing, University College London, Engineering Front Building, Malet Place, London, WC1E 6BT, UK
| | - John H Hipwell
- Department of Medical Physics and Bioengineering, Centre for Medical Image Computing, University College London, Engineering Front Building, Malet Place, London, WC1E 6BT, UK
| | - Chrysovalantis Voutouri
- Cancer Biophysics Laboratory, Department of Mechanical and Manufacturing Engineering, University of Cyprus, 1678, Nicosia, Cyprus
| | - Panagiotis Papageorgis
- Cancer Biophysics Laboratory, Department of Mechanical and Manufacturing Engineering, University of Cyprus, 1678, Nicosia, Cyprus
| | - Triantafyllos Stylianopoulos
- Cancer Biophysics Laboratory, Department of Mechanical and Manufacturing Engineering, University of Cyprus, 1678, Nicosia, Cyprus
| | | | - David J Hawkes
- Department of Medical Physics and Bioengineering, Centre for Medical Image Computing, University College London, Engineering Front Building, Malet Place, London, WC1E 6BT, UK
| |
Collapse
|
18
|
A stochastic model for soft tissue failure using acoustic emission data. J Mech Behav Biomed Mater 2015; 51:328-36. [DOI: 10.1016/j.jmbbm.2015.07.002] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/04/2015] [Revised: 06/30/2015] [Accepted: 07/04/2015] [Indexed: 11/22/2022]
|
19
|
Suki B. Assessing the Functional Mechanical Properties of Bioengineered Organs With Emphasis on the Lung. J Cell Physiol 2014; 229:1134-40. [DOI: 10.1002/jcp.24600] [Citation(s) in RCA: 29] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/27/2014] [Accepted: 03/03/2014] [Indexed: 01/16/2023]
Affiliation(s)
- Béla Suki
- Department of Biomedical Engineering; Boston University; Boston Massachusetts
| |
Collapse
|
20
|
Chen H, Zhao X, Lu X, Kassab G. Non-linear micromechanics of soft tissues. INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS 2013; 58:79-85. [PMID: 24817769 PMCID: PMC4012686 DOI: 10.1016/j.ijnonlinmec.2013.03.002] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
Microstructure-based constitutive models have been adopted in recent studies of non-linear mechanical properties of biological soft tissues. These models provide more accurate predictions of the overall mechanical responses of tissues than phenomenological approaches. Based on standard approximations in non-linear mechanics, we classified the microstructural models into three categories: (1) uniform-field models with solid-like matrix, (2) uniform-field models with fluid-like matrix, and (3) second-order estimate models. The first two categories assume affine deformation field where the deformation of microstructure is the same as that of the tissue, regardless of material heterogeneities; i.e., they represent the upper bounds of the exact effective strain energy and stress of soft tissues. In addition, the first type is not purely structurally motivated and hence cannot accurately predict the microscopic mechanical behaviors of soft tissues. The third category considers realistic geometrical features, material properties of microstructure and interactions among them and allows for flexible deformation in each constituent. The uniform-field model with fluid-like matrix and the second-order estimate model are microstructure-based, and can be applied to different tissues based on micro-structural features.
Collapse
Affiliation(s)
- Huan Chen
- Department of Biomedical Engineering, Indiana University Purdue University Indianapolis, Indianapolis, IN 46202, United States
| | - Xuefeng Zhao
- Department of Biomedical Engineering, Indiana University Purdue University Indianapolis, Indianapolis, IN 46202, United States
| | - Xiao Lu
- Department of Biomedical Engineering, Indiana University Purdue University Indianapolis, Indianapolis, IN 46202, United States
| | - Ghassan Kassab
- Department of Biomedical Engineering, Indiana University Purdue University Indianapolis, Indianapolis, IN 46202, United States
- Department of Surgery, Cellular and Integrative Physiology, Indiana University Purdue University Indianapolis, Indianapolis, IN 46202, United States
| |
Collapse
|
21
|
Wittek A, Karatolios K, Bihari P, Schmitz-Rixen T, Moosdorf R, Vogt S, Blase C. In vivo determination of elastic properties of the human aorta based on 4D ultrasound data. J Mech Behav Biomed Mater 2013; 27:167-83. [PMID: 23668998 DOI: 10.1016/j.jmbbm.2013.03.014] [Citation(s) in RCA: 69] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/16/2012] [Revised: 03/20/2013] [Accepted: 03/22/2013] [Indexed: 11/15/2022]
Abstract
Computational analysis of the biomechanics of the vascular system aims at a better understanding of its physiology and pathophysiology. To be of clinical use, however, these models and thus their predictions, have to be patient specific regarding geometry, boundary conditions and material. In this paper we present an approach to determine individual material properties of human aortae based on a new type of in vivo full field displacement data acquired by dimensional time resolved three dimensional ultrasound (4D-US) imaging. We developed a nested iterative Finite Element Updating method to solve two coupled inverse problems: The prestrains that are present in the imaged diastolic configuration of the aortic wall are determined. The solution of this problem is integrated in an iterative method to identify the nonlinear hyperelastic anisotropic material response of the aorta to physiologic deformation states. The method was applied to 4D-US data sets of the abdominal aorta of five healthy volunteers and verified by a numerical experiment. This non-invasive in vivo technique can be regarded as a first step to determine patient individual material properties of the human aorta.
Collapse
Affiliation(s)
- Andreas Wittek
- Institute for Cell Biology and Neuroscience, Goethe University, Max-von-Laue-Strasse 13, 60438 Frankfurt/Main, Germany
| | | | | | | | | | | | | |
Collapse
|
22
|
Zeinali-Davarani S, Chow MJ, Turcotte R, Zhang Y. Characterization of biaxial mechanical behavior of porcine aorta under gradual elastin degradation. Ann Biomed Eng 2013; 41:1528-38. [PMID: 23297000 DOI: 10.1007/s10439-012-0733-y] [Citation(s) in RCA: 50] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/14/2012] [Accepted: 12/19/2012] [Indexed: 11/29/2022]
Abstract
Arteries are composed of multiple constituents that endow the wall with proper structure and function. Many vascular diseases are associated with prominent mechanical and biological alterations in the wall constituents. In this study, planar biaxial tensile test data of elastase-treated porcine aortic tissue (Chow et al. in Biomech Model Mechanobiol 2013) is re-examined to characterize the altered mechanical behavior at multiple stages of digestion through constitutive modeling. Exponential-based as well as recruitment-based strain energy functions are employed and the associated constitutive parameters for individual digestion stages are identified using nonlinear parameter estimation. It is shown that when the major portion of elastin is degraded from a cut-open artery in the load-free state, the embedded collagen fibers are recruited at lower stretch levels under biaxial loads, leading to a rapid stiffening behavior of the tissue. Multiphoton microscopy illustrates that the collagen waviness decreases significantly with the degradation time, resulting in a rapid recruitment when the tissue is loaded. It is concluded that even when residual stresses are released, there exists an intrinsic mechanical interaction between arterial elastin and collagen that determines the mechanics of arteries and carries important implications to vascular mechanobiology.
Collapse
|
23
|
|
24
|
The layered structure of coronary adventitia under mechanical load. Biophys J 2012; 101:2555-62. [PMID: 22261042 DOI: 10.1016/j.bpj.2011.10.043] [Citation(s) in RCA: 56] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/11/2011] [Revised: 09/01/2011] [Accepted: 10/31/2011] [Indexed: 11/22/2022] Open
Abstract
The mechanical loading-deformation relation of elastin and collagen fibril bundles is fundamental to understanding the microstructural properties of tissue. Here, we use multiphoton microscopy to obtain quantitative data of elastin and collagen fiber bundles under in situ loading of coronary adventitia. Simultaneous loading-imaging experiments on unstained fresh coronary adventitia allowed morphometric measurements of collagen and elastin fibril bundles and their individual deformation. Fiber data were analyzed at five different distension loading points (circumferential stretch ratio λ(θ) = 1.0, 1.2, 1.4, 1.6, and 1.8) at a physiological axial stretch ratio of λ(axial) = 1.3. Four fiber geometrical parameters were used to quantify the fibers: orientation angle, waviness, width, and area fraction. The results show that elastin and collagen fibers in inner adventitia form concentric densely packed fiber sheets, and the fiber orientation angle, width, and area fraction vary transmurally. The extent of fiber deformation depends on the initial orientation angle at no-distension state (λ(θ) = 1.0 and λ(axial) = 1.3). At higher distension loading, the orientation angle and waviness of fibers decrease linearly, but the width of collagen fiber is relatively constant at λ(θ) = 1.0-1.4 and then decrease linearly for λ(θ) ≥ 1.4. A decrease of the relative dispersion (SD/mean) of collagen fiber waviness suggests a heterogeneous mechanical response to loads. This study provides fundamental microstructural data for coronary artery biomechanics and we consider it seminal for structural models.
Collapse
|
25
|
Sunbuloglu E, Bozdag E, Toprak T, Islak C. Experimental parameter estimation method for nonlinear viscoelastic composite material models: an application on arterial tissue. Comput Methods Biomech Biomed Engin 2012; 16:1249-61. [PMID: 22494570 DOI: 10.1080/10255842.2012.666532] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
Abstract
This study is aimed at setting a method of experimental parameter estimation for large-deforming nonlinear viscoelastic continuous fibre-reinforced composite material model. Specifically, arterial tissue was investigated during experimental research and parameter estimation studies, due to medical, scientific and socio-economic importance of soft tissue research. Using analytical formulations for specimens under combined inflation/extension/torsion on thick-walled cylindrical tubes, in vitro experiments were carried out with fresh sheep arterial segments, and parameter estimation procedures were carried out on experimental data. Model restrictions were pointed out using outcomes from parameter estimation. Needs for further studies that can be developed are discussed.
Collapse
Affiliation(s)
- Emin Sunbuloglu
- a Faculty of Mechanical Engineering, Istanbul Technical University , Inonu Cad. No:65, Gumussuyu, Beyoglu, Istanbul , 34437 , Turkey
| | | | | | | |
Collapse
|
26
|
Natali AN, Pavan PG, Venturato C, Komatsu K. Constitutive modeling of the non-linear visco-elasticity of the periodontal ligament. COMPUTER METHODS AND PROGRAMS IN BIOMEDICINE 2011; 104:193-8. [PMID: 21531472 DOI: 10.1016/j.cmpb.2011.03.014] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/29/2010] [Revised: 02/17/2011] [Accepted: 03/26/2011] [Indexed: 05/20/2023]
Abstract
A non-linear visco-elastic constitutive model is adopted to describe the relaxation phenomena of the periodontal ligament (PDL). The introduction of a non-linear formulation of visco-elasticity is necessary because experimental data from the literature referring to animal models show that the relaxation rate depends on the level of strain applied. In particular, the percentage of relaxation increases with decrease of the applied strain. The constitutive model is consistent with the non-linear elastic behavior of the PDL in the case of high rate loading and large strains attained by the tissue. A hyperelastic formulation is adopted for the elastic behavior of the PDL and this formulation is developed adopting suitable measures of stress and strain. The anisotropy of the tissue induced by specific spatial orientation of collagen fibers is included in the model. With respect to recent numerical formulation proposed to describe the non-linear visco-elasticity of the PDL, the proposed model has the advantage of being more consistent with the micro-structural configuration of the tissue and the large strains it can undergo. The results obtained show that a reasonable description of the PDL relaxation phenomena can be obtained by assuming that relaxation times are independent of strain, whereas the relative stiffness results are dependent on strain applied through an exponential function.
Collapse
Affiliation(s)
- Arturo N Natali
- University of Padova, Centre of Mechanics of Biological Materials, Via F. Marzolo 9, I-35131 Padova, Italy.
| | | | | | | |
Collapse
|
27
|
Brunon A, Bruyère-Garnier K, Coret M. Characterization of the nonlinear behaviour and the failure of human liver capsule through inflation tests. J Mech Behav Biomed Mater 2011; 4:1572-81. [DOI: 10.1016/j.jmbbm.2010.12.016] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/13/2010] [Revised: 12/21/2010] [Accepted: 12/22/2010] [Indexed: 11/25/2022]
|
28
|
Zhao X, Raghavan ML, Lu J. Characterizing heterogeneous properties of cerebral aneurysms with unknown stress-free geometry: a precursor to in vivo identification. J Biomech Eng 2011; 133:051008. [PMID: 21599099 DOI: 10.1115/1.4003872] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
Abstract
Knowledge of elastic properties of cerebral aneurysms is crucial for understanding the biomechanical behavior of the lesion. However, characterizing tissue properties using in vivo motion data presents a tremendous challenge. Aside from the limitation of data accuracy, a pressing issue is that the in vivo motion does not expose the stress-free geometry. This is compounded by the nonlinearity, anisotropy, and heterogeneity of the tissue behavior. This article introduces a method for identifying the heterogeneous properties of aneurysm wall tissue under unknown stress-free configuration. In the proposed approach, an accessible configuration is taken as the reference; the unknown stress-free configuration is represented locally by a metric tensor describing the prestrain from the stress-free configuration to the reference configuration. Material parameters are identified together with the metric tensor pointwisely. The paradigm is tested numerically using a forward-inverse analysis loop. An image-derived sac is considered. The aneurysm tissue is modeled as an eightply laminate whose constitutive behavior is described by an anisotropic hyperelastic strain-energy function containing four material parameters. The parameters are assumed to vary continuously in two assigned patterns to represent two types of material heterogeneity. Nine configurations between the diastolic and systolic pressures are generated by forward quasi-static finite element analyses. These configurations are fed to the inverse analysis to delineate the material parameters and the metric tensor. The recovered and the assigned distributions are in good agreement. A forward verification is conducted by comparing the displacement solutions obtained from the recovered and the assigned material parameters at a different pressure. The nodal displacements are found in excellent agreement.
Collapse
Affiliation(s)
- Xuefeng Zhao
- Department of Mechanical and Industrial Engineering, Center for Computer Aided Design, University of Iowa, Iowa City, IA 52242-1527, USA
| | | | | |
Collapse
|
29
|
Chen H, Liu Y, Zhao X, Lanir Y, Kassab GS. A Micromechanics Finite-Strain Constitutive Model of Fibrous Tissue. JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS 2011; 59:1823-1837. [PMID: 21927506 PMCID: PMC3171755 DOI: 10.1016/j.jmps.2011.05.012] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
Biological tissues have unique mechanical properties due to the wavy fibrous collagen and elastin microstructure. In inflation, a vessel easily distends under low pressure but becomes stiffer when the fibers are straightened to take up the load. The current microstructural models of blood vessels assume affine deformation; i.e., the deformation of each fiber is assumed to be identical to the macroscopic deformation of the tissue. This uniform-field (UF) assumption leads to the macroscopic (or effective) strain energy of the tissue that is the volumetric sum of the contributions of the tissue components. Here, a micromechanics-based constitutive model of fibrous tissue is developed to remove the affine assumption and to take into consideration the heterogeneous interactions between the fibers and the ground substance. The development is based on the framework of a recently developed second-order homogenization theory, and takes into account the waviness, orientations, and spatial distribution of the fibers, as well as the material nonlinearity at finite-strain deformation. In an illustrative simulation, the predictions of the macroscopic stress-strain relation, and the statistical deformation of the fibers are compared to the UF model, as well as finite-element (FE) simulation. Our predictions agree well with the FE results, while the UF predictions significantly overestimate. The effects of fiber distribution and waviness on the macroscopic stress-strain relation are also investigated. The present mathematical model may serves as a foundation for native as well as for engineered tissues and biomaterials.
Collapse
Affiliation(s)
- Huan Chen
- Department of Biomedical Engineering, Indiana University Purdue University Indianapolis, Indianapolis, IN 46202, USA
| | - Yi Liu
- Department of Biomedical Engineering, Indiana University Purdue University Indianapolis, Indianapolis, IN 46202, USA
| | - Xuefeng Zhao
- Department of Biomedical Engineering, Indiana University Purdue University Indianapolis, Indianapolis, IN 46202, USA
| | - Yoram Lanir
- Department of Biomedical Engineering, Technion-Israel Institute of Technology, Haifa, Israel
| | - Ghassan S. Kassab
- Department of Biomedical Engineering, Indiana University Purdue University Indianapolis, Indianapolis, IN 46202, USA
- Departments of Surgery, Cellular and Integrative Physiology, Indiana University Purdue University Indianapolis, Indianapolis, IN 46202, USA
| |
Collapse
|
30
|
Natali AN, Pavan PG, Stecco C. A constitutive model for the mechanical characterization of the plantar fascia. Connect Tissue Res 2010; 51:337-46. [PMID: 20175692 DOI: 10.3109/03008200903389127] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 02/03/2023]
Abstract
A constitutive model is proposed to describe the mechanical behavior of the plantar fascia. The mechanical characterization of the plantar fascia regards the role in the foot biomechanics and it is involved in many alterations of its functional behavior, both of mechanical and nonmechanical origin. The structural conformation of the plantar fascia in its middle part is characterized by the presence of collagen fibers reinforcing the tissue along a preferential orientation, which is that supporting the major loading. According to this anatomical evidence, the tissue is described by developing an isotropic fiber-reinforced constitutive model and since the elastic response of the fascia is here considered, the constitutive model is based on the theory of hyperelasticity. The model is consistent with a kinematical description of large strains mechanical behavior, which is typical of soft tissues. A fitting procedure of the constitutive model is implemented making use of experimental curves taken from the literature and referring to specimens of human plantar fascia. A satisfactory fitting of the tensile behavior of the plantar fascia has been performed, showing that the model correctly interprets the mechanical behavior of the tissue in the light of comparison to experimental data at disposal. A critical analysis of the model with respect to the problem of the identification of the constitutive parameters is proposed as the basis for planning a future experimental investigation of mechanical behavior of the plantar fascia.
Collapse
Affiliation(s)
- Arturo N Natali
- Centre of Mechanics of Biological Materials, University of Padova, Padova, Italy
| | | | | |
Collapse
|
31
|
Natali A, Fontanella C, Carniel E. Constitutive formulation and analysis of heel pad tissues mechanics. Med Eng Phys 2010; 32:516-22. [DOI: 10.1016/j.medengphy.2010.02.018] [Citation(s) in RCA: 43] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/28/2009] [Revised: 02/11/2010] [Accepted: 02/18/2010] [Indexed: 10/19/2022]
|
32
|
Zhao X, Raghavan ML, Lu J. Identifying heterogeneous anisotropic properties in cerebral aneurysms: a pointwise approach. Biomech Model Mechanobiol 2010; 10:177-89. [PMID: 20490886 DOI: 10.1007/s10237-010-0225-7] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/20/2009] [Accepted: 05/04/2010] [Indexed: 10/19/2022]
Abstract
The traditional approaches of estimating heterogeneous properties in a soft tissue structure using optimization-based inverse methods often face difficulties because of the large number of unknowns to be simultaneously determined. This article proposes a new method for identifying the heterogeneous anisotropic nonlinear elastic properties in cerebral aneurysms. In this method, the local properties are determined directly from the pointwise stress-strain data, thus avoiding the need for simultaneously optimizing for the property values at all points/regions in the aneurysm. The stress distributions needed for a pointwise identification are computed using an inverse elastostatic method without invoking the material properties in question. This paradigm is tested numerically through simulated inflation tests on an image-based cerebral aneurysm sac. The wall tissue is modeled as an eight-ply laminate whose constitutive behavior is described by an anisotropic hyperelastic strain energy function containing four parameters. The parameters are assumed to vary continuously in the sac. Deformed configurations generated from forward finite element analysis are taken as input to inversely establish the parameter distributions. The delineated and the assigned distributions are in excellent agreement. A forward verification is conducted by comparing the displacement solutions obtained from the delineated and the assigned material parameters at a different pressure. The deviations in nodal displacements are found to be within 0.2% in most part of the sac. The study highlights some distinct features of the proposed method, and demonstrates the feasibility of organ level identification of the distributive anisotropic nonlinear properties in cerebral aneurysms.
Collapse
Affiliation(s)
- Xuefeng Zhao
- Department of Mechanical and Industrial Engineering, Center for Computer Aided Design, The University of Iowa, Iowa City, IA 52242-1527, USA
| | | | | |
Collapse
|
33
|
Abstract
This review article is concerned with the mathematical modelling of the mechanical properties of the soft biological tissues that constitute the walls of arteries. Many important aspects of the mechanical behaviour of arterial tissue can be treated on the basis of elasticity theory, and the focus of the article is therefore on the constitutive modelling of the anisotropic and highly nonlinear elastic properties of the artery wall. The discussion focuses primarily on developments over the last decade based on the theory of deformation invariants, in particular invariants that in part capture structural aspects of the tissue, specifically the orientation of collagen fibres, the dispersion in the orientation, and the associated anisotropy of the material properties. The main features of the relevant theory are summarized briefly and particular forms of the elastic strain-energy function are discussed and then applied to an artery considered as a thick-walled circular cylindrical tube in order to illustrate its extension–inflation behaviour. The wide range of applications of the constitutive modelling framework to artery walls in both health and disease and to the other fibrous soft tissues is discussed in detail. Since the main modelling effort in the literature has been on the passive response of arteries, this is also the concern of the major part of this article. A section is nevertheless devoted to reviewing the limited literature within the continuum mechanics framework on the active response of artery walls, i.e. the mechanical behaviour associated with the activation of smooth muscle, a very important but also very challenging topic that requires substantial further development. A final section provides a brief summary of the current state of arterial wall mechanical modelling and points to key areas that need further modelling effort in order to improve understanding of the biomechanics and mechanobiology of arteries and other soft tissues, from the molecular, to the cellular, tissue and organ levels.
Collapse
Affiliation(s)
- Gerhard A. Holzapfel
- Institute of Biomechanics, Center of Biomedical Engineering, Graz University of Technology, Graz, Austria
- Department of Solid Mechanics, School of Engineering Sciences, Royal Institute of Technology (KTH), Stockholm, Sweden
| | - Ray W. Ogden
- Department of Mathematics, University of Glasgow, Glasgow, UK
| |
Collapse
|
34
|
Girard MJA, Suh JKF, Bottlang M, Burgoyne CF, Downs JC. Scleral biomechanics in the aging monkey eye. Invest Ophthalmol Vis Sci 2009; 50:5226-37. [PMID: 19494203 PMCID: PMC2883469 DOI: 10.1167/iovs.08-3363] [Citation(s) in RCA: 155] [Impact Index Per Article: 10.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022] Open
Abstract
PURPOSE To investigate the age-related differences in the inhomogeneous, anisotropic, nonlinear biomechanical properties of posterior sclera from old (22.9 +/- 5.3 years) and young (1.5 +/- 0.7 years) rhesus monkeys. METHODS The posterior scleral shell of each eye was mounted on a custom-built pressurization apparatus, then intraocular pressure (IOP) was elevated from 5 to 45 mm Hg while the 3D displacements of the scleral surface were measured with speckle interferometry. Each scleral shell's geometry was digitally reconstructed from data generated by a 3-D digitizer (topography) and 20-MHz ultrasound (thickness). An inverse finite element (FE) method incorporating a fiber-reinforced constitutive model was used to extract a unique set of biomechanical properties for each eye. Displacements, thickness, stress, strain, tangent modulus, structural stiffness, and preferred collagen fiber orientation were mapped for each posterior sclera. RESULTS The model yielded 3-D deformations of posterior sclera that matched well with those observed experimentally. The posterior sclera exhibited inhomogeneous, anisotropic, nonlinear mechanical behavior. The sclera was significantly thinner (P = 0.038) and tangent modulus and structural stiffness were significantly higher in old monkeys (P < 0.0001). On average, scleral collagen fibers were circumferentially oriented around the optic nerve head (ONH). No difference was found in the preferred collagen fiber orientation and fiber concentration factor between age groups. CONCLUSIONS Posterior sclera of old monkeys is significantly stiffer than that of young monkeys and is therefore subject to higher stresses but lower strains at all levels of IOP. Age-related stiffening of the sclera may significantly influence ONH biomechanics and potentially contribute to age-related susceptibility to glaucomatous vision loss.
Collapse
Affiliation(s)
- Michaël J. A. Girard
- Department of Biomedical Engineering, Tulane University, 6823 St. Charles Avenue, New Orleans LA, 70118
- Ocular Biomechanics Laboratory, Devers Eye Institute, 1225 NE 2nd Avenue, Portland, OR 97232
- Current affiliation: Department of Bioengineering, Imperial College London, London UK, SW7 2AZ
| | - J-K. Francis Suh
- Department of Biomedical Engineering, Tulane University, 6823 St. Charles Avenue, New Orleans LA, 70118
- Convergence Technology Laboratory, Korea Institute of Science and Technology, Hawolgok-Dong 39-1, Seongbuk-Gu, Seoul, Korea
| | - Michael Bottlang
- Biomechanics Laboratory, Legacy Health Research, 1225 NE 2nd Avenue, Portland, OR 97232
| | - Claude F. Burgoyne
- Department of Biomedical Engineering, Tulane University, 6823 St. Charles Avenue, New Orleans LA, 70118
- Optic Nerve Head Research Laboratory, Devers Eye Institute, 1225 NE 2nd Avenue, Portland, OR 97232
| | - J. Crawford Downs
- Department of Biomedical Engineering, Tulane University, 6823 St. Charles Avenue, New Orleans LA, 70118
- Ocular Biomechanics Laboratory, Devers Eye Institute, 1225 NE 2nd Avenue, Portland, OR 97232
| |
Collapse
|
35
|
Tang H, Buehler MJ, Moran B. A Constitutive Model of Soft Tissue: From Nanoscale Collagen to Tissue Continuum. Ann Biomed Eng 2009; 37:1117-30. [DOI: 10.1007/s10439-009-9679-0] [Citation(s) in RCA: 70] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/09/2008] [Accepted: 03/16/2009] [Indexed: 11/24/2022]
|