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Wiśniewski K, Reorowicz P, Tyfa Z, Price B, Jian A, Fahlström A, Obidowski D, Jaskólski DJ, Jóźwik K, Drummond K, Wessels L, Vajkoczy P, Adamides AA. Computational fluid dynamics; a new diagnostic tool in giant intracerebral aneurysm treatment. Comput Biol Med 2024; 181:109053. [PMID: 39217964 DOI: 10.1016/j.compbiomed.2024.109053] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/05/2024] [Revised: 08/05/2024] [Accepted: 08/20/2024] [Indexed: 09/04/2024]
Abstract
Giant intracerebral aneurysms (GIA) comprise up to 5 % of all intracranial aneurysms. The indirect surgical strategy, which leaves the GIA untouched but reverses the blood flow by performing a bypass in combination with proximal parent artery occlusion is a useful method to achieve spontaneous aneurysm occlusion. The goal of this study was to assess the utility of computational fluid dynamics (CFD) in preoperative GIA treatment planning. We hypothesise that CFD simulations will predict treatment results. A fluid-structure interaction (FSI) CFD investigation was performed for the entire arterial brain circulation. The analyses were performed in three patient-specific CT angiogram models. The first served as the reference geometry with a C6 internal carotid artery (ICA) GIA, the second a proximal parent artery occlusion (PAO) and virtual bypass to the frontal M2 branch of the middle cerebral artery (MCA), and the third a proximal PAO in combination with a temporal M2 branch bypass. The volume of "old blood", flow residence time (FRT), dynamic viscosity and haemodynamic changes were also analysed. The "old blood" within the aneurysm in the bypass models reached 41 % after 20 cardiac cycles while in the reference model it was fully washed out. In Bypass 2 "old blood" was also observed in the main trunk of the MCA after 20 cardiac cycles. Extrapolation of the results yielded a duration of 4 years required to replace the "old blood" inside the aneurysm after bypass revascularization. In both bypass models a 7-fold increase in mean blood viscosity in the aneurysm region was noted. Bypass revascularization combined with proximal PAO favours thrombosis. Areas prone to thrombus formation, and subsequently the treatment outcomes, were accurately identified in the preoperative model. Virtual surgical operations can give a remarkable insight into haemodynamics that could support operative decision-making.
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Affiliation(s)
- Karol Wiśniewski
- Department of Neurosurgery, Royal Melbourne Hospital, 300 Grattan St, Parkville, 3050, Australia; Department of Neurosurgery and Neurooncology, Medical University of Łódź, Kopcińskiego 22, 90-153, Łódź, Poland; Lodz University of Technology, Institute of Turbomachinery, 219/223 Wolczanska Str., 90-924, Lodz, Poland.
| | - Piotr Reorowicz
- Lodz University of Technology, Institute of Turbomachinery, 219/223 Wolczanska Str., 90-924, Lodz, Poland.
| | - Zbigniew Tyfa
- Lodz University of Technology, Institute of Turbomachinery, 219/223 Wolczanska Str., 90-924, Lodz, Poland.
| | - Benjamin Price
- Department of Neurosurgery, Royal Melbourne Hospital, 300 Grattan St, Parkville, 3050, Australia.
| | - Anne Jian
- Department of Neurosurgery, Royal Melbourne Hospital, 300 Grattan St, Parkville, 3050, Australia.
| | - Andreas Fahlström
- Department of Neurosurgery, Royal Melbourne Hospital, 300 Grattan St, Parkville, 3050, Australia; Department of Medical Sciences, Section of Neurosurgery, Uppsala University, Uppsala, 75185, Sweden.
| | - Damian Obidowski
- Lodz University of Technology, Institute of Turbomachinery, 219/223 Wolczanska Str., 90-924, Lodz, Poland.
| | - Dariusz J Jaskólski
- Department of Neurosurgery and Neurooncology, Medical University of Łódź, Kopcińskiego 22, 90-153, Łódź, Poland.
| | - Krzysztof Jóźwik
- Lodz University of Technology, Institute of Turbomachinery, 219/223 Wolczanska Str., 90-924, Lodz, Poland.
| | - Katharine Drummond
- Department of Neurosurgery, Royal Melbourne Hospital, 300 Grattan St, Parkville, 3050, Australia; Department of Surgery, University of Melbourne, 300 Grattan St, Parkville, 3050, Australia.
| | - Lars Wessels
- Department of Neurosurgery and Center for Stroke Research Berlin (CSB), Charité - Universitätsmedizin Berlin, Berlin, Germany.
| | - Peter Vajkoczy
- Department of Neurosurgery and Center for Stroke Research Berlin (CSB), Charité - Universitätsmedizin Berlin, Berlin, Germany.
| | - Alexios A Adamides
- Department of Neurosurgery, Royal Melbourne Hospital, 300 Grattan St, Parkville, 3050, Australia; Department of Surgery, University of Melbourne, 300 Grattan St, Parkville, 3050, Australia.
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2
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Tobe Y, Robertson AM, Ramezanpour M, Cebral JR, Watkins SC, Charbel FT, Amin-Hanjani S, Yu AK, Cheng BC, Woo HH. Comapping Cellular Content and Extracellular Matrix with Hemodynamics in Intact Arterial Tissues Using Scanning Immunofluorescent Multiphoton Microscopy. MICROSCOPY AND MICROANALYSIS : THE OFFICIAL JOURNAL OF MICROSCOPY SOCIETY OF AMERICA, MICROBEAM ANALYSIS SOCIETY, MICROSCOPICAL SOCIETY OF CANADA 2024; 30:342-358. [PMID: 38525887 PMCID: PMC11057816 DOI: 10.1093/mam/ozae025] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/30/2023] [Revised: 03/01/2024] [Accepted: 03/04/2024] [Indexed: 03/26/2024]
Abstract
Deviation of blood flow from an optimal range is known to be associated with the initiation and progression of vascular pathologies. Important open questions remain about how the abnormal flow drives specific wall changes in pathologies such as cerebral aneurysms where the flow is highly heterogeneous and complex. This knowledge gap precludes the clinical use of readily available flow data to predict outcomes and improve treatment of these diseases. As both flow and the pathological wall changes are spatially heterogeneous, a crucial requirement for progress in this area is a methodology for acquiring and comapping local vascular wall biology data with local hemodynamic data. Here, we developed an imaging pipeline to address this pressing need. A protocol that employs scanning multiphoton microscopy was developed to obtain three-dimensional (3D) datasets for smooth muscle actin, collagen, and elastin in intact vascular specimens. A cluster analysis was introduced to objectively categorize the smooth muscle cells (SMC) across the vascular specimen based on SMC actin density. Finally, direct quantitative comparison of local flow and wall biology in 3D intact specimens was achieved by comapping both heterogeneous SMC data and wall thickness to patient-specific hemodynamic results.
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Affiliation(s)
- Yasutaka Tobe
- Department of Mechanical Engineering and Materials Science, University of Pittsburgh, Pittsburgh, PA 15261, USA
| | - Anne M Robertson
- Department of Mechanical Engineering and Materials Science, University of Pittsburgh, Pittsburgh, PA 15261, USA
| | - Mehdi Ramezanpour
- Department of Mechanical Engineering and Materials Science, University of Pittsburgh, Pittsburgh, PA 15261, USA
| | - Juan R Cebral
- Department of Bioengineering, George Mason University, Fairfax, VA 22030, USA
| | - Simon C Watkins
- Department of Cell Biology, University of Pittsburgh, PA 15261, USA
| | - Fady T Charbel
- Department of Neurosurgery, University of Illinois at Chicago, Chicago, IL 60612, USA
| | - Sepideh Amin-Hanjani
- Department of Neurological Surgery, University Hospital Cleveland Medical Center, Cleveland, OH 44106, USA
| | - Alexander K Yu
- Department of Neurological Surgery, Allegheny Health Network, Pittsburgh, PA 15212, USA
| | - Boyle C Cheng
- Neuroscience and Orthopedic Institutes, Allegheny Health Network, Pittsburgh, PA 15212, USA
| | - Henry H Woo
- Department of Neurosurgery, Donald and Barbara Zucker School of Medicine at Hofstra Northwell, Manhasset, NY 11549, USA
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3
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Giudici A, van der Laan KWF, van der Bruggen MM, Parikh S, Berends E, Foulquier S, Delhaas T, Reesink KD, Spronck B. Constituent-based quasi-linear viscoelasticity: a revised quasi-linear modelling framework to capture nonlinear viscoelasticity in arteries. Biomech Model Mechanobiol 2023; 22:1607-1623. [PMID: 37129690 PMCID: PMC10511394 DOI: 10.1007/s10237-023-01711-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/12/2022] [Accepted: 03/08/2023] [Indexed: 05/03/2023]
Abstract
Arteries exhibit fully nonlinear viscoelastic behaviours (i.e. both elastically and viscously nonlinear). While elastically nonlinear arterial models are well established, effective mathematical descriptions of nonlinear viscoelasticity are lacking. Quasi-linear viscoelasticity (QLV) offers a convenient way to mathematically describe viscoelasticity, but its viscous linearity assumption is unsuitable for whole-wall vascular applications. Conversely, application of fully nonlinear viscoelastic models, involving deformation-dependent viscous parameters, to experimental data is impractical and often reduces to identifying specific solutions for each tested loading condition. The present study aims to address this limitation: By applying QLV theory at the wall constituent rather than at the whole-wall level, the deformation-dependent relative contribution of the constituents allows to capture nonlinear viscoelasticity with a unique set of deformation-independent model parameters. Five murine common carotid arteries were subjected to a protocol of quasi-static and harmonic, pseudo-physiological biaxial loading conditions to characterise their viscoelastic behaviour. The arterial wall was modelled as a constrained mixture of an isotropic elastin matrix and four families of collagen fibres. Constituent-based QLV was implemented by assigning different relaxation functions to collagen- and elastin-borne parts of the wall stress. Nonlinearity in viscoelasticity was assessed via the pressure dependency of the dynamic-to-quasi-static stiffness ratio. The experimentally measured ratio increased with pressure, from 1.03 [Formula: see text] 0.03 (mean [Formula: see text] standard deviation) at 80-40 mmHg to 1.58 [Formula: see text] 0.22 at 160-120 mmHg. Constituent-based QLV captured well this trend by attributing the wall viscosity predominantly to collagen fibres, whose recruitment starts at physiological pressures. In conclusion, constituent-based QLV offers a practical and effective solution to model arterial viscoelasticity.
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Affiliation(s)
- Alessandro Giudici
- Department of Biomedical Engineering, CARIM School for Cardiovascular Diseases, Maastricht University, Universiteitssingel 40, Room C5.568, 6229 ER, Maastricht, The Netherlands.
- GROW School for Oncology and Reproduction, Maastricht University, Maastricht, The Netherlands.
| | - Koen W F van der Laan
- Department of Biomedical Engineering, CARIM School for Cardiovascular Diseases, Maastricht University, Universiteitssingel 40, Room C5.568, 6229 ER, Maastricht, The Netherlands
| | - Myrthe M van der Bruggen
- Department of Biomedical Engineering, CARIM School for Cardiovascular Diseases, Maastricht University, Universiteitssingel 40, Room C5.568, 6229 ER, Maastricht, The Netherlands
| | - Shaiv Parikh
- Department of Biomedical Engineering, CARIM School for Cardiovascular Diseases, Maastricht University, Universiteitssingel 40, Room C5.568, 6229 ER, Maastricht, The Netherlands
| | - Eline Berends
- Department of Internal Medicine, CARIM School for Cardiovascular Diseases, Maastricht University, Maastricht, The Netherlands
| | - Sébastien Foulquier
- Department of Pharmacology and Toxicology, CARIM School for Cardiovascular Diseases, Maastricht University, Maastricht, The Netherlands
| | - Tammo Delhaas
- Department of Biomedical Engineering, CARIM School for Cardiovascular Diseases, Maastricht University, Universiteitssingel 40, Room C5.568, 6229 ER, Maastricht, The Netherlands
| | - Koen D Reesink
- Department of Biomedical Engineering, CARIM School for Cardiovascular Diseases, Maastricht University, Universiteitssingel 40, Room C5.568, 6229 ER, Maastricht, The Netherlands
| | - Bart Spronck
- Department of Biomedical Engineering, CARIM School for Cardiovascular Diseases, Maastricht University, Universiteitssingel 40, Room C5.568, 6229 ER, Maastricht, The Netherlands
- Macquarie Medical School, Faculty of Medicine, Health and Human Sciences, Macquarie University, Sydney, Australia
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Sigaeva T, Zhang Y. A novel constitutive model considering the role of elastic lamellae' structural heterogeneity in homogenizing transmural stress distribution in arteries. J R Soc Interface 2023; 20:20220837. [PMID: 37042193 PMCID: PMC10091191 DOI: 10.1098/rsif.2022.0837] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/19/2022] [Accepted: 03/21/2023] [Indexed: 04/13/2023] Open
Abstract
Understanding how the homeostatic stress state can be reached in arterial tissues can provide new insights into vascular physiology. Even though the function of maintaining homeostasis is often linked to the concentric layers of medial elastic lamellae, how the lamellae are capable of evenly distributing the stress transmurally remains to be understood. The recent microstructural study by Yu et al. (2018 J. R. Soc. Interface 15, 20180492) revealed that, circumferentially, lamellar layers closer to the lumen are wavier than the ones further away from it and, thus, experience more unfolding when subjected to blood pressure. Motivated by this peculiar finding, the current study, for the first time, proposes a novel approach to model elastic lamellae and such structural heterogeneity using the extensible worm-like chain model. When implemented into the material description of the conventional two-layer artery model, in which adventitial collagen is modelled using the inextensible worm-like chain model, it is demonstrated that structural heterogeneity in elastic lamellae plays an important role in dictating transmural stress distribution and, therefore, the homeostasis of the arterial wall.
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Affiliation(s)
- Taisiya Sigaeva
- Department of Systems Design Engineering, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
| | - Yanhang Zhang
- Department of Mechanical Engineering, Boston University, Boston, MA 02215, USA
- Department of Biomedical Engineering, Boston University, Boston, MA 02215, USA
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5
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Guo Y, Mofrad MRK, Tepole AB. On modeling the multiscale mechanobiology of soft tissues: Challenges and progress. BIOPHYSICS REVIEWS 2022; 3:031303. [PMID: 38505274 PMCID: PMC10903412 DOI: 10.1063/5.0085025] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/12/2022] [Accepted: 07/12/2022] [Indexed: 03/21/2024]
Abstract
Tissues grow and remodel in response to mechanical cues, extracellular and intracellular signals experienced through various biological events, from the developing embryo to disease and aging. The macroscale response of soft tissues is typically nonlinear, viscoelastic anisotropic, and often emerges from the hierarchical structure of tissues, primarily their biopolymer fiber networks at the microscale. The adaptation to mechanical cues is likewise a multiscale phenomenon. Cell mechanobiology, the ability of cells to transform mechanical inputs into chemical signaling inside the cell, and subsequent regulation of cellular behavior through intra- and inter-cellular signaling networks, is the key coupling at the microscale between the mechanical cues and the mechanical adaptation seen macroscopically. To fully understand mechanics of tissues in growth and remodeling as observed at the tissue level, multiscale models of tissue mechanobiology are essential. In this review, we summarize the state-of-the art modeling tools of soft tissues at both scales, the tissue level response, and the cell scale mechanobiology models. To help the interested reader become more familiar with these modeling frameworks, we also show representative examples. Our aim here is to bring together scientists from different disciplines and enable the future leap in multiscale modeling of tissue mechanobiology.
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Affiliation(s)
- Yifan Guo
- School of Mechanical Engineering, Purdue University, West Lafayette, Indiana 47907, USA
| | - Mohammad R. K. Mofrad
- Departments of Bioengineering and Mechanical Engineering, University of California Berkeley, Berkeley, California 94720, USA
| | - Adrian Buganza Tepole
- School of Mechanical Engineering, Purdue University, West Lafayette, Indiana 47907, USA
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6
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Teixeira FS, Neufeld E, Kuster N, Watton PN. Modeling intracranial aneurysm stability and growth: an integrative mechanobiological framework for clinical cases. Biomech Model Mechanobiol 2020; 19:2413-2431. [PMID: 32533497 PMCID: PMC7603456 DOI: 10.1007/s10237-020-01351-2] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/13/2019] [Accepted: 05/12/2020] [Indexed: 11/03/2022]
Abstract
We present a novel patient-specific fluid-solid-growth framework to model the mechanobiological state of clinically detected intracranial aneurysms (IAs) and their evolution. The artery and IA sac are modeled as thick-walled, non-linear elastic fiber-reinforced composites. We represent the undulation distribution of collagen fibers: the adventitia of the healthy artery is modeled as a protective sheath whereas the aneurysm sac is modeled to bear load within physiological range of pressures. Initially, we assume the detected IA is stable and then consider two flow-related mechanisms to drive enlargement: (1) low wall shear stress; (2) dysfunctional endothelium which is associated with regions of high oscillatory flow. Localized collagen degradation and remodelling gives rise to formation of secondary blebs on the aneurysm dome. Restabilization of blebs is achieved by remodelling of the homeostatic collagen fiber stretch distribution. This integrative mechanobiological modelling workflow provides a step towards a personalized risk-assessment and treatment of clinically detected IAs.
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Affiliation(s)
| | - Esra Neufeld
- IT’IS Foundation & ETH Zürich, Zürich, Switzerland
| | - Niels Kuster
- IT’IS Foundation & ETH Zürich, Zürich, Switzerland
| | - Paul N. Watton
- Department of Computer Science, Insigneo Institute for in silico Medicine, University of Sheffield, Sheffield, UK
- Department of Mechanical Engineering and Materials Science, University of Pittsburgh, Pittsburgh, USA
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7
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Maiti S, Thunes JR, Fortunato RN, Gleason TG, Vorp DA. Computational modeling of the strength of the ascending thoracic aortic media tissue under physiologic biaxial loading conditions. J Biomech 2020; 108:109884. [PMID: 32635998 DOI: 10.1016/j.jbiomech.2020.109884] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/10/2020] [Revised: 05/10/2020] [Accepted: 06/06/2020] [Indexed: 12/23/2022]
Abstract
Type A Aortic Dissection (TAAD) is a life-threatening condition involving delamination of ascending aortic media layers. While current clinical guidelines recommend surgical intervention for aneurysm diameter > 5.5 cm, high incidence of TAAD in patients below this diameter threshold indicates the pressing need for improved evidence-based risk prediction metrics. Construction of such metrics will require the knowledge of the biomechanical failure properties of the aortic wall tissue under biaxial loading conditions. We utilized a fiber-level finite element based structural model of the aortic tissue to quantify the relationship between aortic tissue strength and physiologically relevant biaxial stress state for nonaneurysmal and aneurysmal patient cohorts with tricuspid aortic valve phenotype. We found that the model predicted strength of the aortic tissue under physiologic biaxial loading conditions depends on the stress biaxiality ratio, defined by the ratio of the longitudinal and circumferential components of the tissue stress. We determined that predicted biaxial tissue strength is statistically similar to its uniaxial circumferential strength below biaxiality ratios of 0.68 and 0.69 for nonaneurysmal and aneurysmal cohorts, respectively. Beyond this biaxiality ratio, predicted biaxial strength for both cohorts reduced drastically to a magnitude statistically similar to its longitudinal strength. We identified fiber-level failure mechanisms operative under biaxial stress state governing aforementioned tissue failure behavior. These findings are an important first step towards the development of mechanism-based TAAD risk assessment metrics for early identification of high-risk patients.
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Affiliation(s)
- Spandan Maiti
- Department of Bioengineering, University of Pittsburgh, Pittsburgh, PA, United States; Chemical and Petroleum Engineering, University of Pittsburgh, Pittsburgh, PA, United States; Mechanical Engineering and Materials Science, University of Pittsburgh, Pittsburgh, PA, United States.
| | | | - Ronald N Fortunato
- Mechanical Engineering and Materials Science, University of Pittsburgh, Pittsburgh, PA, United States
| | - Thomas G Gleason
- Department of Bioengineering, University of Pittsburgh, Pittsburgh, PA, United States; Cardiothoracic Surgery, University of Pittsburgh, Pittsburgh, PA, United States; Surgery, University of Pittsburgh, Pittsburgh, PA, United States; Center for Vascular Remodeling and Regeneration, University of Pittsburgh, Pittsburgh, PA, United States; Center for Vascular Remodeling and Regeneration, University of Pittsburgh, Pittsburgh, PA, United States
| | - David A Vorp
- Department of Bioengineering, University of Pittsburgh, Pittsburgh, PA, United States; Chemical and Petroleum Engineering, University of Pittsburgh, Pittsburgh, PA, United States; Cardiothoracic Surgery, University of Pittsburgh, Pittsburgh, PA, United States; Surgery, University of Pittsburgh, Pittsburgh, PA, United States; Center for Vascular Remodeling and Regeneration, University of Pittsburgh, Pittsburgh, PA, United States; McGowan Institute for Regenerative Medicine, University of Pittsburgh, Pittsburgh, PA, United States; Clinical and Translational Sciences Institute, University of Pittsburgh, Pittsburgh, PA, United States
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8
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López-Campos JA, Ferreira JPS, Segade A, Fernández JR, Natal RM. Characterization of hyperelastic and damage behavior of tendons. Comput Methods Biomech Biomed Engin 2020; 23:213-223. [PMID: 31958016 DOI: 10.1080/10255842.2019.1710742] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
Abstract
In this paper, we characterized the hyperelastic and damage behavior of the Extensor Digitorum Longus (EDL) human tendon under loading conditions. The study was conducted in both categories of models, phenomenological and physically motivated, to allow the prediction and the macroscopic response of the tendon under specific loading conditions, assuming that its response follows a hyperelastic anisotropic model in conjunction with damage law. We benchmarked multiple hyperelastic and damage models to fit the response of the tendons in uniaxial tensile loading conditions, and by employing a genetic algorithm, we obtained the material parameters for both elastic and damage models. The objective of this study was to explore different mathematical models to determine which would be the best option to predict the behavior of tendons and ligaments in complex biological systems using Finite Elements (FE) models. Therefore, we took into account accuracy as well as computational features. We considered the model proposed by Shearer and coupled it with a sigmoid function, which governs the evolution of damage in tendons, as the most appropriate for the fitting of the experimental data. The achieved solution shows to be of high interest attributable to the simplicity of the damage law function and its low computational cost.
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Affiliation(s)
- J A López-Campos
- Departamento de Ingeniería Mecánica, Máquinas y Motores Térmicos y Fluídos, Universidade de Vigo, Escola de Enxeñería Industrial, Vigo, Spain
| | - J P S Ferreira
- Faculdade de Engenharia da Universidade do Porto, Porto, Portugal
| | - A Segade
- Departamento de Ingeniería Mecánica, Máquinas y Motores Térmicos y Fluídos, Universidade de Vigo, Escola de Enxeñería Industrial, Vigo, Spain
| | - J R Fernández
- Departamento de Matemática Aplicada I, Universidade de Vigo, ETSI Telecomunicación, Vigo, Spain
| | - R M Natal
- Faculdade de Engenharia da Universidade do Porto, Porto, Portugal
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9
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Niestrawska JA, Augustin CM, Plank G. Computational modeling of cardiac growth and remodeling in pressure overloaded hearts-Linking microstructure to organ phenotype. Acta Biomater 2020; 106:34-53. [PMID: 32058078 PMCID: PMC7311197 DOI: 10.1016/j.actbio.2020.02.010] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/08/2019] [Revised: 02/06/2020] [Accepted: 02/07/2020] [Indexed: 12/25/2022]
Abstract
Cardiac growth and remodeling (G&R) refers to structural changes in myocardial tissue in response to chronic alterations in loading conditions. One such condition is pressure overload where elevated wall stresses stimulate the growth in cardiomyocyte thickness, associated with a phenotype of concentric hypertrophy at the organ scale, and promote fibrosis. The initial hypertrophic response can be considered adaptive and beneficial by favoring myocyte survival, but over time if pressure overload conditions persist, maladaptive mechanisms favoring cell death and fibrosis start to dominate, ultimately mediating the transition towards an overt heart failure phenotype. The underlying mechanisms linking biological factors at the myocyte level to biomechanical factors at the systemic and organ level remain poorly understood. Computational models of G&R show high promise as a unique framework for providing a quantitative link between myocardial stresses and strains at the organ scale to biological regulatory processes at the cellular level which govern the hypertrophic response. However, microstructurally motivated, rigorously validated computational models of G&R are still in their infancy. This article provides an overview of the current state-of-the-art of computational models to study cardiac G&R. The microstructure and mechanosensing/mechanotransduction within cells of the myocardium is discussed and quantitative data from previous experimental and clinical studies is summarized. We conclude with a discussion of major challenges and possible directions of future research that can advance the current state of cardiac G&R computational modeling. STATEMENT OF SIGNIFICANCE: The mechanistic links between organ-scale biomechanics and biological factors at the cellular size scale remain poorly understood as these are largely elusive to investigations using experimental methodology alone. Computational G&R models show high promise to establish quantitative links which allow more mechanistic insight into adaptation mechanisms and may be used as a tool for stratifying the state and predict the progression of disease in the clinic. This review provides a comprehensive overview of research in this domain including a summary of experimental data. Thus, this study may serve as a basis for the further development of more advanced G&R models which are suitable for making clinical predictions on disease progression or for testing hypotheses on pathogenic mechanisms using in-silico models.
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Affiliation(s)
- Justyna A Niestrawska
- Gottfried Schatz Research Center: Division of Biophysics, Medical University of Graz, Graz 8010, Austria
| | - Christoph M Augustin
- Gottfried Schatz Research Center: Division of Biophysics, Medical University of Graz, Graz 8010, Austria.
| | - Gernot Plank
- Gottfried Schatz Research Center: Division of Biophysics, Medical University of Graz, Graz 8010, Austria; BioTechMed-Graz, Austria
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10
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Bhogal P, Pederzani G, Grytsan A, Loh Y, Brouwer PA, Andersson T, Gundiah N, Robertson AM, Watton PN, Söderman M. The unexplained success of stentplasty vasospasm treatment : Insights using Mechanistic Mathematical Modeling. Clin Neuroradiol 2019; 29:763-774. [PMID: 30915482 DOI: 10.1007/s00062-019-00776-2] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/09/2018] [Accepted: 03/08/2019] [Indexed: 11/29/2022]
Abstract
BACKGROUND Cerebral vasospasm (CVS) following subarachnoid hemorrhage occurs in up to 70% of patients. Recently, stents have been used to successfully treat CVS. This implies that the force required to expand spastic vessels and resolve vasospasm is lower than previously thought. OBJECTIVE We develop a mechanistic model of the spastic arterial wall to provide insight into CVS and predict the forces required to treat it. MATERIAL AND METHODS The arterial wall is modelled as a cylindrical membrane using a constrained mixture theory that accounts for the mechanical roles of elastin, collagen and vascular smooth muscle cells (VSMC). We model the pressure diameter curve prior to CVS and predict how it changes following CVS. We propose a stretch-based damage criterion for VSMC and evaluate if several commercially available stents are able to resolve vasospasm. RESULTS The model predicts that dilatation of VSMCs beyond a threshold of mechanical failure is sufficient to resolve CVS without damage to the underlying extracellular matrix. Consistent with recent clinical observations, our model predicts that existing stents have the potential to provide sufficient outward force to successfully treat CVS and that success will be dependent on an appropriate match between stent and vessel. CONCLUSION Mathematical models of CVS can provide insights into biological mechanisms and explore treatment approaches. Improved understanding of the underlying mechanistic processes governing CVS and its mechanical treatment may assist in the development of dedicated stents.
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Affiliation(s)
- P Bhogal
- Department of Interventional Neuroradiology, The Royal London Hospital, Whitechapel Road, E1 1BB, London, UK.
| | - G Pederzani
- Department of Computer Science, University of Sheffield, Sheffield, UK.,Insigneo Institute for in silico Medicine, University of Sheffield, Sheffield, UK
| | - A Grytsan
- Insigneo Institute for in silico Medicine, University of Sheffield, Sheffield, UK
| | - Y Loh
- Uniformed Services University, University of California, Los Angeles, USA.,Swedish Neuroscience Institute, 550 17th Avenue Seattle, 98122, Washington, USA
| | - P A Brouwer
- The Karolinska University Hospital, 171 76, Stockholm, Sweden
| | - T Andersson
- The Karolinska University Hospital, 171 76, Stockholm, Sweden.,AZ Groeninge, Kortrijk, Belgium
| | - Namrata Gundiah
- Department of Mechanical Engineering, Indian Institute of Science, Bangalore, India
| | - Anne M Robertson
- Department of Mechanical Engineering and Materials Science, University of Pittsburgh, Pittsburgh, PA, USA
| | - Paul N Watton
- Department of Computer Science, University of Sheffield, Sheffield, UK.,Insigneo Institute for in silico Medicine, University of Sheffield, Sheffield, UK.,Department of Mechanical Engineering and Materials Science, University of Pittsburgh, Pittsburgh, PA, USA
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11
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Reesink KD, Spronck B. Constitutive interpretation of arterial stiffness in clinical studies: a methodological review. Am J Physiol Heart Circ Physiol 2019; 316:H693-H709. [DOI: 10.1152/ajpheart.00388.2018] [Citation(s) in RCA: 17] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 01/15/2023]
Abstract
Clinical assessment of arterial stiffness relies on noninvasive measurements of regional pulse wave velocity or local distensibility. However, arterial stiffness measures do not discriminate underlying changes in arterial wall constituent properties (e.g., in collagen, elastin, or smooth muscle), which is highly relevant for development and monitoring of treatment. In arterial stiffness in recent clinical-epidemiological studies, we systematically review clinical-epidemiological studies (2012–) that interpreted arterial stiffness changes in terms of changes in arterial wall constituent properties (63 studies included of 514 studies found). Most studies that did so were association studies (52 of 63 studies) providing limited causal evidence. Intervention studies (11 of 63 studies) addressed changes in arterial stiffness through the modulation of extracellular matrix integrity (5 of 11 studies) or smooth muscle tone (6 of 11 studies). A handful of studies (3 of 63 studies) used mathematical modeling to discriminate between extracellular matrix components. Overall, there exists a notable gap in the mechanistic interpretation of stiffness findings. In constitutive model-based interpretation, we first introduce constitutive-based modeling and use it to illustrate the relationship between constituent properties and stiffness measurements (“forward” approach). We then review all literature on modeling approaches for the constitutive interpretation of clinical arterial stiffness data (“inverse” approach), which are aimed at estimation of constitutive properties from arterial stiffness measurements to benefit treatment development and monitoring. Importantly, any modeling approach requires a tradeoff between model complexity and measurable data. Therefore, the feasibility of changing in vivo the biaxial mechanics and/or vascular smooth muscle tone should be explored. The effectiveness of modeling approaches should be confirmed using uncertainty quantification and sensitivity analysis. Taken together, constitutive modeling can significantly improve clinical interpretation of arterial stiffness findings.
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Affiliation(s)
- Koen D. Reesink
- Department of Biomedical Engineering, CARIM School for Cardiovascular Diseases, Maastricht University, Maastricht, The Netherlands
| | - Bart Spronck
- Department of Biomedical Engineering, School of Engineering and Applied Science, Yale University, New Haven, Connecticut
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12
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Holzapfel GA, Ogden RW. Biomechanical relevance of the microstructure in artery walls with a focus on passive and active components. Am J Physiol Heart Circ Physiol 2018; 315:H540-H549. [DOI: 10.1152/ajpheart.00117.2018] [Citation(s) in RCA: 30] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
Abstract
The microstructure of arteries, consisting, in particular, of collagen, elastin, and vascular smooth muscle cells, plays a very significant role in their biomechanical response during a cardiac cycle. In this article, we highlight the microstructure and the contributions of each of its components to the overall mechanical behavior. We also describe the changes of the microstructure that occur as a result of abdominal aortic aneurysms and disease, such as atherosclerosis. We also focus on how the passive and active constituents are incorporated into a mathematical model without going into detail of the mathematical formulation. We conclude by mentioning open problems toward a better characterization of the biomechanical aspects of arteries that will be beneficial for a better understanding of cardiovascular pathophysiology.
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Affiliation(s)
- Gerhard A. Holzapfel
- Institute of Biomechanics, Graz University of Technology, Graz, Austria
- Norwegian University of Science and Technology, Faculty of Engineering Science and Technology, Trondheim, Norway
| | - Ray W. Ogden
- School of Mathematics and Statistics, University of Glasgow, Scotland, United Kingdom
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13
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Watson DJ, Sazonov I, Zawieja DC, Moore JE, van Loon R. Integrated geometric and mechanical analysis of an image-based lymphatic valve. J Biomech 2017; 64:172-179. [PMID: 29061390 DOI: 10.1016/j.jbiomech.2017.09.040] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/12/2017] [Revised: 09/12/2017] [Accepted: 09/25/2017] [Indexed: 02/07/2023]
Abstract
Lymphatic valves facilitate the lymphatic system's role in maintaining fluid homeostasis. Malformed valves are found in several forms of primary lymphœdema, resulting in incurable swelling of the tissues and immune dysfunction. Their experimental study is complicated by their small size and operation in low pressure and low Reynolds number environments. Mathematical models of these structures can give insight and complement experimentation. In this work, we present the first valve geometry reconstructed from confocal imagery and used in the construction of a subject-specific model in a closing mode. A framework is proposed whereby an image is converted into a valve model. An FEA study was performed to identify the significance of the shear modulus, the consequences of smoothing the leaflet surface and the effect of wall motion on valve behaviour. Smoothing is inherent to any analysis from imagery. The nature of the image, segmentation and meshing all cause attenuation of high-frequency features. Smoothing not only causes loss of surface area but also the loss of high-frequency geometric features which may reduce stiffness. This work aimed to consider these effects and inform studies by taking a manual reconstruction and through manifold harmonic analysis, attenuating higher frequency features to replicate lower resolution images or lower degree-of-freedom reconstructions. In conclusion, two metrics were considered: trans-valvular pressure required to close the valve, ΔPc, and the retrograde volume displacement after closure. The higher ΔPc, the greater the volume of lymph that will pass through the valve during closure. Retrograde volume displacement after closure gives a metric of compliance of the valve and for the quality of the valve seal. In the case of the image-specific reconstructed valve, removing features with a wavelength longer than four μm caused changes in ΔPc. Varying the shear modulus from 10 kPa to 60 kPa caused a 3.85-fold increase in the retrograde volume displaced. The inclusion of a non-rigid wall caused ΔPc to increase from 1.56 to 2.52 cmH2O.
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Affiliation(s)
- Daniel J Watson
- ZCCE, College of Engineering, Swansea University, United Kingdom
| | - Igor Sazonov
- ZCCE, College of Engineering, Swansea University, United Kingdom
| | - David C Zawieja
- College of Medicine, Texas A&M Health Sciences Center, United States
| | - James E Moore
- Department of Bioengineering, Imperial College London, United Kingdom
| | - Raoul van Loon
- ZCCE, College of Engineering, Swansea University, United Kingdom.
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14
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Uncertainty quantification and sensitivity analysis of an arterial wall mechanics model for evaluation of vascular drug therapies. Biomech Model Mechanobiol 2017; 17:55-69. [PMID: 28755237 PMCID: PMC5807551 DOI: 10.1007/s10237-017-0944-0] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/18/2017] [Accepted: 07/17/2017] [Indexed: 02/07/2023]
Abstract
Quantification of the uncertainty in constitutive model predictions describing arterial wall mechanics is vital towards non-invasive assessment of vascular drug therapies. Therefore, we perform uncertainty quantification to determine uncertainty in mechanical characteristics describing the vessel wall response upon loading. Furthermore, a global variance-based sensitivity analysis is performed to pinpoint measurements that are most rewarding to be measured more precisely. We used previously published carotid diameter–pressure and intima–media thickness (IMT) data (measured in triplicate), and Holzapfel–Gasser–Ogden models. A virtual data set containing 5000 diastolic and systolic diameter–pressure points, and IMT values was generated by adding measurement error to the average of the measured data. The model was fitted to single-exponential curves calculated from the data, obtaining distributions of constitutive parameters and constituent load bearing parameters. Additionally, we (1) simulated vascular drug treatment to assess the relevance of model uncertainty and (2) evaluated how increasing the number of measurement repetitions influences model uncertainty. We found substantial uncertainty in constitutive parameters. Simulating vascular drug treatment predicted a 6% point reduction in collagen load bearing (\documentclass[12pt]{minimal}
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\begin{document}$$L_\mathrm {coll}$$\end{document}Lcoll), approximately 50% of its uncertainty. Sensitivity analysis indicated that the uncertainty in \documentclass[12pt]{minimal}
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\begin{document}$$L_{\mathrm {coll}}$$\end{document}Lcoll could be decreased by 50% when increasing the number of measurement repetitions from 3 to 10. Model uncertainty, notably that in \documentclass[12pt]{minimal}
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\begin{document}$$L_{\mathrm {coll}}$$\end{document}Lcoll, could conceal effects of vascular drug therapy. However, this uncertainty could be reduced by increasing the number of measurement repetitions of distension and wall thickness measurements used for model parameterisation.
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15
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de Gelidi S, Tozzi G, Bucchi A. The effect of thickness measurement on numerical arterial models. MATERIALS SCIENCE & ENGINEERING. C, MATERIALS FOR BIOLOGICAL APPLICATIONS 2017; 76:1205-1215. [DOI: 10.1016/j.msec.2017.02.123] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/24/2016] [Revised: 02/03/2017] [Accepted: 02/24/2017] [Indexed: 10/20/2022]
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16
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Cyron CJ, Humphrey JD. Growth and Remodeling of Load-Bearing Biological Soft Tissues. MECCANICA 2017; 52:645-664. [PMID: 28286348 PMCID: PMC5342900 DOI: 10.1007/s11012-016-0472-5] [Citation(s) in RCA: 81] [Impact Index Per Article: 11.6] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/03/2023]
Abstract
The past two decades reveal a growing role of continuum biomechanics in understanding homeostasis, adaptation, and disease progression in soft tissues. In this paper, we briefly review the two primary theoretical approaches for describing mechano-regulated soft tissue growth and remodeling on the continuum level as well as hybrid approaches that attempt to combine the advantages of these two approaches while avoiding their disadvantages. We also discuss emerging concepts, including that of mechanobiological stability. Moreover, to motivate and put into context the different theoretical approaches, we briefly review findings from mechanobiology that show the importance of mass turnover and the prestressing of both extant and new extracellular matrix in most cases of growth and remodeling. For illustrative purposes, these concepts and findings are discussed, in large part, within the context of two load-bearing, collagen dominated soft tissues - tendons/ligaments and blood vessels. We conclude by emphasizing further examples, needs, and opportunities in this exciting field of modeling soft tissues.
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Affiliation(s)
- C J Cyron
- Institute for Computational Mechanics, Technische Universität München, Garching, Germany
| | - J D Humphrey
- Department of Biomedical Engineering, Yale University, New Haven, CT, USA; Vascular Biology and Therapeutics Program, Yale School of Medicine, New Haven, CT, USA
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17
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Laksari K, Shahmirzadi D, Acosta CJ, Konofagou E. Energy-based constitutive modelling of local material properties of canine aortas. ROYAL SOCIETY OPEN SCIENCE 2016; 3:160365. [PMID: 27703701 PMCID: PMC5043320 DOI: 10.1098/rsos.160365] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/24/2016] [Accepted: 08/24/2016] [Indexed: 05/05/2023]
Abstract
This study aims at determining the in vitro anisotropic mechanical behaviour of canine aortic tissue. We specifically focused on spatial variations of these properties along the axis of the vessel. We performed uniaxial stretch tests on canine aortic samples in both circumferential and longitudinal directions, as well as histological examinations to derive the tissue's fibre orientations. We subsequently characterized a constitutive model that incorporates both phenomenological and structural elements to account for macroscopic and microstructural behaviour of the tissue. We showed the two fibre families were oriented at similar angles with respect to the aorta's axis. We also found significant changes in mechanical behaviour of the tissue as a function of axial position from proximal to distal direction: the fibres become more aligned with the aortic axis from 46° to 30°. Also, the linear shear modulus of media decreased as we moved distally along the aortic axis from 139 to 64 kPa. These changes derived from the parameters in the nonlinear constitutive model agreed well with the changes in tissue structure. In addition, we showed that isotropic contribution, carried by elastic lamellae, to the total stress induced in the tissue decreases at higher stretch ratios, whereas anisotropic stress, carried by collagen fibres, increases. The constitutive models can be readily used to design computational models of tissue deformation during physiological loading cycles. The findings of this study extend the understanding of local mechanical properties that could lead to region-specific diagnostics and treatment of arterial diseases.
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Affiliation(s)
- Kaveh Laksari
- Department of Bioengineering, Stanford University, Stanford, CA, USA
- Author for correspondence: Kaveh Laksari e-mail:
| | - Danial Shahmirzadi
- Department of Mechanical Engineering, Stevens Institute of Technology, Hoboken, NJ, USA
| | - Camilo J. Acosta
- Ultrasound and Elasticity Imaging Lab (UEIL), Department of Biomedical Engineering, Columbia University, New York, NY, USA
| | - Elisa Konofagou
- Ultrasound and Elasticity Imaging Lab (UEIL), Department of Biomedical Engineering, Columbia University, New York, NY, USA
- Department of Radiology, Columbia University, New York, NY, USA
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18
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Taghizadeh H, Tafazzoli-Shadpour M. Characterization of mechanical properties of lamellar structure of the aortic wall: Effect of aging. J Mech Behav Biomed Mater 2016; 65:20-28. [PMID: 27544616 DOI: 10.1016/j.jmbbm.2016.08.011] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/11/2016] [Revised: 07/18/2016] [Accepted: 08/03/2016] [Indexed: 11/27/2022]
Abstract
Arterial wall tissues are sensitive to their mechanical surroundings and remodel their structure and mechanical properties when subjected to mechanical stimuli such as increased arterial pressure. Such remodeling is evident in hypertension and aging. Aging is characterized by stiffening of the artery wall which is assigned to disturbed elastin function and increased collagen content. To better understand and provide new insight on microstructural changes induced by aging, the lamellar model of the aortic media was utilized to characterize and compare wall structure and mechanical behavior of the young and old human thoracic aortic samples. Such model regards arterial media as two sets of alternating concentric layers, namely sheets of elastin and interlamellar layers. Histological and biaxial tests were performed and microstructural features and stress-strain curves of media were evaluated in young and old age groups. Then using optimization algorithms and hyperelastic constitutive equations the stress-strain curves of layers were evaluated for both age groups. Results indicated slight elevation in the volume fraction of interlamellar layer among old subjects most probably due to age related collagen deposition. Aging indicated substantial stiffening of interlamellar layers accompanied by noticeable softening of elastic lamellae. The general significant stiffening of old samples were attributed to both increase of volume fraction of interlamellar layers and earlier recruitment of collagen fibers during load bearing due to functional loss of elastin within wall lamellae. Mechanical characterization of lamellar structure of wall media is beneficial in study of arterial remodeling in response to alternated mechanical environment in aging and clinical conditions through coupling of wall microstructure and mechanical behavior.
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Affiliation(s)
- Hadi Taghizadeh
- Division of Biomechanics, Mechanical Engineering Department, Sahand University of Technology, Tabriz 51335-1996, Iran.
| | - Mohammad Tafazzoli-Shadpour
- Cardiovascular Engineering Laboratory, Faculty of Biomedical Engineering, Amirkabir University of Technology, 424 Hafez Ave., Tehran 15875-4413, Iran.
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19
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Effects of the three-dimensional residual stresses on the mechanical properties of arterial walls. J Theor Biol 2016; 393:118-26. [DOI: 10.1016/j.jtbi.2015.12.015] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/14/2015] [Revised: 12/25/2015] [Accepted: 12/28/2015] [Indexed: 11/21/2022]
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20
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Tian L, Wang Z, Liu Y, Eickhoff JC, Eliceiri KW, Chesler NC. Validation of an arterial constitutive model accounting for collagen content and crosslinking. Acta Biomater 2016; 31:276-287. [PMID: 26654765 DOI: 10.1016/j.actbio.2015.11.058] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/03/2015] [Revised: 11/20/2015] [Accepted: 11/29/2015] [Indexed: 11/19/2022]
Abstract
During the progression of pulmonary hypertension (PH), proximal pulmonary arteries (PAs) increase in both thickness and stiffness. Collagen, a component of the extracellular matrix, is mainly responsible for these changes via increased collagen fiber amount (or content) and crosslinking. We sought to differentiate the effects of collagen content and cross-linking on mouse PA mechanical changes using a constitutive model with parameters derived from experiments in which collagen content and cross-linking were decoupled during hypoxic pulmonary hypertension (HPH). We employed an eight-chain orthotropic element model to characterize collagen's mechanical behavior and an isotropic neo-Hookean form to represent elastin. Our results showed a strong correlation between the material parameter related to collagen content and measured collagen content (R(2)=0.82, P<0.0001) and a moderate correlation between the material parameter related to collagen crosslinking and measured crosslinking (R(2)=0.24, P=0.06). There was no significant change in either the material parameter related to elastin or the measured elastin content from histology. The model-predicted pressure at which collagen begins to engage was ∼25mmHg, which is consistent with experimental observations. We conclude that this model may allow us to predict changes in the arterial extracellular matrix from measured mechanical behavior in PH patients, which may provide insight into prognoses and the effects of therapy. STATEMENT OF SIGNIFICANCE The literature has proposed several constitutive models to describe the mechanical effects of arterial collagen but none separates collagen content from crosslinking. Given that both are critical to arterial mechanics, the novel model described here does so. Furthermore, our novel model is well tested by experimental data; model parameters were reasonably correlated with measured collagen content and crosslinking and the model-predicted collagen transition stretch was consistent with that obtained experimentally. Given that arterial collagen structural changes and collagen engagement are critical to arterial stiffening in several disease states, this model, by linking mechanical and biological properties, may allow us to predict important biological changes during disease progression from measured mechanical behavior.
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Affiliation(s)
- Lian Tian
- Department of Biomedical Engineering, University of Wisconsin-Madison, Madison, WI, USA
| | - Zhijie Wang
- Department of Biomedical Engineering, University of Wisconsin-Madison, Madison, WI, USA
| | - Yuming Liu
- Laboratory for Optical and Computational Instrumentation, University of Wisconsin-Madison, Madison, WI, USA
| | - Jens C Eickhoff
- Department of Biostatistics and Medical Informatics, University of Wisconsin-Madison, Madison, WI, USA
| | - Kevin W Eliceiri
- Laboratory for Optical and Computational Instrumentation, University of Wisconsin-Madison, Madison, WI, USA
| | - Naomi C Chesler
- Department of Biomedical Engineering, University of Wisconsin-Madison, Madison, WI, USA.
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21
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Farías JG, Herrera EA, Carrasco-Pozo C, Sotomayor-Zárate R, Cruz G, Morales P, Castillo RL. Pharmacological models and approaches for pathophysiological conditions associated with hypoxia and oxidative stress. Pharmacol Ther 2015; 158:1-23. [PMID: 26617218 DOI: 10.1016/j.pharmthera.2015.11.006] [Citation(s) in RCA: 47] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023]
Abstract
Hypoxia is the failure of oxygenation at the tissue level, where the reduced oxygen delivered is not enough to satisfy tissue demands. Metabolic depression is the physiological adaptation associated with reduced oxygen consumption, which evidently does not cause any harm to organs that are exposed to acute and short hypoxic insults. Oxidative stress (OS) refers to the imbalance between the generation of reactive oxygen species (ROS) and the ability of endogenous antioxidant systems to scavenge ROS, where ROS overwhelms the antioxidant capacity. Oxidative stress plays a crucial role in the pathogenesis of diseases related to hypoxia during intrauterine development and postnatal life. Thus, excessive ROS are implicated in the irreversible damage to cell membranes, DNA, and other cellular structures by oxidizing lipids, proteins, and nucleic acids. Here, we describe several pathophysiological conditions and in vivo and ex vivo models developed for the study of hypoxic and oxidative stress injury. We reviewed existing literature on the responses to hypoxia and oxidative stress of the cardiovascular, renal, reproductive, and central nervous systems, and discussed paradigms of chronic and intermittent hypobaric hypoxia. This systematic review is a critical analysis of the advantages in the application of some experimental strategies and their contributions leading to novel pharmacological therapies.
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Affiliation(s)
- Jorge G Farías
- Facultad de Ingeniería y Ciencias, Departamento de Ingeniería Química, Universidad de la Frontera, Casilla 54-D, Temuco, Chile
| | - Emilio A Herrera
- Programa de Fisiopatología, ICBM, Facultad de Medicina, Universidad de Chile, Chile; International Center for Andean Studies (INCAS), Universidad de Chile, Chile
| | | | - Ramón Sotomayor-Zárate
- Centro de Neurobiología y Plasticidad Cerebral (CNPC), Instituto de Fisiología, Facultad de Ciencias, Universidad de Valparaíso, Chile
| | - Gonzalo Cruz
- Centro de Neurobiología y Plasticidad Cerebral (CNPC), Instituto de Fisiología, Facultad de Ciencias, Universidad de Valparaíso, Chile
| | - Paola Morales
- Programa de Farmacología Molecular y Clínica, ICBM, Facultad de Medicina, Universidad de Chile, Chile
| | - Rodrigo L Castillo
- Programa de Fisiopatología, ICBM, Facultad de Medicina, Universidad de Chile, Chile.
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22
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Tonar Z, Kubíková T, Prior C, Demjén E, Liška V, Králíčková M, Witter K. Segmental and age differences in the elastin network, collagen, and smooth muscle phenotype in the tunica media of the porcine aorta. Ann Anat 2015; 201:79-90. [DOI: 10.1016/j.aanat.2015.05.005] [Citation(s) in RCA: 27] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/19/2014] [Revised: 05/26/2015] [Accepted: 05/26/2015] [Indexed: 12/18/2022]
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23
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Wilson JT, van Loon R, Wang W, Zawieja DC, Moore JE. Determining the combined effect of the lymphatic valve leaflets and sinus on resistance to forward flow. J Biomech 2015; 48:3584-90. [PMID: 26315921 DOI: 10.1016/j.jbiomech.2015.07.045] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/16/2015] [Revised: 07/23/2015] [Accepted: 07/30/2015] [Indexed: 10/23/2022]
Abstract
The lymphatic system is vital to a proper maintenance of fluid and solute homeostasis. Collecting lymphatics are composed of actively contracting tubular vessels segmented by bulbous sinus regions that encapsulate bi-leaflet check valves. Valve resistance to forward flow strongly influences pumping performance. However, because of the sub-millimeter size of the vessels with flow rates typically <1 ml/h and pressures of a few cmH2O, resistance is difficult to measure experimentally. Using a newly defined idealized geometry, we employed an uncoupled approach where the solid leaflet deflections of the open valve were computed and lymph flow calculations were subsequently performed. We sought to understand: 1) the effect of sinus and leaflet size on the resulting deflections experienced by the valve leaflets and 2) the effects on valve resistance to forward flow of the fully open valve. For geometries with sinus-to-root diameter ratios >1.39, the average resistance to forward flow was 0.95×10(6)[g/(cm4 s)]. Compared to the viscous pressure drop that would occur in a straight tube the same diameter as the upstream lymphangion, valve leaflets alone increase the pressure drop up to 35%. However, the presence of the sinus reduces viscous losses, with the net effect that when combined with leaflets the overall resistance is less than that of the equivalent continuing straight tube. Accurately quantifying resistance to forward flow will add to the knowledge used to develop therapeutics for treating lymphatic disorders and may eventually lead to understanding some forms of primary lymphedema.
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Affiliation(s)
- John T Wilson
- Department of Bioengineering, Imperial College London, South Kensington Campus, London SW7 2AZ, UK
| | - Raoul van Loon
- College of Engineering, Swansea University, Singleton Park, Swansea SA2 8PP, UK
| | - Wei Wang
- Department of Medical Physiology, Texas A&M Health Science Center, 702 Southwest H.K. Dodgen Loop, Temple, TX 76504, USA
| | - David C Zawieja
- Department of Medical Physiology, Texas A&M Health Science Center, 702 Southwest H.K. Dodgen Loop, Temple, TX 76504, USA
| | - James E Moore
- Department of Bioengineering, Imperial College London, South Kensington Campus, London SW7 2AZ, UK.
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24
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Effect of glucose on the biomechanical function of arterial elastin. J Mech Behav Biomed Mater 2015; 49:244-54. [PMID: 26042769 DOI: 10.1016/j.jmbbm.2015.04.025] [Citation(s) in RCA: 29] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/14/2015] [Revised: 04/16/2015] [Accepted: 04/27/2015] [Indexed: 01/15/2023]
Abstract
Elastin is essential to provide elastic support for blood vessels. As a remarkably long-lived protein, elastin can suffer from cumulative effects of exposure to biochemical damages, which can greatly compromise its biomechanical properties. Non-enzymatic glycation is one of the main mechanisms of aging and its effect is magnified in diabetic patients. The purpose of this study is to investigate the effects of glucose on mechanical properties of isolated porcine aortic elastin. Elastin samples were incubated in 2 M glucose solution and were allowed to equilibrate for 4, 7, 14, 21 or 28 days at 37 °C. Equibiaxial tensile tests were performed to study the changes of elastic properties of elastin due to glycation. Significant decreases in tissue dimension were observed after 7 days glucose incubation. Elastin samples treated for 14, 21 or 28 days demonstrate a significant increase in hysteresis in the stress-stretch curves, indicating a greater energy loss due to glucose treatment. Both the longitudinal and the circumferential directions show significant increases in tangent modulus with glucose treatment, however only significant increases are observed after 7 days for the circumferential direction. An eight-chain statistical mechanics based microstructural model was used to study the hyperelastic and orthotropic behavior of the glucose-treated elastin and the material parameters were estimated using a nonlinear least squares method. Material parameters in the model were related to elastin density and fiber orientation, and, hence, the possible microstructural changes in glucose-treated elastin. Estimated material parameters show a general increasing trend in elastin density per unit volume with glucose incubation. The simulation results also indicate that more elastic fibers are aligned in the longitudinal and circumferential directions, rather than in the radial direction.
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25
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Schriefl AJ, Schmidt T, Balzani D, Sommer G, Holzapfel GA. Selective enzymatic removal of elastin and collagen from human abdominal aortas: uniaxial mechanical response and constitutive modeling. Acta Biomater 2015; 17:125-36. [PMID: 25623592 DOI: 10.1016/j.actbio.2015.01.003] [Citation(s) in RCA: 50] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/23/2014] [Revised: 10/31/2014] [Accepted: 01/05/2015] [Indexed: 02/01/2023]
Abstract
The ability to selectively remove the structurally most relevant components of arterial wall tissues such as collagen and elastin enables ex vivo biomechanical testing of the remaining tissues, with the aim of assessing their individual mechanical contributions. Resulting passive material parameters can be utilized in mathematical models of the cardiovascular system. Using eighteen wall specimens from non-atherosclerotic human abdominal aortas (55 ± 11 years; 9 female, 9 male), we tested enzymatic approaches for the selective digestion of collagen and elastin, focusing on their application to human abdominal aortic wall tissues from different patients with varying sample morphologies. The study resulted in an improved protocol for elastin removal, showing how the enzymatic process is affected by inadequate addition of trypsin inhibitor. We applied the resulting protocol to circumferential and axial specimens from the media and the adventitia, and performed cyclic uniaxial extension tests in the physiological and supra-physiological loading domain. The collagenase-treated samples showed a (linear) response without distinct softening behavior, while the elastase-treated samples exhibited a nonlinear, anisotropic response with pronounced remanent deformations (continuous softening), presumably caused by some sliding of collagen fibers within the damaged regions of the collagen network. In addition, our data showed that the stiffness in the initial linear stress-stretch regime at low loads is lower in elastin-free tissue compared to control samples (i.e. collagen uncrimping requires less force than the stretching of elastin), experimentally confirming that elastin is responsible for the initial stiffness in elastic arteries. Utilizing a continuum mechanical description to mathematically capture the experimental results we concluded that the inclusion of a damage model for the non-collagenous matrix material is, in general, not necessary. To model the softening behavior, continuous damage was included in the fibers by adding a damage variable which led to remanent strains through the consideration of damage.
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Affiliation(s)
| | - Thomas Schmidt
- University of Duisburg-Essen, Institute of Mechanics, Germany
| | - Daniel Balzani
- Dresden University of Technology, Faculty of Civil Engineering, Germany
| | - Gerhard Sommer
- Graz University of Technology, Institute of Biomechanics, Austria
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Grytsan A, Watton PN, Holzapfel GA. A Thick-Walled Fluid–Solid-Growth Model of Abdominal Aortic Aneurysm Evolution: Application to a Patient-Specific Geometry. J Biomech Eng 2015; 137:2020812. [DOI: 10.1115/1.4029279] [Citation(s) in RCA: 36] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/20/2014] [Indexed: 11/08/2022]
Abstract
We propose a novel thick-walled fluid–solid-growth (FSG) computational framework for modeling vascular disease evolution. The arterial wall is modeled as a thick-walled nonlinearly elastic cylindrical tube consisting of two layers corresponding to the media-intima and adventitia, where each layer is treated as a fiber-reinforced material with the fibers corresponding to the collagenous component. Blood is modeled as a Newtonian fluid with constant density and viscosity; no slip and no-flux conditions are applied at the arterial wall. Disease progression is simulated by growth and remodeling (G&R) of the load bearing constituents of the wall. Adaptions of the natural reference configurations and mass densities of constituents are driven by deviations of mechanical stimuli from homeostatic levels. We apply the novel framework to model abdominal aortic aneurysm (AAA) evolution. Elastin degradation is initially prescribed to create a perturbation to the geometry which results in a local decrease in wall shear stress (WSS). Subsequent degradation of elastin is driven by low WSS and an aneurysm evolves as the elastin degrades and the collagen adapts. The influence of transmural G&R of constituents on the aneurysm development is analyzed. We observe that elastin and collagen strains evolve to be transmurally heterogeneous and this may facilitate the development of tortuosity. This multiphysics framework provides the basis for exploring the influence of transmural metabolic activity on the progression of vascular disease.
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Affiliation(s)
- Andrii Grytsan
- Department of Solid Mechanics, Royal Institute of Technology (KTH), Teknikringen 8d, Stockholm 10044, Sweden
| | - Paul N. Watton
- Department of Computer Science, University of Sheffield, Sheffield, UK
- INSIGNEO Institute of In Silico Medicine, University of Sheffield, Sheffield, UK
| | - Gerhard A. Holzapfel
- Institute of Biomechanics, Graz University of Technology, Kronesgasse 5-I, Graz 8010, Austria e-mail:
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Aparício P, Mandaltsi A, Boamah J, Chen H, Selimovic A, Bratby M, Uberoi R, Ventikos Y, Watton PN. Modelling the influence of endothelial heterogeneity on the progression of arterial disease: application to abdominal aortic aneurysm evolution. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2014; 30:563-586. [PMID: 24424963 DOI: 10.1002/cnm.2620] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/27/2013] [Revised: 09/19/2013] [Accepted: 11/18/2013] [Indexed: 06/03/2023]
Abstract
We sophisticate a fluid-solid growth computational framework for modelling aneurysm evolution. A realistic structural model of the arterial wall is integrated into a patient-specific geometry of the vasculature. This enables physiologically representative distributions of haemodynamic stimuli, obtained from a rigid-wall computational fluid dynamics analysis, to be linked to growth and remodelling algorithms. Additionally, a quasistatic structural analysis quantifies the cyclic deformation of the arterial wall so that collagen growth and remodelling can be explicitly linked to the cyclic deformation of vascular cells. To simulate aneurysm evolution, degradation of elastin is driven by reductions in wall shear stress (WSS) below homeostatic thresholds. Given that the endothelium exhibits spatial and temporal heterogeneity, we propose a novel approach to define the homeostatic WSS thresholds: We allow them to be spatially and temporally heterogeneous. We illustrate the application of this novel fluid-solid growth framework to model abdominal aortic aneurysm (AAA) evolution and to examine how the influence of the definition of the WSS homeostatic threshold influences AAA progression. We conclude that improved understanding and modelling of the endothelial heterogeneity is important for modelling aneurysm evolution and, more generally, other vascular diseases where haemodynamic stimuli play an important role.
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Affiliation(s)
- P Aparício
- Systems Biology Doctoral Training Centre, University of Oxford, Oxford, UK
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28
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Weizsäcker HW, Zierler E, Juch H. A simple method for vital staining of elastin in arterial tissue. BIOMED ENG-BIOMED TE 2014; 59:367-73. [PMID: 24762637 DOI: 10.1515/bmt-2013-0089] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/20/2013] [Accepted: 03/26/2014] [Indexed: 11/15/2022]
Abstract
Highly diluted solutions of Gentian Violet and Evans Blue were used to visualize the elastin network in viable porcine right common carotid artery (RCCA) preparations. The two simple, alternative methods of staining were applied to proximal, intermediate, and distal sections of RCCA under various experimental conditions. These included the state of the vessel wall soon after excision, under relaxed smooth muscle condition after preconditioning, and during vasoconstriction. Micrographs of arterial rings, sectors, and axial strips show that the RCCA is an artery of the elastic type at the proximal end and of the muscular type at the distal end. While in sections of freshly dissected or KCl-constricted arteries the elastic lamellae show the well-known waviness, those in sections from arteries with relaxed smooth muscle and after preconditioning appear nearly straight. It is hoped that the inexpensive staining tools will contribute to solve conflicting interpretations existing on elastin structures in the arterial wall.
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29
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Ren JS. Growth and residual stresses of arterial walls. J Theor Biol 2013; 337:80-8. [PMID: 23968891 DOI: 10.1016/j.jtbi.2013.08.008] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/06/2012] [Revised: 08/08/2013] [Accepted: 08/11/2013] [Indexed: 11/19/2022]
Abstract
Growth, residual stresses and mechanical responses of arterial walls under the inner pressure are investigated within the framework of a finite deformation hyper-elasticity theory. A biomechanical model for a two-layer thick-walled circular cylindrical tube is proposed to address the mechanical effects of finite volumetric growth and residual stresses of arterial walls. The active stress due to smooth muscle tone in the media and the dispersion of collagen fiber orientations in the adventitia are also considered. The fields of displacements and stress distributions of arterial walls with growth are solved analytically. Analysis of axial, radial and circumferential growth is considered and residual stress distributions of arterial walls in different cases of growth are compared.
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Affiliation(s)
- Jiu-Sheng Ren
- Shanghai Key Laboratory of Mechanics in Energy and Environment Engineering, Department of Mechanics, Shanghai University, Shanghai 200444, China.
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30
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The role of elastin and collagen in the softening behavior of the human thoracic aortic media. J Biomech 2013; 46:1859-65. [DOI: 10.1016/j.jbiomech.2013.04.025] [Citation(s) in RCA: 61] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/03/2013] [Revised: 04/24/2013] [Accepted: 04/26/2013] [Indexed: 11/21/2022]
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31
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Li W, Hill N, Ogden R, Smythe A, Majeed A, Bird N, Luo X. Anisotropic behaviour of human gallbladder walls. J Mech Behav Biomed Mater 2013; 20:363-75. [DOI: 10.1016/j.jmbbm.2013.02.015] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/23/2012] [Revised: 02/11/2013] [Accepted: 02/20/2013] [Indexed: 10/27/2022]
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32
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Regional variations in the nonlinearity and anisotropy of bovine aortic elastin. Biomech Model Mechanobiol 2013; 12:1181-94. [DOI: 10.1007/s10237-013-0474-3] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/17/2012] [Accepted: 01/18/2013] [Indexed: 10/27/2022]
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33
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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.
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34
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Schmid H, Grytsan A, Poshtan E, Watton PN, Itskov M. Influence of differing material properties in media and adventitia on arterial adaptation — application to aneurysm formation and rupture. Comput Methods Biomech Biomed Engin 2013; 16:33-53. [DOI: 10.1080/10255842.2011.603309] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023]
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35
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Kochová P, Kuncová J, Svíglerová J, Cimrman R, Miklíková M, Liška V, Tonar Z. The contribution of vascular smooth muscle, elastin and collagen on the passive mechanics of porcine carotid arteries. Physiol Meas 2012; 33:1335-51. [PMID: 22813960 DOI: 10.1088/0967-3334/33/8/1335] [Citation(s) in RCA: 32] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
Abstract
The main components responsible for the mechanical behavior of the arterial wall are collagen, elastin, and smooth muscle cells (SMCs) in the medial layer. We determined the structural and mechanical changes in porcine carotid arteries after administration of Triton® X-100, elastase, and collagenase using the inflation-deflation test. The arteries were intraluminarly pressurized from 0 to 200 mmHg, and the outer diameter of the artery was measured. The pressure-strain elastic modulus was determined based on the pressure/diameter ratio. The intima-media thickness, wall thickness, thickness of the tunica adventitia layer, and the area fractions of SMCs, elastin, and collagen within the arterial wall (A(A)(SMC/elastin/collagen, wall)) were measured using stereological methods. The relative changes in the relevant components of the treated samples were as follows: the decrease in A(A)(SMC, wall) after administration of Triton® X-100 was 11% ± 7%, the decrease in A(A)(elastin, wall) after administration of elastase was 40% ± 22%, and the decrease in A(A)(collagen, wall) after the application of collagenase was 51% ± 22%. The Triton® X-100 treatment led to a decrease in the SMC content that was associated with enlargement of the arterial wall (outer diameter) for pressures up to 120 mmHg, and with mechanical stiffening of the arterial wall at higher pressures. Elastase led to a decrease in the elastin content that was associated with enlargement of the arterial wall, but not with stiffening or softening. Collagenase led to a decrease in collagen content that was associated with a change in the stiffness of the arterial wall, although the exact contribution of mechanical loading and the duration of treatment (enlargement) could not be quantified.
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Affiliation(s)
- P Kochová
- New Technologies Research Centre, University of West Bohemia, Univerzitní 8, 306 14 Pilsen, Czech Republic.
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36
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Cheng JK, Stoilov I, Mecham RP, Wagenseil JE. A fiber-based constitutive model predicts changes in amount and organization of matrix proteins with development and disease in the mouse aorta. Biomech Model Mechanobiol 2012; 12:497-510. [PMID: 22790326 DOI: 10.1007/s10237-012-0420-9] [Citation(s) in RCA: 33] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/07/2011] [Accepted: 06/26/2012] [Indexed: 12/16/2022]
Abstract
Decreased elastin in mice (Eln+/-) yields a functioning vascular system with elevated blood pressure and increased arterial stiffness that is morphologically distinct from wild-type mice (WT). Yet, function is retained enough that there is no appreciable effect on life span and some mechanical properties are maintained constant. It is not understood how the mouse modifies the normal developmental process to produce a functioning vascular system despite a deficiency in elastin. To quantify changes in mechanical properties, we have applied a fiber-based constitutive model to mechanical data from the ascending aorta during postnatal development of WT and Eln+/- mice. Results indicate that the fiber-based constitutive model is capable of distinguishing elastin amounts and identifying trends during development. We observe an increase in predicted circumferential stress contribution from elastin with age, which correlates with increased elastin amounts from protein quantification data. The model also predicts changes in the unloaded collagen fiber orientation with age, which must be verified in future work. In Eln+/- mice, elastin amounts are decreased at each age, along with the predicted circumferential stress contribution of elastin. Collagen amounts in Eln+/- aorta are comparable to WT, but the predicted circumferential stress contribution of collagen is increased. This may be due to altered organization or structure of the collagen fibers. Relating quantifiable changes in arterial mechanics with changes in extracellular matrix (ECM) protein amounts will help in understanding developmental remodeling and in producing treatments for human diseases affecting ECM proteins.
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Affiliation(s)
- Jeffrey K Cheng
- Department of Biomedical Engineering, Washington University, St. Louis, MO, USA
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37
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Zou Y, Zhang Y. The biomechanical function of arterial elastin in solutes. J Biomech Eng 2012; 134:1475435. [PMID: 24763624 DOI: 10.1115/1.4006593] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/02/2011] [Indexed: 11/08/2022]
Abstract
Elastin is essential to accommodate physiological deformation and provide elastic support for blood vessels. As a long-lived extracellular matrix protein, elastin can suffer from cumulative effects of exposure to chemical damage, which greatly compromises the mechanical function of elastin. The mechanical properties of elastin are closely related to its microstructure and the external chemical environments. The purpose of this study is to investigate the changes in the macroscopic elastic and viscoelastic properties of isolated porcine aortic elastin under the effects of nonenzymatic mediated in vitro elastin-lipid interactions and glycation. Sodium dodecyl sulfate (SDS) was used for elastin-lipid interaction, while glucose was used for glycation of elastin. Elastin samples were incubated in SDS (20 mM) or glucose (2 M) solutions and were allowed to equilibrate for 48 h at room temperature. Control experiments were performed in 1 × Phosphate buffered saline (PBS). Biaxial tensile and stress relaxation experiments were performed to study the mechanical behavior of elastin with solute effects. Experimental results reveal that both the elastic and viscoelastic behaviors of elastin change in different biochemical solvents environments. The tangent stiffness of SDS treated elastin decreases to 63.57 ± 4.7% of the control condition in circumference and to 58.43 ± 2.65% in the longitude. Glucose treated elastin exhibits an increase in stiffness to 145.06 ± 1.48% of the control condition in the longitude but remains similar mechanical response in the circumferential direction. During stress relaxation experiments with a holding period of half an hour, elastin treated with SDS or glucose shows more prominent stress relaxation than the untreated ones.
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38
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Sforza DM, Putman CM, Cebral JR. Computational fluid dynamics in brain aneurysms. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2012; 28:801-808. [PMID: 25364852 PMCID: PMC4221804 DOI: 10.1002/cnm.1481] [Citation(s) in RCA: 27] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/30/2011] [Revised: 10/04/2011] [Accepted: 10/05/2011] [Indexed: 05/30/2023]
Abstract
Because of its ability to deal with any geometry, image-based computational fluid dynamics (CFD) has been progressively used to investigate the role of hemodynamics in the underlying mechanisms governing the natural history of cerebral aneurysms. Despite great progress in methodological developments and many studies using patient-specific data, there are still significant controversies about the precise governing processes and divergent conclusions from apparently contradictory results. Sorting out these issues requires a global vision of the state of the art and a unified approach to solving this important scientific problem. Towards this end, this paper reviews the contributions made using patient-specific CFD models to further the understanding of these mechanisms, and highlights the great potential of patient-specific computational models for clinical use in the assessment of aneurysm rupture risk and patient management.
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Affiliation(s)
- Daniel M Sforza
- Center for Computational Fluid Dynamics, School of Physics, Astronomy and Computational Sciences, George Mason University, 4400 University Drive, MSN 6A2, Fairfax, VA 22030, USA.
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39
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A theoretical and non-destructive experimental approach for direct inclusion of measured collagen orientation and recruitment into mechanical models of the artery wall. J Biomech 2012; 45:762-71. [PMID: 22305290 PMCID: PMC5962021 DOI: 10.1016/j.jbiomech.2011.11.016] [Citation(s) in RCA: 101] [Impact Index Per Article: 8.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 09/30/2011] [Indexed: 11/27/2022]
Abstract
Gradual collagen recruitment has been hypothesized as the underlying mechanism for the mechanical stiffening with increasing stress in arteries. In this work, we investigated this hypothesis in eight rabbit carotid arteries by directly measuring the distribution of collagen recruitment stretch under increasing circumferential loading using a custom uniaxial (UA) extension device combined with a multi-photon microscope (MPM). This approach allowed simultaneous mechanical testing and imaging of collagen fibers without traditional destructive fixation methods. Fiber recruitment was quantified from 3D rendered MPM images, and fiber orientation was measured in projected stacks of images. Collagen recruitment was observed to initiate at a finite strain, corresponding to a sharp increase in the measured mechanical stiffness, confirming the previous hypothesis and motivating the development of a new constitutive model to capture this response. Previous constitutive equations for the arterial wall have modeled the collagen contribution with either abrupt recruitment at zero strain, abrupt recruitment at finite strain or as gradual recruitment beginning at infinitesimal strain. Based on our experimental data, a new combined constitutive model was presented in which fiber recruitment begins at a finite strain with activation stretch represented by a probability distribution function. By directly including this recruitment data, the collagen contribution was modeled using a simple Neo-Hookean equation. As a result, only two phenomenological material constants were required from the fit to the stress stretch data. Three other models for the arterial wall were then compared with these results. The approach taken here was successful in combining stress-strain analysis with simultaneous microstructural imaging of collagen recruitment and orientation, providing a new approach by which underlying fiber architecture may be quantified and included in constitutive equations.
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40
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Strategies and challenges for the mechanical modeling of biological and bio-inspired materials. MATERIALS SCIENCE & ENGINEERING. C, MATERIALS FOR BIOLOGICAL APPLICATIONS 2011. [DOI: 10.1016/j.msec.2010.11.012] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/30/2022]
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41
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Sokolis DP, Sassani S, Kritharis EP, Tsangaris S. Differential histomechanical response of carotid artery in relation to species and region: mathematical description accounting for elastin and collagen anisotropy. Med Biol Eng Comput 2011; 49:867-79. [PMID: 21626234 DOI: 10.1007/s11517-011-0784-5] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/12/2010] [Accepted: 05/05/2011] [Indexed: 11/24/2022]
Abstract
The selection of a mathematical descriptor for the passive arterial mechanical behavior has been long debated in the literature and customarily constrained by lack of pertinent data on the underlying microstructure. Our objective was to analyze the response of carotid artery subjected to inflation/extension with phenomenological and microstructure-based candidate strain-energy functions (SEFs), according to species (rabbit vs. pig) and region (proximal vs. distal). Histological variations among segments were examined, aiming to explicitly relate them with the differential material response. The Fung-type model could not capture the biphasic response alone. Combining a neo-Hookean with a two-fiber family term alleviated this restraint, but force data were poorly captured, while consideration of low-stress anisotropy via a quadratic term allowed improved simulation of both pressure and force data. The best fitting was achieved with the quadratic and Fung-type or four-fiber family SEF. The latter simulated more closely than the two-fiber family the high-stress response, being structurally justified for all artery types, whereas the quadratic term was justified for transitional and muscular arteries exhibiting notable elastin anisotropy. Diagonally arranged fibers were associated with pericellular medial collagen, and circumferentially and longitudinally arranged fibers with medial and adventitial collagen bundles, evidenced by the significant correlations of SEF parameters with quantitative histology.
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Affiliation(s)
- Dimitrios P Sokolis
- Laboratory of Biomechanics, Center for Experimental Surgery, Foundation of Biomedical Research, Academy of Athens, Athens, Greece.
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42
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Ambrosi D, Ateshian GA, Arruda EM, Cowin SC, Dumais J, Goriely A, Holzapfel GA, Humphrey JD, Kemkemer R, Kuhl E, Olberding JE, Taber LA, Garikipati K. Perspectives on biological growth and remodeling. JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS 2011; 59:863-883. [PMID: 21532929 PMCID: PMC3083065 DOI: 10.1016/j.jmps.2010.12.011] [Citation(s) in RCA: 155] [Impact Index Per Article: 11.9] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/02/2023]
Abstract
The continuum mechanical treatment of biological growth and remodeling has attracted considerable attention over the past fifteen years. Many aspects of these problems are now well-understood, yet there remain areas in need of significant development from the standpoint of experiments, theory, and computation. In this perspective paper we review the state of the field and highlight open questions, challenges, and avenues for further development.
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Affiliation(s)
| | | | | | | | | | | | - G. A. Holzapfel
- Graz University of Technology, Austria, and Royal Institute of Technology, Sweden
| | | | - R. Kemkemer
- Max Planck Institut für Metallforschung, Germany
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43
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Role of elastin anisotropy in structural strain energy functions of arterial tissue. Biomech Model Mechanobiol 2010; 10:599-611. [PMID: 21058025 DOI: 10.1007/s10237-010-0259-x] [Citation(s) in RCA: 35] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/08/2009] [Accepted: 09/20/2010] [Indexed: 10/19/2022]
Abstract
The vascular wall exhibits nonlinear anisotropic mechanical properties. The identification of a strain energy function (SEF) is the preferred method to describe its complex nonlinear elastic properties. Earlier constituent-based SEF models, where elastin is modeled as an isotropic material, failed in describing accurately the tissue response to inflation-extension loading. We hypothesized that these shortcomings are partly due to unaccounted anisotropic properties of elastin. We performed inflation-extension tests on common carotid of rabbits before and after enzymatic degradation of elastin and applied constituent-based SEFs, with both an isotropic and an anisotropic elastin part, on the experimental data. We used transmission electron microscopy (TEM) and serial block-face scanning electron microscopy (SBFSEM) to provide direct structural evidence of the assumed anisotropy. In intact arteries, the SEF including anisotropic elastin with one family of fibers in the circumferential direction fitted better the inflation-extension data than the isotropic SEF. This was supported by TEM and SBFSEM imaging, which showed interlamellar elastin fibers in the circumferential direction. In elastin-degraded arteries, both SEFs succeeded equally well in predicting anisotropic wall behavior. In elastase-treated arteries fitted with the anisotropic SEF for elastin, collagen engaged later than in intact arteries. We conclude that constituent-based models with an anisotropic elastin part characterize more accurately the mechanical properties of the arterial wall when compared to models with simply an isotropic elastin. Microstructural imaging based on electron microscopy techniques provided evidence for elastin anisotropy. Finally, the model suggests a later and less abrupt collagen engagement after elastase treatment.
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44
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Lillie M, Shadwick R, Gosline J. Mechanical anisotropy of inflated elastic tissue from the pig aorta. J Biomech 2010; 43:2070-8. [DOI: 10.1016/j.jbiomech.2010.04.014] [Citation(s) in RCA: 49] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/21/2009] [Revised: 04/08/2010] [Accepted: 04/09/2010] [Indexed: 11/27/2022]
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45
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Ferruzzi J, Vorp DA, Humphrey JD. On constitutive descriptors of the biaxial mechanical behaviour of human abdominal aorta and aneurysms. J R Soc Interface 2010; 8:435-50. [PMID: 20659928 DOI: 10.1098/rsif.2010.0299] [Citation(s) in RCA: 116] [Impact Index Per Article: 8.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
The abdominal aorta (AA) in older individuals can develop an aneurysm, which is of increasing concern in our ageing population. The structural integrity of the ageing aortic wall, and hence aneurysm, depends primarily on effective elastin and multiple families of oriented collagen fibres. In this paper, we show that a structurally motivated phenomenological 'four-fibre family' constitutive relation captures the biaxial mechanical behaviour of both the human AA, from ages less than 30 to over 60, and abdominal aortic aneurysms. Moreover, combining the statistical technique known as non-parametric bootstrap with a modal clustering method provides improved confidence intervals for estimated best-fit values of the eight associated constitutive parameters. It is suggested that this constitutive relation captures the well-known loss of structural integrity of elastic fibres owing to ageing and the development of abdominal aneurysms, and that it provides important insight needed to construct growth and remodelling models for aneurysms, which in turn promise to improve our ability to predict disease progression.
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Affiliation(s)
- J Ferruzzi
- Dipartimento di Ingegneria Meccanica Nucleare e della Produzione, Università di Pisa, Pisa, Italy
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46
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Modelling evolution and the evolving mechanical environment of saccular cerebral aneurysms. Biomech Model Mechanobiol 2010; 10:109-32. [PMID: 20496095 DOI: 10.1007/s10237-010-0221-y] [Citation(s) in RCA: 37] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/20/2009] [Accepted: 05/03/2010] [Indexed: 10/19/2022]
Abstract
A fluid-solid-growth (FSG) model of saccular cerebral aneurysm evolution is developed. It utilises a realistic two-layered structural model of the internal carotid artery and explicitly accounts for the degradation of the elastinous constituents and growth and remodelling (G&R) of the collagen fabric. Aneurysm inception is prescribed: a localised degradation of elastin results in a perturbation in the arterial geometry; the collagen fabric adapts, and the artery achieves a new homeostatic configuration. The perturbation to the geometry creates an altered haemodynamic environment. Subsequent degradation of elastin is explicitly linked to low wall shear stress (WSS) in a confined region of the arterial domain. A sidewall saccular aneurysm develops, the collagen fabric adapts and the aneurysm stabilises in size. A quasi-static analysis is performed to determine the geometry at diastolic pressure. This enables the cyclic stretching of the tissue to be quantified, and we propose a novel index to quantify the degree of biaxial stretching of the tissue. Whilst growth is linked to low WSS from a steady (systolic) flow analysis, a pulsatile flow analysis is performed to compare steady and pulsatile flow parameters during evolution. This model illustrates the evolving mechanical environment for an idealised saccular cerebral aneurysm developing on a cylindrical parent artery and provides the guidance to more sophisticated FSG models of aneurysm evolution which link G&R to the local mechanical stimuli of vascular cells.
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47
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Schmid H, Watton PN, Maurer MM, Wimmer J, Winkler P, Wang YK, Röhrle O, Itskov M. Impact of transmural heterogeneities on arterial adaptation. Biomech Model Mechanobiol 2009; 9:295-315. [DOI: 10.1007/s10237-009-0177-y] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/17/2009] [Accepted: 10/26/2009] [Indexed: 10/20/2022]
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Watton PN, Raberger NB, Holzapfel GA, Ventikos Y. Coupling the Hemodynamic Environment to the Evolution of Cerebral Aneurysms: Computational Framework and Numerical Examples. J Biomech Eng 2009; 131:101003. [DOI: 10.1115/1.3192141] [Citation(s) in RCA: 60] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
Abstract
The physiological mechanisms that give rise to the inception and development of a cerebral aneurysm are accepted to involve the interplay between the local mechanical forces acting on the arterial wall and the biological processes occurring at the cellular level. In fact, the wall shear stresses (WSSs) that act on the endothelial cells are thought to play a pivotal role. A computational framework is proposed to explore the link between the evolution of a cerebral aneurysm and the influence of hemodynamic stimuli that act on the endothelial cells. An aneurysm evolution model, which utilizes a realistic microstructural model of the arterial wall, is combined with detailed 3D hemodynamic solutions. The evolution of the blood flow within the developing aneurysm determines the distributions of the WSS and the spatial WSS gradient (WSSG) that act on the endothelial cell layer of the tissue. Two illustrative examples are considered: Degradation of the elastinous constituents is driven by deviations of WSS or the WSSG from normotensive values. This model provides the basis to further explore the etiology of aneurysmal disease.
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Affiliation(s)
- Paul N. Watton
- Department of Engineering Science and Institute of Biomedical Engineering, University of Oxford, Oxford OX1 3PJ, UK
| | | | - Gerhard A. Holzapfel
- Graz University of Technology, Institute of Biomechanics, Centre of Biomedical Engineering, 8010 Graz, Austria; Department of Solid Mechanics Royal Institute of Technology, School of Engineering Sciences, Osquars Backe 1, 100 44 Stockholm, Sweden
| | - Yiannis Ventikos
- Department of Engineering Science and Institute of Biomedical Engineering, University of Oxford, Oxford OX1 3PJ, UK
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