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Ross CJ, Laurence DW, Aggarwal A, Hsu MC, Mir A, Burkhart HM, Lee CH. Bayesian Optimization-Based Inverse Finite Element Analysis for Atrioventricular Heart Valves. Ann Biomed Eng 2024; 52:611-626. [PMID: 37989903 PMCID: PMC10926997 DOI: 10.1007/s10439-023-03408-6] [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: 07/05/2023] [Accepted: 11/07/2023] [Indexed: 11/23/2023]
Abstract
Inverse finite element analysis (iFEA) of the atrioventricular heart valves (AHVs) can provide insights into the in-vivo valvular function, such as in-vivo tissue strains; however, there are several limitations in the current state-of-the-art that iFEA has not been widely employed to predict the in-vivo, patient-specific AHV leaflet mechanical responses. In this exploratory study, we propose the use of Bayesian optimization (BO) to study the AHV functional behaviors in-vivo. We analyzed the efficacy of Bayesian optimization to estimate the isotropic Lee-Sacks material coefficients in three benchmark problems: (i) an inflation test, (ii) a simplified leaflet contact model, and (iii) an idealized AHV model. Then, we applied the developed BO-iFEA framework to predict the leaflet properties for a patient-specific tricuspid valve under a congenital heart defect condition. We found that the BO could accurately construct the objective function surface compared to the one from a [Formula: see text] grid search analysis. Additionally, in all cases the proposed BO-iFEA framework yielded material parameter predictions with average element errors less than 0.02 mm/mm (normalized by the simulation-specific characteristic length). Nonetheless, the solutions were not unique due to the presence of a long-valley minima region in the objective function surfaces. Parameter sets along this valley can yield functionally equivalent outcomes (i.e., closing behavior) and are typically observed in the inverse analysis or parameter estimation for the nonlinear mechanical responses of the AHV. In this study, our key contributions include: (i) a first-of-its-kind demonstration of the BO method used for the AHV iFEA; and (ii) the evaluation of a candidate AHV in-silico modeling approach wherein the chordae could be substituted with equivalent displacement boundary conditions, rendering the better iFEA convergence and a smoother objective surface.
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Affiliation(s)
- Colton J Ross
- Biomechanics & Biomaterials Design Laboratory, School of Aerospace and Mechanical Engineering, University of Oklahoma, Norman, OK, USA
| | | | - Ankush Aggarwal
- Glasgow Computational Engineering Centre, James Watt School of Engineering, University of Glasgow, Glasgow, UK
| | - Ming-Chen Hsu
- Department of Mechanical Engineering, Iowa State University, Ames, IA, USA
| | - Arshid Mir
- Department of Pediatrics, University of Oklahoma Health Sciences Center, Oklahoma, OK, USA
| | - Harold M Burkhart
- Department of Surgery, University of Oklahoma Health Sciences Center, Oklahoma, OK, USA
| | - Chung-Hao Lee
- Biomechanics & Biomaterials Design Laboratory, School of Aerospace and Mechanical Engineering, University of Oklahoma, Norman, OK, USA.
- Department of Bioengineering, University of California Riverside, Riverside, CA, USA.
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2
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Thiel JN, Steinseifer U, Neidlin M. Generic framework for quantifying the influence of the mitral valve on ventricular blood flow. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2023; 39:e3684. [PMID: 36629779 DOI: 10.1002/cnm.3684] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/24/2022] [Revised: 12/08/2022] [Accepted: 01/06/2023] [Indexed: 06/17/2023]
Abstract
Blood flow within the left ventricle provides important information regarding cardiac function in health and disease. The mitral valve strongly influences the formation of flow structures and there exist various approaches for the representation of the valve in numerical models of left ventricular blood flow. However, a systematic comparison of the various mitral valve models is missing, making a priori decisions considering the overall model's context of use impossible. Within this study, a benchmark setup to compare the influence of mitral valve modeling strategies on intraventricular flow features was developed. Then, five mitral valve models of increasing complexity: no modeling, static wall, 2D and 3D porous medium with time-dependent porosity, and one-way fluid-structure interaction (FSI) were compared with each other. The flow features velocity, kinetic energy, transmitral pressure drop, vortex formation, flow asymmetry as well as computational cost and ease-of-implementation were evaluated. The one-way FSI approach provides the highest level of flow detail, which is accompanied by the highest numerical costs and challenges with the implementation. As an alternative, the porous medium approach with the expansion including time-dependent porosity provides good results with up to 10% deviations in the flow features (except the transmitral pressure drop) in comparison to the FSI model and only a fraction (11%) of numerical costs. However, jet propagation speed is highly underestimated by all alternative approaches to the FSI model. Taken together, our benchmark setup allows a quantitative comparison of various mitral valve modeling approaches and is provided to the scientific community for further testing and expansion.
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Affiliation(s)
- Jan-Niklas Thiel
- Department of Cardiovascular Engineering, Institute of Applied Medical Engineering, Medical Faculty, RWTH Aachen University, Aachen, Germany
| | - Ulrich Steinseifer
- Department of Cardiovascular Engineering, Institute of Applied Medical Engineering, Medical Faculty, RWTH Aachen University, Aachen, Germany
| | - Michael Neidlin
- Department of Cardiovascular Engineering, Institute of Applied Medical Engineering, Medical Faculty, RWTH Aachen University, Aachen, Germany
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3
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Laurence DW, Wang S, Xiao R, Qian J, Mir A, Burkhart HM, Holzapfel GA, Lee CH. An investigation of how specimen dimensions affect biaxial mechanical characterizations with CellScale BioTester and constitutive modeling of porcine tricuspid valve leaflets. J Biomech 2023; 160:111829. [PMID: 37826955 PMCID: PMC10995110 DOI: 10.1016/j.jbiomech.2023.111829] [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: 03/16/2023] [Revised: 08/19/2023] [Accepted: 10/03/2023] [Indexed: 10/14/2023]
Abstract
Biaxial mechanical characterizations are the accepted approach to determine the mechanical response of many biological soft tissues. Although several computational and experimental studies have examined how experimental factors (e.g., clamped vs. suture mounting) affect the acquired tissue mechanical behavior, little is known about the role of specimen dimensions in data acquisition and the subsequent modeling. In this study, we combined our established mechanical characterization framework with an iterative size-reduction protocol to test the hypothesis that specimen dimensions affect the observed mechanical behavior of biaxial characterizations. Our findings indicated that there were non-significant differences in the peak equibiaxial stretches of tricuspid valve leaflets across four specimen dimensions ranging from 4.5×4.5mm to 9 × 9mm. Further analyses revealed that there were significant differences in the low-tensile modulus of the circumferential tissue direction. These differences resulted in significantly different constitutive model parameters for the Tong-Fung model between different specimen dimensions of the posterior and septal leaflets. Overall, our findings demonstrate that specimen dimensions play an important role in experimental characterizations, but not necessarily in constitutive modeling of soft tissue mechanical behavior during biaxial testing with the commercial CellScale BioTester.
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Affiliation(s)
- Devin W Laurence
- Biomechanics and Biomaterials Design Laboratory, The University of Oklahoma, USA
| | - Shuodao Wang
- School of Mechanical and Aerospace Engineering, Oklahoma State University, USA
| | - Rui Xiao
- Department of Engineering Mechanics, Key Laboratory of Soft Machines and Smart Devices of Zhejiang Province, Zhejiang University, Hangzhou 310027, China
| | - Jin Qian
- Department of Engineering Mechanics, Key Laboratory of Soft Machines and Smart Devices of Zhejiang Province, Zhejiang University, Hangzhou 310027, China
| | - Arshid Mir
- Department of Pediatrics, University of Oklahoma Health Sciences Center, USA
| | - Harold M Burkhart
- Department of Surgery, University of Oklahoma Health Sciences Center, USA
| | - Gerhard A Holzapfel
- Institute of Biomechanics, Graz University of Technology, Austria; Department of Structural Engineering, Norwegian University of Science and Technology, Norway
| | - Chung-Hao Lee
- Biomechanics and Biomaterials Design Laboratory, The University of Oklahoma, USA; Institute for Biomedical Engineering, Science and Technology, The University of Oklahoma, USA; Department of Bioengineering, The University of California, Riverside, USA.
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4
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Gaidulis G, Padala M. Computational Modeling of the Subject-Specific Effects of Annuloplasty Ring Sizing on the Mitral Valve to Repair Functional Mitral Regurgitation. Ann Biomed Eng 2023; 51:1984-2000. [PMID: 37344691 PMCID: PMC10826925 DOI: 10.1007/s10439-023-03219-9] [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: 12/21/2022] [Accepted: 04/21/2023] [Indexed: 06/23/2023]
Abstract
Surgical repair of functional mitral regurgitation (FMR) that occurs in nearly 60% of heart failure (HF) patients is currently performed with undersizing mitral annuloplasty (UMA), which lacks short- and long-term durability. Heterogeneity in valve geometry makes tailoring this repair to each patient challenging, and predictive models that can help with planning this surgery are lacking. In this study, we present a 3D echo-derived computational model, to enable subject-specific, pre-surgical planning of the repair. Three computational models of the mitral valve were created from 3D echo data obtained in three pigs with HF and FMR. An annuloplasty ring model in seven sizes was created, each ring was deployed, and post-repair valve closure was simulated. The results indicate that large annuloplasty rings (> 32 mm) were not effective in eliminating regurgitant gaps nor in restoring leaflet coaptation or reducing leaflet stresses and chordal tension. Smaller rings (≤ 32 mm) restored better systolic valve closure in all investigated cases,but excessive valve tethering and restricted motion of the leaflets were still present. This computational study demonstrates that for effective correction of FMR, the extent of annular reduction differs between subjects, and overly reducing the annulus has deleterious effects on the valve.
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Affiliation(s)
- Gediminas Gaidulis
- Structural Heart Research and Innovation Laboratory, Carlyle Fraser Heart Center at Emory University Hospital Midtown, Atlanta, USA
- Division of Cardiothoracic Surgery, Emory University School of Medicine, Atlanta, USA
| | - Muralidhar Padala
- Structural Heart Research and Innovation Laboratory, Carlyle Fraser Heart Center at Emory University Hospital Midtown, Atlanta, USA.
- Division of Cardiothoracic Surgery, Emory University School of Medicine, Atlanta, USA.
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5
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Feng X, Liu Y, Kamensky D, McComb DW, Breuer CK, Sacks MS. Functional mechanical behavior of the murine pulmonary heart valve. Sci Rep 2023; 13:12852. [PMID: 37553466 PMCID: PMC10409802 DOI: 10.1038/s41598-023-40158-w] [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: 05/11/2023] [Accepted: 08/05/2023] [Indexed: 08/10/2023] Open
Abstract
Genetically modified mouse models provide a versatile and efficient platform to extend our understanding of the underlying disease processes and evaluate potential treatments for congenital heart valve diseases. However, applications have been limited to the gene and molecular levels due to the small size of murine heart valves, which prohibits the use of standard mechanical evaluation and in vivo imaging methods. We have developed an integrated imaging/computational mechanics approach to evaluate, for the first time, the functional mechanical behavior of the murine pulmonary heart valve (mPV). We utilized extant mPV high resolution µCT images of 1-year-old healthy C57BL/6J mice, with mPVs loaded to 0, 10, 20 or 30 mmHg then chemically fixed to preserve their shape. Individual mPV leaflets and annular boundaries were segmented and key geometric quantities of interest defined and quantified. The resulting observed inter-valve variations were small and consistent at each TVP level. This allowed us to develop a high fidelity NURBS-based geometric model. From the resultant individual mPV geometries, we developed a mPV shape-evolving geometric model (SEGM) that accurately represented mPV shape changes as a continuous function of transvalvular pressure. The SEGM was then integrated into an isogeometric finite element based inverse model that estimated the individual leaflet and regional mPV mechanical behaviors. We demonstrated that the mPV leaflet mechanical behaviors were highly anisotropic and nonlinear, with substantial leaflet and regional variations. We also observed the presence of strong axial mechanical coupling, suggesting the important role of the underlying collagen fiber architecture in the mPV. When compared to larger mammalian species, the mPV exhibited substantially different mechanical behaviors. Thus, while qualitatively similar, the mPV exhibited important functional differences that will need to accounted for in murine heart valve studies. The results of this novel study will allow detailed murine tissue and organ level investigations of semi-lunar heart valve diseases.
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Affiliation(s)
- Xinzeng Feng
- Willerson Center for Cardiovascular Modeling and Simulation, Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, TX, 78712, USA
| | - Yifei Liu
- Center for Electron Microscopy and Analysis, The Ohio State University, Columbus, OH, 43210, USA
- Department of Materials Science and Engineering, The Ohio State University, Columbus, OH, 43210, USA
| | - David Kamensky
- Department of Mechanical and Aerospace Engineering, University of California San Diego, San Diego, CA, 92093, USA
| | - David W McComb
- Center for Electron Microscopy and Analysis, The Ohio State University, Columbus, OH, 43210, USA
- Department of Materials Science and Engineering, The Ohio State University, Columbus, OH, 43210, USA
| | - Christopher K Breuer
- Center for Regenerative Medicine, Abigail Wexner Research Institute, Nationwide Children's Hospital, Columbus, OH, 43205, USA
- Department of Pediatric Surgery, Nationwide Children's Hospital, Columbus, OH, 43205, USA
| | - Michael S Sacks
- Willerson Center for Cardiovascular Modeling and Simulation, Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, TX, 78712, USA.
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, TX, 78712, USA.
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6
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Wu W, Ching S, Sabin P, Laurence DW, Maas SA, Lasso A, Weiss JA, Jolley MA. The effects of leaflet material properties on the simulated function of regurgitant mitral valves. J Mech Behav Biomed Mater 2023; 142:105858. [PMID: 37099920 PMCID: PMC10199327 DOI: 10.1016/j.jmbbm.2023.105858] [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: 02/09/2023] [Revised: 03/30/2023] [Accepted: 04/12/2023] [Indexed: 04/28/2023]
Abstract
Advances in three-dimensional imaging provide the ability to construct and analyze finite element (FE) models to evaluate the biomechanical behavior and function of atrioventricular valves. However, while obtaining patient-specific valve geometry is now possible, non-invasive measurement of patient-specific leaflet material properties remains nearly impossible. Both valve geometry and tissue properties play a significant role in governing valve dynamics, leading to the central question of whether clinically relevant insights can be attained from FE analysis of atrioventricular valves without precise knowledge of tissue properties. As such we investigated (1) the influence of tissue extensibility and (2) the effects of constitutive model parameters and leaflet thickness on simulated valve function and mechanics. We compared metrics of valve function (e.g., leaflet coaptation and regurgitant orifice area) and mechanics (e.g., stress and strain) across one normal and three regurgitant mitral valve (MV) models with common mechanisms of regurgitation (annular dilation, leaflet prolapse, leaflet tethering) of both moderate and severe degree. We developed a novel fully-automated approach to accurately quantify regurgitant orifice areas of complex valve geometries. We found that the relative ordering of the mechanical and functional metrics was maintained across a group of valves using material properties up to 15% softer than the representative adult mitral constitutive model. Our findings suggest that FE simulations can be used to qualitatively compare how differences and alterations in valve structure affect relative atrioventricular valve function even in populations where material properties are not precisely known.
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Affiliation(s)
- Wensi Wu
- Department of Anesthesiology and Critical Care Medicine, Children's Hospital of Philadelphia, Philadelphia, 19104, PA, USA; Division of Pediatric Cardiology, Children's Hospital of Philadelphia, Philadelphia, 19104, PA, USA
| | - Stephen Ching
- Department of Anesthesiology and Critical Care Medicine, Children's Hospital of Philadelphia, Philadelphia, 19104, PA, USA
| | - Patricia Sabin
- Department of Anesthesiology and Critical Care Medicine, Children's Hospital of Philadelphia, Philadelphia, 19104, PA, USA
| | - Devin W Laurence
- Department of Anesthesiology and Critical Care Medicine, Children's Hospital of Philadelphia, Philadelphia, 19104, PA, USA; Division of Pediatric Cardiology, Children's Hospital of Philadelphia, Philadelphia, 19104, PA, USA
| | - Steve A Maas
- Department of Biomedical Engineering, University of Utah, Salt Lake City, UT 84112, UT, USA; Scientific Computing and Imaging Institute, University of Utah, Salt Lake City, UT 84112, UT, USA
| | - Andras Lasso
- Laboratory for Percutaneous Surgery, Queen's University, Kingston, ON, Canada
| | - Jeffrey A Weiss
- Department of Biomedical Engineering, University of Utah, Salt Lake City, UT 84112, UT, USA; Scientific Computing and Imaging Institute, University of Utah, Salt Lake City, UT 84112, UT, USA
| | - Matthew A Jolley
- Department of Anesthesiology and Critical Care Medicine, Children's Hospital of Philadelphia, Philadelphia, 19104, PA, USA; Division of Pediatric Cardiology, Children's Hospital of Philadelphia, Philadelphia, 19104, PA, USA.
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7
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Wu W, Ching S, Sabin P, Laurence DW, Maas SA, Lasso A, Weiss JA, Jolley MA. The Effects of leaflet material properties on the simulated function of regurgitant mitral valves. ARXIV 2023:arXiv:2302.04939v2. [PMID: 36798457 PMCID: PMC9934730] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Figures] [Subscribe] [Scholar Register] [Indexed: 02/18/2023]
Abstract
Advances in three-dimensional imaging provide the ability to construct and analyze finite element (FE) models to evaluate the biomechanical behavior and function of atrioventricular valves. However, while obtaining patient-specific valve geometry is now possible, non-invasive measurement of patient-specific leaflet material properties remains nearly impossible. Both valve geometry and tissue properties play a significant role in governing valve dynamics, leading to the central question of whether clinically relevant insights can be attained from FE analysis of atrioventricular valves without precise knowledge of tissue properties. As such we investigated 1) the influence of tissue extensibility and 2) the effects of constitutive model parameters and leaflet thickness on simulated valve function and mechanics. We compared metrics of valve function (e.g., leaflet coaptation and regurgitant orifice area) and mechanics (e.g., stress and strain) across one normal and three regurgitant mitral valve (MV) models with common mechanisms of regurgitation (annular dilation, leaflet prolapse, leaflet tethering) of both moderate and severe degree. We developed a novel fully-automated approach to accurately quantify regurgitant orifice areas of complex valve geometries. We found that the relative ordering of the mechanical and functional metrics was maintained across a group of valves using material properties up to 15% softer than the representative adult mitral constitutive model. Our findings suggest that FE simulations can be used to qualitatively compare how differences and alterations in valve structure affect relative atrioventricular valve function even in populations where material properties are not precisely known.
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Affiliation(s)
- Wensi Wu
- Department of Anesthesiology and Critical Care Medicine, Division of Pediatric Cardiology, Children's Hospital of Philadelphia, Philadelphia, PA 19104
| | - Stephen Ching
- Department of Anesthesiology and Critical Care Medicine, Children's Hospital of Philadelphia, Philadelphia, PA 19104
| | - Patricia Sabin
- Department of Anesthesiology and Critical Care Medicine, Children's Hospital of Philadelphia, Philadelphia, PA 19104
| | - Devin W Laurence
- Department of Anesthesiology and Critical Care Medicine, Division of Pediatric Cardiology, Children's Hospital of Philadelphia, Philadelphia, PA 19104
| | - Steve A Maas
- Department of Biomedical Engineering, and Scientific Computing and Imaging Institute, University of Utah, Salt Lake City, UT 84112
| | - Andras Lasso
- Laboratory for Percutaneous Surgery, Queen's University, Kingston, ON
| | - Jeffrey A Weiss
- Department of Biomedical Engineering, and Scientific Computing and Imaging Institute, University of Utah, Salt Lake City, UT 84112
| | - Matthew A Jolley
- Department of Anesthesiology and Critical Care Medicine, Division of Pediatric Cardiology, Children's Hospital of Philadelphia, Philadelphia, PA 19104
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8
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Aggarwal A, Hudson LT, Laurence DW, Lee CH, Pant S. A Bayesian constitutive model selection framework for biaxial mechanical testing of planar soft tissues: Application to porcine aortic valves. J Mech Behav Biomed Mater 2023; 138:105657. [PMID: 36634438 PMCID: PMC10226148 DOI: 10.1016/j.jmbbm.2023.105657] [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: 09/26/2022] [Revised: 12/20/2022] [Accepted: 01/03/2023] [Indexed: 01/06/2023]
Abstract
A variety of constitutive models have been developed for soft tissue mechanics. However, there is no established criterion to select a suitable model for a specific application. Although the model that best fits the experimental data can be deemed the most suitable model, this practice often can be insufficient given the inter-sample variability of experimental observations. Herein, we present a Bayesian approach to calculate the relative probabilities of constitutive models based on biaxial mechanical testing of tissue samples. Forty-six samples of porcine aortic valve tissue were tested using a biaxial stretching setup. For each sample, seven ratios of stresses along and perpendicular to the fiber direction were applied. The probabilities of eight invariant-based constitutive models were calculated based on the experimental data using the proposed model selection framework. The calculated probabilities showed that, out of the considered models and based on the information available through the utilized experimental dataset, the May-Newman model was the most probable model for the porcine aortic valve data. When the samples were further grouped into different cusp types, the May-Newman model remained the most probable for the left- and right-coronary cusps, whereas for non-coronary cusps two models were found to be equally probable: the Lee-Sacks model and the May-Newman model. This difference between cusp types was found to be associated with the first principal component analysis (PCA) mode, where this mode's amplitudes of the non-coronary and right-coronary cusps were found to be significantly different. Our results show that a PCA-based statistical model can capture significant variations in the mechanical properties of soft tissues. The presented framework is applicable to other tissue types, and has the potential to provide a structured and rational way of making simulations population-based.
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Affiliation(s)
- Ankush Aggarwal
- Glasgow Computational Engineering Centre, James Watt School of Engineering, University of Glasgow, Glasgow, G12 8LT, Scotland, United Kingdom.
| | - Luke T Hudson
- Biomechanics and Biomaterials Design Laboratory, School of Aerospace and Mechanical Engineering, The University of Oklahoma, Norman, 73019, OK, United States of America
| | - Devin W Laurence
- Biomechanics and Biomaterials Design Laboratory, School of Aerospace and Mechanical Engineering, The University of Oklahoma, Norman, 73019, OK, United States of America
| | - Chung-Hao Lee
- Biomechanics and Biomaterials Design Laboratory, School of Aerospace and Mechanical Engineering, The University of Oklahoma, Norman, 73019, OK, United States of America
| | - Sanjay Pant
- Faculty of Science and Engineering, Swansea University, Swansea, SA1 8EN, Wales, United Kingdom
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9
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Aggarwal A, Jensen BS, Pant S, Lee CH. Strain energy density as a Gaussian process and its utilization in stochastic finite element analysis: application to planar soft tissues. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 2023; 404:115812. [PMID: 37235184 PMCID: PMC10208436 DOI: 10.1016/j.cma.2022.115812] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/28/2023]
Abstract
Data-based approaches are promising alternatives to the traditional analytical constitutive models for solid mechanics. Herein, we propose a Gaussian process (GP) based constitutive modeling framework, specifically focusing on planar, hyperelastic and incompressible soft tissues. The strain energy density of soft tissues is modeled as a GP, which can be regressed to experimental stress-strain data obtained from biaxial experiments. Moreover, the GP model can be weakly constrained to be convex. A key advantage of a GP-based model is that, in addition to the mean value, it provides a probability density (i.e. associated uncertainty) for the strain energy density. To simulate the effect of this uncertainty, a non-intrusive stochastic finite element analysis (SFEA) framework is proposed. The proposed framework is verified against an artificial dataset based on the Gasser-Ogden-Holzapfel model and applied to a real experimental dataset of a porcine aortic valve leaflet tissue. Results show that the proposed framework can be trained with limited experimental data and fits the data better than several existing models. The SFEA framework provides a straightforward way of using the experimental data and quantifying the resulting uncertainty in simulation-based predictions.
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Affiliation(s)
- Ankush Aggarwal
- Glasgow Computational Engineering Centre, James Watt School of Engineering, University of Glasgow, Glasgow, G12 8LT, Scotland, United Kingdom
| | - Bjørn Sand Jensen
- School of Computing Science, University of Glasgow, Glasgow, G12 8LT, Scotland, United Kingdom
- Department of Applied Mathematics and Computer Science, Technical University of Denmark, Kgs. Lyngby, 2800, Denmark
| | - Sanjay Pant
- Zienkiewicz Centre for Computational Engineering, Swansea University, Swansea, SA18EP, Wales, United Kingdom
| | - Chung-Hao Lee
- School of Aerospace and Mechanical Engineering, The University of Oklahoma, Norman, 73019, OK, United States of America
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10
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You H, Zhang Q, Ross CJ, Lee CH, Hsu MC, Yu Y. A Physics-Guided Neural Operator Learning Approach to Model Biological Tissues From Digital Image Correlation Measurements. J Biomech Eng 2022; 144:121012. [PMID: 36218246 PMCID: PMC9632476 DOI: 10.1115/1.4055918] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/31/2022] [Revised: 10/04/2022] [Indexed: 11/08/2022]
Abstract
We present a data-driven workflow to biological tissue modeling, which aims to predict the displacement field based on digital image correlation (DIC) measurements under unseen loading scenarios, without postulating a specific constitutive model form nor possessing knowledge of the material microstructure. To this end, a material database is constructed from the DIC displacement tracking measurements of multiple biaxial stretching protocols on a porcine tricuspid valve anterior leaflet, with which we build a neural operator learning model. The material response is modeled as a solution operator from the loading to the resultant displacement field, with the material microstructure properties learned implicitly from the data and naturally embedded in the network parameters. Using various combinations of loading protocols, we compare the predictivity of this framework with finite element analysis based on three conventional constitutive models. From in-distribution tests, the predictivity of our approach presents good generalizability to different loading conditions and outperforms the conventional constitutive modeling at approximately one order of magnitude. When tested on out-of-distribution loading ratios, the neural operator learning approach becomes less effective. To improve the generalizability of our framework, we propose a physics-guided neural operator learning model via imposing partial physics knowledge. This method is shown to improve the model's extrapolative performance in the small-deformation regime. Our results demonstrate that with sufficient data coverage and/or guidance from partial physics constraints, the data-driven approach can be a more effective method for modeling biological materials than the traditional constitutive modeling.
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Affiliation(s)
- Huaiqian You
- Department of Mathematics, Lehigh University, Bethlehem, PA 18015
| | - Quinn Zhang
- Department of Mathematics, Lehigh University, Bethlehem, PA 18015
| | - Colton J. Ross
- School of Aerospace and Mechanical Engineering, The University of Oklahoma, Norman, OK 73019
| | - Chung-Hao Lee
- School of Aerospace and Mechanical Engineering, The University of Oklahoma, Norman, OK 73019
| | - Ming-Chen Hsu
- Department of Mechanical Engineering, Iowa State University, Ames, IA 50011
| | - Yue Yu
- Department of Mathematics, Lehigh University, Bethlehem, PA 18015
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11
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Wu W, Ching S, Maas SA, Lasso A, Sabin P, Weiss JA, Jolley MA. A Computational Framework for Atrioventricular Valve Modeling Using Open-Source Software. J Biomech Eng 2022; 144:101012. [PMID: 35510823 PMCID: PMC9254695 DOI: 10.1115/1.4054485] [Citation(s) in RCA: 11] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/31/2022] [Revised: 04/27/2022] [Indexed: 11/08/2022]
Abstract
Atrioventricular valve regurgitation is a significant cause of morbidity and mortality in patients with acquired and congenital cardiac valve disease. Image-derived computational modeling of atrioventricular valves has advanced substantially over the last decade and holds particular promise to inform valve repair in small and heterogeneous populations, which are less likely to be optimized through empiric clinical application. While an abundance of computational biomechanics studies has investigated mitral and tricuspid valve disease in adults, few studies have investigated its application to vulnerable pediatric and congenital heart populations. Further, to date, investigators have primarily relied upon a series of commercial applications that are neither designed for image-derived modeling of cardiac valves nor freely available to facilitate transparent and reproducible valve science. To address this deficiency, we aimed to build an open-source computational framework for the image-derived biomechanical analysis of atrioventricular valves. In the present work, we integrated an open-source valve modeling platform, SlicerHeart, and an open-source biomechanics finite element modeling software, FEBio, to facilitate image-derived atrioventricular valve model creation and finite element analysis. We present a detailed verification and sensitivity analysis to demonstrate the fidelity of this modeling in application to three-dimensional echocardiography-derived pediatric mitral and tricuspid valve models. Our analyses achieved an excellent agreement with those reported in the literature. As such, this evolving computational framework offers a promising initial foundation for future development and investigation of valve mechanics, in particular collaborative efforts targeting the development of improved repairs for children with congenital heart disease.
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Affiliation(s)
- Wensi Wu
- Department of Anesthesiology and Critical Care Medicine, Children's Hospital of Philadelphia, Philadelphia, PA 19104
| | - Stephen Ching
- Department of Anesthesiology and Critical Care Medicine, Children's Hospital of Philadelphia, Philadelphia, PA 19104
| | - Steve A Maas
- Department of Biomedical Engineering, Scientific Computing and Imaging Institute, University of Utah, Salt Lake City, UT 84112
| | - Andras Lasso
- Laboratory for Percutaneous Surgery, Queen's University, Kingston, ON K7L 3N6, Canada
| | - Patricia Sabin
- Department of Anesthesiology and Critical Care Medicine, Children's Hospital of Philadelphia, Philadelphia, PA 19104
| | - Jeffrey A Weiss
- Department of Biomedical Engineering, Scientific Computing and Imaging Institute, University of Utah, Salt Lake City, UT 84112
| | - Matthew A Jolley
- Department of Anesthesiology and Critical Care Medicine, Division of Pediatric Cardiology, Children's Hospital of Philadelphia, Philadelphia, PA 19104
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12
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Benchtop characterization of the tricuspid valve leaflet pre-strains. Acta Biomater 2022; 152:321-334. [PMID: 36041649 DOI: 10.1016/j.actbio.2022.08.046] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/27/2022] [Revised: 08/01/2022] [Accepted: 08/22/2022] [Indexed: 11/21/2022]
Abstract
The pre-strains of biological soft tissues are important when relating their in vitro and in vivo mechanical behaviors. In this study, we present the first-of-its-kind experimental characterization of the tricuspid valve leaflet pre-strains. We use 3D photogrammetry and the reproducing kernel method to calculate the pre-strains within the central 10×10 mm region of the tricuspid valve leaflets from n=8 porcine hearts. In agreement with previous pre-strain studies for heart valve leaflets, our results show that all the three tricuspid valve leaflets shrink after explant from the ex vivo heart. These calculated strains are leaflet-specific and the septal leaflet experiences the most compressive changes. Furthermore, the strains observed after dissection of the central 10×10 mm region of the leaflet are smaller than when the valve is explanted, suggesting that our computed pre-strains are mainly due to the release of in situ annulus and chordae connections. The leaflets are then mounted on a biaxial testing device and preconditioned using force-controlled equibiaxial loading. We show that the employed preconditioning protocol does not 100% restore the leaflet pre-strains as removed during tissue dissection, and future studies are warranted to explore alternative preconditioning methods. Finally, we compare the calculated biomechanically oriented metrics considering five stress-free reference configurations. Interestingly, the radial tissue stretches and material anisotropies are significantly smaller compared to the post-preconditioning configuration. Extensions of this work can further explore the role of this unique leaflet-specific leaflet pre-strains on in vivo valve behavior via high-fidelity in-silico models.
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13
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Gaidulis G, Suresh KS, Xu D, Padala M. Patient-Specific Three-Dimensional Ultrasound Derived Computational Modeling of the Mitral Valve. Ann Biomed Eng 2022; 50:847-859. [PMID: 35380321 PMCID: PMC10826907 DOI: 10.1007/s10439-022-02960-x] [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: 12/27/2021] [Accepted: 03/27/2022] [Indexed: 11/01/2022]
Abstract
Several new techniques to repair the mitral valve affected by functional mitral regurgitation are in development. However, due to the heterogeneity of valve lesions between patients, predicting the outcomes of novel treatment approaches is challenging. We present a patient-specific, 3D ultrasound-derived computational model of the mitral valve for procedure planning, that faithfully mimics the pathological valve dynamics. 3D ultrasound images were obtained in three pigs induced with heart failure and which developed functional mitral regurgitation. For each case, images were segmented, and finite element model of mitral valve was constructed. Annular and papillary muscle dynamics were extracted and imposed as kinematic boundary conditions, and the chordae were pre-strained to induce valve tethering. Valve closure was simulated by applying physiologic transvalvular pressure on the leaflets. Agreement between simulation results and truth datasets was confirmed, with accurate location of regurgitation jets and coaptation defects. Inclusion of kinematic patient-specific boundary conditions was necessary to achieve these results, whereas use of idealized boundary conditions deviated from the truth dataset. Due to the impact of boundary conditions on the model, the effect of repair strategies on valve closure varied as well, indicating that our approach of using patient-specific boundary conditions for mitral valve modeling is valid.
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Affiliation(s)
- Gediminas Gaidulis
- Structural Heart Research and Innovation Laboratory, Carlyle Fraser Heart Center at Emory University Hospital Midtown, 380B Northyards Blvd NW, Atlanta, GA, 30313, USA
- Division of Cardiothoracic Surgery, Emory University School of Medicine, Atlanta, GA, USA
| | - Kirthana Sreerangathama Suresh
- Structural Heart Research and Innovation Laboratory, Carlyle Fraser Heart Center at Emory University Hospital Midtown, 380B Northyards Blvd NW, Atlanta, GA, 30313, USA
| | - Dongyang Xu
- Structural Heart Research and Innovation Laboratory, Carlyle Fraser Heart Center at Emory University Hospital Midtown, 380B Northyards Blvd NW, Atlanta, GA, 30313, USA
| | - Muralidhar Padala
- Structural Heart Research and Innovation Laboratory, Carlyle Fraser Heart Center at Emory University Hospital Midtown, 380B Northyards Blvd NW, Atlanta, GA, 30313, USA.
- Division of Cardiothoracic Surgery, Emory University School of Medicine, Atlanta, GA, USA.
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14
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Bracamonte JH, Saunders SK, Wilson JS, Truong UT, Soares JS. Patient-Specific Inverse Modeling of In Vivo Cardiovascular Mechanics with Medical Image-Derived Kinematics as Input Data: Concepts, Methods, and Applications. APPLIED SCIENCES-BASEL 2022; 12:3954. [PMID: 36911244 PMCID: PMC10004130 DOI: 10.3390/app12083954] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
Inverse modeling approaches in cardiovascular medicine are a collection of methodologies that can provide non-invasive patient-specific estimations of tissue properties, mechanical loads, and other mechanics-based risk factors using medical imaging as inputs. Its incorporation into clinical practice has the potential to improve diagnosis and treatment planning with low associated risks and costs. These methods have become available for medical applications mainly due to the continuing development of image-based kinematic techniques, the maturity of the associated theories describing cardiovascular function, and recent progress in computer science, modeling, and simulation engineering. Inverse method applications are multidisciplinary, requiring tailored solutions to the available clinical data, pathology of interest, and available computational resources. Herein, we review biomechanical modeling and simulation principles, methods of solving inverse problems, and techniques for image-based kinematic analysis. In the final section, the major advances in inverse modeling of human cardiovascular mechanics since its early development in the early 2000s are reviewed with emphasis on method-specific descriptions, results, and conclusions. We draw selected studies on healthy and diseased hearts, aortas, and pulmonary arteries achieved through the incorporation of tissue mechanics, hemodynamics, and fluid-structure interaction methods paired with patient-specific data acquired with medical imaging in inverse modeling approaches.
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Affiliation(s)
- Johane H. Bracamonte
- Department of Mechanical and Nuclear Engineering, Virginia Commonwealth University, Richmond, VA 23284, USA
| | - Sarah K. Saunders
- Department of Mechanical and Nuclear Engineering, Virginia Commonwealth University, Richmond, VA 23284, USA
| | - John S. Wilson
- Department of Biomedical Engineering and Pauley Heart Center, Virginia Commonwealth University, Richmond, VA 23219, USA
| | - Uyen T. Truong
- Department of Pediatrics, School of Medicine, Children’s Hospital of Richmond at Virginia Commonwealth University, Richmond, VA 23219, USA
| | - Joao S. Soares
- Department of Mechanical and Nuclear Engineering, Virginia Commonwealth University, Richmond, VA 23284, USA
- Correspondence:
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15
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Laurence DW, Lee CH, Johnson EL, Hsu MC. An in-silico benchmark for the tricuspid heart valve - Geometry, finite element mesh, Abaqus simulation, and result data set. Data Brief 2021; 39:107664. [PMID: 34917710 PMCID: PMC8668829 DOI: 10.1016/j.dib.2021.107664] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/25/2021] [Revised: 11/22/2021] [Accepted: 11/29/2021] [Indexed: 12/27/2022] Open
Abstract
This article provides Abaqus input files and user subroutines for performing finite element simulations of the tricuspid heart valve with an idealized geometry. Additional post-processing steps to obtain a ParaView visualization file (*.vtk) of the deformed geometry are also provided to allow the readers to use the included ParaView state file (*.pvsm) for customizable visualization and evaluation of the simulation results. We expect this first-of-its-kind in-silico benchmark dataset will facilitate user-friendly simulations considering material nonlinearity, leaflet-to-leaflet contact, and large deformations. Additionally, the information included herein can be used to rapidly evaluate other novel in-silico approaches developed for simulating cardiac valve function. The benchmark can be expanded to consider more complex features of the tricuspid valve function, such as the dynamic annulus motion or the time-varying transvalvular pressure. Interested readers are referred to the companion article (Johnson et al., 2021) for an example application of this in-silico tool for isogeometric analysis of tricuspid valves.
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Affiliation(s)
- Devin W Laurence
- School of Aerospace and Mechanical Engineering, The University of Oklahoma, 865 Asp Ave., Felgar Hall 212, Norman, OK 73019, USA
| | - Chung-Hao Lee
- School of Aerospace and Mechanical Engineering, The University of Oklahoma, 865 Asp Ave., Felgar Hall 212, Norman, OK 73019, USA
| | - Emily L Johnson
- Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, IN 46556, USA
| | - Ming-Chen Hsu
- Department of Mechanical Engineering, Iowa State University, Ames, IA 50011, USA
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16
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Laurence DW, Lee CH. Determination of a Strain Energy Density Function for the Tricuspid Valve Leaflets Using Constant Invariant-Based Mechanical Characterizations. J Biomech Eng 2021; 143:1120829. [PMID: 34596679 DOI: 10.1115/1.4052612] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/19/2021] [Indexed: 11/08/2022]
Abstract
The tricuspid valve (TV) regulates the blood flow within the right side of the heart. Despite recent improvements in understanding TV mechanical and microstructural properties, limited attention has been devoted to the development of TV-specific constitutive models. The objective of this work is to use the first-of-its-kind experimental data from constant invariant-based mechanical characterizations to determine a suitable invariant-based strain energy density function (SEDF). Six specimens for each TV leaflet are characterized using constant invariant mechanical testing. The data is then fit with three candidate SEDF forms: (i) a polynomial model-the transversely isotropic version of the Mooney-Rivlin model, (ii) an exponential model, and (iii) a combined polynomial-exponential model. Similar fitting capabilities were found for the exponential and the polynomial forms (R2=0.92-0.99 versus 0.91-0.97) compared to the combined polynomial-exponential SEDF (R2=0.65-0.95). Furthermore, the polynomial form had larger Pearson's correlation coefficients than the exponential form (0.51 versus 0.30), indicating a more well-defined search space. Finally, the exponential and the combined polynomial-exponential forms had notably smaller but more eccentric model parameter's confidence regions than the polynomial form. Further evaluations of invariant decoupling revealed that the decoupling of the invariant terms within the exponential form leads to a less satisfactory performance. From these results, we conclude that the exponential form is better suited for the TV leaflets owing to its superb fitting capabilities and smaller parameter's confidence regions.
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Affiliation(s)
- Devin W Laurence
- Biomechanics and Biomaterials Design Laboratory, The University of Oklahoma, Norman, OK 73019
| | - Chung-Hao Lee
- Biomechanics and Biomaterials Design Laboratory, The University of Oklahoma, 865 Asp Avenue, Felgar Hall 219C, Norman, OK 73019; Institute for Biomedical Engineering, Science and Technology, The University of Oklahoma, 865 Asp Avenue, Felgar Hall 219C, Norman, OK 73019
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17
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Park MH, Zhu Y, Imbrie-Moore AM, Wang H, Marin-Cuartas M, Paulsen MJ, Woo YJ. Heart Valve Biomechanics: The Frontiers of Modeling Modalities and the Expansive Capabilities of Ex Vivo Heart Simulation. Front Cardiovasc Med 2021; 8:673689. [PMID: 34307492 PMCID: PMC8295480 DOI: 10.3389/fcvm.2021.673689] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/28/2021] [Accepted: 05/17/2021] [Indexed: 01/05/2023] Open
Abstract
The field of heart valve biomechanics is a rapidly expanding, highly clinically relevant area of research. While most valvular pathologies are rooted in biomechanical changes, the technologies for studying these pathologies and identifying treatments have largely been limited. Nonetheless, significant advancements are underway to better understand the biomechanics of heart valves, pathologies, and interventional therapeutics, and these advancements have largely been driven by crucial in silico, ex vivo, and in vivo modeling technologies. These modalities represent cutting-edge abilities for generating novel insights regarding native, disease, and repair physiologies, and each has unique advantages and limitations for advancing study in this field. In particular, novel ex vivo modeling technologies represent an especially promising class of translatable research that leverages the advantages from both in silico and in vivo modeling to provide deep quantitative and qualitative insights on valvular biomechanics. The frontiers of this work are being discovered by innovative research groups that have used creative, interdisciplinary approaches toward recapitulating in vivo physiology, changing the landscape of clinical understanding and practice for cardiovascular surgery and medicine.
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Affiliation(s)
- Matthew H Park
- Department of Cardiothoracic Surgery, Stanford University, Stanford, CA, United States.,Department of Mechanical Engineering, Stanford University, Stanford, CA, United States
| | - Yuanjia Zhu
- Department of Cardiothoracic Surgery, Stanford University, Stanford, CA, United States.,Department of Bioengineering, Stanford University, Stanford, CA, United States
| | - Annabel M Imbrie-Moore
- Department of Cardiothoracic Surgery, Stanford University, Stanford, CA, United States.,Department of Mechanical Engineering, Stanford University, Stanford, CA, United States
| | - Hanjay Wang
- Department of Cardiothoracic Surgery, Stanford University, Stanford, CA, United States
| | - Mateo Marin-Cuartas
- Department of Cardiothoracic Surgery, Stanford University, Stanford, CA, United States.,University Department of Cardiac Surgery, Leipzig Heart Center, Leipzig, Germany
| | - Michael J Paulsen
- Department of Cardiothoracic Surgery, Stanford University, Stanford, CA, United States
| | - Y Joseph Woo
- Department of Cardiothoracic Surgery, Stanford University, Stanford, CA, United States.,Department of Bioengineering, Stanford University, Stanford, CA, United States
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18
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Stanová V, Godio Raboutet Y, Barragan P, Thollon L, Pibarot P, Rieu R. Leaflet stress quantification of porcine vs bovine surgical bioprostheses: an in vitro study. Comput Methods Biomech Biomed Engin 2021; 25:40-51. [PMID: 34219548 DOI: 10.1080/10255842.2021.1928092] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
Abstract
Calcified aortic stenoses are among the most prevalent form of cardiovascular diseases in the industrialized countries. This progressive disease, with no effective medical therapy, ultimately requires aortic valve replacement - either a surgical or very recently transcatheter aortic valve implantation. Increase leaflet mechanical stress is one of the main determinants of the structural deterioration of bioprosthetic aortic valves. We applied a coupled in vitro/in silico method to compare the timing, magnitude, and regional distribution of leaflet mechanical stress in porcine versus pericardial bioprostheses (Mosaic and Trifecta). A double activation simulator was used for in vitro testing of a bioprosthesis with externally mounted pericardium (Abbott, Trifecta) and a bioprosthesis with internally mounted porcine valve (Medtronic, Mosaic). A non-contact system based on stereophotogammetry and digital image correlation (DIC) with high spatial and temporal resolution (2000 img/s) was used to visualize the valve leaflet motion and perform the three-dimensional analysis. A finite element model of the valve was developed, and the leaflet deformation obtained from the DIC analysis was applied to the finite element model calculate local leaflet mechanical stress throughout the cardiac cycle. The maximum leaflet stress was higher with the pericardial versus the porcine bioprosthesis (2.03 vs. 1.30 MPa) For both bioprostheses the highest values of leaflet stress occurred during diastole and were primarily observed in the upper leaflet edge near the commissures and to a lesser extent in the mid-portion of the leaflet body. In conclusion, the coupled in vitro/in silico method described in this study shows that the highest levels of leaflet stress occur in the regions of the commissures and mid-portion of the leaflet body. This method may have important insight with regard to bioprosthetic valve durability. Our results suggest that, compared to porcine bioprostheses, those with externally mounted pericardium have higher leaflet mechanical stress, which may translate into shorter durability.
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Affiliation(s)
- Viktória Stanová
- Laboratoire de Biomécanique Appliquée, UMR T24 Université Gustave Eiffel / Aix Marseille Université, Marseille, France
| | - Yves Godio Raboutet
- Laboratoire de Biomécanique Appliquée, UMR T24 Université Gustave Eiffel / Aix Marseille Université, Marseille, France
| | | | - Lionel Thollon
- Laboratoire de Biomécanique Appliquée, UMR T24 Université Gustave Eiffel / Aix Marseille Université, Marseille, France
| | - Philippe Pibarot
- Quebec Heart and Lung Institute, Laval University, Quebec, Canada
| | - Régis Rieu
- Laboratoire de Biomécanique Appliquée, UMR T24 Université Gustave Eiffel / Aix Marseille Université, Marseille, France
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19
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Redaelli A, Votta E. Cardiovascular patient-specific modeling: Where are we now and what does the future look like? APL Bioeng 2020; 4:040401. [PMID: 33195957 DOI: 10.1063/5.0031452] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/30/2020] [Accepted: 10/23/2020] [Indexed: 12/15/2022] Open
Affiliation(s)
- Alberto Redaelli
- Department of Electronics, Information and Bioengineering, Politecnico di Milano, Milan, Italy
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20
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He Q, Laurence DW, Lee CH, Chen JS. Manifold learning based data-driven modeling for soft biological tissues. J Biomech 2020; 117:110124. [PMID: 33515902 DOI: 10.1016/j.jbiomech.2020.110124] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/16/2020] [Revised: 07/16/2020] [Accepted: 11/03/2020] [Indexed: 02/08/2023]
Abstract
Data-driven modeling directly utilizes experimental data with machine learning techniques to predict a material's response without the necessity of using phenomenological constitutive models. Although data-driven modeling presents a promising new approach, it has yet to be extended to the modeling of large-deformation biological tissues. Herein, we extend our recent local convexity data-driven (LCDD) framework (He and Chen, 2020) to model the mechanical response of a porcine heart mitral valve posterior leaflet. The predictability of the LCDD framework by using various combinations of biaxial and pure shear training protocols are investigated, and its effectiveness is compared with a full structural, phenomenological model modified from Zhang et al. (2016) and a continuum phenomenological Fung-type model (Tong and Fung, 1976). We show that the predictivity of the proposed LCDD nonlinear solver is generally less sensitive to the type of loading protocols (biaxial and pure shear) used in the data set, while more sensitive to the insufficient coverage of the experimental data when compared to the predictivity of the two selected phenomenological models. While no pre-defined functional form in the material model is necessary in LCDD, this study reinstates the importance of having sufficiently rich data coverage in the date-driven and machine learning type of approaches. It is also shown that the proposed LCDD method is an enhancement over the earlier distance-minimization data-driven (DMDD) against noisy data. This study demonstrates that when sufficient data is available, data-driven computing can be an alternative method for modeling complex biological materials.
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Affiliation(s)
- Qizhi He
- Department of Structural Engineering, University of California, San Diego, La Jolla, CA 92093, USA; Physical and Computational Sciences Directorate, Pacific Northwest National Laboratory, Richland, WA 99354, USA
| | - Devin W Laurence
- Biomechanics and Biomaterials Design Laboratory, School of Aerospace and Mechanical Engineering, The University of Oklahoma, Norman, OK 73019, USA
| | - Chung-Hao Lee
- Biomechanics and Biomaterials Design Laboratory, School of Aerospace and Mechanical Engineering, The University of Oklahoma, Norman, OK 73019, USA; Institute for Biomedical Engineering, Science and Technology, The University of Oklahoma, Norman, OK 73019, USA
| | - Jiun-Shyan Chen
- Department of Structural Engineering, University of California, San Diego, La Jolla, CA 92093, USA.
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21
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Ticar JM, Gaidulis G, Veith K, Rath C, Jarman J, Mohl W. Mitral Butterfly: Preclinical Experience of a Novel Chordal Repair Device Using an Artificial Papillary Muscle. ACTA ACUST UNITED AC 2020; 5:1002-1014. [PMID: 33145463 PMCID: PMC7591935 DOI: 10.1016/j.jacbts.2020.08.007] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/17/2020] [Revised: 08/10/2020] [Accepted: 08/12/2020] [Indexed: 01/08/2023]
Abstract
Transcatheter mitral repair is based on the principle of artificial monochordal repair. In this paper, the authors show an alternative, based on the realization of an artificial papillary muscle concept that avoids multiple chordal replacements and fixation in the myocardium. Unlike the interposition of artificial chordae between the free edge of the leaflet and the myocardium, the so-called Mitral Butterfly device collects a multitude of chordae in a matrix connected to a swing arm, stabilizing prolapsing forces with a broad atrial support. Device testing in chronic animal models and in silico substantiated the underlying device concept and performance after 90 days.
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Affiliation(s)
| | - Gediminas Gaidulis
- Department of Biomechanical Engineering, Vilnius Gediminas Technical University, Vilnius, Lithuania
| | | | - Claus Rath
- Department of Anatomy, Medical University of Vienna, Vienna, Austria
| | | | - Werner Mohl
- AVVie GmbH, Vienna, Austria
- Department of Surgery, Medical University of Vienna, Vienna, Austria
- Address for correspondence: Dr. Werner Mohl, Medical University of Vienna, AVVie GmbH, Lazarettgasse 12/1, 1090 Vienna, Austria.
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22
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Introduction to the Special Issue on Advances in Biological Tissue Biomechanics. Bioengineering (Basel) 2020; 7:bioengineering7030095. [PMID: 32824476 PMCID: PMC7552630 DOI: 10.3390/bioengineering7030095] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Key Words] [Track Full Text] [Download PDF] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/13/2020] [Accepted: 08/14/2020] [Indexed: 11/20/2022] Open
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23
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Laurence DW, Johnson EL, Hsu MC, Baumwart R, Mir A, Burkhart HM, Holzapfel GA, Wu Y, Lee CH. A pilot in silico modeling-based study of the pathological effects on the biomechanical function of tricuspid valves. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2020; 36:e3346. [PMID: 32362054 PMCID: PMC8039906 DOI: 10.1002/cnm.3346] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/08/2020] [Revised: 03/23/2020] [Accepted: 04/22/2020] [Indexed: 05/12/2023]
Abstract
Current clinical assessment of functional tricuspid valve regurgitation relies on metrics quantified from medical imaging modalities. Although these clinical methodologies are generally successful, the lack of detailed information about the mechanical environment of the valve presents inherent challenges for assessing tricuspid valve regurgitation. In the present study, we have developed a finite element-based in silico model of one porcine tricuspid valve (TV) geometry to investigate how various pathological conditions affect the overall biomechanical function of the TV. There were three primary observations from our results. Firstly, the results of the papillary muscle (PM) displacement study scenario indicated more pronounced changes in the TV biomechanical function. Secondly, compared to uniform annulus dilation, nonuniform dilation scenario induced more evident changes in the von Mises stresses (83.8-125.3 kPa vs 65.1-84.0 kPa) and the Green-Lagrange strains (0.52-0.58 vs 0.47-0.53) for the three TV leaflets. Finally, results from the pulmonary hypertension study scenario showed opposite trends compared to the PM displacement and annulus dilation scenarios. Furthermore, various chordae rupture scenarios were simulated, and the results showed that the chordae tendineae attached to the TV anterior and septal leaflets may be more critical to proper TV function. This in silico modeling-based study has provided a deeper insight into the tricuspid valve pathologies that may be useful, with moderate extensions, for guiding clinical decisions. NOVELTY STATEMENT: The novelties of the research are summarized below: A comprehensive in silico pilot study of how isolated functional tricuspid regurgitation pathologies and ruptured chordae tendineae would alter the tricuspid valve function; An extensive analysis of the tricuspid valve function, including mechanical quantities (eg, the von Mises stress and the Green-Lagrange strain) and clinically-relevant geometry metrics (eg, the tenting area and the coaptation height); and A developed computational modeling pipeline that can be extended to evaluate patient-specific tricuspid valve geometries and enhance the current clinical diagnosis and treatment of tricuspid regurgitation.
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Affiliation(s)
- Devin W. Laurence
- Biomechanics and Biomaterials Design Laboratory, School of Aerospace and Mechanical Engineering, The University of Oklahoma, Norman, OK 73019, USA
| | - Emily L. Johnson
- Computational Fluid-Structure Interaction Laboratory, Department of Mechanical Engineering, Iowa State University, Ames, IA 50011, USA
| | - Ming-Chen Hsu
- Computational Fluid-Structure Interaction Laboratory, Department of Mechanical Engineering, Iowa State University, Ames, IA 50011, USA
| | - Ryan Baumwart
- Center for Veterinary Health Sciences, Oklahoma State University, Stillwater, OK 74078, USA
| | - Arshid Mir
- Division of Pediatric Cardiology, Department of Pediatrics, The University of Oklahoma Health Sciences Center, Oklahoma City, OK 73104, USA
| | - Harold M. Burkhart
- Division of Cardiothoracic Surgery, Department of Surgery, The University of Oklahoma Health Sciences Center, Oklahoma City, OK 73104, USA
| | - Gerhard A. Holzapfel
- Institute of Biomechanics, Graz University of Technology, Stremayrgasse 16/2 8010 Graz, Austria
- Department of Structural Engineering, Norwegian University of Science and Technology (NTNU), 7491 Trondheim, Norway
| | - Yi Wu
- Biomechanics and Biomaterials Design Laboratory, School of Aerospace and Mechanical Engineering, The University of Oklahoma, Norman, OK 73019, USA
| | - Chung-Hao Lee
- Biomechanics and Biomaterials Design Laboratory, School of Aerospace and Mechanical Engineering, The University of Oklahoma, Norman, OK 73019, USA
- Institute for Biomedical Engineering, Science, and Technology, The University of Oklahoma, Norman, OK 73019, USA
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24
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Wu MCH, Muchowski HM, Johnson EL, Rajanna MR, Hsu MC. Immersogeometric fluid-structure interaction modeling and simulation of transcatheter aortic valve replacement. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 2019; 357:112556. [PMID: 32831419 PMCID: PMC7442159 DOI: 10.1016/j.cma.2019.07.025] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/10/2023]
Abstract
The transcatheter aortic valve replacement (TAVR) has emerged as a minimally invasive alternative to surgical treatments of valvular heart disease. TAVR offers many advantages, however, the safe anchoring of the transcatheter heart valve (THV) in the patients anatomy is key to a successful procedure. In this paper, we develop and apply a novel immersogeometric fluid-structure interaction (FSI) framework for the modeling and simulation of the TAVR procedure to study the anchoring ability of the THV. To account for physiological realism, methods are proposed to model and couple the main components of the system, including the arterial wall, blood flow, valve leaflets, skirt, and frame. The THV is first crimped and deployed into an idealized ascending aorta. During the FSI simulation, the radial outward force and friction force between the aortic wall and the THV frame are examined over the entire cardiac cycle. The ratio between these two forces is computed and compared with the experimentally estimated coefficient of friction to study the likelihood of valve migration.
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Affiliation(s)
- Michael C. H. Wu
- Department of Mechanical Engineering, Iowa State University, 2043 Black Engineering, Ames, Iowa 50011, USA
- School of Engineering, Brown University, 184 Hope Street, Providence, Rhode Island 02912, USA
| | - Heather M. Muchowski
- Department of Mechanical Engineering, Iowa State University, 2043 Black Engineering, Ames, Iowa 50011, USA
- Department of Mathematics, Iowa State University, 396 Carver Hall, Ames, Iowa 50011, USA
| | - Emily L. Johnson
- Department of Mechanical Engineering, Iowa State University, 2043 Black Engineering, Ames, Iowa 50011, USA
| | - Manoj R. Rajanna
- Department of Mechanical Engineering, Iowa State University, 2043 Black Engineering, Ames, Iowa 50011, USA
| | - Ming-Chen Hsu
- Department of Mechanical Engineering, Iowa State University, 2043 Black Engineering, Ames, Iowa 50011, USA
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Aggarwal A. Effect of Residual and Transformation Choice on Computational Aspects of Biomechanical Parameter Estimation of Soft Tissues. Bioengineering (Basel) 2019; 6:bioengineering6040100. [PMID: 31671871 PMCID: PMC6956274 DOI: 10.3390/bioengineering6040100] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/19/2019] [Revised: 10/28/2019] [Accepted: 10/28/2019] [Indexed: 12/30/2022] Open
Abstract
Several nonlinear and anisotropic constitutive models have been proposed to describe the biomechanical properties of soft tissues, and reliably estimating the unknown parameters in these models using experimental data is an important step towards developing predictive capabilities. However, the effect of parameter estimation technique on the resulting biomechanical parameters remains under-analyzed. Standard off-the-shelf techniques can produce unreliable results where the parameters are not uniquely identified and can vary with the initial guess. In this study, a thorough analysis of parameter estimation techniques on the resulting properties for four multi-parameter invariant-based constitutive models is presented. It was found that linear transformations have no effect on parameter estimation for the presented cases, and nonlinear transforms are necessary for any improvement. A distinct focus is put on the issue of non-convergence, and we propose simple modifications that not only improve the speed of convergence but also avoid convergence to a wrong solution. The proposed modifications are straightforward to implement and can avoid severe problems in the biomechanical analysis. The results also show that including the fiber angle as an unknown in the parameter estimation makes it extremely challenging, where almost all of the formulations and models fail to converge to the true solution. Therefore, until this issue is resolved, a non-mechanical—such as optical—technique for determining the fiber angle is required in conjunction with the planar biaxial test for a robust biomechanical analysis.
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Affiliation(s)
- Ankush Aggarwal
- Glasgow Computational Engineering Centre, School of Engineering, University of Glasgow, Glasgow G12 8LT, UK.
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Pant AD, Dorairaj SK, Amini R. Appropriate Objective Functions for Quantifying Iris Mechanical Properties Using Inverse Finite Element Modeling. J Biomech Eng 2019; 140:2676340. [PMID: 29570756 DOI: 10.1115/1.4039679] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/07/2017] [Indexed: 01/08/2023]
Abstract
Quantifying the mechanical properties of the iris is important, as it provides insight into the pathophysiology of glaucoma. Recent ex vivo studies have shown that the mechanical properties of the iris are different in glaucomatous eyes as compared to normal ones. Notwithstanding the importance of the ex vivo studies, such measurements are severely limited for diagnosis and preclude development of treatment strategies. With the advent of detailed imaging modalities, it is possible to determine the in vivo mechanical properties using inverse finite element (FE) modeling. An inverse modeling approach requires an appropriate objective function for reliable estimation of parameters. In the case of the iris, numerous measurements such as iris chord length (CL) and iris concavity (CV) are made routinely in clinical practice. In this study, we have evaluated five different objective functions chosen based on the iris biometrics (in the presence and absence of clinical measurement errors) to determine the appropriate criterion for inverse modeling. Our results showed that in the absence of experimental measurement error, a combination of iris CL and CV can be used as the objective function. However, with the addition of measurement errors, the objective functions that employ a large number of local displacement values provide more reliable outcomes.
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Affiliation(s)
- Anup D Pant
- Department of Biomedical Engineering, The University of Akron, Akron, OH 44325 e-mail:
| | - Syril K Dorairaj
- Department of Ophthalmology, Mayo Clinic, Jacksonville, FL 32224 e-mail:
| | - Rouzbeh Amini
- Mem. ASME Department of Biomedical Engineering, The University of Akron, Akron, OH 44325 e-mail:
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Some Effects of Different Constitutive Laws on FSI Simulation for the Mitral Valve. Sci Rep 2019; 9:12753. [PMID: 31484963 PMCID: PMC6726639 DOI: 10.1038/s41598-019-49161-6] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/01/2019] [Accepted: 08/20/2019] [Indexed: 12/23/2022] Open
Abstract
In this paper, three different constitutive laws for mitral leaflets and two laws for chordae tendineae are selected to study their effects on mitral valve dynamics with fluid-structure interaction. We first fit these three mitral leaflet constitutive laws and two chordae tendineae laws with experimental data. The fluid-structure interaction is implemented in an immersed boundary framework with finite element extension for solid, that is the hybrid immersed boundary/finite element(IB/FE) method. We specifically compare the fluid-structure results of different constitutive laws since fluid-structure interaction is the physiological loading environment. This allows us to look at the peak jet velocity, the closure regurgitation volume, and the orifice area. Our numerical results show that different constitutive laws can affect mitral valve dynamics, such as the transvalvular flow rate, closure regurgitation and the orifice area, while the differences in fiber strain and stress are insignificant because all leaflet constitutive laws are fitted to the same set of experimental data. In addition, when an exponential constitutive law of chordae tendineae is used, a lower closure regurgitation flow is observed compared to that of a linear material model. In conclusion, combining numerical dynamic simulations and static experimental tests, we are able to identify suitable constitutive laws for dynamic behaviour of mitral leaflets and chordae under physiological conditions.
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Ross CJ, Laurence DW, Richardson J, Babu AR, Evans LE, Beyer EG, Childers RC, Wu Y, Towner RA, Fung KM, Mir A, Burkhart HM, Holzapfel GA, Lee CH. An investigation of the glycosaminoglycan contribution to biaxial mechanical behaviours of porcine atrioventricular heart valve leaflets. J R Soc Interface 2019; 16:20190069. [PMID: 31266416 PMCID: PMC6685018 DOI: 10.1098/rsif.2019.0069] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/03/2019] [Accepted: 06/03/2019] [Indexed: 01/06/2023] Open
Abstract
The atrioventricular heart valve (AHV) leaflets have a complex microstructure composed of four distinct layers: atrialis, ventricularis, fibrosa and spongiosa. Specifically, the spongiosa layer is primarily proteoglycans and glycosaminoglycans (GAGs). Quantification of the GAGs' mechanical contribution to the overall leaflet function has been of recent focus for aortic valve leaflets, but this characterization has not been reported for the AHV leaflets. This study seeks to expand current GAG literature through novel mechanical characterizations of GAGs in AHV leaflets. For this characterization, mitral and tricuspid valve anterior leaflets (MVAL and TVAL, respectively) were: (i) tested by biaxial mechanical loading at varying loading ratios and by stress-relaxation procedures, (ii) enzymatically treated for removal of the GAGs and (iii) biaxially mechanically tested again under the same protocols as in step (i). Removal of the GAG contents from the leaflet was conducted using a 100 min enzyme treatment to achieve approximate 74.87% and 61.24% reductions of all GAGs from the MVAL and TVAL, respectively. Our main findings demonstrated that biaxial mechanical testing yielded a statistically significant difference in tissue extensibility after GAG removal and that stress-relaxation testing revealed a statistically significant smaller stress decay of the enzyme-treated tissue than untreated tissues. These novel findings illustrate the importance of GAGs in AHV leaflet behaviour, which can be employed to better inform heart valve therapeutics and computational models.
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Affiliation(s)
- Colton J. Ross
- Biomechanics and Biomaterials Design Laboratory, School of Aerospace and Mechanical Engineering, The University of Oklahoma, Norman, OK, USA
| | - Devin W. Laurence
- Biomechanics and Biomaterials Design Laboratory, School of Aerospace and Mechanical Engineering, The University of Oklahoma, Norman, OK, USA
| | - Jacob Richardson
- Biomechanics and Biomaterials Design Laboratory, School of Aerospace and Mechanical Engineering, The University of Oklahoma, Norman, OK, USA
| | - Anju R. Babu
- Biomechanics and Biomaterials Design Laboratory, School of Aerospace and Mechanical Engineering, The University of Oklahoma, Norman, OK, USA
| | - Lauren E. Evans
- Biomechanics and Biomaterials Design Laboratory, School of Aerospace and Mechanical Engineering, The University of Oklahoma, Norman, OK, USA
| | - Ean G. Beyer
- Biomechanics and Biomaterials Design Laboratory, School of Aerospace and Mechanical Engineering, The University of Oklahoma, Norman, OK, USA
| | - Rachel C. Childers
- Stephenson School of Biomedical Engineering, The University of Oklahoma, Norman, OK, USA
| | - Yi Wu
- Biomechanics and Biomaterials Design Laboratory, School of Aerospace and Mechanical Engineering, The University of Oklahoma, Norman, OK, USA
| | - Rheal A. Towner
- Advanced Magnetic Resonance Center, MS 60, Oklahoma Medical Research Foundation, Oklahoma City, OK, USA
| | - Kar-Ming Fung
- Department of Pathology, The University of Oklahoma Health Sciences Center, Oklahoma City, OK, USA
- Stephenson Cancer Center, The University of Oklahoma Health Sciences Center, Oklahoma City, OK, USA
| | - Arshid Mir
- Division of Pediatric Cardiology, Department of Pediatrics, The University of Oklahoma Health Sciences Center, Oklahoma City, OK, USA
| | - Harold M. Burkhart
- Division of Cardiothoracic Surgery, Department of Surgery, The University of Oklahoma Health Sciences Center, Oklahoma City, OK, USA
| | - Gerhard A. Holzapfel
- Institute of Biomechanics, Graz University of Technology, Graz, Austria
- Department of Structural Engineering, Norwegian University of Science and Technology (NTNU), Trondheim, Norway
| | - Chung-Hao Lee
- Biomechanics and Biomaterials Design Laboratory, School of Aerospace and Mechanical Engineering, The University of Oklahoma, Norman, OK, USA
- Institute for Biomedical Engineering, Science and Technology, The University of Oklahoma, Norman, OK, USA
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Lee CH, Laurence DW, Ross CJ, Kramer KE, Babu AR, Johnson EL, Hsu MC, Aggarwal A, Mir A, Burkhart HM, Towner RA, Baumwart R, Wu Y. Mechanics of the Tricuspid Valve-From Clinical Diagnosis/Treatment, In-Vivo and In-Vitro Investigations, to Patient-Specific Biomechanical Modeling. Bioengineering (Basel) 2019; 6:E47. [PMID: 31121881 PMCID: PMC6630695 DOI: 10.3390/bioengineering6020047] [Citation(s) in RCA: 25] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/28/2019] [Revised: 05/16/2019] [Accepted: 05/17/2019] [Indexed: 12/29/2022] Open
Abstract
Proper tricuspid valve (TV) function is essential to unidirectional blood flow through the right side of the heart. Alterations to the tricuspid valvular components, such as the TV annulus, may lead to functional tricuspid regurgitation (FTR), where the valve is unable to prevent undesired backflow of blood from the right ventricle into the right atrium during systole. Various treatment options are currently available for FTR; however, research for the tricuspid heart valve, functional tricuspid regurgitation, and the relevant treatment methodologies are limited due to the pervasive expectation among cardiac surgeons and cardiologists that FTR will naturally regress after repair of left-sided heart valve lesions. Recent studies have focused on (i) understanding the function of the TV and the initiation or progression of FTR using both in-vivo and in-vitro methods, (ii) quantifying the biomechanical properties of the tricuspid valve apparatus as well as its surrounding heart tissue, and (iii) performing computational modeling of the TV to provide new insight into its biomechanical and physiological function. This review paper focuses on these advances and summarizes recent research relevant to the TV within the scope of FTR. Moreover, this review also provides future perspectives and extensions critical to enhancing the current understanding of the functioning and remodeling tricuspid valve in both the healthy and pathophysiological states.
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Affiliation(s)
- Chung-Hao Lee
- Biomechanics and Biomaterials Design Laboratory, School of Aerospace and Mechanical Engineering, The University of Oklahoma, Norman, OK 73019, USA.
- Institute for Biomedical Engineering, Science and Technology (IBEST), The University of Oklahoma, Norman, OK 73019, USA.
| | - Devin W Laurence
- Biomechanics and Biomaterials Design Laboratory, School of Aerospace and Mechanical Engineering, The University of Oklahoma, Norman, OK 73019, USA.
| | - Colton J Ross
- Biomechanics and Biomaterials Design Laboratory, School of Aerospace and Mechanical Engineering, The University of Oklahoma, Norman, OK 73019, USA.
| | - Katherine E Kramer
- Biomechanics and Biomaterials Design Laboratory, School of Aerospace and Mechanical Engineering, The University of Oklahoma, Norman, OK 73019, USA.
| | - Anju R Babu
- Biomechanics and Biomaterials Design Laboratory, School of Aerospace and Mechanical Engineering, The University of Oklahoma, Norman, OK 73019, USA.
- Department of Biotechnology and Medical Engineering, National Institute of Technology Rourkela, Rourkela, Odisha 769008, India.
| | - Emily L Johnson
- Department of Mechanical Engineering, Iowa State University, Ames, IA 50011, USA.
| | - Ming-Chen Hsu
- Department of Mechanical Engineering, Iowa State University, Ames, IA 50011, USA.
| | - Ankush Aggarwal
- Glasgow Computational Engineering Centre, School of Engineering, University of Glasgow, Scotland G12 8LT, UK.
| | - Arshid Mir
- Division of Pediatric Cardiology, Department of Pediatrics, The University of Oklahoma Health Sciences Center, Oklahoma City, OK 73104, USA.
| | - Harold M Burkhart
- Division of Cardiothoracic Surgery, Department of Surgery, The University of Oklahoma Health Sciences Center, Oklahoma City, OK 73104, USA.
| | - Rheal A Towner
- Advance Magnetic Resonance Center, MS 60, Oklahoma Medical Research Foundation, Oklahoma City, OK 73104, USA.
| | - Ryan Baumwart
- Center for Veterinary Health Sciences, Oklahoma State University, Stillwater, OK 74078, USA.
| | - Yi Wu
- Biomechanics and Biomaterials Design Laboratory, School of Aerospace and Mechanical Engineering, The University of Oklahoma, Norman, OK 73019, USA.
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Adham Esfahani S, Hassani K, Espino DM. Fluid-structure interaction assessment of blood flow hemodynamics and leaflet stress during mitral regurgitation. Comput Methods Biomech Biomed Engin 2019; 22:288-303. [PMID: 30596526 DOI: 10.1080/10255842.2018.1552683] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/11/2023]
Abstract
The aim of this study is to simulate the Mitral Regurgitation (MR) disease progression from mild to severe intensity. A Fluid Structure Interaction (FSI) model was developed to extract the hemodynamic parameters of blood flow in mitral regurgitation (MR) during systole. A two-dimensional (2D) geometry of the mitral valve was built based on the data resulting from Magnetic Resonance Imaging (MRI) dimensional measurements. The leaflets were assumed to be elastic. Using COMSOL software, the hemodynamic parameters of blood flow including velocity, pressure, and Von Mises stress contours were obtained by moving arbitrary Lagrange-Euler mesh. The results were obtained for normal and MR cases. They showed the effects of the abnormal distance between the leaflets on the amount of returned flow. Furthermore, the deformation of the leaflets was measured during systole. The results were found to be consistent with the relevant literature.
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Affiliation(s)
- Saeed Adham Esfahani
- a Mechanical Engineering Department, Majlesi Branch , Islamic Azad University , Isfahan , Iran
| | - Kamran Hassani
- b Department of Biomechanics, Science and Research Branch , Islamic Azad University , Tehran , Iran
| | - Daniel M Espino
- c Department of Mechanical Engineering , University of Birmingham , Birmingham , UK
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31
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A material modeling approach for the effective response of planar soft tissues for efficient computational simulations. J Mech Behav Biomed Mater 2019; 89:168-198. [DOI: 10.1016/j.jmbbm.2018.09.016] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/18/2018] [Revised: 08/22/2018] [Accepted: 09/14/2018] [Indexed: 11/23/2022]
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32
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Laurence D, Ross C, Jett S, Johns C, Echols A, Baumwart R, Towner R, Liao J, Bajona P, Wu Y, Lee CH. An investigation of regional variations in the biaxial mechanical properties and stress relaxation behaviors of porcine atrioventricular heart valve leaflets. J Biomech 2018; 83:16-27. [PMID: 30497683 PMCID: PMC8008702 DOI: 10.1016/j.jbiomech.2018.11.015] [Citation(s) in RCA: 34] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/10/2018] [Revised: 10/17/2018] [Accepted: 11/08/2018] [Indexed: 10/27/2022]
Abstract
The facilitation of proper blood flow through the heart depends on proper function of heart valve components, and alterations to any component can lead to heart disease or failure. Comprehension of these valvular diseases is reliant on thorough characterization of healthy heart valve structures for use in computational models. Previously, computational models have treated these leaflet structures as a structurally and mechanically homogenous material, which may not be an accurate description of leaflet mechanical response. In this study, we aimed to characterize the mechanics of the heart valve leaflet as a structurally heterogenous material. Specifically, porcine mitral valve and tricuspid valve anterior leaflets were sectioned into six regions and biaxial mechanical tests with various loading ratios and stress-relaxation test were performed on each regional tissue sample. Three main findings from this study were summarized as follows: (i) the central regions of the leaflet had a more anisotropic nature than edge regions, (ii) the mitral valve anterior leaflet was more extensible in regions closer to the annulus, and (iii) there was variance in the stress-relaxation behavior among all six regions, with mitral valve leaflet tissue regions exhibiting a greater decay than the tricuspid valve regions. This study presents a novel investigation of the regional variations in the heart valve biomechanics that has not been comprehensively examined. Our results thus allow for a refinement of computational models for more accurately predicting diseased or surgically-intervened condition, where tissue heterogeneity plays an essential role in the heart valve function.
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Affiliation(s)
- Devin Laurence
- Biomechanics and Biomaterials Design Laboratory (BBDL), School of Aerospace and Mechanical Engineering, The University of Oklahoma, Norman, OK 73019, USA
| | - Colton Ross
- Biomechanics and Biomaterials Design Laboratory (BBDL), School of Aerospace and Mechanical Engineering, The University of Oklahoma, Norman, OK 73019, USA
| | - Samuel Jett
- Biomechanics and Biomaterials Design Laboratory (BBDL), School of Aerospace and Mechanical Engineering, The University of Oklahoma, Norman, OK 73019, USA
| | - Cortland Johns
- Biomechanics and Biomaterials Design Laboratory (BBDL), School of Aerospace and Mechanical Engineering, The University of Oklahoma, Norman, OK 73019, USA
| | - Allyson Echols
- Biomechanics and Biomaterials Design Laboratory (BBDL), School of Aerospace and Mechanical Engineering, The University of Oklahoma, Norman, OK 73019, USA
| | - Ryan Baumwart
- Center for Veterinary Health Sciences, Oklahoma State University, Stillwater, OK 74078, USA
| | - Rheal Towner
- Advanced Magnetic Resonance Center, MS 60, Oklahoma Medical Research Foundation, Oklahoma City, OK 73104, USA
| | - Jun Liao
- Department of Bioengineering, The University of Texas at Arlington, Arlington, TX 76019, USA
| | - Pietro Bajona
- Department of Cardiovascular and Thoracic Surgery, The University of Texas Southwestern Medical Center, Dallas, TX 75390, USA
| | - Yi Wu
- Biomechanics and Biomaterials Design Laboratory (BBDL), School of Aerospace and Mechanical Engineering, The University of Oklahoma, Norman, OK 73019, USA
| | - Chung-Hao Lee
- Biomechanics and Biomaterials Design Laboratory (BBDL), School of Aerospace and Mechanical Engineering, The University of Oklahoma, Norman, OK 73019, USA; Institute for Biomedical Engineering, Science and Technology, The University of Oklahoma, Norman, OK 73019, USA.
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A Non-Invasive Material Characterization Framework for Bioprosthetic Heart Valves. Ann Biomed Eng 2018; 47:97-112. [PMID: 30229500 DOI: 10.1007/s10439-018-02129-5] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/17/2018] [Accepted: 09/11/2018] [Indexed: 10/28/2022]
Abstract
Computational modeling and simulation has become more common in design and development of bioprosthetic heart valves. To have a reliable computational model, considering accurate mechanical properties of biological soft tissue is one of the most important steps. The goal of this study was to present a non-invasive material characterization framework to determine mechanical propertied of soft tissue employed in bioprosthetic heart valves. Using integrated experimental methods (i.e., digital image correlation measurements and hemodynamic testing in a pulse duplicator system) and numerical methods (i.e., finite element modeling and optimization), three-dimensional anisotropic mechanical properties of leaflets used in two commercially available transcatheter aortic valves (i.e., Edwards SAPIEN 3 and Medtronic CoreValve) were characterized and compared to that of a commonly used and well-examined surgical bioprosthesis (i.e., Carpentier-Edwards PERIMOUNT Magna aortic heart valve). The results of the simulations showed that the highest stress value during one cardiac cycle was at the peak of systole in the three bioprostheses. In addition, in the diastole, the peak of maximum in-plane principal stress was 0.98, 0.96, and 2.95 MPa for the PERIMOUNT Magna, CoreValve, and SAPIEN 3, respectively. Considering leaflet stress distributions, there might be a difference in the long-term durability of different TAV models.
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Material characterization of cardiovascular biomaterials using an inverse finite-element method and an explicit solver. J Biomech 2018; 79:207-211. [PMID: 30060921 DOI: 10.1016/j.jbiomech.2018.07.026] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/02/2017] [Revised: 05/28/2018] [Accepted: 07/14/2018] [Indexed: 11/23/2022]
Abstract
The ability to accurately model soft tissue behavior, such as that of heart valve tissue, is essential for developing reliable numerical simulations and determining patient-specific care options. Although several material models can predict soft tissue behavior, complications may arise when these models are implemented into finite element (FE) programs, due to the addition of an arbitrary penalty parameter for numerically enforcing material incompressibility. Herein, an inverse methodology was developed in MATLAB to use previously published stress-strain data from experimental planar equibiaxial testing of five biomaterials used in heart valve cusp replacements, in conjunction with commercial explicit FE solver LS-DYNA, to optimize the material parameters and the penalty parameter for an anisotropic hyperelastic strain energy function. A two-parameter optimization involving the scaling constant of the strain energy function and the penalty parameter proved sufficient to produce acceptable material responses when compared with experimental behaviors under the same testing conditions, as long as analytically derived material constants were available for the other non-optimized parameters and the actual tissue thickness was not much less than 1 mm. Variations in the penalty parameter had a direct effect on the accuracy of the simulated responses, with a practical range determined to be 5×108-9×108 times the scaling constant of the strain energy function.
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Jett S, Laurence D, Kunkel R, Babu AR, Kramer K, Baumwart R, Towner R, Wu Y, Lee CH. An investigation of the anisotropic mechanical properties and anatomical structure of porcine atrioventricular heart valves. J Mech Behav Biomed Mater 2018; 87:155-171. [PMID: 30071486 PMCID: PMC8008704 DOI: 10.1016/j.jmbbm.2018.07.024] [Citation(s) in RCA: 48] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/14/2018] [Revised: 05/05/2018] [Accepted: 07/15/2018] [Indexed: 11/18/2022]
Abstract
Valvular heart diseases are complex disorders, varying in pathophysiological mechanism and affected valve components. Understanding the effects of these diseases on valve functionality requires a thorough characterization of the mechanics and structure of the healthy heart valves. In this study, we performed biaxial mechanical experiments with extensive testing protocols to examine the mechanical behaviors of the mitral valve and tricuspid valve leaflets. We also investigated the effect of loading rate, testing temperatures, species (porcine versus ovine hearts), and age (juvenile vs adult ovine hearts) on the mechanical responses of the leaflet tissues. In addition, we evaluated the structure of chordae tendineae within each valve and performed histological analysis on each atrioventricular leaflet. We found all tissues displayed a characteristic nonlinear anisotropic mechanical response, with radial stretches on average 30.7% higher than circumferential stretches under equibiaxial physiological loading. Tissue mechanical responses showed consistent mechanical stiffening in response to increased loading rate and minor temperature dependence in all five atrioventricular heart valve leaflets. Moreover, our anatomical study revealed similar chordae quantities in the porcine mitral (30.5 ± 1.43 chords) and tricuspid valves (35.3 ± 2.45 chords) but significantly more chordae in the porcine than the ovine valves (p < 0.010). Our histological analyses quantified the relative thicknesses of the four distinct morphological layers in each leaflet. This study provides a comprehensive database of the mechanics and structure of the atrioventricular valves, which will be beneficial to development of subject-specific atrioventricular valve constitutive models and toward multi-scale biomechanical investigations of heart valve function to improve valvular disease treatments.
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Affiliation(s)
- Samuel Jett
- School of Aerospace and Mechanical Engineering, The University of Oklahoma, 865 Asp Ave., Felgar Hall Rm. 219 C, Norman, OK 73019, USA
| | - Devin Laurence
- School of Aerospace and Mechanical Engineering, The University of Oklahoma, 865 Asp Ave., Felgar Hall Rm. 219 C, Norman, OK 73019, USA
| | - Robert Kunkel
- School of Aerospace and Mechanical Engineering, The University of Oklahoma, 865 Asp Ave., Felgar Hall Rm. 219 C, Norman, OK 73019, USA
| | - Anju R Babu
- School of Aerospace and Mechanical Engineering, The University of Oklahoma, 865 Asp Ave., Felgar Hall Rm. 219 C, Norman, OK 73019, USA
| | - Katherine Kramer
- School of Aerospace and Mechanical Engineering, The University of Oklahoma, 865 Asp Ave., Felgar Hall Rm. 219 C, Norman, OK 73019, USA
| | - Ryan Baumwart
- Center for Veterinary Health Sciences, Oklahoma State University, 208 S. McFarland Street, Stillwater, OK 74078, USA
| | - Rheal Towner
- Advanced Magnetic Resonance Center, MS 60, Oklahoma Medical Research Foundation 825 N.E. 13th Street, Oklahoma City, OK 73104, USA
| | - Yi Wu
- School of Aerospace and Mechanical Engineering, The University of Oklahoma, 865 Asp Ave., Felgar Hall Rm. 219 C, Norman, OK 73019, USA
| | - Chung-Hao Lee
- School of Aerospace and Mechanical Engineering, The University of Oklahoma, 865 Asp Ave., Felgar Hall Rm. 219 C, Norman, OK 73019, USA; Institute for Biomedical Engineering, Science and Technology (IBEST), The University of Oklahoma, Norman, OK 73019, USA.
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36
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Gaidulis G, Votta E, Selmi M, Aidietienė S, Aidietis A, Kačianauskas R. Numerical simulation of transapical off-pump mitral valve repair with neochordae implantation. Technol Health Care 2018; 26:635-645. [PMID: 29843286 DOI: 10.3233/thc-182510] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Abstract
BACKGROUND Transapical off-pump mitral valve (MV) repair is a novel minimally-invasive surgical technique, allowing to correct mitral regurgitation (MR) caused by chordae tendineae rupture. While numerical simulation of the MV structure has proven to be useful to evaluate the effects of the MV surgical repair techniques, no numerical simulation studies on the outcomes of transapical MV repair have been done up to now. OBJECTIVE The purpose of this study is to evaluate the transapical MV repair using finite element modeling and to determine the effect of the neochordal length on the function of the prolapsing MV. METHODS The reconstruction of the MV geometry based on the patient-specific data was performed. In order to simulate prolapse, chordae inserted into the middle segment of the posterior leaflet (P2) were ruptured. A total of four virtual transapical repairs using neochordae of different length were performed. The function of the MV before and after virtual repairs was simulated. RESULTS The evaluation of the effect of the neochordal length on post-repair MV function showed that the length of the implanted neochordae has a significant impact on the correction of MR caused by chordae tendineae rupture. CONCLUSIONS The presented results can improve the understanding of the effects of transapical MV repair.
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Affiliation(s)
- Gediminas Gaidulis
- Department of Biomechanical Engineering, Vilnius Gediminas Technical University, Vilnius, Lithuania
| | - Emiliano Votta
- Department of Electronics, Information and Bioengineering, Politecnico di Milano, Milan, Italy
| | - Matteo Selmi
- Department of Electronics, Information and Bioengineering, Politecnico di Milano, Milan, Italy.,Division of Cardiac Surgery, Department of Surgery, Università di Verona, Verona, Italy
| | - Sigita Aidietienė
- Department of Cardiovascular Medicine, Vilnius University, Vilnius, Lithuania
| | - Audrius Aidietis
- Department of Cardiovascular Medicine, Vilnius University, Vilnius, Lithuania
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Dehiscence of patch augmentation of a left-sided atrioventricular valve related to strenuous isometric exercise: Case report and failure analysis. J Thorac Cardiovasc Surg 2018; 156:e165-e168. [PMID: 29804663 DOI: 10.1016/j.jtcvs.2018.04.101] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 02/13/2018] [Revised: 04/09/2018] [Accepted: 04/24/2018] [Indexed: 11/22/2022]
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Potter S, Graves J, Drach B, Leahy T, Hammel C, Feng Y, Baker A, Sacks MS. A Novel Small-Specimen Planar Biaxial Testing System With Full In-Plane Deformation Control. J Biomech Eng 2018; 140:2666965. [PMID: 29247251 PMCID: PMC5816250 DOI: 10.1115/1.4038779] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/01/2017] [Revised: 12/11/2017] [Indexed: 01/12/2023]
Abstract
Simulations of soft tissues require accurate and robust constitutive models, whose form is derived from carefully designed experimental studies. For such investigations of membranes or thin specimens, planar biaxial systems have been used extensively. Yet, all such systems remain limited in their ability to: (1) fully prescribe in-plane deformation gradient tensor F2D, (2) ensure homogeneity of the applied deformation, and (3) be able to accommodate sufficiently small specimens to ensure a reasonable degree of material homogeneity. To address these issues, we have developed a novel planar biaxial testing device that overcomes these difficulties and is capable of full control of the in-plane deformation gradient tensor F2D and of testing specimens as small as ∼4 mm × ∼4 mm. Individual actuation of the specimen attachment points, combined with a robust real-time feedback control, enabled the device to enforce any arbitrary F2D with a high degree of accuracy and homogeneity. Results from extensive device validation trials and example tissues illustrated the ability of the device to perform as designed and gather data needed for developing and validating constitutive models. Examples included the murine aortic tissues, allowing for investigators to take advantage of the genetic manipulation of murine disease models. These capabilities highlight the potential of the device to serve as a platform for informing and verifying the results of inverse models and for conducting robust, controlled investigation into the biomechanics of very local behaviors of soft tissues and membrane biomaterials.
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Affiliation(s)
- Samuel Potter
- Department of Mechanical Engineering, Willerson Center for Cardiovascular Modeling and Simulation, Institute for Computational Engineering and Sciences, The University of Texas at Austin, 240 East 24th Street, Austin, TX 78712
| | - Jordan Graves
- Department of Biomedical Engineering, Willerson Center for Cardiovascular Modeling and Simulation, Institute for Computational Engineering and Sciences, The University of Texas at Austin, , Austin, TX 78712
| | - Borys Drach
- Department of Mechanical and Aerospace Engineering, New Mexico State University, Las Cruces, NM 88003
| | - Thomas Leahy
- Department of Biomedical Engineering, Willerson Center for Cardiovascular Modeling and Simulation, Institute for Computational Engineering and Sciences, The University of Texas at Austin, , Austin, TX 78712
| | - Chris Hammel
- Department of Mechanical Engineering, Willerson Center for Cardiovascular Modeling and Simulation, Institute for Computational Engineering and Sciences, The University of Texas at Austin, , Austin, TX 78712
| | - Yuan Feng
- Center for Molecular Imaging and Nuclear Medicine, School of Radiological and Interdisciplinary Sciences (RAD-X), Soochow University, Collaborative Innovation Center of Radiation Medicine of Jiangsu Higher Education Institutions, Suzhou 215123, China
| | - Aaron Baker
- Department of Biomedical Engineering, Willerson Center for Cardiovascular Modeling and Simulation, The University of Texas at Austin, , Austin, TX 78712
| | - Michael S Sacks
- Department of Biomedical Engineering, Willerson Center for Cardiovascular Modeling and Simulation, Institute for Computational Engineering and Sciences, The University of Texas at Austin, , Austin, TX 78712
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Wu MCH, Zakerzadeh R, Kamensky D, Kiendl J, Sacks MS, Hsu MC. An anisotropic constitutive model for immersogeometric fluid-structure interaction analysis of bioprosthetic heart valves. J Biomech 2018; 74:23-31. [PMID: 29735263 DOI: 10.1016/j.jbiomech.2018.04.012] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/02/2017] [Revised: 02/25/2018] [Accepted: 04/04/2018] [Indexed: 12/01/2022]
Abstract
This paper considers an anisotropic hyperelastic soft tissue model, originally proposed for native valve tissue and referred to herein as the Lee-Sacks model, in an isogeometric thin shell analysis framework that can be readily combined with immersogeometric fluid-structure interaction (FSI) analysis for high-fidelity simulations of bioprosthetic heart valves (BHVs) interacting with blood flow. We find that the Lee-Sacks model is well-suited to reproduce the anisotropic stress-strain behavior of the cross-linked bovine pericardial tissues that are commonly used in BHVs. An automated procedure for parameter selection leads to an instance of the Lee-Sacks model that matches biaxial stress-strain data from the literature more closely, over a wider range of strains, than other soft tissue models. The relative simplicity of the Lee-Sacks model is attractive for computationally-demanding applications such as FSI analysis and we use the model to demonstrate how the presence and direction of material anisotropy affect the FSI dynamics of BHV leaflets.
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Affiliation(s)
- Michael C H Wu
- Department of Mechanical Engineering, Iowa State University, 2025 Black Engineering, Ames, IA 50011, USA
| | - Rana Zakerzadeh
- Willerson Center for Cardiovascular Modeling and Simulation, Institute for Computational Engineering and Sciences, The University of Texas at Austin, 201 East 24th St, Stop C0200, Austin, TX 78712, USA
| | - David Kamensky
- Department of Structural Engineering, University of California, San Diego, 9500 Gilman Drive, Mail Code 0085, La Jolla, CA 92093, USA
| | - Josef Kiendl
- Department of Marine Technology, Norwegian University of Science and Technology, O. Nielsens veg 10, 7052 Trondheim, Norway
| | - Michael S Sacks
- Willerson Center for Cardiovascular Modeling and Simulation, Institute for Computational Engineering and Sciences, The University of Texas at Austin, 201 East 24th St, Stop C0200, Austin, TX 78712, USA
| | - Ming-Chen Hsu
- Department of Mechanical Engineering, Iowa State University, 2025 Black Engineering, Ames, IA 50011, USA.
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Kamensky D, Xu F, Lee CH, Yan J, Bazilevs Y, Hsu MC. A contact formulation based on a volumetric potential: Application to isogeometric simulations of atrioventricular valves. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 2018; 330:522-546. [PMID: 29736092 PMCID: PMC5935269 DOI: 10.1016/j.cma.2017.11.007] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/10/2023]
Abstract
This work formulates frictionless contact between solid bodies in terms of a repulsive potential energy term and illustrates how numerical integration of the resulting forces is computationally similar to the "pinball algorithm" proposed and studied by Belytschko and collaborators in the 1990s. We thereby arrive at a numerical approach that has both the theoretical advantages of a potential-based formulation and the algorithmic simplicity, computational efficiency, and geometrical versatility of pinball contact. The singular nature of the contact potential requires a specialized nonlinear solver and an adaptive time stepping scheme to ensure reliable convergence of implicit dynamic calculations. We illustrate the effectiveness of this numerical method by simulating several benchmark problems and the structural mechanics of the right atrioventricular (tricuspid) heart valve. Atrioventricular valve closure involves contact between every combination of shell surfaces, edges of shells, and cables, but our formulation handles all contact scenarios in a unified manner. We take advantage of this versatility to demonstrate the effects of chordal rupture on tricuspid valve coaptation behavior.
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Affiliation(s)
- David Kamensky
- Department of Structural Engineering, University of California, San Diego, La Jolla, CA 92093, USA
- Corresponding author: (David Kamensky)
| | - Fei Xu
- Department of Mechanical Engineering, Iowa State University, Ames, IA 50011, USA
| | - Chung-Hao Lee
- School of Aerospace and Mechanical Engineering, The University of Oklahoma, Norman, OK 73019, USA
| | - Jinhui Yan
- Department of Mechanical Engineering, Northwestern University, Evanston, IL 60208, USA
| | - Yuri Bazilevs
- Department of Structural Engineering, University of California, San Diego, La Jolla, CA 92093, USA
| | - Ming-Chen Hsu
- Department of Mechanical Engineering, Iowa State University, Ames, IA 50011, USA
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41
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Pant AD, Thomas VS, Black AL, Verba T, Lesicko JG, Amini R. Pressure-induced microstructural changes in porcine tricuspid valve leaflets. Acta Biomater 2018; 67:248-258. [PMID: 29199067 DOI: 10.1016/j.actbio.2017.11.040] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/10/2017] [Revised: 10/24/2017] [Accepted: 11/13/2017] [Indexed: 12/20/2022]
Abstract
Quantifying mechanically-induced changes in the tricuspid valve extracellular matrix (ECM) structural components, e.g. collagen fiber spread and distribution, is important as it determines the overall macro-scale tissue responses and subsequently its function/malfunction in physiological/pathophysiological states. For example, functional tricuspid regurgitation, a common tricuspid valve disorder, could be caused by elevated right ventricular pressure due to pulmonary hypertension. In such patients, the geometry and the normal function of valve leaflets alter due to chronic pressure overload, which could cause remodeling responses in the ECM and change its structural components. To understand such a relation, we developed an experimental setup and measured alteration of leaflet microstructure in response to pressure increase in porcine tricuspid valves using the small angle light scattering technique. The anisotropy index, a measure of the fiber spread and distribution, was obtained and averaged for each region of the anterior, posterior, and septal leaflet using four averaging methods. The average anisotropy indices (mean ± standard error) in the belly region of the anterior, posterior, and septal leaflets of non-pressurized valves were found to be 12 ± 2%, 21 ± 3% and 12 ± 1%, respectively. For the pressurized valve, the average values of the anisotropy index in the belly region of the anterior, posterior, and septal leaflets were 56 ± 5%, 39 ± 7% and 32 ± 5%, respectively. Overall, the average anisotropy index was found to be higher for all leaflets in the pressurized valves as compared to the non-pressurized valves, indicating that the ECM fibers became more aligned in response to an increased ventricular pressure. STATEMENT OF SIGNIFICANCE Mechanics plays a critical role in development, regeneration, and remodeling of tissues. In the current study, we have conducted experiments to examine how increasing the ventricular pressure leads to realignment of protein fibers comprising the extracellular matrix (ECM) of the tricuspid valve leaflets. Like many other tissues, in cardiac valves, cell-matrix interactions and gene expressions are heavily influenced by changes in the mechanical microenvironment at the ECM/cellular level. We believe that our study will help us better understand how abnormal increases in the right ventricular pressure (due to pulmonary hypertension) could change the structural architecture of tricuspid valve leaflets and subsequently the mechanical microenvironment at the ECM/cellular level.
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Affiliation(s)
- Anup D Pant
- Department of Biomedical Engineering, The University of Akron, Akron, OH, United States.
| | - Vineet S Thomas
- Department of Biomedical Engineering, The University of Akron, Akron, OH, United States.
| | - Anthony L Black
- Department of Biomedical Engineering, The University of Akron, Akron, OH, United States.
| | - Taylor Verba
- Department of Biomedical Engineering, The University of Akron, Akron, OH, United States.
| | | | - Rouzbeh Amini
- Department of Biomedical Engineering, The University of Akron, Akron, OH, United States.
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42
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Pagnozzi LA, Butcher JT. Mechanotransduction Mechanisms in Mitral Valve Physiology and Disease Pathogenesis. Front Cardiovasc Med 2017; 4:83. [PMID: 29312958 PMCID: PMC5744129 DOI: 10.3389/fcvm.2017.00083] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/15/2017] [Accepted: 12/07/2017] [Indexed: 01/13/2023] Open
Abstract
The mitral valve exists in a mechanically demanding environment, with the stress of each cardiac cycle deforming and shearing the native fibroblasts and endothelial cells. Cells and their extracellular matrix exhibit a dynamic reciprocity in the growth and formation of tissue through mechanotransduction and continuously adapt to physical cues in their environment through gene, protein, and cytokine expression. Valve disease is the most common congenital heart defect with watchful waiting and valve replacement surgery the only treatment option. Mitral valve disease (MVD) has been linked to a variety of mechano-active genes ranging from extracellular components, mechanotransductive elements, and cytoplasmic and nuclear transcription factors. Specialized cell receptors, such as adherens junctions, cadherins, integrins, primary cilia, ion channels, caveolae, and the glycocalyx, convert mechanical cues into biochemical responses via a complex of mechanoresponsive elements, shared signaling modalities, and integrated frameworks. Understanding mechanosensing and transduction in mitral valve-specific cells may allow us to discover unique signal transduction pathways between cells and their environment, leading to cell or tissue specific mechanically targeted therapeutics for MVD.
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Affiliation(s)
- Leah A. Pagnozzi
- Meinig School of Biomedical Engineering, Cornell University, Ithaca, NY, United States
| | - Jonathan T. Butcher
- Meinig School of Biomedical Engineering, Cornell University, Ithaca, NY, United States
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43
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Ayoub S, Lee CH, Driesbaugh KH, Anselmo W, Hughes CT, Ferrari G, Gorman RC, Gorman JH, Sacks MS. Regulation of valve interstitial cell homeostasis by mechanical deformation: implications for heart valve disease and surgical repair. J R Soc Interface 2017; 14:20170580. [PMID: 29046338 PMCID: PMC5665836 DOI: 10.1098/rsif.2017.0580] [Citation(s) in RCA: 34] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/07/2017] [Accepted: 09/21/2017] [Indexed: 11/12/2022] Open
Abstract
Mechanical stress is one of the major aetiological factors underlying soft-tissue remodelling, especially for the mitral valve (MV). It has been hypothesized that altered MV tissue stress states lead to deviations from cellular homeostasis, resulting in subsequent cellular activation and extracellular matrix (ECM) remodelling. However, a quantitative link between alterations in the organ-level in vivo state and in vitro-based mechanobiology studies has yet to be made. We thus developed an integrated experimental-computational approach to elucidate MV tissue and interstitial cell responses to varying tissue strain levels. Comprehensive results at different length scales revealed that normal responses are observed only within a defined range of tissue deformations, whereas deformations outside of this range lead to hypo- and hyper-synthetic responses, evidenced by changes in α-smooth muscle actin, type I collagen, and other ECM and cell adhesion molecule regulation. We identified MV interstitial cell deformation as a key player in leaflet tissue homeostatic regulation and, as such, used it as the metric that makes the critical link between in vitro responses to simulated equivalent in vivo behaviour. Results indicated that cell responses have a delimited range of in vivo deformations that maintain a homeostatic response, suggesting that deviations from this range may lead to deleterious tissue remodelling and failure.
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Affiliation(s)
- Salma Ayoub
- Center for Cardiovascular Simulation, Institute for Computational Engineering and Sciences (ICES), Department of Biomedical Engineering, The University of Texas at Austin, Austin, TX 78712, USA
| | - Chung-Hao Lee
- School of Aerospace and Mechanical Engineering, The University of Oklahoma, Norman, OK 73019, USA
| | - Kathryn H Driesbaugh
- Gorman Cardiovascular Research Group, University of Pennsylvania, Philadelphia, PA 19104, USA
| | - Wanda Anselmo
- Gorman Cardiovascular Research Group, University of Pennsylvania, Philadelphia, PA 19104, USA
| | - Connor T Hughes
- Center for Cardiovascular Simulation, Institute for Computational Engineering and Sciences (ICES), Department of Biomedical Engineering, The University of Texas at Austin, Austin, TX 78712, USA
| | - Giovanni Ferrari
- Gorman Cardiovascular Research Group, University of Pennsylvania, Philadelphia, PA 19104, USA
| | - Robert C Gorman
- Gorman Cardiovascular Research Group, University of Pennsylvania, Philadelphia, PA 19104, USA
| | - Joseph H Gorman
- Gorman Cardiovascular Research Group, University of Pennsylvania, Philadelphia, PA 19104, USA
| | - Michael S Sacks
- Center for Cardiovascular Simulation, Institute for Computational Engineering and Sciences (ICES), Department of Biomedical Engineering, The University of Texas at Austin, Austin, TX 78712, USA
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44
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Gao H, Qi N, Feng L, Ma X, Danton M, Berry C, Luo X. Modelling mitral valvular dynamics-current trend and future directions. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2017; 33:e2858. [PMID: 27935265 PMCID: PMC5697636 DOI: 10.1002/cnm.2858] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/09/2016] [Revised: 09/30/2016] [Accepted: 11/26/2016] [Indexed: 05/19/2023]
Abstract
Dysfunction of mitral valve causes morbidity and premature mortality and remains a leading medical problem worldwide. Computational modelling aims to understand the biomechanics of human mitral valve and could lead to the development of new treatment, prevention and diagnosis of mitral valve diseases. Compared with the aortic valve, the mitral valve has been much less studied owing to its highly complex structure and strong interaction with the blood flow and the ventricles. However, the interest in mitral valve modelling is growing, and the sophistication level is increasing with the advanced development of computational technology and imaging tools. This review summarises the state-of-the-art modelling of the mitral valve, including static and dynamics models, models with fluid-structure interaction, and models with the left ventricle interaction. Challenges and future directions are also discussed.
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Affiliation(s)
- Hao Gao
- School of Mathematics and StatisticsUniversity of GlasgowUK
| | - Nan Qi
- School of Mathematics and StatisticsUniversity of GlasgowUK
| | - Liuyang Feng
- School of Mathematics and StatisticsUniversity of GlasgowUK
| | | | - Mark Danton
- Department of Cardiac SurgeryRoyal Hospital for ChildrenGlasgowUK
| | - Colin Berry
- Institute of Cardiovascular and Medical SciencesUniversity of GlasgowUK
| | - Xiaoyu Luo
- School of Mathematics and StatisticsUniversity of GlasgowUK
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45
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Votta E, Presicce M, Della Corte A, Dellegrottaglie S, Bancone C, Sturla F, Redaelli A. A novel approach to the quantification of aortic root in vivo structural mechanics. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2017; 33:e2849. [PMID: 28029755 DOI: 10.1002/cnm.2849] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/15/2015] [Revised: 09/05/2016] [Accepted: 10/25/2016] [Indexed: 06/06/2023]
Abstract
Understanding aortic root in vivo biomechanics can help in elucidating key mechanisms involved in aortic root pathologies and in the outcome of their surgical treatment. Numerical models can provide useful quantitative information. For this to be reliable, detailed aortic root anatomy should be captured. Also, since the aortic root is never unloaded throughout the cardiac cycle, the modeled geometry should be consistent with the in vivo loads acting on it. Achieving such consistency is still a challenge, which was tackled only by few numerical studies. Here we propose and describe in detail a new approach to the finite element modeling of aortic root in vivo structural mechanics. Our approach exploits the anatomical information yielded by magnetic resonance imaging by reconstructing the 3-dimensional end-diastolic geometry of the aortic root and makes the reconstructed geometry consistent with end-diastolic loading conditions through the estimation of the corresponding prestresses field. We implemented our approach through a semiautomated modeling pipeline, and we applied it to quantify aortic root biomechanics in 4 healthy participants. Computed results highlighted that including prestresses into the model allowed for pressurizing the aortic root to the end-diastolic pressure while matching the image-based ground truth data. Aortic root dynamics, tissues strains, and stresses computed at relevant time points through the cardiac cycle were consistent with a broad set of data from previous computational and in vivo studies, strongly suggesting the potential of the method. Also, results highlighted the major role played by the anatomy in driving aortic root biomechanics.
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Affiliation(s)
- E Votta
- Department of Electronics, Information, and Bioengineering, Politecnico di Milano, Milan, Italy
| | - M Presicce
- Department of Electronics, Information, and Bioengineering, Politecnico di Milano, Milan, Italy
| | - A Della Corte
- Department of Cardiothoracic and Respiratory Sciences, Second University of Naples, Naples, Italy
| | - S Dellegrottaglie
- Department of Advanced Biomedical Sciences, Federico II University, Naples, Italy
- Division of Cardiology, Ospedale Medico-Chirurgico Accreditato Villa dei Fiori, Acerra, Naples, Italy
| | - C Bancone
- Department of Cardiothoracic and Respiratory Sciences, Second University of Naples, Naples, Italy
| | - F Sturla
- Department of Electronics, Information, and Bioengineering, Politecnico di Milano, Milan, Italy
| | - A Redaelli
- Department of Electronics, Information, and Bioengineering, Politecnico di Milano, Milan, Italy
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46
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Pappalardo O, Sturla F, Onorati F, Puppini G, Selmi M, Luciani G, Faggian G, Redaelli A, Votta E. Mass-spring models for the simulation of mitral valve function: Looking for a trade-off between reliability and time-efficiency. Med Eng Phys 2017; 47:93-104. [DOI: 10.1016/j.medengphy.2017.07.001] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/16/2017] [Revised: 06/23/2017] [Accepted: 07/03/2017] [Indexed: 11/27/2022]
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47
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Lee CH, Zhang W, Feaver K, Gorman RC, Gorman JH, Sacks MS. On the in vivo function of the mitral heart valve leaflet: insights into tissue-interstitial cell biomechanical coupling. Biomech Model Mechanobiol 2017; 16:1613-1632. [PMID: 28429161 DOI: 10.1007/s10237-017-0908-4] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/01/2016] [Accepted: 04/07/2017] [Indexed: 10/19/2022]
Abstract
There continues to be a critical need for developing data-informed computational modeling techniques that enable systematic evaluations of mitral valve (MV) function. This is important for a better understanding of MV organ-level biomechanical performance, in vivo functional tissue stresses, and the biosynthetic responses of MV interstitial cells (MVICs) in the normal, pathophysiological, and surgically repaired states. In the present study, we utilized extant ovine MV population-averaged 3D fiducial marker data to quantify the MV anterior leaflet (MVAL) deformations in various kinematic states. This approach allowed us to make the critical connection between the in vivo functional and the in vitro experimental configurations. Moreover, we incorporated the in vivo MVAL deformations and pre-strains into an enhanced inverse finite element modeling framework (Path 1) to estimate the resulting in vivo tissue prestresses [Formula: see text] and the in vivo peak functional tissue stresses [Formula: see text]. These in vivo stress estimates were then cross-verified with the results obtained from an alternative forward modeling method (Path 2), by taking account of the changes in the in vitro and in vivo reference configurations. Moreover, by integrating the tissue-level kinematic results into a downscale MVIC microenvironment FE model, we were able to estimate, for the first time, the in vivo layer-specific MVIC deformations and deformation rates of the normal and surgically repaired MVALs. From these simulations, we determined that the placement of annuloplasty ring greatly reduces the peak MVIC deformation levels in a layer-specific manner. This suggests that the associated reductions in MVIC deformation may down-regulate MV extracellular matrix maintenance, ultimately leading to reduction in tissue mechanical integrity. These simulations provide valuable insight into MV cellular mechanobiology in response to organ- and tissue-level alternations induced by MV disease or surgical repair. They will also assist in the future development of computer simulation tools for guiding MV surgery procedure with enhanced durability and improved long-term surgical outcomes.
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Affiliation(s)
- Chung-Hao Lee
- School of Aerospace and Mechanical Engineering, The University of Oklahoma, 865 Asp Ave., Felgar Hall, Rm. 219C, Norman, OK, 73019, USA.,Department of Biomedical Engineering, Center for Cardiovascular Simulation, Institute for Computational Engineering and Sciences, The University of Texas at Austin, 201 East 24th St, POB 5.236, 1 University Station, C0200, Austin, TX, 78712, USA
| | - Will Zhang
- Department of Biomedical Engineering, Center for Cardiovascular Simulation, Institute for Computational Engineering and Sciences, The University of Texas at Austin, 201 East 24th St, POB 5.236, 1 University Station, C0200, Austin, TX, 78712, USA
| | - Kristen Feaver
- Department of Biomedical Engineering, Center for Cardiovascular Simulation, Institute for Computational Engineering and Sciences, The University of Texas at Austin, 201 East 24th St, POB 5.236, 1 University Station, C0200, Austin, TX, 78712, USA
| | - Robert C Gorman
- Gorman Cardiovascular Research Group, University of Pennsylvania, 3400 Civic Center Blvd, Philadelphia, PA, 19104, USA
| | - Joseph H Gorman
- Gorman Cardiovascular Research Group, University of Pennsylvania, 3400 Civic Center Blvd, Philadelphia, PA, 19104, USA
| | - Michael S Sacks
- Department of Biomedical Engineering, Center for Cardiovascular Simulation, Institute for Computational Engineering and Sciences, The University of Texas at Austin, 201 East 24th St, POB 5.236, 1 University Station, C0200, Austin, TX, 78712, USA. .,W. A. Moncrief, Jr. Simulation-Based Engineering Science Chair I, Department of Biomedical Engineering, Institute for Computational Engineering and Sciences, The University of Texas at Austin, 201 East 24th Street, ACES 5.438, 1 University Station, C0200, Austin, TX, 78712-0027, USA.
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48
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Feng Y, Qiu S, Xia X, Ji S, Lee CH. A computational study of invariant I 5 in a nearly incompressible transversely isotropic model for white matter. J Biomech 2017; 57:146-151. [PMID: 28433390 DOI: 10.1016/j.jbiomech.2017.03.025] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/12/2016] [Revised: 03/25/2017] [Accepted: 03/31/2017] [Indexed: 12/16/2022]
Abstract
The aligned axonal fiber bundles in white matter make it suitable to be modeled as a transversely isotropic material. Recent experimental studies have shown that a minimal form, nearly incompressible transversely isotropic (MITI) material model, is capable of describing mechanical anisotropy of white matter. Here, we used a finite element (FE) computational approach to demonstrate the significance of the fifth invariant (I5) when modeling the anisotropic behavior of white matter in the large-strain regime. We first implemented and validated the MITI model in an FE simulation framework for large deformations. Next, we applied the model to a plate-hole structural problem to highlight the significance of the invariant I5 by comparing with the standard fiber reinforcement (SFR) model. We also compared the two models by fitting the experiment data of asymmetric indentation, shear test, and uniaxial stretch of white matter. Our results demonstrated the significance of I5 in describing shear deformation/anisotropy, and illustrated the potential of the MITI model to characterize transversely isotropic white matter tissues in the large-strain regime.
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Affiliation(s)
- Yuan Feng
- Center for Molecular Imaging and Nuclear Medicine, School of Radiological and Interdisciplinary Sciences (RAD-X), Soochow University, Collaborative Innovation Center of Radiation Medicine of Jiangsu Higher Education Institutions, Suzhou, Jiangsu 215123, China; School of Mechanical and Electronic Engineering, Soochow University, Suzhou, Jiangsu 215021, China.
| | - Suhao Qiu
- Center for Molecular Imaging and Nuclear Medicine, School of Radiological and Interdisciplinary Sciences (RAD-X), Soochow University, Collaborative Innovation Center of Radiation Medicine of Jiangsu Higher Education Institutions, Suzhou, Jiangsu 215123, China; School of Electronic and Information Engineering, Soochow University, Suzhou, Jiangsu 215021, China
| | - Xiaolong Xia
- Center for Molecular Imaging and Nuclear Medicine, School of Radiological and Interdisciplinary Sciences (RAD-X), Soochow University, Collaborative Innovation Center of Radiation Medicine of Jiangsu Higher Education Institutions, Suzhou, Jiangsu 215123, China; School of Electronic and Information Engineering, Soochow University, Suzhou, Jiangsu 215021, China
| | - Songbai Ji
- Thayer School of Engineering, Dartmouth College, Hanover, NH 03755, USA
| | - Chung-Hao Lee
- School of Aerospace and Mechanical Engineering, The University of Oklahoma, Norman, OK 73019, USA; Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, TX 78712, USA
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49
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An improved parameter estimation and comparison for soft tissue constitutive models containing an exponential function. Biomech Model Mechanobiol 2017; 16:1309-1327. [PMID: 28251368 PMCID: PMC5511618 DOI: 10.1007/s10237-017-0889-3] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/12/2016] [Accepted: 02/10/2017] [Indexed: 01/05/2023]
Abstract
Motivated by the well-known result that stiffness of soft tissue is proportional to the stress, many of the constitutive laws for soft tissues contain an exponential function. In this work, we analyze properties of the exponential function and how it affects the estimation and comparison of elastic parameters for soft tissues. In particular, we find that as a consequence of the exponential function there are lines of high covariance in the elastic parameter space. As a result, one can have widely varying mechanical parameters defining the tissue stiffness but similar effective stress–strain responses. Drawing from elementary algebra, we propose simple changes in the norm and the parameter space, which significantly improve the convergence of parameter estimation and robustness in the presence of noise. More importantly, we demonstrate that these changes improve the conditioning of the problem and provide a more robust solution in the case of heterogeneous material by reducing the chances of getting trapped in a local minima. Based upon the new insight, we also propose a transformed parameter space which will allow for rational parameter comparison and avoid misleading conclusions regarding soft tissue mechanics.
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Rausch MK, Zöllner AM, Genet M, Baillargeon B, Bothe W, Kuhl E. A virtual sizing tool for mitral valve annuloplasty. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2017; 33:10.1002/cnm.2788. [PMID: 27028496 PMCID: PMC5289896 DOI: 10.1002/cnm.2788] [Citation(s) in RCA: 23] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/02/2015] [Revised: 02/16/2016] [Accepted: 03/19/2016] [Indexed: 05/08/2023]
Abstract
Functional mitral regurgitation, a backward leakage of the mitral valve, is a result of left ventricular growth and mitral annular dilatation. Its gold standard treatment is mitral annuloplasty, the surgical reduction in mitral annular area through the implantation of annuloplasty rings. Recurrent regurgitation rates may, however, be as high as 30% and more. While the degree of annular downsizing has been linked to improved long-term outcomes, too aggressive downsizing increases the risk of ring dehiscences and significantly impairs repair durability. Here, we prototype a virtual sizing tool to quantify changes in annular dimensions, surgically induced tissue strains, mitral annular stretches, and suture forces in response to mitral annuloplasty. We create a computational model of dilated cardiomyopathy onto which we virtually implant annuloplasty rings of different sizes. Our simulations confirm the common intuition that smaller rings are more invasive to the surrounding tissue, induce higher strains, and require larger suture forces than larger rings: The total suture force was 2.2 N for a 24-mm ring, 1.9 N for a 28-mm ring, and 0.8 N for a 32-mm ring. Our model predicts the highest risk of dehiscence in the septal and postero-lateral annulus where suture forces are maximal. These regions co-localize with regional peaks in myocardial strain and annular stretch. Our study illustrates the potential of realistic predictive simulations in cardiac surgery to identify areas at risk for dehiscence, guide the selection of ring size and shape, rationalize the design of smart annuloplasty rings and, ultimately, improve long-term outcomes after surgical mitral annuloplasty. Copyright © 2016 John Wiley & Sons, Ltd.
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Affiliation(s)
- Manuel K. Rausch
- Department of Biomedical Engineering, Yale University, New Haven, CT 06511, USA
| | - Alexander M. Zöllner
- Department of Mechanical Engineering, Stanford University, Stanford, CA 94305, USA
| | - Martin Genet
- Laboratoire de Mécanique des Solides CNRS-UMR 7649, Ecole Polytechnique, 91128 Palaiseau, France
| | | | - Wolfgang Bothe
- University Heart Center Freiburg, 79106 Freiburg, Germany
| | - E. Kuhl
- Departments of Mechanical Engineering, Bioengineering and Cardiothoracic Surgery, Stanford University, Stanford, CA 94305, USA
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