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Torre M, Morganti S, Pasqualini FS, Reali A. Current progress toward isogeometric modeling of the heart biophysics. BIOPHYSICS REVIEWS 2023; 4:041301. [PMID: 38510845 PMCID: PMC10903424 DOI: 10.1063/5.0152690] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/31/2023] [Accepted: 10/24/2023] [Indexed: 03/22/2024]
Abstract
In this paper, we review a powerful methodology to solve complex numerical simulations, known as isogeometric analysis, with a focus on applications to the biophysical modeling of the heart. We focus on the hemodynamics, modeling of the valves, cardiac tissue mechanics, and on the simulation of medical devices and treatments. For every topic, we provide an overview of the methods employed to solve the specific numerical issue entailed by the simulation. We try to cover the complete process, starting from the creation of the geometrical model up to the analysis and post-processing, highlighting the advantages and disadvantages of the methodology.
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Affiliation(s)
- Michele Torre
- Department of Civil Engineering and Architecture, University of Pavia, Via Ferrata 3, 27100 Pavia, Italy
| | - Simone Morganti
- Department of Electrical, Computer, and Biomedical Engineering, University of Pavia, Via Ferrata 5, 27100 Pavia, Italy
| | - Francesco S. Pasqualini
- Department of Civil Engineering and Architecture, University of Pavia, Via Ferrata 3, 27100 Pavia, Italy
| | - Alessandro Reali
- Department of Civil Engineering and Architecture, University of Pavia, Via Ferrata 3, 27100 Pavia, Italy
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2
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Sacks MS, Motiwale S, Goodbrake C, Zhang W. Neural Network Approaches for Soft Biological Tissue and Organ Simulations. J Biomech Eng 2022; 144:121010. [PMID: 36193891 PMCID: PMC9632474 DOI: 10.1115/1.4055835] [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: 05/09/2022] [Revised: 09/27/2022] [Indexed: 11/08/2022]
Abstract
Given the functional complexities of soft tissues and organs, it is clear that computational simulations are critical in their understanding and for the rational basis for the development of therapies and replacements. A key aspect of such simulations is accounting for their complex, nonlinear, anisotropic mechanical behaviors. While soft tissue material models have developed to the point of high fidelity, in-silico implementation is typically done using the finite element (FE) method, which remains impractically slow for translational clinical time frames. As a potential path toward addressing the development of high fidelity simulations capable of performing in clinically relevant time frames, we review the use of neural networks (NN) for soft tissue and organ simulation using two approaches. In the first approach, we show how a NN can learn the responses for a detailed meso-structural soft tissue material model. The NN material model not only reproduced the full anisotropic mechanical responses but also demonstrated a considerable efficiency improvement, as it was trained over a range of realizable fibrous structures. In the second approach, we go a step further with the use of a physics-based surrogate model to directly learn the displacement field solution without the need for raw training data or FE simulation datasets. In this approach we utilize a finite element mesh to define the domain and perform the necessary integrations, but not the finite element method (FEM) itself. We demonstrate with this approach, termed neural network finite element (NNFE), results in a trained NNFE model with excellent agreement with the corresponding "ground truth" FE solutions over the entire physiological deformation range on a cuboidal myocardium specimen. More importantly, the NNFE approach provided a significantly decreased computational time for a range of finite element mesh sizes. Specifically, as the FE mesh size increased from 2744 to 175,615 elements, the NNFE computational time increased from 0.1108 s to 0.1393 s, while the "ground truth" FE model increased from 4.541 s to 719.9 s, with the same effective accuracy. These results suggest that NNFE run times are significantly reduced compared with the traditional large-deformation-based finite element solution methods. We then show how a nonuniform rational B-splines (NURBS)-based approach can be directly integrated into the NNFE approach as a means to handle real organ geometries. While these and related approaches are in their early stages, they offer a method to perform complex organ-level simulations in clinically relevant time frames without compromising accuracy.
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Affiliation(s)
- Michael S. Sacks
- James T. Willerson Center for Cardiovascular Modeling and Simulation, The Oden Institute for Computational Engineering and Sciences, Department of Biomedical Engineering, The University of Texas at Austin, Austin, TX 78712
| | - Shruti Motiwale
- James T. Willerson Center for Cardiovascular Modeling and Simulation, The Oden Institute for Computational Engineering and Sciences, Department of Biomedical Engineering, The University of Texas at Austin, Austin, TX 78712
| | - Christian Goodbrake
- James T. Willerson Center for Cardiovascular Modeling and Simulation, The Oden Institute for Computational Engineering and Sciences, Department of Biomedical Engineering, The University of Texas at Austin, Austin, TX 78712
| | - Wenbo Zhang
- James T. Willerson Center for Cardiovascular Modeling and Simulation, The Oden Institute for Computational Engineering and Sciences, Department of Biomedical Engineering, The University of Texas at Austin, Austin, TX 78712
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3
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Coupling of IGA and peridynamics for air-blast fluid-structure interaction using an immersed approach. FORCES IN MECHANICS 2021. [DOI: 10.1016/j.finmec.2021.100045] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
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4
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Kang S, Masud A. A Variational Multiscale method with immersed boundary conditions for incompressible flows. MECCANICA 2021; 56:1397-1422. [PMID: 37655308 PMCID: PMC10470433 DOI: 10.1007/s11012-020-01227-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/03/2020] [Accepted: 08/10/2020] [Indexed: 09/02/2023]
Abstract
This paper presents a new stabilized form of incompressible Navier-Stokes equations for weak enforcement of Dirichlet boundary conditions at immersed boundaries. The boundary terms are derived via the Variational Multiscale (VMS) method which involves solving the fine-scale variational problem locally within a narrow band along the boundary. The fine-scale model is then variationally embedded into the coarse-scale form that yields a stabilized method which is free of user defined parameters. The derived boundary terms weakly enforce the Dirichlet boundary conditions along the immersed boundaries that may not align with the inter-element edges in the mesh. A unique feature of this rigorous derivation is that the structure of the stabilization tensor which emerges is naturally endowed with the mathematical attributes of area-averaging and stress-averaging. The method is implemented using 4-node quadrilateral and 8-node hexahedral elements. A set of 2D and 3D benchmark problems is presented that investigate the mathematical attributes of the method. These test cases show that the proposed method is mathematically robust as well as computationally stable and accurate for modeling boundary layers around immersed objects in the fluid domain.
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Affiliation(s)
- Soonpil Kang
- Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
| | - Arif Masud
- Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
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5
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Xu F, Johnson EL, Wang C, Jafari A, Yang CH, Sacks MS, Krishnamurthy A, Hsu MC. Computational investigation of left ventricular hemodynamics following bioprosthetic aortic and mitral valve replacement. MECHANICS RESEARCH COMMUNICATIONS 2021; 112:103604. [PMID: 34305195 PMCID: PMC8301225 DOI: 10.1016/j.mechrescom.2020.103604] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/07/2023]
Abstract
The left ventricle of the heart is a fundamental structure in the human cardiac system that pumps oxygenated blood into the systemic circulation. Several valvular conditions can cause the aortic and mitral valves associated with the left ventricle to become severely diseased and require replacement. However, the clinical outcomes of such operations, specifically the postoperative ventricular hemodynamics of replacing both valves, are not well understood. This work uses computational fluid-structure interaction (FSI) to develop an improved understanding of this effect by modeling a left ventricle with the aortic and mitral valves replaced with bioprostheses. We use a hybrid Arbitrary Lagrangian-Eulerian/immersogeometric framework to accommodate the analysis of cardiac hemodynamics and heart valve structural mechanics in a moving fluid domain. The motion of the endocardium is obtained from a cardiac biomechanics simulation and provided as an input to the proposed numerical framework. The results from the simulations in this work indicate that the replacement of the native mitral valve with a tri-radially symmetric bioprosthesis dramatically changes the ventricular hemodynamics. Most significantly, the vortical motion in the left ventricle is found to reverse direction after mitral valve replacement. This study demonstrates that the proposed computational FSI framework is capable of simulating complex multiphysics problems and can provide an in-depth understanding of the cardiac mechanics.
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Affiliation(s)
- Fei Xu
- Ansys Inc., Austin, TX 78746, USA
| | - Emily L. Johnson
- Department of Mechanical Engineering, Iowa State University, Ames, IA 50011, USA
| | | | - Arian Jafari
- Department of Mechanical Engineering, Iowa State University, Ames, IA 50011, USA
| | - Cheng-Hau Yang
- Department of Mechanical Engineering, Iowa State University, Ames, IA 50011, USA
| | - Michael S. Sacks
- 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
| | - Adarsh Krishnamurthy
- 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
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6
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Balmus M, Massing A, Hoffman J, Razavi R, Nordsletten DA. A partition of unity approach to fluid mechanics and fluid-structure interaction. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 2020; 362:112842. [PMID: 34093912 PMCID: PMC7610902 DOI: 10.1016/j.cma.2020.112842] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
For problems involving large deformations of thin structures, simulating fluid-structure interaction (FSI) remains a computationally expensive endeavour which continues to drive interest in the development of novel approaches. Overlapping domain techniques have been introduced as a way to combine the fluid-solid mesh conformity, seen in moving-mesh methods, without the need for mesh smoothing or re-meshing, which is a core characteristic of fixed mesh approaches. In this work, we introduce a novel overlapping domain method based on a partition of unity approach. Unified function spaces are defined as a weighted sum of fields given on two overlapping meshes. The method is shown to achieve optimal convergence rates and to be stable for steady-state Stokes, Navier-Stokes, and ALE Navier-Stokes problems. Finally, we present results for FSI in the case of 2D flow past an elastic beam simulation. These initial results point to the potential applicability of the method to a wide range of FSI applications, enabling boundary layer refinement and large deformations without the need for re-meshing or user-defined stabilization.
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Affiliation(s)
- Maximilian Balmus
- Department of Biomedical Engineering, School of Imaging Sciences and Biomedical Engineering, King’s College London, King’s Health Partners, London SE1 7EH, United Kingdom
| | - André Massing
- Department of Mathematics and Mathematical Statistics, Umeå University, SE-90187 Umeå, Sweden
- Department of Mathematical Sciences, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway
| | - Johan Hoffman
- Division of Computational Science and Technology, KTH Royal Institute of Technology, Sweden
| | - Reza Razavi
- Department of Biomedical Engineering, School of Imaging Sciences and Biomedical Engineering, King’s College London, King’s Health Partners, London SE1 7EH, United Kingdom
| | - David A. Nordsletten
- Department of Biomedical Engineering, School of Imaging Sciences and Biomedical Engineering, King’s College London, King’s Health Partners, London SE1 7EH, United Kingdom
- Department of Biomedical Engineering and Cardiac Surgery, University of Michigan, MI, USA
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7
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This A, Boilevin-Kayl L, Fernández MA, Gerbeau JF. Augmented resistive immersed surfaces valve model for the simulation of cardiac hemodynamics with isovolumetric phases. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2020; 36:e3223. [PMID: 31206245 DOI: 10.1002/cnm.3223] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/14/2018] [Revised: 04/12/2019] [Accepted: 05/21/2019] [Indexed: 06/09/2023]
Abstract
In order to reduce the complexity of heart hemodynamics simulations, uncoupling approaches are often considered for the modeling of the immersed valves as an alternative to complex fluid-structure interaction (FSI) models. A possible shortcoming of these simplified approaches is the difficulty to correctly capture the pressure dynamics during the isovolumetric phases. In this work, we propose an enhanced resistive immersed surfaces (RIS) model of cardiac valves, which overcomes this issue. The benefits of the model are investigated and tested in blood flow simulations of the left heart where the physiological behavior of the intracavity pressure during the isovolumetric phases is recovered without using fully coupled fluid-structure models and without important alteration of the associated velocity field.
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Affiliation(s)
- Alexandre This
- Medisys, Philips Research, Suresnes, France
- COMMEDIA, Inria Paris, Paris, France
- Sorbonne Université, UMR 7598 LJLL, Paris, France
| | - Ludovic Boilevin-Kayl
- COMMEDIA, Inria Paris, Paris, France
- Sorbonne Université, UMR 7598 LJLL, Paris, France
| | - Miguel A Fernández
- COMMEDIA, Inria Paris, Paris, France
- Sorbonne Université, UMR 7598 LJLL, Paris, France
| | - Jean-Frédéric Gerbeau
- COMMEDIA, Inria Paris, Paris, France
- Sorbonne Université, UMR 7598 LJLL, Paris, France
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8
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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: 11] [Impact Index Per Article: 2.2] [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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9
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Lavon K, Halevi R, Marom G, Ben Zekry S, Hamdan A, Joachim Schäfers H, Raanani E, Haj-Ali R. Fluid-Structure Interaction Models of Bicuspid Aortic Valves: The Effects of Nonfused Cusp Angles. J Biomech Eng 2019; 140:2661744. [PMID: 29098290 DOI: 10.1115/1.4038329] [Citation(s) in RCA: 20] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/20/2017] [Indexed: 12/21/2022]
Abstract
Bicuspid aortic valve (BAV) is the most common type of congenital heart disease, occurring in 0.5-2% of the population, where the valve has only two rather than the three normal cusps. Valvular pathologies, such as aortic regurgitation and aortic stenosis, are associated with BAVs, thereby increasing the need for a better understanding of BAV kinematics and geometrical characteristics. The aim of this study is to investigate the influence of the nonfused cusp (NFC) angle in BAV type-1 configuration on the valve's structural and hemodynamic performance. Toward that goal, a parametric fluid-structure interaction (FSI) modeling approach of BAVs is presented. Four FSI models were generated with varying NFC angles between 120 deg and 180 deg. The FSI simulations were based on fully coupled structural and fluid dynamic solvers and corresponded to physiologic values, including the anisotropic hyper-elastic behavior of the tissue. The simulated angles led to different mechanical behavior, such as eccentric jet flow direction with a wider opening shape that was found for the smaller NFC angles, while a narrower opening orifice followed by increased jet flow velocity was observed for the larger NFC angles. Smaller NFC angles led to higher concentrated flow shear stress (FSS) on the NFC during peak systole, while higher maximal principal stresses were found in the raphe region during diastole. The proposed biomechanical models could explain the early failure of BAVs with decreased NFC angles, and suggests that a larger NFC angle is preferable in suture annuloplasty BAV repair surgery.
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Affiliation(s)
- Karin Lavon
- Faculty of Engineering, School of Mechanical Engineering, Tel Aviv University, Tel Aviv 6997801, Israel
| | - Rotem Halevi
- Faculty of Engineering, School of Mechanical Engineering, Tel Aviv University, Tel Aviv 6997801, Israel
| | - Gil Marom
- Biomedical Engineering Department, Stony Brook University, Stony Brook, NY 11794
| | - Sagit Ben Zekry
- Echocardiography Laboratory, Chaim Sheba Medical Center, Tel Hashomer 52621, Israel
| | - Ashraf Hamdan
- Department of Cardiology, Rabin Medical Center, Petach Tikva 4941492, Israel
| | - Hans Joachim Schäfers
- Department of Thoracic and Cardiovascular Surgery, University Hospitals of Saarland, Homburg 66421, Germany
| | - Ehud Raanani
- Department of Cardio-thoracic Surgery, Chaim Sheba Medical Center, Tel Hashomer 52621, Israel
| | - Rami Haj-Ali
- School of Mechanical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 6997801, Israel
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10
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Ghosh R, Marom G, Rotman O, Slepian MJ, Prabhakar S, Horner M, Bluestein D. Comparative Fluid-Structure Interaction Analysis of Polymeric Transcatheter and Surgical Aortic Valves' Hemodynamics and Structural Mechanics. J Biomech Eng 2018; 140:2686528. [PMID: 30029207 DOI: 10.1115/1.4040600] [Citation(s) in RCA: 27] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/06/2017] [Indexed: 02/28/2024]
Abstract
Transcatheter aortic valve replacement (TAVR) has emerged as an effective alternative to conventional surgical aortic valve replacement (SAVR) in high-risk elderly patients with calcified aortic valve disease. All currently FDA-approved TAVR devices use tissue valves that were adapted to but not specifically designed for TAVR use. Emerging clinical evidence indicates that these valves may get damaged during crimping and deployment- leading to valvular calcification, thrombotic complications, and limited durability. This impedes the expected expansion of TAVR to lower-risk and younger patients. Viable polymeric valves have the potential to overcome such limitations. We have developed a polymeric SAVR valve, which was optimized to reduce leaflet stresses and offer a thromboresistance profile similar to that of a tissue valve. This study compares the polymeric SAVR valve's hemodynamic performance and mechanical stresses to a new version of the valve- specifically designed for TAVR. Fluid-structure interaction (FSI) models were utilized and the valves' hemodynamics, flexural stresses, strains, orifice area, and wall shear stresses were compared. The TAVR valve had 42% larger opening area and 27% higher flow rate versus the SAVR valve, while wall shear stress distribution and mechanical stress magnitudes were of the same order, demonstrating the enhanced performance of the TAVR valve prototype. The TAVR valve FSI simulation and Vivitro pulse duplicator experiments were compared in terms of the leaflets' kinematics and the effective orifice area. The numerical methodology presented can be further used as a predictive tool for valve design optimization for enhanced hemodynamics and durability.
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Affiliation(s)
- Ram Ghosh
- Department of Biomedical Engineering, Stony Brook University, Stony Brook, NY 11794-8151, USA
| | - Gil Marom
- School of Mechanical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 6997801, Israel; Biomedical Engineering Department, Stony Brook University, Stony Brook 11794, NY, USA
| | - Oren Rotman
- Department of Biomedical Engineering, Stony Brook University, Stony Brook, NY 11794-8151, USA
| | - Marvin J Slepian
- Department of Biomedical Engineering and Department of Medicine, Sarver Heart Center, University of Arizona, Tucson, AZ 85724, USA
| | - Saurabh Prabhakar
- ANSYS Fluent India Pvt Ltd., MIDC, Plot No. 34/1, Rajiv Gandhi IT Park, Hinjewadi, Pune 411057, India
| | - Marc Horner
- ANSYS, Inc., 1007 Church St, Suite 250, Evanston, IL 60201, USA
| | - Danny Bluestein
- Department of Biomedical Engineering, Stony Brook University, Stony Brook, NY 11794-8151, USA
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11
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Xu F, Morganti S, Zakerzadeh R, Kamensky D, Auricchio F, Reali A, Hughes TJ, Sacks MS, Hsu MC. A framework for designing patient-specific bioprosthetic heart valves using immersogeometric fluid-structure interaction analysis. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2018; 34:e2938. [PMID: 29119728 PMCID: PMC5893448 DOI: 10.1002/cnm.2938] [Citation(s) in RCA: 25] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/17/2017] [Revised: 09/08/2017] [Accepted: 10/22/2017] [Indexed: 05/07/2023]
Abstract
Numerous studies have suggested that medical image derived computational mechanics models could be developed to reduce mortality and morbidity due to cardiovascular diseases by allowing for patient-specific surgical planning and customized medical device design. In this work, we present a novel framework for designing prosthetic heart valves using a parametric design platform and immersogeometric fluid-structure interaction (FSI) analysis. We parameterize the leaflet geometry using several key design parameters. This allows for generating various perturbations of the leaflet design for the patient-specific aortic root reconstructed from the medical image data. Each design is analyzed using our hybrid arbitrary Lagrangian-Eulerian/immersogeometric FSI methodology, which allows us to efficiently simulate the coupling of the deforming aortic root, the parametrically designed prosthetic valves, and the surrounding blood flow under physiological conditions. A parametric study is performed to investigate the influence of the geometry on heart valve performance, indicated by the effective orifice area and the coaptation area. Finally, the FSI simulation result of a design that balances effective orifice area and coaptation area reasonably well is compared with patient-specific phase contrast magnetic resonance imaging data to demonstrate the qualitative similarity of the flow patterns in the ascending aorta.
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Affiliation(s)
- Fei Xu
- Department of Mechanical Engineering, Iowa State University, 2025 Black Engineering, Ames, IA 50011, USA
| | - Simone Morganti
- Department of Electrical, Computer, and Biomedical Engineering, University of Pavia, via Ferrata 3, 27100, Pavia Italy
| | - Rana Zakerzadeh
- Center for Cardiovascular 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
| | - Ferdinando Auricchio
- Department of Civil Engineering and Architecture, University of Pavia, via Ferrata 3, 27100, Pavia, Italy
| | - Alessandro Reali
- Department of Civil Engineering and Architecture, University of Pavia, via Ferrata 3, 27100, Pavia, Italy
| | - Thomas J.R. Hughes
- Center for Cardiovascular Simulation, Institute for Computational Engineering and Sciences, The University of Texas at Austin, 201 East 24th St, Stop C0200, Austin, TX 78712, USA
| | - Michael S. Sacks
- Center for Cardiovascular 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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12
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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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13
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Kamensky D, Evans JA, Hsu MC, Bazilevs Y. Projection-based stabilization of interface Lagrange multipliers in immersogeometric fluid-thin structure interaction analysis, with application to heart valve modeling. COMPUTERS & MATHEMATICS WITH APPLICATIONS (OXFORD, ENGLAND : 1987) 2017; 74:2068-2088. [PMID: 29225420 PMCID: PMC5720179 DOI: 10.1016/j.camwa.2017.07.006] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/25/2023]
Abstract
This paper discusses a method of stabilizing Lagrange multiplier fields used to couple thin immersed shell structures and surrounding fluids. The method retains essential conservation properties by stabilizing only the portion of the constraint orthogonal to a coarse multiplier space. This stabilization can easily be applied within iterative methods or semi-implicit time integrators that avoid directly solving a saddle point problem for the Lagrange multiplier field. Heart valve simulations demonstrate applicability of the proposed method to 3D unsteady simulations. An appendix sketches the relation between the proposed method and a high-order-accurate approach for simpler model problems.
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Affiliation(s)
- David Kamensky
- Department of Structural Engineering, University of California, San Diego, 9500 Gilman Drive, Mail Code 0085, La Jolla, CA 92093, USA
| | - John A. Evans
- Department of Aerospace Engineering Sciences, University of Colorado at Boulder, 429 UCB, Boulder, CO 80309, USA
| | - Ming-Chen Hsu
- Department of Mechanical Engineering, Iowa State University, 2025 Black Engineering, Ames, IA 50011, USA
| | - Yuri Bazilevs
- Department of Structural Engineering, University of California, San Diego, 9500 Gilman Drive, Mail Code 0085, La Jolla, CA 92093, USA
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Costabal FS, Concha FA, Hurtado DE, Kuhl E. The importance of mechano-electrical feedback and inertia in cardiac electromechanics. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 2017; 320:352-368. [PMID: 29056782 PMCID: PMC5646712 DOI: 10.1016/j.cma.2017.03.015] [Citation(s) in RCA: 35] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/08/2023]
Abstract
In the past years, a number cardiac electromechanics models have been developed to better understand the excitation-contraction behavior of the heart. However, there is no agreement on whether inertial forces play a role in this system. In this study, we assess the influence of mass in electromechanical simulations, using a fully coupled finite element model. We include the effect of mechano-electrical feedback via stretch activated currents. We compare five different models: electrophysiology, electromechanics, electromechanics with mechano-electrical feedback, electromechanics with mass, and electromechanics with mass and mechano-electrical feedback. We simulate normal conduction to study conduction velocity and spiral waves to study fibrillation. During normal conduction, mass in conjunction with mechano-electrical feedback increased the conduction velocity by 8.12% in comparison to the plain electrophysiology case. During the generation of a spiral wave, mass and mechano-electrical feedback generated secondary wavefronts, which were not present in any other model. These secondary wavefronts were initiated in tensile stretch regions that induced electrical currents. We expect that this study will help the research community to better understand the importance of mechanoelectrical feedback and inertia in cardiac electromechanics.
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Affiliation(s)
| | - Felipe A Concha
- Department of Structural and Geotechnical Engineering, School of Engineering, Pontificia Universidad Católica de Chile, Santiago, Chile
| | - Daniel E Hurtado
- Department of Structural and Geotechnical Engineering, School of Engineering, Pontificia Universidad Católica de Chile, Santiago, Chile
- Institute for Biological and Medical Engineering, Schools of Engineering, Medicine and Biological Sciences, Pontificia Universidad Catoólica de Chile, Santiago, Chile
| | - Ellen Kuhl
- Departments of Mechanical Engineering, Bioengineering, and Cardiothoracic Surgery, Stanford University, Stanford, CA 94305, USA
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