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Bennati L, Giambruno V, Renzi F, Di Nicola V, Maffeis C, Puppini G, Luciani GB, Vergara C. Turbulent blood dynamics in the left heart in the presence of mitral regurgitation: a computational study based on multi-series cine-MRI. Biomech Model Mechanobiol 2023; 22:1829-1846. [PMID: 37400622 PMCID: PMC10613156 DOI: 10.1007/s10237-023-01735-0] [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: 03/28/2023] [Accepted: 06/04/2023] [Indexed: 07/05/2023]
Abstract
In this work, we performed a computational image-based study of blood dynamics in the whole left heart, both in a healthy subject and in a patient with mitral valve regurgitation. We elaborated multi-series cine-MRI with the aim of reconstructing the geometry and the corresponding motion of left ventricle, left atrium, mitral and aortic valves, and aortic root of the subjects. This allowed us to prescribe such motion to computational blood dynamics simulations where, for the first time, the whole left heart motion of the subject is considered, allowing us to obtain reliable subject-specific information. The final aim is to investigate and compare between the subjects the occurrence of turbulence and the risk of hemolysis and of thrombi formation. In particular, we modeled blood with the Navier-Stokes equations in the arbitrary Lagrangian-Eulerian framework, with a large eddy simulation model to describe the transition to turbulence and a resistive method to manage the valve dynamics, and we used a finite element discretization implemented in an in-house code for the numerical solution.
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Affiliation(s)
- Lorenzo Bennati
- Department of Surgery, Dentistry, Pediatrics, and Obstetrics/Gynecology, University of Verona, Piazzale Ludovico Antonio Scuro 10, 37134, Verona, Italy
| | - Vincenzo Giambruno
- Division of Cardiac Surgery, Department of Surgery, Dentistry, Pediatrics, and Obstetrics/Gynecology, University of Verona, Piazzale Stefani 1, 37126, Verona, Italy
| | - Francesca Renzi
- Department of Surgery, Dentistry, Pediatrics, and Obstetrics/Gynecology, University of Verona, Piazzale Ludovico Antonio Scuro 10, 37134, Verona, Italy
| | - Venanzio Di Nicola
- Division of Cardiac Surgery, Department of Surgery, Dentistry, Pediatrics, and Obstetrics/Gynecology, University of Verona, Piazzale Stefani 1, 37126, Verona, Italy
| | - Caterina Maffeis
- Department of Surgery, Dentistry, Pediatrics, and Obstetrics/Gynecology, University of Verona, Piazzale Ludovico Antonio Scuro 10, 37134, Verona, Italy
| | - Giovanni Puppini
- Department of Radiology, University of Verona, Piazzale Stefani 1, 37126, Verona, Italy
| | - Giovanni Battista Luciani
- Division of Cardiac Surgery, Department of Surgery, Dentistry, Pediatrics, and Obstetrics/Gynecology, University of Verona, Piazzale Stefani 1, 37126, Verona, Italy
| | - Christian Vergara
- LaBS, Dipartimento di Chimica, Materiali e Ingegneria Chimica "Giulio Natta", Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133, Milan, Italy.
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Kaiser AD, Schiavone NK, Elkins CJ, McElhinney DB, Eaton JK, Marsden AL. Comparison of Immersed Boundary Simulations of Heart Valve Hemodynamics Against In Vitro 4D Flow MRI Data. Ann Biomed Eng 2023; 51:2267-2288. [PMID: 37378877 PMCID: PMC10775908 DOI: 10.1007/s10439-023-03266-2] [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: 03/14/2023] [Accepted: 05/31/2023] [Indexed: 06/29/2023]
Abstract
The immersed boundary (IB) method is a mathematical framework for fluid-structure interaction problems (FSI) that was originally developed to simulate flows around heart valves. Direct comparison of FSI simulations around heart valves against experimental data is challenging, however, due to the difficulty of performing robust and effective simulations, the complications of modeling a specific physical experiment, and the need to acquire experimental data that is directly comparable to simulation data. Such comparators are a necessary precursor for further formal validation studies of FSI simulations involving heart valves. In this work, we performed physical experiments of flow through a pulmonary valve in an in vitro pulse duplicator, and measured the corresponding velocity field using 4D flow MRI (4-dimensional flow magnetic resonance imaging). We constructed a computer model of this pulmonary artery setup, including modeling valve geometry and material properties via a technique called design-based elasticity, and simulated flow through it with the IB method. The simulated flow fields showed excellent qualitative agreement with experiments, excellent agreement on integral metrics, and reasonable relative error in the entire flow domain and on slices of interest. These results illustrate how to construct a computational model of a physical experiment for use as a comparator.
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Affiliation(s)
- Alexander D Kaiser
- Department of Pediatrics (Cardiology), Stanford University, Stanford, CA, USA
- Stanford Cardiovascular Institute, Stanford, CA, USA
| | - Nicole K Schiavone
- Department of Mechanical Engineering, Stanford University, Stanford, CA, USA
| | | | - Doff B McElhinney
- Department of Pediatrics (Cardiology), Stanford University, Stanford, CA, USA
- Stanford Cardiovascular Institute, Stanford, CA, USA
- Department of Cardiothoracic Surgery, Stanford University, Stanford, CA, USA
| | - John K Eaton
- Department of Mechanical Engineering, Stanford University, Stanford, CA, USA
| | - Alison L Marsden
- Department of Pediatrics (Cardiology), Stanford University, Stanford, CA, USA.
- Stanford Cardiovascular Institute, Stanford, CA, USA.
- Department of Mechanical Engineering, Stanford University, Stanford, CA, USA.
- Institute for Computational and Mathematical Engineering, Stanford University, Stanford, CA, USA.
- Department of Bioengineering, Stanford University, Stanford, CA, USA.
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Bennati L, Vergara C, Giambruno V, Fumagalli I, Corno AF, Quarteroni A, Puppini G, Luciani GB. An Image-Based Computational Fluid Dynamics Study of Mitral Regurgitation in Presence of Prolapse. Cardiovasc Eng Technol 2023; 14:457-475. [PMID: 37069336 PMCID: PMC10412498 DOI: 10.1007/s13239-023-00665-3] [Citation(s) in RCA: 6] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 04/11/2022] [Accepted: 03/12/2023] [Indexed: 04/19/2023]
Abstract
PURPOSE In this work we performed an imaged-based computational study of the systolic fluid dynamics in presence of mitral valve regurgitation (MVR). In particular, we compared healthy and different regurgitant scenarios with the aim of quantifying different hemodynamic quantities. METHODS We performed computational fluid dynamic (CFD) simulations in the left ventricle, left atrium and aortic root, with a resistive immersed method, a turbulence model, and with imposed systolic wall motion reconstructed from Cine-MRI images, which allowed us to segment also the mitral valve. For the regurgitant scenarios we considered an increase of the heart rate and a dilation of the left ventricle. RESULTS Our results highlighted that MVR gave rise to regurgitant jets through the mitral orifice impinging against the atrial walls and scratching against the mitral valve leading to high values of wall shear stresses (WSSs) with respect to the healthy case. CONCLUSION CFD with prescribed wall motion and immersed mitral valve revealed to be an effective tool to quantitatively describe hemodynamics in case of MVR and to compare different regurgitant scenarios. Our findings highlighted in particular the presence of transition to turbulence in the atrium and allowed us to quantify some important cardiac indices such as cardiac output and WSS.
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Affiliation(s)
- Lorenzo Bennati
- Department of Surgery, Dentistry, Pediatrics, and Obstetrics/Gynecology, University of Verona, Piazzale Ludovico Antonio Scuro 10, 37134 Verona, Italy
| | - Christian Vergara
- LaBS, Dipartimento di Chimica, Materiali e Ingegneria Chimica “Giulio Natta”, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milan, Italy
| | - Vincenzo Giambruno
- Division of Cardiac Surgery, Department of Surgery, Dentistry, Pediatrics, and Obstetrics/Gynecology, University of Verona, O. C. M. Piazzale Stefani 1, 37126 Verona, Italy
| | - Ivan Fumagalli
- MOX, Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milan, Italy
| | - Antonio Francesco Corno
- Children’s Heart Institute, McGovern Medical School, UT Health, 6431 Fannin Street, Houston, TX 77030 USA
| | - Alfio Quarteroni
- MOX, Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milan, Italy
- École Polytechnique Fédérale de Lausanne, Rte Cantonale, 1015 Lausanne, Switzerland
| | - Giovanni Puppini
- Department of Radiology, University of Verona, O. C. M. Piazzale Stefani 1, 37126 Verona, Italy
| | - Giovanni Battista Luciani
- Division of Cardiac Surgery, Department of Surgery, Dentistry, Pediatrics, and Obstetrics/Gynecology, University of Verona, O. C. M. Piazzale Stefani 1, 37126 Verona, Italy
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Katz S, Caiazzo A, Moreau B, Wilbrandt U, Brüning J, Goubergrits L, John V. Impact of turbulence modeling on the simulation of blood flow in aortic coarctation. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2023; 39:e3695. [PMID: 36914373 DOI: 10.1002/cnm.3695] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/26/2022] [Revised: 02/10/2023] [Accepted: 02/20/2023] [Indexed: 05/13/2023]
Abstract
Numerical simulations of pulsatile blood flow in an aortic coarctation require the use of turbulence modeling. This paper considers three models from the class of large eddy simulation (LES) models (Smagorinsky, Vreman, σ -model) and one model from the class of variational multiscale models (residual-based) within a finite element framework. The influence of these models on the estimation of clinically relevant biomarkers used to assess the degree of severity of the pathological condition (pressure difference, secondary flow degree, normalized flow displacement, wall shear stress) is investigated in detail. The simulations show that most methods are consistent in terms of severity indicators such as pressure difference and stenotic velocity. Moreover, using second-order velocity finite elements, different turbulence models might lead to considerably different results concerning other clinically relevant quantities such as wall shear stresses. These differences may be attributed to differences in numerical dissipation introduced by the turbulence models.
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Affiliation(s)
- Sarah Katz
- Numerical Mathematics and Scientific Computing Research Group, Weierstrass Institute for Applied Analysis and Stochastics (WIAS), Berlin, Germany
| | - Alfonso Caiazzo
- Numerical Mathematics and Scientific Computing Research Group, Weierstrass Institute for Applied Analysis and Stochastics (WIAS), Berlin, Germany
| | - Baptiste Moreau
- Numerical Mathematics and Scientific Computing Research Group, Weierstrass Institute for Applied Analysis and Stochastics (WIAS), Berlin, Germany
| | - Ulrich Wilbrandt
- Numerical Mathematics and Scientific Computing Research Group, Weierstrass Institute for Applied Analysis and Stochastics (WIAS), Berlin, Germany
| | - Jan Brüning
- Deutsches Herzzentrum der Charité, Institute of Computer-assisted Cardiovascular Medicine, Charité - Universitätsmedizin Berlin, corporate member of Freie Universität Berlin and Humboldt Universität zu Berlin, Berlin, Germany
| | - Leonid Goubergrits
- Deutsches Herzzentrum der Charité, Institute of Computer-assisted Cardiovascular Medicine, Charité - Universitätsmedizin Berlin, corporate member of Freie Universität Berlin and Humboldt Universität zu Berlin, Berlin, Germany
- Einstein Center Digital Future, Berlin, Germany
| | - Volker John
- Numerical Mathematics and Scientific Computing Research Group, Weierstrass Institute for Applied Analysis and Stochastics (WIAS), Berlin, Germany
- Department of Mathematics and Computer Science, Freie Universität Berlin, Berlin, Germany
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Kaiser AD, Shad R, Schiavone N, Hiesinger W, Marsden AL. Controlled Comparison of Simulated Hemodynamics Across Tricuspid and Bicuspid Aortic Valves. Ann Biomed Eng 2022; 50:1053-1072. [PMID: 35748961 PMCID: PMC10775905 DOI: 10.1007/s10439-022-02983-4] [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: 10/13/2021] [Accepted: 05/16/2022] [Indexed: 11/01/2022]
Abstract
Bicuspid aortic valve is the most common congenital heart defect, affecting 1-2% of the global population. Patients with bicuspid valves frequently develop dilation and aneurysms of the ascending aorta. Both hemodynamic and genetic factors are believed to contribute to dilation, yet the precise mechanism underlying this progression remains under debate. Controlled comparisons of hemodynamics in patients with different forms of bicuspid valve disease are challenging because of confounding factors, and simulations offer the opportunity for direct and systematic comparisons. Using fluid-structure interaction simulations, we simulate flows through multiple aortic valve models in a patient-specific geometry. The aortic geometry is based on a healthy patient with no known aortic or valvular disease, which allows us to isolate the hemodynamic consequences of changes to the valve alone. Four fully-passive, elastic model valves are studied: a tricuspid valve and bicuspid valves with fusion of the left- and right-, right- and non-, and non- and left-coronary cusps. The resulting tricuspid flow is relatively uniform, with little secondary or reverse flow, and little to no pressure gradient across the valve. The bicuspid cases show localized jets of forward flow, excess streamwise momentum, elevated secondary and reverse flow, and clinically significant levels of stenosis. Localized high flow rates correspond to locations of dilation observed in patients, with the location related to which valve cusps are fused. Thus, the simulations support the hypothesis that chronic exposure to high local flow contributes to localized dilation and aneurysm formation.
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Affiliation(s)
- Alexander D Kaiser
- Institute for Computational & Mathematical Engineering, Stanford University, Stanford, CA, USA
- Department of Pediatrics (Cardiology), Stanford University, Stanford, CA, USA
- Stanford Cardiovascular Institute, Stanford, CA, USA
| | - Rohan Shad
- Stanford Cardiovascular Institute, Stanford, CA, USA
- Department of Cardiothoracic Surgery, Stanford University, Stanford, CA, USA
| | - Nicole Schiavone
- Department of Mechanical Engineering, Stanford University, Stanford, CA, USA
| | - William Hiesinger
- Stanford Cardiovascular Institute, Stanford, CA, USA
- Department of Cardiothoracic Surgery, Stanford University, Stanford, CA, USA
| | - Alison L Marsden
- Institute for Computational & Mathematical Engineering, Stanford University, Stanford, CA, USA.
- Department of Pediatrics (Cardiology), Stanford University, Stanford, CA, USA.
- Stanford Cardiovascular Institute, Stanford, CA, USA.
- Department of Mechanical Engineering, Stanford University, Stanford, CA, USA.
- Department of Bioengineering, Stanford University, Stanford, CA, USA.
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Nolte D, Bertoglio C. Inverse problems in blood flow modeling: A review. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2022; 38:e3613. [PMID: 35526113 PMCID: PMC9541505 DOI: 10.1002/cnm.3613] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 07/17/2021] [Revised: 12/29/2021] [Accepted: 03/18/2022] [Indexed: 06/14/2023]
Abstract
Mathematical and computational modeling of the cardiovascular system is increasingly providing non-invasive alternatives to traditional invasive clinical procedures. Moreover, it has the potential for generating additional diagnostic markers. In blood flow computations, the personalization of spatially distributed (i.e., 3D) models is a key step which relies on the formulation and numerical solution of inverse problems using clinical data, typically medical images for measuring both anatomy and function of the vasculature. In the last years, the development and application of inverse methods has rapidly expanded most likely due to the increased availability of data in clinical centers and the growing interest of modelers and clinicians in collaborating. Therefore, this work aims to provide a wide and comparative overview of literature within the last decade. We review the current state of the art of inverse problems in blood flows, focusing on studies considering fully dimensional fluid and fluid-solid models. The relevant physical models and hemodynamic measurement techniques are introduced, followed by a survey of mathematical data assimilation approaches used to solve different kinds of inverse problems, namely state and parameter estimation. An exhaustive discussion of the literature of the last decade is presented, structured by types of problems, models and available data.
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Affiliation(s)
- David Nolte
- Bernoulli InstituteUniversity of GroningenGroningenThe Netherlands
- Center for Mathematical ModelingUniversidad de ChileSantiagoChile
- Department of Fluid DynamicsTechnische Universität BerlinBerlinGermany
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Kaiser AD, Shad R, Hiesinger W, Marsden AL. A design-based model of the aortic valve for fluid-structure interaction. Biomech Model Mechanobiol 2021; 20:2413-2435. [PMID: 34549354 PMCID: PMC10752438 DOI: 10.1007/s10237-021-01516-7] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/25/2020] [Accepted: 08/22/2021] [Indexed: 11/27/2022]
Abstract
This paper presents a new method for modeling the mechanics of the aortic valve and simulates its interaction with blood. As much as possible, the model construction is based on first principles, but such that the model is consistent with experimental observations. We require that tension in the leaflets must support a pressure, then derive a system of partial differential equations governing its mechanical equilibrium. The solution to these differential equations is referred to as the predicted loaded configuration; it includes the loaded leaflet geometry, fiber orientations and tensions needed to support the prescribed load. From this configuration, we derive a reference configuration and constitutive law. In fluid-structure interaction simulations with the immersed boundary method, the model seals reliably under physiological pressures and opens freely over multiple cardiac cycles. Further, model closure is robust to extreme hypo- and hypertensive pressures. Then, exploiting the unique features of this model construction, we conduct experiments on reference configurations, constitutive laws and gross morphology. These experiments suggest the following conclusions: (1) The loaded geometry, tensions and tangent moduli primarily determine model function. (2) Alterations to the reference configuration have little effect if the predicted loaded configuration is identical. (3) The leaflets must have sufficiently nonlinear material response to function over a variety of pressures. (4) Valve performance is highly sensitive to free edge length and leaflet height. These conclusions suggest appropriate gross morphology and material properties for the design of prosthetic aortic valves. In future studies, our aortic valve modeling framework can be used with patient-specific models of vascular or cardiac flow.
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Affiliation(s)
- Alexander D Kaiser
- Institute for Computational and Mathematical Engineering, Stanford University, Stanford, CA, USA.
- Department of Pediatrics (Cardiology), Stanford University, Stanford, CA, USA.
- Stanford Cardiovascular Institute, Stanford, CA, USA.
| | - Rohan Shad
- Stanford Cardiovascular Institute, Stanford, CA, USA
- Department of Cardiothoracic Surgery, Stanford University, Stanford, CA, USA
| | - William Hiesinger
- Stanford Cardiovascular Institute, Stanford, CA, USA
- Department of Cardiothoracic Surgery, Stanford University, Stanford, CA, USA
| | - Alison L Marsden
- Institute for Computational and Mathematical Engineering, Stanford University, Stanford, CA, USA
- Department of Pediatrics (Cardiology), Stanford University, Stanford, CA, USA
- Stanford Cardiovascular Institute, Stanford, CA, USA
- Department of Bioengineering, Stanford University, Stanford, CA, USA
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Galarce F, Lombardi D, Mula O. Reconstructing haemodynamics quantities of interest from Doppler ultrasound imaging. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2021; 37:e3416. [PMID: 33219632 DOI: 10.1002/cnm.3416] [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: 06/15/2020] [Revised: 11/06/2020] [Accepted: 11/07/2020] [Indexed: 06/11/2023]
Abstract
The present contribution deals with the estimation of haemodynamics Quantities of Interest by exploiting Ultrasound Doppler measurements. A fast method is proposed, based on the Parameterized Background Data-Weak (PBDW) method. Several methodological contributions are described: a sub-manifold partitioning is introduced to improve the reduced-order approximation, two different ways to estimate the pressure drop are compared, and an error estimation is derived. A fully synthetic test-case on a realistic common carotid geometry is presented, showing that the proposed approach is promising in view of realistic applications.
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Affiliation(s)
- Felipe Galarce
- Centre de Recherche INRIA de Paris, Laboratoire Jacques-Louis Lions Faculté des Sciences de Sorbonne Université, INRIA, Paris, France
| | - Damiano Lombardi
- Centre de Recherche INRIA de Paris, Laboratoire Jacques-Louis Lions Faculté des Sciences de Sorbonne Université, INRIA, Paris, France
| | - Olga Mula
- Centre de Recherche INRIA de Paris, Laboratoire Jacques-Louis Lions Faculté des Sciences de Sorbonne Université, INRIA, Paris, France
- CEREMADE, Paris-Dauphine University, PSL Research University, CNRS, Paris, France
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Lynch SR, Nama N, Xu Z, Arthurs CJ, Sahni O, Figueroa CA. Numerical considerations for advection-diffusion problems in cardiovascular hemodynamics. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2020; 36:e3378. [PMID: 32573092 PMCID: PMC11129875 DOI: 10.1002/cnm.3378] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/26/2020] [Revised: 04/21/2020] [Accepted: 06/07/2020] [Indexed: 06/11/2023]
Abstract
Numerical simulations of cardiovascular mass transport pose significant challenges due to the wide range of Péclet numbers and backflow at Neumann boundaries. In this paper we present and discuss several numerical tools to address these challenges in the context of a stabilized finite element computational framework. To overcome numerical instabilities when backflow occurs at Neumann boundaries, we propose an approach based on the prescription of the total flux. In addition, we introduce a "consistent flux" outflow boundary condition and demonstrate its superior performance over the traditional zero diffusive flux boundary condition. Lastly, we discuss discontinuity capturing (DC) stabilization techniques to address the well-known oscillatory behavior of the solution near the concentration front in advection-dominated flows. We present numerical examples in both idealized and patient-specific geometries to demonstrate the efficacy of the proposed procedures. The three contributions discussed in this paper successfully address commonly found challenges when simulating mass transport processes in cardiovascular flows.
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Affiliation(s)
- Sabrina R. Lynch
- Department of Biomedical Engineering, University of Michigan, Ann Arbor, Michigan
| | - Nitesh Nama
- Department of Surgery, University of Michigan, Ann Arbor, Michigan
| | - Zelu Xu
- Mechanical, Aerospace and Nuclear Engineering, Rensselaer Polytechnic Institute, New York, New York
| | | | - Onkar Sahni
- Mechanical, Aerospace and Nuclear Engineering, Rensselaer Polytechnic Institute, New York, New York
| | - C. Alberto Figueroa
- Department of Biomedical Engineering, University of Michigan, Ann Arbor, Michigan
- Department of Surgery, University of Michigan, Ann Arbor, Michigan
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Liu J, Yang W, Dong M, Marsden AL. The nested block preconditioning technique for the incompressible Navier-Stokes equations with emphasis on hemodynamic simulations. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 2020; 367:113122. [PMID: 32675836 PMCID: PMC7365595 DOI: 10.1016/j.cma.2020.113122] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/17/2023]
Abstract
We develop a novel iterative solution method for the incompressible Navier-Stokes equations with boundary conditions coupled with reduced models. The iterative algorithm is designed based on the variational multiscale formulation and the generalized-α scheme. The spatiotemporal discretization leads to a block structure of the resulting consistent tangent matrix in the Newton-Raphson procedure. As a generalization of the conventional block preconditioners, a three-level nested block preconditioner is introduced to attain a better representation of the Schur complement, which plays a key role in the overall algorithm robustness and efficiency. This approach provides a flexible, algorithmic way to handle the Schur complement for problems involving multiscale and multiphysics coupling. The solution method is implemented and benchmarked against experimental data from the nozzle challenge problem issued by the US Food and Drug Administration. The robustness, efficiency, and parallel scalability of the proposed technique are then examined in several settings, including moderately high Reynolds number flows and physiological flows with strong resistance effect due to coupled downstream vasculature models. Two patient-specific hemodynamic simulations, covering systemic and pulmonary flows, are performed to further corroborate the efficacy of the proposed methodology.
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Affiliation(s)
- Ju Liu
- Department of Pediatrics (Cardiology), Department of Bioengineering, and Institute for Computational and Mathematical Engineering, Stanford University, Clark Center E1.3, 318 Campus Drive, Stanford, CA 94305, USA
| | - Weiguang Yang
- Department of Pediatrics (Cardiology), Department of Bioengineering, and Institute for Computational and Mathematical Engineering, Stanford University, Clark Center E1.3, 318 Campus Drive, Stanford, CA 94305, USA
| | - Melody Dong
- Department of Pediatrics (Cardiology), Department of Bioengineering, and Institute for Computational and Mathematical Engineering, Stanford University, Clark Center E1.3, 318 Campus Drive, Stanford, CA 94305, USA
| | - Alison L Marsden
- Department of Pediatrics (Cardiology), Department of Bioengineering, and Institute for Computational and Mathematical Engineering, Stanford University, Clark Center E1.3, 318 Campus Drive, Stanford, CA 94305, USA
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11
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Liu J, Yang W, Lan IS, Marsden AL. Fluid-structure interaction modeling of blood flow in the pulmonary arteries using the unified continuum and variational multiscale formulation. MECHANICS RESEARCH COMMUNICATIONS 2020; 107:103556. [PMID: 32773906 PMCID: PMC7405952 DOI: 10.1016/j.mechrescom.2020.103556] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/02/2023]
Abstract
In this work, we present a computational fluid-structure interaction (FSI) study for a healthy patient-specific pulmonary arterial tree using the unified continuum and variational multiscale (VMS) formulation we previously developed. The unified framework is particularly well-suited for FSI, as the fluid and solid sub-problems are addressed in essentially the same manner and can thus be uniformly integrated in time with the generalized-α method. In addition, the VMS formulation provides a mechanism for large-eddy simulation in the fluid sub-problem and pressure stabilization in the solid sub-problem. The FSI problem is solved in a quasi-direct approach, in which the pressure and velocity in the unified continuum body are first solved, and the solid displacement is then obtained via a segregated algorithm and prescribed as a boundary condition for the mesh motion. Results of the pulmonary arterial FSI simulation are presented and compared against those of a rigid wall simulation.
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Affiliation(s)
- Ju Liu
- Department of Pediatrics (Cardiology), Department of Bioengineering, and Institute for Computational and Mathematical Engineering, Stanford University, Clark Center E1.3, 318 Campus Drive, Stanford, CA 94305, USA
| | - Weiguang Yang
- Department of Pediatrics (Cardiology), Department of Bioengineering, and Institute for Computational and Mathematical Engineering, Stanford University, Clark Center E1.3, 318 Campus Drive, Stanford, CA 94305, USA
| | - Ingrid S Lan
- Department of Pediatrics (Cardiology), Department of Bioengineering, and Institute for Computational and Mathematical Engineering, Stanford University, Clark Center E1.3, 318 Campus Drive, Stanford, CA 94305, USA
| | - Alison L Marsden
- Department of Pediatrics (Cardiology), Department of Bioengineering, and Institute for Computational and Mathematical Engineering, Stanford University, Clark Center E1.3, 318 Campus Drive, Stanford, CA 94305, USA
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12
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Joly F, Soulez G, Lessard S, Kauffmann C, Vignon-Clementel I. A Cohort Longitudinal Study Identifies Morphology and Hemodynamics Predictors of Abdominal Aortic Aneurysm Growth. Ann Biomed Eng 2019; 48:606-623. [DOI: 10.1007/s10439-019-02375-1] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/25/2019] [Accepted: 09/24/2019] [Indexed: 12/19/2022]
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13
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B V, Dubey A, Bég OA. Finite element analysis of non-Newtonian magnetohemodynamic flow conveying nanoparticles through a stenosed coronary artery. ACTA ACUST UNITED AC 2019. [DOI: 10.1002/htj.21598] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022]
Affiliation(s)
- Vasu B
- Department of Mathematics; Motilal Nehru National Institute of Technology Allahabad; Prayagraj Uttar Pradesh India
| | - Ankita Dubey
- Department of Mathematics; Motilal Nehru National Institute of Technology Allahabad; Prayagraj Uttar Pradesh India
| | - O. Anwar Bég
- Department of Mechanical and Aeronautical Engineering; Salford University; Manchester UK
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Wei ZA, Huddleston C, Trusty PM, Singh-Gryzbon S, Fogel MA, Veneziani A, Yoganathan AP. Analysis of Inlet Velocity Profiles in Numerical Assessment of Fontan Hemodynamics. Ann Biomed Eng 2019; 47:2258-2270. [PMID: 31236791 DOI: 10.1007/s10439-019-02307-z] [Citation(s) in RCA: 16] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/11/2018] [Accepted: 06/08/2019] [Indexed: 12/16/2022]
Abstract
Computational fluid dynamic (CFD) simulations are widely utilized to assess Fontan hemodynamics that are related to long-term complications. No previous studies have systemically investigated the effects of using different inlet velocity profiles in Fontan simulations. This study implements real, patient-specific velocity profiles for numerical assessment of Fontan hemodynamics using CFD simulations. Four additional, artificial velocity profiles were used for comparison: (1) flat, (2) parabolic, (3) Womersley, and (4) parabolic with inlet extensions [to develop flow before entering the total cavopulmonary connection (TCPC)]. The differences arising from the five velocity profiles, as well as discrepancies between the real and each of the artificial velocity profiles, were quantified by examining clinically important metrics in TCPC hemodynamics: power loss (PL), viscous dissipation rate (VDR), hepatic flow distribution, and regions of low wall shear stress. Statistically significant differences were observed in PL and VDR between simulations using real and flat velocity profiles, but differences between those using real velocity profiles and the other three artificial profiles did not reach statistical significance. These conclusions suggest that the artificial velocity profiles (2)-(4) are acceptable surrogates for real velocity profiles in Fontan simulations, but parabolic profiles are recommended because of their low computational demands and prevalent applicability.
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Affiliation(s)
- Zhenglun Alan Wei
- Wallace H. Coulter School of Biomedical Engineering, Georgia Institute of Technology, 387 Technology Circle, Suite 232, Atlanta, GA, 30313-2412, USA
| | - Connor Huddleston
- School of Chemistry and Biochemistry, Georgia Institute of Technology, Atlanta, GA, USA
| | - Phillip M Trusty
- Wallace H. Coulter School of Biomedical Engineering, Georgia Institute of Technology, 387 Technology Circle, Suite 232, Atlanta, GA, 30313-2412, USA
| | - Shelly Singh-Gryzbon
- Wallace H. Coulter School of Biomedical Engineering, Georgia Institute of Technology, 387 Technology Circle, Suite 232, Atlanta, GA, 30313-2412, USA
| | - Mark A Fogel
- Department of Cardiology, Children's Hospital of Philadelphia, Philadelphia, PA, USA
| | - Alessandro Veneziani
- Department of Mathematics, Department of Computer Science, Emory University, Atlanta, GA, USA
| | - Ajit P Yoganathan
- Wallace H. Coulter School of Biomedical Engineering, Georgia Institute of Technology, 387 Technology Circle, Suite 232, Atlanta, GA, 30313-2412, USA.
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15
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Nolte D, Bertoglio C. Reducing the impact of geometric errors in flow computations using velocity measurements. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2019; 35:e3203. [PMID: 30932361 PMCID: PMC6619346 DOI: 10.1002/cnm.3203] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 12/12/2018] [Revised: 02/26/2019] [Accepted: 03/12/2019] [Indexed: 06/09/2023]
Abstract
Numerical blood flow simulations are typically set up from anatomical medical images and calibrated using velocity measurements. However, the accuracy of the computational geometry itself is limited by the resolution of the anatomical image. We first show that applying standard no-slip boundary conditions on inaccurately extracted boundaries can cause large errors in the results, in particular the pressure gradient. In this work, we therefore propose to augment the flow model calibration by slip/transpiration boundary conditions, whose parameters are then estimated using velocity measurements. Numerical experiments show that this methodology can considerably improve the accuracy of the estimated pressure gradients and 3D velocity fields when the vessel geometry is uncertain.
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Affiliation(s)
- David Nolte
- Bernoulli InstituteUniversity of GroningenGroningenNetherlands
- Center of Mathematical ModelingUniversity of ChileSantiagoChile
| | - Cristóbal Bertoglio
- Bernoulli InstituteUniversity of GroningenGroningenNetherlands
- Center of Mathematical ModelingUniversity of ChileSantiagoChile
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16
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Bergersen AW, Mortensen M, Valen-Sendstad K. The FDA nozzle benchmark: "In theory there is no difference between theory and practice, but in practice there is". INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2019; 35:e3150. [PMID: 30211982 DOI: 10.1002/cnm.3150] [Citation(s) in RCA: 22] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/01/2017] [Revised: 08/30/2018] [Accepted: 08/31/2018] [Indexed: 06/08/2023]
Abstract
The utility of flow simulations relies on the robustness of computational fluid dynamics (CFD) solvers and reproducibility of results. The aim of this study was to validate the Oasis CFD solver against in vitro experimental measurements of jet breakdown location from the FDA nozzle benchmark at Reynolds number 3500, which is in the particularly challenging transitional regime. Simulations were performed on meshes consisting of 5, 10, 17, and 28 million (M) tetrahedra, with Δt = 10-5 seconds. The 5M and 10M simulation jets broke down in reasonable agreement with the experiments. However, the 17M and 28M simulation jets broke down further downstream. But which of our simulations are "correct"? From a theoretical point of view, they are all wrong because the jet should not break down in the absence of disturbances. The geometry is axisymmetric with no geometrical features that can generate angular velocities. A stable flow was supported by linear stability analysis. From a physical point of view, a finite amount of "noise" will always be present in experiments, which lowers transition point. To replicate noise numerically, we prescribed minor random angular velocities (approximately 0.31%), much smaller than the reported flow asymmetry (approximately 3%) and model accuracy (approximately 1%), at the inlet of the 17M simulation, which shifted the jet breakdown location closer to the measurements. Hence, the high-resolution simulations and "noise" experiment can potentially explain discrepancies in transition between sometimes "sterile" CFD and inherently noisy "ground truth" experiments. Thus, we have shown that numerical simulations can agree with experiments, but for the wrong reasons.
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Affiliation(s)
- Aslak W Bergersen
- Department of Computational Physiology, Simula Research Laboratory AS, Fornebu, Norway
| | - Mikael Mortensen
- Department of Mathematics, University of Oslo Mathematics and Natural Sciences, Oslo, Norway
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17
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Karabelas E, Gsell MAF, Augustin CM, Marx L, Neic A, Prassl AJ, Goubergrits L, Kuehne T, Plank G. Towards a Computational Framework for Modeling the Impact of Aortic Coarctations Upon Left Ventricular Load. Front Physiol 2018; 9:538. [PMID: 29892227 PMCID: PMC5985756 DOI: 10.3389/fphys.2018.00538] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/15/2017] [Accepted: 04/26/2018] [Indexed: 01/04/2023] Open
Abstract
Computational fluid dynamics (CFD) models of blood flow in the left ventricle (LV) and aorta are important tools for analyzing the mechanistic links between myocardial deformation and flow patterns. Typically, the use of image-based kinematic CFD models prevails in applications such as predicting the acute response to interventions which alter LV afterload conditions. However, such models are limited in their ability to analyze any impacts upon LV load or key biomarkers known to be implicated in driving remodeling processes as LV function is not accounted for in a mechanistic sense. This study addresses these limitations by reporting on progress made toward a novel electro-mechano-fluidic (EMF) model that represents the entire physics of LV electromechanics (EM) based on first principles. A biophysically detailed finite element (FE) model of LV EM was coupled with a FE-based CFD solver for moving domains using an arbitrary Eulerian-Lagrangian (ALE) formulation. Two clinical cases of patients suffering from aortic coarctations (CoA) were built and parameterized based on clinical data under pre-treatment conditions. For one patient case simulations under post-treatment conditions after geometric repair of CoA by a virtual stenting procedure were compared against pre-treatment results. Numerical stability of the approach was demonstrated by analyzing mesh quality and solver performance under the significantly large deformations of the LV blood pool. Further, computational tractability and compatibility with clinical time scales were investigated by performing strong scaling benchmarks up to 1536 compute cores. The overall cost of the entire workflow for building, fitting and executing EMF simulations was comparable to those reported for image-based kinematic models, suggesting that EMF models show potential of evolving into a viable clinical research tool.
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Affiliation(s)
- Elias Karabelas
- Computational Cardiology Laboratory, Institute of Biophysics, Medical University of Graz, Graz, Austria
| | - Matthias A F Gsell
- Computational Cardiology Laboratory, Institute of Biophysics, Medical University of Graz, Graz, Austria
| | - Christoph M Augustin
- Computational Cardiology Laboratory, Institute of Biophysics, Medical University of Graz, Graz, Austria.,Shadden Research Group, Department of Mechanical Engineering, University of California, Berkeley, Berkeley, CA, United States
| | - Laura Marx
- Computational Cardiology Laboratory, Institute of Biophysics, Medical University of Graz, Graz, Austria
| | - Aurel Neic
- Computational Cardiology Laboratory, Institute of Biophysics, Medical University of Graz, Graz, Austria
| | - Anton J Prassl
- Computational Cardiology Laboratory, Institute of Biophysics, Medical University of Graz, Graz, Austria
| | - Leonid Goubergrits
- Department of Congenital Heart Disease/Pediatric Cardiology, German Heart Institute Berlin, Berlin, Germany.,Institute for Imaging Science and Computational Modeling in Cardiovascular Medicine, Charité - University Medicine Berlin, Berlin, Germany
| | - Titus Kuehne
- Department of Congenital Heart Disease/Pediatric Cardiology, German Heart Institute Berlin, Berlin, Germany.,Institute for Imaging Science and Computational Modeling in Cardiovascular Medicine, Charité - University Medicine Berlin, Berlin, Germany
| | - Gernot Plank
- Computational Cardiology Laboratory, Institute of Biophysics, Medical University of Graz, Graz, Austria
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