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Karabelas E, Longobardi S, Fuchsberger J, Razeghi O, Rodero C, Strocchi M, Rajani R, Haase G, Plank G, Niederer S. Global Sensitivity Analysis of Four Chamber Heart Hemodynamics Using Surrogate Models. IEEE Trans Biomed Eng 2022; 69:3216-3223. [PMID: 35353691 PMCID: PMC9491017 DOI: 10.1109/tbme.2022.3163428] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/31/2022] [Accepted: 03/19/2022] [Indexed: 11/15/2022]
Abstract
Computational Fluid Dynamics (CFD) is used to assist in designing artificial valves and planning procedures, focusing on local flow features. However, assessing the impact on overall cardiovascular function or predicting longer-term outcomes may requires more comprehensive whole heart CFD models. Fitting such models to patient data requires numerous computationally expensive simulations, and depends on specific clinical measurements to constrain model parameters, hampering clinical adoption. Surrogate models can help to accelerate the fitting process while accounting for the added uncertainty. We create a validated patient-specific four-chamber heart CFD model based on the Navier-Stokes-Brinkman (NSB) equations and test Gaussian Process Emulators (GPEs) as a surrogate model for performing a variance-based global sensitivity analysis (GSA). GSA identified preload as the dominant driver of flow in both the right and left side of the heart, respectively. Left-right differences were seen in terms of vascular outflow resistances, with pulmonary artery resistance having a much larger impact on flow than aortic resistance. Our results suggest that GPEs can be used to identify parameters in personalized whole heart CFD models, and highlight the importance of accurate preload measurements.
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Affiliation(s)
- Elias Karabelas
- Institute of Mathematics and Scientific ComputingUniversity of GrazAustria
| | - Stefano Longobardi
- Cardiac Electromechanics Research Group, School of Biomedical Engineering and Imaging SciencesKing’s College LondonU.K.
| | - Jana Fuchsberger
- Institute of Mathematics and Scientific ComputingUniversity of GrazAustria
| | - Orod Razeghi
- Research IT Services DepartmentUniversity College LondonU.K.
| | - Cristobal Rodero
- Cardiac Electromechanics Research Group, School of Biomedical Engineering and Imaging SciencesKing’s College LondonU.K.
| | - Marina Strocchi
- Cardiac Electromechanics Research Group, School of Biomedical Engineering and Imaging SciencesKing’s College LondonU.K.
| | - Ronak Rajani
- Department of Adult EchocardiographyGuy’s and St Thomas’ Hospitals NHS Foundation TrustU.K.
| | - Gundolf Haase
- Institute of Mathematics and Scientific ComputingUniversity of GrazAustria
| | - Gernot Plank
- Gottfried Schatz Research Center (for Cell Signaling, Metabolism and Aging), Division BiophysicsMedical University of GrazAustria
| | - Steven Niederer
- Cardiac Electromechanics Research Group, School of Biomedical Engineering and Imaging SciencesKing’s College LondonSE1 7EHLondonU.K.
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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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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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Bertoglio C, Caiazzo A, Bazilevs Y, Braack M, Esmaily M, Gravemeier V, L Marsden A, Pironneau O, E Vignon-Clementel I, A Wall W. Benchmark problems for numerical treatment of backflow at open boundaries. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2018; 34:e2918. [PMID: 28744968 DOI: 10.1002/cnm.2918] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/06/2017] [Revised: 07/21/2017] [Accepted: 07/21/2017] [Indexed: 06/07/2023]
Abstract
In computational fluid dynamics, incoming velocity at open boundaries, or backflow, often yields unphysical instabilities already for moderate Reynolds numbers. Several treatments to overcome these backflow instabilities have been proposed in the literature. However, these approaches have not yet been compared in detail in terms of accuracy in different physiological regimes, in particular because of the difficulty to generate stable reference solutions apart from analytical forms. In this work, we present a set of benchmark problems in order to compare different methods in different backflow regimes (with a full reversal flow and with propagating vortices after a stenosis). The examples are implemented in FreeFem++, and the source code is openly available, making them a solid basis for future method developments.
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Affiliation(s)
- Cristóbal Bertoglio
- Center for Mathematical Modeling, Universidad de Chile, Santiago, Chile
- Johann Bernoulli Institute, University of Groningen, Groningen, The Netherlands
| | - Alfonso Caiazzo
- Weierstrass Institute for Applied Analysis and Stochastics (WIAS) Leibniz Institute in Forschungsverbund Berlin e.V., Berlin, Germany
| | - Yuri Bazilevs
- Department of Structural Engineering, University of California, San Diego, CA, USA
| | - Malte Braack
- Research Group for Applied Mathematics, Christian-Albrechts-Universität, Kiel, Germany
| | - Mahdi Esmaily
- Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14850, USA
- Center for Turbulence Research, Stanford University, Stanford, CA, USA
| | - Volker Gravemeier
- Institute for Computational Mechanics, Technical University of Munich, Garching b., Munich, Germany
- AdCo EngineeringGW GmbH, Garching b., Munich, Germany
| | - Alison L Marsden
- Cardiovascular Biomechanics Computational Lab, Stanford University, Stanford, CA, USA
| | - Olivier Pironneau
- Laboratoire Jacques-Louis Lions, Pierre-and-Marie-Curie University, Paris, France
| | - Irene E Vignon-Clementel
- Laboratoire Jacques-Louis Lions, Pierre-and-Marie-Curie University, Paris, France
- REO Project Team, INRIA, Paris, France
| | - Wolfgang A Wall
- Institute for Computational Mechanics, Technical University of Munich, Garching b., Munich, Germany
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