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Liu Y, Qi F, Cai XC. An aneurysm-specific preconditioning technique for the acceleration of Newton-Krylov method with application in the simulation of blood flows. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2023; 39:e3771. [PMID: 37688432 DOI: 10.1002/cnm.3771] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/04/2023] [Revised: 07/25/2023] [Accepted: 08/19/2023] [Indexed: 09/10/2023]
Abstract
In this paper, we develop an algorithm to simulate blood flows in aneurysmal arteries and focus on the construction of robust and efficient multilevel preconditioners to speed up the convergence of both linear and nonlinear solvers. The work is motivated by the observation that in the local aneurysmal region, the flow is often quite complicated with one or more vortices, but in the healthy section of the artery, the principal component of blood flows along the centerline of the artery. Based on this observation, we introduce a novel two-level additive Schwarz method with a mixed-dimensional coarse preconditioner. The key components of the preconditioner include (1) a three-dimensional coarse preconditioner covering the aneurysm; (2) a one-dimensional coarse preconditioner covering the central line of the healthy section of the artery; (3) a collection of three-dimensional overlapping subdomain preconditioners covering the fine meshes of the entire artery; (4) extension/restriction operators constructed by radial basis functions. The blood flow is modeled by the unsteady incompressible Navier-Stokes equations with resistance outflow boundary conditions discretized by a stabilized finite element method on fully unstructured meshes and the second-order backward differentiation formula in time. The resulting large nonlinear algebraic systems are solved by a Newton-Krylov algorithm accelerated by the new preconditioner in two ways: (1) the initial guess of Newton is obtained by solving a linear system defined by the coarse preconditioner; (2) the Krylov solver of the Jacobian system is preconditioned by the new preconditioner. Numerical experiments indicate that the proposed preconditioner is highly effective and robust for complex flows in a patient-specific artery with aneurysm, and it significantly reduces the numbers of linear and nonlinear iterations.
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Affiliation(s)
- Yingzhi Liu
- Department of Mathematics, University of Macau, Macau, People's Republic of China
| | - Fenfen Qi
- Department of Mathematics, University of Macau, Macau, People's Republic of China
| | - Xiao-Chuan Cai
- Department of Mathematics, University of Macau, Macau, People's Republic of China
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Rahma AG, Yousef K, Abdelhamid T. Blood flow CFD simulation on a cerebral artery of a stroke patient. SN APPLIED SCIENCES 2022. [DOI: 10.1007/s42452-022-05149-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/14/2022] Open
Abstract
Abstract
The purpose of this paper is to conduct a numerical simulation of the stroke patient's cerebral arteries and investigate the flow parameters due to the presence of stenosis. The computational fluid dynamics (CFD) simulations are based on simplified and realistic cerebral artery models. The seven simplified models (benchmarks) include straight cylindrical vessels with idealized stenosis with variable d/D (0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1). The realistic model of the cerebral artery is based on magnetic resonance imaging (MRI) for patient-specific cerebral arteries. The simulation for the realistic model of the cerebral artery is performed at boundary conditions measured by ultrasonography of the input and the output flow profiles (velocity and pressure). The obtained CFD results of the benchmarks are validated with actual data from the literature. Furthermore, a previous vascular contraction is assumed to be exist and the effect of this contraction area ratio on the blood flow regime is discussed and highlighted. Furthermore, CFD results show that a certain vascular contraction area critically affects the blood flow which shows increasing the wall shear stress WSS at the stenosis site. An increase in the blood velocity and vortex appears after the contraction zone, this lead to vessel occlusion and strokes.
Article highlights
The pressure drop across the arterial contraction is reduced when the area ratio d/D is increased.
In some cases, the vortex can prevent blood flow from crossing, this leads to vessel occlusion especially at low d/D
The WSS near the contraction area is high. Increasing the WSS can cause embolism that leads to lead to vessel occlusion.
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Zhou J, Li J, Qin S, Liu J, Lin Z, Xie J, Zhang Z, Chen R. High-resolution cerebral blood flow simulation with a domain decomposition method and verified by the TCD measurement. COMPUTER METHODS AND PROGRAMS IN BIOMEDICINE 2022; 224:107004. [PMID: 35841853 DOI: 10.1016/j.cmpb.2022.107004] [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: 02/22/2022] [Revised: 06/24/2022] [Accepted: 07/03/2022] [Indexed: 06/15/2023]
Abstract
BACKGROUND An efficient and accurate blood flow simulation can be useful for understanding many vascular diseases. Accurately resolving the blood flow velocity based on patient-specific geometries and model parameters is still a major challenge because of complex geomerty and turbulence issues. In addition, obtaining results in a short amount of computing time is important so that the simulation can be used in the clinical environment. In this work, we present a parallel scalable method for the patient-specific blood flow simulation with focuses on its parallel performance study and clinical verification. METHODS We adopt a fully implicit unstructured finite element method for a patient-specific simulation of blood flow in a full precerebral artery. The 3D artery is constructed from MRI images, and a parallel Newton-Krylov method preconditioned with a two-level domain decomposition method is adopted to solve the large nonlinear system discretized from the time-dependent 3D Navier-Stokes equations in the artery with an integral outlet boundary condition. The simulated results are verified using the clinical data measured by transcranial Doppler ultrasound, and the parallel performance of the algorithm is studied on a supercomputer. RESULTS The simulated velocity matches the clinical measured data well. Other simulated blood flow parameters, such as pressure and wall shear stress, are within reasonable ranges. The results show that the parallel algorithm scales up to 2160 processors with a 49% parallel efficiency for solving a problem with over 20 million unstructured elements on a supercomputer. For a standard cerebral blood flow simulation case with approximately 4 million finite elements, the calculation of one cardiac cycle can be finished within one hour with 1000 processors. CONCLUSION The proposed method is able to perform high-resolution 3D blood flow simulations in a patient-specific full precerebral artery within an acceptable time, and the simulated results are comparable with the clinical measured data, which demonstrates its high potential for clinical applications.
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Affiliation(s)
- Jie Zhou
- School of Mathematics and Statistics, Changsha University of Science and Technology, Changsha, China
| | - Jing Li
- School of Mathematics and Statistics, Changsha University of Science and Technology, Changsha, China
| | - Shanlin Qin
- Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen, China.
| | - Jia Liu
- Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen, China
| | - Zeng Lin
- Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen, China
| | - Jian Xie
- Department of Neurology, Affiliated ZhongDa Hospital, School of Medicine, Southeast University, Nanjing, China
| | - Zhijun Zhang
- Department of Neurology, Affiliated ZhongDa Hospital, School of Medicine, Southeast University, Nanjing, China
| | - Rongliang Chen
- Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen, China; Shenzhen Key Laboratory for Exascale Engineering and Scientific Computing, Shenzhen, China.
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Qin S, Wu B, Liu J, Shiu WS, Yan Z, Chen R, Cai XC. Efficient parallel simulation of hemodynamics in patient-specific abdominal aorta with aneurysm. Comput Biol Med 2021; 136:104652. [PMID: 34329862 DOI: 10.1016/j.compbiomed.2021.104652] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/17/2021] [Revised: 06/30/2021] [Accepted: 07/13/2021] [Indexed: 10/20/2022]
Abstract
Surgical planning for aortic aneurysm repair is a difficult task. In addition to the morphological features obtained from medical imaging, alternative features obtained with computational modeling may provide additional useful information. Though numerical studies are noninvasive, they are often time-consuming, especially when we need to study and compare multiple repair scenarios, because of the high computational complexity. In this paper, we present a highly parallel algorithm for the numerical simulation of unsteady blood flows in the patient-specific abdominal aorta before and after the aneurysmic repair. We model the blood flow with the unsteady incompressible Navier-Stokes equations with different outlet boundary conditions, and solve the discretized system with a highly scalable domain decomposition method. With this approach, a high resolution simulation of a full-size adult aorta can be obtained in less than an hour, instead of days with older methods and software. In addition, we show that the parallel efficiency of the proposed method is near 70% on a parallel computer with 2, 880 processor cores.
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Affiliation(s)
- Shanlin Qin
- Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen, China
| | - Bokai Wu
- Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen, China
| | - Jia Liu
- Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen, China
| | - Wen-Shin Shiu
- Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen, China
| | - Zhengzheng Yan
- Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen, China
| | - Rongliang Chen
- Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen, China; Shenzhen Key Laboratory for Exascale Engineering and Scientific Computing, Shenzhen, China.
| | - Xiao-Chuan Cai
- Department of Mathematics, University of Macau, Macau, China.
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Wu X, Wu B, He W, Wang X, Wang K, Yan Z, Cheng Z, Huang Y, Zhang W, Chen R, Liu J, Wang J, Hu X. Expanding the coronary tree reconstruction to smaller arteries improves the accuracy of FFR CT. Eur Radiol 2021; 31:8967-8974. [PMID: 34032918 DOI: 10.1007/s00330-021-08012-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/26/2021] [Revised: 04/16/2021] [Accepted: 04/26/2021] [Indexed: 11/29/2022]
Abstract
OBJECTIVES We attempted to improve the accuracy of coronary CT angiography (CCTA)-derived fractional flow reserve (FFR) (FFRCT) by expanding the coronary tree in the computational fluid dynamics (CFD) domain. An observational study was performed to evaluate the effects of extending the coronary tree analysis for FFRCT from a minimal diameter of 1.2 to 0.8 mm. METHODS Patients who underwent CCTA and interventional FFR were enrolled retrospectively. Seventy-six patients qualified based on the inclusion criteria. The three-dimensional (3D) coronary artery tree was reconstructed to generate a finite element mesh for each subject with different lower limits of luminal diameter (1.2 mm and 0.8 mm). Outlet boundary conditions were defined according to Murray's law. The Newton-Krylov-Schwarz (NKS) method was applied to solve the governing equations of CFD to derive FFRCT. RESULTS At the individual patient level, extending the minimal diameter of the coronary tree from 1.2 to 0.8 mm improved the sensitivity of FFRCT by 16.7% (p = 0.022). This led to the conversion of four false-negative cases into true-positive cases. The AUC value of the ROC curve increased from 0.74 to 0.83. Moreover, the NKS method can solve the computational problem of extending the coronary tree to an 0.8-mm luminal diameter in 10.5 min with 2160 processor cores. CONCLUSIONS Extending the reconstructed coronary tree to a smaller luminal diameter can considerably improve the sensitivity of FFRCT. The NKS method can achieve favorable computational times for future clinical applications. KEY POINTS • Extending the reconstructed coronary tree to a smaller luminal diameter can considerably improve the sensitivity of FFRCT. • The NKS method applied in our study can effectively reduce the computational time of this process for future clinical applications.
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Affiliation(s)
- Xianpeng Wu
- Department of Cardiology, The Second Affiliated Hospital, Zhejiang University School of Medicine, Hangzhou, 310009, Zhejiang, China.,Cardiovascular Key Laboratory of Zhejiang Province, Hangzhou, 310009, Zhejiang, China
| | - Bokai Wu
- Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences, Shenzhen, 518055, Guangdong, China
| | - Wenming He
- Department of Cardiology, The Second Affiliated Hospital, Zhejiang University School of Medicine, Hangzhou, 310009, Zhejiang, China.,Department of Cardiology, The Affiliated Hospital of Medical School, Ningbo University, Ningbo, 315020, Zhejiang, China
| | - Xinhong Wang
- Department of Radiology, The Second Affiliated Hospital, Zhejiang University School of Medicine, Hangzhou, 310009, Zhejiang, China
| | - Kan Wang
- Department of Cardiology, The Second Affiliated Hospital, Zhejiang University School of Medicine, Hangzhou, 310009, Zhejiang, China.,Cardiovascular Key Laboratory of Zhejiang Province, Hangzhou, 310009, Zhejiang, China
| | - Zhengzheng Yan
- Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences, Shenzhen, 518055, Guangdong, China
| | - Zaiheng Cheng
- Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences, Shenzhen, 518055, Guangdong, China
| | - Yuyu Huang
- Guangzhou First People's Hospital, School of Medicine, South China University of Technology, Guangzhou, 510180, Guangdong, China
| | - Wei Zhang
- Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences, Shenzhen, 518055, Guangdong, China
| | - Rongliang Chen
- Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences, Shenzhen, 518055, Guangdong, China
| | - Jia Liu
- Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences, Shenzhen, 518055, Guangdong, China
| | - Jian'an Wang
- Department of Cardiology, The Second Affiliated Hospital, Zhejiang University School of Medicine, Hangzhou, 310009, Zhejiang, China. .,Cardiovascular Key Laboratory of Zhejiang Province, Hangzhou, 310009, Zhejiang, China.
| | - Xinyang Hu
- Department of Cardiology, The Second Affiliated Hospital, Zhejiang University School of Medicine, Hangzhou, 310009, Zhejiang, China. .,Cardiovascular Key Laboratory of Zhejiang Province, Hangzhou, 310009, Zhejiang, China.
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