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Huang Y, Wang S, Luo T, Du MHF, Sun C, Sadat U, Schönlieb CB, Gillard JH, Zhang J, Teng Z. Estimation of the zero-pressure computational start shape of atherosclerotic plaques: Improving the backward displacement method with deformation gradient tensor. J Biomech 2022; 131:110910. [PMID: 34954525 DOI: 10.1016/j.jbiomech.2021.110910] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/20/2021] [Revised: 10/16/2021] [Accepted: 12/10/2021] [Indexed: 01/06/2023]
Abstract
Advances in medical imaging have enabled patient-specific biomechanical modelling of arterial lesions such as atherosclerosis and aneurysm. Geometry acquired from in-vivo imaging is already pressurized and a zero-pressure computational start shape needs to be identified. The backward displacement algorithm was proposed to solve this inverse problem, utilizing fixed-point iterations to gradually approach the start shape. However, classical fixed-point implementations were reported with suboptimal convergence properties under large deformations. In this paper, a dynamic learning rate guided by the deformation gradient tensor was introduced to control the geometry update. The effectiveness of this new algorithm was demonstrated for both idealized and patient-specific models. The proposed algorithm led to faster convergence by accelerating the initial steps and helped to avoid the non-convergence in large-deformation problems.
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Affiliation(s)
- Yuan Huang
- EPSRC Cambridge Mathematics of Information in Healthcare, University of Cambridge, Cambridge, UK; Department of Radiology, University of Cambridge, Cambridge, UK
| | - Shuo Wang
- Department of Radiology, University of Cambridge, Cambridge, UK; Shanghai Key Laboratory of Medical Imaging Computing and Computer Assisted Intervention, Fudan University, Shanghai, China; Digital Medical Research Center, School of Basic Medical Sciences, Fudan University, Shanghai, China
| | - Tao Luo
- Department of Engineering, University of Cambridge, Cambridge, UK
| | - Michael Hong-Fei Du
- Department of Radiology, University of Cambridge, Cambridge, UK; John Farman Intensive Care Unit, Cambridge University Hospitals NHS Foundation Trust, Cambridge, UK
| | - Chang Sun
- Department of Radiology, University of Cambridge, Cambridge, UK
| | - Umar Sadat
- Cambridge Vascular Unit, Cambridge University Hospitals NHS Foundation Trust, Cambridge, UK
| | - Carola-Bibiane Schönlieb
- EPSRC Cambridge Mathematics of Information in Healthcare, University of Cambridge, Cambridge, UK; Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, UK
| | | | - Jianjun Zhang
- Department of Radiology, Zhejiang Hospital, Zhejiang University School of Medicine, Hangzhou, China
| | - Zhongzhao Teng
- Department of Radiology, University of Cambridge, Cambridge, UK; Nanjing Jingsan Medical Science and Technology, Ltd, Jiangsu, China.
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