{"title":"A Computational Comparison of Variational Formulations for the Direct Solution of Hybrid Elastography Inverse Problems","authors":"Quinn T. Kolt, Olalekan A. Babaniyi","doi":"10.1002/nme.70072","DOIUrl":null,"url":null,"abstract":"<div>\n \n <p>We consider the inverse problem of reconstructing the complex shear modulus distribution within an object from measurements of the displacement field within that object. This problem is motivated by applications in the dynamic elastography field, where the shear modulus is used for noninvasive detection and diagnosis of various diseases. The displacements are assumed to obey a scalar wave model. We extend previously proposed direct error in constitutive equations (DECE) and equation error (EE) formulations to the scalar wave inverse problem, and compare them to each other and three other direct methods for the same problem. All the methods considered perform well in some scenarios. Only DECE and EE perform well in all scenarios considered. In particular, only DECE and EE methods can accurately reconstruct both continuous and discontinuous modulus fields in the presence of noise.</p>\n </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 13","pages":""},"PeriodicalIF":2.9000,"publicationDate":"2025-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal for Numerical Methods in Engineering","FirstCategoryId":"5","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/nme.70072","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
We consider the inverse problem of reconstructing the complex shear modulus distribution within an object from measurements of the displacement field within that object. This problem is motivated by applications in the dynamic elastography field, where the shear modulus is used for noninvasive detection and diagnosis of various diseases. The displacements are assumed to obey a scalar wave model. We extend previously proposed direct error in constitutive equations (DECE) and equation error (EE) formulations to the scalar wave inverse problem, and compare them to each other and three other direct methods for the same problem. All the methods considered perform well in some scenarios. Only DECE and EE perform well in all scenarios considered. In particular, only DECE and EE methods can accurately reconstruct both continuous and discontinuous modulus fields in the presence of noise.
期刊介绍：
The International Journal for Numerical Methods in Engineering publishes original papers describing significant, novel developments in numerical methods that are applicable to engineering problems.
The Journal is known for welcoming contributions in a wide range of areas in computational engineering, including computational issues in model reduction, uncertainty quantification, verification and validation, inverse analysis and stochastic methods, optimisation, element technology, solution techniques and parallel computing, damage and fracture, mechanics at micro and nano-scales, low-speed fluid dynamics, fluid-structure interaction, electromagnetics, coupled diffusion phenomena, and error estimation and mesh generation. It is emphasized that this is by no means an exhaustive list, and particularly papers on multi-scale, multi-physics or multi-disciplinary problems, and on new, emerging topics are welcome.
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