Extended Kalman Filter Nonlinear Finite Element Method for Nonlinear Soft Tissue Deformation

Xie, Hujin; Song, Jialu; Zhong, Yongmin; Li, Jiankun; Gu, Chengfan; Choi, Kup‐Sze

doi:10.1016/j.cmpb.2020.105828

Cited by 20 publications

(7 citation statements)

References 39 publications

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“…This method allows online estimation of softtissue deformation from the local measurement of displacement by formulating the deformation of the soft tissue as a filtering identification process. To analyze the nonlinear soft tissue behavior, an extended (nonlinear) Kalman filter is combined with the traditional nonlinear FEM [84]. The computational head can be further reduced by lowering the number of states of model without compromising its physics [85].…”

Section: ) Mesh-based Modeling Methodsmentioning

confidence: 99%

Toward a Digital Twin for Arthroscopic Knee Surgery: A Systematic Review

et al. 2022

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The use of digital twins to represent a product or process digitally is trending in many engineering disciplines. This term has also been recently introduced in the medical field. In arthroscopic surgery education, the paradigm shift from apprenticeship to simulation training has driven the need for better simulators, and the current focus is on improving simulators with respect to computational efficiency and system accuracy. However, expanding surgical simulations towards digital twins has not yet been explored. This paper introduces the digital twin concept for arthroscopic surgery, and explores its potential in light of the existing scientific literature. Thus, a systematic review was conducted to summarize and analyze the literature with respect to fast and robust design of an arthroscopic digital twin using patientspecific information, and methods for interactive surgical soft tissue simulation. The review was conducted using the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) protocol with three reliable scientific search engines: IEEE Explore, ScienceDirect and PubMed. Eighty papers were included in the review, and the extracted data included modeling methods, tissue types, constitutive behavior, computational efficiency or accuracy, hardware configuration, haptic device description, software tools, and system architectures. Considering the review, a novel macro-level conceptual arthroscopic digital twin system is presented, and the applicability of the review findings for the identified subsystems are discussed. The proposed system integrates patient-specific images, diagnostic data, intraoperative sensor data, and surgical practice as inputs, and conceptually enables surgical skills training, preoperative planning, and a database of virtual surgeries.

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Section: ) Mesh-based Modeling Methodsmentioning

confidence: 99%

Toward a Digital Twin for Arthroscopic Knee Surgery: A Systematic Review

et al. 2022

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“…They applied different force fields to the outer surface of the geometry and used FEM software Abaqus as a nonlinear finite element solver to simulate tumor deformation under different load cases. Xie et al 36 proposed an approach that combines the traditional nonlinear finite element method and nonlinear Kalman filtering to address both physical fidelity and real-time performance for soft tissue modeling. This approach defines mechanical tissue deformation as a nonlinear filtering process for the dynamic estimation of nonlinear deformation behaviors of biological tissues.…”

Section: Resolution Methods Of Nonlinear Continuum Mechanicsmentioning

confidence: 99%

Fast and accurate nonlinear hyper‐elastic deformation with a posteriori numerical verification of the convergence of solution: Application to the simulation of liver deformation

Saidi

Malti

2021

Numer Methods Biomed Eng

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In this paper, we propose a new method to reduce the computational complexity of calculating the tangential stiffness matrix in a nonlinear finite element formulation. Our approach consists in partially updating the tangential stiffness matrix during a classic Newton–Raphson iterative process. The complexity of such an update process has the order of the number of mesh vertices to the power of two. With our approach, this complexity is reduced to the power of two of only the number of updated vertices. We numerically study the convergence of the solution with our modified algorithm. We describe the deformation through a strain energy density function which is defined with respect to the Lagrangian strain. We derive the conditions of convergence for a given tangential stiffness matrix and a given set of updated vertices. We use nonlinear geometric deformation and the nonlinear Mooney‐Rivilin model with both tetrahedron and hexahedron element meshing. We provide extensive results using a cube with small and large number of elements. We provide results on nonlinearly deformed liver with multiple deformation ranges of updated vertices. We compare the proposed method to state‐of‐the‐art work and we prove its efficiency at three levels: accuracy, speed of convergence and small radius of convergence.

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“…This task is not easy because these biological characteristics represent very complex phenomena such as nonlinearity, direction-dependent anisotropy, and time-dependent viscoelasticity. Some scholars began to notice the influence of these biological characteristics on the deformation of virtual surgical models, and some research results have been achieved [ [10] , [11] , [12] , [13] , [14] ]. Wei Zhang et al [ 10 ] used the generalized Maxwell model to fit the relaxation data of the aorta and capture the significant features of vascular viscoelasticity by taking the rate insensitive characteristics of biological materials into account.…”

Section: Related Workmentioning

confidence: 99%