Radial Basis Functions for Combining Shape and Speckle Tracking in 4D Echocardiography

Compas, Colin B.; Wong, Emily Y.; Huang, Xiaojie; Sampath, Smita; Lin, Ben A.; Pal, Prasanta; Papademetris, Xenophon; Thiele, Karl; Dione, Donald P.; Stacy, Mitchel R.; Staib, Lawrence H.; Sinusas, Albert J.; O’Donnell, Matthew; Duncan, James S.

doi:10.1109/tmi.2014.2308894

Cited by 26 publications

(28 citation statements)

References 68 publications

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“…In addition, both examples used the plane stress assumption to reduce the computational expense. A Gaussian radial basis function (RBF) representation was chosen to define the localized elastic modulus variations, which was based upon several other similar works [36][37][38]. The RBF representation of elastic modulus distribution was defined as:…”

Section: Numerically Simulated Examplesmentioning

confidence: 99%

A computationally efficient approach for inverse material characterization combining Gappy POD with direct inversion

Wang

Dutta

Kim

et al. 2015

Computer Methods in Applied Mechanics and Engineering

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Section: Numerically Simulated Examplesmentioning

confidence: 99%

A computationally efficient approach for inverse material characterization combining Gappy POD with direct inversion

Wang

Dutta

Kim

et al. 2015

Computer Methods in Applied Mechanics and Engineering

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“…It was assumed that a priori knowledge would be available that the elastic modulus distributions to be characterized in the examples would be localized (e.g., as could be expected in applications of damage characterization of civil structures [26] or tumor characterization of biological structures [13]). As such, the snapshot response fields used for the Gappy POD procedure were generated using a Gaussian radial basis function (RBF) representation of the elastic modulus (see [27,28,29] for other similar works utilizing a RBF representation to define localized elastic modulus variations), as:…”

Section: Examples and Discussionmentioning

confidence: 99%

A generalized computationally efficient inverse characterization approach combining direct inversion solution initialization with gradient-based optimization

Wang

Brigham

2016

Comput Mech

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The nal publication is available at Springer via https://doi.org/10.1007/s00466-016-1362-3Additional information: Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. AbstractA computationally efficient gradient-based optimization approach for inverse material characterization from incomplete system response measurements that can utilize a generally applicable parameterization (e.g., finite elementtype parameterization) is presented and evaluated. The key to this inverse characterization algorithm is the use of a direct inversion strategy with Gappy proper orthogonal decomposition (POD) response field estimation to initialize the inverse solution estimate prior to gradient-based optimization. Gappy POD is used to estimate the complete (i.e., all components over the entire spatial domain) system response field from incomplete (e.g., partial spatial distribution) measurements obtained from some type of system testing along with some amount of a priori information regarding the potential distribution of the unknown material property. The estimated complete system response is used within a physics-based direct inversion procedure with a finite element-type parameterization to estimate the spatial distribution of the desired unknown material property with minimal computational expense. Then, this estimated spatial distribution of the unknown material property is used to initialize a gradient-based optimization approach, which * Corresponding author Email addresses: mengyu_wang@meei.harvard.edu (Mengyu Wang), john.brigham@durham.ac.uk (John C. Brigham) Preprint submitted to Computational MechanicsNovember 23, 2016 uses the adjoint method for computationally efficient gradient calculations, to produce the final estimate of the material property distribution. The three-step ((1) Gappy POD, (2) direct inversion, and (3) gradient-based optimization) inverse characterization approach is evaluated through simulated test problems based on the characterization of elastic modulus distributions with localized variations (e.g., inclusions) within simple structures. Overall, this inverse characterization approach is shown to efficiently and consistently provide accurate inverse characterization estimates for material property distributions from incomplete response field measurements. Moreover, the solution procedure is shown to be capable of extrapolating significantly beyond the initial assumptions regarding the potential nature of the unknown material property distribution.

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“…The mesh correspondence condition may be satisfied by using 4D (3D+t) ultrasound image data processed with speckle tracking algorithms [18], or 4D CT image data processed with surface tracking algorithms [19]; the heterogeneous thickness of the aortic wall may be extracted by using CT [20–22], MR[23] and ultrasound [24, 25] imaging techniques.…”

Section: Methodsmentioning

confidence: 99%

A new inverse method for estimation of in vivo mechanical properties of the aortic wall

Liu

Liang

Sun

2017

Journal of the Mechanical Behavior of Biomedical Materials

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The aortic wall is always loaded in vivo, which makes it challenging to estimate the material parameters of its nonlinear, anisotropic constitutive equation from in vivo image data. Previous approaches largely relied on either computationally expensive finite element models or simplifications of the geometry or material models. In this study, we investigated a new inverse method based on aortic wall stress computation. This approach consists of the following two steps: (1) computing an “almost true” stress field from the in vivo geometries and loading conditions, (2) building an objective function based on the “almost true” stress fields, constitutive equations and deformation relations, and estimating the material parameters by minimizing the objective function. The method was validated through numerical experiments by using the in vivo data from four ascending aortic aneurysm (AsAA) patients. The results demonstrated that the method is computationally efficient. This novel approach may facilitate the personalized biomechanical analysis of aortic tissues in clinical applications, such as in the rupture risk analysis of ascending aortic aneurysms.

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Radial Basis Functions for Combining Shape and Speckle Tracking in 4D Echocardiography

Cited by 26 publications

References 68 publications

A computationally efficient approach for inverse material characterization combining Gappy POD with direct inversion

A computationally efficient approach for inverse material characterization combining Gappy POD with direct inversion

A generalized computationally efficient inverse characterization approach combining direct inversion solution initialization with gradient-based optimization

A new inverse method for estimation of in vivo mechanical properties of the aortic wall

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