A Review of the Mathematical and Computational Foundations of Biomechanical Imaging

Barbone, Paul E.; Oberai, Assad A.

doi:10.1007/978-90-481-3575-2_13

Cited by 26 publications

(20 citation statements)

References 86 publications

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“…To reduce the computational time required to perform the shear modulus inversion, we further down-sample the number of points in the inversion ROI. The down-sampling rates used for Subject 1 and Subject 2, are [4,4,4] and [3,6,8], respectively, in x , y , z directions. The final mesh for modulus reconstruction contains 41 × 32 × 8 nodes for Subject 1, and 36 × 40 × 8 nodes for Subject 2, in x , y , z directions, respectively.…”

Section: Resultsmentioning

confidence: 99%

Improving three‐dimensional mechanical imaging of breast lesions with principal component analysis

et al. 2017

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Purpose: Elastography has emerged as a new tool for detecting and diagnosing many types of diseases including breast cancer. To date, most clinical applications of elastography have utilized two-dimensional strain images. The goal of this paper is to present a new quasi-static elastography technique that yields shear modulus images in three dimensions. Methods: An automated breast volume scanner was used to acquire ultrasound images of the breast as it was gently compressed. Cross-correlation between successive images was used to determine the displacement within the tissue. The resulting displacement field was filtered of all but compressive motion through principal component analysis. This displacement field was used to infer spatial distribution of shear modulus by solving a 3D elastic inverse problem. Results: Three dimensional shear modulus images of benign breast lesions for two subjects were generated using the techniques described above. It was found that the lesions were visualized more clearly in images generated using the displacement data de-noised through the use of principal components. Conclusions: We have presented experimental and algorithmic techniques that lead to three- dimensional imaging of shear modulus using quasi-static elastography. This work demonstrates feasibility of this approach, and lays the foundation for images of other, more informative, mechanical parameters.

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Section: Resultsmentioning

confidence: 99%

Improving three‐dimensional mechanical imaging of breast lesions with principal component analysis

et al. 2017

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“…Using medical imaging techniques from a branch of medical imaging known as “elastography,” the deformation of breast tissue may be measured in vivo [11, 12, 13, 14]. The availability of such data motivates the study and solution 10 of the following inverse problem of incompressible linear elasticity: Given a displacement field measured everywhere in an incompressible linear elastic solid, determine the heterogeneous shear modulus distribution within the solid.…”

Section: Introductionmentioning

confidence: 99%

“…direct approaches, offer a computationally efficient alternative to iterative approaches [11, 13]. In this approach, the measurements are treated as coefficients in a partial differential equation (PDE) for the desired material parameters.…”

Section: Introductionmentioning

confidence: 99%

Direct error in constitutive equation formulation for plane stress inverse elasticity problem

Babaniyi

Oberai²,

Barbone

2017

Computer Methods in Applied Mechanics and Engineering

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We present a new computational formulation for inverse problems in elasticity with full field data. The formulation is a variant of an error in the constitutive equation formulation, but allows direct solution for the modulus field and accommodates discontinuous strain fields. The development of the formulation is motivated by the relatively poor performance of current direct formulations, reported so far in literature, in dealing with discontinuities in the strain and material property distribution. The formulation relies on minimizing the error in the constitutive equation, and a momentum equation constraint. Numerical results on model problems show that the formulation is capable handling discontinuous, and noisy strain fields, and also converging with mesh refinement for continuous and discontinuous material property distributions. The application to reconstruct the elastic modulus distribution in solid breast tumors is shown.

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“…Furthermore, one goal of measuring the displacement field is as input to an inverse problem to estimate material property distributions [7, 13]. Computing the material properties from only one component of the displacement field is computationally intensive [7, 13]. In that situation, an iterative inversion approach is required, which may takes hundreds to thousands of iterations to converge.…”

Section: Introductionmentioning

confidence: 99%

Recovering vector displacement estimates in quasistatic elastography using sparse relaxation of the momentum equation

Babaniyi

Oberai

Barbone

2016

Inverse Problems in Science and Engineering

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We consider the problem of estimating the 2D vector displacement field in a heterogeneous elastic solid deforming under plane stress conditions. The problem is motivated by applications in quasistatic elastography. From precise and accurate measurements of one component of the 2D vector displacement field and very limited information of the second component, the method reconstructs the second component quite accurately. No a priori knowledge of the heterogeneous distribution of material properties is required. This method relies on using a special form of the momentum equations to filter ultrasound displacement measurements to produce more precise estimates. We verify the method with applications to simulated displacement data. We validate the method with applications to displacement data measured from a tissue mimicking phantom, and in-vivo data; significant improvements are noticed in the filtered displacements recovered from all the tests. In verification studies, error in lateral displacement estimates decreased from about 50% to about 2%, and strain error decreased from more than 250% to below 2%.

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A Review of the Mathematical and Computational Foundations of Biomechanical Imaging

Cited by 26 publications

References 86 publications

Improving three‐dimensional mechanical imaging of breast lesions with principal component analysis

Improving three‐dimensional mechanical imaging of breast lesions with principal component analysis

Direct error in constitutive equation formulation for plane stress inverse elasticity problem

Recovering vector displacement estimates in quasistatic elastography using sparse relaxation of the momentum equation

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