On the Numerical Solution of the Inverse Elastography Problem for Time-harmonic Excitation

Serranho, Pedro; Barbeiro, Sílvia; Henriques, Rafael; Batista, Ana; Santos, M.L.A.S.; Correia, Carlos; Domingues, José Paulo; Loureiro,; Cardoso, João Muralha; Bernardes, Rui; Morgado, Miguel

doi:10.5220/0011125900003209

Cited by 3 publications

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“…Although the benefits of increased displacement measurement accuracy in wave-based OCE may not be readily apparent, they can have a significant impact on elasticity estimation when considering numerical methods. An example is the application of Newton's method to a wave solution represented by the method of fundamental solutions [26]. We have recently shown that, when using Newton's-type iterations to recover the elastic properties of the medium, 1% noise in the data can lead to a two-to three-orders-of-magnitude higher error in the recovered elastic coefficients [26].…”

Section: Discussionmentioning

confidence: 99%

Phase-Resolved Optical Coherence Elastography: An Insight into Tissue Displacement Estimation

Batista

Serranho

Santos

et al. 2023

Sensors

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Robust methods to compute tissue displacements in optical coherence elastography (OCE) data are paramount, as they play a significant role in the accuracy of tissue elastic properties estimation. In this study, the accuracy of different phase estimators was evaluated on simulated OCE data, where the displacements can be accurately set, and on real data. Displacement (∆d) estimates were computed from (i) the original interferogram data (Δφori) and two phase-invariant mathematical manipulations of the interferogram: (ii) its first-order derivative (Δφd) and (iii) its integral (Δφint). We observed a dependence of the phase difference estimation accuracy on the initial depth location of the scatterer and the magnitude of the tissue displacement. However, by combining the three phase-difference estimates (Δdav), the error in phase difference estimation could be minimized. By using Δdav, the median root-mean-square error associated with displacement prediction in simulated OCE data was reduced by 85% and 70% in data with and without noise, respectively, in relation to the traditional estimate. Furthermore, a modest improvement in the minimum detectable displacement in real OCE data was also observed, particularly in data with low signal-to-noise ratios. The feasibility of using Δdav to estimate agarose phantoms’ Young’s modulus is illustrated.

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Section: Discussionmentioning

confidence: 99%

Phase-Resolved Optical Coherence Elastography: An Insight into Tissue Displacement Estimation

Batista

Serranho

Santos

et al. 2023

Sensors

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“…To calculate the global stiffness matrix B * and the vector F * of problem (13) we will make use of a reference tetrahedron.…”

Section: Reference Tetrahedronmentioning

confidence: 99%

“…Let us now compute the vector F * in (13), such that V ⊺ F * = l 1,h (v h ) with l 1,h given by (11).…”

Section: Vector F *mentioning

confidence: 99%

“…Let us compute the matrix B * in (13). We will determine b(v h , v h ) in terms of the coefficients V ji .…”

Section: Global Matrix B *mentioning

confidence: 99%

“…The predominant approaches in the literature are based on minimizing the difference between the measured and simulated displacements (e.g. [7,11,13]). Differently, in our method, we use the direct problem to define the objective function.…”

Section: Introductionmentioning

confidence: 99%

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A quadratic optimization program for the inverse elastography problem

Barbeiro,

Henriques,

Santos

2024

Preprint

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In this work we focus on the development of a numerical algorithm for the inverse elastography problem. The goal is to perform an efficient material parameter identification knowing the elastic displacement field induced by a mechanical load. We propose to define the inverse problem through a quadratic optimization program which uses the direct problem formulation to define the objective function. In this way, we end up with a convex minimization problem which attains its minimum at the solution of a linear system. The effectiveness of our method is illustrated through numeral examples.

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Retinal imaging in animal models: Searching for biomarkers of neurodegeneration

et al. 2023

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There is a pressing need for novel diagnostic and progression biomarkers of neurodegeneration. However, the inability to determine disease duration and stage in patients with Alzheimer’s disease (AD) hinders their discovery. Because animal models of disease allow us to circumvent some of these limitations, they have proven to be of paramount importance in clinical research. Due to the clear optics of the eye, the retina combined with optical coherence tomography (OCT) offers the perfect opportunity to image neurodegeneration in the retina in vivo, non-invasively, directly, quickly, and inexpensively. Based on these premises, our group has worked towards uncovering neurodegeneration-associated changes in the retina of the triple-transgenic mouse model of familial AD (3×Tg-AD). In this work, we present an overview of our work on this topic. We report on thickness variations of the retina and retinal layers/layer aggregates caused by healthy aging and AD-like conditions and discuss the implications of focusing research efforts solely on retinal thickness. We explore what other information is embedded in the OCT data, extracted based on texture analysis and deep-learning approaches, to further identify biomarkers that could be used for early detection and diagnosis. We were able to detect changes in the retina of the animal model of AD as early as 1 month of age. We also discuss our work to develop an optical coherence elastography system to measure retinal elasticity, which can be used in conjunction with conventional OCT. Finally, we discuss the potential application of these technologies in human patients and the steps needed to make OCT a helpful screening tool for the detection of neurodegeneration.

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On the Numerical Solution of the Inverse Elastography Problem for Time-harmonic Excitation

Cited by 3 publications

References 0 publications

Phase-Resolved Optical Coherence Elastography: An Insight into Tissue Displacement Estimation

Phase-Resolved Optical Coherence Elastography: An Insight into Tissue Displacement Estimation

A quadratic optimization program for the inverse elastography problem

Retinal imaging in animal models: Searching for biomarkers of neurodegeneration

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