Vector method of strain estimation in OCT-elastography with adaptive choice of scale for estimating interframe phase-variation gradients

Zykov, Alexey A.; Matveyev, Alexander L.; Sovetsky, Alexander A.; Matveev, Lev A.; Zaitsev, Vladimir Yu.

doi:10.1088/1612-202x/ace253

Cited by 9 publications

(10 citation statements)

References 34 publications

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“…Axial strain, 𝜀 𝑧 , is calculated by measuring the axial displacement, 𝑢 𝑧 , due to compression at every (𝑥, 𝑧) location and computing the gradient of 𝑢 𝑧 with respect to 𝑧, i.e., . Methods for computing the gradient include linear regression [27,28] and finite difference [50] methods; however, the presence of noise typically necessitates increasing the fitting range or performing spatial averaging to improve sensitivity, at the expense of resolution [38,39].…”

Section: Methodsmentioning

confidence: 99%

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Tumor spheroid elasticity estimation using mechano-microscopy combined with a conditional generative adversarial network

Foo,

Shaddy,

Murgoitio-Esandi

et al. 2024

Preprint

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Techniques for imaging the mechanical properties of cells are needed to study how cell mechanics influence cell function and disease progression. Mechano-microscopy (a high-resolution variant of compression optical coherence elastography) generates elasticity images of a sample undergoing compression from the phase difference between optical coherence microscopy (OCM) B-scans. However, the existing mechano-microscopy signal processing chain (referred to as the algebraic method) assumes the sample stress is uniaxial and axially uniform, such that violation of these assumptions reduces the accuracy and precision of elasticity images. Furthermore, it does not account for prior information regarding the sample geometry or mechanical property distribution. In this study, we investigate the feasibility of training a conditional generative adversarial network (cGAN) to generate elasticity images from phase difference images of samples containing a cell spheroid embedded in a hydrogel. To train and test the cGAN, we constructed 30,000 elasticity and phase difference image pairs, where elasticity images were generated using a parametric model to simulate artificial samples, and phase difference images were computed using finite element analysis to simulate compression applied to the artificial samples. By applying both the cGAN and algebraic methods to simulated phase difference images, our results indicate the cGAN elasticity images exhibit better spatial resolution and sensitivity. We also evaluated the cGAN on experimental phase difference images of real spheroids embedded in hydrogels and compared the cGAN elasticity with the algebraic elasticity, OCM, and confocal fluorescence microscopy, and found the cGAN elasticity is often more robust to noise, especially within stiff nuclei.

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Section: Methodsmentioning

confidence: 99%

“…Methods for computing the gradient include linear regression [27,28] and finite difference [50] methods; however, the presence of noise typically necessitates increasing the fitting range or performing spatial averaging to improve sensitivity, at the expense of resolution [38,39].…”

Section: 𝜕𝑢 𝑧mentioning

confidence: 99%

Tumor spheroid elasticity estimation using mechano-microscopy combined with a conditional generative adversarial network

Foo,

Shaddy,

Murgoitio-Esandi

et al. 2024

Preprint

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“…Recently, the problem of adaptive choice of the gradientestimation scale g was considered in [17], and [18] discussed the problem of adaptive choice of window size W z × W x for vector averaging for strain estimation in optical coherence elastography (OCE) based on the vector method. In those papers, solution of both problems required repetition of enumerative procedures for a set of values g with verification of correctness of the estimated-strain sign.…”

Section: Elucidation Of How the Quality Of Strain Estimation Depends ...mentioning

confidence: 99%

“…In this approach, OCT signals are represented as vectors in the complex plane and all the operations are performed with such vectors (also called phasors [16]). A recent study [17] considered optimization of the choice of scale (or step) over which gradients of interframe phase variations are estimated. The main idea is to choose a scale such that the phase gradient approaches the maximal unambiguously evaluated value, i.e.…”

Section: Introductionmentioning

confidence: 99%

Computationally efficient adaptive optimization of vector-method parameters for phase-sensitive strain estimation in optical coherence elastography

Zykov,

Matveyev,

Matveev

et al. 2024

Laser Phys. Lett.

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A new method for automatic adaptive optimization of strain estimation in phase-sensitive optical coherence tomography (OCT) is introduced. More specifically, this paper focuses on optimizing the estimation of strain using the vector method, in which OCT signals are treated as vectors in the complex plane. In phase-sensitive optical coherence elastography, the tissue strain is extracted from the interframe phase variation between the complex-valued scans acquired for the initial and deformed tissue. This phase variation is proportional to interframe displacements of scatterers and corresponds to the argument of the pixel-by-pixel product of the initial OCT scan and complex-conjugate deformed scan. Measurement noises and the so-called ‘speckle noise’ that are intrinsic to OCT scans cause degradation of the derived scan obtained by such multiplication. To mitigate the noise influence, complex-valued pixel amplitudes in the derived scan are usually averaged over a certain window. The interframe strain is found by estimating the gradient of the interframe phase difference. The noise influence on the strain estimation can also be reduced by increasing the scale over which the phase-variation gradient is estimated. However, choosing a too large window for preliminary averaging may significantly distort the reconstructed strain distribution. Similarly, a too large scale for gradient estimation may also cause errors in the estimated-strain magnitude and even its sign (because of possible phase wrapping). Therefore, appropriately performed adaptive choice of the strain-estimation parameters can greatly improve the quality of strain estimation. Here, we present a unified approach for adaptive choice of both the averaging-window size and gradient-estimation scale that were initially considered separately. The new method is computationally simplified but enables approximately the same strain-estimation quality, as demonstrated using both simulated and experimental OCT data.

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“…The following equations (Matveyev et al, 2018;Za et al, 2016;Zykov et al, 2023) were used to obtain the pixel-wise strain in the direction of the optical axis z [m], ε zz [-]:…”

Section: Strain Computationmentioning

confidence: 99%

Optomechanical assessment of photorefractive corneal cross-linking via optical coherence elastography

Frigelli,

Büchler,

Kling

2023

Front. Bioeng. Biotechnol.

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Purpose: Corneal cross-linking (CXL) has recently been used with promising results to positively affect corneal refractive power in the treatment of hyperopia and mild myopia. However, understanding and predicting the optomechanical changes induced by this procedure are challenging.Methods: We applied ambient pressure modulation based optical coherence elastography (OCE) to quantify the refractive and mechanical effects of patterned CXL and their relationship to energy delivered during the treatment on porcine corneas. Three different patterned treatments were performed, designed according to Zernike polynomial functions (circle, astigmatism, coma). In addition, three different irradiation protocols were analyzed: standard Dresden CXL (fluence of 5.4 J/cm2), accelerated CXL (fluence of 5.4 J/cm2), and high-fluence CXL (fluence of 16.2 J/cm2). The axial strain distribution in the stroma induced by ocular inflation (Δp = 30 mmHg) was quantified, maps of the anterior sagittal curvature were constructed and cylindrical refraction was assessed.Results: Thirty minutes after CXL, there was a statistically significant increase in axial strain amplitude (p < 0.050) and a reduction in sagittal curvature (p < 0.050) in the regions treated with all irradiation patterns compared to the non-irradiated ones. Thirty-6 hours later, the non-irradiated regions showed compressive strains, while the axial strain in the CXL-treated regions was close to zero, and the reduction in sagittal curvature observed 30 minutes after the treatment was maintained. The Dresden CXL and accelerated CXL produced comparable amounts of stiffening and refractive changes (p = 0.856), while high-fluence CXL produced the strongest response in terms of axial strain (6.9‰ ± 1.9‰) and refractive correction (3.4 ± 0.9 D). Tripling the energy administered during CXL resulted in a 2.4-fold increase in the resulting refractive correction.Conclusion: OCE showed that refractive changes and alterations in corneal biomechanics are directly related. A patient-specific selection of both, the administered UV fluence and the irradiation pattern during CXL is promising to allow customized photorefractive corrections in the future.

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Vector method of strain estimation in OCT-elastography with adaptive choice of scale for estimating interframe phase-variation gradients

Cited by 9 publications

References 34 publications

Tumor spheroid elasticity estimation using mechano-microscopy combined with a conditional generative adversarial network

Tumor spheroid elasticity estimation using mechano-microscopy combined with a conditional generative adversarial network

Computationally efficient adaptive optimization of vector-method parameters for phase-sensitive strain estimation in optical coherence elastography

Optomechanical assessment of photorefractive corneal cross-linking via optical coherence elastography

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