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- Phase-resolved optical coherence elastography: an insight into tissue displacement estimationPublication . Batista, Ana; Serranho, Pedro; Santos, Mário; Correia, Carlos; Domingues, José P.; Loureiro, Custódio; Cardoso, João; Barbeiro, Sílvia; Morgado, António Miguel; Bernardes, RuiRobust 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.
- Swept-source phase-stabilized optical coherence tomography setup for elastographyPublication . Batista, Ana; Correia, Carlos; Barbeiro, Sílvia; Cardoso, João; Domingues, José Paulo; Henriques, Rafael; Loureiro, Custódio; Santos, Mário; Serranho, Pedro; Bernardes, Rui; Morgado, António MiguelWe present an Optical Coherence Elastography (OCE) system, based on a swept-source Optical Coherence Tomography (OCT) setup, and evaluate its performance in terms of phase stability and minimum detectable displacement. The ability to record sub-pixel movements in samples under dynamic conditions was also assessed. The OCE system has a time stability of 396.9 ± 46.7 ps. The phase stability, given by the standard deviation of the measured phase difference, was 72.44 mrad, which corresponds to a minimum detectable displacement of 6.11 nm. Tests showed that the OCE system can detect and measure sub-pixel movements in samples under dynamic mechanical excitation.
- On the numerical solution of the inverse elastography problem for time-harmonic excitationPublication . Serranho, Pedro; Barbeiro, Sílvia; Henriques, Rafael; Batista, Ana; Santos, Mário; Correia, Carlos; Domingues, José Paulo; Loureiro, Custódio; Cardoso, João M. R.; Bernardes, Rui; Morgado, António MiguelIn this paper we address the numerical solution of the inverse elastography problem, from the knowledge of the excitation field on the boundary and the displacement field in a grid of points within the domain. We suggest using a representation of the solution by the method of fundamental solutions and using a Newtontype method to iteratively approximate the Lam´e coefficients of the medium from elastography displacement measurements. We consider a toy model to illustrate the performance of the method.