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  • Time-dependent elastic numerical model for Optical Coherence Elastography of the murine retina
    Publication . Correia, Carlos; Batista, Ana; Barbeiro, Sílvia; Cardoso, João; Domingues, José Paulo; Henriques, Rafael; Loureiro, Custódio; Santos, Mário J.; Serranho, Pedro; Bernardes, Rui; Morgado, Miguel
    We present the initial stages of development of a Finite Element Method-based time-dependent elastic numerical model which seeks to support the employment of our Optical Coherence Elastography system for assessing murine retinal elasticity. The current model is able to reconstruct displacement maps in both homogeneous and heterogeneous domains with errors up to a few hundredths relatively to a known exact displacement map, within 1 millisecond. The results demonstrate the robustness of the numerical algorithm under different elastic domains, and model parametrization with real Optical Coherence Elastography data is already in progress.
  • Ocular fundus Imaging: from structure to function
    Publication . Serranho, Pedro; Maduro, Cristina; Santos, Torcato; Bernardes, Rui; Vaz, José Cunha; Araújo, Adérito; Barbeiro, Sílvia
    Imaging the ocular fundus, namely the retina, to detect and/or monitor changes over time from the healthy condition is of fundamental importance to assess onset and disease progression and is a valuable tool to understand the basic mechanisms of ocular diseases. Current trends point to the need for less or non-invasive approaches, to the need for detailed (higher spatial and temporal resolution) imaging systems and to the quantification as opposed to qualitative classification of any findings. In this work we present a snapshot of our research by presenting two examples of technical development aiming to obtain structural and function information from the human retina, in vivo, using non-invasive techniques, namely optical coherence tomography imaging. Based on our experience and developed work, we are now starting to bridge the gap to brain imaging as the eye is only the starting point of vision.
  • Phase-resolved optical coherence elastography: an insight into tissue displacement estimation
    Publication . Batista, Ana; Serranho, Pedro; Santos, Mário; Correia, Carlos; Domingues, José P.; Loureiro, Custódio; Cardoso, João; Barbeiro, Sílvia; Morgado, António Miguel; Bernardes, Rui
    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.
  • The method of fundamental solutions for the direct elastography problem in the human retina
    Publication . Barbeiro, Sílvia; Serranho, Pedro
    This paper addresses the numerical simulation of the mechanical waves propagation and induced displacements in the human retina, for the elastography imaging modality. In this way, we use a model for the human eye and numerically approximate the propagation of time-harmonic acoustic waves through the different media of the eye and the respective elastic excitation in the retina, through a layered representation approach based on the method of fundamental solutions. We present numerical results showing the feasibility of the method.
  • Improved adaptive complex diffusion despeckling filter
    Publication . Bernardes, Rui; Maduro, Cristina; Serranho, Pedro; Araújo, Adérito; Barbeiro, Sílvia; Cunha-Vaz, José
    Despeckling optical coherence tomograms from the human retina is a fundamental step to a better diagnosis or as a preprocessing stage for retinal layer segmentation. Both of these applications are particularly important in monitoring the progression of retinal disorders. In this study we propose a new formulation for a well-known nonlinear complex diffusion filter. A regularization factor is now made to be dependent on data, and the process itself is now an adaptive one. Experimental results making use of synthetic data show the good performance of the proposed formulation by achieving better quantitative results and increasing computation speed.
  • Swept-source phase-stabilized optical coherence tomography setup for elastography
    Publication . Batista, Ana; Correia, Carlos; Barbeiro, Sílvia; Cardoso, João; Domingues, José Paulo; Henriques, Rafael; Loureiro, Custódio; Santos, Mário; Serranho, Pedro; Bernardes, Rui; Morgado, António Miguel
    We 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 excitation
    Publication . 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 Miguel
    In 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.
  • Stability of finite difference schemes for nonlinear complex reaction-diffusion processes
    Publication . Araújo, Adérito; Barbeiro, Sílvia; Serranho, Pedro
    In this paper we consider explicit, implicit and semiimplicit finite difference schemes for a general nonlinear reaction–diffusion equation. The stability condition for each method is established and several particular cases are highlighted. To illustrate the theoretical results we present some numerical examples.
  • Stability of finite difference schemes for complex diffusion processes
    Publication . Araújo, Adérito; Barbeiro, Sílvia; Serranho, Pedro
    In this paper we present a rigorous proof for the stability of a class of finite difference schemes applied to nonlinear complex diffusion equations. Complex diffusion is a common and broadly used denoising procedure in image processing. To illustrate the theoretical results we present some numerical examples based on an explicit scheme applied to a nonlinear equation in the context of image denoising.
  • Convergence of finite difference schemes for nonlinear complex reaction-diffusion processes
    Publication . Araújo, Adérito; Barbeiro, Sílvia; Serranho, Pedro
    This paper is devoted to the proof of the convergence properties of a class of finite difference schemes applied to nonlinear complex reaction-diffusion equations. We investigate the accuracy of the numerical solution considering implicit and semi-implicit discretizations. To illustrate the theoretical results we present some numerical examples computed with a semi-implicit scheme applied to a nonlinear equation.