Directional analysis of cardiac motion field from gated fluorodeoxyglucose PET images using the Discrete Helmholtz Hodge Decomposition

Sims, John A.; Giorgi, Maria Clementina Pinto; Oliveira, Marco Antônio Condé de; Meneghetti, José Cláudio; Gutierrez, Marco Antônio

doi:10.1016/j.compmedimag.2017.06.004

Cited by 6 publications

(3 citation statements)

References 16 publications

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“…Sparse OF provides a vector field for special features, normally pixels corresponding to edges or corners of objects, while dense OF provides a vector field for all pixels in the image. Dense algorithms related to motion vector field (MVF) analysis are known to have medical imaging applications, in particular for temporal analysis of cardiac images [4,[10][11][12][13]. A number of different methods exist for quantification of OF [14][15][16] of which the dense OF algorithms by Horn and Schunck (HS) and Farneback (FOF) have been used extensively in the literature.…”

Section: Optical Flowmentioning

confidence: 99%

Tracking Atrial Fibrillation Mechanisms: a Computational Method for Locating Rotors and Ectopic Activity Using Curl and Divergence Operators

Oliveira¹,

Sims²,

Salinet"³

2022

Computing in Cardiology Conference (CinC)

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Atrial Fibrillation (AF) is the most common supraventricular arrhythmia and has different underlying activation mechanism, including functional rotors (FR) and ectopic foci (EF). In this work we propose an approach for locating FR and EF in potential maps, which were tested with mathematical phantoms. 12 phantoms were created (128x128 array, 4 s, Fs 500 Hz), simulating the motion of: FR (4 maps), EF (4 maps) and superpositions of these (4 maps). These were downsampled to different grids from 16x16 to 8x8, simulating electrode acquisition. Noise (SNR from 2 to 60) was added. To locate the mechanism, the signals were filtered and interpolated. Farneback optical flow was applied to compute the motion vector field (MVF). The MVF was normalized and its temporal average was calculated. Finally, we computed curl and divergence, by using a x and y oriented 11 × 11 Sobel filter as a estimation of the of the partial derivatives. The location of extrema in the curl and divergence maps were used for locating FR and EF respectively. Method robustness was tested by comparing the algorithm performance on different grid sizes and SNR. The mechanism was considered to be detected accurately if the position was within a normalized error of 5% from its respective phantom location. The results showed that our approach was able to locate both mechanisms, but revealed a dependency on spatial resolution.

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Section: Optical Flowmentioning

confidence: 99%

Tracking Atrial Fibrillation Mechanisms: a Computational Method for Locating Rotors and Ectopic Activity Using Curl and Divergence Operators

Oliveira¹,

Sims²,

Salinet"³

2022

Computing in Cardiology Conference (CinC)

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“…The Helmholtz Hodge decomposition of a vector field into irrotational and solenoidal components and their respective scalar and vector potentials is a classical result that appears in many different variants both in the traditional fields of mathematics and physics and more recently in applied sciences like medical imaging [51]. Especially in the context of classical electromagnetism and plasma physics, the Helmholtz Hodge decomposition has been used for many years to help analyse turbulent velocity fields [4,26] or separate current systems into source-free and irrotational components [17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Discrete Vector Calculus and Helmholtz Hodge Decomposition for Classical Finite Difference Summation by Parts Operators

Ranocha

Ostaszewski

Heinisch

2020

Commun. Appl. Math. Comput.

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In this article, discrete variants of several results from vector calculus are studied for classical finite difference summation by parts operators in two and three space dimensions. It is shown that existence theorems for scalar/vector potentials of irrotational/solenoidal vector fields cannot hold discretely because of grid oscillations, which are characterised explicitly. This results in a non-vanishing remainder associated to grid oscillations in the discrete Helmholtz Hodge decomposition. Nevertheless, iterative numerical methods based on an interpretation of the Helmholtz Hodge decomposition via orthogonal projections are proposed and applied successfully.In numerical experiments, the discrete remainder vanishes and the potentials converge with the same order of accuracy as usual in other first order partial differential equations. Motivated by the successful application of the Helmholtz Hodge decomposition in theoretical plasma physics, applications to the discrete analysis of magnetohydrodynamic (MHD) wave modes are presented and discussed.

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“…Buckberg (2004), according to Notomi et al [1], notes that research in clinical cardiac mechanics has moved towards three-dimensional ventricular deformation studies, which include investigations of LV torsion. We have previously applied the Discrete Helmholtz Hodge Decomposition (DHHD) to 3D cardiac motion fields, calculated from in-vivo 4D image sequences using optical flow techniques ( [2]), and show that the DHHD algorithm presents the following possibilities for analysis: (i) an automated method for decomposing the motion field into components, such as LV torsion, which can then be studied independently and in a simpler manner; (ii) a method for tracking the centres of flow phenomena from frame to frame.…”

Section: Introductionmentioning

confidence: 99%

Directional Analysis of 2D Cardiac Motion Slices Using the Discrete Helmholtz Hodge Decomposition

Sims¹,

Santiago²,

Salinet³

et al. 2019

2019 Computing in Cardiology Conference (CinC)

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The 2D Discrete Helmholtz Hodge Decomposition (DHHD) is a candidate for decomposition of cardiac motion vector field (MVFs)from modalities such as echocardiography, allowing analyses of rotational, radial and harmonic MVFs separately and the tracking of centers of flow phenomena. However, the literature contains differing opinions about how boundary conditions (BCs) should be applied. In the proposed study, we investigate two sets of BCs, found in the literature, using synthetic motion vector fields: (i) zero BCs for all nodes along the domain boundary; (ii) a single zero BC for the first node. We found that (i) produces a decomposition with Normalised Root Mean Square Error (NRMSE) below 1%, while (ii) produces NRMSE greater than 200% when the input field contains a harmonic component. Further, we demonstrate the decomposition of a synthetic motion field from the Extended Cardiac Torso Phantom v2 into radial, rotational and harmonic components.

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Directional analysis of cardiac motion field from gated fluorodeoxyglucose PET images using the Discrete Helmholtz Hodge Decomposition

Cited by 6 publications

References 16 publications

Tracking Atrial Fibrillation Mechanisms: a Computational Method for Locating Rotors and Ectopic Activity Using Curl and Divergence Operators

Tracking Atrial Fibrillation Mechanisms: a Computational Method for Locating Rotors and Ectopic Activity Using Curl and Divergence Operators

Discrete Vector Calculus and Helmholtz Hodge Decomposition for Classical Finite Difference Summation by Parts Operators

Directional Analysis of 2D Cardiac Motion Slices Using the Discrete Helmholtz Hodge Decomposition

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