Resulting Phase Maps Research Articles

Pulmonary Veins Function as Echo Chambers in Persistent Atrial Fibrillation: Circuitous Re-Entry Generates Outgoing Wavefronts

BackgroundAlthough the substrate in persistent atrial fibrillation (PeAF) is not limited to the pulmonary veins (PVs), PV isolation (PVI) remains the cornerstone ablation strategy. ObjectivesThe aim of this study was to describe the mechanism of outgoing wavefronts (WFs) originating in the PV sleeves during PeAF. MethodsEleven patients presenting for first-time PeAF ablation were recruited (mean age 63.1 ± 10.9 years, 91% men). A 64-electrode catheter (Constellation; 38 mm) was positioned within the PV under fluoroscopic guidance. An inverse mapping technique was used to reconstruct unipolar atrial electrograms on the PV surface, and the resulting phase maps were used to identify incoming and outgoing WFs at the PV junction and to classify focal and re-entrant activity within the PV sleeves. ResultsDuring PeAF, the PVs gave rise to outgoing WFs with a frequency of 3.7 s−1 (Q1-Q3: 3.4-5.4 s−1) compared with 3.6 s−1 (Q1-Q3: 2.8-4.2 s−1) for incoming WFs. Circuitous macroscopic re-entry was the dominant mechanism driving outgoing WFs (frequency of re-entry 2.7 s−1 [Q1-Q3: 2.0-3.3 s−1] compared with focal activity 1.4 s−1 [Q1-Q3: 1.1-1.5 s−1]; P < 0.006). This was initiated by incoming WFs in 80% of cases. Consecutive focal activation from the same location was infrequent (10.0% ± 6.6%, n = 10). Rotors ≥360° were never observed. The median ratio (R) of outgoing to incoming WF frequency was 1.14 (Q1-Q3: 0.84-1.75), with R > 1 in 6 of 11 PVs. ConclusionsElectric activity generated by PV sleeves during PeAF is due mainly to circuitous re-entry initiated by incoming waves, frequently with R > 1. That is, the PVs act less as drivers of atrial fibrillation than as “echo chambers” that sustain and amplify fibrillatory activity.

Moire profilometry through simultaneous dual fringe projection for accurate phase demodulation: a comparative study.

In optical metrology, fringe projection and moire techniques have been widely used to measure the topography of objects. We can combine the advantages of the two techniques by applying a configuration of simultaneous dual projection in the fringe projection technique, which generates a superimposed fringe pattern containing a moire pattern that is phase modulated according to the topography. In this work, we present an analytic and comparative study of three methods to demodulate the phase of the moire pattern: the spatial, spatial-temporal, and temporal methods. Those methods consist of two steps: first, the moire pattern is extracted from the superimposed fringe pattern; next, the phase of the moire pattern is demodulated. The analytical results show that the resulting phase map has double phase sensitivity compared to that of the classical fringe projection technique. Experimental and numeric results prove the feasibility of this technique.

Analysis of different phase unwrapping methods to optimize quantitative susceptibility mapping in the abdomen.

Quantitative susceptibility mapping (QSM) is heavily impacted by phase processing of gradient echo imaging data. So far, phase unwrapping algorithms have mostly been developed and tested for neuroimaging applications. In this work, a numerical human abdomen phantom was created and used to assess the feasibility of different phase unwrapping algorithms in abdominal QSM. Furthermore, in vivo data were acquired to evaluate consistency with the simulations. Laplacian-based, quality-guided region growing and graph-cuts unwrapping techniques were evaluated using the numerical phantom as well as an in vivo measurement. As a quality metric, root mean square error (RMSE) was calculated in order to analyze the performance of the examined unwrapping algorithms. Subsequently, susceptibility maps were generated from the resulting phase maps and compared to the ground truth. The evaluation was carried out on the whole phantom as well as individual organs. Graph-cuts led to the most accurate and robust results among the investigated unwrapping methods. The other algorithms showed severe errors in regions with large susceptibility changes (i.e., around the lungs). Deviations from the ground-truth susceptibility were higher than in the previous brain simulations for all tested algorithms. Graph-cuts-based unwrapping algorithms should be preferred in QSM studies in the human abdomen, where large susceptibility changes occur. For further improvement of QSM studies, unwrapping algorithms should be optimized for abdominal applications.

Application of 3D electronic speckle pattern interferometry for the analysis of thermal response in printed circuit boards

The present work reports the development of a method for measurement of sub-micrometer displacements due to the thermal response of printed circuit boards.The developed system employs Electronic Speckle Pattern Interferometry in three dimensions, obtaining three orthogonal displacements of the specimen’s surface from the resulting phase maps. Afterwards, the displacements are corrected, removing the rigid rotation of the physical support and the relative rotation between the two regions of interest is calculated.This method provides a very high-resolution displacement measurement tool, which is very important, for example, in the design phase of outdoor surveillance cameras to optimize image quality.

Ferrimagnetic/ferroelastic domain interactions in magnetite below the Verwey transition: Part II. Micromagnetic and image simulations

Micromagnetic simulations have been used to explore the interaction between ferrimagnetic domain walls (DWs) and ferroelastic twin walls (TWs) below the Verwey transition in magnetite (Fe3O4). Simulations were performed using a thin-foil geometry in order to replicate the domain patterns observed experimentally using transmission electron microscopy. The magnetic microstructure is shown to be highly sensitive to the physical dimensions and crystallographic orientation of the foil, the spatial distribution and crystallographic classification of the TWs and the temperature/field history of the sample. A method to calculate the phase shift of a beam of electrons passing through the micromagnetic simulations is applied. The resulting phase maps provide a robust interpretation of experimental images obtained using Fresnel-mode Lorentz microscopy and off-axis electron holography. The interaction between ferrimagnetic and ferroelastic DWs during field cycling provides an explanation for the low-temperature ‘field-memory effect’ in magnetite.

Eikonal-based initiation of fibrillatory activity in thin-walled cardiac propagation models

Reentrant arrhythmias can be simulated in electrophysiological models of electrical impulse propagation governed by a reaction-diffusion system. To facilitate the initiation of a large number of independent episodes of simulated arrhythmias with controllable level of complexity, a new approach is proposed for thin-walled geometries in which depolarization wave dynamics is essentially two-dimensional. Points representing phase singularities are first randomly distributed over the epicardial surface and are assigned a topological charge (direction of rotation). A qualitatively-correct phase map is then reconstructed on the whole surface by interpolation. The eikonal-diffusion equation is used to iteratively regularize the phase map based on a priori information on wavefront propagation. An initial condition for the reaction-diffusion model is created from the resulting phase map with multiple functional/anatomical reentries. Results in an atrial model demonstrate the ability to generate statistical realizations of the same dynamics and to vary the level of complexity measured by the number of phase singularities. A library of 100 simulations with an average number of phase singularities ranging from 1 to 10 is created. An extension to volumetric patient-specific atrial models including fiber orientation and a fast conducting system is presented to illustrate possible applications.

A simple method for phase wraps elimination or reduction in spatial fringe patterns

In this paper, we propose a simple method for processing a 2D wrapped phase map that contains a spatial carrier signal in order to completely eliminate, or greatly reduce, the number of phase wraps in the image. The 2D Fourier transform of the wrapped phase map is calculated. Then the spectrum is shifted to the origin in frequency space. After that, the inverse 2D Fourier transform is computed. Finally, a four-quadrant arctangent function is used to calculate the angle of the complex array that was produced by the inverse 2D Fourier transform. This produces a phase map with a smaller number of 2π phase jumps than the original phase map. In some cases, all of the phase wraps are eliminated and there is therefore no need to unwrap the resultant phase map. The reduction of the number of 2π phase jumps can reduce the execution time and improve the noise performance of some phase unwrapping algorithms such as the Flynn method. The validation of the proposed algorithm is demonstrated experimentally and also via computer-simulation.

Three-dimensional Fourier transform evaluation of sequences of spatially and temporally modulated speckle interferograms

Phase evaluation methods based on the 2D spatial Fourier transform of a speckle interferogram with spatial carrier usually assume that the Fourier spectrum of the interferogram has a trimodal distribution, i. e. that the side lobes corresponding to the interferential terms do not overlap the other two spectral terms, which are related to the intensity of the object and reference beams, respectively. Otherwise, part of the spectrum of the object beam is inside the inverse-transform window of the selected interference lobe and induces an error in the resultant phase map. We present a technique for the acquisition and processing of speckle interferogram sequences that separates the interference lobes from the other spectral terms when the aforementioned assumption does not apply and regardless of the temporal bandwidth of the phase signal. It requires the recording of a sequence of interferograms with spatial and temporal carriers, and their processing with a 3D Fourier transform. In the resultant 3D spectrum, the spatial and temporal carriers separate the conjugate interferential terms from each other and from the term related to the object beam. Experimental corroboration is provided through the measurement of the amplitude of surface acoustic waves in plates with a double-pulsed TV holography setup. The results obtained with the proposed method are compared to those obtained with the processing of individual interferograms with the regular spatial-carrier 2D Fourier transform method.

Measurement of low-derivative surface lenses by two-laser holography with Bi_12TiO_20 crystals

Refractive and profilometric analyses of lenses with large radii of curvature and/or large focal distance were performed through photorefractive holography using a Bi12TiO20 crystal as the recording medium and two red diode lasers as light sources. Both lasers were properly aligned and tuned in order to provide submillimetric synthetic wavelengths providing real-time interferograms in a two-color holography experiment. The resulting contour interferogram describes the form of the wavefront after the beam traveled back and forth through the lens. The fringe quantitative evaluation was carried out through the four-stepping technique, and the resulting phase map and the branch-cut method were employed for phase unwrapping. Exact ray tracing calculation was performed in order to establish a relation between the output wavefront geometry and the lens parameters such as radii of curvature, thickness, and refractive index. By quantitatively comparing the theoretically calculated wavefront geometry with the experimental results, errors below 1% for both refractive index and focal length were obtained.

Distance measurement with adjustable range by interferometry with Gaussian beams

We describe a technique for distance measurement in applications that require moderate precision. The technique is based on interference fringes resulting from the differing optical path lengths of two Gaussian beams traveling through the arms of a Michelson interferometer. From a propagation analysis of the beams, we find an expression that relates the distance between two surfaces and the resulting phase map from intensity images, making unnecessary the continuous tracking of the order of interference. The range of measurement of the method can be varied by the proper selection of the focal length of an expanding lens, from a fraction of a millimeter to a few centimeters.

Measurement of the complex amplitude of transient surface acoustic waves usingdouble-pulsed TV holography and a two-stage spatial Fourier transform method

We present a technique to measure the mechanical complex amplitude, i.e. themechanical amplitude and phase of vibration, of an ultrasonic plane wavefield ofnanometric amplitude that propagates on a surface. Our aim is to detect perturbationsof the initially smooth wavefronts that indicate the presence of flaws in thematerial. We use bursts of surface acoustic waves (SAWs) and a double-pulsed TVholography system that records two correlograms with time separations down to1.5 µs.The phases of the correlograms are calculated separately using the spatial Fouriertransform method (SFTM) and operated on to obtain the phase change between exposures.In the resultant optical phase map, the field of instantaneous displacements of the surface(that comprises several periods of the SAW) acts as a modulated spatial carrier, nowrelated to the mechanical phase and amplitude, that are extracted by applying the SFTMagain.

Electronic speckle interferometry, phase-mapping, and nondestructive testing techniques applied to real-time, thermal loading

A digital phase-mapping method has been developed for application in real-time electronic speckle interferometry studies. Its principles and application to a continuously deforming object are described. An efficient digital image-processing algorithm has been developed that permits quantitative interpretation of the resulting phase maps.

Radio frequency field intensity mapping using a composite spin-echo sequence

A novel radio frequency (RF) field intensity mapping or imaging method using a composite NMR spin-echo sequence is proposed. A composite spin-echo RF pulse with 90° y -180° x -90° y sequence makes phase change in the final image depending on the RF field intensity on the object. The resultant phase change or phase map can be used to obtain the actual RF flip-angle map for a given condition which includes the status of tuning and RF inhomogeneity, etc. Bloch equation has been solved numerically to obtain the effects of the RF field intensity as well as the main magnetic field inhomogeneity and the results are used for the mapping (imaging) of the RF field intensity. Phantom studies have been performed using a 1.5 Tesla whole body MRI system and the results are presented.