Estimation of myocardial deformation using correlation image velocimetry.

BACKGROUND: Tagged Magnetic Resonance (tMR) imaging is a powerful technique for determining cardiovascular abnormalities. One of the reasons for tMR not being used in routine clinical practice is the lack of easy-to-use tools for image analysis and strain mapping. In this paper, we introduce a novel interdisciplinary method based on correlation image velocimetry (CIV) to estimate cardiac deformation and strain maps from tMR images. METHODS: CIV, a cross-correlation based pattern matching algorithm, analyses a pair of images to obtain the displacement field at sub-pixel accuracy with any desired spatial resolution. This first time application of CIV to tMR image analysis is implemented using an existing open source Matlab-based software called UVMAT. The method, which requires two main input parameters namely correlation box size (C B ) and search box size (S B ), is first validated using a synthetic grid image with grid sizes representative of typical tMR images. Phantom and patient images obtained from a Medical Imaging grand challenge dataset ( http://stacom.cardiacatlas.org/motion-tracking-challenge/ ) were then analysed to obtain cardiac displacement fields and strain maps. The results were then compared with estimates from Harmonic Phase analysis (HARP) technique. RESULTS: For a known displacement field imposed on both the synthetic grid image and the phantom image, CIV is accurate for 3-pixel and larger displacements on a 512 × 512 image with (C B ,S B )=(25,55) pixels. Further validation of our method is achieved by showing that our estimated landmark positions on patient images fall within the inter-observer variability in the ground truth. The effectiveness of our approach to analyse patient images is then established by calculating dense displacement fields throughout a cardiac cycle, and were found to be physiologically consistent. Circumferential strains were estimated at the apical, mid and basal slices of the heart, and were shown to compare favorably with those of HARP over the entire cardiac cycle, except in a few (∼4) of the segments in the 17-segment AHA model. The radial strains, however, are underestimated by our method in most segments when compared with HARP. CONCLUSIONS: In summary, we have demonstrated the capability of CIV to accurately and efficiently quantify cardiac deformation from tMR images. Furthermore, physiologically consistent displacement fields and circumferential strain curves in most regions of the heart indicate that our approach, upon automating some pre-processing steps and testing in clinical trials, can potentially be implemented in a clinical setting.

Lagrangian coherent structures during combustion instability in a premixed-flame backward-step combustor.

This paper quantitatively examines the occurrence of large-scale coherent structures in the flow field during combustion instability in comparison with the flow-combustion-acoustic system when it is stable. For this purpose, the features in the recirculation zone of the confined flow past a backward-facing step are studied in terms of Lagrangian coherent structures. The experiments are conducted at a Reynolds number of 18600 and an equivalence ratio of 0.9 of the premixed fuel-air mixture for two combustor lengths, the long duct corresponding to instability and the short one to the stable case. Simultaneous measurements of the velocity field using time-resolved particle image velocimetry and the CH^{*} chemiluminescence of the flame along with pressure time traces are obtained. The extracted ridges of the finite-time Lyapunov exponent (FTLE) fields delineate dynamically distinct regions of the flow field. The presence of large-scale vortical structures and their modulation over different time instants are well captured by the FTLE ridges for the long combustor where high-amplitude acoustic oscillations are self-excited. In contrast, small-scale vortices signifying Kelvin-Helmholtz instability are observed in the short duct case. Saddle-type flow features are found to separate the distinct flow structures for both combustor lengths. The FTLE ridges are found to align with the flame boundaries in the upstream regions, whereas farther downstream, the alignment is weaker due to dilatation of the flow by the flame's heat release. Specifically, the FTLE ridges encompass the flame curl-up for both the combustor lengths, and thus act as the surrogate flame boundaries. The flame is found to propagate upstream from an earlier vortex roll-up to a newer one along the backward-time FTLE ridge connecting the two structures.

Internal wave interferometry.

Internal waves are a ubiquitous and significant means of momentum and energy transport in the oceans, atmosphere, and astrophysical bodies. Here, we show that internal wave propagation in nonuniform density stratifications, which are prevalent throughout nature, has a direct mathematical analogy with the classical optical problem of a Fabry-Perot multiple-beam light interferometer. We rigorously establish this correspondence, and furthermore provide the first experimental demonstration of an internal wave interferometer, based on the theory of resonant transmission of internal waves.

Stochastic bimodalities in deterministically monostable reversible chemical networks due to network topology reduction.

Recently, stochastic simulations of networks of chemical reactions have shown distributions of steady states that are inconsistent with the steady state solutions of the corresponding deterministic ordinary differential equations. One such class of systems is comprised of networks that have irreversible reactions, and the origin of the anomalous behavior in these cases is understood to be due to the existence of absorbing states. More puzzling is the report of such anomalies in reaction networks without irreversible reactions. One such biologically important example is the futile cycle. Here we show that, in these systems, nonclassical behavior can originate from a stochastic elimination of all the molecules of a key species. This leads to a reduction in the topology of the network and the sampling of steady states corresponding to a truncated network. Surprisingly, we find that, in spite of the purely discrete character of the topology reduction mechanism revealed by "exact" numerical solutions of the master equations, this phenomenon is reproduced by the corresponding Fokker-Planck equations.

Uncovering the Lagrangian skeleton of turbulence.

We present a technique that uncovers the Lagrangian building blocks of turbulence, and apply this technique to a quasi-two-dimensional turbulent flow experiment. Our analysis identifies an intricate network of attracting and repelling material lines. This chaotic tangle, the Lagrangian skeleton of turbulence, shows a level of complexity found previously only in theoretical and numerical examples of strange attractors. We quantify the strength (hyperbolicity) of each material line in the skeleton and demonstrate dramatically different mixing properties in different parts of the tangle.

Gravity-free hydraulic jumps and metal femtoliter cups.

Hydraulic jumps created by gravity are seen everyday in the kitchen sink. We show that at small scales a circular hydraulic jump can be created in the absence of gravity by surface tension. The theory is motivated by our experimental finding of a height discontinuity in spreading submicron molten metal droplets created by pulsed-laser ablation. By careful control of initial conditions, this leads to solid femtoliter cups of gold, silver, copper, niobium, and tin.

A facile method of producing femtoliter metal cups by pulsed laser ablation.

Cuplike structures of Au, Ag, Cu, Zn, Nb, Cd, Al, In, and Sn in the size range of 300 nm to a few micrometers with an internal volume of a few femtoliters have been produced by the laser ablation of metal targets in a vacuum, by optimizing, in each case, the laser fluence and the substrate temperature. The metal droplets impinging on the substrate seem to undergo a hydraulic jump driven by the surface tension forces before solidifying into cups. The cups are robust and can be functionalized with biomarkers, filled with nanoparticle sols, oxidized to crucibles, or detached from the substrate without causing any deformation. We envisage their potential applications as femtoliter metal containers.