Vector Flow Field Research Articles

Near-field electromagnetic holography for high-resolution analysis of network interactions in neuronal tissue

BackgroundBrain function is dependent upon the concerted, dynamical interactions between a great many neurons distributed over many cortical subregions. Current methods of quantifying such interactions are limited by consideration only of single direct or indirect measures of a subsample of all neuronal population activity. New methodHere we present a new derivation of the electromagnetic analogy to near-field acoustic holography allowing high-resolution, vectored estimates of interactions between sources of electromagnetic activity that significantly improves this situation. In vitro voltage potential recordings were used to estimate pseudo-electromagnetic energy flow vector fields, current and energy source densities and energy dissipation in reconstruction planes at depth into the neural tissue parallel to the recording plane of the microelectrode array. ResultsThe properties of the reconstructed near-field estimate allowed both the utilization of super-resolution techniques to increase the imaging resolution beyond that of the microelectrode array, and facilitated a novel approach to estimating causal relationships between activity in neocortical subregions. Comparison with existing methodsThe holographic nature of the reconstruction method allowed significantly better estimation of the fine spatiotemporal detail of neuronal population activity, compared with interpolation alone, beyond the spatial resolution of the electrode arrays used. Pseudo-energy flow vector mapping was possible with high temporal precision, allowing a near-realtime estimate of causal interaction dynamics. ConclusionsBasic near-field electromagnetic holography provides a powerful means to increase spatial resolution from electrode array data with careful choice of spatial filters and distance to reconstruction plane. More detailed approaches may provide the ability to volumetrically reconstruct activity patterns on neuronal tissue, but the ability to extract vectored data with the method presented already permits the study of dynamic causal interactions without bias from any prior assumptions on anatomical connectivity.

Existence and Uniqueness of Maximal Regular Flows for Non-smooth Vector Fields

In this paper we provide a complete analogy between the Cauchy–Lipschitz and the DiPerna–Lions theories for ODE’s, by developing a local version of the DiPerna–Lions theory. More precisely, we prove the existence and uniqueness of a maximal regular flow for the DiPerna–Lions theory using only local regularity and summability assumptions on the vector field, in analogy with the classical theory, which uses only local regularity assumptions. We also study the behaviour of the ODE trajectories before the maximal existence time. Unlike the Cauchy–Lipschitz theory, this behaviour crucially depends on the nature of the bounds imposed on the spatial divergence of the vector field. In particular, a global assumption on the divergence is needed to obtain a proper blow-up of the trajectories.

STRAIN ANALYSIS OF CARDIAC TISSUES FROM 3D ULTRASOUND IMAGES USING SNAKES AND SPECKLE TRACKING

In this paper, we are presenting a method for achieving strain analysis of cardiac tissues from 3D ultrasound images. First of all, the left ventricle was segmented by an iterative snake algorithm which exploits the gradient vector flow field estimated from the 3D images. Once the ventricle was segmented, a set of points located on the external surface of the ventricle was selected. The movement of all these points along the entire cardiac cycle was calculated by using speckle tracking techniques. The strain of all the segments connecting two of the considered points was computed, together with the rotation of the points along the long axis of the ventricle. The method was tested on images acquired from 10 subjects: three with heart pathologies, five healthy subjects, and two patients with mild hypertrophy. Preliminary results showed the feasibility of characterizing healthy subjects and patients with well-defined heart pathologies by using the outcomes achieved with the strain analysis.

Piv Method and Numerical Computation for Prediction of Liquid Steel Flow Structure in Tundish

AbstractThis paper presents the results of computer simulations and laboratory experiments carried out to describe the motion of steel flow in the tundish. The facility under investigation is a single-nozzle tundish designed for casting concast slabs. For the validation of the numerical model and verification of the hydrodynamic conditions occurring in the examined tundish furniture variants, obtained from the computer simulations, a physical model of the tundish was employed. State-of-the-art vector flow field analysis measuring systems developed by Lavision were used in the laboratory tests. Computer simulations of liquid steel flow were performed using the commercial program Ansys-Fluent¯. In order to obtain a complete hydrodynamic picture in the tundish furniture variants tested, the computer simulations were performed for both isothermal and non-isothermal conditions.

Optimal-mass-transfer-based estimation of glymphatic transport in living brain.

It was recently shown that the brain-wide cerebrospinal fluid (CSF) and interstitial fluid exchange system designated the 'glymphatic pathway' plays a key role in removing waste products from the brain, similarly to the lymphatic system in other body organs1,2. It is therefore important to study the flow patterns of glymphatic transport through the live brain in order to better understand its functionality in normal and pathological states. Unlike blood, the CSF does not flow rapidly through a network of dedicated vessels, but rather through para-vascular channels and brain parenchyma in a slower time-domain, and thus conventional fMRI or other blood-flow sensitive MRI sequences do not provide much useful information about the desired flow patterns. We have accordingly analyzed a series of MRI images, taken at different times, of the brain of a live rat, which was injected with a paramagnetic tracer into the CSF via the lumbar intrathecal space of the spine. Our goal is twofold: (a) find glymphatic (tracer) flow directions in the live rodent brain; and (b) provide a model of a (healthy) brain that will allow the prediction of tracer concentrations given initial conditions. We model the liquid flow through the brain by the diffusion equation. We then use the Optimal Mass Transfer (OMT) approach3 to derive the glymphatic flow vector field, and estimate the diffusion tensors by analyzing the (changes in the) flow. Simulations show that the resulting model successfully reproduces the dominant features of the experimental data.

Evaporation and convective flow pattern of a heated pendant silicone oil droplet

The evaporation and convective flow pattern of a heated pendant silicone oil droplet have been investigated under the steady-state conditions. Due to the light deflection across a curved interface, a direct velocity recovery method has been developed to recover the distorted vector field of convective flow in the Particle Image Velocimetry analysis. The relation between convection and evaporation is demonstrated in the study. A higher temperature difference at the droplet surface generates a larger convection velocity, indicated in the recovered return flow at the center area of the droplet. Such recovery method can supply a fast solution towards the further quantitative study of the energy transportation of Marangoni flow on droplet evaporation.

Congenital heart disease assessment with 4D flow MRI.

With improvements in surgical and medical management, patients with congenital heart disease (CHD) are often living well into adulthood. MRI provides critical data for diagnosis and monitoring of these patients, yielding information on cardiac anatomy, blood flow, and cardiac function. Though historically these exams have been complex and lengthy, four-dimensional (4D) flow is emerging as a single fast technique for comprehensive assessment of CHD. The 4D flow consists of a volumetric time-resolved acquisition that is gated to the cardiac cycle, providing a time-varying vector field of blood flow as well as registered anatomic images. In this article, we provide an overview of MRI evaluation of congenital heart disease by means of example of three relatively common representative conditions: tetralogy of Fallot, aortic coarctation, and anomalous pulmonary venous drainage. Then 4D flow data acquisition, data correction, and postprocessing techniques are reviewed. We conclude with several examples that highlight the comprehensive nature of the evaluation of congenital heart disease with 4D flow.

2086303 High Frame Rate Ultrasound Can Dynamically Visualize Fast-Changing Vector Flow Fields in The Carotid Bifurcation

Our aim is to track spatiotemporal variations in cardiovascular flow fields by using high frame rate ultrasound to derive flow vectors at millisecond time resolution. Achieving such diagnostic capability is practically important because it may foster clinical detection of abnormal vascular conditions. So far, complex flow patterns have not been visualized lucidly using color Doppler imaging due to flaws like Doppler angle ambiguity and limited time resolution. New solutions are needed. We have devised a new technique called vector projectile imaging (VPI) to facilitate flow vector estimation over the entire field of view at fine temporal resolution. First, using a reconfigurable ultrasound scanner (SonixTouch) and a linear array, slow-time sampling was performed using a plane wave firing approach, and it was carried out from three different angles (-10, 0, +10 deg) at kHz-range PRF. This allowed parallel acquisition of Doppler information over all pixel positions. No contrast agent was used in the process. For each pulsing event, three angle steered frames (-10, 0, +10 deg) were beamformed, and these were used to calculate the flow vector at every pixel position in the field of view using multi-angle Doppler analysis principles. Performance analysis was conducted using carotid bifurcation models with well-characterized pulsatile flow conditions. Both healthy and stenotic vasculatures were included in the analysis. Using VPI, we have successfully tracked time-varying vector flow fields inside the carotid arteries. Using a 416 fps frame rate (2.4 ms time resolution), the main transit path of blood flow in a healthy bifurcation was mapped accurately. In a diseased case with 50% eccentric stenosis at the entrance to the internal carotid artery, VPI effectively highlighted the high velocity jet emerging at the stenosis site, curvy transit path downstream from the stenosis, and significant recirculatory flow in the carotid bulb. Corresponding cineloops will be shown at the meeting. Complex flow fields in the cardiovascular system can be mapped through ultrasound imaging innovations. This can help expand ultrasound’s present role in cardiovascular diagnostics.

Dissipative energy loss within the left ventricle detected by vector flow mapping in children: Normal values and effects of age and heart rate

BackgroundVector flow mapping (VFM) is a novel echocardiographic technology which enables visualization of the intraventricular flow velocity vector. Dissipative energy loss (EL) derived from the velocity vector field of intraventricular blood flow is considered to reflect the efficiency of blood flow, and could be an indicator of left ventricular function. We aimed to determine the reference values of the EL derived from VFM within the left ventricle. MethodsVFM analysis was performed using echocardiography in 64 healthy children. The velocity vector fields of the intra-left ventricular blood flow were obtained from the apical 5-chamber view, and the EL values during systole and diastole were calculated. The measurements were averaged over three cardiac cycles, and indexed to body surface area (BSA). ResultsThe mean subject age was 6.8±4.3 years. The mean EL was 4.10±2.35mW/m/m2 BSA during systole and 16.24±11.63mW/m/m2 BSA during diastole. On multivariate analysis, age and heart rate (HR) were independent predictors of systolic EL, whereas age, HR, and E wave peak velocity were independent predictors of diastolic EL. The regression equations used to predict the BSA-indexed systolic and diastolic EL were as follows: log10 (systolic EL)=−0.0332−0.00213×age (months)+0.00789×HR (beats/min) (adjusted R2, 0.833; p<0.0001); and log10 (diastolic EL)=0.277−0.00346×age (months)+0.00570×HR (beats/min)+0.00564×E wave peak velocity (cm/s) (adjusted R2, 0.867; p<0.0001). ConclusionsThe systolic and diastolic EL were positively correlated with HR and negatively correlated with age. Moreover, the diastolic EL was positively correlated with the E wave peak velocity. The present study provides reference values for the systolic and diastolic EL that can be used in future studies examining patients with heart disease.

Magnetic microbubble-mediated ultrasound-MRI registration based on robust optical flow model.

BackgroundAs a dual-modality contrast agent, magnetic microbubbles (MMBs) can not only improve contrast of ultrasound (US) image, but can also serve as a contrast agent of magnetic resonance image (MRI). With the help of MMBs, a new registration method between US image and MRI is presented.MethodsIn this method, MMBs were used in both ultrasound and magnetic resonance imaging process to enhance the most important information of interest. In order to reduce the influence of the speckle noise to registration, semi-automatic segmentations of US image and MRI were carried out by using active contour model. After that, a robust optical flow model between US image segmentation (floating image) and MRI segmentation (reference image) was built, and the vector flow field was estimated by using the Coarse-to-fine Gaussian pyramid and graduated non-convexity (GNC) schemes.ResultsQualitative and quantitative analyses of multiple group comparison experiments showed that registration results using all methods tested in this paper without MMBs were unsatisfactory. On the contrary, the proposed method combined with MMBs led to the best registration results.ConclusionThe proposed algorithm combined with MMBs contends with larger deformation and performs well not only for local deformation but also for global deformation. The comparison experiments also demonstrated that ultrasound-MRI registration using the above-mentioned method might be a promising method for obtaining more accurate image information.

A Novel Contour Closure Method using Ending Point Restrained Gradient Vector Flow Field

This paper presents a novel variational and Partial Differential Equation (PDE)-based method to link edge points into closed contours. First, an ending point restrained energy function, which improves the one used in the Gradient Vector Flow (GVF) Snake model, is proposed to derive an ending point restrained Gradient Vector Flow (ERGVF) field. When there are broken edges in the edge map, the GVF field cannot recover the object's original shape, especially the broken corners of the object's boundary. The new ERGVF field can solve this problem by diffusing the gradient vectors in the continuous edge regions of the edge map into the broken edge regions. To detect the linked edge map based on the ERGVF field, this paper proposes a vector-based Mean Vector Difference (VMVD) method, which optimizes the original Mean Vector Difference (MVD) method by employing a new vector-based formula. The VMVD method has better performance than the MVD method when coping with images with broken edges. The proposed contour closure method can link broken edges belonging to multiple objects simultaneously and recover the objects' original shapes, especially the corners. Synthetic images with different edge structures and real cell images have been tested to show its validity and effectiveness in closed contour extraction and shape recovery.

Differential geometry via infinitesimal displacements

We present a new formulation of some basic differential geometric notions on a smooth manifold M, in the setting of nonstandard analysis. In place of classical vector fields, for which one needs to construct the tangent bundle of M, we define a prevector field, which is an internal map from ∗ M to itself, implementing the intuitive notion of vectors as infinitesimal displacements. We introduce regularity conditions for prevector fields, defined by finite differences, thus purely combinatorial conditions involving no analysis. These conditions replace the more elaborate analytic regularity conditions appearing in previous similar approaches, e.g. by Stroyan and Luxemburg or Lutz and Goze. We define the flow of a prevector field by hyperfinite iteration of the given prevector field, in the spirit of Euler’s method. We define the Lie bracket of two prevector fields by appropriate iteration of their commutator. We study the properties of flows and Lie brackets, particularly in relation with our proposed regularity conditions. We note several simple applications to the classical setting, such as bounds related to the flow of vector fields, analysis of small oscillations of a pendulum, and an instance of Frobenius’ Theorem regarding the complete integrability of independent vector fields.

Extension of Chronological Calculus for dynamical systems on manifolds

We propose an extension of the Chronological Calculus, developed by Agrachev and Gamkrelidze for the case of C∞-smooth dynamical systems on finite-dimensional C∞-smooth manifolds, to the case of Cm-smooth dynamical systems and infinite-dimensional Cm-manifolds. Due to a relaxation in the underlying structure of the calculus, this extension provides a powerful computational tool without recourse to the theory of calculus in Fréchet spaces required by the classical Chronological Calculus. In addition, this extension accounts for flows of vector fields which are merely measurable in time. To demonstrate the utility of this extension, we prove a variant of Chow–Rashevskii theorem for infinite-dimensional manifolds.

Experimental investigation on the natural convection flow in pool boiling

In the present study, the key thermal hydraulic phenomena within a passive condensate cooling tank (PCCT) of a small-scale pool test rig with a single heater rod are experimentally investigated. The volumetric scaling ratio of the test rig is 1/910 the size of the passive auxiliary feedwater system (PAFS) condensing heat removal assessment loop (PASCAL), which is a PAFS performance evaluation test facility. The two-dimensional velocity vector fields that occur as the water level decreases are experimentally investigated in a pool that contains a horizontal heater rod. The 2D particle image velocimetry (PIV) measurement technique is adopted to determine the velocity vector field of the natural convection flow. The experimental results indicate that a large natural convection flow occurs above the heater rod and that thermal stratification occurs below the heater rod. The thermal stratification and the stagnant region begin to disappear when the pool temperature reaches approximately 90°C. The experimental results can provide benchmark data to validate computational fluid dynamics (CFD) calculations of thermal hydraulic phenomena that occur in a pool with a heat source.

4DGVF : segmentation variationnelle pour images 3D multicomposantes

In this paper, we generalize the gradient vector flow field to vector-valued images. We base our method on the definition of a structure tensor that is calculated according to a blind estimation of contrast in the different channels and that exploits the whole spatio- spectral information, hence reducing sensitivity to noise and better defining orientations of the force field. The resulting field takes profit of both magnitude and direction of the vector- valued gradient. Applied to biological volume delineation in 3D dynamic Positron Emission Tomography (PET) imaging, we validate our method on realistic Monte Carlo simulations of numerical phantoms and present results on real dynamic PET data. Performances observed on such images confirm the potential of the proposed active surface approach for vector-valued data.

Active spline model: A shape based model—interactive segmentation

We propose to formulate point distribution model in terms of centripetal-parameterized Catmull–Rom spline, so that the model-based segmentation is augmented to permit quick edit, and the consequent shape is independent of scale. We train the model in a fashion similar to active shape model, but with fewer salient/landmark points. We use gradient vector flow field as the external force field to drive the segmentation, but we did not adopt the procedures panned out by Cootes et al. to update a shape. Instead, we transform the shape back and forth between model scale and image scale to get the shape converged to the object of interest. To test the method, we turned the solution into an automated algorithm to segment lung on chest radiographs, and achieved an average overlap of 0.879. With edit, the average overlap increased to 0.945, with a minimum of 0.925. The method can be applied on a variety of images, as illustrated in Appendix C. The source code of the algorithm and the demo video can be located at http://jenh.co/2014/01/09/active-spline-models/.

The projective translation equation and unramified 2-dimensional flows with rational vector fields

Let x = (x, y). Previously we have found all rational solutions of the 2-dimensional projective translation equation, or PrTE, (1−z)ϕ(x) = ϕ(ϕ(xz)(1−z)/z); here ϕ(x) = (u(x,y),v(x,y)) is a pair of two (real or complex) functions. Solutions of this functional equation are called projective flows. A vector field of a rational flow is a pair of 2-homogenic rational functions. On the other hand, only special pairs of 2-homogenic rational functions give rise to rational flows. In this paper we are interested in all non-singular (satisfying the boundary condition) and unramified (without branching points, i.e. single-valued functions in \({\mathbb{C}^{2}\setminus\{\text{union of curves}\}}\)) projective flows whose vector field is still rational. If an orbit of the flow is given by a homogeneous rational function of degree N, then N is called the level of the flow. We prove that, up to conjugation with 1-homogenic birational plane transformation, unramified non-singular flows are of 6 types: (1) the identity flow; (2) one flow for each non-negative integer N—these flows are rational of level N; (3) the level 1 exponential flow, which is also conjugate to the level 1 tangent flow; (4) the level 3 flow expressable in terms of Dixonian (equianharmonic) elliptic functions; (5) the level 4 flow expressable in terms of lemniscatic elliptic functions; (6) the level 6 flow expressable in terms of Dixonian elliptic functions again. This reveals another aspect of the PrTE: in the latter four cases this equation is equivalent and provides a uniform framework to addition formulas for exponential, tangent, or special elliptic functions (also addition formulas for polynomials and the logarithm, though the latter appears only in branched flows). Moreover, the PrTE turns out to have a connection with Pólya–Eggenberger urn models. Another purpose of this study is expository, and we provide the list of open problems and directions in the theory of PrTE; for example, we define the notion of quasi-rational projective flows which includes curves of arbitrary genus. This study, though seemingly analytic, is in fact algebraic and our method reduces to algebraic transformations in various quotient rings of rational function fields.

Variational segmentation of vector-valued images with gradient vector flow.

In this paper, we extend the gradient vector flow field for robust variational segmentation of vector-valued images. Rather than using scalar edge information, we define a vectorial edge map derived from a weighted local structure tensor of the image that enables the diffusion of the gradient vectors in accurate directions through the 4D gradient vector flow equation. To reduce the contribution of noise in the structure tensor, image channels are weighted according to a blind estimator of contrast. The method is applied to biological volume delineation in dynamic PET imaging, and validated on realistic Monte Carlo simulations of numerical phantoms as well as on real images.

Complements of graphs of meromorphic functions and complete vector fields

Given a meromorphic function $s: \mathbb{C}\to \mathbb{P}^{1}$, we obtain a family of fiber-preserving dominating holomorphic maps from $\mathbb{C}^{2}$ onto $\mathbb{C}^{2}\setminus graph(s)$ defined in terms of the flows of complete vector fields of type $\mathbb{C}^{\ast}$ and of an entire function $h:\mathbb{C}\to\mathbb{C}$ whose graph does not meet $graph(s)$, which was determined by Buzzard and Lu. In particular, we prove that the dominating map constructed by these authors to prove the dominability of $\mathbb{C}^{2}\setminus graph(s)$ is in the above family. We also study the complement of a double section in $\mathbb{C}\times\mathbb{P}^{1}$ in terms of a complex flow. Moreover, when $s$ has at most one pole, we prove that there are infinitely many complete vector fields tangent to $graph(s)$, describing explicit families of them with all their trajectories proper and of the same type ($\mathbb{C}$ or $\mathbb{C}^{\ast}$), if $graph(s)$ does not contain zeros; and families with almost all trajectories non-proper and of type $\mathbb{C}$, or of type $\mathbb{C}^{\ast}$, if $graph(s)$ contains zeros. We also study the dominability of $\mathbb{C}^{2}\setminus A$ when $A\subset \mathbb{C}^{2}$ is invariant by the flow of a complete holomorphic vector field.

Almost Ricci solitons and $$K$$ K -contact geometry

We give a short Lie-derivative theoretic proof of the following recent result of Barros et al. “A compact non-trivial almost Ricci soliton with constant scalar curvature is gradient, and isometric to a Euclidean sphere”. Next, we obtain the result: a complete almost Ricci soliton whose metric \(g\) is \(K\)-contact and flow vector field \(X\) is contact, becomes a Ricci soliton with constant scalar curvature. In particular, for \(X\) strict, \(g\) becomes compact Sasakian Einstein.