Gradient Moment Research Articles

Scaling laws of velocity gradient moments of attached eddies

Scaling laws of velocity gradient moments of attached eddies

BSSFP Phase Contrast (PC-SSFP) at 0.55 T Applied to Aortic Flow

BackgroundThere is a growing interest in the development and application of mid-field (0.55T) for cardiac MR, including flow imaging. However, aortic flow imaging at 0.55T has limited SNR, especially in diastolic phases where there is reduced inflow-driven contrast for spoiled gradient echo (GRE) sequences. The low SNR can limit the accuracy of flow and regurgitant fraction measurements. MethodsIn this work, we developed a 2D phase contrast (PC) acquisition with balanced steady state free precession (bSSFP), termed PC-SSFP, for flow imaging and quantification at 0.55T. This PC-SSFP approach precisely nulls the 0th and 1st gradient moments at both the TE and TR, except for the flow-encoded acquisition, for which the 1st gradient moment at the TE is determined by the VENC. Our proposed sequence was tested in both phantoms and in healthy volunteers (n=11), to measure aortic flow. In volunteers, both a breath-hold and a free-breathing protocol, with averaging to increase SNR, were obtained. Total flow, peak flow, cardiac output and SNR were compared for PC-SSFP and PC-GRE. Stroke volumes were also measured and compared to planimetry method. ResultsIn a phantom, SNR was significantly higher using PC-SSFP compared to PC-GRE (25.5±9.6 vs 8.2±2.9), and the velocity measurements agreed well (R = 1.00). In healthy subjects, for both breath-hold (bh) and free-breathing (fb) protocols, PC-SSFP measured accurate peak flow (fb: R = 0.99, bh: R = 0.96) and cardiac output (fb: R = 0.98, bh: R = 0.88), compared to PC-GRE, accurate stroke volume (fb: R = 0.94, bh: R = 0.97), compared to planimetry measurement, and offered constant high SNR (fb: 28±9 vs 18±6, bh: 24±7 vs 11±3) over the cardiac cycle in 11 subjects. ConclusionPC-SSFP is a more reliable evaluation tool for aortic flow quantification, when compared to the conventional PC-GRE method at 0.55T, providing higher SNR, and thus potentially more accurate flows.

Towards Understanding Convergence and Generalization of AdamW.

AdamW modifies Adam by adding a decoupled weight decay to decay network weights per training iteration. For adaptive algorithms, this decoupled weight decay does not affect specific optimization steps, and differs from the widely used l2-regularizer which changes optimization steps via changing the first- and second-order gradient moments. Despite its great practical success, for AdamW, its convergence behavior and generalization improvement over Adam and l2-regularized Adam ( l2-Adam) remain absent yet. To solve this issue, we prove the convergence of AdamW and justify its generalization advantages over Adam and l2-Adam. Specifically, AdamW provably converges but minimizes a dynamically regularized loss that combines vanilla loss and a dynamical regularization induced by decoupled weight decay, thus yielding different behaviors with Adam and l2-Adam. Moreover, on both general nonconvex problems and PŁ-conditioned problems, we establish stochastic gradient complexity of AdamW to find a stationary point. Such complexity is also applicable to Adam and l2-Adam, and improves their previously known complexity, especially for over-parametrized networks. Besides, we prove that AdamW enjoys smaller generalization errors than Adam and l2-Adam from the Bayesian posterior aspect. This result, for the first time, explicitly reveals the benefits of decoupled weight decay in AdamW. Experimental results validate our theory.

Small-scale turbulent characteristics in transcritical wall-bounded flows

Considerable efforts have been devoted to the understanding of the small-scale characteristics in turbulent flows. While the universality of small-scale quantities has been established for incompressible flows, their extension to high-pressure transcritical flows remains an open area of research. To address this question, we investigate the real-fluid thermodynamic effects on small-scale velocity statistics of high-pressure transcritical wall-bounded turbulence. We show that in the locally isotropic region for transcritical flows, low-order moments of small-scale statistics collapse for all cases and Kolmogorov's (1941) theory holds. However, real-fluid thermodynamic effects introduce deviations in the tails of the probability density function for the velocity derivative and, consequently, high-order moments of velocity gradients and dissipation rate in transcritical flows cannot collapse in the locally isotropic region. Analysis of the intermittency shows that the low-order structure functions in transcritical flows follow extended self-similarity, while the dependence of the intermittency factor on real-fluid effects is observed for high-order structure functions. The real-fluid effects on intermittency are explained by turbulent structures related to rare events. Additionally, the dissipation rate moments for transcritical flows follow a universal scaling with Reynolds number, and the scaling exponents are different from those of incompressible flows. These results extend the small-scale universality in incompressible flows (Schumacher et al., Proc. Natl Acad. Sci. USA, vol. 111, 2014, pp. 10961–10965) to realistic flows with significant changes in thermodynamic properties, and provide a physical underpinning of the scaling laws of small-scale statistics at transcritical conditions.

Development and validation of cardiac diffusion weighted magnetic resonance imaging for the diagnosis of myocardial injury in small animal models

Cardiac diffusion weighted-magnetic resonance imaging (DWI) has slowly developed due to its technical difficulties. However, this limitation could be overcome by advanced techniques, including a stimulated echo technique and a gradient moment nulling technique. This study aimed to develop and validate a high-order DWI sequence, using echo-planar imaging (EPI) and second-order motion-compensated (M012) diffusion gradient applied to cardiac imaging in small-sized animals with fast heart and respiratory rates, and to investigate the feasibility of cardiac DWI, diagnosing acute myocardial injury in isoproterenol-induced myocardial injury rat models. The M012 diffusion gradient sequence was designed for diffusion tensor imaging of the rat myocardium and validated in the polyvinylpyrrolidone phantom. Following sequence optimization, 23 rats with isoproterenol-induced acute myocardial injury and five healthy control rats underwent cardiac MRI, including cine imaging, T1 mapping, and DWI. Diffusion gradient was applied using a 9.4-T MRI scanner (Bruker, BioSpec 94/20, gradient amplitude = 440 mT/m, maximum slew rate = 3440 T/m/s) with double gating (electrocardiogram and respiratory gating). Troponin I was used as a serum biomarker for myocardial injury. Histopathologic examination of the heart was subsequently performed. The developed DWI sequence using EPI and M012 provided the interpretable images of rat hearts. The apparent diffusion coefficient (ADC) values were significantly higher in rats with acute myocardial injury than in the control group (1.847 ± 0.326 * 10–3 mm2/s vs. 1.578 ± 0.144 * 10–3 mm2/s, P < 0.001). Troponin I levels were increased in the blood samples of rats with acute myocardial injury (P < 0.001). Histopathologic examinations detected myocardial damage and subendocardial fibrosis in rats with acute myocardial injury. The newly developed DWI technique has the ability to detect myocardial injury in small animal models, representing high ADC values on the myocardium with isoproterenol-induced injury.

Riemann’s wave and an exact solution of the main turbulence problem

ABSTRACT The paper presents a review of the results that allowed us to find an exact analytical solution to the main problem of the turbulence theory consisting in a closed description of any moments and spectra of all random fields that are described by the Euler hydrodynamic equations for a compressible medium. This solution is based on an exact and explicit analytical solution to n-dimensional Euler equations in the limit of large Mach numbers (S. G. Chefranov, 1991). Based on the Dirac delta function theory, this solution gives an n-dimensional generalization of the well-known implicit Riemann (1860) solution to the one-dimensional Euler equations. In the one-dimensional case, the resulting solution exactly coincides with the explicit form of the Riemann solution for an arbitrary Mach numbers. We have obtained for the first time the exact value of the universal scaling exponent -2/3 for a spectrum of the turbulence energy dissipation rate corresponds to the exact analytical solution to fourth-order two-point moments of the velocity field gradient. We have noted a good agreement between this value and the observational data of turbulence intermittency in the surface atmosphere layer (M. Z. Kholmyansky, 1972) and with the findings of the well-known turbulence intermittency model by Novikov-Stewart (1964).

Multiclass Apple Varieties Classification Using Machine Learning with Histogram of Oriented Gradient and Color Moments

It is critically necessary to maximize the efficiency of agricultural methods while concurrently reducing the cost of production. Varieties, types, and fruit classification grades are crucial to fruit production. High expenditure, inconsistent subjectivity, and tedious labor characterize traditional and manual varieties classification. This study developed machine learning (ML) models to classify ten apple varieties, extracting the histogram of oriented gradient (HOG) and color moments from RGB apple images. Support vector machine (SVM), random forest classifier (RFC), multilayer perceptron (MLP), and K-nearest neighbor (KNN) classification models were trained with 10-fold stratified cross-validation (Skfold) by using the textural and color features, and a GridSearch was implemented to fine-tune the hyperparameters. The trained models, SVM, RFC, MLP, and KNN were tested with separate test data and performed well, having an accuracy of 98.17%, 96.67%, 98.62%, and 91.28%, respectively. Having the top results, the MLP and SVM models demonstrated the potential of applying HOG and color moments to train ML models for classifying apple varieties. This study suggests conducting further research to thoroughly examine additional image features and determine the impact of combining features and utilizing different classifiers.

Emergence of universal scaling in isotropic turbulence.

Universal properties of turbulence have been associated traditionally with very high Reynolds numbers, but recent work has shown that the onset of the power laws in derivative statistics occurs at modest microscale Reynolds numbers of the order of 10, with the corresponding exponents being consistent with those for the inertial range structure functions at very high Reynolds numbers. In this paper we use well-resolved direct numerical simulations of homogeneous and isotropic turbulence to establish this result for a range of initial conditions with different forcing mechanisms. We also show that the moments of transverse velocity gradients possess larger scaling exponents than those of the longitudinal moments, confirming past results that the former are more intermittent than the latter.

Homogeneity constraints on the mixed moments of velocity gradient and pressure Hessian in incompressible turbulence

We derive a relation for the correlation between pressure Hessian and velocity gradient in homogeneous flows. This relation provides restrictions to the parameters in the closure models of pressure hessian in velocity gradient dynamics, and together with the Poisson equation, we could obtain an integral expression for the fourth-order moment of velocity gradient in isotropic flows. Furthermore, this relation could be generalized to shear flows, and it is approximately satisfied even in the presence of a shear and of a wall, as occurs in turbulent channel flows.

A new efficient algorithm based on feedforward neural network for solving differential equations of fractional order

Artificial neural network (ANN) have shown great success in various scientific fields over several decades. Recently, one of its variants known as deep feedforward neural network (FNN) led to dramatic improvement in many tasks, including getting more accurate approximation solution for integer-order differential equations. However, its capability on solving FDEs is still remain questionable. Thus, this paper aims to design new scheme based on deep feedforward neural network (FNN) with vectorized algorithm (FNNVA) using selected first-order optimization techniques which are gradient descent (GD), momentum method (MM) and adaptive moment estimation method (Adam) to solve Caputo FDEs. At the first stage, a detailed method formulations on solving Caputo FDEs using FNN are presented. Then, a vectorized algorithm is developed for the scheme to be computationally efficient. The effectiveness and applicability of the scheme were validate on linear and nonlinear FDEs through comparison based on different number of hidden layers with varying learning rates and number of neurons. The results show that FNNVA with Adam technique with one and two hidden layers outperformed among others by appropriate selection value of learning rates and number of neurons respectively. This scheme also provide high accuracy and low computational cost compared to several existing numerical methods.

Low-order moments of the velocity gradient in homogeneous compressible turbulence

We derive from first principles analytic relations for the second- and third-order moments of $\boldsymbol{\mathsf{m}}$ , the spatial gradient of fluid velocity $\boldsymbol{u}$ , $\boldsymbol{\mathsf{m}} = \nabla \boldsymbol{u}$ , in compressible turbulence, which generalize known relations in incompressible flows. These relations, although derived for homogeneous flows, hold approximately for a mixing layer. We also discuss how to apply these relations to determine all the second- and third-order moments of the velocity gradient experimentally for isotropic compressible turbulence.

Automated slice-specific z-shimming for functional magnetic resonance imaging of the human spinal cord.

Functional magnetic resonance imaging (fMRI) of the human spinal cord faces many challenges, such as signal loss due to local magnetic field inhomogeneities. This issue can be addressed with slice-specific z-shimming, which compensates for the dephasing effect of the inhomogeneities using a slice-specific gradient pulse. Here, we aim to address outstanding issues regarding this technique by evaluating its effects on several aspects that are directly relevant for spinal fMRI and by developing two automated procedures in order to improve upon the time-consuming and subjective nature of manual selection of z-shims: one procedure finds the z-shim that maximizes signal intensity in each slice of an EPI reference-scan and the other finds the through-slice field inhomogeneity for each EPI-slice in field map data and calculates the required compensation gradient moment. We demonstrate that the beneficial effects of z-shimming are apparent across different echo times, hold true for both the dorsal and ventral horn, and are also apparent in the temporal signal-to-noise ratio (tSNR) of EPI time-series data. Both of our automated approaches were faster than the manual approach, lead to significant improvements in gray matter tSNR compared to no z-shimming and resulted in beneficial effects that were stable across time. While the field-map-based approach performed slightly worse than the manual approach, the EPI-based approach performed as well as the manual one and was furthermore validated on an external corticospinal data-set (N > 100). Together, automated z-shimming may improve the data quality of future spinal fMRI studies and lead to increased reproducibility in longitudinal studies.

Computerized Texture Analysis of Optical Coherence Tomography Angiography of Choriocapillaris in Normal Eyes of Young and Healthy Subjects.

Computerized texture analysis uses higher-order mathematics to identify patterns beyond what the naked eye can recognize. We tested its feasibility in optical coherence tomography angiography imaging of choriocapillaris. Our objective was to determine sets of parameters that provide coherent and consistent output when applied to a homogeneous, healthy group of patients. This observational cross-sectional study involved 19 eyes of 10 young and healthy Caucasian subjects. En-face macular optical coherence tomography angiography of superficial choriocapillaris was obtained by the RTVue-XR Avanti system. Various algorithms were used to extract texture features. The mean and standard deviation were used to assess the distribution and dispersion of data points in each metric among eyes, which included: average gray level, gray level yielding 70% threshold and 30% threshold, balance, skewness, energy, entropy, contrast, edge mean gradient, root-mean-square variation, and first moment of power spectrum, which was compared between images, showing a highly concordant homology between all eyes of participants. We conclude that computerized texture analysis for en-face optical coherence tomography angiography images of choriocapillaris is feasible and provides values that are coherent and tightly distributed around the mean in a homogenous, healthy group of patients. Homology of blob size among subjects may represent a “repeat pattern” in signal density and thus a perfusion in the superficial choriocapillaris of healthy young individuals of the same ethnic background.

Research on mechanism of springback control by viscous medium with different mechanical properties

Viscous pressure forming has shown its advantages in precision forming of complex surface components. However, there are very few reports focusing on revealing the mechanism of springback control by viscous medium. This paper aims to study the effect of viscous medium on springback and the mechanism of springback control by viscous medium. The viscous pressure forming of a bulging axisymmetric geometry is studied. The effect of viscous medium on springback and stress path of sheet is analyzed in numerical simulation by unloading the sheet and viscous medium together. Then, the experiments are conducted using different kinds of viscous medium and loading speeds. The digital correlation image (DIC) technology is employed to measure the springback. The stress and membrane force of the bulging sheet are calculated and analyzed. Results show that non-uniformly distributed force of viscous medium changes the shape and stress path of the sheet. The viscous medium simultaneously possessing good strain rate sensitivity and viscosity can well control the springback. This is because the coupling effect of non-uniform normal force and tangential adhesion promotes the uniformity of stress distribution on the whole sheet and reduces the bending moment of sheet near the die corner. • The mechanism of springback control by viscous medium is investigated. • The effect of viscous medium properties and loading speeds on springback is studied experimentally. • The viscous medium simultaneously possessing good strain rate sensitivity and viscosity can well control the springback. • The coupling effect of non-uniform normal force and tangential adhesion reduces the stress gradient and bending moment.

Deep learning LSTM for predicting thermally induced geometric errors using rotary axes’ powers as input parameters

Temperature changes within a machine tool, which are partly due to internal heat sources related to the power consumption at the machine drives, result in thermally induced geometric errors of the machine. Predicting the thermally affected machine geometry facilitates the prediction of volumetric errors throughout the 5-axis machine volume. Measuring power instead of temperature is easier to implement in practice but causes drift issues. Stacked Long Short Term Memory (LSTM) with two hidden LSTM layers is applied to determine the relationship between powers and the thermal variation of geometric error parameters by remembering previous states and learning complex non-linear relationships through optimized generalized parameters of the predicting model. Optimizers Adam, RMSprop, and SGD based on exponential moving average of first order and second order moments of gradients are combined with Stacked LSTM for faster learning convergence to an optimal solution. Validation trials with various B- and C-axis motion sequences demonstrate a capability of predicting multi time steps ahead over a 40 hours period without re-measuring the geometric error parameters of the model. Stacked LSTM with the Adam optimizer has the best capability by predicting up to 93% of the main geometric error compared to the other optimizers.

Stay on the Beat With Tensor-Valued Encoding: Time-Dependent Diffusion and Cell Size Estimation in ex vivo Heart

Diffusion encoding with free gradient waveforms can provide increased microstructural specificity in heterogeneous tissues compared to conventional encoding approaches. This is achieved by considering specific aspects of encoding, such as b-tensor shape, sensitivity to bulk motion and to time-dependent diffusion (TDD). In tensor-valued encoding, different b-tensor shapes are used, such as in linear tensor encoding (LTE) or spherical tensor encoding (STE). STE can be employed for estimation of mean diffusivity (MD) or in combination with LTE to probe average microscopic anisotropy unconfounded by orientation dispersion. While tensor-valued encoding has been successfully applied in the brain and other organs, its potential and limitations have not yet been fully explored in cardiac applications. To avoid artefacts due to motion, which are particularly challenging in cardiac imaging, arbitrary b-tensors can be designed with motion compensation, i.e. gradient moment nulling, while also nulling the adverse effects of concomitant gradients. Encoding waveforms with varying degrees of motion compensation may however have significantly different sensitivities to TDD. This effect can be prominent in tissues with relatively large cell sizes such as in the heart and can be used advantageously to provide further tissue information. To account for TDD in tensor-valued encoding, the interplay between asynchronous gradients simultaneously applied along different directions needs to be considered. As the first step toward in vivo cardiac applications, our overarching goal was to explore the feasibility of acceleration compensated tensor-valued encoding on preclinical and clinical scanners ex vivo. We have demonstrated strong and predictable variation of MD due to TDD in mouse and pig hearts using a wide range of LTE and STE with progressively increasing degrees of motion compensation. Our preliminary data from acceleration compensated STE and LTE at high b-values, attainable on the preclinical scanner, indicate that TDD needs to be considered in experiments with varying b-tensor shapes. We have presented a novel theoretical framework, which enables cell size estimation, helps to elucidate limitations and provides a basis for further optimizations of experiments probing both mean diffusivity and microscopic anisotropy in the heart.

Hybrid Feature-Based Disease Detection in Plant Leaf Using Convolutional Neural Network, Bayesian Optimized SVM, and Random Forest Classifier

Plant diseases are unfavourable factors that cause a significant decrease in the quality and quantity of crops. Experienced biologists or farmers often observe plants with the naked eye for disease, but this method is often imprecise and can take a long time. In this study, we use artificial intelligence and computer vision techniques to achieve the goal of designing and developing an intelligent classification mechanism for leaf diseases. This paper follows two methodologies and their simulation outcomes are compared for performance evaluation. In the first part, data augmentation is performed on the PlantVillage data set images (for apple, corn, potato, tomato, and rice plants), and their deep features are extracted using convolutional neural network (CNN). These features are classified by a Bayesian optimized support vector machine classifier and the results attained in terms of precision, sensitivity, f-score, and accuracy. The above-said methodologies will enable farmers all over the world to take early action to prevent their crops from becoming irreversibly damaged, thereby saving the world and themselves from a potential economic crisis. The second part of the methodology starts with the preprocessing of data set images, and their texture and color features are extracted by histogram of oriented gradient (HoG), GLCM, and color moments. Here, the three types of features, that is, color, texture, and deep features, are combined to form hybrid features. The binary particle swarm optimization is applied for the selection of these hybrid features followed by the classification with random forest classifier to get the simulation results. Binary particle swarm optimization plays a crucial role in hybrid feature selection; the purpose of this Algorithm is to obtain the suitable output with the least features. The comparative analysis of both techniques is presented with the use of the above-mentioned evaluation parameters.

Free‐breathing three‐dimensional isotropic‐resolution MR sequence for simultaneous vessel wall imaging of bilateral renal arteries and abdominal aorta: Feasibility and reproducibility

Many diseases can simultaneously involve renal arteries and the adjacent abdominal aorta. This study proposed a free-breathing three-dimensional (3D) isotropic-resolution magnetic resonance sequence for simultaneous vessel wall imaging (VWI) of bilateral renal arteries and adjacent abdominal aorta. A respiratory-triggered isotropic-resolution sequence that combined the improved motion-sensitized driven-equilibrium (iMSDE) preparation with the spoiled gradient recalled (SPGR) readout (iMSDE-SPGR) was proposed for simultaneous VWI of renal arteries and abdominal aorta. The proposed iMSDE-SPGR sequence was optimized by positioning spatial saturation pulses (i.e., REST slabs) elaborately to further alleviate respiratory and gastrointestinal motion artifacts and selecting appropriate first-order gradient moment (m1 ) of the iMSDE preparation. Thirteen healthy subjects and 13 patients with renal artery stenosis underwent simultaneous VWI with the optimized iMSDE-SPGR sequence at 3.0 T. Signal-to-noise ratio (SNR), contrast-to-noise ratio (CNR), and morphology of renal arterial wall and aortic wall were measured. Reproducibility of intra-observer, inter-observer, and scan-rescan (n=13 healthy subjects) in measuring SNR, CNR, and morphology was evaluated. For the reproducibility test, the agreement was determined using intraclass correlation coefficients (ICC), and the differences were compared using paired t-test or nonparametric Wilcoxon test when appropriate. Bland-Altman plots were used to calculate the bias between observers and between scans. The proposed iMSDE-SPGR sequence was feasible for simultaneous VWI both in the healthy subjects and the patients. The sequence showed good to excellent inter-observer (ICC: 0.615-0.999), excellent intra-observer (ICC: 0.801-0.998), and scan-rescan (ICC: 0.768-0.998) reproducibility in measuring morphology, SNR, and CNR. There were no significant differences in SNR, CNR, and morphology measurements between observers and between scans (all p>0.05). Bland-Altman plots showed small bias in assessing SNR, CNR, and morphology. The proposed free-breathing 3D isotropic-resolution iMSDE-SPGR technique is feasible and reproducible for simultaneous VWI of bilateral renal arteries and adjacent abdominal aorta.

Numerical finite element simulation and structural behaviour of cold-formed steel members

Cold-formed steel (CFS) is going through an interesting phase of development. Thin-walled cold-rolled steel structures are adopted widely for low-mid rise construction. The CFS sections find its application, not for construction but alternate sectors too, such as automobile and aerospace applications. Many research on the CFS members have been conducted in past but yet there is a scarcity of research done for flexural members, especially under the 3-point loading scenario. Unlikely most common 4-point loading, in the case of 3-point loading the member is under gradient moment distribution as well as is exposed to uniform shear along the span of the member. This paper attempts to bridge this gap and explains the developed finite element (FE) model, validating the developed model, followed by a parametric study. Commercially available FE program ABAQUS was adopted for numerical simulations. An extensive parametric study was conducted considering, 7 geometric sections, having 12 spans and two grades of steel, making a total of 168 simulations. The member non-dimensional slenderness (λ) ranged from 0.40 to 2.17. Preliminary results of this research indicate the significant effect of geometry, grade and non-dimensional slenderness on member moment behaviour and capacity. A higher grade of steel is found to be more sensitive to the effects of non-dimensional slenderness.

Fundamentals of turbulent flow spectrum imaging.

PurposeTo introduce a mathematical framework and in‐silico validation of turbulent flow spectrum imaging (TFSI) of stenotic flow using phase‐contrast MRI, evaluate systematic errors in quantitative turbulence parameter estimation, and propose a novel method for probing the Lagrangian velocity spectra of turbulent flows.Theory and MethodsThe spectral response of velocity‐encoding gradients is derived theoretically and linked to turbulence parameter estimation including the velocity autocorrelation function spectrum. Using a phase‐contrast MRI simulation framework, the encoding properties of bipolar gradient waveforms with identical first gradient moments but different duration are investigated on turbulent flow data of defined characteristics as derived from computational fluid dynamics. Based on theoretical insights, an approach using velocity‐compensated gradient waveforms is proposed to specifically probe desired ranges of the velocity autocorrelation function spectrum with increased accuracy.ResultsPractical velocity‐encoding gradients exhibit limited encoding power of typical turbulent flow spectra, resulting in up to 50% systematic underestimation of intravoxel SD values. Depending on the turbulence level in fluids, the error due to a single encoding gradient spectral response can vary by 20%. When using tailored velocity‐compensated gradients, improved quantification of the Lagrangian velocity spectrum on a voxel‐by‐voxel basis is achieved and used for quantitative correction of intravoxel SD values estimated with velocity‐encoding gradients.ConclusionTo address systematic underestimation of turbulence parameters using bipolar velocity‐encoding gradients in phase‐contrast MRI of stenotic flows with short correlation times, tailored velocity‐compensated gradients are proposed to improve quantitative mapping of turbulent blood flow characteristics.