Browsing by Author "Bertoglio, Cristobal"

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    A comparison of phase unwrapping methods in velocity-encoded MRI for aortic flows
    (2023) Locke, Miriam; Labra, Jeremias Esteban Garay; Franco, Pamela; Uribe, Sergio; Bertoglio, Cristobal
    PurposeThe phase of a MRI signal is used to encode the velocity of blood flow. Phase unwrapping artifacts may appear when aiming to improve the velocity-to-noise ratio (VNR) of the measured velocity field. This study aims to compare various unwrapping algorithms on ground-truth synthetic data generated using computational fluid dynamics (CFD) simulations. MethodsWe compare four different phase unwrapping algorithms on two different synthetic datasets of four-dimensional flow MRI and 26 datasets of 2D PC-MRI acquisitions including the ascending and descending aorta. The synthetic datasets are constructed using CFD simulations of an aorta with a coarctation, with different levels of spatiotemporal resolutions and noise. The error of the unwrapped images was assessed by comparison against the ground truth velocity field in the synthetic data and dual-VENC reconstructions in the in vivo data. ResultsUsing the unwrapping algorithms, we were able to remove aliased voxels in the data almost entirely, reducing the L2-error compared to the ground truth by 50%-80%. Results indicated that the best choice of algorithm depend on the spatiotemporal resolution and noise level of the dataset. Temporal unwrapping is most successful with a high temporal and low spatial resolution (& delta;t=30$$ \delta t=30 $$ ms, h=2.5$$ h=2.5 $$ mm), reducing the L2-error by 70%-85%, while Laplacian unwrapping performs better with a lower temporal or better spatial resolution (& delta;t=60$$ \delta t=60 $$ ms, h=1.5$$ h=1.5 $$ mm), especially for signal-to-noise ratio (SNR) 12 as opposed to SNR 15, with an error reduction of 55%-85% compared to the 50%-75% achieved by the Temporal method. The differences in performance between the methods are statistically significant. ConclusionsThe temporal method and spatiotemporal Laplacian method provide the best results, with the spatiotemporal Laplacian being more robust. However, single-Venc$$ {V}_{\mathrm{enc}} $$ methods only situationally and not generally reach the performance of dual-Venc$$ {V}_{\mathrm{enc}} $$ unwrapping methods.
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    Assessment of 4D flow MRI's quality by verifying its Navier-Stokes compatibility
    (2022) Garay, Jeremias; Mella, Hernan; Sotelo, Julio; Carcamo, Cristian; Uribe, Sergio; Bertoglio, Cristobal; Mura, Joaquin
    4D Flow Magnetic Resonance Imaging (MRI) is the state-of-the-art technique to comprehensively measure the complex spatio-temporal and multidirectional patterns of blood flow. However, it is subject to artifacts such as noise and aliasing, which due to the 3D and dynamic structure is difficult to detect in clinical practice. In this work, a new mathematical and computational model to determine the quality of 4D Flow MRI is presented. The model is derived by assuming the true velocity satisfies the incompressible Navier-Stokes equations and that can be decomposed by the measurements u -> meas$$ {\overrightarrow{u}}_{meas} $$ plus an extra field w ->$$ \overrightarrow{w} $$. Therefore, a non-linear problem with w ->$$ \overrightarrow{w} $$ as unknown arises, which serves as a measure of data quality. A stabilized finite element formulation tailored to this problem is proposed and analyzed. Then, extensive numerical examples-using synthetic 4D Flow MRI data as well as real measurements on experimental phantom and subjects-illustrate the ability to use w ->$$ \overrightarrow{w} $$ for assessing the quality of 4D Flow MRI measurements over space and time.
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    Comparison of Improved Unidirectional Dual Velocity-Encoding MRI Methods
    (2023) Franco, Pamela; Ma, Liliana; Schnell, Susanne; Carrillo, Hugo; Montalba, Cristian; Markl, Michael; Bertoglio, Cristobal; Uribe, Sergio
    Background In phase-contrast (PC) MRI, several dual velocity encoding methods have been proposed to robustly increase velocity-to-noise ratio (VNR), including a standard dual-VENC (SDV), an optimal dual-VENC (ODV), and bi- and triconditional methods. Purpose To develop a correction method for the ODV approach and to perform a comparison between methods. Study Type Case-control study. Population Twenty-six volunteers. Field Strength/Sequence 1.5 T phase-contrast MRI with VENCs of 50, 75, and 150 cm/second. Assessment Since we acquired single-VENC protocols, we used the background phase from high-VENC (VENCH) to reconstruct the low-VENC (VENCL) phase. We implemented and compared the unwrapping methods for different noise levels and also developed a correction of the ODV method. Statistical Tests Shapiro-Wilk's normality test, two-way analysis of variance with homogeneity of variances was performed using Levene's test, and the significance level was adjusted by Tukey's multiple post hoc analysis with Bonferroni (P < 0.05). Results Statistical analysis revealed no extreme outliers, normally distributed residuals, and homogeneous variances. We found statistically significant interaction between noise levels and the unwrapping methods. This implies that the number of non-unwrapped pixels increased with the noise level. We found that for beta = VENCL/VENCH = 1/2, unwrapping methods were more robust to noise. The post hoc test showed a significant difference between the ODV corrected and the other methods, offering the best results regarding the number of unwrapped pixels. Data Conclusions All methods performed similarly without noise, but the ODV corrected method was more robust to noise at the price of a higher computational time. Level of Evidence 4 Technical Efficacy Stage 1
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    Convergence analysis of pressure reconstruction methods from discrete velocities
    (2023) Araya, Rodolfo; Bertoglio, Cristobal; Carcamo, Cristian; Nolte, David; Uribe, Sergio
    Magnetic resonance imaging allows the measurement of the three-dimensional velocity field in blood flows. Therefore, several methods have been proposed to reconstruct the pressure field from such measurements using the incompressible Navier-Stokes equations, thereby avoiding the use of invasive technologies. However, those measurements are obtained at limited spatial resolution given by the voxel sizes in the image. In this paper, we propose a strategy for the convergence analysis of state-of-the-art pressure reconstruction methods. The methods analyzed are the so-called Pressure Poisson Estimator (PPE) and Stokes Estimator (STE). In both methods, the right-hand side corresponds to the terms that involving the field velocity in the Navier-Stokes equations, with a piecewise linear interpolation of the exact velocity. In the theoretical error analysis, we show that many terms of different order of convergence appear. These are certainly dominated by the lowest-order term, which in most cases stems from the interpolation of the velocity field. However, the numerical results in academic examples indicate that only the PPE may profit of increasing the polynomial order, and that the STE presents a higher accuracy than the PPE, but the interpolation order of the velocity field always prevails. Furthermore, we compare the pressure estimation methods on real MRI data, assessing the impact of different spatial resolutions and polynomial degrees on each method. Here, the results are consistent with the academic test cases in terms of sensitivity to polynomial order as well as the STE showing to be potentially more accurate when compared to reference pressure measurements.
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    Multiple motion encoding in phase-contrast MRI: A general theory and application to elastography imaging
    (2022) Herthum, Helge; Carrillo, Hugo; Osses, Axel; Uribe, Sergio; Sack, Ingolf; Bertoglio, Cristobal
    While MRI allows to encode the motion of tissue in the magnetization's phase, it remains yet a challenge to obtain high fidelity motion images due to wraps in the phase for high encoding efficiencies. Therefore, we propose an optimal multiple motion encoding method (OMME) and exemplify it in Magnetic Resonance Elastography (MRE) data. OMME is formulated as a non-convex least-squares problem for the motion using an arbitrary number of phase-contrast measurements with different motion encoding gradients (MEGs). The mathematical properties of OMME are proved in terms of standard deviation and dynamic range of the motion's estimate for arbitrary MEGs combination which are confirmed using synthetically generated data. OMME's performance is assessed on MRE data from in vivo human brain experiments and compared to dual encoding strategies. The unwrapped images are further used to reconstruct stiffness maps and compared to the ones obtained using conventional unwrapping methods. OMME allowed to successfully combine several MRE phase images with different MEGs, outperforming dual encoding strategies in either motion-to-noise ratio (MNR) or number of successfully reconstructed voxels with good noise stability. This lead to stiffness maps with greater resolution of details than obtained with conventional unwrapping methods. The proposed OMME method allows for a flexible and noise robust increase in the dynamic range and thus provides wrap-free phase images with high MNR. In MRE, the method may be especially suitable when high resolution images with high MNR are needed. (c) 2022 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ )
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    Optimal Dual-VENC Unwrapping in Phase-Contrast MRI
    (2019) Carrillo, Hugo; Osses, Axel; Uribe, Sergio; Bertoglio, Cristobal
    Dual-VENC strategies have been proposed to improve the velocity-to-noise ratio in phase-contrast MRI. However, they are based on aliasing-free high-VENC data. The aim of this paper is to propose a dual-VENC velocity estimation method allowing high-VENC aliased data. For this purpose, we reformulate the phase-contrast velocity as a least squares estimator, providing a natural framework for including multiple encoding gradient measurements. By analyzing the mathematical properties of both single-and dual-VENCproblems, we can justify theoretically high/low-VENC ratios such that the aliasing velocity can be minimized. The resulting reconstruction algorithm was assessed using three types of data: numerical, experimental, and volunteers. In clinical practice, this method would allow shorter examination times by avoiding tedious adaptation of VENC values by repeated scans.
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    Validation of 4D Flow based relative pressure maps in aortic flows
    (2021) Nolte, David; Urbina, Jesus; Sotelo, Julio; Sok, Leo; Montalba, Cristian; Valverde, Israel; Osses, Axel; Uribe, Sergio; Bertoglio, Cristobal
    While the clinical gold standard for pressure difference measurements is invasive catheterization, 4D Flow MRI is a promising tool for enabling a non-invasive quantification, by linking highly spatially resolved velocity measurements with pressure differences via the incompressible Navier-Stokes equations. In this work we provide a validation and comparison with phantom and clinical patient data of pressure difference maps estimators. We compare the classical Pressure Poisson Estimator (PPE) and the new Stokes Estimator (STE) against catheter pressure measurements under a variety of stenosis severities and flow intensities. Specifically, we use several 4D Flow data sets of realistic aortic phantoms with different anatomic and hemodynamic severities and two patients with aortic coarctation. The phantom data sets are enriched by subsampling to lower resolutions, modification of the segmentation and addition of synthetic noise, in order to study the sensitivity of the pressure difference estimators to these factors. Overall, the STE method yields more accurate results than the PPE method compared to catheterization data. The superiority of the STE becomes more evident at increasing Reynolds numbers with a better capacity of capturing pressure gradients in strongly convective flow regimes. The results indicate an improved robustness of the STE method with respect to variation in lumen segmentation. However, with heuristic removal of the wall-voxels, the PPE can reach a comparable accuracy for lower Reynolds' numbers. (c) 2021 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ )