The stress and strain pattern in the ligaments of the acromioclavicular joint using a quasi-static model.

BACKGROUND: The precise role of the acromioclavicular and coracoclavicular ligaments during shoulder motion is unclear. We evaluate changes in the stress-strain distribution of the acromioclavicular joint's ligaments during different shoulder passive motion positions. METHODS: A 3D acromioclavicular joint model was reconstructed. A constitutive hyperelastic model was used for the ligaments. The kinematics of the shoulder girdle was taken to simulate shoulder abduction (Motion 1) and horizontal adduction (Motion 2). A computer-generated quasi-static and non-linear finite element model was used to predict the 3D stress-strain distribution pattern of the acromioclavicular ligament and the coracoclavicular ligament complex. FINDINGS: In motion 1, from 20 to 90° the peak von Mises stress was found in the conoid (4.14 MPa) and the anteroinferior bundle (2.46 MPa), while from 90 to 120° it was found in the conoid and the trapezoid. However, there were no significant differences between the mean stress values between anteroinferior bundle and trapezoid throughout the motion (p = 0.98). In Motion 2, from 20 to 80° the maximum equivalent elastic strain was found in the anteroinferior bundle (0.68 mm/mm) and the conoid (0.57 mm/mm), while from 80 to 100° it was higher in the conoid (0.88 mm/mm) than in the anteroinferior bundle (0.77 mm/mm). INTERPRETATION: The coracoclavicular ligament complex demonstrated a high stress-strain concentration during simulated passive shoulder abduction. Additionally, it was shown that the acromioclavicular ligament plays an important role in joint restraint during passive horizontal adduction, changing the primary role with the trapezoid and conoid at different motion intervals.

Fully Three-Dimensional Hemodynamic Characterization of Altered Blood Flow in Bicuspid Aortic Valve Patients With Respect to Aortic Dilatation: A Finite Element Approach.

Background and Purpose: Prognostic models based on cardiovascular hemodynamic parameters may bring new information for an early assessment of patients with bicuspid aortic valve (BAV), playing a key role in reducing the long-term risk of cardiovascular events. This work quantifies several three-dimensional hemodynamic parameters in different patients with BAV and ranks their relationships with aortic diameter. Materials and Methods: Using 4D-flow CMR data of 74 patients with BAV (49 right-left and 25 right-non-coronary) and 48 healthy volunteers, aortic 3D maps of seventeen 17 different hemodynamic parameters were quantified along the thoracic aorta. Patients with BAV were divided into two morphotype categories, BAV-Non-AAoD (where we include 18 non-dilated patients and 7 root-dilated patients) and BAV-AAoD (where we include the 49 patients with dilatation of the ascending aorta). Differences between volunteers and patients were evaluated using MANOVA with Pillai's trace statistic, Mann-Whitney U test, ROC curves, and minimum redundancy maximum relevance algorithm. Spearman's correlation was used to correlate the dilation with each hemodynamic parameter. Results: The flow eccentricity, backward velocity, velocity angle, regurgitation fraction, circumferential wall shear stress, axial vorticity, and axial circulation allowed to discriminate between volunteers and patients with BAV, even in the absence of dilation. In patients with BAV, the diameter presented a strong correlation (> |+/-0.7|) with the forward velocity and velocity angle, and a good correlation (> |+/-0.5|) with regurgitation fraction, wall shear stress, wall shear stress axial, and vorticity, also for morphotypes and phenotypes, some of them are correlated with the diameter. The velocity angle proved to be an excellent biomarker in the differentiation between volunteers and patients with BAV, BAV morphotypes, and BAV phenotypes, with an area under the curve bigger than 0.90, and higher predictor important scores. Conclusions: Through the application of a novel 3D quantification method, hemodynamic parameters related to flow direction, such as flow eccentricity, velocity angle, and regurgitation fraction, presented the best relationships with a local diameter and effectively differentiated patients with BAV from healthy volunteers.

Assessment of 4D flow MRI's quality by verifying its Navier-Stokes compatibility.

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 plus an extra field w→ . Therefore, a non-linear problem with 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→ for assessing the quality of 4D Flow MRI measurements over space and time.

Three-dimensional quantification of circulation using finite-element methods in four-dimensional flow MR data of the thoracic aorta.

PURPOSE: Three-dimensional (3D) quantification of circulation using a Finite Elements methodology. METHODS: We validate our 3D method using an in-silico arch model, for different mesh resolutions, image resolution and noise levels, and we compared this with a currently used 2D method. Finally, we evaluated the application of our methodology in 4D Flow MRI data of ascending aorta of six healthy volunteers, and six bicuspid aortic valve (BAV) patients, three with right and three with left handed flow, at peak systole. The in-vivo data was compared using a Mann-Whitney U-test between volunteers and patients (right and left handed flow). RESULTS: The robustness of our method throughout different image resolutions and noise levels showed subestimation of circulation less than 45 cm2 /s in comparison with the 55cm2 /s generated by the current 2D method. The circulation (mean ± SD) of the healthy volunteer group was 13.83 ± 28.78 cm2 /s, in BAV patients with right-handed flow 724.37 ± 317.53 cm2 /s, and BAV patients with left-handed flow -480.99 ± 387.29 cm2 /s. There were significant differences between healthy volunteers and BAV patients groups (P-value < .01), and also between BAV patients with a right-handed or left-handed helical flow and healthy volunteers (P-value < .01). CONCLUSION: We propose a novel 3D formulation to estimate the circulation in the thoracic aorta, which can be used to assess the differences between normal and diseased hemodynamic from 4D-Flow MRI data. This method also can correctly differentiate between the visually seen right- and left-handed helical flow, which suggests that this approach may have high clinical sensitivity, but requires confirmation in longitudinal studies with a large cohort.

A comprehensive comparison between shortest-path HARP refinement, SinMod, and DENSEanalysis processing tools applied to CSPAMM and DENSE images.

We addressed comprehensively the performance of Shortest-Path HARP Refinement (SP-HR), SinMod, and DENSEanalysis using 2D slices of synthetic CSPAMM and DENSE images with realistic contrasts obtained from 3D phantoms. The three motion estimation techniques were interrogated under ideal and no-ideal conditions (with MR induced artifacts, noise, and through-plane motion), considering several resolutions and noise levels. Under noisy conditions, and for isotropic pixel sizes of 1.5 mm and 3.0 mm in CSPAMM and DENSE images respectively, the nRMSE obtained for the circumferential and radial strain components were 10.7 ±â€¯10.8% and 25.5 ±â€¯14.8% using SP-HR, 11.9 ±â€¯2.5% and 29.3 ±â€¯6.5% using SinMod, and 6.4 ±â€¯2.0% and 18.2 ±â€¯4.6% using DENSEanalysis. Overall, the results showed that SP-HR tends to fail for large tissue motions, whereas SinMod and DENSEanalysis gave accurate displacement and strain field estimations, being the last which performed the best.

HARP-I: A Harmonic Phase Interpolation Method for the Estimation of Motion From Tagged MR Images.

We proposed a novel method called HARP-I, which enhances the estimation of motion from tagged Magnetic Resonance Imaging (MRI). The harmonic phase of the images is unwrapped and treated as noisy measurements of reference coordinates on a deformed domain, obtaining motion with high accuracy using Radial Basis Functions interpolations. Results were compared against Shortest Path HARP Refinement (SP-HR) and Sine-wave Modeling (SinMod), two harmonic image-based techniques for motion estimation from tagged images. HARP-I showed a favorable similarity with both methods under noise-free conditions, whereas a more robust performance was found in the presence of noise. Cardiac strain was better estimated using HARP-I at almost any motion level, giving strain maps with less artifacts. Additionally, HARP-I showed better temporal consistency as a new method was developed to fix phase jumps between frames. In conclusion, HARP-I showed to be a robust method for the estimation of motion and strain under ideal and non-ideal conditions.

MAPL1: q-space reconstruction using ℓ1 -regularized mean apparent propagator.

PURPOSE: To improve the quality of mean apparent propagator (MAP) reconstruction from a limited number of q-space samples. METHODS: We implement an ℓ1 -regularised MAP (MAPL1) to consider higher order basis functions and to improve the fit without increasing the number of q-space samples. We compare MAPL1 with the least-squares optimization subject to non-negativity (MAP), and the Laplacian-regularized MAP (MAPL). We use simulations of crossing fibers and compute the normalized mean squared error (NMSE) and the Pearson's correlation coefficient to evaluate the reconstruction quality in q-space. We also compare coefficient-based diffusion indices in the simulations and in in vivo data. RESULTS: Results indicate that MAPL1 improves NMSE in 1 to 3% when compared to MAP or MAPL in a high undersampling regime. Additionally, MAPL1 produces more reproducible and accurate results for all sampling rates when there are enough basis functions to meet the sparsity criterion for the regularizer. These improved reconstructions also produce better coefficient-based diffusion indices for in vivo data. CONCLUSIONS: Adding an ℓ1 regularizer to MAP allows the use of more basis functions and a better fit without increasing the number of q-space samples. The impact of our research is that a complete diffusion spectrum can be reconstructed from an acquisition time very similar to a diffusion tensor imaging protocol.

An analytical solution to the dispersion-by-inversion problem in magnetic resonance elastography.

PURPOSE: Magnetic resonance elastography (MRE) measures stiffness of soft tissues by analyzing their spatial harmonic response to externally induced shear vibrations. Many MRE methods use inversion-based reconstruction approaches, which invoke first- or second-order derivatives by finite difference operators (first- and second-FDOs) and thus give rise to a biased frequency dispersion of stiffness estimates. METHODS: We here demonstrate analytically, numerically, and experimentally that FDO-based stiffness estimates are affected by (1) noise-related underestimation of values in the range of high spatial wave support, that is, at lower vibration frequencies, and (2) overestimation of values due to wave discretization at low spatial support, that is, at higher vibration frequencies. RESULTS: Our results further demonstrate that second-FDOs are more susceptible to noise than first-FDOs and that FDO dispersion depends both on signal-to-noise ratio (SNR) and on a lumped parameter A, which is defined as wavelength over pixel size and over a number of pixels per stencil of the FDO. Analytical FDO dispersion functions are derived for optimizing A parameters at a given SNR. As a simple rule of thumb, we show that FDO artifacts are minimized when A/2 is in the range of the square root of 2SNR for the first-FDO or cubic root of 5SNR for the second-FDO. CONCLUSIONS: Taken together, the results of our study provide an analytical solution to a long-standing, well-recognized, yet unsolved problem in MRE postprocessing and might thus contribute to the ongoing quest for minimizing inversion artifacts in MRE.

Pediatric heterozygous familial hypercholesterolemia patients have locally increased aortic pulse wave velocity and wall thickness at the aortic root.

Familial hypercholesterolemia (FH) is an autosomal dominant disorder that affects 1 in 250 people. Aortic stiffness, measured by pulse wave velocity (PWV), is an independent predictor for cardiovascular events. Young FH patients are a unique group with early vessel wall disease that may serve to elucidate the determinants of aortic stiffness. We hypothesized that young FH patients would have early changes in aortic stiffness compared to healthy, age- and sex-matched reference values. Thirty-three FH patients ( ≥ 7 years age; mean age 14.6 ± 3.3 years; 26/33 on statin therapy) underwent cardiac MRI. PWV was determined using propagation of flow waveform from aortic arch phase contrast images. Distensibility and aortic wall thickness (AWT) were measured at the ascending, proximal descending, and diaphragmatic aorta. Ventricular volumes and left ventricular (LV) myocardial mass were measured from 2D cine images. These parameters were compared to age- and sex-matched reference values. FH patients had significantly higher PWV (4.5 ± 0.8 vs. 3.5 ± 0.3 m/s; p < 0.001), aortic distensibility, and ascending aortic wall thickness (1.37 ± 0.18 vs. 1.30 ± 0.02 mm; p < 0.05) compared to reference. There was no difference in aortic area or descending aortic wall thickness between groups. Young FH patients had aortic changes with increased aortic pulse wave velocity in the setting of increased aortic distensibility, accompanied by increased thickness of the ascending aortic wall. Presence of these early findings in young patients despite the majority being on statin therapy support enhanced screening and aggressive treatment of familial hypercholesterolemia to prevent potential future cardiovascular events.

Three-dimensional quantification of vorticity and helicity from 3D cine PC-MRI using finite-element interpolations.

PURPOSE: We propose a 3D finite-element method for the quantification of vorticity and helicity density from 3D cine phase-contrast (PC) MRI. METHODS: By using a 3D finite-element method, we seamlessly estimate velocity gradients in 3D. The robustness and convergence were analyzed using a combined Poiseuille and Lamb-Ossen equation. A computational fluid dynamics simulation was used to compared our method with others available in the literature. Additionally, we computed 3D maps for different 3D cine PC-MRI data sets: phantom without and with coarctation (18 healthy volunteers and 3 patients). RESULTS: We found a good agreement between our method and both the analytical solution of the combined Poiseuille and Lamb-Ossen. The computational fluid dynamics results showed that our method outperforms current approaches to estimate vorticity and helicity values. In the in silico model, we observed that for a tetrahedral element of 2 mm of characteristic length, we underestimated the vorticity in less than 5% with respect to the analytical solution. In patients, we found higher values of helicity density in comparison to healthy volunteers, associated with vortices in the lumen of the vessels. CONCLUSIONS: We proposed a novel method that provides entire 3D vorticity and helicity density maps, avoiding the used of reformatted 2D planes from 3D cine PC-MRI. Magn Reson Med 79:541-553, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

3D axial and circumferential wall shear stress from 4D flow MRI data using a finite element method and a laplacian approach.

PURPOSE: To decompose the 3D wall shear stress (WSS) vector field into its axial (WSSA ) and circumferential (WSSC ) components using a Laplacian finite element approach. METHODS: We validated our method with in silico experiments involving different geometries and a modified Poiseuille flow. We computed 3D maps of the WSS, WSSA , and WSSC using 4D flow MRI data obtained from 10 volunteers and 10 patients with bicuspid aortic valve (BAV). We compared our method with the centerline method. The mean value, standard deviation, root mean-squared error, and Wilcoxon signed rank test are reported. RESULTS: We obtained an error <0.05% processing analytical geometries. We found good agreement between our method and the modified Poiseuille flow for the WSS, WSSA , and WSSC . We found statistically significance differences between our method and a 3D centerline method. In BAV patients, we found a 220% significant increase in the WSSC in the ascending aorta with respect to volunteers. CONCLUSION: We developed a novel methodology to decompose the WSS vector in WSSA and WSSC in 3D domains, using 4D flow MRI data. Our method provides a more robust quantification of WSSA and WSSC in comparison with other reported methods. Magn Reson Med 79:2816-2823, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

Enhancing the Velocity Data From 4D Flow MR Images by Reducing its Divergence.

Velocity measurements from 4D flow MRI are prone to be affected by several imperfections of the MR system. Assuming that blood is incompressible, we propose a novel method for enhancing the velocity field by reducing its divergence. To enhance the velocity data, we added a corrector velocity to each voxel such that the divergence is minimized. The method was validated using an analytical Womersley flow model for different settings of resolution and noise levels. The performance of the proposed method was also assessed in volunteers and patients. Results demonstrated a significant reduction of the divergence depending on the size of the regularization term, obtaining a reduction close to 50% of the mean divergence with negligible modification of flow parameters. Remarkably, we found that the reduction of the divergence, in percentage, was independent of volunteers, resolution or noise.