Automatic 4D Flow MRI Segmentation Using the Standardized Difference of Means Velocity.

We present a method to automatically segment 4D flow magnetic resonance imaging (MRI) by identifying net flow effects using the standardized difference of means (SDM) velocity. The SDM velocity quantifies the ratio between the net flow and observed flow pulsatility in each voxel. Vessel segmentation is performed using an F-test, identifying voxels with significantly higher SDM velocity values than background voxels. We compare the SDM segmentation algorithm against pseudo-complex difference (PCD) intensity segmentation of 4D flow measurements in in vitro cerebral aneurysm models and 10 in vitro Circle of Willis (CoW) datasets. We also compared the SDM algorithm to convolutional neural network (CNN) segmentation in 5 thoracic vasculature datasets. The in vitro flow phantom geometry is known, while the ground truth geometries for the CoW and thoracic aortas are derived from high-resolution time-of-flight (TOF) magnetic resonance angiography and manual segmentation, respectively. The SDM algorithm demonstrates greater robustness than PCD and CNN approaches and can be applied to 4D flow data from other vascular territories. The SDM to PCD comparison demonstrated an approximate 48% increase in sensitivity in vitro and 70% increase in the CoW, respectively; the SDM and CNN sensitivities were similar. The vessel surface derived from the SDM method was 46% closer to the in vitro surfaces and 72% closer to the in vitro TOF surfaces than the PCD approach. The SDM and CNN approaches both accurately identify vessel surfaces. The SDM algorithm is a repeatable segmentation method, enabling reliable computation of hemodynamic metrics associated with cardiovascular disease.

Wall Shear Stress Estimation for 4D Flow MRI Using Navier-Stokes Equation Correction.

This study introduces a novel wall shear stress (WSS) estimation method for 4D flow MRI. The method improves the WSS accuracy by using the reconstructed pressure gradient and the flow-physics constraints to correct velocity gradient estimation. The method was tested on synthetic 4D flow data of analytical Womersley flow and flow in cerebral aneurysms and applied to in vivo 4D flow data acquired in cerebral aneurysms and aortas. The proposed method's performance was compared to the state-of-the-art method based on smooth-spline fitting of velocity profile and the WSS calculated from uncorrected velocity gradient. The proposed method improved the WSS accuracy by as much as 100% for the Womersley flow and reduced the underestimation of mean WSS by 39 to 50% for the synthetic aneurysmal flow. The predicted mean WSS from the in vivo aneurysmal data using the proposed method was 31 to 50% higher than the other methods. The predicted aortic WSS using the proposed method was 3 to 6 times higher than the other methods and was consistent with previous CFD studies and the results from recently developed methods that take into account the limited spatial resolution of 4D flow MRI. The proposed method improves the accuracy of WSS estimation from 4D flow MRI, which can help predict blood vessel remodeling and progression of cardiovascular diseases.

Modeling Bias Error in 4D Flow MRI Velocity Measurements.

We present a model to estimate the bias error of 4D flow magnetic resonance imaging (MRI) velocity measurements. The local instantaneous bias error is defined as the difference between the expectation of the voxel's measured velocity and actual velocity at the voxel center. The model accounts for bias error introduced by the intra-voxel velocity distribution and partial volume (PV) effects. We assess the intra-voxel velocity distribution using a 3D Taylor Series expansion. PV effects and numerical errors are considered using a Richardson extrapolation. The model is applied to synthetic Womersley flow and in vitro and in vivo 4D flow MRI measurements in a cerebral aneurysm. The bias error model is valid for measurements with at least 3.75 voxels across the vessel diameter and signal-to-noise ratio greater than 5. All test cases exceeded this diameter to voxel size ratio with diameters, isotropic voxel sizes, and velocity ranging from 3-15mm, 0.5-1mm, and 0-60cm/s, respectively. The model accurately estimates the bias error in voxels not affected by PV effects. In PV voxels, the bias error is an order of magnitude higher, and the accuracy of the bias error estimation in PV voxels ranges from 67.3% to 108% relative to the actual bias error. The bias error estimated for in vivo measurements increased two-fold at systole compared to diastole in partial volume and non-partial volume voxels, suggesting the bias error varies over the cardiac cycle. This bias error model quantifies 4D flow MRI measurement accuracy and can help plan 4D flow MRI scans.

A multi-modality approach for enhancing 4D flow magnetic resonance imaging via sparse representation.

This work evaluates and applies a multi-modality approach to enhance blood flow measurements and haemodynamic analysis with phase-contrast magnetic resonance imaging (4D flow MRI) in cerebral aneurysms (CAs). Using a library of high-resolution velocity fields from patient-specific computational fluid dynamic simulations and in vitro particle tracking velocimetry measurements, the flow field of 4D flow MRI data is reconstructed as the sparse representation of the library. The method was evaluated with synthetic 4D flow MRI data in two CAs. The reconstruction enhanced the spatial resolution and velocity accuracy of the synthetic MRI data, leading to reliable pressure and wall shear stress (WSS) evaluation. The method was applied on in vivo 4D flow MRI data acquired in the same CAs. The reconstruction increased the velocity and WSS by 6-13% and 39-61%, respectively, suggesting that the accuracy of these quantities was improved since the raw MRI data underestimated the velocity and WSS by 10-20% and 40-50%, respectively. The computed pressure fields from the reconstructed data were consistent with the observed flow structures. The results suggest that using the sparse representation flow reconstruction with in vivo 4D flow MRI enhances blood flow measurement and haemodynamic analysis.

Design and validation of a modular micro-robotic system for the mechanical characterization of soft tissues.

The mechanical properties of tissues are critical design parameters for biomaterials and regenerative therapies seeking to restore functionality after disease or injury. Characterizing the mechanical properties of native tissues and extracellular matrix throughout embryonic development helps us understand the microenvironments that promote growth and remodeling, activities critical for biomaterials to support. The mechanical characterization of small, soft materials like the embryonic tissues of the mouse, an established mammalian model for development, is challenging due to difficulties in handling minute geometries and resolving forces of low magnitude. While uniaxial tensile testing is the physiologically relevant modality to characterize tissues that are loaded in tension in vivo, there are no commercially available instruments that can simultaneously measure sufficiently low tensile force magnitudes, directly measure sample deformation, keep samples hydrated throughout testing, and effectively grip minute geometries to test small tissues. To address this gap, we developed a micromanipulator and spring system that can mechanically characterize small, soft materials under tension. We demonstrate the capability of this system to measure the force contribution of soft materials, silicone, fibronectin sheets, and fibrin gels with a 5 nN - 50 µN force resolution and perform a variety of mechanical tests. Additionally, we investigated murine embryonic tendon mechanics, demonstrating the instrument can measure differences in mechanics of small, soft tissues as a function of developmental stage. This system can be further utilized to mechanically characterize soft biomaterials and small tissues and provide physiologically relevant parameters for designing scaffolds that seek to emulate native tissue mechanics. STATEMENT OF SIGNIFICANCE: The mechanical properties of cellular microenvironments are critical parameters that contribute to the modulation of tissue growth and remodeling. The field of tissue engineering endeavors to recapitulate these microenvironments in order to construct tissues de novo. Therefore, it is crucial to uncover the mechanical properties of the cellular microenvironment during tissue formation. Here, we present a system capable of acquiring microscale forces and optically measuring sample deformation to calculate the stress-strain response of soft, embryonic tissues under tension, and easily adaptable to accommodate biomaterials of various sizes and stiffnesses. Altogether, this modular system enables researchers to probe the unknown mechanical properties of soft tissues throughout development to inform the engineering of physiologically relevant microenvironments.

Divergence-Free Constrained Phase Unwrapping and Denoising for 4D Flow MRI Using Weighted Least-Squares.

A novel divergence-free constrained phase unwrapping method was proposed and evaluated for 4D flow MRI. The unwrapped phase field was obtained by integrating the phase variations estimated from the wrapped phase data using weighted least-squares. The divergence-free constraint for incompressible blood flow was incorporated to regulate and denoise the resulting phase field. The proposed method was tested on synthetic phase data of left ventricular flow and in vitro 4D flow measurement of Poiseuille flow. The method was additionally applied to in vivo 4D flow measurements in the thoracic aorta from 30 human subjects. The performance of the proposed method was compared to the state-of-the-art 4D single-step Laplacian algorithm. The synthetic phase data were completely unwrapped by the proposed method for all the cases with velocity encoding (venc) as low as 20% of the maximum velocity and signal-to-noise ratio as low as 5. The in vitro Poiseuille flow data were completely unwrapped with a 60% increase in the velocity-to-noise ratio. For the in-vivo aortic datasets with venc ratio less than 0.4, the proposed method significantly improved the success rate by as much as 40% and reduced the velocity error levels by a factor of 10 compared to the state-of-the-art method. The divergence-free constrained method exhibits reliability and robustness on phase unwrapping and shows improved accuracy of velocity and hemodynamic quantities by unwrapping the low-venc 4D flow MRI data.

Computational Hemodynamic Modeling of Arterial Aneurysms: A Mini-Review.

Arterial aneurysms are pathological dilations of blood vessels, which can be of clinical concern due to thrombosis, dissection, or rupture. Aneurysms can form throughout the arterial system, including intracranial, thoracic, abdominal, visceral, peripheral, or coronary arteries. Currently, aneurysm diameter and expansion rates are the most commonly used metrics to assess rupture risk. Surgical or endovascular interventions are clinical treatment options, but are invasive and associated with risk for the patient. For aneurysms in locations where thrombosis is the primary concern, diameter is also used to determine the level of therapeutic anticoagulation, a treatment that increases the possibility of internal bleeding. Since simple diameter is often insufficient to reliably determine rupture and thrombosis risk, computational hemodynamic simulations are being developed to help assess when an intervention is warranted. Created from subject-specific data, computational models have the potential to be used to predict growth, dissection, rupture, and thrombus-formation risk based on hemodynamic parameters, including wall shear stress, oscillatory shear index, residence time, and anomalous blood flow patterns. Generally, endothelial damage and flow stagnation within aneurysms can lead to coagulation, inflammation, and the release of proteases, which alter extracellular matrix composition, increasing risk of rupture. In this review, we highlight recent work that investigates aneurysm geometry, model parameter assumptions, and other specific considerations that influence computational aneurysm simulations. By highlighting modeling validation and verification approaches, we hope to inspire future computational efforts aimed at improving our understanding of aneurysm pathology and treatment risk stratification.

4D Flow MRI Pressure Estimation Using Velocity Measurement-Error-Based Weighted Least-Squares.

This work introduces a 4D flow magnetic resonance imaging (MRI) pressure reconstruction method which employs weighted least-squares (WLS) for pressure integration. Pressure gradients are calculated from the velocity fields, and velocity errors are estimated from the velocity divergence for incompressible flow. Pressure gradient errors are estimated by propagating the velocity errors through Navier-Stokes momentum equation. A weight matrix is generated based on the pressure gradient errors, then employed for pressure reconstruction. The pressure reconstruction method was demonstrated and analyzed using synthetic velocity fields as well as Poiseuille flow measured using in vitro 4D flow MRI. Performance of the proposed WLS method was compared to the method of solving the pressure Poisson equation which has been the primary method used in the previous studies. Error analysis indicated that the proposed method is more robust to velocity measurement errors. Improvement on pressure results was found to be more significant for the cases with spatially-varying velocity error level, with reductions in error ranging from 50% to over 200%. Finally, the method was applied to flow in patient-specific cerebral aneurysms. Validation was performed with in vitro flow data collected using Particle Tracking Velocimetry (PTV) and in vivo flow measurement obtained using 4D flow MRI. Pressure calculated by WLS, as opposed to the Poisson equation, was more consistent with the flow structures and showed better agreement between the in vivo and in vitro data. These results suggest the utility of WLS method to obtain reliable pressure field from clinical flow measurement data.

Multi-modality cerebral aneurysm haemodynamic analysis: in vivo 4D flow MRI, in vitro volumetric particle velocimetry and in silico computational fluid dynamics.

Typical approaches to patient-specific haemodynamic studies of cerebral aneurysms use image-based computational fluid dynamics (CFD) and seek to statistically correlate parameters such as wall shear stress (WSS) and oscillatory shear index (OSI) to risk of growth and rupture. However, such studies have reported contradictory results, emphasizing the need for in-depth multi-modality haemodynamic metric evaluation. In this work, we used in vivo 4D flow MRI data to inform in vitro particle velocimetry and CFD modalities in two patient-specific cerebral aneurysm models (basilar tip and internal carotid artery). Pulsatile volumetric particle velocimetry experiments were conducted, and the particle images were processed using Shake-the-Box, a particle tracking method. Distributions of normalized WSS and relative residence time were shown to be highly yet inconsistently affected by minor flow field and spatial resolution variations across modalities, and specific relationships among these should be explored in future work. Conversely, OSI, a non-dimensional parameter, was shown to be more robust to the varying assumptions, limitations and spatial resolutions of each subject and modality. These results suggest a need for further multi-modality analysis as well as development of non-dimensional haemodynamic parameters and correlation of such metrics to aneurysm risk of growth and rupture.

Strain Mapping From Four-Dimensional Ultrasound Reveals Complex Remodeling in Dissecting Murine Abdominal Aortic Aneurysms.

Current in vivo abdominal aortic aneurysm (AAA) imaging approaches tend to focus on maximum diameter but do not measure three-dimensional (3D) vascular deformation or strain. Complex vessel geometries, heterogeneous wall compositions, and surrounding structures can all influence aortic strain. Improved understanding of complex aortic kinematics has the potential to increase our ability to predict aneurysm expansion and eventual rupture. Here, we describe a method that combines four-dimensional (4D) ultrasound and direct deformation estimation to compute in vivo 3D Green-Lagrange strain in murine angiotensin II-induced suprarenal dissecting aortic aneurysms, a commonly used small animal model. We compared heterogeneous patterns of the maximum, first-component 3D Green-Lagrange strain with vessel composition from mice with varying AAA morphologies. Intramural thrombus and focal breakage in the medial elastin significantly reduced aortic strain. Interestingly, a dissection that was not detected with high-frequency ultrasound also experienced reduced strain, suggesting medial elastin breakage that was later confirmed via histology. These results suggest that in vivo measurements of 3D strain can provide improved insight into aneurysm disease progression. While further work is needed with both preclinical animal models and human imaging studies, this initial murine study indicates that vessel strain should be considered when developing an improved metric for predicting aneurysm growth and rupture.