Computational fluid dynamics simulations of blood flow regularized by 3D phase contrast MRI

On the importance of fundamental computational fluid dynamics toward a robust and reliable model of left atrial flows

Computational fluid dynamics (CFD) studies of left atrial flows have reached a sophisticated level, for example, revealing plausible relationships between hemodynamics and stresses with atrial fibrillation. However, little focus has been on fundamental fluid modeling of LA flows. The purpose of this study was to investigate the spatiotemporal convergence, along with the differences between high- (HR) versus normal-resolution/accuracy (NR) solution strategies, respectively. Rigid wall CFD simulations were conducted on 12 patient-specific left atrial geometries obtained from computed tomography scans, utilizing a second-order accurate and space/time-centered solver. The convergence studies showed an average variability of around 30% and 55% for time averaged wall shear stress (WSS), oscillatory shear index (OSI), relative residence time (RRT), and endothelial cell activation potential (ECAP), even between intermediate spatial and temporal resolutions, in the left atrium (LA) and left atrial appendage (LAA), respectively. The comparison between HR and NR simulations showed good correlation in the LA for WSS, RRT, and ECAP (R 2 > .9 ), but not for OSI (R 2 = .63 ). However, there were poor correlations in the LAA especially for OSI, RRT, and ECAP (R 2 = .55, .63, and .61, respectively), except for WSS (R 2 = .81 ). The errors are comparable to differences previously reported with disease correlations. To robustly predict atrial hemodynamics and stresses, numerical resolutions of 10 M elements (i.e., Δ x = ∼ .5 mm) and 10 k time-steps per cycle seem necessary (i.e., one order of magnitude higher than normally used in both space and time). In conclusion, attention to fundamental numerical aspects is essential toward establishing a plausible, robust, and reliable model of LA flows.

Implicit neural representations for unsupervised super-resolution and denoising of 4D flow MRI

BACKGROUND AND OBJECTIVE

4D flow magnetic resonance imaging provides time-resolved blood flow velocity measurements, but suffers from limitations in spatio-temporal resolution and noise. In this study, we investigated the use of sinusoidal representation networks (SIRENs) to improve denoising and super-resolution of velocity fields measured by 4D flow MRI in the thoracic aorta.

METHODS

Efficient training of SIRENs in 4D was achieved by sampling voxel coordinates and enforcing the no-slip condition at the vessel wall. A set of synthetic measurements were generated from computational fluid dynamics simulations, reproducing different noise levels. The influence of SIREN architecture was systematically investigated, and the performance of our method was compared to existing approaches for 4D flow denoising and super-resolution.

RESULTS

Compared to existing techniques, a SIREN with 300 neurons per layer and 20 layers achieved lower errors (up to 50% lower vector normalized root mean square error, 42% lower magnitude normalized root mean square error, and 15% lower direction error) in velocity and wall shear stress fields. Applied to real 4D flow velocity measurements in a patient-specific aortic aneurysm, our method produced denoised and super-resolved velocity fields while maintaining accurate macroscopic flow measurements.

CONCLUSIONS

This study demonstrates the feasibility of using SIRENs for complex blood flow velocity representation from clinical 4D flow, with quick execution and straightforward implementation.

Effect of rheological models on pulsatile hemodynamics in a multiply afflicted descending human aortic network

In the cardiovascular diseased (CVD) conditions, it is essential to choose a suitable rheological model for capturing the correct physics behind the hemodynamic in the multiply afflicted diseased arterial network. This study investigates the effect of blood rheology on hemodynamics in a blood vessel with abdominal aortic aneurysm (AAA) and right internal iliac stenosis (RIIAS). A model with AAA and RIIAS is reconstructed from a human subject's computed tomography (CT) data. Localized mesh generation and pulsatile inflow condition are considered. Non-Newtonian models such as the Power-law, Carreau, Cross, and Herschel Berkley models are used in simulations. The outcome from a validated computational model is compared with the Newtonian model to identify the suitable model for dealing with pathological complications under consideration. The capabilities and significance of various rheological models are also examined via Wall Pressure (WP), Wall Shear Stress (WSS), velocity, Global non-Newtonian importance factor (IG), Vorticity Streamlines, and Swirling Strength. It is noted that during the entire cardiac cycle, the IG factor of the cross model is found to be relatively more significant. Power Law depicts larger IG factor during peak systole and early diastole. Also, the cross model depicts larger WSS, WPS, swirling strength distribution and vorticity during the peak systolic and diastolic phases It is noted that IG ∼0.02 is an appropriate non-Newtonian blood activity cut-off value in the descending abdominal artery having AAA and RIIAS. The critical important WSS values are in the range of 0-9 Pa which is stated in WSS contour plot.

Recent developments in modeling, imaging, and monitoring of cardiovascular diseases using machine learning

Cardiovascular diseases are the leading cause of mortality, morbidity, and hospitalization around the world. Recent technological advances have facilitated analyzing, visualizing, and monitoring cardiovascular diseases using emerging computational fluid dynamics, blood flow imaging, and wearable sensing technologies. Yet, computational cost, limited spatiotemporal resolution, and obstacles for thorough data analysis have hindered the utility of such techniques to curb cardiovascular diseases. We herein discuss how leveraging machine learning techniques, and in particular deep learning methods, could overcome these limitations and offer promise for translation. We discuss the remarkable capacity of recently developed machine learning techniques to accelerate flow modeling, enhance the resolution while reduce the noise and scanning time of current blood flow imaging techniques, and accurate detection of cardiovascular diseases using a plethora of data collected by wearable sensors.

Automated analysis of mitochondrial dimensions in mesenchymal stem cells: Current methods and future perspectives

As centre of energy production and key regulators of metabolic and cellular signaling pathways, the integrity of mitochondria is essential for mesenchymal stem cell function in tissue regeneration. Alterations in the size, shape and structural organization of mitochondria are correlated with the physiological state of the cell and its environment and could be used as diagnostic biomarkers. Therefore, high-throughput experimental and computational techniques are crucial to ensure adequate correlations between mitochondrial function and disease phenotypes. The emerge of microfluidic technologies can address the shortcomings of traditional methods to determine mitochondrial dimensions for diagnostic and therapeutic use. This review discusses optical detection methods compatible with microfluidics to measure mitochondrial dynamics and their potential for clinical stem cell research targeting mitochondrial dysfunction.

On the identification of hypoxic regions in subject-specific cerebral vasculature by combined CFD/MRI

A long-time exposure to lack of oxygen (hypoxia) in some regions of the cerebrovascular system is believed to be one of the causes of cerebral neurological diseases. In the present study, we show how a combination of magnetic resonance imaging (MRI) and computational fluid dynamics (CFD) can provide a non-invasive alternative for studying blood flow and transport of oxygen within the cerebral vasculature. We perform computer simulations of oxygen mass transfer in the subject-specific geometry of the circle of Willis. The computational domain and boundary conditions are based on four-dimensional (4D)-flow MRI measurements. Two different oxygen mass transfer models are considered: passive (where oxygen is treated as a dilute chemical species in plasma) and active (where oxygen is bonded to haemoglobin) models. We show that neglecting haemoglobin transport results in a significant underestimation of the arterial wall mass transfer of oxygen. We identified the hypoxic regions along the arterial walls by introducing the critical thresholds that are obtained by comparison of the estimated range of Damköhler number (Da ⊂ 〈9; 57〉) with the local Sherwood number. Finally, we recommend additional validations of the combined MRI/CFD approach proposed here for larger groups of subject- or patient-specific brain vasculature systems.

The impact of 4D-Flow MRI spatial resolution on patient-specific CFD simulations of the thoracic aorta

Magnetic Resonance Imaging (MRI) is considered the gold standard of medical imaging technologies as it allows for accurate imaging of blood vessels. 4-Dimensional Flow Magnetic Resonance Imaging (4D-Flow MRI) is built on conventional MRI, and provides flow data in the three vector directions and a time resolved magnitude data set. As such it can be used to retrospectively calculate haemodynamic parameters of interest, such as Wall Shear Stress (WSS). However, multiple studies have indicated that a significant limitation of the imaging technique is the spatiotemporal resolution that is currently available. Recent advances have proposed and successfully integrated 4D-Flow MRI imaging techniques with Computational Fluid Dynamics (CFD) to produce patient-specific simulations that have the potential to aid in treatments,surgical decision making, and risk stratification. However, the consequences of using insufficient 4D-Flow MRI spatial resolutions on any patient-specific CFD simulations is currently unclear, despite being a recognised limitation. The research presented in this study aims to quantify the inaccuracies in patient-specific 4D-Flow MRI based CFD simulations that can be attributed to insufficient spatial resolutions when acquiring 4D-Flow MRI data. For this research, a patient has undergone four 4D-Flow MRI scans acquired at various isotropic spatial resolutions and patient-specific CFD simulations have subsequently been run using geometry and velocity data produced from each scan. It was found that compared to CFD simulations based on a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1.5\,{\text {mm}} \times 1.5\,{\text {mm}} \times 1.5\,{\text {mm}}$$\end{document}1.5mm×1.5mm×1.5mm, using a spatial resolution of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$4\,{\text {mm}} \times 4\,{\text {mm}} \times 4\,{\text {mm}}$$\end{document}4mm×4mm×4mm substantially underestimated the maximum velocity magnitude at peak systole by \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$110.55\%$$\end{document}110.55%. The impacts of 4D-Flow MRI spatial resolution on WSS calculated from CFD simulations have been investigated and it has been shown that WSS is underestimated in CFD simulations that are based on a coarse 4D-Flow MRI spatial resolution. The authors have concluded that a minimum 4D-Flow MRI spatial resolution of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1.5\,{\text {mm}} \times 1.5\,{\text {mm}} \times 1.5\,{\text {mm}}$$\end{document}1.5mm×1.5mm×1.5mm must be used when acquiring 4D-Flow MRI data to perform patient-specific CFD simulations. A coarser spatial resolution will produce substantial differences within the flow field and geometry.

Inverse problems in blood flow modeling: A review

Mathematical and computational modeling of the cardiovascular system is increasingly providing non-invasive alternatives to traditional invasive clinical procedures. Moreover, it has the potential for generating additional diagnostic markers. In blood flow computations, the personalization of spatially distributed (i.e., 3D) models is a key step which relies on the formulation and numerical solution of inverse problems using clinical data, typically medical images for measuring both anatomy and function of the vasculature. In the last years, the development and application of inverse methods has rapidly expanded most likely due to the increased availability of data in clinical centers and the growing interest of modelers and clinicians in collaborating. Therefore, this work aims to provide a wide and comparative overview of literature within the last decade. We review the current state of the art of inverse problems in blood flows, focusing on studies considering fully dimensional fluid and fluid-solid models. The relevant physical models and hemodynamic measurement techniques are introduced, followed by a survey of mathematical data assimilation approaches used to solve different kinds of inverse problems, namely state and parameter estimation. An exhaustive discussion of the literature of the last decade is presented, structured by types of problems, models and available data.

Patient-Specific Inverse Modeling of In Vivo Cardiovascular Mechanics with Medical Image-Derived Kinematics as Input Data: Concepts, Methods, and Applications

Inverse modeling approaches in cardiovascular medicine are a collection of methodologies that can provide non-invasive patient-specific estimations of tissue properties, mechanical loads, and other mechanics-based risk factors using medical imaging as inputs. Its incorporation into clinical practice has the potential to improve diagnosis and treatment planning with low associated risks and costs. These methods have become available for medical applications mainly due to the continuing development of image-based kinematic techniques, the maturity of the associated theories describing cardiovascular function, and recent progress in computer science, modeling, and simulation engineering. Inverse method applications are multidisciplinary, requiring tailored solutions to the available clinical data, pathology of interest, and available computational resources. Herein, we review biomechanical modeling and simulation principles, methods of solving inverse problems, and techniques for image-based kinematic analysis. In the final section, the major advances in inverse modeling of human cardiovascular mechanics since its early development in the early 2000s are reviewed with emphasis on method-specific descriptions, results, and conclusions. We draw selected studies on healthy and diseased hearts, aortas, and pulmonary arteries achieved through the incorporation of tissue mechanics, hemodynamics, and fluid-structure interaction methods paired with patient-specific data acquired with medical imaging in inverse modeling approaches.

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.

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.

Data Assimilation by Stochastic Ensemble Kalman Filtering to Enhance Turbulent Cardiovascular Flow Data From Under-Resolved Observations

We propose a data assimilation methodology that can be used to enhance the spatial and temporal resolution of voxel-based data as it may be obtained from biomedical imaging modalities. It can be used to improve the assessment of turbulent blood flow in large vessels by combining observed data with a computational fluid dynamics solver. The methodology is based on a Stochastic Ensemble Kalman Filter (SEnKF) approach and geared toward pulsatile and turbulent flow configurations. We describe the observed flow fields by a mean value and its covariance. These flow fields are combined with forecasts obtained from a direct numerical simulation of the flow field. The method is validated against canonical pulsatile and turbulent flows. Finally, it is applied to a clinically relevant configuration, namely the flow downstream of a bioprosthetic valve in an aorta phantom. It is demonstrated how the 4D flow field obtained from experimental observations can be enhanced by the data assimilation algorithm. Results show that the presented method is promising for future use with in vivo data from 4D Flow Magnetic Resonance Imaging (4D Flow MRI). 4D Flow MRI returns spatially and temporally averaged flow fields that are limited by the spatial and the temporal resolution of the tool. These averaged flow fields and the associated uncertainty might be used as observation data in the context of the proposed methodology.

A Hybrid Approach for Cardiac Blood Flow Vortex Ring Identification Based on Optical Flow and Lagrangian Averaged Vorticity Deviation

Objective: The measurement of cardiac blood flow vortex characteristics can help to facilitate the analysis of blood flow dynamics that regulates heart function. However, the complexity of cardiac flow along with other physical limitations makes it difficult to adequately identify the dominant vortices in a heart chamber, which play a significant role in regulating the heart function. Although the existing vortex quantification methods can achieve this goal, there are still some shortcomings: such as low precision, and ignoring the center of the vortex without the description of vortex deformation processes. To address these problems, an optical flow Lagrangian averaged vorticity deviation (Optical flow-LAVD) method is proposed.

Methodology: We examined the flow within the right atrium (RA) of the participants’ hearts, by using a single set of scans pertaining to a slice at two-chamber short-axis orientation. Toward adequate extraction of the vortex ring characteristics, a novel approach driven by the Lagrangian averaged vorticity deviation (LAVD) was implemented and applied to characterize the trajectory integral associated with vorticity deviation and the spatial mean of rings, by using phase-contrast magnetic resonance imaging (PC-MRI) datasets as a case study. To interpolate the time frames between every larger discrete frame and minimize the error caused by constructing a continuous velocity field for the integral process of LAVD, we implemented the optical flow as an interpolator and introduced the backward warping as an intermediate frame synthesis basis, which is then used to generate higher quality continuous velocity fields.

Results: Our analytical study results showed that the proposed Optical flow-LAVD method can accurately identify vortex ring and continuous velocity fields, based on optical flow information, for yielding high reconstruction outcomes. Compared with the linear interpolation and phased-based frame interpolation methods, our proposed algorithm can generate more accurate synthesized PC-MRI.

Conclusion: This study has developed a novel Optical flow-LAVD model to accurately identify cardiac vortex rings, and minimize the associated errors caused by the construction of a continuous velocity field. Our paper presents a superior vortex characteristics detection method that may potentially aid the understanding of medical experts on the dynamics of blood flow within the heart.

Enhancement of cerebrovascular 4D flow MRI velocity fields using machine learning and computational fluid dynamics simulation data

Blood flow metrics obtained with four-dimensional (4D) flow phase contrast (PC) magnetic resonance imaging (MRI) can be of great value in clinical and experimental cerebrovascular analysis. However, limitations in both quantitative and qualitative analyses can result from errors inherent to PC MRI. One method that excels in creating low-error, physics-based, velocity fields is computational fluid dynamics (CFD). Augmentation of cerebral 4D flow MRI data with CFD-informed neural networks may provide a method to produce highly accurate physiological flow fields. In this preliminary study, the potential utility of such a method was demonstrated by using high resolution patient-specific CFD data to train a convolutional neural network, and then using the trained network to enhance MRI-derived velocity fields in cerebral blood vessel data sets. Through testing on simulated images, phantom data, and cerebrovascular 4D flow data from 20 patients, the trained network successfully de-noised flow images, decreased velocity error, and enhanced near-vessel-wall velocity quantification and visualization. Such image enhancement can improve experimental and clinical qualitative and quantitative cerebrovascular PC MRI analysis.

Application of physics-based flow models in cardiovascular medicine: Current practices and challenges

Personalized physics-based flow models are becoming increasingly important in cardiovascular medicine. They are a powerful complement to traditional methods of clinical decision-making and offer a wealth of physiological information beyond conventional anatomic viewing using medical imaging data. These models have been used to identify key hemodynamic biomarkers, such as pressure gradient and wall shear stress, which are associated with determining the functional severity of cardiovascular diseases. Importantly, simulation-driven diagnostics can help researchers understand the complex interplay between geometric and fluid dynamic parameters, which can ultimately improve patient outcomes and treatment planning. The possibility to compute and predict diagnostic variables and hemodynamics biomarkers can therefore play a pivotal role in reducing adverse treatment outcomes and accelerate development of novel strategies for cardiovascular disease management.

Data-driven cardiovascular flow modelling: examples and opportunities

High-fidelity blood flow modelling is crucial for enhancing our understanding of cardiovascular disease. Despite significant advances in computational and experimental characterization of blood flow, the knowledge that we can acquire from such investigations remains limited by the presence of uncertainty in parameters, low resolution, and measurement noise. Additionally, extracting useful information from these datasets is challenging. Data-driven modelling techniques have the potential to overcome these challenges and transform cardiovascular flow modelling. Here, we review several data-driven modelling techniques, highlight the common ideas and principles that emerge across numerous such techniques, and provide illustrative examples of how they could be used in the context of cardiovascular fluid mechanics. In particular, we discuss principal component analysis (PCA), robust PCA, compressed sensing, the Kalman filter for data assimilation, low-rank data recovery, and several additional methods for reduced-order modelling of cardiovascular flows, including the dynamic mode decomposition and the sparse identification of nonlinear dynamics. All techniques are presented in the context of cardiovascular flows with simple examples. These data-driven modelling techniques have the potential to transform computational and experimental cardiovascular research, and we discuss challenges and opportunities in applying these techniques in the field, looking ultimately towards data-driven patient-specific blood flow modelling.

Super-resolution and denoising of 4D-Flow MRI using physics-Informed deep neural nets

BACKGROUND AND OBJECTIVE

Time resolved three-dimensional phase contrast magnetic resonance imaging (4D-Flow MRI) has been used to non-invasively measure blood velocities in the human vascular system. However, issues such as low spatio-temporal resolution, acquisition noise, velocity aliasing, and phase-offset artifacts have hampered its clinical application. In this research, we developed a purely data-driven method for super-resolution and denoising of 4D-Flow MRI.

METHODS

The flow velocities, pressure, and the MRI image magnitude are modeled as a patient-specific deep neural net (DNN). For training, 4D-Flow MRI images in the complex Cartesian space are used to impose data-fidelity. Physics of fluid flow is imposed through regularization. Creative loss function terms have been introduced to handle noise and super-resolution. The trained patient-specific DNN can be sampled to generate noise-free high-resolution flow images. The proposed method has been implemented using the TensorFlow DNN library and tested on numerical phantoms and validated in-vitro using high-resolution particle image velocitmetry (PIV) and 4D-Flow MRI experiments on transparent models subjected to pulsatile flow conditions.

RESULTS

In case of numerical phantoms, we were able to increase spatial resolution by a factor of 100 and temporal resolution by a factor of 5 compared to the simulated 4D-Flow MRI. There is an order of magnitude reduction of velocity normalized root mean square error (vNRMSE). In case of the in-vitro validation tests with PIV as reference, there is similar improvement in spatio-temporal resolution. Although the vNRMSE is reduced by 50%, the method is unable to negate a systematic bias with respect to the reference PIV that is introduced by the 4D-Flow MRI measurement.

CONCLUSIONS

This work has demonstrated the feasibility of using the readily available machinery of deep learning to enhance 4D-Flow MRI using a purely data-driven method. Unlike current state-of-the-art methods, the proposed method is agnostic to geometry and boundary conditions and therefore eliminates the need for tedious tasks such as accurate image segmentation for geometry, image registration, and estimation of boundary flow conditions. Arbitrary regions of interest can be selected for processing. This work will lead to user-friendly analysis tools that will enable quantitative hemodynamic analysis of vascular diseases in a clinical setting.

Hemodynamic Data Assimilation in a Subject-specific Circle of Willis Geometry

PURPOSE

The anatomy of the circle of Willis (CoW), the brain's main arterial blood supply system, strongly differs between individuals, resulting in highly variable flow fields and intracranial vascularization patterns. To predict subject-specific hemodynamics with high certainty, we propose a data assimilation (DA) approach that merges fully 4D phase-contrast magnetic resonance imaging (PC-MRI) data with a numerical model in the form of computational fluid dynamics (CFD) simulations.

METHODS

To the best of our knowledge, this study is the first to provide a transient state estimate for the three-dimensional velocity field in a subject-specific CoW geometry using DA. High-resolution velocity state estimates are obtained using the local ensemble transform Kalman filter (LETKF).

RESULTS

Quantitative evaluation shows a considerable reduction (up to 90%) in the uncertainty of the velocity field state estimate after the data assimilation step. Velocity values in vessel areas that are below the resolution of the PC-MRI data (e.g., in posterior communicating arteries) are provided. Furthermore, the uncertainty of the analysis-based wall shear stress distribution is reduced by a factor of 2 for the data assimilation approach when compared to the CFD model alone.

CONCLUSION

This study demonstrates the potential of data assimilation to provide detailed information on vascular flow, and to reduce the uncertainty in such estimates by combining various sources of data in a statistically appropriate fashion.

Towards multi-modal data fusion for super-resolution and denoising of 4D-Flow MRI

4D-Flow magnetic resonance imaging (MRI) has enabled in vivo time-resolved measurement of three-dimensional blood flow velocities in the human vascular system. However, its clinical use has been hampered by two main issues, namely, low spatio-temporal resolution and acquisition noise. While patient-specific computational fluid dynamics (CFD) simulations can address the resolution and noise issues, its fidelity is impacted by accuracy of estimation of boundary conditions, model parameters, vascular geometry, and flow model assumptions. In this paper a scheme to address limitations of both modalities through data-fusion is presented. The solutions of the patient-specific CFD simulation are characterized using proper orthogonal decomposition (POD). Next, a process of projecting the 4D-Flow MRI data onto the POD basis and projection coefficient mapping using generalized dynamic mode decomposition (DMD) enables simultaneous super-resolution and denoising of 4D-Flow MRI. The method has been tested using numerical phantoms derived from patient-specific aneurysmal geometries and applied to in vivo 4D-Flow MRI data.

A Systematic Review for the Design of In Vitro Flow Studies of the Carotid Artery Bifurcation

PURPOSE

In vitro blood flow studies in carotid artery bifurcation models may contribute to understanding the influence of hemodynamics on carotid artery disease. However, the design of in vitro blood flow studies involves many steps and selection of imaging techniques, model materials, model design, and flow visualization parameters. Therefore, an overview of the possibilities and guidance for the design process is beneficial for researchers with less experience in flow studies.

METHODS

A systematic search to in vitro flow studies in carotid artery bifurcation models aiming at quantification and detailed flow visualization of blood flow dynamics results in inclusion of 42 articles.

RESULTS

Four categories of imaging techniques are distinguished: MRI, optical particle image velocimetry (PIV), ultrasound and miscellaneous techniques. Parameters for flow visualization are categorized into velocity, flow, shear-related, turbulent/disordered flow and other parameters. Model materials and design characteristics vary between study type.

CONCLUSIONS

A simplified three-step design process is proposed for better fitting and adequate match with the pertinent research question at hand and as guidance for less experienced flow study researchers. The three consecutive selection steps are: flow parameters, image modality, and model materials and designs. Model materials depend on the chosen imaging technique, whereas choice of flow parameters is independent from imaging technique and is therefore only determined by the goal of the study.

Hemodynamics of Cerebral Aneurysms: Connecting Medical Imaging and Biomechanical Analysis

In the last two decades, numerous studies have conducted patient-specific computations of blood flow dynamics in cerebral aneurysms and reported correlations between various hemodynamic metrics and aneurysmal disease progression or treatment outcomes. Nevertheless, intra-aneurysmal flow analysis has not been adopted in current clinical practice, and hemodynamic factors usually are not considered in clinical decision making. This review presents the state of the art in cerebral aneurysm imaging and image-based modeling, discussing the advantages and limitations of each approach and focusing on the translational value of hemodynamic analysis. Combining imaging and modeling data obtained from different flow modalities can improve the accuracy and fidelity of resulting velocity fields and flow-derived factors that are thought to affect aneurysmal disease progression. It is expected that predictive models utilizing hemodynamic factors in combination with patient medical history and morphological data will outperform current risk scores and treatment guidelines. Possible future directions include novel approaches enabling data assimilation and multimodality analysis of cerebral aneurysm hemodynamics.

Computational investigation of hemodynamics in hardshell venous reservoirs: A comparative study

Extracorporeal circulation using heart-lung-machines is associated with a profound activation of corpuscular and plasmatic components of circulating blood, which can also lead to deleterious events such as systemic inflammatory response and hemolysis. Individual components used to install the extracorporeal circulation have an impact on the level of activation, most predominantly membrane oxygenators and hardshell venous reservoirs as used in extracorporeal systems. The blood flows in two different hardshell reservoirs are computationally investigated. A special emphasis is placed on the prediction of an onset of transition and turbulence generation. Reynolds-averaged numerical simulations (RANS) based on a transitional turbulence model, as well as large eddy simulations (LES) are applied to achieve an accurate prediction. In the LES analysis, the non-Newtonian behavior of the blood is considered via the Carreau model. Blood damage potential is quantified applying the Modified Index of Hemolysis (MIH) based on the predicted flow fields. The results indicate that the flows in both reservoirs remain predominantly laminar. For one of the reservoirs, considerable turbulence generation is observed near the exit site, caused by the specific design for the connection with the drainage tube. This difference causes the MIH of this reservoir to be nearly twice as large as compared to the alternative design. However, a substantial improvement of these performance criteria can be expected by a local geometry modification.

Cerebral arteriovenous malformation venous stenosis is associated with hemodynamic changes at the draining vein-venous sinus junction

Cerebral arteriovenous malformations (AVMs) are an uncommon vascular anomaly that carry the risk of rupture and hemorrhage. Several factors have been implicated in the propensity of an AVM to bleed. One such factor is stenosis of AVM draining veins, as impairment of the AVM venous drainage system is associated with increased risk of intracranial hemorrhage. Currently, our understanding of the pathogenesis of AVM venous outflow stenosis is limited, as there is insufficient data on the blood flow patterns and local hemodynamic parameters of these draining veins. The angioarchitecture of AVMs features a nidus lacking a high resistance capillary network. Accordingly, our previous studies on AVM arterial feeders have demonstrated an abnormally high flow volume rate along with low pulsatility and resistance indices on quantitative magnetic resonance angiography. As such, AVM vessels endure high, non-physiologic levels of flow that may partially contribute to ectasia or stenosis depending on whether wall shear stress (WSS) is high or low, respectively. We hypothesize that AVM venous outflow stenosis occurs most commonly near the junction of the draining vein and the dural venous sinus. Increased flow volume rate through the AVM circuit coupled with the variation in compliance and rigidity between the walls of the draining vein and the dural venous sinus likely create turbulence of blood flow. The resulting flow separation, low WSS, and departure from axially aligned, unidirectional flow may create atherogenic conditions that can be implicated in venous intimal hyperplasia and outflow stenosis. We have previously found there to be a significant association between intimal hyperplasia risk factors and venous outflow stenosis. Additionally, we have found a significant association between age and likelihood as well as degree of stenosis, suggesting a progressive disease process. Similar conditions have been demonstrated in the pathophysiology of stenosis of the carotid artery and dialysis arteriovenous fistulas. In both of these conditions, the use of computational fluid dynamics (CFD) has been employed to characterize the local hemodynamic features that contribute to the pathogenesis of intimal hyperplasia and stenosis. We recommend the utilization of CFD to characterize the anatomic and hemodynamic features of AVM venous outflow stenosis. An improved understanding of the possible causative features of venous outflow stenosis may impact how clinicians choose to manage the treatment of patients with AVMs.

Blind blur assessment of MRI images using parallel multiscale difference of Gaussian filters

Background

Rician noise, bias fields and blur are the common distortions that degrade MRI images during acquisition. Blur is unique in comparison to Rician noise and bias fields because it can be introduced into an image beyond the acquisition stage such as postacquisition processing and the manifestation of pathological conditions. Most current blur assessment algorithms are designed and validated on consumer electronics such as television, video and mobile appliances. The few algorithms dedicated to medical images either requires a reference image or incorporate manual approach. For these reasons it is difficult to compare quality measures from different images and images with different contents. Furthermore, they will not be suitable in environments where large volumes of images are processed. In this report we propose a new blind blur assessment method for different types of MRI images and for different applications including automated environments.

Methods

Two copies of the test image are generated. Edge map is extracted by separately convolving each copy of the test image with two parallel difference of Gaussian filters. At the start of the multiscale representation, the initial output of the filters are equal. In subsequent scales of the multiscale representation, each filter is tuned to different operating parameters over the same fixed range of Gaussian scales. The filters are termed low and high energy filters based on their characteristics to successively attenuate and highlight edges over the range of multiscale representation. Quality score is predicted from the distance between the normalized mean of the edge maps at the final output of the filters.

Results

The proposed method was evaluated on cardiac and brain MRI images. Performance evaluation shows that the quality index has very good correlation with human perception and will be suitable for application in routine clinical practice and clinical research.

SIMULATION ANALYSIS OF BLOOD FLOW IN ARTERIES OF THE HUMAN ARM

Arteries in the upper limb play important roles in the circulation system of the human body. In particular, the radial artery has received considerable attention in traditional Chinese medicine for thousands of years. Here, a 3D model for the arm arteries has been created uncomplicated, in a Chinese adult's left hand, from the magnetic resonance imaging data, using professional modeling software to restore the basic structure of the arm artery in human body, before being imported to Ansys software for simulation. Blood model has been only simulated, and using the blood density of constant parameter and viscosity using the Carreau fluid model, and using viscous-laminar model of Fluent to obtain the velocity profile, static pressure and shear stress in the brachial, interosseous, ulnar, radial and palmar arch arteries. In particular, the brachial and bifurcations have the high pressure and velocity profiles. The simulation results obtained here are also validated by those published in the literature and proved the ulnar artery prevails over the radial artery as a blood supplier to the vessels in the wrist and hand.

Merging computational fluid dynamics and 4D Flow MRI using proper orthogonal decomposition and ridge regression

Time resolved phase-contrast magnetic resonance imaging 4D-PCMR (also called 4D Flow MRI) data while capable of non-invasively measuring blood velocities, can be affected by acquisition noise, flow artifacts, and resolution limits. In this paper, we present a novel method for merging 4D Flow MRI with computational fluid dynamics (CFD) to address these limitations and to reconstruct de-noised, divergence-free high-resolution flow-fields. Proper orthogonal decomposition (POD) is used to construct the orthonormal basis of the local sampling of the space of all possible solutions to the flow equations both at the low-resolution level of the 4D Flow MRI grid and the high-level resolution of the CFD mesh. Low-resolution, de-noised flow is obtained by projecting in vivo 4D Flow MRI data onto the low-resolution basis vectors. Ridge regression is then used to reconstruct high-resolution de-noised divergence-free solution. The effects of 4D Flow MRI grid resolution, and noise levels on the resulting velocity fields are further investigated. A numerical phantom of the flow through a cerebral aneurysm was used to compare the results obtained using the POD method with those obtained with the state-of-the-art de-noising methods. At the 4D Flow MRI grid resolution, the POD method was shown to preserve the small flow structures better than the other methods, while eliminating noise. Furthermore, the method was shown to successfully reconstruct details at the CFD mesh resolution not discernible at the 4D Flow MRI grid resolution. This method will improve the accuracy of the clinically relevant flow-derived parameters, such as pressure gradients and wall shear stresses, computed from in vivo 4D Flow MRI data.

Computational Fluid Dynamics modeling of contrast transport in basilar aneurysms following flow-altering surgeries

In vivo measurement of blood velocity fields and flow descriptors remains challenging due to image artifacts and limited resolution of current imaging methods; however, in vivo imaging data can be used to inform and validate patient-specific computational fluid dynamics (CFD) models. Image-based CFD can be particularly useful for planning surgical interventions in complicated cases such as fusiform aneurysms of the basilar artery, where it is crucial to alter pathological hemodynamics while preserving flow to the distal vasculature. In this study, patient-specific CFD modeling was conducted for two basilar aneurysm patients considered for surgical treatment. In addition to velocity fields, transport of contrast agent was simulated for the preoperative and postoperative conditions using two approaches. The transport of a virtual contrast passively following the flow streamlines was simulated to predict post-surgical flow regions prone to thrombus deposition. In addition, the transport of a mixture of blood with an iodine-based contrast agent was modeled to compare and verify the CFD results with X-ray angiograms. The CFD-predicted patterns of contrast flow were qualitatively compared to in vivo X-ray angiograms acquired before and after the intervention. The results suggest that the mixture modeling approach, accounting for the flow rates and properties of the contrast injection, is in better agreement with the X-ray angiography data. The virtual contrast modeling assessed the residence time based on flow patterns unaffected by the injection procedure, which makes the virtual contrast modeling approach better suited for prediction of thrombus deposition, which is not limited to the peri-procedural state.

Hemodynamic changes in a rat parietal cortex after endothelin-1-induced middle cerebral artery occlusion monitored by optical coherence tomography

A blockage of the middle cerebral artery (MCA) on the cortical branch will seriously affect the blood supply of the cerebral cortex. Real-time monitoring of MCA hemodynamic parameters is critical for therapy and rehabilitation. Optical coherence tomography (OCT) is a powerful imaging modality that can produce not only structural images but also functional information on the tissue. We use OCT to detect hemodynamic changes after MCA branch occlusion. We injected a selected dose of endothelin-1 (ET-1) at a depth of 1 mm near the MCA and let the blood vessels follow a process first of occlusion and then of slow reperfusion as realistically as possible to simulate local cerebral ischemia. During this period, we used optical microangiography and Doppler OCT to obtain multiple hemodynamic MCA parameters. The change trend of these parameters from before to after ET-1 injection clearly reflects the dynamic regularity of the MCA. These results show the mechanism of the cerebral ischemia-reperfusion process after a transient middle cerebral artery occlusion and confirm that OCT can be used to monitor hemodynamic parameters.