Flow imaging and computing: large artery hemodynamics

A GPU-Based, Real-Time Dealiasing Framework for High-Frame-Rate Vector Doppler Imaging

Vector Doppler is well regarded as a potential way of deriving flow vectors to intuitively visualize complex flow profiles, especially when it is implemented at high frame rates. However, this technique's performance is known to suffer from aliasing artifacts. There is a dire need to devise real-time dealiasing solutions for vector Doppler. In this article, we present a new methodological framework for achieving aliasing-resistant flow vector estimation at real-time throughput from precalculated Doppler frequencies. Our framework comprises a series of compute kernels that have synergized: 1) an extended least squares vector Doppler (ELS-VD) algorithm; 2) single-instruction, multiple-thread (SIMT) processing principles; and 3) implementation on a graphical processing unit (GPU). Results show that this new framework, when executed on an RTX-2080 GPU, can effectively generate aliasing-free flow vector maps using high-frame-rate imaging datasets acquired from multiple transmit-receive angle pairs in a carotid phantom imaging scenario. Over the entire cardiac cycle, the frame processing time for aliasing-resistant vector estimation was measured to be less than 16 ms, which corresponds to a minimum processing throughput of 62.5 frames/s. In a human femoral bifurcation imaging trial with fast flow (150 cm/s), our framework was found to be effective in resolving two-cycle aliasing artifacts at a minimum throughput of 53 frames/s. The framework's processing throughput was generally in the real-time range for practical combinations of ELS-VD algorithmic parameters. Overall, this work represents the first demonstration of real-time, GPU-based aliasing-resistant vector flow imaging using vector Doppler estimation principles.

Evidence Accumulates: Patients with Ascending Aneurysms Are Strongly Protected from Atherosclerotic Disease

Ascending thoracic aortic aneurysms may be fatal upon rupture or dissection and remain a leading cause of death in the developed world. Understanding the pathophysiology of the development of ascending thoracic aortic aneurysms may help reduce the morbidity and mortality of this disease. In this review, we will discuss our current understanding of the protective relationship between ascending thoracic aortic aneurysms and the development of atherosclerosis, including decreased carotid intima-media thickness, low-density lipoprotein levels, coronary and aortic calcification, and incidence of myocardial infarction. We also propose several possible mechanisms driving this relationship, including matrix metalloproteinase proteins and transforming growth factor-β.

Direct 0D-3D coupling of a lattice Boltzmann methodology for fluid-structure aortic flow simulations

This work introduces a numerical approach and implementation for the direct coupling of arbitrary complex ordinary differential equation- (ODE-)governed zero-dimensional (0D) boundary conditions to three-dimensional (3D) lattice Boltzmann-based fluid-structure systems for hemodynamics studies. In particular, a most complex configuration is treated by considering a dynamic left ventricle- (LV-)elastance heart model which is governed by (and applied as) a nonlinear, non-stationary hybrid ODE-Dirichlet system. Other ODE-based boundary conditions, such as lumped parameter Windkessel models for truncated vasculature, are also considered. Performance studies of the complete 0D-3D solver, including its treatment of the lattice Boltzmann fluid equations and elastodynamics equations as well as their interactions, is conducted through a variety of benchmark and convergence studies that demonstrate the ability of the coupled 0D-3D methodology in generating physiological pressure and flow waveforms-ultimately enabling the exploration of various physical and physiological parameters for hemodynamics studies of the coupled LV-arterial system. The methods proposed in this paper can be easily applied to other ODE-based boundary conditions as well as to other fluid problems that are modeled by 3D lattice Boltzmann equations and that require direct coupling of dynamic 0D boundary conditions.

Reducing Geometric Uncertainty in Computational Hemodynamics by Deep Learning-Assisted Parallel-Chain MCMC

Computational hemodynamic modeling has been widely used in cardiovascular research and healthcare. However, the reliability of model predictions is largely dependent on the uncertainties of modeling parameters and boundary conditions, which should be carefully quantified and further reduced with available measurements. In this work, we focus on propagating and reducing the uncertainty of vascular geometries within a Bayesian framework. A novel deep learning (DL)-assisted parallel Markov chain Monte Carlo (MCMC) method is presented to enable efficient Bayesian posterior sampling and geometric uncertainty reduction. A DL model is built to approximate the geometry-to-hemodynamic map, which is trained actively using online data collected from parallel MCMC chains and utilized for early rejection of unlikely proposals to facilitate convergence with less expensive full-order model evaluations. Numerical studies on two-dimensional aortic flows are conducted to demonstrate the effectiveness and merit of the proposed method.

Characterization of Flow Dynamics in the Pulmonary Bifurcation of Patients With Repaired Tetralogy of Fallot: A Computational Approach

The hemodynamic environment of the pulmonary bifurcation is of great importance for adult patients with repaired tetralogy of Fallot (rTOF) due to possible complications in the pulmonary valve and narrowing of the left pulmonary artery (LPA). The aim of this study was to computationally investigate the effect of geometrical variability and flow split on blood flow characteristics in the pulmonary trunk of patient-specific models. Data from a cohort of seven patients was used retrospectively and the pulmonary hemodynamics was investigated using averaged and MRI-derived patient-specific boundary conditions on the individualized models, as well as a statistical mean geometry. Geometrical analysis showed that curvature and tortuosity are higher in the LPA branch, compared to the right pulmonary artery (RPA), resulting in complex flow patterns in the LPA. The computational analysis also demonstrated high time-averaged wall shear stress (TAWSS) at the outer wall of the LPA and the wall of the RPA proximal to the junction. Similar TAWSS patterns were observed for averaged boundary conditions, except for a significantly modified flow split assigned at the outlets. Overall, this study enhances our understanding about the flow development in the pulmonary bifurcation of rTOF patients and associates some morphological characteristics with hemodynamic parameters, highlighting the importance of patient-specificity in the models. To confirm these findings, further studies are required with a bigger cohort of patients.

Seven Mathematical Models of Hemorrhagic Shock

Although mathematical modelling of pressure-flow dynamics in the cardiocirculatory system has a lengthy history, readily finding the appropriate model for the experimental situation at hand is often a challenge in and of itself. An ideal model would be relatively easy to use and reliable, besides being ethically acceptable. Furthermore, it would address the pathogenic features of the cardiovascular disease that one seeks to investigate. No universally valid model has been identified, even though a host of models have been developed. The object of this review is to describe several of the most relevant mathematical models of the cardiovascular system: the physiological features of circulatory dynamics are explained, and their mathematical formulations are compared. The focus is on the whole-body scale mathematical models that portray the subject's responses to hypovolemic shock. The models contained in this review differ from one another, both in the mathematical methodology adopted and in the physiological or pathological aspects described. Each model, in fact, mimics different aspects of cardiocirculatory physiology and pathophysiology to varying degrees: some of these models are geared to better understand the mechanisms of vascular hemodynamics, whereas others focus more on disease states so as to develop therapeutic standards of care or to test novel approaches. We will elucidate key issues involved in the modeling of cardiovascular system and its control by reviewing seven of these models developed to address these specific purposes.

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.

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.

Fluid shear stress modulates endothelial inflammation by targeting LIMS2

Mechanosensitive genes regulate multiple cardiovascular pathophysiological processes and disorders; however, the role of flow-sensitive genes in atherosclerosis is still unknown. In this study, we identify LIM Zinc Finger Domain Containing 2 (LIMS2) that acts as a mechanosensitive gene downregulated by disturbed flow (d-flow) both in human endothelial cells (ECs) in vitro and in mice in vivo. Mechanistically, d-flow suppresses LIMS2 expression, which leads to endothelial inflammation by upregulating typical inflammatory factors, VCAM-1, and ICAM-1 in human ECs. The findings indicate that LIMS2, the new flow-sensitive gene, may help us to find a new insight to explain how d-flow caused endothelial inflammation and provide a new therapeutic approach for atherosclerosis in the future.

Role of flow-sensitive microRNAs and long noncoding RNAs in vascular dysfunction and atherosclerosis

Atherosclerosis is the primary underlying cause of myocardial infarction, ischemic stroke, and peripheral artery disease. The disease preferentially occurs in arterial regions exposed to disturbed blood flow, in part, by altering expression of flow-sensitive coding- and non-coding genes. In this review, we summarize the role of noncoding RNAs, [microRNAs (miRNAs) and long noncoding RNAs(lncRNAs)], as regulators of gene expression and outline their relationship to the pathogenesis of atherosclerosis. While miRNAs are small noncoding genes that post-transcriptionally regulate gene expression by targeting mRNA transcripts, the lncRNAs regulate gene expression by diverse mechanisms, which are still emerging and incompletely understood. We focused on multiple flow-sensitive miRNAs such as, miR-10a, -19a, -23b, -17~92, -21, -663, -92a, -143/145, -101, -126, -712, -205, and -155 that play a critical role in endothelial function and atherosclerosis by targeting inflammation, cell cycle, proliferation, migration, apoptosis, and nitric oxide signaling. Flow-dependent regulation of lncRNAs is just emerging, and their role in vascular dysfunction and atherosclerosis is unknown. Here, we discuss the flow-sensitive lncRNA STEEL along with other lncRNAs studied in the context of vascular pathophysiology and atherosclerosis such as MALAT1, MIAT1, ANRIL, MYOSLID, MEG3, SENCR, SMILR, LISPR1, and H19. Also discussed is the use of these noncoding RNAs as potential biomarkers and therapeutics to reduce and regress atherosclerosis.

Bayesian sensitivity analysis of a 1D vascular model with Gaussian process emulators

One-dimensional models of the cardiovascular system can capture the physics of pulse waves but involve many parameters. Since these may vary among individuals, patient-specific models are difficult to construct. Sensitivity analysis can be used to rank model parameters by their effect on outputs and to quantify how uncertainty in parameters influences output uncertainty. This type of analysis is often conducted with a Monte Carlo method, where large numbers of model runs are used to assess input-output relations. The aim of this study was to demonstrate the computational efficiency of variance-based sensitivity analysis of 1D vascular models using Gaussian process emulators, compared to a standard Monte Carlo approach. The methodology was tested on four vascular networks of increasing complexity to analyse its scalability. The computational time needed to perform the sensitivity analysis with an emulator was reduced by the 99.96% compared to a Monte Carlo approach. Despite the reduced computational time, sensitivity indices obtained using the two approaches were comparable. The scalability study showed that the number of mechanistic simulations needed to train a Gaussian process for sensitivity analysis was of the order O(d), rather than O(d×103) needed for Monte Carlo analysis (where d is the number of parameters in the model). The efficiency of this approach, combined with capacity to estimate the impact of uncertain parameters on model outputs, will enable development of patient-specific models of the vascular system, and has the potential to produce results with clinical relevance.

Modeling of coarctation of aorta in human fetuses using 3D/4D fetal echocardiography and computational fluid dynamics

OBJECTIVES

We sought to develop a hemodynamic model of aortic and ductal arches using computational fluid dynamics (CFD) and 3D/4D spatio-temporal image correlation (STIC) fetal echocardiography and to investigate the hemodynamics of coarctation of aorta (CoA) in human fetuses using this approach.

METHODS

We obtained 3D/4D STIC fetal echocardiographic images of the aortic and ductal arches (DA) in five normal fetuses. Based on these images, we simulated the hemodynamics in the two arches using CFD. Subsequently, we reduced the dimensions of aortic isthmus from 100% to 85%, 70%, 55%, 40%, and 25% of the original dimension digitally. Numerical simulation was repeated in each condition, and flow profile, velocity, pressure, and wall shear stress (WSS) were compared with those of the baseline normal aortic and ductal arches.

RESULTS

With the progressive narrowing in the aortic isthmus, there were alterations in the flow profile, velocity, pressure, and WSS. The downstream vortexes disappeared, and the double helix profile became single helix. When the aortic isthmus reduced by 55% in dimension, there was an exponential increase in velocity and WSS and decrease in pressure.

CONCLUSIONS

The aortic and ductal arch geometry and flow lead to the alterations in flow profile, velocity, pressure, and WSS in the aortic isthmus in normal and CoA models, which are conductive of ductal issue migration into these areas. A 55% reduction in the dimension of aortic isthmus is associated with exponential change in velocity, pressure, and WSS, a probable threshold for hemodynamically significant CoA.

Imaging in Vascular Access

This review examines four imaging modalities; ultrasound (US), digital subtraction angiography (DSA), magnetic resonance imaging (MRI) and computed tomography (CT), that have common or potential applications in vascular access (VA). The four modalities are reviewed under their primary uses, techniques, advantages and disadvantages, and future directions that are specific to VA. Currently, US is the most commonly used modality in VA because it is cheaper (relative to other modalities), accessible, non-ionising, and does not require the use of contrast agents. DSA is predominantly only performed when an intervention is indicated. MRI is limited by its cost and the time required for image acquisition that mainly confines it to the realm of research where high resolution is required. CT’s short acquisition times and high resolution make it useful as a problem-solving tool in complex cases, although accessibility can be an issue. All four imaging modalities have advantages and disadvantages that limit their use in this particular patient cohort. Current imaging in VA comprises an integrated approach with each modality providing particular uses dependent on their capabilities. MRI and CT, which currently have limited use, may have increasingly important future roles in complex cases where detailed analysis is required.

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.

Investigation of Ultrasound-Measured Flow Velocity, Flow Rate and Wall Shear Rate in Radial and Ulnar Arteries Using Simulation

Parameters of blood flow measured by ultrasound in radial and ulnar arteries, such as flow velocity, flow rate and wall shear rate, are widely used in clinical practice and clinical research. Investigation of these measurements is useful for evaluating accuracy and providing knowledge of error sources. A method for simulating the spectral Doppler ultrasound measurement process was developed with computational fluid dynamics providing flow-field data. Specific scanning factors were adjusted to investigate their influence on estimation of the maximum velocity waveform, and flow rate and wall shear rate were derived using the Womersley equation. The overestimation in maximum velocity increases greatly (peak systolic from about 10% to 30%, time-averaged from about 30% to 50%) when the beam-vessel angle is changed from 30° to 70°. The Womersley equation was able to estimate flow rate in both arteries with less than 3% error, but performed better in the radial artery (2.3% overestimation) than the ulnar artery (15.4% underestimation) in estimating wall shear rate. It is concluded that measurements of flow parameters in the radial and ulnar arteries with clinical ultrasound scanners are prone to clinically significant errors.

A Robust and Subject-Specific Hemodynamic Model of the Lower Limb Based on Noninvasive Arterial Measurements

Cardiovascular diseases are currently the leading cause of mortality in the population of developed countries, due to the constant increase in cardiovascular risk factors, such as high blood pressure, cholesterol, overweight, tobacco use, lack of physical activity, etc. Numerous prospective and retrospective studies have shown that arterial stiffening is a relevant predictor of these diseases. Unfortunately, the arterial stiffness distribution across the human body is difficult to measure experimentally. We propose a numerical approach to determine the arterial stiffness distribution of an arterial network using a subject-specific one-dimensional model. The proposed approach calibrates the optimal parameters of the reduced-order model, including the arterial stiffness, by solving an inverse problem associated with the noninvasive in vivo measurements. An uncertainty quantification analysis has also been carried out to measure the contribution of the model input parameters variability, alone or by interaction with other inputs, to the variation of clinically relevant hemodynamic indices, here the arterial pulse pressure. The results obtained for a lower limb model, demonstrate that the numerical approach presented here can provide a robust and subject-specific tool to the practitioner, allowing an early and reliable diagnosis of cardiovascular diseases based on a noninvasive clinical examination.

Computational Hemodynamic Analysis for the Diagnosis of Atherosclerotic Changes in Intracranial Aneurysms: A Proof-of-Concept Study Using 3 Cases Harboring Atherosclerotic and Nonatherosclerotic Aneurysms Simultaneously

This was a proof-of-concept computational fluid dynamics (CFD) study designed to identify atherosclerotic changes in intracranial aneurysms. We selected 3 patients with multiple unruptured aneurysms including at least one with atherosclerotic changes and investigated whether an image-based CFD study could provide useful information for discriminating the atherosclerotic aneurysms. Patient-specific geometries were constructed from three-dimensional data obtained using rotational angiography. Transient simulations were conducted under patient-specific inlet flow rates measured by phase-contrast magnetic resonance velocimetry. In the postanalyses, we calculated time-averaged wall shear stress (WSS), oscillatory shear index, and relative residence time (RRT). The volume of blood flow entering aneurysms through the neck and the mean velocity of blood flow inside aneurysms were examined. We applied the age-of-fluid method to quantitatively assess the residence of blood inside aneurysms. Atherosclerotic changes coincided with regions exposed to disturbed blood flow, as indicated by low WSS and long RRT. Blood entered aneurysms in phase with inlet flow rates. The mean velocities of blood inside atherosclerotic aneurysms were lower than those inside nonatherosclerotic aneurysms. Blood in atherosclerotic aneurysms was older than that in nonatherosclerotic aneurysms, especially near the wall. This proof-of-concept study demonstrated that CFD analysis provided detailed information on the exchange and residence of blood that is useful for the diagnosis of atherosclerotic changes in intracranial aneurysms.

Omics-based approaches to understand mechanosensitive endothelial biology and atherosclerosis

Atherosclerosis is a multifactorial disease that preferentially occurs in arterial regions exposed to d-flow can be used to indicate disturbed flow or disturbed blood flow. The mechanisms by which d-flow induces atherosclerosis involve changes in the transcriptome, methylome, proteome, and metabolome of multiple vascular cells, especially endothelial cells. Initially, we begin with the pathogenesis of atherosclerosis and the changes that occur at multiple levels owing to d-flow, especially in the endothelium. Also, there are a variety of strategies used for the global profiling of the genome, transcriptome, miRNA-ome, DNA methylome, and metabolome that are important to define the biological and pathophysiological mechanisms of endothelial dysfunction and atherosclerosis. Finally, systems biology can be used to integrate these 'omics' datasets, especially those that derive data based on a single animal model, in order to better understand the pathophysiology of atherosclerosis development in a holistic manner and how this integrative approach could be used to identify novel molecular diagnostics and therapeutic targets to prevent or treat atherosclerosis. WIREs Syst Biol Med 2016, 8:378-401. doi: 10.1002/wsbm.1344 For further resources related to this article, please visit the WIREs website.

The role of endothelial mechanosensitive genes in atherosclerosis and omics approaches

Atherosclerosis is the leading cause of morbidity and mortality in the U.S., and is a multifactorial disease that preferentially occurs in regions of the arterial tree exposed to disturbed blood flow. The detailed mechanisms by which d-flow induces atherosclerosis involve changes in the expression of genes, epigenetic patterns, and metabolites of multiple vascular cells, especially endothelial cells. This review presents an overview of endothelial mechanobiology and its relation to the pathogenesis of atherosclerosis with special reference to the anatomy of the artery and the underlying fluid mechanics, followed by a discussion of a variety of experimental models to study the role of fluid mechanics and atherosclerosis. Various in vitro and in vivo models to study the role of flow in endothelial biology and pathobiology are discussed in this review. Furthermore, strategies used for the global profiling of the genome, transcriptome, miR-nome, DNA methylome, and metabolome, as they are important to define the biological and pathophysiological mechanisms of atherosclerosis. These "omics" approaches, especially those which derive data based on a single animal model, provide unprecedented opportunities to not only better understand the pathophysiology of atherosclerosis development in a holistic and integrative manner, but also to identify novel molecular and diagnostic targets.

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

Background

Phase contrast magnetic resonance imaging (PC-MRI) is used clinically for quantitative assessment of cardiovascular flow and function, as it is capable of providing directly-measured 3D velocity maps. Alternatively, vascular flow can be estimated from model-based computation fluid dynamics (CFD) calculations. CFD provides arbitrarily high resolution, but its accuracy hinges on model assumptions, while velocity fields measured with PC-MRI generally do not satisfy the equations of fluid dynamics, provide limited resolution, and suffer from partial volume effects. The purpose of this study is to develop a proof-of-concept numerical procedure for constructing a simulated flow field that is influenced by both direct PC-MRI measurements and a fluid physics model, thereby taking advantage of both the accuracy of PC-MRI and the high spatial resolution of CFD. The use of the proposed approach in regularizing 3D flow fields is evaluated.

Methods

The proposed algorithm incorporates both a Newtonian fluid physics model and a linear PC-MRI signal model. The model equations are solved numerically using a modified CFD algorithm. The numerical solution corresponds to the optimal solution of a generalized Tikhonov regularization, which provides a flow field that satisfies the flow physics equations, while being close enough to the measured PC-MRI velocity profile. The feasibility of the proposed approach is demonstrated on data from the carotid bifurcation of one healthy volunteer, and also from a pulsatile carotid flow phantom.

Results

The proposed solver produces flow fields that are in better agreement with direct PC-MRI measurements than CFD alone, and converges faster, while closely satisfying the fluid dynamics equations. For the implementation that provided the best results, the signal-to-error ratio (with respect to the PC-MRI measurements) in the phantom experiment was 6.56 dB higher than that of conventional CFD; in the in vivo experiment, it was 2.15 dB higher.

Conclusions

The proposed approach allows partial or complete measurements to be incorporated into a modified CFD solver, for improving the accuracy of the resulting flow fields estimates. This can be used for reducing scan time, increasing the spatial resolution, and/or denoising the PC-MRI measurements.

Outflow boundary conditions for blood flow in arterial trees

In the modeling of the pulse wave in the systemic arterial tree, it is necessary to truncate small arterial crowns representing the networks of small arteries and arterioles. Appropriate boundary conditions at the truncation points are required to represent wave reflection effects of the truncated arterial crowns. In this work, we provide a systematic method to extract parameters of the three-element Windkessel model from the impedance of a truncated arterial tree or from experimental measurements of the blood pressure and flow rate at the inlet of the truncated arterial crown. In addition, we propose an improved three-element Windkessel model with a complex capacitance to accurately capture the fundamental-frequency time lag of the reflection wave with respect to the incident wave. Through our numerical simulations of blood flow in a single artery and in a large arterial tree, together with the analysis of the modeling error of the pulse wave in large arteries, we show that both a small truncation radius and the complex capacitance in the improved Windkessel model play an important role in reducing the modeling error, defined as the difference in dynamics induced by the structured tree model and the Windkessel models.

Vector projectile imaging: time-resolved dynamic visualization of complex flow patterns

Achieving non-invasive, accurate and time-resolved imaging of vascular flow with spatiotemporal fluctuations is well acknowledged to be an ongoing challenge. In this article, we present a new ultrasound-based framework called vector projectile imaging (VPI) that can dynamically render complex flow patterns over an imaging view at millisecond time resolution. VPI is founded on three principles: (i) high-frame-rate broad-view data acquisition (based on steered plane wave firings); (ii) flow vector estimation derived from multi-angle Doppler analysis (coupled with data regularization and least-squares fitting); (iii) dynamic visualization of color-encoded vector projectiles (with flow speckles displayed as adjunct). Calibration results indicated that by using three transmit angles and three receive angles (-10°, 0°, +10° for both), VPI can consistently compute flow vectors in a multi-vessel phantom with three tubes positioned at different depths (1.5, 4, 6 cm), oriented at different angles (-10°, 0°, +10°) and of different sizes (dilated diameter: 2.2, 4.4 and 6.3 mm; steady flow rate: 2.5 mL/s). The practical merit of VPI was further illustrated through an anthropomorphic flow phantom investigation that considered both healthy and stenosed carotid bifurcation geometries. For the healthy bifurcation with 1.2-Hz carotid flow pulses, VPI was able to render multi-directional and spatiotemporally varying flow patterns (using a nominal frame rate of 416 fps or 2.4-ms time resolution). In the case of stenosed bifurcations (50% eccentric narrowing), VPI enabled dynamic visualization of flow jet and recirculation zones. These findings suggest that VPI holds promise as a new tool for complex flow analysis.

Simulation based planning of surgical interventions in pediatric cardiology

Hemodynamics plays an essential role in the progression and treatment of cardiovascular disease. However, while medical imaging provides increasingly detailed anatomical information, clinicians often have limited access to hemodynamic data that may be crucial to patient risk assessment and treatment planning. Computational simulations can now provide detailed hemodynamic data to augment clinical knowledge in both adult and pediatric applications. There is a particular need for simulation tools in pediatric cardiology, due to the wide variation in anatomy and physiology in congenital heart disease patients, necessitating individualized treatment plans. Despite great strides in medical imaging, enabling extraction of flow information from magnetic resonance and ultrasound imaging, simulations offer predictive capabilities that imaging alone cannot provide. Patient specific simulations can be used for in silico testing of new surgical designs, treatment planning, device testing, and patient risk stratification. Furthermore, simulations can be performed at no direct risk to the patient. In this paper, we outline the current state of the art in methods for cardiovascular blood flow simulation and virtual surgery. We then step through pressing challenges in the field, including multiscale modeling, boundary condition selection, optimization, and uncertainty quantification. Finally, we summarize simulation results of two representative examples from pediatric cardiology: single ventricle physiology, and coronary aneurysms caused by Kawasaki disease. These examples illustrate the potential impact of computational modeling tools in the clinical setting.

Computational Fluid Dynamic Analysis of Intracranial Aneurysmal Bleb Formation

BACKGROUND:

The management of unruptured aneurysms is controversial, with the decision to treat influenced by aneurysm characteristics including size and morphology. Aneurysmal bleb formation is thought to be associated with an increased risk of rupture.

OBJECTIVE:

To correlate computational fluid dynamic (CFD) indices with bleb formation.

METHODS:

Anatomic models were constructed from 3-dimensional rotational angiography data in 27 patients with cerebral aneurysms harboring a single bleb. Additional models representing the aneurysm before bleb formation were constructed by digitally removing the bleb. We characterized hemodynamic features of models both with and without the blebs using CFDs. Flow structure, wall shear stress (WSS), pressure, and oscillatory shear index (OSI) were analyzed.

RESULTS:

There was a statistically significant association between bleb location at or adjacent to the point of maximal WSS (74%, P = .019), irrespective of rupture status. Aneurysmal blebs were related to the inflow or outflow jet in 89% of cases (P < .001), whereas 11% were unrelated. Maximal wall pressure and OSI were not significantly related to bleb location. The bleb region attained a lower WSS after its formation in 96% of cases (P < .001) and was also lower than the average aneurysm WSS in 86% of cases (P < .001).

CONCLUSION:

Cerebral aneurysm blebs generally form at or adjacent to the point of maximal WSS and are aligned with major flow structures. Wall pressure and OSI do not contribute to determining bleb location. The measurement of WSS using CFD models may potentially predict bleb formation and thus improve the assessment of rupture risk in unruptured aneurysms.

Understanding the role of hemodynamics in the initiation, progression, rupture, and treatment outcome of cerebral aneurysm from medical image-based computational studies

About a decade ago, the first image-based computational hemodynamic studies of cerebral aneurysms were presented. Their potential for clinical applications was the result of a right combination of medical image processing, vascular reconstruction, and grid generation techniques used to reconstruct personalized domains for computational fluid and solid dynamics solvers and data analysis and visualization techniques. A considerable number of studies have captivated the attention of clinicians, neurosurgeons, and neuroradiologists, who realized the ability of those tools to help in understanding the role played by hemodynamics in the natural history and management of intracranial aneurysms. This paper intends to summarize the most relevant results in the field reported during the last years.

Computational fluid dynamic simulations of image-based stented coronary bifurcation models

One of the relevant phenomenon associated with in-stent restenosis in coronary arteries is an altered haemodynamics in the stented region. Computational fluid dynamics (CFD) offers the possibility to investigate the haemodynamics at a level of detail not always accessible within experimental techniques. CFD can quantify and correlate the local haemodynamics structures which might lead to in-stent restenosis. The aim of this work is to study the fluid dynamics of realistic stented coronary artery models which replicate the complete clinical procedure of stent implantation. Two cases of pathologic left anterior descending coronary arteries with their bifurcations are reconstructed from computed tomography angiography and conventional coronary angiography images. Results of wall shear stress and relative residence time show that the wall regions more prone to the risk of restenosis are located next to stent struts, to the bifurcations and to the stent overlapping zone for both investigated cases. Considering a bulk flow analysis, helical flow structures are generated by the curvature of the zone upstream from the stent and by the bifurcation regions. Helical recirculating microstructures are also visible downstream from the stent struts. This study demonstrates the feasibility to virtually investigate the haemodynamics of patient-specific coronary bifurcation geometries.

Effect of head posture on the healthy human carotid bifurcation hemodynamics

Head and neck postures may cause morphology changes to the geometry of the carotid bifurcation (CB) that alter the low and oscillating wall shear stress (WSS) regions previously reported as important in the development of atherosclerosis. Here the right and left CB were imaged by MRI in two healthy subjects in the neutral head posture with the subject in the supine position and in two other head postures with the subject in the prone position: (1) rightward rotation up to 80°, and (2) leftward rotation up to 80°. Image-based computational models were constructed to investigate the effect of posture on arterial geometry and local hemodynamics. The area exposure to unfavorable hemodynamics, based on thresholds set for oscillatory shear index (OSI), WSS and relative residence time, was used to quantify the hemodynamic impact on the wall. Torsion of the head was found to: (1) cause notable changes in the bifurcation and internal carotid artery angles and, in most cases, on cross-sectional area ratios for common, internal and external carotid artery, (2) change the spatial distribution of wall regions exposed to unfavorable hemodynamics, and (3) cause a marked change in the hemodynamic burden on the wall when the OSI was considered. These findings suggest that head posture may be associated with the genesis and development of atherosclerotic disease as well as complications in stenotic and stented vessels.

Computational simulations for aortic coarctation: representative results from a sampling of patients

Treatments for coarctation of the aorta (CoA) can alleviate blood pressure (BP) gradients (Δ), but long-term morbidity still exists that can be explained by altered indices of hemodynamics and biomechanics. We introduce a technique to increase our understanding of these indices for CoA under resting and nonresting conditions, quantify their contribution to morbidity, and evaluate treatment options. Patient-specific computational fluid dynamics (CFD) models were created from imaging and BP data for one normal and four CoA patients (moderate native CoA: Δ12 mmHg, severe native CoA: Δ25 mmHg and postoperative end-to-end and end-to-side patients: Δ0 mmHg). Simulations incorporated vessel deformation, downstream vascular resistance and compliance. Indices including cyclic strain, time-averaged wall shear stress (TAWSS), and oscillatory shear index (OSI) were quantified. Simulations replicated resting BP and blood flow data. BP during simulated exercise for the normal patient matched reported values. Greatest exercise-induced increases in systolic BP and mean and peak ΔBP occurred for the moderate native CoA patient (SBP: 115 to 154 mmHg; mean and peak ΔBP: 31 and 73 mmHg). Cyclic strain was elevated proximal to the coarctation for native CoA patients, but reduced throughout the aorta after treatment. A greater percentage of vessels was exposed to subnormal TAWSS or elevated OSI for CoA patients. Local patterns of these indices reported to correlate with atherosclerosis in normal patients were accentuated by CoA. These results apply CFD to a range of CoA patients for the first time and provide the foundation for future progress in this area.

Assessment of the accuracy of MRI wall shear stress estimation using numerical simulations

PURPOSE

To investigate the accuracy of wall shear stress (WSS) estimation using MRI. Specifically, to investigate the impact of different parameters and if MRI WSS estimates are monotonically related to actual WSS.

MATERIALS AND METHODS

The accuracy of WSS estimation using methods based on phase-contrast (PC) MRI velocity mapping, Fourier velocity encoding (FVE) and intravoxel velocity standard deviation mapping were studied using numerical simulations. The influence of spatial resolution, velocity encoding, wall segmentation, and voxel location were investigated over a range of WSS values.

RESULTS

WSS estimates were found to be sensitive to parameter settings in general and spatial resolution in particular. All methods underestimated WSS, except for the FVE-based method, which instead was extremely sensitive to voxel position relative to the wall. Methods using PC-based WSS estimation with wall segmentation showed to be accurate for low WSS, but were sensitive to segmentation errors.

CONCLUSION

Even in the absence of noise and for relatively simple velocity profiles, MRI WSS estimates cannot always be assumed to be linearly or even monotonically related to actual WSS. High WSS values cannot be resolved and the estimates depend on parameter setting. Nevertheless, distinguishing areas of low and moderate WSS may be feasible.

Virtual Interventions for Image-based Blood Flow Computation

Image-based blood flow computation provides great promise for evaluation of vascular devices and assessment of surgical procedures. However, many previous studies employ idealized arterial and device models or only patient-specific models from the image data after device deployment, since the tools for model construction are unavailable or limited and tedious to use. Moreover, in contrast to retrospective studies from existing data, there is a pressing need for prospective analysis with the goal of surgical planning. Therefore, it is necessary to construct models with deployed devices in a fast, virtual and interactive fashion. The goal of this paper is to develop new geometric methods to deploy stents or stent grafts virtually to patient-specific geometric models constructed from a 3D segmentation of medical images. A triangular surface representing the vessel lumen boundary is extracted from the segmentation. The diseased portion is either clipped and replaced by the surface of a deployed device or rerouted in the case of a bypass graft. For diseased arteries close to bifurcations, bifurcated device models are generated. A method to map a 2D strut pattern on the surface of a device is also presented. We demonstrate three applications of our methods in personalized surgical planning for aortic aneurysms, aortic coarctation, and coronary artery stenosis using blood flow computation. Our approach enables prospective model construction and may help to expand the throughput required by routine clinical uses in the future.

Interdependencies of aortic arch secondary flow patterns, geometry, and age analysed by 4-dimensional phase contrast magnetic resonance imaging at 3 Tesla

OBJECTIVE

It was the aim to analyse the impact of age, aortic arch geometry, and size on secondary flow patterns such as helix and vortex flow derived from flow-sensitive magnetic resonance imaging (4D PC-MRI).

METHODS

62 subjects (age range = 20-80 years) without circumscribed pathologies of the thoracic aorta (ascending aortic (AAo) diameter: 3.2 ± 0.6 cm [range 2.2-5.1]) were examined by 4D PC-MRI after IRB-approval and written informed consent. Blood flow visualisation based on streamlines and time-resolved 3D particle traces was performed. Aortic diameter, shape (gothic, crook-shaped, cubic), angle, and age were correlated with existence and extent of secondary flow patterns (helicity, vortices); statistical modelling was performed.

RESULTS

Helical flow was the typical pattern in standard crook-shaped aortic arches. With altered shapes and increasing age, helicity was less common. AAo diameter and age had the highest correlation (r = 0.69 and 0.68, respectively) with number of detected vortices. None of the other arch geometric or demographic variables (for all, P ≥ 0.177) improved statistical modelling.

CONCLUSION

Substantially different secondary flow patterns can be observed in the normal thoracic aorta. Age and the AAo diameter were the parameters correlating best with presence and amount of vortices. Findings underline the importance of age- and geometry-matched control groups for haemodynamic studies.

KEY POINTS

• Secondary blood flow patterns (helices, vortices) are commonly observed in the aorta • Secondary flow patterns predominantly depend on patient age and aortic diameter • Geometric factors show a lesser impact on blood flow patterns than age and diameter • Future analyses of flow patterns should incorporate age- and diameter dependencies.

Pulmonary vascular stiffness: measurement, modeling, and implications in normal and hypertensive pulmonary circulations

This article introduces the concept of pulmonary vascular stiffness, discusses its increasingly recognized importance as a diagnostic marker in the evaluation of pulmonary vascular disease, and describes methods to measure and model it clinically, experimentally, and computationally. It begins with a description of systems-level methods to evaluate pulmonary vascular compliance and recent clinical efforts in applying such techniques to better predict patient outcomes in pulmonary arterial hypertension. It then progresses from the systems-level to the local level, discusses proposed methods by which upstream pulmonary vessels increase in stiffness, introduces concepts around vascular mechanics, and concludes by describing recent work incorporating advanced numerical methods to more thoroughly evaluate changes in local mechanical properties of pulmonary arteries.

Simulation of blood flow in deformable vessels using subject-specific geometry and spatially varying wall properties

Simulation of blood flow using image-based models and computational fluid dynamics has found widespread application to quantifying hemodynamic factors relevant to the initiation and progression of cardiovascular diseases and for planning interventions. Methods for creating subject-specific geometric models from medical imaging data have improved substantially in the last decade but for many problems, still require significant user interaction. In addition, while fluid-structure interaction methods are being employed to model blood flow and vessel wall dynamics, tissue properties are often assumed to be uniform. In this paper, we propose a novel workflow for simulating blood flow using subject-specific geometry and spatially varying wall properties. The geometric model construction is based on 3D segmentation and geometric processing. Variable wall properties are assigned to the model based on combining centerline-based and surface-based methods. We finally demonstrate these new methods using an idealized cylindrical model and two subject-specific vascular models with thoracic and cerebral aneurysms.

Review of zero-D and 1-D models of blood flow in the cardiovascular system

Background

Zero-dimensional (lumped parameter) and one dimensional models, based on simplified representations of the components of the cardiovascular system, can contribute strongly to our understanding of circulatory physiology. Zero-D models provide a concise way to evaluate the haemodynamic interactions among the cardiovascular organs, whilst one-D (distributed parameter) models add the facility to represent efficiently the effects of pulse wave transmission in the arterial network at greatly reduced computational expense compared to higher dimensional computational fluid dynamics studies. There is extensive literature on both types of models.

Method and Results

The purpose of this review article is to summarise published 0D and 1D models of the cardiovascular system, to explore their limitations and range of application, and to provide an indication of the physiological phenomena that can be included in these representations. The review on 0D models collects together in one place a description of the range of models that have been used to describe the various characteristics of cardiovascular response, together with the factors that influence it. Such models generally feature the major components of the system, such as the heart, the heart valves and the vasculature. The models are categorised in terms of the features of the system that they are able to represent, their complexity and range of application: representations of effects including pressure-dependent vessel properties, interaction between the heart chambers, neuro-regulation and auto-regulation are explored. The examination on 1D models covers various methods for the assembly, discretisation and solution of the governing equations, in conjunction with a report of the definition and treatment of boundary conditions. Increasingly, 0D and 1D models are used in multi-scale models, in which their primary role is to provide boundary conditions for sophisticate, and often patient-specific, 2D and 3D models, and this application is also addressed. As an example of 0D cardiovascular modelling, a small selection of simple models have been represented in the CellML mark-up language and uploaded to the CellML model repository http://models.cellml.org/. They are freely available to the research and education communities.

Conclusion

Each published cardiovascular model has merit for particular applications. This review categorises 0D and 1D models, highlights their advantages and disadvantages, and thus provides guidance on the selection of models to assist various cardiovascular modelling studies. It also identifies directions for further development, as well as current challenges in the wider use of these models including service to represent boundary conditions for local 3D models and translation to clinical application.

Towards treatment planning for the embolization of arteriovenous malformations of the brain: intranidal hemodynamics modeling

This paper presents a patient-derived model for the simulation of the hemodynamics of arteriovenous malformations of the brain (BAVM). This new approach is a step toward the simulation of the outcome of the embolization of the BAVM during treatment planning. More specifically, two aspects of the planning are pursued: simulation of the change of blood flow in the brain vasculature after the blocking of the malformation and simulation of the transport of the embolic liquid. The method we propose is tested on 3 BAVM cases of varying complexity. Twenty two out of 24 main BAVM flow paths have been identified well by simulation.