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Dynamically Scaled Phantom Phase Contrast MRI Compared to True-Scale Computational Modeling of Coronary Artery Flow
Abstract
Purpose:
To examine the feasibility of combining computational fluid dynamics (CFD) and dynamically scaled phantom phase-contrast magnetic resonance imaging (PC-MRI) for coronary flow assessment.
Materials and methods:
Left main coronary bifurcations segmented from computed tomography with bifurcation angles of 33°, 68°, and 117° were scaled-up ∼7× and 3D printed. Steady coronary flow was reproduced in these phantoms using the principle of dynamic similarity to preserve the true-scale Reynolds number, using blood analog fluid and a pump circuit in a 3T MRI scanner. After PC-MRI acquisition, the data were segmented and coregistered to CFD simulations of identical, but true-scale geometries. Velocities at the inlet region were extracted from the PC-MRI to define the CFD inlet boundary condition.
Results:
The PC-MRI and CFD flow data agreed well, and comparison showed: 1) small velocity magnitude discrepancies (2-8%); 2) with a Spearman's rank correlation ≥0.72; and 3) a velocity vector correlation (including direction) of r(2) ≥ 0.82. The highest agreement was achieved for high velocity regions with discrepancies being located in slow or recirculating zones with low MRI signal-to-noise ratio (SNRv ) in tortuous segments and large bifurcating vessels.
Conclusion:
Characterization of coronary flow using a dynamically scaled PC-MRI phantom flow is feasible and provides higher resolution than current in vivo or true-scale in vitro methods, and may be used to provide boundary conditions for true-scale CFD simulations. J. Magn. Reson. Imaging 2016.
... MRI has not been *This work was financially supported by the Auckland Charitable Heart Trust, the Auckland Medical Research Foundation (AMRF) and the Auckland Academic Health Alliance (AAHA). 1 applied to coronary flow before because of limited temporal and spatial resolution. Previously we successfully used dynamically scaled in vitro coronary blood flow experiments to over-come these imaging limitations [5]. In this study, we explore if the same methodology is sufficiently adequate to capture changes to blood flow on the micro scale that are a result of stents in coronary arteries. ...
... Both a Newtonian and a non-Newtonian fluid was used experimentally. The experimental and numerical methods have been previously described in [5] and [8] and are summarized here briefly. ...
... The lumen was smoothed using Poisson surface reconstruction, cut and rendered and extended in the open-source VMTK software (Vascular modelling tool kit, www.vmtk.org) as detailed in an earlier publication [5]. The virtual geometry was then imported into AutoCAD Inventor (2016, AutoDesk, SanRafael, CA, USA). ...
We investigated if blood flow changes induced through the presence of a stent could be detected using in vitro dynamically scaled 4D Phase-Contrast Magnetic Resonance Imaging (PC-MRI). Using idealized and patient-specific left main coronary artery bifurcations, we 3D-printed the dynamically large scaled geometries and incorporated them into a flow circuit for non-invasive acquisition with a higher effective spatial resolution. We tested the effects of using non-Newtonian and Newtonian fluids for the experiment. We also numerically simulated the same geometries in true scale for comparison using computational fluid dynamics (CFD). We found that the experimental setup increased the effective spatial resolution enough to reveal stent induced blood flow changes close to the vessel wall. Non-Newtonian fluid replicated all of the flow field well with a strong agreement with the computed flow field (R2 > 0.9). Fine flow structures were not as prominent for the Newtonian compared to non-Newtonian fluid consideration. In the patient-specific geometry, arterial non-planarity increased the difficulty to capture the near wall slow velocity changes. Findings demonstrate the potential to dynamically scale in vitro 4D MRI flow acquisition for micro blood flow considerations.
... In some locations, these stresses can influence or even injure the endothelial cells lining the wall [3]. Vessel branching or bifurcations have complex shapes which create complex flow regions with a higher likelihood of adverse stresses, making them more susceptible to atherosclerotic disease [4,5]. ...
... Computational modeling with computational fluid dynamics (CFD) is a wellestablished technique which provides numerical prediction of velocity, pressure, and stress in the fluid domain of interest. With an accurate description of the boundary conditions, it provides insights into the effects of stent design [8] and deployment [9], and vessel shape effects on blood flow [5]. Vessel regions exposed to adverse stress can be identified, which enables predictions of sites for plaque development and evolution [10]. ...
... The Law of Dynamic Similarity ensures the development of identical flow patterns in scaled-up and true-scale cases by preserving the relationship between geometric scales and fluid forces with the constant ratios of forces expressed as nondimensional numbers such as the Reynolds number [23]. This is a common engineering procedure [24], and was recently applied to the problem of coronary artery flow, where a close correlation for true-scale computational fluid dynamics (CFD) and scaled-up PC-MRI flow was demonstrated for patient-specific arteries [5]. ...
This chapter discusses coronary artery flow assessment for atherosclerosis investigations. The overall goal is to foster the reader’s understanding of coronary flow assessment with CFD and experimental MRI, including advantages, shortcomings, and potential for clinical applicability. In Section 1 , we begin by introducing coronary artery disease and how it links to local blood flow and hemodynamic parameters, before introducing strategies to investigating coronary flow for risk assessment—computational modeling and experimental studies. Both of these need the artery geometry and embedded stents to be retrieved first, as detailed in Section 2 . Section 3 details the concepts of computational coronary flow modeling with computational fluid dynamics (CFD) including the governing equations, mesh discretization, and boundary and initial conditions. Section 4 introduces experimental approaches using in vitro flow sensitive magnetic resonance imaging (MRI), including dynamic scaling for steady or transient state considerations, creation of phantom, consideration of vessel compliance and motion, non-Newtonian blood properties, and the design of an experimental circuit. Postprocessing, analysis, and comparison of both methods are explained in Section 5 , before discussion of the accuracy and reliability of the results in Section 6 . Finally, current developments, particularly patient-specific profiling, are discussed in Section 7 .
... Such a priori hypotheses on the velocity profiles to be used as conditions at inflow boundaries represent a source of uncertainty in the estimation of helical and WSS patterns [31], potentially masking their relationship with atherosclerosis initiation and progression. Moreover, in vitro and in silico hemodynamic studies revealed the presence of skewed velocity profiles in the left coronary artery [32][33][34], with a not negligible presence of secondary flows in the entire coronary tree, as it can be expected by considering the vessel tortuosity and the presence of bifurcations and branching. ...
... The 3D velocity profile on a generic cross-section of a vessel can be described as a combination of (1) a principal, through-plane (TP) component, in the direction of the axis of the vessel, and (2) a secondary, in-plane (IP) component, lying on the plane orthogonal to the axis of the vessel. To test the impact of the velocity profile on the hemodynamics of LAD coronary arteries, different 3D velocity profiles were generated using analytical formulations based on previous observations demonstrating the presence of secondary flows in coronary arteries [32,34]. ...
Patient-specific computational fluid dynamics is a powerful tool for investigating the hemodynamic risk in coronary arteries. Proper setting of flow boundary conditions in computational hemodynamic models of coronary arteries is one of the sources of uncertainty weakening the findings of in silico experiments, in consequence of the challenging task of obtaining in vivo 3D flow measurements within the clinical framework. Accordingly, in this study we evaluated the influence of assumptions on inflow velocity profile shape on coronary artery hemodynamics. To do that, (1) ten left anterior descending coronary artery (LAD) geometries were reconstructed from clinical angiography, and (2) eleven velocity profiles with realistic 3D features such as eccentricity and differently shaped (single- and double-vortex) secondary flows were generated analytically and imposed as inflow boundary conditions. Wall shear stress and helicity-based descriptors obtained prescribing the commonly used parabolic velocity profile were compared with those obtained with the other velocity profiles. Our findings indicated that the imposition of idealized velocity profiles as inflow boundary condition is acceptable as long the results of the proximal vessel segment are not considered, in LAD coronary arteries. As a pragmatic rule of thumb, a conservative estimation of the length of influence of the shape of the inflow velocity profile on LAD local hemodynamics can be given by the theoretical entrance length for cylindrical conduits in laminar flow conditions.
... Device manufacturers and researchers with an interest in cardiovascular modelling, prediction and treatment of coronary artery disease can analyse this data directly or combine it with other available datasets. The smooth surface meshes and centrelines can be directly used for computational modelling 16 , directly 3D printed for experiments [18][19][20][21] , assist in developing and testing medical devices such as stents [22][23][24] , and can be used for Virtual Reality applications for education and training [25][26][27] . Moreover, our dataset allows for the development and benchmarking of new segmentation algorithms aiming to efficiently annotate the coronary arteries automatically as per ASOCA challenge 28 . ...
Computed Tomography Coronary Angiography (CTCA) is a non-invasive method to evaluate coronary artery anatomy and disease. CTCA is ideal for geometry reconstruction to create virtual models of coronary arteries. To our knowledge there is no public dataset that includes centrelines and segmentation of the full coronary tree. We provide anonymized CTCA images, voxel-wise annotations and associated data in the form of centrelines, calcification scores and meshes of the coronary lumen in 20 normal and 20 diseased cases. Images were obtained along with patient information with informed, written consent as part of the Coronary Atlas. Cases were classified as normal (zero calcium score with no signs of stenosis) or diseased (confirmed coronary artery disease). Manual voxel-wise segmentations by three experts were combined using majority voting to generate the final annotations. Provided data can be used for a variety of research purposes, such as 3D printing patient-specific models, development and validation of segmentation algorithms, education and training of medical personnel and in-silico analyses such as testing of medical devices.
... Device manufacturers and researchers with an interest in cardiovascular modelling, prediction and treatment of coronary artery disease can analyse this data directly or combine it with other available datasets. The smooth surface meshes and centrelines can be directly used for computational modelling 17 , directly 3D printed for experiments [19][20][21][22] , assist in developing and testing medical devices such as stents [23][24][25] , and can be used for Virtual Reality applications for education and training [26][27][28] . Moreover, our dataset allows for the development and benchmarking of new segmentation algorithms aiming to efficiently annotate the coronary arteries automatically as per ASOCA challenge 29 . ...
Computed Tomography Coronary Angiography (CTCA) is a non-invasive method to evaluate coronary artery anatomy and disease. CTCA is ideal for geometry reconstruction to create virtual models of coronary arteries. To our knowledge there is no public dataset that includes centrelines and segmentation of the full coronary tree. We provide anonymized CTCA images, voxel-wise annotations and associated data in the form of centrelines, calcification scores and meshes of the coronary lumen in 20 normal and 20 diseased cases. Images were obtained along with patient information with informed, written consent as part of Coronary Atlas (https://www.coronaryatlas.org/). Cases were classified as normal (zero calcium score with no signs of stenosis) or diseased (confirmed coronary artery disease). Manual voxel-wise segmentations by three experts were combined using majority voting to generate the final annotations. Provided data can be used for a variety of research purposes, such as 3D printing patient-specific models, development and validation of segmentation algorithms, education and training of medical personnel and in-silico analyses such as testing of medical devices.
... A parabolic flow profile was prescribed at the inlet and constant pressure of 0 atm at the outlet 24 . The constant pressure outlet has also been a common assumption in published literature 42,43 and is generally accepted for healthy vessels since realistic outlet conditions are often not available, and because of previous published validation with in vitro data 44 . The velocity-time profile and flow rate were adapted from previous studies 45 , and the flow was scaled according to equation developed by Giessen et al. ( q = 1.43d 1.55 ) 46 using the inlet radii 47 . ...
Severe coronary tortuosity has previously been linked to low shear stresses at the luminal surface, yet this relationship is not fully understood. Several previous studies considered different tortuosity metrics when exploring its impact of on the wall shear stress (WSS), which has likely contributed to the ambiguous findings in the literature. Here, we aim to analyze different tortuosity metrics to determine a benchmark for the highest correlating metric with low time-averaged WSS (TAWSS). Using Computed Tomography Coronary Angiogram (CTCA) data from 127 patients without coronary artery disease, we applied all previously used tortuosity metrics to the left main coronary artery bifurcation, and to its left anterior descending and left circumflex branches, before modelling their TAWSS using computational fluid dynamics (CFD). The tortuosity measures included tortuosity index, average absolute-curvature, root-mean-squared (RMS) curvature, and average squared-derivative-curvature. Each tortuosity measure was then correlated with the percentage of vessel area that showed a < 0.4 Pa TAWSS, a threshold associated with altered endothelial cell cytoarchitecture and potentially higher disease risk. Our results showed a stronger correlation between curvature-based versus non-curvature-based tortuosity measures and low TAWSS, with the average-absolute-curvature showing the highest coefficient of determination across all left main branches ( p < 0.001), followed by the average-squared-derivative-curvature ( p = 0.001), and RMS-curvature ( p = 0.002). The tortuosity index, the most widely used measure in literature, showed no significant correlation to low TAWSS ( p = 0.86). We thus recommend the use of average-absolute-curvature as a tortuosity measure for future studies.
... Although cardiovascular models based on imaging data were demonstrated to produce results comparable to clinical diagnostic methods 22,37,38 , their combination with interventional study designs remained challenging and complex in heart valve disease. A technically and clinically oriented approach has recently helped to identify anatomical and functional target parameters in degenerative mitral valve disease with potential use for treatment planning 39 , and Kassab et al. recently highlighted the capabilities of new modelling technologies and quantitative approaches to surgical decision making 7 . ...
... Although cardiovascular models based on imaging data were demonstrated to produce results comparable to clinical diagnostic methods 22,37,38 , their combination with interventional study designs remained challenging and complex in heart valve disease. A technically and clinically oriented approach has recently helped to identify anatomical and functional target parameters in degenerative mitral valve disease with potential use for treatment planning 39 , and Kassab et al. recently highlighted the capabilities of new modelling technologies and quantitative approaches to surgical decision making 7 . ...
Optimizing treatment planning is essential for advances in patient care and outcomes. Precisely tailored therapy for each patient remains a yearned-for goal. Cardiovascular modelling has the potential to simulate and predict the functional response before the actual intervention is performed. The objective of this study was to proof the validity of model-based prediction of haemodynamic outcome after aortic valve replacement. In a prospective study design virtual (model-based) treatment of the valve and the surrounding vasculature were performed alongside the actual surgical procedure (control group). The resulting predictions of anatomic and haemodynamic outcome based on information from magnetic resonance imaging before the procedure were compared to post-operative imaging assessment of the surgical control group in ten patients. Predicted vs. post-operative peak velocities across the valve were comparable (2.97 ± 1.12 vs. 2.68 ± 0.67 m/s; p = 0.362). In wall shear stress (17.3 ± 12.3 Pa vs. 16.7 ± 16.84 Pa; p = 0.803) and secondary flow degree (0.44 ± 0.32 vs. 0.49 ± 0.23; p = 0.277) significant linear correlations (p < 0.001) were found between predicted and post-operative outcomes. Between groups blood flow patterns showed good agreement (helicity p = 0.852, vorticity p = 0.185, eccentricity p = 0.333). Model-based therapy planning is able to accurately predict post-operative haemodynamics after aortic valve replacement. These validated virtual treatment procedures open up promising opportunities for individually targeted interventions.
Congenital heart defect interventions may benefit from the fabrication of patient-specific vascular grafts because of the wide array of anatomies present in children with cardiovascular defects. Three-dimensional (3D) bioprinting is used to establish a platform to produce custom vascular grafts, which are biodegradable , mechanically compatible with vascular tissues, and support neotissue formation and growth. It is an advanced and emerging technology having great potential in the field of tissue engineering. Bioprinting uses cell-laden biomaterials, generally called bio-inks, to deposit in a layer-by-layer fashion. The goal of 3D bioprinting is to offer an alternative to autologous or allogeneic tissue grafts to replace or treat damaged tissues. This chapter aims to offer a synopsis of the current state of 3D bioprinting techniques in analysis, research potentials, and applications. This new and exciting technology has the potential to not only provide better treatment options, but also to improve the quality of life for patients suffering from chronic illnesses.
3D printing as a means of fabrication has seen increasing applications in medicine in the last decade, becoming invaluable for cardiovascular applications. This rapidly developing technology has had a significant impact on cardiovascular research, its clinical translation and education. It has expanded our understanding of the cardiovascular system resulting in better devices, tools and consequently improved patient outcomes. This review discusses the latest developments and future directions of generating medical replicas (‘phantoms’) for use in the cardiovascular field, detailing the end-to-end process from medical imaging to capture structures of interest, to production and use of 3D printed models. We provide comparisons of available imaging modalities and overview of segmentation and post-processing techniques to process images for printing, detailed exploration of latest 3D printing methods and materials, and a comprehensive, up-to-date review of milestone applications and their impact within the cardiovascular domain across research, clinical use and education. We then provide an in-depth exploration of future technologies and innovations around these methods, capturing opportunities and emerging directions across increasingly realistic representations, bioprinting and tissue engineering, and complementary virtual and mixed reality solutions. The next generation of 3D printing techniques allow patient-specific models that are increasingly realistic, replicating properties, anatomy and function.
This is a consensus document from the European Bifurcation Club concerning bench testing in coronary artery bifurcations. It is intended to provide guidelines for bench assessment of stents and other strategies in coronary bifurcation treatment where the United States Food and Drug Administration (FDA) or International Organization for Standardization (ISO) guidelines are limited or absent. These recommendations provide guidelines rather than a step-by-step manual. We provide data on the anatomy of bifurcations and elastic response of coronary arteries to aid model construction. We discuss testing apparatus, bench testing endpoints and bifurcation nomenclature.
3D-printed models fabricated from CT, MRI, or echocardiography data provide the advantage of haptic feedback, direct manipulation, and enhanced understanding of cardiovascular anatomy and underlying pathologies. Reported applications of cardiovascular 3D printing span from diagnostic assistance and optimization of management algorithms in complex cardiovascular diseases, to planning and simulating surgical and interventional procedures. The technology has been used in practically the entire range of structural, valvular, and congenital heart diseases, and the added-value of 3D printing is established. Patient-specific implants and custom-made devices can be designed, produced, and tested, thus opening new horizons in personalized patient care and cardiovascular research. Physicians and trainees can better elucidate anatomical abnormalities with the use of 3D-printed models, and communication with patients is markedly improved. Cardiovascular 3D bioprinting and molecular 3D printing, although currently not translated into clinical practice, hold revolutionary potential. 3D printing is expected to have a broad influence in cardiovascular care, and will prove pivotal for the future generation of cardiovascular imagers and care providers. In this Review, we summarize the cardiovascular 3D printing workflow, from image acquisition to the generation of a hand-held model, and discuss the cardiovascular applications and the current status and future perspectives of cardiovascular 3D printing.
Magnetic resonance imaging (MRI) has become an important tool for the clinical evaluation of patients with cardiovascular disease. Since its introduction in the late 1980s, 2-dimensional phase contrast MRI (2D PC-MRI) has become a routine part of standard-of-care cardiac MRI for the assessment of regional blood flow in the heart and great vessels. More recently, time-resolved PC-MRI with velocity encoding along all three flow directions and three-dimensional (3D) anatomic coverage (also termed '4D flow MRI') has been developed and applied for the evaluation of cardiovascular hemodynamics in multiple regions of the human body. 4D flow MRI allows for the comprehensive evaluation of complex blood flow patterns by 3D blood flow visualization and flexible retrospective quantification of flow parameters. Recent technical developments, including the utilization of advanced parallel imaging techniques such as k-t GRAPPA, have resulted in reasonable overall scan times, e.g., 8-12 minutes for 4D flow MRI of the aorta and 10-20 minutes for whole heart coverage. As a result, the application of 4D flow MRI in a clinical setting has become more feasible, as documented by an increased number of recent reports on the utility of the technique for the assessment of cardiac and vascular hemodynamics in patient studies. A number of studies have demonstrated the potential of 4D flow MRI to provide an improved assessment of hemodynamics which might aid in the diagnosis and therapeutic management of cardiovascular diseases. The purpose of this review is to describe the methods used for 4D flow MRI acquisition, post-processing and data analysis. In addition, the article provides an overview of the clinical applications of 4D flow MRI and includes a review of applications in the heart, thoracic aorta and hepatic system.
Coronary artery disease (CAD) is the most common cardiovascular disease. Early diagnosis of CAD's physiological significance is of utmost importance for guiding individualized risk-tailored treatment strategies. In this paper, we first review the state-of-the-art clinical diagnostic indices to quantify the severity of CAD and the associated invasive and noninvasive imaging technologies in order to quantify the anatomical parameters of diameter stenosis, area stenosis, and hemodynamic indices of coronary flow reserve and fractional flow reserve. With the development of computational technologies and CFD methods, tremendous progress has been made in applying image-based CFD simulation techniques to elucidate the effects of hemodynamics in vascular pathophysiology toward the initialization and progression of CAD. So then, we review the advancements of CFD technologies in patient-specific modeling, involving the development of geometry reconstruction, boundary conditions, and fluid-structure interaction. Next, we review the applications of CFD to stenotic sites, in order to compute their hemodynamic parameters and study the relationship between the hemodynamic conditions and the clinical indices, to thereby assess the amount of viable myocardium and candidacy for percutaneous coronary intervention. Finally, we review the strengths and limitations of current researches of applying CFD to CAD studies. Copyright © 2014 John Wiley & Sons, Ltd.
Though conventional coronary angiography (CCA) has been the standard of reference for diagnosing coronary artery disease in the past decades, computed tomography angiography (CTA) has rapidly emerged, and is nowadays widely used in clinical practice. Here, we introduce a standardized evaluation framework to reliably evaluate and compare the performance of the algorithms devised to detect and quantify the coronary artery stenoses, and to segment the coronary artery lumen in CTA data. The objective of this evaluation framework is to demonstrate the feasibility of dedicated algorithms to: (1) (semi-)automatically detect and quantify stenosis on CTA, in comparison with quantitative coronary angiography (QCA) and CTA consensus reading, and (2) (semi-)automatically segment the coronary lumen on CTA, in comparison with expert's manual annotation. A database consisting of 48 multicenter multivendor cardiac CTA datasets with corresponding reference standards are described and made available. The algorithms from 11 research groups were quantitatively evaluated and compared. The results show that (1) some of the current stenosis detection/quantification algorithms may be used for triage or as a second-reader in clinical practice, and that (2) automatic lumen segmentation is possible with a precision similar to that obtained by experts. The framework is open for new submissions through the website, at http://coronary.bigr.nl/stenoses/.
Dimensional analysis has been applied to an unsteady pulsatile flow of a shear-thinning power-law non-Newtonian liquid. An
experiment was then designed in which both Newtonian and non-Newtonian liquids were used to model blood flow through a large-scale
(38.5mm dia.), simplified, rigid arterial junction (a distal anastomosis of a femorodistal bypass). The flow field within
the junction was obtained by Particle Imaging Velocimetry and near-wall velocities were used to calculate the wall shear stresses.
Dimensionless wall shear stresses were obtained at different points in the cardiac cycle for two different but dynamically
similar non-Newtonian fluids; the good agreement between the measured dimensionless wall shear stresses confirm the validity
of the dimensional analysis. However, blood exhibits a constant viscosity at high-shear rates and to obtain complete dynamic
similarity between large-scale experiments and life-scale flows, the high-shear viscosity also needs to be included in the
analysis. How this might be done is discussed in the paper.
Object
A new software module for coronary artery segmentation and visualization in CT angiography (CTA) datasets is presented, which aims to interactively segment coronary arteries and visualize them in 3D with maximum intensity projection (MIP) and volume rendering (VRT).
Materials and Methods
The software was built as a plug-in for the open-source PACS workstation OsiriX. The main segmentation function is based an optimized “virtual contrast injection” algorithm, which uses fuzzy connectedness of the vessel lumen to separate the contrast-filled structures from each other. The software was evaluated in 42 clinical coronary CTA datasets acquired with 64-slice CT using isotropic voxels of 0.3–0.5 mm.
Results
The median processing time was 6.4 min, and 100% of main branches (right coronary artery, left circumflex artery and left anterior descending artery) and 86.9% (219/252) of visible minor branches were intact. Visually correct centerlines were obtained automatically in 94.7% (321/339) of the intact branches.
Conclusion
The new software is a promising tool for coronary CTA post-processing providing good overviews of the coronary artery with limited user interaction on low-end hardware, and the coronary CTA diagnosis procedure could potentially be more time-efficient than using thin-slab technique.
Point set registration is a key component in many computer vision tasks. The goal of point set registration is to assign correspondences between two sets of points and to recover the transformation that maps one point set to the other. Multiple factors, including an unknown nonrigid spatial transformation, large dimensionality of point set, noise, and outliers, make the point set registration a challenging problem. We introduce a probabilistic method, called the Coherent Point Drift (CPD) algorithm, for both rigid and nonrigid point set registration. We consider the alignment of two point sets as a probability density estimation problem. We fit the Gaussian mixture model (GMM) centroids (representing the first point set) to the data (the second point set) by maximizing the likelihood. We force the GMM centroids to move coherently as a group to preserve the topological structure of the point sets. In the rigid case, we impose the coherence constraint by reparameterization of GMM centroid locations with rigid parameters and derive a closed form solution of the maximization step of the EM algorithm in arbitrary dimensions. In the nonrigid case, we impose the coherence constraint by regularizing the displacement field and using the variational calculus to derive the optimal transformation. We also introduce a fast algorithm that reduces the method computation complexity to linear. We test the CPD algorithm for both rigid and nonrigid transformations in the presence of noise, outliers, and missing points, where CPD shows accurate results and outperforms current state-of-the-art methods.
The Froude number (a ratio of inertial to gravitational forces) predicts the occurrence of dynamic similarity in legged animals over a wide range of sizes and velocities for both walking and running gaits at Earth gravity. This is puzzling because the Froude number ignores elastic forces that are crucial for understanding running gaits. We used simulated reduced gravity as a tool for exploring dynamic similarity in human running. We simulated reduced gravity by applying a nearly constant upward force to the torsos of our subjects while they ran on a treadmill. We found that at equal Froude numbers, achieved through different combinations of velocity and levels of gravity, our subjects did not run in a dynamically similar manner. Thus, the inertial and gravitational forces that comprise the Froude number were not sufficient to characterize running in reduced gravity. Further, two dimensionless numbers that incorporate elastic forces, the Groucho number and the vertical Strouhal number, also failed to predict dynamic similarity in reduced-gravity running. To better understand the separate effects of velocity and gravity, we also studied running mechanics at fixed absolute velocities under different levels of gravity. The effects of velocity and gravity on the requirements of dynamic similarity differed in both magnitude and direction, indicating that there are no two velocity and gravity combinations at which humans will prefer to run in a dynamically similar manner. A comparison of walking and running results demonstrated that reduced gravity had different effects on the mechanics of each gait. This suggests that a single unifying hypothesis for the effects of size, velocity and gravity on both walking and running gaits will not be successful.
The pressure drop-flow relations in myocardial bridges and the assessment of vascular heart disease via fractional flow reserve (FFR) have motivated many researchers the last decades. The aim of this study is to simulate several clinical conditions present in myocardial bridges to determine the flow reserve and consequently the clinical relevance of the disease. From a fluid mechanical point of view the pathophysiological situation in myocardial bridges involves fluid flow in a time dependent flow geometry, caused by contracting cardiac muscles overlying an intramural segment of the coronary artery. These flows mostly involve flow separation and secondary motions, which are difficult to calculate and analyse.
Because a three dimensional simulation of the haemodynamic conditions in myocardial bridges in a network of coronary arteries is time-consuming, we present a boundary layer model for the calculation of the pressure drop and flow separation. The approach is based on the assumption that the flow can be sufficiently well described by the interaction of an inviscid core and a viscous boundary layer. Under the assumption that the idealised flow through a constriction is given by near-equilibrium velocity profiles of the Falkner-Skan-Cooke (FSC) family, the evolution of the boundary layer is obtained by the simultaneous solution of the Falkner-Skan equation and the transient von-Kármán integral momentum equation.
The model was used to investigate the relative importance of several physical parameters present in myocardial bridges. Results have been obtained for steady and unsteady flow through vessels with 0 - 85% diameter stenosis. We compare two clinical relevant cases of a myocardial bridge in the middle segment of the left anterior descending coronary artery (LAD). The pressure derived FFR of fixed and dynamic lesions has shown that the flow is less affected in the dynamic case, because the distal pressure partially recovers during re-opening of the vessel in diastole. We have further calculated the wall shear stress (WSS) distributions in addition to the location and length of the flow reversal zones in dependence on the severity of the disease.
The described boundary layer method can be used to simulate frictional forces and wall shear stresses in the entrance region of vessels. Earlier models are supplemented by the viscous effects in a quasi three-dimensional vessel geometry with a prescribed wall motion. The results indicate that the translesional pressure drop and the mean FFR compares favourably to clinical findings in the literature. We have further shown that the mean FFR under the assumption of Hagen-Poiseuille flow is overestimated in developing flow conditions.
To develop and validate a method for creating realistic, patient specific replicas of cerebral aneurysms by means of fused deposition modeling.
The luminal boundaries of 10 cerebral aneurysms, together with adjacent proximal and distal sections of the parent artery, were segmented based on DSA images, and corresponding virtual three-dimensional (3D) surface reconstructions were created. From these, polylactic acid and MakerBot Flexible Filament replicas of each aneurysm were created by means of fused deposition modeling. The accuracy of the replicas was assessed by quantifying statistical significance in the variations of their inner dimensions relative to 3D DSA images. Feasibility for using these replicas as flow phantoms in combination with phase contrast MRI was demonstrated.
3D printed aneurysm models were created for all 10 subjects. Good agreement was seen between the models and the source anatomy. Aneurysm diameter measurements of the printed models and source images correlated well (r=0.999; p<0.001), with no statistically significant group difference (p=0.4) or observed bias. The SDs of the measurements were 0.5 mm and 0.2 mm for source images and 3D models, respectively. 3D printed models could be imaged with flow via MRI.
The 3D printed aneurysm models presented were accurate and were able to be produced inhouse. These models can be used for previously cited applications, but their anatomical accuracy also enables their use as MRI flow phantoms for comparison with ongoing studies of computational fluid dynamics. Proof of principle imaging experiments confirm MRI flow phantom utility.
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Purpose:
The level-set method is known to require long computation time for 3D image segmentation, which limits its usage in clinical workflow. The goal of this study was to develop a fast level-set algorithm based on the coherent propagation method and explore its character using clinical datasets.
Methods:
The coherent propagation algorithm allows level set functions to converge faster by forcing the contour to move monotonically according to a predicted developing trend. Repeated temporary backwards propagation, caused by noise or numerical errors, is then avoided. It also makes it possible to detect local convergence, so that the parts of the boundary that have reached their final position can be excluded in subsequent iterations, thus reducing computation time. To compensate for the overshoot error, forward and backward coherent propagation is repeated periodically. This can result in fluctuations of great magnitude in parts of the contour. In this paper, a new gradual convergence scheme using a damping factor is proposed to address this problem. The new algorithm is also generalized to non-narrow band cases. Finally, the coherent propagation approach is combined with a new distance-regularized level set, which eliminates the needs of reinitialization of the distance.
Results:
Compared with the sparse field method implemented in the widely available ITKSnap software, the proposed algorithm is about 10 times faster when used for brain segmentation and about 100 times faster for aorta segmentation. Using a multiresolution approach, the new method achieved 50 times speed-up in liver segmentation. The Dice coefficient between the proposed method and the sparse field method is above 99% in most cases.
Conclusions:
A generalized coherent propagation algorithm for level set evolution yielded substantial improvement in processing time with both synthetic datasets and medical images.
Blood flow in arteries is dominated by unsteady flow phenomena. The
cardiovascular system is an internal flow loop with multiple branches in
which a complex liquid circulates. A nondimensional frequency parameter,
the Womersley number, governs the relationship between the unsteady and
viscous forces. Normal arterial flow is laminar with secondary flows
generated at curves and branches. The arteries are living organs that
can adapt to and change with the varying hemodynamic conditions. In
certain circumstances, unusual hemodynamic conditions create an abnormal
biological response. Velocity profile skewing can create pockets in
which the direction of the wall shear stress oscillates. Atherosclerotic
disease tends to be localized in these sites and results in a narrowing
of the artery lumena stenosis. The stenosis can cause turbulence and
reduce flow by means of viscous head losses and flow choking. Very high
shear stresses near the throat of the stenosis can activate platelets
and thereby induce thrombosis, which can totally block blood flow to the
heart or brain. Detection and quantification of stenosis serve as the
basis for surgical intervention. In the future, the study of arterial
blood flow will lead to the prediction of individual hemodynamic flows
in any patient, the development of diagnostic tools to quantify disease,
and the design of devices that mimic or alter blood flow. This field is
rich with challenging problems in fluid mechanics involving
three-dimensional, pulsatile flows at the edge of turbulence.
Phase contrast MRI allows access to tri-directional encoded velocity information and therefore, measurement of flow in the human hemodynamic system. The aim of this work was to investigate whether this technology could be applied to support the grading of stenosis in mid-size arteries. Using a specially constructed flow phantom and a stenosis model with tube diameter of 5mm and 8mm and a stenosis of 50%, experiments at different flow rates (180–640ml/min), slice thickness (1–4mm), field strength (1.5 and 3.0T), and multi-slice as well as 3D volume acquisition were performed. The observations were assessed visually and evaluated by signal-to-noise (SNR) ratios in regions before and after the stenosis. The obtained results show that examinations should be performed at high field (3.0T) and at flow rates up to 500ml/min without hampering the measurements by areas of signal loss. In comparison, no detectable differences in the flow patterns of the two acquisition schemes could be observed. However, the SNR was higher using the 3D volume acquisition and thick slices. In summary, 3D PC-MRI of mid-size vessels with stenosis is feasible for certain flow rates. The presented results could be seen as guidance for in vivo situations to assess if an examination of a patient is reasonable in terms of outcome.
Purpose:
Coronary plaque has been shown to directly affect the blood parameters, however, haemodynamic variations based on the plaque configuration has not been studied. In this study we investigate the haemodynamic effects of various types of plaques in the left coronary bifurcation.
Methods:
Eight types of plaque configurations were simulated and located in various positions in the left main stem, the left anterior descending and left circumflex to produce a >50% narrowing of the coronary lumen. We analyse and characterise haemodynamic effects caused by each type of plaque. Computational fluid dynamics was performed to simulate realistic physiological conditions that reveal the in vivo cardiac haemodynamics. Velocity, wall shear stress (WSS) and pressure gradient (PSG) in the left coronary artery were calculated and compared in all plaque configurations during cardiac cycles.
Results:
Our results showed that the highest velocity and PSG were found in the type of plaque configuration which involved all of the three left coronary branches. Plaques located in the left circumflex branch resulted in highly significant changes of the velocity, WSS and PSG (p<0.001) when compared to the other types of plaque configurations.
Conclusion:
Our analysis provides an insight into the distribution of plaque at the left bifurcation, and corresponding haemodynamic effects, thus, improving our understanding of atherosclerosis.
In the last two decades, numerical models have become well-recognized and widely adopted tools to investigate stenting procedures. Due to limited computational resources and modeling capabilities, early numerical studies only involved simplified cases and idealized stented arteries. Nowadays, increased computational power allows for numerical models to meet clinical needs and include more complex cases such as the implantation of multiple stents in bifurcations or curved vessels. Interesting progresses have been made in the numerical modeling of stenting procedures both from a structural and a fluid dynamics points of view. Moreover, in the drug eluting stents era, new insights on drug elution capabilities are becoming essential in the stent development. Lastly, image-based methods able to reconstruct realistic geometries from medical images have been proposed in the recent literature aiming to better describe the peculiar anatomical features of coronary vessels and increase the accuracy of the numerical models. In this light, this review provides a comprehensive analysis of the current state-of-the-art in this research area, discussing the main methodological advances and remarkable results drawn from a number of significant studies.
Key Words blood flow, cardiovascular disease, magnetic resonance imaging s Abstract The characterization of blood flow is important for understanding the function of the cardiovascular system under normal and diseased conditions, designing cardiovascular devices, and diagnosing and treating congenital and acquired cardio-vascular disease. Experimental methods, especially magnetic resonance imaging tech-niques can be used to noninvasively quantify blood flow for diagnosing cardiovascular disease, researching disease mechanisms, and validating assumptions and predictions of mathematical models. Computational methods can be used to simulate blood flow and vessel dynamics, test hypotheses of disease formation under controlled condi-tions, and evaluate devices that have not yet been built and treatments that have not yet been implemented. In this article we review experimental and computational methods for quantifying blood flow velocity and pressure fields in human arteries. We place particular emphasis on providing an introduction to the physics and applications of magnetic resonance imaging, and surveying lumped parameter, one-dimensional, and three-dimensional numerical methods used to model blood flow.
Atherosclerotic plaques progress in a highly individual manner. The purposes of the Prediction of Progression of Coronary Artery Disease and Clinical Outcome Using Vascular Profiling of Shear Stress and Wall Morphology (PREDICTION) Study were to determine the role of local hemodynamic and vascular characteristics in coronary plaque progression and to relate plaque changes to clinical events.
Vascular profiling, using coronary angiography and intravascular ultrasound, was used to reconstruct each artery and calculate endothelial shear stress and plaque/remodeling characteristics in vivo. Three-vessel vascular profiling (2.7 arteries per patient) was performed at baseline in 506 patients with an acute coronary syndrome treated with a percutaneous coronary intervention and in a subset of 374 (74%) consecutive patients 6 to 10 months later to assess plaque natural history. Each reconstructed artery was divided into sequential 3-mm segments for serial analysis. One-year clinical follow-up was completed in 99.2%. Symptomatic clinical events were infrequent: only 1 (0.2%) cardiac death; 4 (0.8%) patients with new acute coronary syndrome in nonstented segments; and 15 (3.0%) patients hospitalized for stable angina. Increase in plaque area (primary end point) was predicted by baseline large plaque burden; decrease in lumen area (secondary end point) was independently predicted by baseline large plaque burden and low endothelial shear stress. Large plaque size and low endothelial shear stress independently predicted the exploratory end points of increased plaque burden and worsening of clinically relevant luminal obstructions treated with a percutaneous coronary intervention at follow-up. The combination of independent baseline predictors had a 41% positive and 92% negative predictive value to predict progression of an obstruction treated with a percutaneous coronary intervention.
Large plaque burden and low local endothelial shear stress provide independent and additive prediction to identify plaques that develop progressive enlargement and lumen narrowing.
URL: http:www.//clinicaltrials.gov. Unique Identifier: NCT01316159.
Coupled fluid–structure interaction (FSI) analysis of the human right coronary artery (RCA) has been carried out to investigate the effects of wall compliance on coronary hemodynamics. A 3-D model of a stenosed RCA was reconstructed based on multislice computerized tomography images. A velocity waveform in the proximal RCA and a pressure waveform in the distal RCA of a patient with a severe stenosis were acquired with a catheter delivered wire probe and applied as boundary conditions. The arterial wall was modeled as a Mooney–Rivlin hyperelastic material. The predicted maximum wall displacement (3.85 mm) was comparable with the vessel diameter (∼4 mm), but the diameter variation was much smaller, 0.134 mm at the stenosis and 0.486 mm in the distal region. Comparison of the computational results between the FSI and rigid-wall models showed that the instantaneous wall shear stress (WSS) distributions were affected by diameter variation in the arterial wall; increasing systolic blood pressure dilated the vessel and consequently lowered WSS, whereas the opposite occurred when pressure started to decrease. However, the effects of wall compliance on time-averaged WSS (TAWSS) and oscillatory shear index (OSI) were insignificant (4.5 and 2.7% difference in maximum TAWSS and OSI, respectively). Copyright © 2009 John Wiley & Sons, Ltd.
The knowledge of local vascular anatomy and function in the human body is of high interest for the diagnosis and treatment of cardiovascular disease. A comprehensive analysis of the hemodynamics in the thoracic aorta is presented based on the integration of flow-sensitive 4D MRI with state-of-the-art rapid prototyping technology and computational fluid dynamics (CFD). Rapid prototyping was used to transform aortic geometries as measured by contrast-enhanced MR angiography into realistic vascular models with large anatomical coverage. Integration into a flow circuit with patient-specific pulsatile in-flow conditions and application of flow-sensitive 4D MRI permitted detailed analysis of local and global 3D flow dynamics in a realistic vascular geometry. Visualization of characteristic 3D flow patterns and quantitative comparisons of the in vitro experiments with in vivo data and CFD simulations in identical vascular geometries were performed to evaluate the accuracy of vascular model systems. The results indicate the potential of such patient-specific model systems for detailed experimental simulation of realistic vascular hemodynamics. Further studies are warranted to examine the influence of refined boundary conditions of the human circulatory system such as fluid-wall interaction and their effect on normal and pathological blood flow characteristics associated with vascular geometry. Magn Reson Med 59:535–546, 2008. © 2008 Wiley-Liss, Inc.
The scope of this work is to study the pulsatile flow of a blood mimicking fluid in a micro channel that simulates a bifurcated small artery, in which the Fahraeus-Lindqvist effect is insignificant. An aqueous glycerol solution with small amounts of xanthan gum was used for simulating viscoelastic properties of blood and in vivo flow conditions were reproduced. Local flow velocities were measured using micro Particle Image Velocimetry (μ-PIV). From the measured velocity distributions, the wall shear stress (WSS) and its variation during a pulse were estimated. The Reynolds numbers employed are relatively low, i.e. similar to those prevailing during blood flow in small arteries. Experiments both with a Newtonian and a non-Newtonian fluid (having asymptotic viscosity equal to the viscosity of the Newtonian one) proved that the common assumption that blood behaves as a Newtonian fluid is not valid for blood flow in small arteries. It was also shown that the outer wall of the bifurcation, which is exposed to a lower WSS, is more predisposed to atherosclerotic plaque formation. Moreover, this region in small vessels is shorter than the one in large arteries, as the developed secondary flow decays faster. Finally, the WSS values in small arteries were found to be lower than those in large ones.
A significant amount of evidence linking wall shear stress to neointimal hyperplasia has been reported in the literature. As a result, numerical and experimental models have been created to study the influence of stent design on wall shear stress. Traditionally, blood has been assumed to behave as a Newtonian fluid, but recently that assumption has been challenged. The use of a linear model; however, can reduce computational cost, and allow the use of Newtonian fluids (e.g., glycerine and water) instead of a blood analog fluid in an experimental setup. Therefore, it is of interest whether a linear model can be used to accurately predict the wall shear stress caused by a non-Newtonian fluid such as blood within a stented arterial segment. The present work compares the resulting wall shear stress obtained using two linear and one nonlinear model under the same flow waveform. All numerical models are fully three-dimensional, transient, and incorporate a realistic stent geometry. It is shown that traditional linear models (based on blood's lowest viscosity limit, 3.5 Pa s) underestimate the wall shear stress within a stented arterial segment, which can lead to an overestimation of the risk of restenosis. The second linear model, which uses a characteristic viscosity (based on an average strain rate, 4.7 Pa s), results in higher wall shear stress levels, but which are still substantially below those of the nonlinear model. It is therefore shown that nonlinear models result in more accurate predictions of wall shear stress within a stented arterial segment.
Using human pathologic specimens from the CVPath registry, we aimed to investigate the location of the atherosclerotic plaque at bifurcation in native coronary atherosclerotic lesions and to determine the responses at bifurcation after implantation of bare-metal stents (BMS) and drug-eluting stents (DES).
Greater atherosclerotic plaque burden has been reported to occur at low-shear regions of bifurcation.
Twenty-six randomly selected human atherosclerotic nonstented coronary bifurcation lesions were examined longitudinally for plaque distribution in patients dying of severe coronary artery disease. Forty stented bifurcation lesions (21 BMS and 19 DES) were reviewed and analyzed by morphometry.
In nonstented coronary bifurcations, the lateral wall showed significantly greater intima as well as necrotic core thickness than the flow divider. In the stented lesion, the frequency of late stent thrombosis was greater in the DES group (75%) than in the BMS group (36%), whereas restenosis was more frequent in the BMS group (33%) than in the DES group (5%). Neointimal formation was significantly less at the flow divider compared with the lateral wall in the DES group (0.07 mm [interquartile range (IQR) 0.03 to 0.15 mm] vs. 0.17 mm [IQR 0.09 to 0.23 mm]; p = 0.001), whereas this difference was not significant in the BMS group. Similarly, uncovered struts and fibrin deposition was significantly greater at the flow divider compared with the lateral wall in the DES group (uncovered: 40% [IQR 16% to 76%] vs. 0% [IQR 0% to 15%]; p = 0.001; fibrin: 60% [IQR 21% to 67%] vs. 17% [IQR 0% to 55%]; p = 0.01), but not in the BMS group.
Plaque formation in native coronary bifurcations and neointimal growth after DES implantation was significantly less at the flow divider versus the lateral wall. A higher prevalence of late stent thrombosis in DES compared with BMS was associated with greater uncovered struts at flow divider sites, which is likely due to flow disturbances.
The aim of this study was to develop a fully subject-specific model of the right coronary artery (RCA), including dynamic vessel motion, for computational analysis to assess the effects of cardiac-induced motion on hemodynamics and resulting wall shear stress (WSS). Vascular geometries were acquired in the right coronary artery (RCA) of a healthy volunteer using a navigator-gated interleaved spiral sequence at 14 time points during the cardiac cycle. A high temporal resolution velocity waveform was also acquired in the proximal region. Cardiac-induced dynamic vessel motion was calculated by interpolating the geometries with an active contour model and a computational fluid dynamic (CFD) simulation with fully subject-specific information was carried out using this model. The results showed the expected variation of vessel radius and curvature throughout the cardiac cycle, and also revealed that dynamic motion of the right coronary artery consequent to cardiac motion had significant effects on instantaneous WSS and oscillatory shear index. Subject-specific MRI-based CFD is feasible and, if scan duration could be shortened, this method may have potential as a non-invasive tool to investigate the physiological and pathological role of hemodynamics in human coronary arteries.
Phase contrast MRI allows access to tri-directional encoded velocity information and therefore, measurement of flow in the human hemodynamic system. The aim of this work was to investigate whether this technology could be applied to support the grading of stenosis in mid-size arteries. Using a specially constructed flow phantom and a stenosis model with tube diameter of 5mm and 8mm and a stenosis of 50%, experiments at different flow rates (180-640 ml/min), slice thickness (1-4 mm), field strength (1.5 and 3.0 T), and multi-slice as well as 3D volume acquisition were performed. The observations were assessed visually and evaluated by signal-to-noise (SNR) ratios in regions before and after the stenosis. The obtained results show that examinations should be performed at high field (3.0 T) and at flow rates up to 500 ml/min without hampering the measurements by areas of signal loss. In comparison, no detectable differences in the flow patterns of the two acquisition schemes could be observed. However, the SNR was higher using the 3D volume acquisition and thick slices. In summary, 3D PC-MRI of mid-size vessels with stenosis is feasible for certain flow rates. The presented results could be seen as guidance for in vivo situations to assess if an examination of a patient is reasonable in terms of outcome.
Efficiently obtaining a reliable coronary artery centerline from computed tomography angiography data is relevant in clinical practice. Whereas numerous methods have been presented for this purpose, up to now no standardized evaluation methodology has been published to reliably evaluate and compare the performance of the existing or newly developed coronary artery centerline extraction algorithms. This paper describes a standardized evaluation methodology and reference database for the quantitative evaluation of coronary artery centerline extraction algorithms. The contribution of this work is fourfold: (1) a method is described to create a consensus centerline with multiple observers, (2) well-defined measures are presented for the evaluation of coronary artery centerline extraction algorithms, (3) a database containing 32 cardiac CTA datasets with corresponding reference standard is described and made available, and (4) 13 coronary artery centerline extraction algorithms, implemented by different research groups, are quantitatively evaluated and compared. The presented evaluation framework is made available to the medical imaging community for benchmarking existing or newly developed coronary centerline extraction algorithms.
Image processing and Computer Numerical Controlled (CNC) machining techniques have been used to prepare a large-than-life investment cast of an aortic bifurcation from magnetic resonance images of a replica of the vessel. The technique will facilitate experimental studies of vascular fluid dynamics and permit the in vitro reproduction of flows in living subjects.
Coronary flow velocity varies widely between individuals, even at rest. Because of this variation, indices with less apparent deviation, such as the ratio of hyperemic to resting velocity (coronary flow reserve), have been more commonly studied. We tested the hypothesis that the flow continuity principle could be used to model resting coronary flow, and we examined the resulting velocity relationship.
We studied coronary velocity in 59 patients using a Doppler wire to measure resting and hyperemic average peak velocities in the left anterior descending artery. Quantitative techniques were used to calculate lumen cross-sectional area and the lengths of all distal coronary branches. Branch lengths were used to estimate regional left ventricular mass. We then calculated the ratio of lumen area to regional mass (A/m). Regional perfusion was estimated from the double product of heart rate and systolic blood pressure. Resting velocity (V) varied inversely with A/m ratio [V=46.5/(A/m); r=0.68, P<0.001]. Disease in the left anterior descending artery was categorized as none or luminal irregularities only (n=22), mild (n=15), or moderate (n=22). The A/m ratio declined across these groups (8.7+/-4.0, 8.5+/-6.2, and 5. 6+/-3.0 mm(2)/100 g, respectively; P<0.04), and the resting average peak velocity increased (27+/-16, 33+/-11, and 37+/-20 cm/s, respectively; P=0.06).
Resting coronary artery flow velocity is inversely related to the ratio of lumen area to regional left ventricular mass. Higher resting velocities are found when insufficient lumen size exists for the distal myocardial bed, as occurs with diffuse mild or moderate coronary atherosclerosis.
The purpose of this work was to investigate the effects of physiologically realistic cardiac-induced motion on hemodynamics in human right coronary arteries. The blood flow patterns were numerically simulated in a modeled right coronary artery (RCA) having a uniform circular cross section of 2.48 mm diam. Arterial motion was specified based on biplane cineangiograms, and incorporated physiologically realistic bending and torsion. Simulations were carried out with steady and pulsatile inflow conditions (mean ReD=233, α =1.82) in both fixed and moving RCA models, to evaluate the relative importance of RCA motion, flow pulsation, and the interaction between motion and flow pulsation. RCA motion with a steady inlet flow rate caused variations in wall shear stress (WSS) magnitude up to 150% of the inlet Poiseuille value. There was significant spatial variability in the magnitude of this motion-induced WSS variation. However, the time-averaged WSS distribution was similar to that predicted in a static model representing the time-averaged geometry. Furthermore, the effects of flow pulsatility dominated RCA motion-induced effects; specifically, there were only modest differences in the WSS history between simulations conducted in fixed and moving RCA models with pulsatile inflow. RCA motion has little effect on time-averaged WSS patterns. It has a larger effect on the temporal variation of WSS, but even this effect is overshadowed by the variations in WSS due to flow pulsation. The hemodynamic effects of RCA motion can, therefore, be ignored as a first approximation in modeling studies. © 2003 Biomedical Engineering Society.
PAC2003: 8719Uv, 8719Hh, 8719St, 8719Rr
A computational fluid dynamic (CFD) analysis is pre sented to describe local flow dynamics in both 3-D spatial and 4-D spatial and temporal domains from reconstructions of intravascular ultrasound (IVUS) and bi-plane angiographic fusion images. A left anterior descending (LAD) coronary artery segment geometry was accurately reconstructed and subsequently its motion was incorporated into the CFD model. The results indicate that the incorporation of motion had appreciable effects on blood flow patterns. The velocity profiles in the region of a stenosis and the circumferential distribution of the axial wall shear stress (WSS) patterns in the vessel are altered with the wall motion introduced in the simulation. The time-averaged axial WSS between simulations of steady flow and unsteady flow without arterial motion were comparable (-0.3 to 13.7 Pa in unsteady flow versus -0.2 to 10.1 Pa in steady flow) while the magnitudes decreased when motion was introduced (0.3-4.5 Pa). The arterial wall motion affects the time-mean WSS and the oscillatory shear index in the coronary vessel fluid dynamics and may provide more realistic predictions on the progression of atherosclerotic disease.
Computational fluid dynamics (CFD) methods based on in vivo three-dimensional vessel reconstructions have recently been shown to provide prognostically relevant hemodynamic data. However, the geometry reconstruction and the assessment of clinically relevant hemodynamic parameters may depend on the used imaging modality. This study compares geometric reconstruction and calculated wall shear stress (WSS) values based on magnetic resonance imaging (MRI) and computed tomography (CT). Both imaging methods were applied to a same 2.5-fold upscale silicon model of the left coronary artery (LCA) main bifurcation. The original model is an optically digitized post mortem vessel cast. This digitized geometry is considered as a "gold standard" or original geometry for the MRI versus CT comparative study. The use of the upscale model allowed generating a high resolution CT raw data set with voxel size of 0.156 x 0.156 x 0.36 mm(3) and a high resolution MRI data set with an equivalent voxel size of 0.196 x 0.196 x 0.196 mm(3) for corresponding in vivo conditions. MRI based reconstruction achieved a mean Hausdorff surface distance of 0.1 mm to the original geometry. This is 2.5 times better than CT based reconstruction with mean Hausdorff surface distance of 0.252 mm. A comparison of the calculated mean WSS shows good correlation (r = 0.97) and good agreement among the three modalities with a WSS of 0.65 Pa in the original model, of 0.68 Pa in the CT based model and of 0.67 Pa in the MRI based model.
A validation study and early results for non-invasive, in vivo measurement of coronary artery blood flow using phase contrast magnetic resonance imaging (PC-MRI) at 3.0T is presented. Accuracy of coronary artery blood flow measurements by phase contrast MRI is limited by heart and respiratory motion as well as the small size of the coronary arteries. In this study, a navigator echo gated, cine phase velocity mapping technique is described to obtain time-resolved velocity and flow waveforms of small diameter vessels at 3.0T. Phantom experiments using steady, laminar flow are presented to validate the technique and show flow rates measured by 3.0T phase contrast MRI to be accurate within 15% of true flow rates. Subsequently, in vivo scans on healthy volunteers yield velocity measurements for blood flow in the right, left anterior descending, and left circumflex arteries. Measurements of average, cross-sectional velocity were obtainable in 224/243 (92%) of the cardiac phases. Time-averaged, cross-sectional velocity of the blood flow was 6.8+/-4.3cm/s in the LAD, 8.0+/-3.8cm/s in the LCX, and 6.0+/-1.6cm/s in the RCA.
A computational model incorporating physiological motion and uniform transient wall deformation of a branchless right coronary artery (RCA) was developed to assess the influence of artery compliance on wall shear stress (WSS). Arterial geometry and deformation were derived from modern medical imaging techniques, whereas the blood flow was solved numerically employing a moving-grid approach using a well-validated in-house finite element code. The simulation results indicate that artery compliance affects the WSS in the RCA heterogeneously, with the distal region mostly experiencing these effects. Under physiological inflow conditions, coronary compliance contributed to phase changes in the WSS time history, without affecting the temporal gradient of the local WSS nor the bounds of the WSS magnitude. Compliance does not cause considerable changes to the topology of WSS vector patterns nor to the localization of WSS minima along the RCA. We conclude that compliance is not an important factor affecting local hemodynamics in the proximal region of the RCA while the influence of compliance in the distal region needs to be evaluated in conjunction with the outflow to the myocardium through the major branches of the RCA.
Patient specific hemodynamics: combined 4D flow-sensitive MRI and CFD. In: Computational biomechanics for medicine: soft tissues and the musculoskeletal system
- A F Stalder
- Z Liu
- J Hennig
- J G Korvink
- K C Li
- M Markl
Stalder AF, Liu Z, Hennig J, Korvink JG, Li KC, Markl M. Patient specific hemodynamics: combined 4D flow-sensitive MRI and CFD. In:
Computational biomechanics for medicine: soft tissues and the musculoskeletal system. New York: Springer; 2011.
Construction of a coronary atlas from CT angiography. In: Medical image computing and computer assisted intervention
- P Medrano-Gracia
- J Ormiston
- M Webster
Medrano-Gracia P, Ormiston J, Webster M, et al. (eds.). Construction
of a coronary atlas from CT angiography. In: Medical image computing and computer assisted intervention. 2014. Boston: MICCAI.