Left atrial (LA) blood flow plays an important role in diseases such as atrial fibrillation (AF) and atrial cardiomyopathy since alterations in the blood flow might lead to thrombus formation and stroke. Using traditional techniques, such as echocardiography, atrial flow velocities can be measured at the pulmonary veins and the mitral valve, but a comprehensive understanding of the three-dimensional atrial flow field is missing. Previously, ventricular flow has been analyzed using flow component analysis, revealing new insights into ventricular flow and function. Thus, the aim of this project was to develop a comprehensive flow component analysis method for the LA and explore its utility in 21 patients with paroxysmal atrial fibrillation compared with a control group of 8 participants. The flow field was derived from time-resolved CT acquired during sinus rhythm using computational fluid dynamics. Flow components were computed from particle tracking. We identified six atrial flow components: conduit, reservoir, delayed ejection, retained inflow, residual volume, and pulmonary vein backflow. It was shown that conduit flow, defined as blood entering and leaving the LA within the same diastolic phase, exists in most subjects. Although the volume of conduit and reservoir is similar in patients with paroxysmal AF in sinus rhythm and controls, the volume of the other components is increased in paroxysmal AF. Comprehensive quantification of LA flow using flow component analysis makes atrial blood flow quantifiable, thus facilitating investigation of mechanisms underlying atrial dysfunction and can increase understanding of atrial blood flow in disease progression and stroke risk. NEW & NOTEWORTHY We developed a new comprehensive approach to atrial blood component analysis that includes both conduit flow and residual volume and compared the flow components of atrial fibrillation (AF) patients in sinus rhythm with controls. Conduit and reservoir flow were similar between the groups, whereas components with longer residence time in the left atrium were increased in the AF group. This could add to the pathophysiological understanding of atrial diseases and possibly clinical management.

Introduction: Atrial fibrillation (AF) is associated with an increased risk of stroke, often caused by thrombi that form in the left atrium (LA), and especially in the left atrial appendage (LAA). The underlying mechanism is not fully understood but is thought to be related to stagnant blood flow, which might be present despite sinus rhythm. However, measuring blood flow and stasis in the LAA is challenging due to its small size and low velocities. We aimed to compare the blood flow and stasis in the left atrium of paroxysmal AF patients with controls using computational fluid dynamics (CFD) simulations.Methods : The CFD simulations were based on time-resolved computed tomography including the patient-specific cardiac motion. The pipeline allowed for analysis of 21 patients with paroxysmal AF and 8 controls. Stasis was estimated by computing the blood residence time.Results and Discussion: Residence time was elevated in the AF group (p < 0.001). Linear regression analysis revealed that stasis was strongest associated with LA ejection ratio (p < 0.001, R-2 = 0.68) and the ratio of LA volume and left ventricular stroke volume (p < 0.001, R-2 = 0.81). Stroke risk due to LA thrombi could already be elevated in AF patients during sinus rhythm. In the future, patient specific CFD simulations may add to the assessment of this risk and support diagnosis and treatment.

Difficulties in achieving knowledge about physiology and anatomy of the beating heart highlight the challenges with more traditional pedagogical methods. Recent research regarding anatomy education has mainly focused on digital three-dimensional models. However, these pedagogical improvements may not be entirely applicable to cardiac anatomy and physiology due to the multidimensional complexity with moving anatomy and complex blood flow. The aim of this study was therefore to evaluate whether high quality time-resolved anatomical images combined with realistic blood flow simulations improve the understanding of cardiac structures and function. Three time-resolved datasets were acquired using time-resolved computed tomography and blood flow was computed using Computational Fluid Dynamics. The anatomical and blood flow information was combined and interactively visualized using volume rendering on an advanced stereo projection system. The setup was tested in interactive lectures for medical students. Ninety-seven students participated. Summative assessment of examinations showed significantly improved mean score (18.1 +/- 4.5 vs 20.3 +/- 4.9, p = 0.002). This improvement was driven by knowledge regarding myocardial hypertrophy and pressure-velocity differences over a stenotic valve. Additionally, a supplementary formative assessment showed significantly more agreeing answers than disagreeing answers (p < 0.001) when the participants subjectively evaluated the contribution of the visualizations to their education and knowledge. In conclusion, the use of simultaneous visualization of time-resolved anatomy data and simulated blood flow improved medical students results, with a particular effect on understanding of cardiac physiology and these simulations may be useful educational tools for teaching complex anatomical and physiological concepts.

Recent studies have correlated kinetic energy (KE) and viscous dissipation rate (VDR) in the left ventricle (LV) with heart health. These studies have relied on 4D-flow imaging or computational fluid dynamics modeling, which are able to measure, or compute, all 3 components (3C) of the blood flow velocity in 3 dimensional (3D) space. This richness of data is difficult to acquire clinically. Alternatively, color Doppler echocardiography (CDE) is more widespread clinically, but only measures a single radial component of velocity and typically only over a planar section. Because of this limitation, prior CDE-based studies have first reconstructed a second component of velocity in the measurement plane prior to evaluating VDR or KE. Herein, we propose 1C-based surrogates of KE and VDR that can be derived directly from the radial component of the flow velocity in the LV. Our results demonstrate that the proposed 1C-based surrogates of KE and VDR are generally as well-correlated with the true KE and VDR values as surrogates that use reconstructed 2C flow data. Moreover, the correlation of these 1C-based surrogates with the true values indicate that CDE (3D in particular) may be useful in evaluating these metrics in practice.

Significant mitral valve regurgitation creates progressive adverse remodeling of the left ventricle (LV). Replacement of the failing valve with a prosthesis generally improves patient outcomes but leaves the patient with non-physiological intracardiac flow patterns that might contribute to their future risk of thrombus formation and embolism. It has been suggested that the angular orientation of the implanted valve might modify the postoperative distortion of the intraventricular flow field. In this study, we investigated the effect of prosthetic valve orientation on LV flow patterns by using heart geometry from a patient with LV dysfunction and a competent native mitral valve to calculate intracardiac flow fields with computational fluid dynamics (CFD). Results were validated using in vivo 4D Flow MRI. The computed flow fields were compared to calculations following virtual implantation of a mechanical heart valve oriented in four different angles to assess the effect of leaflet position. Flow patterns were visualized in longand short-axes and quantified with flow component analysis. In comparison to a native valve, valve implantation increased the proportion of the mitral inflow remaining in the basal region and further increased the residual volume in the apical area. Only slight changes due to valve orientation were observed. Using our numerical framework, we demonstrated quantitative changes in left ventricular blood flow due to prosthetic mitral replacement. This framework may be used to improve design of prosthetic heart valves and implantation procedures to minimize the potential for apical flow stasis, and potentially assist personalized treatment planning. (c) 2020 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

Blood flow simulations are making their way into the clinic, and much attention is given to estimation of fractional flow reserve in coronary arteries. Intracardiac blood flow simulations also show promising results, and here the flow field is expected to depend on the pulmonary venous (PV) flow rates. In the absence of in vivo measurements, the distribution of the flow from the individual PVs is often unknown and typically assumed. Here, we performed intracardiac blood flow simulations based on time-resolved computed tomography on three patients, and investigated the effect of the distribution of PV flow rate on the flow field in the left atrium and ventricle. A design-of-experiment approach was used, where PV flow rates were varied in a systematic manner. In total 20 different simulations were performed per patient, and compared to in vivo 4D flow MRI measurements. Results were quantified by kinetic energy, mitral valve velocity profiles and root-mean-square errors of velocity. While large differences in atrial flow were found for varying PV inflow distributions, the effect on ventricular flow was negligible, due to a regularizing effect by mitral valve. Equal flow rate through all PVs most closely resembled in vivo measurements and is recommended in the absence of a priori knowledge.

Purpose: To examine methods for visualizing and quantifying flow stasis in abdominal aortic aneurysms (AAA) using 4D Flow MRI. Methods: Three methods were investigated: conventional volumetric residence time (VRT), mean velocity analysis (MVA), and particle travel distance analysis (TDA). First, ideal 4D Flow MRI data was generated using numerical simulations and used as a platform to explore the effects of noise and background phase-offset errors, both of which are common 4D Flow MRI artifacts. Error-free results were compared to noise or offset affected results using linear regression. Subsequently, 4D Flow MRI data for thirteen (13) subjects with AAA was acquired and used to compare the stasis quantification methods against conventional flow visualization. Results: VRT (R-2 = 0.69) was more sensitive to noise than MVA (R-2 = 0.98) and TDA (R-2 = 0.99) at typical noncontrast signal-to-noise ratio levels (SNR = 20). VRT (R-2 = 0.14) was more sensitive to background phase-offsets than MVA (R-2 = 0.99) and TDA (R-2 = 0.96) when considering a 95% effective background phase-offset correction. Qualitatively, TDA outperformed MVA (Wilcoxon p amp;lt; 0.005, mean score improvement 1.6/5), and had good agreement (median score 4/5) with flow visualizations. Conclusion: Flow stasis can be quantitatively assessed using 4D Flow MRI. While conventional residence time calculations fail due to error accumulation as a result of imperfect measured velocity fields, methods that do not require lengthy particle tracking perform better. MVA and TDA are less sensitive to measurement errors, and TDA generates results most similar to those obtained using conventional flow visualization.

PurposeTo measure the Reynolds stress tensor using 4D flow MRI, and to evaluate its contribution to computed pressure maps. MethodsA method to assess both velocity and Reynolds stress using 4D flow MRI is presented and evaluated. The Reynolds stress is compared by cross-sectional integrals of the Reynolds stress invariants. Pressure maps are computed using the pressure Poisson equationboth including and neglecting the Reynolds stress. ResultGood agreement is seen for Reynolds stress between computational fluid dynamics, simulated MRI, and MRI experiment. The Reynolds stress can significantly influence the computed pressure loss for simulated (eg, -0.52% vs -15.34% error; Pamp;lt;0.001) and experimental (eg, 30611 vs 203 +/- 6 Pa; Pamp;lt;0.001) data. A 54% greater pressure loss is seen at the highest experimental flow rate when accounting for Reynolds stress (Pamp;lt;0.001). Conclusion4D flow MRI with extended motion-encoding enables quantification of both the velocity and the Reynolds stress tensor. The additional information provided by this method improves the assessment of pressure gradients across a stenosis in the presence of turbulence. Unlike conventional methods, which are only valid if the flow is laminar, the proposed method is valid for both laminar and disturbed flow, a common presentation in diseased vessels. Magn Reson Med 79:1962-1971, 2018. (c) 2017 International Society for Magnetic Resonance in Medicine.

Background Assessment of myocardial deformation from time-resolved cardiac computed tomography (4D CT) would augment the already available functional information from such an examination without incurring any additional costs. A deformable image registration (DIR) based approach is proposed to allow fast and automatic myocardial tracking in clinical 4D CT images.

Methods Left ventricular myocardial tissue displacement through a cardiac cycle was tracked using a B-spline transformation based DIR. Gradient of such displacements allowed Lagrangian strain estimation with respect to end-diastole in clinical 4D CT data from ten subjects with suspected coronary artery disease. Dice similarity coefficient (DSC), point-to-curve error (PTC), and tracking error were used to assess the tracking accuracy. Wilcoxon signed rank test provided significance of tracking errors. Topology preservation was verified using Jacobian of the deformation. Reliability of estimated strains and torsion (normalized twist angle) was tested in subjects with normal function by comparing them with normal strain in the literature.

Results Comparison with manual tracking showed high accuracy (DSC: 0.99± 0.05; PTC: 0.56mm± 0.47 mm) and resulted in determinant(Jacobian) > 0 for all subjects, indicating preservation of topology. Average radial (0.13 mm), angular (0.64) and longitudinal (0.10 mm) tracking errors for the entire cohort were not significant (p > 0.9). For patients with normal function, average strain [circumferential, radial, longitudinal] and peak torsion estimates were: [-23.5%, 31.1%, −17.2%] and 7.22°, respectively. These estimates were in conformity with the reported normal ranges in the existing literature.

Conclusions Accurate wall deformation tracking and subsequent strain estimation are feasible with the proposed method using only routine time-resolved 3D cardiac CT.

Purpose

To investigate four-dimensional (4D) flow CT for the assessment of intracardiac blood flow patterns as compared with 4D flow MRI.

Materials and Methods

This prospective study acquired coronary CT angiography and 4D flow MRI data between February and December 2016 in a cohort of 12 participants (age range, 36–74 years; mean age, 57 years; seven men [age range, 36–74 years; mean age, 57 years] and five women [age range, 52–73 years; mean age, 64 years]). Flow simulations based solely on CT-derived cardiac anatomy were assessed together with 4D flow MRI measurements. Flow patterns, flow rates, stroke volume, kinetic energy, and flow components were quantified for both techniques and were compared by using linear regression.

Results

Cardiac flow patterns obtained by using 4D flow CT were qualitatively similar to 4D flow MRI measurements, as graded by three independent observers. The Cohen κ score was used to assess intraobserver variability (0.83, 0.79, and 0.70) and a paired Wilcoxon rank-sum test showed no significant change (P > .05) between gradings. Peak flow rate and stroke volumes between 4D flow MRI measurements and 4D flow CT measurements had high correlation (r = 0.98 and r = 0.81, respectively; P < .05 for both). Integrated kinetic energy quantified at peak systole correlated well (r = 0.95, P < .05), while kinetic energy levels at early and late filling showed no correlation. Flow component analysis showed high correlation for the direct and residual components, respectively (r = 0.93, P < .05 and r = 0.87, P < .05), while the retained and delayed components showed no correlation.

Conclusion

Four-dimensional flow CT produced qualitatively and quantitatively similar intracardiac blood flow patterns compared with the current reference standard, four-dimensional flow MRI.

Purpose: To explore the use of MR-estimated turbulence quantities for the assessment of turbulent flow effects on the vessel wall. Methods: Numerical velocity data for two patient-derived models was obtained using computational fluid dynamics (CFD) for two physiological flow rates. The four-dimensional (4D) Flow MRI measurements were simulated at three different spatial resolutions and used to investigate the estimation of turbulent wall shear stress (tWSS) using the intravoxel standard deviation (IVSD) of velocity and turbulent kinetic energy (TKE) estimated near the vessel wall. Results: Accurate estimation of tWSS using the IVSD is limited by the spatial resolution achievable with 4D Flow MRI. TKE, estimated near the wall, has a strong linear relationship to the tWSS (mean R(2=)0.84). Near-wall TKE estimates from MR simulations have good agreement to CFD-derived ground truth (mean R-2=0.90). Maps of near-wall TKE have strong visual correspondence to tWSS. Conclusion: Near-wall estimation of TKE permits assessment of relative maps of tWSS, but direct estimation of tWSS is challenging due to limitations in spatial resolution. Assessment of tWSS and near-wall TKE may open new avenues for analysis of different pathologies. (C) 2016 International Society for Magnetic Resonance in Medicine

Lumped parameter models of the cardiovascular system have the potential to assist researchers and clinicians to better understand cardiovascular function. The value of such models increases when they are subject specific. However, most approaches to personalize lumped parameter models have thus far required invasive measurements or fall short of being subject specific due to a lack of the necessary clinical data. Here, we propose an approach to personalize parameters in a model of the heart and the systemic circulation using exclusively non-invasive measurements. The personalized model is created using flow data from four-dimensional magnetic resonance imaging and cuff pressure measurements in the brachial artery. We term this personalized model the cardiovascular avatar. In our proof-of-concept study, we evaluated the capability of the avatar to reproduce pressures and flows in a group of eight healthy subjects. Both quantitatively and qualitatively, the model-based results agreed well with the pressure and flow measurements obtained in vivo for each subject. This non-invasive and personalized approach can synthesize medical data into clinically relevant indicators of cardiovascular function, and estimate hemodynamic variables that cannot be assessed directly from clinical measurements.

In this study, cardiac blood flow was simulated using Computational Fluid Dynamics and compared to in vivo flow measurements by 4D Flow MRI. In total, nine patients with various heart diseases were studied. Geometry and heart wall motion for the simulations were obtained from clinical CT measurements, with 0.3x0.3x0.3 mm spatial resolution and 20 time frames covering one heartbeat. The CFD simulations included pulmonary veins, left atrium and ventricle, mitral and aortic valve, and ascending aorta. Mesh sizes were on the order of 6-16 million cells, depending on the size of the heart, in order to resolve both papillary muscles and trabeculae. The computed flow field agreed visually very well with 4D Flow MRI, with characteristic vortices and flow structures seen in both techniques. Regression analysis showed that peak flow rate as well as stroke volume had an excellent agreement for the two techniques. We demonstrated the feasibility, and more importantly, fidelity of cardiac flow simulations by comparing CFD results to in vivo measurements. Both qualitative and quantitative results agreed well with the 4D Flow MRI measurements. Also, the developed simulation methodology enables “what if” scenarios, such as optimization of valve replacement and other surgical procedures.

The pressure drop across a stenotic vessel is an important parameter in medicine, providing a commonly used and intuitive metric for evaluating the severity of the stenosis. However, non-invasive estimation of the pressure drop under pathological conditions has remained difficult. This study demonstrates a novel method to quantify the irreversible pressure drop across a stenosis using 4D Flow MRI by calculating the total turbulence production of the flow. Simulation MRI acquisitions showed that the energy lost to turbulence production can be accurately quantified with 4D Flow MRI within a range of practical spatial resolutions (1-3 mm; regression slope = 0.91, R-2 = 0.96). The quantification of the turbulence production was not substantially influenced by the signal-to-noise ratio (SNR), resulting in less than 2% mean bias at SNR amp;gt; 10. Pressure drop estimation based on turbulence production robustly predicted the irreversible pressure drop, regardless of the stenosis severity and post-stenosis dilatation (regression slope = 0.956, R-2 = 0.96). In vitro validation of the technique in a 75% stenosis channel confirmed that pressure drop prediction based on the turbulence production agreed with the measured pressure drop (regression slope = 1.15, R-2 = 0.999, Bland-Altman agreement = 0.75 +/- 3.93 mmHg).

Wall shear stress (WSS) disturbances are commonly expressed at sites of abnormal flow obstructions and may play an essential role in the pathogenesis of various vascular diseases. In laminar flows these disturbances have recently been assessed by the transverse wall shear stress (transWSS), which accounts for the WSS multidirectionality. Site-specific estimations of WSS disturbances in pulsatile transitional and turbulent type of flows are more challenging due to continuous and unpredictable changes in WSS behavior. In these complex flow settings, the transWSS may serve as a more comprehensive descriptor for assessing WSS disturbances of general nature compared to commonly used parameters. In this study large eddy simulations (LES) were used to investigate the transWSS properties in flows subjected to different pathological turbulent flow conditions, governed by a patient-specific model of an aortic coarctation pre and post balloon angioplasty. Results showed that regions of strong near-wall turbulence were collocated with regions of elevated transWSS and turbulent WSS, while in more transitional-like near-wall flow regions a closer resemblance was found between transWSS and low, and oscillatory WSS. Within the frame of this study, the transWSS parameter demonstrated a more multi-featured picture of WSS disturbances when exposed to different types of flow regimes, characteristics which were not depicted by the other parameters alone. (C) 2016 Published by Elsevier Ltd.

Purpose: To assess how 4D flow MRI-based pressure and energy loss estimates correspond to net transstenotic pressure gradients (TPG(net)) and their dependence on spatial resolution. Methods: Numerical velocity data of stenotic flow were obtained from computational fluid dynamics (CFD) simulations in geometries with varying stenosis degrees, poststenotic diameters and flow rates. MRI measurements were simulated at different spatial resolutions. The simplified and extended Bernoulli equations, Pressure-Poisson equation (PPE), and integration of turbulent kinetic energy (TKE) and viscous dissipation were compared against the true TPG(net). Results: The simplified Bernoulli equation overestimated the true TPG(net) (8.74 +/- 0.67 versus 6.76 +/- 0.54 mmHg). The extended Bernoulli equation performed better (6.57 +/- 0.53 mmHg), although errors remained at low TPG(net). TPG(net) estimations using the PPE were always close to zero. Total TKE and viscous dissipation correlated strongly with TPG(net) for each geometry (r(2) &gt; 0.93) and moderately considering all geometries (r(2) = 0.756 and r(2) = 0.776, respectively). TKE estimates were accurate and minorly impacted by resolution. Viscous dissipation was overall underestimated and resolution dependent. Conclusion: Several parameters overestimate or are not linearly related to TPG(net) and/or depend on spatial resolution. Considering idealized axisymmetric geometries and in absence of noise, TPG(net) was best estimated using the extended Bernoulli equation. (C) 2015 The Authors. Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance.

Flow-induced blood damage plays an important role in determining the hemodynamic impact of abnormal blood flow, but quantifying of these effects, which are dominated by shear stresses in highly fluctuating turbulent flow, has not been feasible. This study evaluated the novel application of turbulence tensor measurements using simulated 4D Flow MRI data with six-directional velocity encoding for assessing hemodynamic stresses and corresponding blood damage index (BDI) in stenotic turbulent blood flow. The results showed that 4D Flow MRI underestimates the maximum principal shear stress of laminar viscous stress (PLVS), and overestimates the maximum principal shear stress of Reynolds stress (PRSS) with increasing voxel size. PLVS and PRSS were also overestimated by about 1.2 and 4.6 times at medium signal to noise ratio (SNR) = 20. In contrast, the square sum of the turbulent viscous shear stress (TVSS), which is used for blood damage index (BDI) estimation, was not severely affected by SNR and voxel size. The square sum of TVSS and the BDI at SNR amp;gt;20 were underestimated by less than 1% and 10%, respectively. In conclusion, this study demonstrated the feasibility of 4D Flow MRI based quantification of TVSS and BDI which are closely linked to blood damage.

Cardiac hemodynamics can be computed from medical imaging data, and results could potentially aid in cardiac diagnosis and treatment optimization. However, simulations are often based on simplified geometries, ignoring features such as papillary muscles and trabeculae due to their complex shape, limitations in image acquisitions, and challenges in computational modeling. This severely hampers the use of computational fluid dynamics in clinical practice. The overall aim of this study was to develop a novel numerical framework that incorporated these geometrical features. The model included the left atrium, ventricle, ascending aorta, and heart valves. The framework used image registration to obtain patient-specific wall motion, automatic remeshing to handle topological changes due to the complex trabeculae motion, and a fast interpolation routine to obtain intermediate meshes during the simulations. Velocity fields and residence time were evaluated, and they indicated that papillary muscles and trabeculae strongly interacted with the blood, which could not be observed in a simplified model. The framework resulted in a model with outstanding geometrical detail, demonstrating the feasibility as well as the importance of a framework that is capable of simulating blood flow in physiologically realistic hearts.

PurposeEvaluate spiral three-dimensional (3D) phase contrast MRI for the assessment of turbulence and velocity in stenotic flow. MethodsA-stack-of-spirals 3D phase contrast MRI sequence was evaluated in vitro against a conventional Cartesian sequence. Measurements were made in a flow phantom with a 75% stenosis. Both spiral and Cartesian imaging were performed using different scan orientations and flow rates. Volume flow rate, maximum velocity and turbulent kinetic energy (TKE) were computed for both methods. Moreover, the estimated TKE was compared with computational fluid dynamics (CFD) data. ResultsThere was good agreement between the turbulent kinetic energy from the spiral, Cartesian and CFD data. Flow rate and maximum velocity from the spiral data agreed well with Cartesian data. As expected, the short echo time of the spiral sequence resulted in less prominent displacement artifacts compared with the Cartesian sequence. However, both spiral and Cartesian flow rate estimates were sensitive to displacement when the flow was oblique to the encoding directions. ConclusionSpiral 3D phase contrast MRI appears favorable for the assessment of stenotic flow. The spiral sequence was more than three times faster and less sensitive to displacement artifacts when compared with a conventional Cartesian sequence.

Turbulence and flow eccentricity can be measured by magnetic resonance imaging (MRI) and may play an important role in the pathogenesis of numerous cardiovascular diseases. In the present study, we propose quantitative techniques to assess turbulent kinetic energy (TKE) and flow eccentricity that could assist in the evaluation and treatment of stenotic severities. These hemodynamic parameters were studied in a pre-treated aortic coarctation (CoA) and after several virtual interventions using computational fluid dynamics (CFD), to demonstrate the effect of different dilatation options on the flow field. Patient-specific geometry and flow conditions were derived from MRI data. The unsteady pulsatile flow was resolved by large eddy simulation (LES) including non-Newtonian blood rheology. Results showed an inverse asymptotic relationship between the total amount of TKE and degree of dilatation of the stenosis, where the pre-stenotic hypoplastic segment may limit the possible improvement by treating the CoA alone. Spatiotem-poral maps of TKE and flow eccentricity could be linked to the characteristics of the post-stenotic jet, showing a versatile response between the CoA dilatations. By including these flow markers into a combined MRI-CFD intervention framework, CoA therapy has not only the possibility to produce predictions via simulation, but can also be validated pre-and immediate post treatment, as well as during follow-up studies.

The size of the larger arteries increases during the entire life, but not much is known about how the change in size affects the blood flow. This study compares the flow field in a group of young males (N = 10, age = 23.5 +/- 1.4), with a group of older males (N = 8, age = 58.0 +/- 2.8). Aortic geometries were obtained by magnetic resonance imaging, and the aortic blood flow field was computed using computational fluid dynamics. The aortic wall shear stress was obtained from the computations, and it was concluded that time-averaged wall shear stress decreased with increased age, probably as a consequence of increased aortic diameter and decreased stroke volume, which in turn reduces the shear rates in the aorta. However, the oscillatory shear index, which is a measure of the oscillatory nature of the wall shear stress vector, seemed to be unaffected by aging.

Turbulence and flow eccentricity can be measured by magnetic resonance imaging (MRI) and may play an important role in the pathogenesis of numerous cardiovascular diseases. In the present study, we propose quantitative techniques to assess turbulent kinetic energy (TKE) and flow eccentricity that could assist in the evaluation and treatment of stenotic severities. These hemodynamic parameters were studied in a pre-treated aortic coarctation (CoA) and after several virtual interventions using computational fluid dynamics (CFD), to demonstrate the effect of different dilatation options on the flow field. Patient-specific geometry and flow conditions were derived from MRI data. The unsteady pulsatile flow was resolved by large eddy simulation (LES) including non-Newtonian blood rheology. Results showed an inverse asymptotic relationship between the total amount of TKE and degree of dilatation of the stenosis, where turbulent flow proximal the constriction limits the possible improvement by treating the CoA alone. Spatiotemporal maps of TKE and flow eccentricity could be linked to the characteristics of the jet, where improved flow conditions were favored by an eccentric dilatation of the CoA. By including these flow markers into a combined MRI-CFD intervention framework, CoA therapy has not only the possibility to produce predictions via simulation, but can also be validated pre- and immediate post treatment, as well as during follow-up studies.

Physiologically relevant simulations of blood flow require models that allow for wall deformation. Normally a fluid–structure interaction (FSI) approach is used; however, this method relies on several assumptions and patient-specific material parameters that are difficult or impossible to measure in vivo. In order to circumvent the assumptions inherent in FSI models, aortic wall motion was measured with MRI and prescribed directly in a numerical solver. In this way is not only the displacement of the vessel accounted for, but also the interaction with the beating heart and surrounding organs. In order to highlight the effect of wall motion, comparisons with standard rigid wall models was performed in a healthy human aorta. The additional computational cost associated with prescribing the wall motion was low (17%). Standard hemodynamic parameters such as time-averaged wall shear stress and oscillatory shear index seemed largely unaffected by the wall motion, as a consequence of the smoothing effect inherent in time-averaging. Conversely, instantaneous wall shear stress was greatly affected by the wall motion; the wall dynamics seemed to produce a lower wall shear stress magnitude compared to a rigid wall model. In addition, it was found that if wall motion was taken into account the computed flow field agreed better with in vivo measurements. This article shows that it is feasible to include measured subject-specific wall motion into numerical simulations, and that the wall motion greatly affects the flow field. This approach to incorporate measured motion should be considered in future studies of arterial blood flow simulations.

Turbulent blood flow is often associated with some sort of cardiovascular disease, e.g. sharp bends and/or sudden constrictions/expansions of the vessel wall. The energy losses associated with the turbulent flow may increase the heart workload in order to maintain cardiac output (CO). In the present study, the amount of turbulent kinetic energy (TKE) developed in the vicinity of an aortic coarctation was estimated pre-intervention and in a variety of post-intervention configurations, using scale-resolved image-based computational fluid dynamics (CFD). TKE can be measured using magnet resonance imaging (MRI) and have also been validated with CFD simulations [1], i.e. a parameter that not only can be quantified using simulations but can also be measured by MRI.

Patient-specific geometry and inlet flow conditions were obtained using contrast-enhanced MR angiography and 2D cine phase-contrast MRI, respectively. The intervention procedure was mimicked using an inflation simulation, where six different geometries were obtained. A scale-resolving turbulence model, large eddy simulation (LES), was utilized to resolve the largest turbulent scales and also to capture the laminar-to-turbulent transition. All cases were simulated using baseline CO and with a 20% CO increase to simulate a possible flow adaption after intervention.

For this patient, results shows a non-linear decay of the total amount of TKE integrated over the cardiac phase as the stenotic cross-sectional area is increased by the intervention.  Figure 1 shows the original segmented geometry and two dilated coarctation with corresponding volume rendering of the TKE at peak systole. Due to turbulent transition at a kink upstream the stenosis further dilation of the coarctation tends to restrict the TKE to a plateau, and continued vessel expansion may therefore only induce unnecessary stresses onto the arterial wall. 

This patient-specific non-invasive framework has shown the geometrical impact on the TKE estimates. New insight in turbulence development indicates that the studied coarctation can only be improved to a certain extent, where focus should be on the upstream region, if further TKE reduction is motivated. The possibility of including MRI in a combined framework could have great potential for future intervention planning and follow-up studies.  

[1] J. Lantz, T. Ebbers, J. Engvall and M. Karlsson, Numerical and Experimental Assessment of Turbulent Kinetic Energy in an Aortic Coarctation, Journal of Biomechnics, 2013. 46(11): p. 1851-1858.

The aim of this paper is to investigate the influence of the internal fluid flow characteristics of a special hydraulic solenoid valve, developed by Öhlins Racing AB, on its overall dynamic behavior. This valve is a two stage hydraulic pressure control valve and is typically mounted on each shock absorber of an on-road vehicle, allowing the implementation of semi-active suspension functionality. This technology is referred as CES (Continuously Controlled Electronic Suspension). The CES valve allows continuously controlling the vehicle shock absorbers damping characteristic by proportionally adjusting the metering geometry offered to its damping element, i.e. hydraulic oil. The electronic valve actuation and control, obtained through an electromagnetic solenoid, is based on the input from several vehicle dynamics sensors, such as accelerometers, gyroscopes and other displacement sensors. The CES valve’s unconventional design significantly influences the fluid flow, making the use of numerical modeling essential to discover its physical behavior and to support further product development. In this paper, a CFD (Computational Fluid Dynamics) analysis on the main and pilot stages of the hydraulic valve is discussed. This 3D numerical analysis is used to extract critical physical variables, affecting the valve behavior, such as flow coefficients and pressure distributions on the moving elements, i.e. flow forces. This information is coupled with a detailed lumped parameter model of the hydraulic valve, which solves for the valve moving element dynamics considering the action of the main external forces. Moreover, the 1D model allows predicting the valve critical pressure/flow characteristics. It is shown how the coupling of 3D modeling results with the CES valve 1D model strongly improves the whole valve dynamics numerical predictions over traditional methods for considering the effect of fluid inertia and discharge in lumped parameter simulations. Comparisons with measurement both on single regions of the CES hydraulic valve and on the entire valve are discussed in order to validate the various phases of numerical modeling.

The turbulent blood flow through an aortic coarctation in a 63-year old female patient was studied experimentally using magnetic resonance imaging (MRI), and numerically using computational fluid dynamics (CFD), before and after catheter intervention. Turbulent kinetic energy (TKE) was computed in the numerical model using large eddy simulation and compared with direct in vivo MRI measurements. Despite the two totally different methods to obtain TKE values, both quantitative and qualitative results agreed very well. The results showed that even though both blood flow rate and Reynolds number increased after intervention, total turbulent kinetic energy levels decreased in the coarctation. Therefore, the use of the Reynolds number alone as a measure of turbulence in cardiovascular flows should be used with caution. Furthermore, the change in flow field and kinetic energy were assessed, and it was found that before intervention a jet formed in the throat of the coarctation, which impacted the arterial wall just downstream the constriction. After intervention the jet was significantly weaker and broke up almost immediately, presumably resulting in less stress on the wall. As there was a good agreement between measurements and numerical results (the increase and decrease of integrated TKE matched measurements almost perfectly while peak values differed by approximately 1 mJ), the CFD results confirmed the MRI measurements while at the same time providing high-resolution details about the flow. Thus, this preliminary study indicates that MR-based TKE measurements might be useful as a diagnostic tool when evaluating intervention outcome, while the detailed numerical results might be useful for further understanding of the flow for treatment planning.

This thesis focuses on modeling and simulation of the blood flow in the aorta, the largest artery in the human body. It is an accepted fact that abnormal biological and mechanical interactions between the blood flow and the vessel wall are involved in the genesis and progression of cardiovascular diseases. The transport of low-density lipoprotein into the wall has been linked to the initiation of atherosclerosis. The mechanical forces acting on the wall can impede the endothelial cell layer function, which normally acts as a barrier to harmful substances. The wall shear stress (WSS) affects endothelial cell function, and is a direct consequence of the flow field; steady laminar flows are generally considered atheroprotective, while the unsteady turbulent flow could contribute to atherogenesis. Quantification of regions with abnormal wall shear stress is therefore vital in order to understand the initiation and progression of atherosclerosis.However, flow forces such as WSS cannot today be measured with significant accuracy using present clinical measurement techniques. Instead, researches rely on image-based computational modeling and simulation. With the aid of advanced mathematical models it is possible to simulate the blood flow, vessel dynamics, and even biochemical reactions, enabling information and insights that are currently unavailable through other techniques. During the cardiac cycle, the normally laminar aortic blood flow can become unstable and undergo transition to turbulence, at least in pathological cases such as coarctation of the aorta where the vessel is locally narrowed. The coarctation results in the formation of a jet with a high velocity, which will create the transition to turbulent flow. The high velocity will also increase the forces on the vessel wall. Turbulence is generally very difficult to model, requiring advanced mathematical models in order to resolve the flow features. As the flow is highly dependent on geometry, patient-specific representations of the in vivo arterial walls are needed, in order to perform an accurate and reliable simulation. Scale-resolving flow simulations were used to compute the WSS on the aortic wall and resolve the turbulent scales in the complex flow field. In addition to WSS, the turbulent flow before and after surgical intervention in an aortic coarctation was assessed. Numerical results were compared to state-of-the-art magnetic resonance imaging measurements. The results agreed very well, suggesting that that the measurement technique is reliable and could be used as a complement to standard clinical procedures when evaluating the outcome of an intervention.The work described in the thesis deals with patient-specific flows, and is, when possible, validated with experimental measurements. The results provide new insights to turbulent aortic flows, and show that image-based computational modeling and simulation are now ready for clinical practice.

Purpose: To evaluate the feasibility of spiral 3D phase contrast MRI for the assessment of velocity, volume flow rate, peak velocity and turbulent kinetic energy in stenotic flow.

Materials and Methods: A-stack-of-spirals 3D phase contrast MRI sequence was evaluated in-vitro against a conventional Cartesian sequence. Measurements were made in a flow phantom with a 75% stenosis. Both spiral and Cartesian imaging were performed using different scan orientations and flow rates. Volume flow rate, peak velocity and turbulent kinetic energy (TKE) were computed for both methods. For further validation, the estimated TKE was compared to computational fluid dynamics (CFD) data.

Results: The volume flow rate, peak velocity and TKE obtained with spiral 4D flow MRI agreed well with Cartesian data and CFD data. As expected, the short echo time of the spiral sequence resulted in less prominent displacement artifacts compared to the Cartesian sequence. However, both spiral and Cartesian flow rate estimates were sensitive to displacement when the flow was oblique to the encoding directions.

Conclusion: Spiral 3D phase contrast MRI appears favorable for the assessment of stenotic flow. The spiral sequence was more than three times faster and less sensitive to displacement artifacts when compared to a conventional Cartesian sequence.

The development of atherosclerosis is correlated to the accumulation of lipids in the arterial wall, which, in turn, may be caused by the build-up of low-density lipoproteins (LDL) on the arterial surface. The goal of this study was to model blood flow within a subject specific human aorta, and to study how the LDL surface concentration changed during a cardiac cycle. With measured velocity profiles as boundary conditions, a scale-resolving technique (large eddy simulation, LES) was used to compute the pulsatile blood flow that was in the transitional regime. The relationship between wall shear stress (WSS) and LDL surface concentration was investigated, and it was found that the accumulation of LDL correlated well with WSS. In general, regions of low WSS corresponded to regions of increased LDL concentration and vice versa. The instantaneous LDL values changed significantly during a cardiac cycle; during systole the surface concentration was low due to increased convective fluid transport, while in diastole there was an increased accumulation of LDL on the surface. Therefore, the near-wall velocity was investigated at four representative locations, and it was concluded that in regions with disturbed flow the LDL concentration had significant temporal changes, indicating that LDL accumulation is sensitive to not only the WSS but also near-wall flow.

In this study, large-eddy simulation (LES) is employed to calculate the disturbed flow field and the wall shear stress (WSS) in a subject specific human aorta. Velocity and geometry measurements using magnetic resonance imaging (MRI) are taken as input to the model to provide accurate boundary conditions and to assure the physiological relevance. In total, 50 consecutive cardiac cycles were simulated from which a phase average was computed to get a statistically reliable result. A decomposition similar to Reynolds decomposition is introduced, where the WSS signal is divided into a pulsating part (due to the mass flow rate) and a fluctuating part (originating from the disturbed flow). Oscillatory shear index (OSI) is plotted against time-averaged WSS in a novel way, and locations on the aortic wall where elevated values existed could easily be found. In general, high and oscillating WSS values were found in the vicinity of the branches in the aortic arch, while low and oscillating WSS were present in the inner curvature of the descending aorta. The decomposition of WSS into a pulsating and a fluctuating part increases the understanding of how WSS affects the aortic wall, which enables both qualitative and quantitative comparisons.

In the presented work, two studies using ComputationalFluid Dynamics (CFD) have been conducted on a generictruck-like model with and without a trailer unit at a speed of 80km/h. The purpose is to evaluate drag reduction possibilitiesusing externally fitted devices. A first study deals with a flapplaced at the back of a rigid truck and inclined at seven differentangles with two lengths. Results show that it is possible todecrease drag by 4%. In a second study, the flap has been fittedon the tractor and trailer units of a truck-trailer combination.Four settings were surveyed for this investigation, one of whichproved to decrease drag by up to 15%. A last configurationwhere the gap between the units has been closed has also beenevaluated. This configuration offers a 15% decrease in drag.Adding a flap to the closed gap configuration decreases drag by18%. New means of reducing aerodynamic drag of heavy-duty(HD) vehicles will be important in the foreseeable future inorder to improve the fuel economy. The possibilities of reducingdrag are prevalent using conceptual design.

Turbulent flow in the cardiovascular system may increase the risk for severe arterial disease. This workaddresses the feasibility of Large Eddy Simulation (LES) using a general purpose code as a tool for assessmentof cardiovascular flow and investigates Wall Shear Stress (WSS) in steady as well as pulsating turbulent pipeflow. Poiseuille flow was specified at the inlet, and with a suitable ammount of perturbations at the inlet it waspossible to predict experimental data. The extent of the recirculation zone was affected by the inlet disturbances,and magnitude as well as direction of the WSS vector varied significantly at the reattachment point. For thepulsating flow, WSS shows a complex pattern with different spatial and temporal variation along the pipe. Thewall shear stress gradient was calculated on the entire post-stenotic surface and each component in the gradientwas investigated. The off-diagonal components in the gradient are usually assumed to be small, but here they werefound to be on the same order of magnitude as the diagonal terms. This work demonstrates the need for a scaleresolving simulation technique to accurately model cardiovascular flows.

Modeling of Subject Specific Arterial Segments Using 3D Fluid Structure Interaction and a 1D-0D Arterial Tree Network Boundary Condition

Magnus Andersson, Jonas Lantz , Matts Karlsson

Department of Management and Engineering, Linköping University, SE-581 83 Linköping, Sweden

Introduction

In recent years it has been possible to simulate 3D blood flow through CFD including the dilatation effect in elastic arteries using Fluid-Structure Interaction (FSI) to better match in vivo data. Patient specific imposed boundary condition (BC) is often used as the velocity profiles at the inlets. However, for the outlet BC a time-resolved pressure is required and often lacking as it is obtained by an invasive procedure. Numerous models have been developed for capturing the main effects of the vascular bed at these sites, which have been shown crucial and difficult to implement accurately. This work focus on a full scaled FSI simulation at an arterial section including the abdominal aorta, renal arteries and iliac bifurcations, obtained from MRI of an healthy individual. The outlet BC at the iliac arteries is connected with a 1D systemic arterial tree which is truncated with a 0D lumped model. This 3D-(0D-1D) connection can provide the essential features of the peripheral flow and, in contrast to the imposed BC, the 1D-0D coupling allow for investigation of cardiovascular diseases including stenoses and/or hypertension.

Methods

The MRI images were segmented using an in-house software to obtain a 3D surface of the vessel lumen, Figure 1. The surfaces were meshed with high quality hexahedral element using ANSYS ICEM CFD 12.0 (ANSYS Inc, Canonsburg, PA, USA). A PC-MRI time-resolved massflow at the descending aorta were used as inlet BC, where 22% of the flow was forced into the renal bifurcations assuming negligible pressure wave reflection. The wall was modelled with an isotropic elastic model with addition of an elastic support mimicking the damping effect of the surrounding tissue. The 1D model is based on transmission-line theory which involves an impedance model for the pressure-flow relationship. The arterial topology was extracted from literature and only the central arteries after the iliacs was considered. At the truncation sites a 3-element Windkessel model (known as RRC) was implemented and is the most common model of choice for describing the main effects of all the distal vessels.  The 1D system solves the Fourier frequency impedance coefficients over one heart cycle accounting for wave reflection by using the 15 first harmonics to obtain the corresponding pressure. The 3D-1D connection is done offline, which allows for an independent and more stable 3D simulation. This step is iteratively repeated until convergence is reach between the present 3D outlet flow and previous implemented 1D outlet flow. The simulation was utilized in ANSYS CFX, ANSYS Mechanical, and coupled by ANSYS Multi-Field.

Results

The (0D-1D)-3D model showed convergence of pressure/flow at the iliac outlets, Figure 2. The method provides realistic pressure and flow responses based on the input parameters and even capture the relative difference in flow/pressure distribution between the right and left illiac artery due to subject specific geometric variability. Parameters such as velocity profiles and WSS can be extracted in the 3D domain.

Conclusions

This method allows for a better insight of large scale vascular networks effect of the local 3D flow features and also gives a better representation of the peripheral flow compared to a pure 0D (lumped parameter/Windkessel) model. PC-MRI will provide data for validation of velocity profiles in the 3D model. Future work includes a subject specific 1D vascular topology to be combined with the 3D model.   

Vascular wall shear stress (WSS) has been correlated to the development of atherosclerosis in arteries. As WSS depends on the blood flow dynamics, it is sensitive to pulsatile effects and local changes in geometry. The aim of this study is therefore to investigate if the effect of wall motion changes the WSS or if a rigid wall assumption is sufficient. Magnetic resonance imaging (MRI) was used to acquire subject specific geometry and flow rates in a human aorta, which were used as inputs in numerical models. Both rigid wall models and fluid-structure interaction (FSI) models were considered, and used to calculate the WSS on the aortic wall. A physiological range of different wall stiffnesses in the FSI simulations was used in order to investigate its effect on the flow dynamics. MRI measurements of velocity in the descending aorta were used as validation of the numerical models, and good agreement was achieved. It was found that the influence of wall motion was low on time-averaged WSS and oscillating shear index, but when regarding instantaneous WSS values the e.ect from the wall motion was clearly visible. Therefore, if instantaneous WSS is to be investigated, a FSI simulation should be considered.