A mathematical description of blood spiral flow in vessels: application to a numerical study of flow in arterial bending

Patient-specific analysis of bicuspid aortic valve hemodynamics using a fully coupled fluid-structure interaction model

Bicuspid aortic valve (BAV), the most common congenital heart disease, is prone to develop significant valvular dysfunction and aortic wall abnormalities such as ascending aortic aneurysm. Growing evidence has suggested that abnormal BAV hemodynamics could contribute to disease progression. In order to investigate BAV hemodynamics, we performed 3D patient-specific fluid-structure interaction (FSI) simulations with fully coupled blood flow dynamics and valve motion throughout the cardiac cycle. Results showed that the hemodynamics during systole can be characterized by a systolic jet and two counter-rotating recirculation vortices. At peak systole, the jet was usually eccentric, with asymmetric recirculation vortices and helical flow motion in the ascending aorta. The flow structure at peak systole was quantified using the vorticity, flow rate reversal ratio and local normalized helicity (LNH) at four locations from the aortic root to the ascending aorta. The systolic jet was evaluated with the peak velocity, normalized flow displacement, and jet angle. It was found that peak velocity and normalized flow displacement (rather than jet angle) gave a strong correlation with the vorticity and LNH in the ascending aorta, which suggests that these two metrics could be used for clinical noninvasive evaluation of abnormal blood flow patterns in BAV patients.

Hemodynamic analysis of hybrid treatment for thoracoabdominal aortic aneurysm based on Newtonian and non-Newtonian models in a patient-specific model

The accuracy of the Newtonian model used in retrograde visceral revascularization (RVR) of hybrid surgery for thoracoabdominal aortic aneurysm (TAAA) hemodynamic simulation remains unclear. Noting that an appropriate blood viscosity model is a significant factor to capture hemodynamic changes in numerical studies. Therefore, both Newtonian and non-Newtonian blood viscosity models were adopted in this study to investigate the importance of hemodynamics when non-Newtonian blood property was accounted for in a patient-specific RVR simulation. The results revealed that disturbed flow and unfavorable WSS distribution can be observed in the anastomosis region under both blood viscosity models due to the retrograde flow pattern in the RVR model. However, although the non-Newtonian blood model has negligible effect on flow pattern and pressure drop, there were of significance quantitative and qualitative difference of local normalized helicity and wall shear stress distribution under pulsatile flow condition. In particular, the unfavorable WSS indicators distribution was better matched with a patient-specific follow-up report when non-Newtonian blood viscosity was accounted for. To conclude, the use of a Newtonian blood model is a reasonable approximation to obtain the general features of the flow field under steady flow condition. However, to study the hemodynamic parameters within retrograde flow under pulsatile flow condition, a non-Newtonian model may be more appropriate.

Haemodynamic Analysis of Branched Endografts for Complex Aortic Arch Repair

This study aims to investigate the haemodynamic response induced by implantation of a double-branched endograft used in thoracic endovascular aortic repair (TEVAR) of the aortic arch. Anatomically realistic models were reconstructed from CT images obtained from patients who underwent TEVAR using the RelayPlus double-branched endograft implanted in the aortic arch. Two cases (Patient 1, Patient 2) were included here, both patients presented with type A aortic dissection before TEVAR. To examine the influence of inner tunnel branch diameters on localised flow patterns, three tunnel branch diameters were tested using the geometric model reconstructed for Patient 1. Pulsatile blood flow through the models was simulated by numerically solving the Navier–Stokes equations along with a transitional flow model. The physiological boundary conditions were imposed at the model inlet and outlets, while the wall was assumed to be rigid. Our simulation results showed that the double-branched endograft allowed for the sufficient perfusion of blood to the supra-aortic branches and restored flow patterns expected in normal aortas. The diameter of tunnel branches in the device plays a crucial role in the development of flow downstream of the branches and thus must be selected carefully based on the overall geometry of the vessel. Given the importance of wall shear stress in vascular remodelling and thrombus formation, longitudinal studies should be performed in the future in order to elucidate the role of tunnel branch diameters in long-term patency of the supra-aortic branches following TEVAR with the double-branched endograft.

'Heart-like' cross-sectional shape can better improve the hemodynamics in spiral laminar flow graft for small-caliber bypass application: a numerical study

Small-caliber grafts remain disappointed in the long-term bypass surgeries of coronary and peripheral arterial diseases. In order to improve the hemodynamics in small-caliber artery bypass grafts (ABGs), an improved spiral laminar flow (improved-SLF) graft with a 'heart-like' cross-sectional shape was proposed and verified by computational fluid dynamics simulation in this study. The results show that such graft can indeed induce a spiral flow and enhance the WSS distribution on the graft section. Furthermore, the helically distributed ribbon of unfavorable WSS observed in the original SLF graft was eliminated in the improved-SLF graft due to its smoothed and gentle helical ridge. On the other hand, improved-SLF ABG improved the WSS distribution in the distal anastomosis as well, because it maintained the strength of spiral flow when entering the anastomosis region. Finally, the improved-SLF ABG slightly increased the pressure drop along the bypass due to its small change of the general graft structure. As a proof-of-concept study, it can be concluded that improved-SLF graft can not only evenly enhance the WSS distribution in the graft section, but also improve the hemodynamic environment in the distal anastomosis without significantly increasing the pressure drop along the bypass, indicating such new helical-type graft may be more suitable to be used in the small-caliber graft bypass surgeries.

A Hemodynamic Comparison of Myocardial Bridging and Coronary Atherosclerotic Stenosis: A Computational Model With Experimental Evaluation

Myocardial bridging (MB) and coronary atherosclerotic stenosis can impair coronary blood flow and may cause myocardial ischemia or even heart attack. It remains unclear how MB and stenosis are similar or different regarding their impacts on coronary hemodynamics. The purpose of this study was to compare the hemodynamic effects of coronary stenosis and MB using experimental and computational fluid dynamics (CFD) approaches. For CFD modeling, three MB patients with different levels of lumen obstruction, mild, moderate, and severe were selected. Patient-specific left anterior descending (LAD) coronary artery models were reconstructed from biplane angiograms. For each MB patient, the virtually healthy and stenotic models were also simulated for comparison. In addition, an in vitro flow-loop was developed, and the pressure drop was measured for comparison. The CFD simulations results demonstrated that the difference between MB and stenosis increased with increasing MB/stenosis severity and flowrate. Experimental results showed that increasing the MB length (by 140%) only had significant impact on the pressure drop in the severe MB (39% increase at the exercise), but increasing the stenosis length dramatically increased the pressure drop in both moderate and severe stenoses at all flow rates (31% and 93% increase at the exercise, respectively). Both CFD and experimental results confirmed that the MB had a higher maximum and a lower mean pressure drop in comparison with the stenosis, regardless of the degree of lumen obstruction. A better understanding of MB and atherosclerotic stenosis may improve the therapeutic strategies in coronary disease patients and prevent acute coronary syndromes.

Three dimensional numerical analysis of hemodynamic of stenosed artery considering realistic outlet boundary conditions

BACKGROUND AND OBJECTIVE

Mortality rate increases globally among which one third is due to diseased blood vessels. Due to late diagnoses of the disease in vessels (severe stenoses), qualitative and rapid assessment becomes difficult. Earlier assessment of stenoses can lead to formulation of effective treatment protocol. It is often found that proliferation of secondary stenoses at downstream of a stenosed vessel depends on the degree of severity of primary stenoses. Numerical investigation of flow dynamics of blood in such condition helps in prediction of distributed field of secondarystenoses. This investigation also requires consideration of rigorous boundary conditions at inlet and outlet of defined flow domain.

METHODS

Patient-specific geometry of aortic arch with stenoses in descending aorta was considered for numerical estimation of biofluid dynamics. Boundary conditionsat inlet and outlet were extracted from time-resolved pulsed Doppler Ultrasound imaging at appropriate sections of the vessel. Womersley inlet flux was considered. Flow parameters like wall shear stress, oscillatory shear index, etc. were evaluated at upper and lower aortic arch of the vessel at different combinations of boundary conditions at inlet and four outlets respectively.

RESULTS

Effect of outlet boundary conditions were acknowledged for the progression of secondary stenoses. Severity of primary stenoses was found influencing the progression of secondary stenoses. It was found that the outlets Left Subclavian Artery and Left Common Carotid Artery greatly influence the flow dynamic structure within the stenosed aortic arch. Simultaneously, lower wall of aortic-arch had shown more affinity for secondary stenoses progression.

CONCLUSION

Aortic arch is a vital anatomical region of circulatory system which is vulnerable to progression of secondary stenoses in presence of primary stenoses in ascending or descending aorta. It also drives the author to speculate the influence of anurysm in descending aorta on this landmark of aortic arch.

Geometrical effects in the hemodynamics of stenotic and non-stenotic left coronary arteries-numerical and in vitro approaches

Atherosclerosis is a common cardiovascular disease found in the left coronary artery (LCA), closely linked to local hemodynamic, which, in turn, is highly influenced by the artery geometry. The hemodynamics in the LCA was studied in a patient-specific geometry without any sign of disease using both numerical and in vitro approaches. The influence of non-planarity was evaluated through two models of the patient-specific LCA that deviate from its original geometry in their planarity. Afterwards, in all models, irregular stenoses were created by a procedure in which the stenosis emerges by diffusion from low wall shear stress (WSS) areas. The WSS distribution and flow patterns were evaluated in all the models. The experimental results validate the numerical code developed to study the blood flow assuming a steady state Newtonian behavior. Comparison between the planar and non-planar idealized LCA revealed no significant differences in low WSS regions forming stenotic regions with identical shape. In the patient-specific LCA, the low WSS regions are not consistent with the idealized models leading to a different stenosis shape. The results revealed that the non-planarity has an unquestionable effect in helicity. It was also demonstrated that eccentricity of the vessels cross section and the position of the apex in relation to the axis of the parent branch contribute to the flow patterns observed. Numerical results of pulsatile blood flow assuming a non-Newtonian behavior, in the patient-specific LCA, reinforce the non-planarity effect in local hemodynamics.

Segment-specific associations between local haemodynamic and imaging markers of early atherosclerosis at the carotid artery: an in vivo human study

Low and oscillatory wall shear stress (WSS) has long been hypothesized as a risk factor for atherosclerosis; however, evidence has been inferred primarily from model and post-mortem studies, or clinical studies of patients with already-developed plaques. This study aimed to identify associations between local haemodynamic and imaging markers of early atherosclerosis. Comprehensive magnetic resonance imaging allowed quantification of contrast enhancement (CE) (a marker of endothelial dysfunction) and vessel wall thickness at two distinct segments: the internal carotid artery bulb and the common carotid artery (CCA). Strict criteria were applied to a large dataset to exclude inward remodelling, resulting in 41 cases for which personalized computational fluid dynamic simulations were performed. After controlling for cardiovascular risk factors, bulb wall thickening was found to be weakly, but not significantly, associated with oscillatory WSS. CE at the bulb was significantly associated with low WSS (p < 0.001) and low flow helicity (p < 0.05). No significant associations were found for the CCA segment. Local haemodynamics at the bulb were significantly correlated with blood flow rates and heart rates, but not carotid bifurcation geometry (flare and curvature). Therefore low, but not oscillatory, WSS is an early independent marker of atherosclerotic changes preceding intimal thickening at the carotid bulb.

Numerical and Experimental Investigation of Novel Blended Bifurcated Stent Grafts with Taper to Improve Hemodynamic Performance

The typical helical flow within the human arterial system is widely used when designing cardiovascular devices, as this helical flow can be generated using the “crossed limbs” strategy of the bifurcated stent graft (BSG) and enhanced by the tapered structure of arteries. Here, we propose the use of a deflected blended bifurcated stent graft (BBSG) with various tapers, using conventional blended BSGs with the same degree of taper as a comparison. Hemodynamic performances, including helical strength and wall shear stress- (WSS-) based indicators, were assessed. Displacement forces that may induce stent-graft migration were assessed using numerical simulations and in vitro experiments. The results showed that as the taper increased, the displacement force, helicity strength, and time-averaged wall shear stress (TAWSS) within the iliac grafts increased, whereas the oscillating shear index (OSI) and relative residence time (RRT) gradually decreased for both types of BBSGs. With identical tapers, deflected BBSGs, compared to conventional BBSGs, exhibited a wider helical structure and lower RRT on the iliac graft and lower displacement force; however, there were no differences in hemodynamic indicators. In summary, the presence of tapering facilitated helical flow and produced better hemodynamic performance but posed a higher risk of graft migration. Conventional and deflected BBSGs with taper might be the two optimal configurations for endovascular aneurysm repair, given the helical flow. The deflected BBSG provides a better configuration, compared to the conventional BBSG, when considering the reduction of migration risk.

Bulk Flow and Near Wall Hemodynamics of the Rabbit Aortic Arch: A 4D PC-MRI Derived CFD Study

Animal models offer a flexible experimental environment for studying atherosclerosis. The mouse is the most commonly used animal, however, the underlying hemodynamics in larger animals such as the rabbit are far closer to that of humans. The aortic arch is a vessel with complex helical flow and highly heterogeneous shear stress patterns which may influence where atherosclerotic lesions form. A better understanding of intra-species flow variation and the impact of geometry on flow may improve our understanding of where disease forms. In this work we use Magnetic Resonance Angiography (MRA) and 4D Phase contrast magnetic resonance imaging (PC-MRI) to image and measure blood velocity in the rabbit aortic arch. Measured flow rates from the PC-MRI were used as boundary conditions in computational fluid dynamics models of the arches. Helical flow, cross flow index (CFI) and time-averaged wall shear stress (TAWSS) were determined from the simulated flow field. Both traditional geometric metrics and shape modes derived from statistical shape analysis were analyzed with respect to flow helicity. High CFI and low TAWSS were found to co-localize in the ascending aorta and to a lesser extent on the inner curvature of the aortic arch. The Reynolds number was linearly associated with an increase in helical flow intensity (R=0.85, p<.05). Both traditional and statistical shape analysis correlated with increased helical flow symmetry. However, a stronger correlation was obtained from the statistical shape analysis demonstrating its potential for discerning the role of shape in hemodynamic studies.

Impact of Patient-Specific Inflow Velocity Profile on Hemodynamics of the Thoracic Aorta

Computational fluid dynamics (CFD) provides a noninvasive method to functionally assess aortic hemodynamics. The thoracic aorta has an anatomically complex inlet comprising of the aortic valve and root, which is highly prone to different morphologies and pathologies. We investigated the effect of using patient-specific (PS) inflow velocity profiles compared to idealized profiles based on the patient's flow waveform. A healthy 31 yo with a normally functioning tricuspid aortic valve (subject A), and a 52 yo with a bicuspid aortic valve (BAV), aortic valvular stenosis, and dilated ascending aorta (subject B) were studied. Subjects underwent MR angiography to image and reconstruct three-dimensional (3D) geometric models of the thoracic aorta. Flow-magnetic resonance imaging (MRI) was acquired above the aortic valve and used to extract the patient-specific velocity profiles. Subject B's eccentric asymmetrical inflow profile led to highly complex velocity patterns, which were not replicated by the idealized velocity profiles. Despite having identical flow rates, the idealized inflow profiles displayed significantly different peak and radial velocities. Subject A's results showed some similarity between PS and parabolic inflow profiles; however, other parameters such as Flowasymmetry were significantly different. Idealized inflow velocity profiles significantly alter velocity patterns and produce inaccurate hemodynamic assessments in the thoracic aorta. The complex structure of the aortic valve and its predisposition to pathological change means the inflow into the thoracic aorta can be highly variable. CFD analysis of the thoracic aorta needs to utilize fully PS inflow boundary conditions in order to produce truly meaningful results.

Does the Ventrica Magnetic Vascular Positioner (MVP®) for Coronary Artery Bypass Grafting Significantly alter Local Fluid Dynamics? a Numeric Study

Objective

Automatic devices have been recently introduced to make the anastomosis procedure quick and efficient when creating a coronary bypass on the beating heart. However, the implantation of these devices could modify the graft configuration, consistently affecting the hemodynamics usually found in the traditional anastomosis. As local fluid dynamics could play a significant role in the onset of vessel wall pathologies, in this article a computational approach was designed to investigate flow patterns in the presence of the Ventrica magnetic vascular positioner (Ventrica MVP®) device.

Methods

A model of standard hand-sewn anastomosis and of automated magnetic anastomosis were constructed, and the finite volume method was used to simulate in silico realistic graft hemodynamics. Synthetic analytical descriptors - i.e., time-averaged wall shear stress (TAWSS), oscillating shear index (OSI) and helical flow index (HFI) - were calculated and compared for quantitative assessment of the anastomosis geometry hemodynamic performance.

Results

In this case study, the same most critical region was identified for the 2 models as the one with the lowest TAWSS and the highest OSI (TAWSS=0.229, OSI=0.255 for the hand-sewn anastomosis; TAWSS=0.297, OSI=0.171 for the Ventrica MVP®). However, the shape of the Ventrica MVP® does not induce more critical wall shear stresses, oscillating flow and damped helicity in the graft fluid dynamics, as compared with conventional anastomosis.

Conclusions

We found that the use of the Ventrica MVP® for the case study under investigation was not associated with more critical fluid dynamics than with conventional hand-sewn anastomosis. Thereby, the device could facilitate beating heart and minimally invasive coronary artery bypass grafting without increasing local hemodynamic-related risks of failure. (Int J Artif Organs 2007; 30: 628–39)

Arterial pulse attenuation prediction using the decaying rate of a pressure wave in a viscoelastic material model

The present study examines the possibility of attenuating blood pulses by means of introducing prosthetic viscoelastic materials able to absorb energy and damp such pulses. Vascular prostheses made of polymeric materials modify the mechanical properties of blood vessels. The effect of these materials on the blood pulse propagation remains to be fully understood. Several materials for medical applications, such as medical polydimethylsiloxane or polytetrafluoroethylene, show viscoelastic behavior, modifying the original vessel stiffness and affecting the propagation of blood pulses. This study focuses on the propagation of pressure waves along a pipe with viscoelastic materials using the Maxwell and the Zener models. An expression of exponential decay has been obtained for the Maxwell material model and also for low viscous coefficient values in the Zener model. For relatively high values of the viscous term in the Zener model, the steepest part of the pulse can be damped quickly, leaving a smooth, slowly decaying wave. These mathematical models are critical to tailor those materials used in cardiovascular implants to the mechanical environment they are confronted with to repair or improve blood vessel function.

Healthy and diseased coronary bifurcation geometries influence near-wall and intravascular flow: A computational exploration of the hemodynamic risk

Local hemodynamics has been identified as one main determinant in the onset and progression of atherosclerotic lesions at coronary bifurcations. Starting from the observation that atherosensitive hemodynamic conditions in arterial bifurcation are majorly determined by the underlying anatomy, the aim of the present study is to investigate how peculiar coronary bifurcation anatomical features influence near-wall and intravascular flow patterns. Different bifurcation angles and cardiac curvatures were varied in population-based, idealized models of both stenosed and unstenosed bifurcations, representing the left anterior descending (LAD) coronary artery with its diagonal branch. Local hemodynamics was analyzed in terms of helical flow and exposure to low/oscillatory shear stress by performing computational fluid dynamics simulations. Results show that bifurcation angle impacts lowly hemodynamics in both stenosed and unstenosed cases. Instead, curvature radius influences the generation and transport of helical flow structures, with smaller cardiac curvature radius associated to higher helicity intensity. Stenosed bifurcation models exhibit helicity intensity values one order of magnitude higher than the corresponding unstenosed cases. Cardiac curvature radius moderately affects near-wall hemodynamics of the stenosed cases, with smaller curvature radius leading to higher exposure to low shear stress and lower exposure to oscillatory shear stress. In conclusion, the proposed controlled benchmark allows investigating the effect of various geometrical features on local hemodynamics at the LAD/diagonal bifurcation, highlighting that cardiac curvature influences near wall and intravascular hemodynamics, while bifurcation angle has a minor effect.

Improvement of hemodynamic performance using novel helical flow vena cava filter design

We propose a vena cava filter in which helical flow is created in the filter’s working zone to minimize filter blockage by trapped clots and facilitate the lysis of trapped clots. To validate this new design, we compared five helical flow inducers with different thread pitches in terms of blood flow patterns in the filter. The vena cava was reconstructed based on computed tomography images. Both the numerical simulation and in vitro experiment revealed that the helical flow inducer can effectively create a helical flow in the vessel, thereby subduing the filter structure’s adverse disruption to blood flow, and increasing flow-induced shear stress in the filter center. In addition, the smaller thread pitch helical flow inducer reduced the oscillating shear index and relative residence time on the vessel wall. Moreover, we observed that the helical flow inducer in the vena cava could induce flow rotation both in clockwise and counterclockwise directions. In conclusion, the new design of the filter with the smaller thread pitch inducer is advantageous over the traditional filter in terms of improving local hemodynamics, which may reduce thrombosis build-up after deployment.

The manifestation of vortical and secondary flow in the cerebral venous outflow tract: An in vivo MR velocimetry study

Aberrations in flow in the cerebral venous outflow tract (CVOT) have been implicated as the cause of several pathologic conditions including idiopathic intracranial hypertension (IIH), multiple sclerosis (MS), and pulsatile tinnitus (PT). The advent of 4D flow magnetic resonance imaging (4D-flow MRI) has recently allowed researchers to evaluate blood flow patterns in the arterial structures with great success. We utilized similar imaging techniques and found several distinct flow characteristics in the CVOT of subjects with and without lumenal irregularities. We present the flow patterns of 8 out of 38 subjects who have varying heights of the internal jugular bulb and varying lumenal irregularities including stenosis and diverticulum. In the internal jugular vein (IJV) with an elevated jugular bulb (JB), 4Dflow MRI revealed a characteristic spiral flow that was dependent on the level of JB elevation. Vortical flow was also observed in the diverticula of the venous sinuses and IJV. The diversity of flow complexity in the CVOT illustrates the potential importance of hemodynamic investigations in elucidating venous pathologies.

Link between deviations from Murray's Law and occurrence of low wall shear stress regions in the left coronary artery

Murray developed two laws for the geometry of bifurcations in the circulatory system. Based on the principle of energy minimization, Murray found restrictions for the relation between the diameters and also between the angles of the branches. It is known that bifurcations are prone to the development of atherosclerosis, in regions associated to low wall shear stresses (WSS) and high oscillatory shear index (OSI). These indicators (size of low WSS regions, size of high OSI regions and size of high helicity regions) were evaluated in this work. All of them were normalized by the size of the outflow branches. The relation between Murray's laws and the size of low WSS regions was analysed in detail. It was found that the main factor leading to large regions of low WSS is the so called expansion ratio, a relation between the cross section areas of the outflow branches and the cross section area of the main branch. Large regions of low WSS appear for high expansion ratios. Furthermore, the size of low WSS regions is independent of the ratio between the diameters of the outflow branches. Since the expansion ratio in bifurcations following Murray's law is kept in a small range (1 and 1.25), all of them have regions of low WSS with similar size. However, the expansion ratio is not small enough to completely prevent regions with low WSS values and, therefore, Murray's law does not lead to atherosclerosis minimization. A study on the effect of the angulation of the bifurcation suggests that the Murray's law for the angles does not minimize the size of low WSS regions.

Influence of the Accuracy of Angiography-Based Reconstructions on Velocity and Wall Shear Stress Computations in Coronary Bifurcations: A Phantom Study

INTRODUCTION

Wall shear stress (WSS) plays a key role in the onset and progression of atherosclerosis in human coronary arteries. Especially sites with low and oscillating WSS near bifurcations have a higher propensity to develop atherosclerosis. WSS computations in coronary bifurcations can be performed in angiography-based 3D reconstructions. It is essential to evaluate how reconstruction errors influence WSS computations in mildly-diseased coronary bifurcations. In mildly-diseased lesions WSS could potentially provide more insight in plaque progression.

MATERIALS METHODS

Four Plexiglas phantom models of coronary bifurcations were imaged with bi-plane angiography. The lumens were segmented by two clinically experienced readers. Based on the segmentations 3D models were generated. This resulted in three models per phantom: one gold-standard from the phantom model itself, and one from each reader. Steady-state and transient simulations were performed with computational fluid dynamics to compute the WSS. A similarity index and a noninferiority test were used to compare the WSS in the phantoms and their reconstructions. The margin for this test was based on the resolution constraints of angiography.

RESULTS

The reconstruction errors were similar to previously reported data; in seven out of eight reconstructions less than 0.10 mm. WSS in the regions proximal and far distal of the stenosis showed a good agreement. However, the low WSS areas directly distal of the stenosis showed some disagreement between the phantoms and the readers. This was due to small deviations in the reconstruction of the stenosis that caused differences in the resulting jet, and consequently the size and location of the low WSS area.

DISCUSSION

This study showed that WSS can accurately be computed within angiography-based 3D reconstructions of coronary arteries with early stage atherosclerosis. Qualitatively, there was a good agreement between the phantoms and the readers. Quantitatively, the low WSS regions directly distal to the stenosis were sensitive to small reconstruction errors.

Aortic flow patterns before and after personalised external aortic root support implantation in Marfan patients

Implantation of a personalised external aortic root support (PEARS) in the Marfan aorta is a new procedure that has emerged recently, but its haemodynamic implication has not been investigated. The objective of this study was to compare the flow characteristics and hemodynamic indices in the aorta before and after insertion of PEARS, using combined cardiovascular magnetic resonance imaging (CMR) and computational fluid dynamics (CFD). Pre- and post-PEARS MR images were acquired from 3 patients and used to build patient-specific models and upstream flow conditions, which were incorporated into the CFD simulations. The results revealed that while the qualitative patterns of the haemodynamics were similar before and after PEARS implantation, the post-PEARS aortas had slightly less disturbed flow at the sinuses, as a result of reduced diameters in the post-PEARS aortic roots. Quantitative differences were observed between the pre- and post-PEARS aortas, in that the mean values of helicity flow index (HFI) varied by -10%, 35% and 20% in post-PEARS aortas of Patients 1, 2 and 3, respectively, but all values were within the range reported for normal aortas. Comparisons with MR measured velocities in the descending aorta of Patient 2 demonstrated that the computational models were able to reproduce the important flow features observed in vivo.

Haemodynamics and Flow Modification Stents for Peripheral Arterial Disease: A Review

Endovascular stents are widely used for the treatment of peripheral arterial disease (PAD). However, the development of in-stent restenosis and downstream PAD progression remain a challenge. Stent revascularisation of PAD causes arterial trauma and introduces abnormal haemodynamics, which initiate complicated biological processes detrimental to the arterial wall. The interaction between stent struts and arterial cells in contact, and the blood flow field created in a stented region, are highly affected by stent design. Spiral flow is known as a normal physiologic characteristic of arterial circulation and is believed to prevent the development of flow disturbances. This secondary flow motion is lost in atheromatous disease and its re-introduction after endovascular treatment of PAD has been suggested as a method to induce stabilised and coherent haemodynamics. Stent designs able to generate spiral flow may support endothelial function and therefore increase patency rates. This review is focused on secondary flow phenomena in arteries and the development of flow modification stent technologies for the treatment of PAD.

Spiral blood flow in aorta-renal bifurcation models

The presence of a spiral arterial blood flow pattern in humans has been widely accepted. It is believed that this spiral component of the blood flow alters arterial haemodynamics in both positive and negative ways. The purpose of this study was to determine the effect of spiral flow on haemodynamic changes in aorta-renal bifurcations. In this regard, a computational fluid dynamics analysis of pulsatile blood flow was performed in two idealised models of aorta-renal bifurcations with and without flow diverter. The results show that the spirality effect causes a substantial variation in blood velocity distribution, while causing only slight changes in fluid shear stress patterns. The dominant observed effect of spiral flow is on turbulent kinetic energy and flow recirculation zones. As spiral flow intensity increases, the rate of turbulent kinetic energy production decreases, reducing the region of potential damage to red blood cells and endothelial cells. Furthermore, the recirculation zones which form on the cranial sides of the aorta and renal artery shrink in size in the presence of spirality effect; this may lower the rate of atherosclerosis development and progression in the aorta-renal bifurcation. These results indicate that the spiral nature of blood flow has atheroprotective effects in renal arteries and should be taken into consideration in analyses of the aorta and renal arteries.

Assessment of Hemodynamic Conditions in the Aorta Following Root Replacement with Composite Valve-Conduit Graft

This paper presents the analysis of detailed hemodynamics in the aortas of four patients following replacement with a composite bio-prosthetic valve-conduit. Magnetic resonance image-based computational models were set up for each patient with boundary conditions comprising subject-specific three-dimensional inflow velocity profiles at the aortic root and central pressure waveform at the model outlet. Two normal subjects were also included for comparison. The purpose of the study was to investigate the effects of the valve-conduit on flow in the proximal and distal aorta. The results suggested that following the composite valve-conduit implantation, the vortical flow structure and hemodynamic parameters in the aorta were altered, with slightly reduced helical flow index, elevated wall shear stress and higher non-uniformity in wall shear compared to normal aortas. Inter-individual analysis revealed different hemodynamic conditions among the patients depending on the conduit configuration in the ascending aorta, which is a key factor in determining post-operative aortic flow. Introducing a natural curvature in the conduit to create a smooth transition between the conduit and native aorta may help prevent the occurrence of retrograde and recirculating flow in the aortic arch, which is particularly important when a large portion or the entire ascending aorta needs to be replaced.

Computation of Hemodynamics in Tortuous Left Coronary Artery: A Morphological Parametric Study

Coronary tortuosity (CT) would alter the local wall shear stress (WSS) and may become a risk factor for atherosclerosis. Here we performed a systematic computational study to relate CT morphological parameters to abnormal WSS, which is a predisposing factor to the formation of atherosclerotic lesions. Several idealized left coronary artery (LCA) models were created to conduct a series of morphological parametric studies, in which we concentrate on three specific morphological parameters, the center line radius (CLR), the bend angle (BA), and the length between two adjust bends (LBB). The time averaged WSS (TAWSS), the oscillatory shear index (OSI), and the time averaged WSS gradient (WSSGnd) were explored by using the computational fluid dynamics (CFD) method, in order to determine susceptible sites for the onset of early atherosclerosis. In addition, two realistic LCA models were reconstructed to further validate the finding's credibility. The CLR and LBB had great impact on the distributions of WSS-derived parameters, while the BA had minor impact on the hemodynamic of the tortuous arteries. Abnormal regions with low TAWSS (TAWSS < 0.5 Pa), high OSI (OSI > 0.1) and high WSSGnd (WSSGnd > 8) were observed at the inner wall of bend sections in the models with small CLR or small LBB. These findings were also confirmed in the realistic models. Severe CT with small CLR or LBB would lead to the formation of abnormal WSS regions at the bend sections and providing these regions with favorable conditions for the onset and/or progression of atherosclerosis.

An in vitro investigation of the influence of stenosis severity on the flow in the ascending aorta

Cardiovascular diseases can lead to abnormal blood flows, some of which are linked to hemolysis and thrombus formation. Abnormal turbulent flows of blood in the vessels with stenosis create strong shear stresses on blood elements and may cause blood cell destruction or platelet activation. We implemented a Lagrangian (following the fluid elements) measurement technique of three dimensional particle tracking velocimetry that provides insight on the evolution of viscous and turbulent stresses along blood element trajectories. We apply this method to study a pulsatile flow in a compliant phantom of an aorta and compare the results in three cases: the reference case (called "healthy" case), and two cases of abnormal flows due to mild and severe stenosis, respectively. The chosen conditions can mimic a clinical application of an abnormal flow due to a calcific valve. We estimate the effect of aortic stenosis on the kinetic energy of the mean flow and the turbulent kinetic energy, which increases about two orders of magnitude as compared with the healthy flow case. Measuring the total flow stress acting on a moving fluid element that incorporates viscous stresses and the apparent turbulent-induced stresses (the so-called Reynolds stresses) we find out similar increase of the stresses with the increased severity of the stenosis. Furthermore, these unique Lagrangian measurements provide full acceleration and, consequently, the forces acting on the blood elements that are estimated to reach the level that can considerably deform red blood cells. These forces are strong and abrupt due to the contribution of the turbulent fluctuations which is much stronger than the typically measured phase-averaged values.

Lagrangian postprocessing of computational hemodynamics

Recent advances in imaging, modeling, and computing have rapidly expanded our capabilities to model hemodynamics in the large vessels (heart, arteries, and veins). This data encodes a wealth of information that is often under-utilized. Modeling (and measuring) blood flow in the large vessels typically amounts to solving for the time-varying velocity field in a region of interest. Flow in the heart and larger arteries is often complex, and velocity field data provides a starting point for investigating the hemodynamics. This data can be used to perform Lagrangian particle tracking, and other Lagrangian-based postprocessing. As described herein, Lagrangian methods are necessary to understand inherently transient hemodynamic conditions from the fluid mechanics perspective, and to properly understand the biomechanical factors that lead to acute and gradual changes of vascular function and health. The goal of the present paper is to review Lagrangian methods that have been used in post-processing velocity data of cardiovascular flows.

Comparison of patient-specific inlet boundary conditions in the numerical modelling of blood flow in abdominal aortic aneurysm disease

Three inlet boundary condition datasets were derived from phase-contrast MRI: (i) centre line velocity data converted to two-dimensional (2D) velocity profile using Womersley equations (Womersley), (ii) 2D velocity profile with one axial component of velocity (1CV), (iii) 2D velocity profile with three components of velocity (3CV). Computational fluid dynamics was performed using a rigid wall approach with geometry data extracted from the computed tomography dataset. Helical flow was present in the 1CV and 3CV simulations, with more complex patterns for the 3CV case. The Womersley method produced simplified flow patterns with an absence of helical flow. Mean values of quantitative indices (helical flow index, mean wall shear stress, oscillatory index) were compared with the 3CV inlet data. These were lower for both the Womersley inlet data (28%, 71%, 56%) and the 1CV inlet data (9%, 24%, 69%). It was concluded that inlet methods based on centre line velocity, such as might be obtained from Doppler ultrasound, lead to significantly simplified abdominal aortic aneurysm haemodynamics and thus are not recommended. Single velocity component (axial) data from MRI might suffice when general flow characteristics and spatial wall shear stress are required. Ideally 2D MRI velocity profiles with 3-velocity component data are preferred to fully account for helical flow.

A computational exploration of helical arterio-venous graft designs

Although arterio-venous grafts (AVGs) are the second best option as long-term vascular access for hemodialysis, they suffer from complications caused by intimal hyperplasia, mainly located in vessel regions of low and oscillating wall shear stress. However, certain flow patterns in the bulk may reduce these unfavorable hemodynamic conditions. We therefore studied, with computational fluid dynamics (CFD), the impact of a helical AVG design on the occurrence of (un)favorable hemodynamic conditions at the venous anastomosis. Six CFD-models of an AVG in closed-loop configuration were constructed: one conventional straight graft, and five helical designed grafts with a pitch of 105 mm down to 35 mm. At the venous anastomosis, disturbed shear was assessed by quantifying the area with unfavorable conditions, and by analyzing averaged values in a case-specific patch. The bulk hemodynamics were assessed by analyzing the kinetic helicity in and the pressure drop over the graft. The most helical design scores best, being instrumental to suppress disturbed shear in the venous segment. There is, however, no trivial relationship between the number of helix turns of the graft and disturbed shear in the venous segment, when a realistic closed-loop AVG model is investigated. Bulk flow investigation showed a marked increase of helicity intensity in, and a moderate pressure drop over the AVG by introducing a lower pitch. At the venous anastomosis, unfavorable hemodynamic conditions can be reduced by introducing a helical design. However, due to the complex flow conditions, the optimal helical design for an AVG cannot be derived without studying case by case.

ASSESSING HEMODYNAMIC PERFORMANCES OF SMALL DIAMETER HELICAL GRAFTS: TRANSIENT SIMULATION

The present study numerically simulated the physiological pulsatile flow in helical grafts to increase understanding of its flow mechanism which may contribute to the design of better grafts. The wall-indices like time-averaged wall shear stress (WSS) and oscillatory shear index (OSI), joint with a quantitative index for helical flow by means of Lagrangian approach, were introduced as effective instruments to classify the hemodynamic performance of helical grafts. The simulation suggests that the helical geometry created amplified WSS magnitudes as well as elevated velocities near the wall. The calculated oscillatory shear index (OSI) values were never exceeded to 0.07 which is not considered physiologically significant. In addition, the strong secondary flow in helical graft helped the flow mixing between low-momentum fluid closer to the surface and high-momentum fluid at the center which brought the high-momentum fluid to the surface. Furthermore, Helicity analysis revealed that most of the fluid particles experienced counter-clockwise rotation during the whole cardiac cycle which helps to protect the graft wall from damage by reducing the laterally directed forces and keep flow stability. It concluded that a helical graft provides guaranties for the graft wall surface to get smooth and even washing by the blood and eliminates mechanical trauma to blood cells so that atherosclerotic plaques can hardly form in the graft wall.

NUMERICAL INVESTIGATION OF PULSATILE FLOW IN AN S-TYPE BYPASS GRAFT

Intimal hyperplasia developed at the end-to-side anastomosis of artery bypass is closely related to unphysiological hemodynamics. The helical flow as a normal physiological phenomenon in arteries is beneficial to endothelial damage repair. To deeply understand the physiological flow properties in a S-type bypass (StB) graft, four end-to-side bypass models including 30°, 45°, 60° conventional bypasses and a 45° StB were compared numerically under physiological pulsatile flow. The results showed that strong helical flow was observed at the distal anastomosis of StB. The distribution of hemodynamic parameters such as helicity, average wall shear stress and oscillating shear index, etc. were significantly improved at the S-type anastomosis as compared with those of three conventional models. The area-averaged normalized helicity in StB reached maxima at the moments of maximum flow rate and systolic deceleration. The hemodynamic performance in a 45° StB was improved as compared with a 30° conventional model. It is concluded that large StB anastomosis angle can be taken to achieve good hemodynamic performance while much smaller anastomosis angle has to be adopted for conventional bypass. As such, a S-type anastomosis should be a feasible choice of clinical artery bypass grafting due to its significant improvement in hemodynamic performance.

Synthetic dataset generation for the analysis and the evaluation of image-based hemodynamics of the human aorta

Here, we consider the issue of generating a suitable controlled environment for the evaluation of phase contrast (PC) MRI measurements. The computational framework, tailored to build synthetic datasets, is based on a two-step approach, i.e., define and implement (1) an accurate CFD model and (2) an image generator able to mime the overall outcomes of a PC MRI acquisition starting from datasets retrieved by the computational model. About 20 different datasets were built by changing relevant image parameters (pixel size, slice thickness, time frames per cardiac cycle). Focusing our attention on the thoracic aorta, synthetic images were processed in order to: (1) verify to which extent the fluid dynamics into the aortic arch is influenced by the image parameters; (2) establish the effect of spatial and temporal interpolation. Our study demonstrates that the integral scale of the aortic bulk flow could be described satisfactorily even when using images which are nowadays acquirable with MRI scanners. However, attention must be paid to near-wall velocities that can be affected by large inaccuracy. In detail, in bulk flow regions error values are well bounded (below 5% for most of the analyzed resolutions), while errors greater than 100% are systematically present at the vessel's wall. Moreover, also the data interpolation process can be responsible for large inaccuracies in new data generation, due to the inherent complexity of the flow field in some connected regions.

Accuracy vs. computational time: translating aortic simulations to the clinic

State of the art simulations of aortic haemodynamics feature full fluid-structure interaction (FSI) and coupled 0D boundary conditions. Such analyses require not only significant computational resource but also weeks to months of run time, which compromises the effectiveness of their translation to a clinical workflow. This article employs three computational fluid methodologies, of varying levels of complexity with coupled 0D boundary conditions, to simulate the haemodynamics within a patient-specific aorta. The most comprehensive model is a full FSI simulation. The simplest is a rigid walled incompressible fluid simulation while an alternative middle-ground approach employs a compressible fluid, tuned to elicit a response analogous to the compliance of the aortic wall. The results demonstrate that, in the context of certain clinical questions, the simpler analysis methods may capture the important characteristics of the flow field.

Importance of realistic LVAD profiles for assisted aortic simulations: evaluation of optimal outflow anastomosis locations

Left ventricular assist devices (LVADs) are carefully designed, but the significance of the implantation configuration and interaction with the vasculature is complex and not fully determined. The present study employs computational fluid dynamics to investigate the importance of applying a realistic LVAD profile when evaluating assisted aortic flow fields and subsequently compares a number of potential anastomosis locations in a patient-specific aortic geometry. The outflow profile of the Berlin Heart INCOR® device was provided by Berlin Heart GmbH (Berlin, Germany) and the cannula was attached at a number of locations on the aorta. Simulations were conducted to compare a flat profile against the real LVAD profile. The results illustrate the importance of applying an LVAD profile. It not only affects the magnitude and distribution of oscillatory shear index, but also the distribution of flow to the great arteries. The ascending aorta was identified as the optimal location for the anastomosis.

Outflow Conditions for Image-Based Hemodynamic Models of the Carotid Bifurcation: Implications for Indicators of Abnormal Flow

Computational fluid dynamics (CFD) models have become very effective tools for predicting the flow field within the carotid bifurcation, and for understanding the relationship between local hemodynamics, and the initiation and progression of vascular wall pathologies. As prescribing proper boundary conditions can affect the solutions of the equations governing blood flow, in this study, we investigated the influence to assumptions regarding the outflow boundary conditions in an image-based CFD model of human carotid bifurcation. Four simulations were conducted with identical geometry, inlet flow rate, and fluid parameters. In the first case, a physiological time-varying flow rate partition at branches along the cardiac cycle was obtained by coupling the 3D model of the carotid bifurcation at outlets with a lumped-parameter model of the downstream vascular network. Results from the coupled model were compared with those obtained by imposing three fixed flow rate divisions (50/50, 60/40, and 70/30) between the two branches of the isolated 3D model of the carotid bifurcation. Three hemodynamic wall parameters were considered as indicators of vascular wall dysfunction. Our findings underscore that the overall effect of the assumptions done in order to simulate blood flow within the carotid bifurcation is mainly in the hot-spot modulation of the hemodynamic descriptors of atherosusceptible areas, rather than in their distribution. In particular, the more physiological, time-varying flow rate division deriving from the coupled simulation has the effect of damping wall shear stress (WSS) oscillations (differences among the coupled and the three fixed flow partition models are up to 37.3% for the oscillating shear index). In conclusion, we recommend to adopt more realistic constraints, for example, by coupling models at different scales, as in this study, when the objective is the outcome prediction of alternate therapeutic interventions for individual patients, or to test hypotheses related to the role of local fluid dynamics and other biomechanical factors in vascular diseases.

Mechanistic insight into the physiological relevance of helical blood flow in the human aorta: an in vivo study

The hemodynamics within the aorta of five healthy humans were investigated to gain insight into the complex helical flow patterns that arise from the existence of asymmetries in the aortic region. The adopted approach is aimed at (1) overcoming the relative paucity of quantitative data regarding helical blood flow dynamics in the human aorta and (2) identifying common characteristics in physiological aortic flow topology, in terms of its helical content. Four-dimensional phase-contrast magnetic resonance imaging (4D PC MRI) was combined with algorithms for the calculation of advanced fluid dynamics in this study. These algorithms allowed us to obtain a 4D representation of intra-aortic flow fields and to quantify the aortic helical flow. For our purposes, helicity was used as a measure of the alignment of the velocity and the vorticity. There were two key findings of our study: (1) intra-individual analysis revealed a statistically significant difference in the helical content at different phases of systole and (2) group analysis suggested that aortic helical blood flow dynamics is an emerging behavior that is common to normal individuals. Our results also suggest that helical flow might be caused by natural optimization of fluid transport processes in the cardiovascular system, aimed at obtaining efficient perfusion. The approach here applied to assess in vivo helical blood flow could be the starting point to elucidate the role played by helicity in the generation and decay of rotating flows in the thoracic aorta.

The role of biofluid mechanics in the assessment of clinical and pathological observations: sixth International Bio-Fluid Mechanics Symposium and Workshop, March 28-30, 2008 Pasadena, California

Biofluid mechanics is increasingly applied in support of diagnosis and decision-making for treatment of clinical pathologies. Exploring the relationship between blood flow phenomena and pathophysiological observations is enhanced by continuing advances in the imaging modalities, measurement techniques, and capabilities of computational models. When combined with underlying physiological models, a powerful set of tools becomes available to address unmet clinical needs, predominantly in the direction of enhanced diagnosis, as well as assessment and prediction of treatment outcomes. This position paper presents an overview of current approaches and future developments along this theme that were discussed at the 5th International Biofluid Symposium and Workshop held at the California Institute of Technology in 2008. The introduction of novel mechanical biomarkers in device design and optimization, and applications in the characterization of more specific and focal conditions such as aneurysms, are at the center of attention. Further advances in integrative modeling, incorporating multiscale and multiphysics techniques are also discussed.

The influences of stenosis on the downstream flow pattern in curved arteries

The influence of stenosis on the pulsatile blood flow pattern in curved arteries with stenosis at inner wall was investigated by computer simulations. Numerical calculations were performed with various values of physiological parameters to examine the effect of a stenosis on the hemodynamic characteristics such as secondary flow, flow separation, wall shear stress (WSS) and pressure drop. The results demonstrated that when the severity of a stenosis at the inner wall of a curved artery reaches a certain level, the flow pattern in the downstream of the artery shows a dramatic change compared to that of a curved artery with no stenosis. According to previous studies, a flow separation occurs at the inner wall of the bend in a curved artery. The present work reports an analysis of such a flow separation area at the inner wall of the post stenosis region in curved arteries with a stenosis. In addition, another area of flow separation with low and oscillating WSS and blood pressure at the outer wall in a downstream tube was also found and investigated. The observed characteristic change of the flow downstream may suggest a formation of a new plaque at the outer wall downstream.