Turbulent blood flow in the ascending aorta of humans with normal and diseased aortic valves

Literature Survey for In-Vivo Reynolds and Womersley Numbers of Various Arteries and Implications for Compliant In-Vitro Modelling

PURPOSE

In-vitro modelling can be used to investigate haemodynamics of arterial geometry and stent implants. However, in-vitro model fidelity relies on precise matching of in-vivo conditions. In pulsatile flow, velocity distribution and wall shear stress depend on compliance, and the Reynolds and Womersley numbers. However, matching such values may lead to unachievable tolerances in phantom fabrication.

METHODS

Published Reynolds and Womersley numbers for 14 major arteries in the human body were determined via a literature search. Preference was given to in-vivo publications but in-vitro and in-silico values were presented when in-vivo values were not found. Subsequently ascending aorta and carotid artery case studies were presented to highlight the limitations dynamic matching would apply to phantom fabrication.

RESULTS

Seven studies reported the in-vivo Reynolds and Womersley numbers for the aorta and two for the carotid artery. However, only one study each reported in-vivo numbers for the remaining ten arteries. No in-vivo data could be found for the femoral, superior mesenteric and renal arteries. Thus, information derived in-vitro and in-silico were provided instead. The ascending aorta and carotid artery models required scaling to 1.5× and 3× life-scale, respectively, to achieve dimensional tolerance restrictions. Modelling the ascending aorta with the comparatively high viscosity water/glycerine solution will lead to high pump power demands. However, all the working fluids considered could be dynamically matched with low pump demand for the carotid model.

CONCLUSION

This paper compiles available human haemodynamic information, and highlights the paucity of information for some arteries. It also provides a method for optimal in-vitro experimental configuration.

In vivo fluid dynamics of the Ventura interatrial shunt device in patients with heart failure

AIMS

Interatrial shunts are under evaluation as a treatment for heart failure (HF); however, their in vivo flow performance has not been quantitatively studied. We aimed to investigate the fluid dynamics properties of the 0.51 cm orifice diameter Ventura shunt and assess its lumen integrity with serial transesophageal echocardiography (TEE).

METHODS AND RESULTS

Computational fluid dynamics (CFD) and bench flow tests were used to establish the flow-pressure relationship of the shunt. Open-label patients from the RELIEVE-HF trial underwent TEE at shunt implant and at 6 and 12 month follow-up. Shunt effective diameter (Deff) was derived from the vena contracta, and flow was determined by the continuity equation. CFD and bench studies independently validated that the shunt's discharge coefficient was 0.88 to 0.89. The device was successfully implanted in all 97 enrolled patients; mean age was 70 ± 11 years, 97% were NYHA class III, and 51% had LVEF ≤40%. Patency was confirmed in all instances, except for one stenotic shunt at 6 months. Deff remained unchanged from baseline at 12 months (0.47 ± 0.01 cm, P = 0.376), as did the trans-shunt mean pressure gradient (5.1 ± 3.9 mmHg, P = 0.316) and flow (1137 ± 463 mL/min, P = 0.384). TEE measured flow versus pressure closely correlated (R2 ≥ 0.98) with a fluid dynamics model. At 12 months, the pulmonary/systemic flow Qp/Qs ratio was 1.22 ± 0.12.

CONCLUSIONS

When implanted in patients with advanced HF, this small interatrial shunt demonstrated predictable and durable patency and performance.

Enhancing the implantation of mechanical circulatory support devices using computational simulations

Introduction: Patients with end-stage heart failure (HF) may need mechanical circulatory support such as a left ventricular assist device (LVAD). However, there are a range of complications associated with LVAD including aortic regurgitation (AR) and thrombus formation. This study assesses whether the risk of developing aortic conditions can be minimised by optimising LVAD implantation technique. Methods: In this work, we evaluate the aortic flow patterns produced under different geometrical parameters for the anastomosis of the outflow graft (OG) to the aorta using computational fluid dynamics (CFD). A three-dimensional aortic model is created and the HeartMate III OG positioning is simulated by modifying (i) the distance from the anatomic ventriculo-arterial junction (AVJ) to the OG, (ii) the cardinal position around the aorta, and (iii) the angle between the aorta and the OG. The continuous LVAD flow and the remnant native cardiac cycle are used as inlet boundaries and the three-element Windkessel model is applied at the pressure outlets. Results: The analysis quantifies the impact of OG positioning on different haemodynamic parameters, including velocity, wall shear stress (WSS), pressure, vorticity and turbulent kinetic energy (TKE). We find that WSS on the aortic root (AoR) is around two times lower when the OG is attached to the coronal side of the aorta using an angle of 45° ± 10° at a distance of 55 mm. Discussion: The results show that the OG placement may significantly influence the haemodynamic patterns, demonstrating the potential application of CFD for optimising OG positioning to minimise the risk of cardiovascular complications after LVAD implantation.

Biomechanical Evaluation of Aortic Valve Stenosis by Means of a Virtual Stress Test: A Fluid-Structure Interaction Study

The impact of aortic valve stenosis (AS) extends beyond the vicinity of the narrowed leaflets into the left ventricle (LV) and into the systemic vasculature because of highly unpredictable valve behavior and complex blood flow in the ascending aorta that can be attributed to the strong interaction between the narrowed cusps and the ejected blood. These effects can become exacerbated during exercise and may have implications for disease progression, accurate diagnosis, and timing of intervention. In this 3-D patient-specific study, we employ strongly coupled fluid-structure interaction (FSI) modeling to perform a comprehensive biomechanical evaluation of systolic ejection dynamics in a stenosed aortic valve (AV) during increasing LV contraction. Our model predictions reveal that the heterogeneous ∆P vs. Q relationship that was observed in our previous clinical study can be attributed to a non-linear increase (by ~ 1.5-fold) in aortic valve area as LV heart rate increases from 70 to 115 bpm. Furthermore, our results show that even for a moderately stenotic valve, increased LV contraction during exercise can lead to high-velocity flow turbulence (Re = 11,700) in the aorta similar to that encountered with a severely stenotic valve (Re ~ 10,000), with concomitant greater viscous loss (~3-fold increase) and elevated wall stress in the ascending aorta. Our FSI predictions also reveal that individual valve cusps undergo distinct and highly non-linear increases (>100%) in stress during exercise, potentially contributing to progressive calcification. Such quantitative biomechanical evaluations from realistic FSI workflows provide insights into disease progression and can be integrated with current stress testing for AS patients to comprehensively predict hemodynamics and valve function under both baseline and exercise conditions.

Aortic regurgitation provokes phenotypic modulation of smooth muscle cells in the normal ascending aorta

BACKGROUND

Aortic complications are more likely to occur in patients with ascending aortic aneurysms and concomitant aortic regurgitation (AR). AR may have a negative influence on the aortic wall structure even in patients with tricuspid aortic valves and absence of aortic dilatation. It is unknown whether smooth muscle cell (SMC) changes are a feature of AR-associated aortic remodeling.

METHODS

Nondilated aortic samples were harvested intraoperatively from individuals with normal aortic valves (n = 10) or those with either predominant aortic stenosis (AS) (n = 20) or AR (n = 35). Tissue from each patient was processed for immunohistochemistry or used for the extraction of medial SMCs. Tissue and cells were stained for markers of SMC contraction (alpha-smooth muscle actin), synthesis (vimentin) and senescence (p16INK4A and p21Cip1 [p16/p21]). Replicative capacity was analyzed in cultured SMCs from AS- and AR-associated aortas. A subanalysis compared SMCs from individuals with either tricuspid aortic valves or bicuspid aortic valves to evaluate the effect of aortic valve morphology.

RESULTS

In aortic tissue samples, AR was associated with decreased alpha-smooth muscle actin and increased vimentin, p16 and p21 compared with normal aortic valves and AS. In cell culture, SMCs from AR-aortas had decreased alpha-smooth muscle actin and increased vimentin compared with SMCs from AS-aortas. AR-associated SMCs had increased p16 and p21 expression, and they reached senescence earlier than SMCs from AS-aortas. In AR, SMC changes were more pronounced with the presence of a bicuspid aortic valve.

CONCLUSIONS

AR itself negatively influences SMC phenotype in the ascending aortic wall. This AR-specific effect is independent of aortic diameter and aortic valve morphology, although it is more pronounced with bicuspid aortic valves. These findings provide insight into the mechanisms of AR-related aortic remodeling, and they provide a model for studying SMC-specific therapies in culture.

Assessing turbulent effects in ascending aorta in presence of bicuspid aortic valve

Aortic valves with bicuspids have two rather than three leaflets, which is a congenital heart condition. About 0.5-2% of people have a bicuspid aortic valve. Blood flow through the aorta is commonly believed to be laminar, although aortic valve disorders can cause turbulent transitions. Understanding the impact of turbulence is crucial for foreseeing how the disease will progress. The study's objective was use large eddy simulation to provide a thorough analysis of the turbulence in bicuspid aortic valve dysfunction. Using a large eddy simulation, the blood flow patterns of the bicuspid and tricuspid aortic valves were compared, and significant discrepancies were found. The velocity field in flow in bicuspid configurations was asymmetrically distributed toward the ascending aorta. In tricuspid aortic valve (TAV) the flow, on the other hand, was symmetrical within the same aortic segment. Moreover, we looked into standard deviation, Q-criterion, viscosity ratio and wall shear stresses for each cases to understand transition to turbulence. Our findings indicate that in the bicuspid aortic valve (BAV) case, the fluid-dynamic abnormalities increase. The global turbulent kinetic energy and time-averaged wall shear stress for the TAV and BAV scenarios were also examined. We discovered that the global turbulent kinetic energy was higher in the BAV case compared to TAV, in addition to the increased wall shear stress induced by the BAV in the ascending aorta.

Wall shear stress and pressure patterns in aortic stenosis patients with and without aortic dilation captured by high-performance image-based computational fluid dynamics

Spatial patterns of elevated wall shear stress and pressure due to blood flow past aortic stenosis (AS) are studied using GPU-accelerated patient-specific computational fluid dynamics. Three cases of moderate to severe AS, one with a dilated ascending aorta and two within the normal range (root diameter less than 4cm) are simulated for physiological waveforms obtained from echocardiography. The computational framework is built based on sharp-interface Immersed Boundary Method, where aortic geometries segmented from CT angiograms are integrated into a high-order incompressible Navier-Stokes solver. The key question addressed here is, given the presence of turbulence due to AS which increases wall shear stress (WSS) levels, why some AS patients undergo much less aortic dilation. Recent case studies of AS have linked the existence of an elevated WSS hotspot (due to impingement of AS on the aortic wall) to the dilation process. Herein we further investigate the WSS distribution for cases with and without dilation to understand the possible hemodynamics which may impact the dilation process. We show that the spatial distribution of elevated WSS is significantly more focused for the case with dilation than those without dilation. We further show that this focal area accommodates a persistent pocket of high pressure, which may have contributed to the dilation process through an increased wall-normal forcing. The cases without dilation, on the contrary, showed a rather oscillatory pressure behaviour, with no persistent pressure "buildup" effect. We further argue that a more proximal branching of the aortic arch could explain the lack of a focal area of elevated WSS and pressure, because it interferes with the impingement process due to fluid suction effects. These phenomena are further illustrated using an idealized aortic geometry. We finally show that a restored inflow eliminates the focal area of elevated WSS and pressure zone from the ascending aorta.

Turbulence suppression by cardiac-cycle-inspired driving of pipe flow

Flows through pipes and channels are, in practice, almost always turbulent, and the multiscale eddying motion is responsible for a major part of the encountered friction losses and pumping costs1. Conversely, for pulsatile flows, in particular for aortic blood flow, turbulence levels remain low despite relatively large peak velocities. For aortic blood flow, high turbulence levels are intolerable as they would damage the shear-sensitive endothelial cell layer2-5. Here we show that turbulence in ordinary pipe flow is diminished if the flow is driven in a pulsatile mode that incorporates all the key features of the cardiac waveform. At Reynolds numbers comparable to those of aortic blood flow, turbulence is largely inhibited, whereas at much higher speeds, the turbulent drag is reduced by more than 25%. This specific operation mode is more efficient when compared with steady driving, which is the present situation for virtually all fluid transport processes ranging from heating circuits to water, gas and oil pipelines.

Smooth Muscle Heterogeneity and Plasticity in Health and Aortic Aneurysmal Disease

Vascular smooth muscle cells (VSMCs) are the predominant cell type in the medial layer of the aorta, which plays a critical role in the maintenance of aortic wall integrity. VSMCs have been suggested to have contractile and synthetic phenotypes and undergo phenotypic switching to contribute to the deteriorating aortic wall structure. Recently, the unprecedented heterogeneity and diversity of VSMCs and their complex relationship to aortic aneurysms (AAs) have been revealed by high-resolution research methods, such as lineage tracing and single-cell RNA sequencing. The aortic wall consists of VSMCs from different embryonic origins that respond unevenly to genetic defects that directly or indirectly regulate VSMC contractile phenotype. This difference predisposes to hereditary AAs in the aortic root and ascending aorta. Several VSMC phenotypes with different functions, for example, secreting VSMCs, proliferative VSMCs, mesenchymal stem cell-like VSMCs, immune-related VSMCs, proinflammatory VSMCs, senescent VSMCs, and stressed VSMCs are identified in non-hereditary AAs. The transformation of VSMCs into different phenotypes is an adaptive response to deleterious stimuli but can also trigger pathological remodeling that exacerbates the pathogenesis and development of AAs. This review is intended to contribute to the understanding of VSMC diversity in health and aneurysmal diseases. Papers that give an update on VSMC phenotype diversity in health and aneurysmal disease are summarized and recent insights on the role of VSMCs in AAs are discussed.

Deep reinforcement learning for turbulent drag reduction in channel flows

We introduce a reinforcement learning (RL) environment to design and benchmark control strategies aimed at reducing drag in turbulent fluid flows enclosed in a channel. The environment provides a framework for computationally efficient, parallelized, high-fidelity fluid simulations, ready to interface with established RL agent programming interfaces. This allows for both testing existing deep reinforcement learning (DRL) algorithms against a challenging task, and advancing our knowledge of a complex, turbulent physical system that has been a major topic of research for over two centuries, and remains, even today, the subject of many unanswered questions. The control is applied in the form of blowing and suction at the wall, while the observable state is configurable, allowing to choose different variables such as velocity and pressure, in different locations of the domain. Given the complex nonlinear nature of turbulent flows, the control strategies proposed so far in the literature are physically grounded, but too simple. DRL, by contrast, enables leveraging the high-dimensional data that can be sampled from flow simulations to design advanced control strategies. In an effort to establish a benchmark for testing data-driven control strategies, we compare opposition control, a state-of-the-art turbulence-control strategy from the literature, and a commonly used DRL algorithm, deep deterministic policy gradient. Our results show that DRL leads to 43% and 30% drag reduction in a minimal and a larger channel (at a friction Reynolds number of 180), respectively, outperforming the classical opposition control by around 20 and 10 percentage points, respectively.

A Bayesian approach to blood rheological uncertainties in aortic hemodynamics

Computational hemodynamics has received increasing attention recently. Patient-specific simulations require questionable model assumptions, for example, for geometry, boundary conditions, and material parameters. Consequently, the credibility of these simulations is much doubted, and rightly so. Yet, the matter may be addressed by a rigorous uncertainty quantification. In this contribution, we investigated the impact of blood rheological models on wall shear stress uncertainties in aortic hemodynamics obtained in numerical simulations. Based on shear-rheometric experiments, we compare the non-Newtonian Carreau model to a simple Newtonian model and a Reynolds number-equivalent Newtonian model. Bayesian Probability Theory treats uncertainties consistently and allows to include elusive assumptions such as the comparability of flow regimes. We overcome the prohibitively high computational cost for the simulation with a surrogate model, and account for the uncertainties of the surrogate model itself, too. We have two main findings: (1) The Newtonian models mostly underestimate the uncertainties as compared to the non-Newtonian model. (2) The wall shear stresses of specific persons cannot be distinguished due to largely overlapping uncertainty bands, implying that a more precise determination of person-specific blood rheological properties is necessary for person-specific simulations. While we refrain from a general recommendation for one rheological model, we have quantified the error of the uncertainty quantification associated with these modeling choices.

Assessment of flow mechanics in the lower extremity venous system

BACKGROUND

The Reynolds number (R_e) is a dimensionless parameter that describes fluid flow mechanics. Veins are compliant and collapsible vascular conduits that can accommodate large volume changes in response to small pressure changes. However, only sparse information is available about flow parameters such as the R_e in the venous system.

METHODS

Bilateral duplex ultrasound examination of 15 healthy volunteers (30 limbs) was performed before and after exercise (four flights of stairs) of the veins of the lower extremity (left and right sides) and inferior vena cava. These volunteers had been confirmed to not have any signs or symptoms of lower extremity venous disease via focused history and physical examination findings.

RESULTS

Most of the volunteers were women (73%). Their mean age was 37 ± 12.8 years. The R_e was highest in the inferior vena cava among all the veins examined (470 ± 144 before exercise and 589 ± 205 after exercise; P = .04). The association between the change in R_e before and after exercise and the specific vein examined was also significant for the right and left external iliac veins, right and left common femoral veins, right and left profunda femoris veins, right and left femoral veins, and right common iliac vein. Resistance and velocity maps for the lower extremity venous system were also created. The velocity increased and the resistance decreased as one moved up the venous tree toward the right atrium.

CONCLUSIONS

The R_e increased for most of the lower extremity veins after exercise in our healthy volunteers. However, the critical value for turbulent flow was not reached despite the exercise.

Vascular regulation of disseminated tumor cells during metastatic spread

Cancer cells can travel to other organs via interconnected vascular systems to form new lesions in a process known as metastatic spread. Unfortunately, metastasis remains the leading cause of patient lethality. In recent years, it has been demonstrated that physical cues are just as important as chemical and genetic perturbations in driving changes in gene expression, cell motility, and survival. In this concise review, we focus on the physical cues that cancer cells experience as they migrate through the lymphatic and blood vascular networks. We also present an overview of steps that may facilitate organ specific metastasis.

Helical flow in tortuous aortas and its relationship to turbulence: A whole-aorta 4D flow MRI study

Background

Increased vascular tortuosity is a hallmark of ageing of the vascular system, including the aorta. However, the impact of tortuosity on aortic blood flow is unknown. We hypothesized that increased tortuosity would be associated with increased blood flow helicity and with decreased degree of blood flow turbulence as measured by the turbulent kinetic energy (TKE).

Methods

4D Flow MR images covering the entire aorta from the aortic valve to the iliac bifurcation were acquired in 23 normal volunteers aged 18-30 years ("Young") and 23 normal volunteers aged 66-76 years ("Old") without aortic disease. The aorta was segmented and divided into four regions: the ascending, descending, suprarenal abdominal and infrarenal abdominal aorta. Tortuosity, helicity, TKE, flow velocity, and Reynolds number were computed for the whole aorta and for each section.

Results

Tortuosity and helicity were higher whereas TKE, velocity, and Reynolds number were lower in Old than in Young, for all aortic regions (p < 0.05) except for helicity in the descending aorta. Tortuosity correlated positively with helicity and negatively with TKE for all aortic regions (Spearman rho=±0.45-±0.72, p < =0.002) except for TKE in the ascending aorta. Further, helicity correlated with TKE in the descending, suprarenal abdominal and infrarenal abdominal aorta (Spearman rho=-0.56--0.77).

Conclusion

Tortuosity increases with age and blood flow in tortuous aortas is more helical. Increasing helicity, in turn, is associated with decreasing TKE.

Effect of aortic curvature on bioprosthetic aortic valve performance

Transvalvular pressure gradient (ΔP) after aortic valve replacement is an important surrogate of aortic bioprostheses performance. Invasive ΔP is often measured after transcatheter aortic valve replacement to exclude patient-prosthetic mismatch. However, invasive aortic pressures are usually recorded in the pressure recovery (PR) zone downstream of the valve, potentially resulting in ΔP underestimation compared to noninvasive measurements. PR was extensively studied in straight ascending aortas. However, the impact of various aortic arch configurations on ΔP has not been explored. PR was assessed in a pulse duplicating simulator at various cardiac conditions of cardiac output, heart rates and pressures. Three different aortic geometries with identical root dimensions but with different aortic arches were used: (1) curvature 1, (2) curvature 2, and (3) straight aortic models. Instantaneous pressure and peak ΔP measurements were recorded incrementally along the models for each cardiac condition. The models with aortic arches produced two distinct PR zones (after the valve and after the aortic arch), whereas the model without an aortic arch produced only one PR zone (after the valve). The trend of the pressure and ΔP curves for each model was independent of the cardiac condition used, but the individually measured pressure magnitudes did change with different conditions. In this study, we illustrated the differences in PR between distinct aortic curvatures and straight aorta. PR affects pressure and ΔP measurements. These effects are clear when recording aortic pressures by catheterization and echocardiography.

Semi-Automated Construction of Patient-Specific Aortic Valves from Computed Tomography Images

This paper presents a semi-automatic method for the construction of volumetric models of the aortic valve using computed tomography angiography images. Although the aortic valve typically cannot be segmented directly from a computed tomography angiography image, the method described herein uses manually selected samples of an aortic segmentation derived from this image to inform the construction. These samples capture certain physiologic landmarks and are used to construct a volumetric valve model. As a demonstration of the capabilities of this method, valve models for 25 pediatric patients are created. A selected valve anatomy is used to perform fluid-structure interaction simulations using the immersed finite element/difference method with physiologic driving and loading conditions. Simulation results demonstrate this method creates a functional valve that opens and closes normally and generates pressure and flow waveforms that are similar to those observed clinically.

Evaluation of aortic stenosis: From Bernoulli and Doppler to Navier-Stokes

Uni-dimensional Doppler echocardiography data provide the mainstay of quantative assessment of aortic stenosis, with the transvalvular pressure drop a key indicator of haemodynamic burden. Sophisticated methods of obtaining velocity data, combined with improved computational analysis, are facilitating increasingly robust and reproducible measurement. Imaging modalities which permit acquisition of three-dimensional blood velocity vector fields enable angle-independent valve interrogation and calculation of enhanced measures of the transvalvular pressure drop. This manuscript clarifies the fundamental principles of physics that underpin the evaluation of aortic stenosis and explores modern techniques that may provide more accurate means to grade aortic stenosis and inform appropriate management.

An artificial intelligence-based platform for automatically estimating time-averaged wall shear stress in the ascending aorta

Aims

Aortopathies are a series of disorders requiring multiple indicators to assess risk. Time-averaged wall shear stress (TAWSS) is currently considered as the primary indicator of aortopathies progression, which can only be calculated by Computational Fluid Dynamics (CFD). However, CFD's complexity and high computational cost, greatly limit its application. The study aimed to construct a deep learning platform which could accurately estimate TAWSS in ascending aorta.

Methods and results

A total of 154 patients who had thoracic computed tomography angiography were included and randomly divided into two parts: training set (90%, n = 139) and testing set (10%, n = 15). TAWSS were calculated via CFD. The artificial intelligence (AI)-based model was trained and assessed using the dice coefficient (DC), normalized mean absolute error (NMAE), and root mean square error (RMSE). Our AI platform brought into correspondence with the manual segmentation (DC = 0.86) and the CFD findings (NMAE, 7.8773% ± 4.7144%; RMSE, 0.0098 ± 0.0097), while saving 12000-fold computational cost.

Conclusion

The high-efficiency and robust AI platform can automatically estimate value and distribution of TAWSS in ascending aorta, which may be suitable for clinical applications and provide potential ideas for CFD-based problem solving.

Enhanced 4D Flow MRI-Based CFD with Adaptive Mesh Refinement for Flow Dynamics Assessment in Coarctation of the Aorta

4D Flow MRI is a diagnostic tool that can visualize and quantify patient-specific hemodynamics and help interventionalists optimize treatment strategies for repairing coarctation of the aorta (COA). Despite recent developments in 4D Flow MRI, shortcomings include phase-offset errors, limited spatiotemporal resolution, aliasing, inaccuracies due to slow aneurysmal flows, and distortion of images due to metallic artifact from vascular stents. To address these limitations, we developed a framework utilizing Computational Fluid Dynamics (CFD) with Adaptive Mesh Refinement (AMR) that enhances 4D Flow MRI visualization/quantification. We applied this framework to five pediatric patients with COA, providing in-vivo and in-silico datasets, pre- and post-intervention. These two data sets were compared and showed that CFD flow rates were within 9.6% of 4D Flow MRI, which is within a clinically acceptable range. CFD simulated slow aneurysmal flow, which MRI failed to capture due to high relative velocity encoding (Venc). CFD successfully predicted in-stent blood flow, which was not visible in the in-vivo data due to susceptibility artifact. AMR improved spatial resolution by factors of 101 to 103 and temporal resolution four-fold. This computational framework has strong potential to optimize visualization/quantification of aneurysmal and in-stent flows, improve spatiotemporal resolution, and assess hemodynamic efficiency post-COA treatment.

Pulsatile blood flow in healthy aorta: An application of nonlinear evolution equation

Fluid flow dynamics in nature and its applications including hemodynamics are subjected to periodic velocity modulations. The nonlinear evolution equations are perused to understand such fundamental dynamical challenges in hemodynamics. Assuming cardiovascular hemodynamic system as a finite dissipative system and blood as an incompressible Newtonian fluid, a nonlinear evolution equation for pulsatile blood flow in the aorta during the cardiac cycle is modeled. The main results for generalized [Formula: see text]-dimensional nonlinear evolution equation, using the Lie group of transformations method are introduced. The implications of traveling wave solutions to describe the pulsatile blood flow in the aorta are discussed. It is found that the self-interactions among solitary waves along with generation of relatively small-scale and unstable wave fields contribute to turbulence.

Review of the Development of Hemodynamic Modeling Techniques to Capture Flow Behavior in Arteries Affected by Aneurysm, Atherosclerosis, and Stenting

Cardiovascular diseases (CVDs) are the leading cause of death in the developed world. CVD can include atherosclerosis, aneurysm, dissection, or occlusion of the main arteries. Many CVDs are caused by unhealthy hemodynamics. Some CVDs can be treated with the implantation of stents and stent grafts. Investigations have been carried out to understand the effects of stents and stent grafts have on arteries and the hemodynamic changes post-treatment. Numerous studies on stent hemodynamics have been carried out using computational fluid dynamics (CFD) which has yielded significant insight into the effect of stent mesh design on near-wall blood flow and improving hemodynamics. Particle image velocimetry (PIV) has also been used to capture behavior of fluids that mimic physiological hemodynamics. However, PIV studies have largely been restricted to unstented models or intra-aneurysmal flow rather than peri or distal stent flow behaviors. PIV has been used both as a standalone measurement method and as a comparison to validate the CFD studies. This article reviews the successes and limitations of CFD and PIV-based modeling methods used to investigate the hemodynamic effects of stents. The review includes an overview of physiology and relevant mechanics of arteries as well as consideration of boundary conditions and the working fluids used to simulate blood for each modeling method along with the benefits and limitations introduced.

Computational Modeling of Aortic Stenosis With a Reduced Degree-of-Freedom Fluid-Structure Interaction Valve Model

In this study, a novel reduced degree-of-freedom (rDOF) aortic valve model is employed to investigate the fluid-structure interaction (FSI) and hemodynamics associated with aortic stenosis. The dynamics of the valve leaflets are determined by an ordinary differential equation with two parameters and this rDOF model is shown to reproduce key features of more complex valve models. The hemodynamics associated with aortic stenosis is studied for three cases: a healthy case and two stenosed cases. The focus of the study is to correlate the hemodynamic features with the source generation mechanism of systolic murmurs associated with aortic stenosis. In the healthy case, extremely weak flow fluctuations are observed. However, in the stenosed cases, simulations show significant turbulent fluctuations in the ascending aorta, which are responsible for the generation of strong wall pressure fluctuations after the aortic root mostly during the deceleration phase of the systole. The intensity of the murmur generation increases with the severity of the stenosis, and the source locations for the two diseased cases studied here lie around 1.0 inlet duct diameters (Do) downstream of the ascending aorta.

Scale-Resolving Simulations of Steady and Pulsatile Flow Through Healthy and Stenotic Heart Valves

Blood-flow downstream of stenotic and healthy aortic valves exhibits intermittent random fluctuations in the velocity field which are associated with turbulence. Such flows warrant the use of computationally demanding scale-resolving models. The aim of this work was to compute and quantify this turbulent flow in healthy and stenotic heart valves for steady and pulsatile flow conditions. Large eddy simulations (LESs) and Reynolds-averaged Navier-Stokes (RANS) simulations were used to compute the flow field at inlet Reynolds numbers of 2700 and 5400 for valves with an opening area of 70 mm2 and 175 mm2 and their projected orifice-plate type counterparts. Power spectra and turbulent kinetic energy were quantified on the centerline. Projected geometries exhibited an increased pressure-drop (>90%) and elevated turbulent kinetic energy levels (>147%). Turbulence production was an order of magnitude higher in stenotic heart valves compared to healthy valves. Pulsatile flow stabilizes flow in the acceleration phase, whereas onset of deceleration triggered (healthy valve) or amplified (stenotic valve) turbulence. Simplification of the aortic valve by projecting the orifice area should be avoided in computational fluid dynamics (CFD). RANS simulations may be used to predict the transvalvular pressure-drop, but scale-resolving models are recommended when detailed information of the flow field is required.

Improving transcatheter aortic valve interventional predictability via fluid-structure interaction modelling using patient-specific anatomy

Transcatheter aortic valve replacement (TAVR) is now a standard treatment for high-surgical-risk patients with severe aortic valve stenosis. TAVR is being explored for broader indications including degenerated bioprosthetic valves, bicuspid valves and for aortic valve (AV) insufficiency. It is, however, challenging to predict whether the chosen valve size, design or its orientation would produce the most-optimal haemodynamics in the patient. Here, we present a novel patient-specific evaluation framework to realistically predict the patient's AV performance with a high-fidelity fluid-structure interaction analysis that included the patient's left ventricle and ascending aorta (AAo). We retrospectively evaluated the pre- and post-TAVR dynamics of a patient who underwent a 23 mm TAVR and evaluated against the patient's virtually de-calcified AV serving as a hypothetical benchmark. Our model predictions were consistent with clinical data. Stenosed AV produced a turbulent flow during peak-systole, while aortic flow with TAVR and de-calcified AV were both in the laminar-to-turbulent transitional regime with an estimated fivefold reduction in viscous dissipation. For TAVR, dissipation was highest during early systole when valve deformation was the greatest, suggesting that an efficient valve opening may reduce energy loss. Our study demonstrates that such patient-specific modelling frameworks can be used to improve predictability and in the planning of AV interventions.

WSSNet: Aortic Wall Shear Stress Estimation Using Deep Learning on 4D Flow MRI

Wall shear stress (WSS) is an important contributor to vessel wall remodeling and atherosclerosis. However, image-based WSS estimation from 4D Flow MRI underestimates true WSS values, and the accuracy is dependent on spatial resolution, which is limited in 4D Flow MRI. To address this, we present a deep learning algorithm (WSSNet) to estimate WSS trained on aortic computational fluid dynamics (CFD) simulations. The 3D CFD velocity and coordinate point clouds were resampled into a 2D template of 48 × 93 points at two inward distances (randomly varied from 0.3 to 2.0 mm) from the vessel surface (“velocity sheets”). The algorithm was trained on 37 patient-specific geometries and velocity sheets. Results from 6 validation and test cases showed high accuracy against CFD WSS (mean absolute error 0.55 ± 0.60 Pa, relative error 4.34 ± 4.14%, 0.92 ± 0.05 Pearson correlation) and noisy synthetic 4D Flow MRI at 2.4 mm resolution (mean absolute error 0.99 ± 0.91 Pa, relative error 7.13 ± 6.27%, and 0.79 ± 0.10 Pearson correlation). Furthermore, the method was applied on in vivo 4D Flow MRI cases, effectively estimating WSS from standard clinical images. Compared with the existing parabolic fitting method, WSSNet estimates showed 2–3 × higher values, closer to CFD, and a Pearson correlation of 0.68 ± 0.12. This approach, considering both geometric and velocity information from the image, is capable of estimating spatiotemporal WSS with varying image resolution, and is more accurate than existing methods while still preserving the correct WSS pattern distribution.

In-vitro and In-Vivo Assessment of 4D Flow MRI Reynolds Stress Mapping for Pulsatile Blood Flow

Imaging hemodynamics play an important role in the diagnosis of abnormal blood flow due to vascular and valvular diseases as well as in monitoring the recovery of normal blood flow after surgical or interventional treatment. Recently, characterization of turbulent blood flow using 4D flow magnetic resonance imaging (MRI) has been demonstrated by utilizing the changes in signal magnitude depending on intravoxel spin distribution. The imaging sequence was extended with a six-directional icosahedral (ICOSA6) flow-encoding to characterize all elements of the Reynolds stress tensor (RST) in turbulent blood flow. In the present study, we aimed to demonstrate the feasibility of full RST analysis using ICOSA6 4D flow MRI under physiological conditions. First, the turbulence analysis was performed through in vitro experiments with a physiological pulsatile flow condition. Second, a total of 12 normal subjects and one patient with severe aortic stenosis were analyzed using the same sequence. The in-vitro study showed that total turbulent kinetic energy (TKE) was less affected by the signal-to-noise ratio (SNR), however, maximum principal turbulence shear stress (MPTSS) and total turbulence production (TP) had a noise-induced bias. Smaller degree of the bias was observed for TP compared to MPTSS. In-vivo study showed that the subject-variability on turbulence quantification was relatively low for the consistent scan protocol. The in vivo demonstration of the stenosis patient showed that the turbulence analysis could clearly distinguish the difference in all turbulence parameters as they were at least an order of magnitude larger than those from the normal subjects.

Fundamentals of turbulent flow spectrum imaging

PURPOSE

To introduce a mathematical framework and in-silico validation of turbulent flow spectrum imaging (TFSI) of stenotic flow using phase-contrast MRI, evaluate systematic errors in quantitative turbulence parameter estimation, and propose a novel method for probing the Lagrangian velocity spectra of turbulent flows.

THEORY AND METHODS

The spectral response of velocity-encoding gradients is derived theoretically and linked to turbulence parameter estimation including the velocity autocorrelation function spectrum. Using a phase-contrast MRI simulation framework, the encoding properties of bipolar gradient waveforms with identical first gradient moments but different duration are investigated on turbulent flow data of defined characteristics as derived from computational fluid dynamics. Based on theoretical insights, an approach using velocity-compensated gradient waveforms is proposed to specifically probe desired ranges of the velocity autocorrelation function spectrum with increased accuracy.

RESULTS

Practical velocity-encoding gradients exhibit limited encoding power of typical turbulent flow spectra, resulting in up to 50% systematic underestimation of intravoxel SD values. Depending on the turbulence level in fluids, the error due to a single encoding gradient spectral response can vary by 20%. When using tailored velocity-compensated gradients, improved quantification of the Lagrangian velocity spectrum on a voxel-by-voxel basis is achieved and used for quantitative correction of intravoxel SD values estimated with velocity-encoding gradients.

CONCLUSION

To address systematic underestimation of turbulence parameters using bipolar velocity-encoding gradients in phase-contrast MRI of stenotic flows with short correlation times, tailored velocity-compensated gradients are proposed to improve quantitative mapping of turbulent blood flow characteristics.

Impact of calcific aortic valve disease on valve mechanics

The aortic valve is a highly dynamic structure characterized by a transvalvular flow that is unsteady, pulsatile, and characterized by episodes of forward and reverse flow patterns. Calcific aortic valve disease (CAVD) resulting in compromised valve function and increased pressure overload on the ventricle potentially leading to heart failure if untreated, is the most predominant valve disease. CAVD is a multi-factorial disease involving molecular, tissue and mechanical interactions. In this review, we aim at recapitulating the biomechanical loads on the aortic valve, summarizing the current and most recent research in the field in vitro, in-silico, and in vivo, and offering a clinical perspective on current strategies adopted to mitigate or approach CAVD.

Comparison of Four-Dimensional Flow Magnetic Resonance Imaging and Particle Image Velocimetry to Quantify Velocity and Turbulence Parameters

Although recent advances of four-dimensional (4D) flow magnetic resonance imaging (MRI) has introduced a new way to measure Reynolds stress tensor (RST) in turbulent flows, its measurement accuracy and possible bias have remained to be revealed. The purpose of this study was to compare the turbulent flow measurement of 4D flow MRI and particle image velocimetry (PIV) in terms of velocity and turbulence quantification. Two difference flow rates of 10 and 20 L/min through a 50% stenosis were measured with both PIV and 4D flow MRI. Not only velocity through the stenosis but also the turbulence parameters such as turbulence kinetic energy and turbulence production were quantitatively compared. Results shows that 4D flow MRI velocity measurement well agreed with the that of PIV, showing the linear regression slopes of two methods are 0.94 and 0.89, respectively. Although turbulence mapping of 4D flow MRI was qualitatively agreed with that of PIV, the quantitative comparison shows that the 4D flow MRI overestimates RST showing the linear regression slopes of 1.44 and 1.66, respectively. In this study, we demonstrate that the 4D flow MRI visualize and quantify not only flow velocity and also turbulence tensor. However, further optimization of 4D flow MRI for better accuracy might be remained.

Analysis of Turbulence Effects in a Patient-Specific Aorta with Aortic Valve Stenosis

Blood flow in the aorta is often assumed laminar, however aortic valve pathologies may induce transition to turbulence and our understanding of turbulence effects is incomplete. The aim of the study was to provide a detailed analysis of turbulence effects in aortic valve stenosis (AVS).

METHODS

Large-eddy simulation (LES) of flow through a patient-specific aorta with AVS was conducted. Magnetic resonance imaging (MRI) was performed and used for geometric reconstruction and patient-specific boundary conditions. Computed velocity field was compared with 4D flow MRI to check qualitative and quantitative consistency. The effect of turbulence was evaluated in terms of fluctuating kinetic energy, turbulence-related wall shear stress (WSS) and energy loss.

RESULTS

Our analysis suggested that turbulence was induced by a combination of a high velocity jet impinging on the arterial wall and a dilated ascending aorta which provided sufficient space for turbulence to develop. Turbulent WSS contributed to 40% of the total WSS in the ascending aorta and 38% in the entire aorta. Viscous and turbulent irreversible energy losses accounted for 3.9 and 2.7% of the total stroke work, respectively.

CONCLUSIONS

This study demonstrates the importance of turbulence in assessing aortic haemodynamics in a patient with AVS. Neglecting the turbulent contribution to WSS could potentially result in a significant underestimation of the total WSS. Further work is warranted to extend the analysis to more AVS cases and patients with other aortic valve diseases.

A review of dynamical systems approaches for the detection of chaotic attractors in cancer networks

Cancers are complex dynamical systems. They remain the leading cause of disease-related pediatric mortality in North America. To overcome this burden, we must decipher the state-space attractor dynamics of gene expression patterns and protein oscillations orchestrated by cancer stemness networks. The review provides an overview of dynamical systems theory to steer cancer research in pattern science. While most of our current tools in network medicine rely on statistical correlation methods, causality inference remains primitively developed. As such, a survey of attractor reconstruction methods and machine algorithms for the detection of causal structures applicable in experimentally derived time series cancer datasets is presented. A toolbox of complex systems approaches are discussed for reconstructing the signaling state space of cancer networks, interpreting causal relationships in their time series gene expression patterns, and assisting clinical decision making in computational oncology. As a proof of concept, the applicability of some algorithms are demonstrated on pediatric brain cancer datasets and the requirement of their time series analysis is highlighted.

Characterization of the dynamic viscoelastic response of the ascending aorta imposed via pulsatile flow

This study characterizes the material properties of a viscoelastic, ex vivo porcine ascending aorta under dynamic-loading conditions via pulsatile flow. The deformation of the opaque vessel wall and the pulsatile flow field inside the vessel were recorded using ultrasound imaging. The internal pressure was extracted from the pulsatile flow results and, when coupled with the vessel-wall expansion, was used to calculate the instantaneous elastic modulus from a novel, time-resolved two-dimensional (i.e. axial and circumferential) stress model. The circumferential instantaneous elasticity obtained from the two-dimensional stress model was found to match the uniaxial tensile test for strains below 50%. The agreement in elasticity between the two stress states reveals that the two-dimensional stress model accurately resolves the circumferential stress of the viscoelastic aorta at physiological strains (8%-30%). At higher strains, results from pulsatile flow generated a more compliant response than the uniaxial measurements. Viscoelastic properties (storage modulus and loss factor) were also calculated using the two-dimensional stress model and compared to those obtained from uniaxial tests. While instantaneous elasticity matched between the cylindrical and uniaxial loading, the viscoelastic behaviour significantly diverged between stress states. The storage modulus obtained from the pulsatile flow data was dependent on mean Reynolds number, while the uniaxial storage modulus results exhibited a strong inverse dependency on the frequency. The loss factor for the pulsatile flow data increased alongside the frequency, while the uniaxial data indicated a constant loss factor over the entire frequency range. The results of the current study show that the two-dimensional stress model can accurately extract the material properties of the ex vivo porcine aorta.

Aortic aneurysms with tricuspid aortic valve have more degeneration than unicuspid aortic valve aneurysms

 

OBJECTIVES

The unicuspid aortic valve (UAV) is a rare cardiac malformation and is associated with the formation of ascending aortic aneurysms. To characterize its associated aortic wall changes, normal and aneurysmatic ascending aortic wall specimens were analysed, focusing on the potential mechanisms of aneurysm formation. Patients with tricuspid aortic valve (TAV) served as controls.

METHODS

In a retrospective observational study, 74 specimens (dilated and non-dilated aortas; individuals with UAV and TAV) obtained intraoperatively were studied. Standard stains and immunohistochemical labelling of cleaved caspase-3, cluster of differentiation 31 and endothelial nitric oxide synthase (eNOS) were performed to assess the degree of apoptosis, distribution of eNOS within the aortic wall, smooth muscle cell (SMC) nuclei loss and mucoid extracellular matrix accumulation (MEMA).

RESULTS

Deeper ingrowth of vasa vasorum was found in dilated aortas. Interestingly, eNOS was expressed mostly in vasa vasorum. More apoptosis was seen in UAV aortas compared to TAV aortas (P < 0.001). Both UAV and TAV aortas were comparable regarding SMC nuclei loss (P = 0.419). In dilated compared to non-dilated aortas regardless valve morphology SMC nuclei loss was increased (P = 0.005) and more pronounced translamellar MEMA was present (P = 0.011). The highest grade of distribution (P = 0.043) and the highest severity (P = 0.005) regarding MEMA were seen in TAV dilated specimens compared to UAV dilated specimens.

CONCLUSIONS

Aneurysms with UAV show increased apoptosis, the role of which is unclear. Strikingly, more severe MEMA was found in TAV aneurysms compared to UAV aneurysms. Thus, UAV-associated aortic wall changes and resulting aneurysm may be less aggressive than aneurysms with TAV.

Heritability of haemodynamics in the ascending aorta

Blood flow in the vasculature can be characterised by dimensionless numbers commonly used to define the level of instabilities in the flow, for example the Reynolds number, Re. Haemodynamics play a key role in cardiovascular disease (CVD) progression. Genetic studies have identified mechanosensitive genes with causal roles in CVD. Given that CVD is highly heritable and abnormal blood flow may increase risk, we investigated the heritability of fluid metrics in the ascending aorta calculated using patient-specific data from cardiac magnetic resonance (CMR) imaging. 341 participants from 108 British Caucasian families were phenotyped by CMR and genotyped for 557,124 SNPs. Flow metrics were derived from the CMR images to provide some local information about blood flow in the ascending aorta, based on maximum values at systole at a single location, denoted max, and a 'peak mean' value averaged over the area of the cross section, denoted pm. Heritability was estimated using pedigree-based (QTDT) and SNP-based (GCTA-GREML) methods. Estimates of Reynolds number based on spatially averaged local flow during systole showed substantial heritability ([Formula: see text], [Formula: see text]), while the estimated heritability for Reynolds number calculated using the absolute local maximum velocity was not statistically significant (12-13%; [Formula: see text]). Heritability estimates of the geometric quantities alone; e.g. aortic diameter ([Formula: see text], [Formula: see text]), were also substantially heritable, as described previously. These findings indicate the potential for the discovery of genetic factors influencing haemodynamic traits in large-scale genotyped and phenotyped cohorts where local spatial averaging is used, rather than instantaneous values. Future Mendelian randomisation studies of aortic haemodynamic estimates, which are swift to derive in a clinical setting, will allow for the investigation of causality of abnormal blood flow in CVD.

In vitro experiments on ICOSA6 4D flow MRI measurement for the quantification of velocity and turbulence parameters

PURPOSE

To perform comprehensive in vitro experiments using six-directional icosahedral flow encoding (ICOSA6) 4D flow magnetic resonance imaging (MRI) under various scan conditions to analyze the robustness of velocity and turbulence quantification.

MATERIALS AND METHODS

In vitro flow phantoms with steady flow rates of 10 and 20 L/min were scanned using both conventional 4D flow MRI and ICOSA6. Experiments focused on comparisons between ICOSA6 and conventional four point (4P) methods, and the effects of contrast agents, velocity encoding range (Venc), and scan direction on velocity and turbulence quantification.

RESULTS

The results demonstrated that 1) ICOSA6 improves the velocity-to-noise ratio (VNR) of velocity estimation by 33% (on average) and results in similar turbulent kinetic energy (TKE) estimation as the 4P method. 2) Measurements with a contrast agent resulted in more than a 2.5 fold increase in average VNR. However, the improvement of total TKE quantification was not obvious. 3) TKE estimation was less affected by Venc and the scan direction, whereas turbulence production (TP) estimation was largely affected by these measurement conditions. The effects of Venc and scan direction accounted for less than 11.63% of TKE estimation, but up to 33.89% of TP estimation.

CONCLUSION

The ICOSA6 scheme is compatible with conventional 4D flow MRI for velocity and TKE measurement. Contrast agents are effective at increasing VNR, but not signal-to-noise ratio for TKE quantification. The effects of Venc and scan direction influence total TP more than total TKE.

Accelerating massively parallel hemodynamic models of coarctation of the aorta using neural networks

Comorbidities such as anemia or hypertension and physiological factors related to exertion can influence a patient’s hemodynamics and increase the severity of many cardiovascular diseases. Observing and quantifying associations between these factors and hemodynamics can be difficult due to the multitude of co-existing conditions and blood flow parameters in real patient data. Machine learning-driven, physics-based simulations provide a means to understand how potentially correlated conditions may affect a particular patient. Here, we use a combination of machine learning and massively parallel computing to predict the effects of physiological factors on hemodynamics in patients with coarctation of the aorta. We first validated blood flow simulations against in vitro measurements in 3D-printed phantoms representing the patient’s vasculature. We then investigated the effects of varying the degree of stenosis, blood flow rate, and viscosity on two diagnostic metrics – pressure gradient across the stenosis (ΔP) and wall shear stress (WSS) - by performing the largest simulation study to date of coarctation of the aorta (over 70 million compute hours). Using machine learning models trained on data from the simulations and validated on two independent datasets, we developed a framework to identify the minimal training set required to build a predictive model on a per-patient basis. We then used this model to accurately predict ΔP (mean absolute error within 1.18 mmHg) and WSS (mean absolute error within 0.99 Pa) for patients with this disease.

Fluid Structure Interaction on Paravalvular Leakage of Transcatheter Aortic Valve Implantation Related to Aortic Stenosis: A Patient-Specific Case

This study investigated the impact of paravalvular leakage (PVL) in relation to the different valve openings of the transcatheter aortic valve implantation (TAVI) valve using the fluid structure interaction (FSI) approach. Limited studies were found on the subject of FSI with regards to TAVI-PVL condition, which involves both fluid and structural responses in coupling interaction. Hence, further FSI simulation with the two-way coupling method is implemented to investigate the effects of hemodynamics blood flow along the patient-specific aorta model subjected to the interrelationship between PVL and the different valve openings using the established FSI software ANSYS 16.1. A 3D patient-specific aorta model is constructed using MIMICS software. The TAVI valve identical to Edward SAPIEN XT 26 (Edwards Lifesciences, Irvine, California), at different Geometrical Orifice Areas (GOAs), is implanted into the patient's aortic annulus. The leaflet opening of the TAVI valve is drawn according to severity of GOA opening represented in terms of 100%, 80%, 60%, and 40% opening, respectively. The result proved that the smallest percentage of GOA opening produced the highest possibility of PVL, increased the recirculatory flow proximally to the inner wall of the ascending aorta, and produced lower backflow velocity streamlines through the side area of PVL region. Overall, 40% GOA produced 89.17% increment of maximum velocity magnitude, 19.97% of pressure drop, 65.70% of maximum WSS magnitude, and a decrement of 33.62% total displacement magnitude with respect to the 100% GOA.

ESTIMATION OF WALL SHEAR STRESS OF COMPLIANT THORACIC AORTA WITH ANEURYSM

In this paper, a numerical estimation of wall shear stress (WSS) in a compliant Thoracic Aorta (TA) with aneurysm is modeled and the hemodynamic pattern is studied using Computational Fluid Dynamics (CFD). Thoracic Aortic Aneurysm (TAA) is an excessively localized enlargement of TA caused by weakness in the arterial wall and it can rupture the inner wall intima and continue on to the outer wall adventitia. WSS is a tangential force exerted by blood flow on the vessel wall, and its estimation is clinically very important because any change in WSS is considered as a vital cue in the onset of aneurysm. In this work, a three-dimensional (3D) model of a TAA reconstructed from computed tomography (CT) images comprising of 600 slices with 1-mm resolution from neck to hip is considered and patient-specific simulations have been carried out in compliant TA under rest and exercise conditions. The findings show that the change in wall geometry was marginal due to variation in pressure forces inside and is not the primary source for expansion of an aneurysm. It was inferred that expansion was rather due to thinning of the wall, owing to damage caused to the inner lining of the tissues, at regions of high WSS. It was found that the geometry extraction is important as any change in length causes a corresponding variation in mass flow through it. Although mass conservation is maintained irrespective of the length, it does affect the rate of flow due to shifting in the pressure boundary conditions with the length as it varies the pressure inside the system. Modeling of the geometry is very important as the change in mass flow will affect the outlet velocity and strength of vortices. Surprisingly, the split-up of flow is consistent but the geometric change in the model has no effect on WSS values and flow pattern. The results of this study provide important information such as blood flow pattern and pressure drops in the compliant TA on WSS estimations with TAA diseases.

Non-invasive estimation of relative pressure in turbulent flow using virtual work-energy

Vascular pressure differences are established risk markers for a number of cardiovascular diseases. Relative pressures are, however, often driven by turbulence-induced flow fluctuations, where conventional non-invasive methods may yield inaccurate results. Recently, we proposed a novel method for non-turbulent flows, νWERP, utilizing the concept of virtual work-energy to accurately probe relative pressure through complex branching vasculature. Here, we present an extension of this approach for turbulent flows: νWERP-t. We present a theoretical method derivation based on flow covariance, quantifying the impact of flow fluctuations on relative pressure. νWERP-t is tested on a set of in-vitro stenotic flow phantoms with data acquired by 4D flow MRI with six-directional flow encoding, as well as on a patient-specific in-silico model of an acute aortic dissection. Over all tests νWERP-t shows improved accuracy over alternative energy-based approaches, with excellent recovery of estimated relative pressures. In particular, the use of a guaranteed divergence-free virtual field improves accuracy in cases where turbulent flows skew the apparent divergence of the acquired field. With the original νWERP allowing for assessment of relative pressure into previously inaccessible vasculatures, the extended νWERP-t further enlarges the method's clinical scope, underlining its potential as a novel tool for assessing relative pressure in-vivo.

Design of nanorobots for exposing cancer cells

We discuss in detail, the design of a nanorobot that can navigate, detect cancer cells in the blood and actuate the exposure of drugs. The nanorobot is designed with blood energy harvesting capability and the accumulation of electricity in a capacitor, which forms the main body of the nanorobot. Glucose hunger-based cancer detectors immobilized on a carbon nanotube sensor, reduces its electrical resistance when attached to a cancer cell. This mechanism in turn allows electric current to activate a nano-electrical-mechanical relay (mechanical transistor) to break the chamber ceiling exposing a drug identified by the immune system for cell elimination. This concept is in line with the effort to design an autonomous computational nanorobot for in vivo medical diagnosis and treatment. We present this facile approach to design a collective system to visualize the programmability in nanorobots. The calculations and simulation results provide a proof-of-concept towards a plausible implementation. Through this work, we present an overall picture towards an inorganic autonomous computational nanorobot for cancer diagnosis and treatment.

Embolus Analog Trajectory Paths Under Physiological Flowrates Through Patient-Specific Aortic Arch Models

Atrial fibrillation (AF) is the most common irregular heartbeat among the world's population and is a major contributor to cardiogenic embolisms and acute ischemic stroke (AIS). However, the role AF flow plays in the trajectory paths of cardiogenic emboli has not been experimentally investigated. A physiological simulation system was designed to analyze the trajectory patterns of bovine embolus analogs (EAs) (n = 720) through four patient-specific models, under three flow conditions: steady flow, normal pulsatile flow, and AF pulsatile flow. It was seen that EA trajectory paths were proportional to the percentage flowrate split of 25–31% along the branching vessels. Overall, AF flow conditions increased trajectories through the left- (LCCA) and right (RCCA)-common carotid artery by 25% with respect to normal pulsatile flow. There was no statistical difference in the distribution of clot trajectories when the clot was released from the right, left, or anterior positions. Significantly, more EAs traveled through the brachiocephalic trunk (BCT) than through the LCCA or the left subclavian. Yet of the EAs that traveled through the common carotid arteries, there was a greater affiliation toward the LCCA compared to the RCCA (p < 0.05).

Suitability of lattice Boltzmann inlet and outlet boundary conditions for simulating flow in image-derived vasculature

The lattice Boltzmann method (LBM) is a popular alternative to solving the Navier-Stokes equations for modeling blood flow. When simulating flow using the LBM, several choices for inlet and outlet boundary conditions exist. While boundary conditions in the LBM have been evaluated in idealized geometries, there have been no extensive comparisons in image-derived vasculature, where the geometries are highly complex. In this study, the Zou-He (ZH) and finite difference (FD) boundary conditions were evaluated in image-derived vascular geometries by comparing their stability, accuracy, and run times. The boundary conditions were compared in four arteries: a coarctation of the aorta, dissected aorta, femoral artery, and left coronary artery. The FD boundary condition was more stable than ZH in all four geometries. In general, simulations using the ZH and FD method showed similar convergence rates within each geometry. However, the ZH method proved to be slightly more accurate compared with experimental flow using three-dimensional printed vasculature. The total run times necessary for simulations using the ZH boundary condition were significantly higher as the ZH method required a larger relaxation time, grid resolution, and number of time steps for a simulation representing the same physiological time. Finally, a new inlet velocity profile algorithm is presented for complex inlet geometries. Overall, results indicated that the FD method should generally be used for large-scale blood flow simulations in image-derived vasculature geometries. This study can serve as a guide to researchers interested in using the LBM to simulate blood flow.

Combined In Silico and In Vitro Approach Predicts Low Wall Shear Stress Regions in a Hemofilter that Correlate with Thrombus Formation In Vivo

A major challenge in developing blood-contacting medical devices is mitigating thrombogenicity of an intravascular device. Thrombi may interfere with device function or embolize from the device to occlude distant vascular beds with catastrophic consequences. Chemical interactions between plasma proteins and bioengineered surface occur at the nanometer scale; however, continuum models of blood predict local shear stresses that lead to platelet activation or aggregation and thrombosis. Here, an iterative approach to blood flow path design incorporating in silico, in vitro, and in vivo experiments predicted the occurrence and location of thrombi in an implantable hemofilter. Low wall shear stress (WSS) regions identified by computational fluid dynamics (CFD) predicted clot formation in vivo. Revised designs based on CFD demonstrated superior performance, illustrating the importance of a multipronged approach for a successful design process.

Use of Computational Fluid Dynamics to Analyze Blood Flow, Hemolysis and Sublethal Damage to Red Blood Cells in a Bileaflet Artificial Heart Valve

Artificial heart valves may expose blood to flow conditions that lead to unnaturally high stress and damage to blood cells as well as issues with thrombosis. The purpose of this research was to predict the trauma caused to red blood cells (RBCs), including hemolysis, from the stresses applied to them and their exposure time as determined by analysis of simulation results for blood flow through both a functioning and malfunctioning bileaflet artificial heart valve. The calculations provided the spatial distribution of the Kolmogorov length scales that were used to estimate the spatial and size distributions of the smallest turbulent flow eddies in the flow field. The number and surface area of these eddies in the blood were utilized to predict the amount of hemolysis experienced by RBCs. Results indicated that hemolysis levels are low while suggesting stresses at the leading edge of the leaflet may contribute to subhemolytic damage characterized by shortened circulatory lifetimes and reduced RBC deformability.

Validation of pressure drop assessment using 4D flow MRI-based turbulence production in various shapes of aortic stenoses

PURPOSE

To validate pressure drop measurements using 4D flow MRI-based turbulence production in various shapes of stenotic stenoses.

METHODS

In vitro flow phantoms with seven different 3D-printed aortic valve geometries were constructed and scanned with 4D flow MRI with six-directional flow encoding (ICOSA6). The pressure drop through the valve was non-invasively predicted based on the simplified Bernoulli, the extended Bernoulli, the turbulence production, and the shear-scaling methods. Linear regression and agreement of the predictions with invasively measured pressure drop were analyzed.

RESULTS

All pressure drop predictions using 4D Flow MRI were linearly correlated to the true pressure drop but resulted in different regression slopes. The regression slope and 95% limits of agreement for the simplified Bernoulli method were 1.35 and 11.99 ± 21.72 mm Hg. The regression slope and 95% limits of agreement for the extended Bernoulli method were 1.02 and 0.74 ± 8.48 mm Hg. The regression slope and 95% limits of agreement for the turbulence production method were 0.89 and 0.96 ± 8.01 mm Hg. The shear-scaling method presented good correlation with an invasively measured pressure drop, but the regression slope varied between 0.36 and 1.00 depending on the shear-scaling coefficient.

CONCLUSION

The pressure drop assessment based on the turbulence production method agrees well with the extended Bernoulli method and invasively measured pressure drop in various shapes of the aortic valve. Turbulence-based pressure drop estimation can, as a complement to the conventional Bernoulli method, play a role in the assessment of valve diseases.