Use of factor analysis to characterize arterial geometry and predict hemodynamic risk: application to the human carotid bifurcation

The detailed geometry of atherosclerosis-prone vascular segments may influence their susceptibility by mediating local hemodynamics. An appreciation of the role of specific geometric variables is complicated by the considerable correlation among the many parameters that can be used to describe arterial shape and size. Factor analysis is a useful tool for identifying the essential features of such an inter-related data set, as well as for predicting hemodynamic risk in terms of these features and for interpreting the role of specific geometric variables. Here, factor analysis is applied to a set of 14 geometric variables obtained from magnetic resonance images of 50 human carotid bifurcations. Two factors alone were capable of predicting 12 hemodynamic metrics related to shear and near-wall residence time with adjusted squared Pearson's correlation coefficient as high as 0.54 and P-values less than 0.0001. One factor measures cross-sectional expansion at the bifurcation; the other measures the colinearity of the common and internal carotid artery axes at the bifurcation. The factors explain the apparent lack of an effect of branch angle on hemodynamic risk. The relative risk among the 50 bifurcations, based on time-average wall shear stress, could be predicted with a sensitivity and specificity as high as 0.84. The predictability of the hemodynamic metrics and relative risk is only modestly sensitive to assumptions about flow rates and flow partitions in the bifurcation.     

Hemodynamics and wall mechanics in human carotid bifurcation and its consequences for atherogenesis: investigation of inter-individual variation

Finite element simulations of fluid-solid interactions were used to investigate inter-individual variations in flow dynamics and wall mechanics at the carotid artery bifurcation, and its effects on atherogenesis, in three healthy humans (normal volunteers: NV1, NV2, NV4). Subject-specific calculations were based on MR images of structural anatomy and ultrasound measurements of flow at domain boundaries. For all subjects, the largest contiguous region of low wall shear stress (WSS) occurred at the carotid bulb, WSS was high (6-10 Pa) at the apex, and a small localized region of WSS > 10 Pa occurred close to the inner wall of the external carotid artery (ECA). NV2 and NV4 had a "spot" of low WSS distal to the bifurcation at the inner wall of the ECA. Low WSS patches in the common carotid artery (CCA) were contiguous with the carotid bulb low WSS region in NV1 and NV2, but not in NV4. In all three subjects, areas of high oscillatory shear index (OSI) were confined to regions of low WSS. Only NV4 exhibited high levels of OSI on the external adjoining wall of the ECA and CCA. For all subjects, the maximum wall shear stress temporal gradient (WSSTG) was highest at the flow divider (reaching 1,000 Pa/s), exceeding 300 Pa/s at the walls connecting the ECA and CCA, but remaining below 250 Pa/s outside of the ECA. In all subjects, (maximum principle) cyclic strain (CS) was greatest at the apex (NV1: 14%; NV2: 11%; NV4: 6%), and a second high CS region occurred at the ECA-CCA adjoining wall (NV1: 11%, NV2: 9%, NV4: 5%). Wall deformability was included in one simulation (NV2) to verify that it had little influence on the parameters studied. Location and magnitude of low WSS were similar, except for the apex (differences of up to 25%). Wall distensibility also influenced OSI, doubling it in most of the CCA, separating the single high OSI region of the carotid bulb into two smaller regions, and shrinking the ECA internal and external walls' high OSI regions. These observations provide further evidence that significant intra-subject variability exists in those factors thought to impact atherosclerosis.     

Carotid geometry effects on blood flow and on risk for vascular disease

It has been widely observed that atherosclerotic diseases occur at sites with complex hemodynamics, such as artery bifurcations, junctions, and regions of high curvature. These regions usually have very low or highly oscillatory wall shear stress (WSS). In the present work, 3D pulsatile blood flow through a model of the carotid artery bifurcation was simulated using a finite volume numerical method. The goal was to quantify the risk of atherogenesis associated with different carotid artery geometries. A risk scale based on the average WSS on the sinus wall of the internal carotid artery was proposed-a scale that can be used to quantify the effect of the carotid geometry on the relative risk for developing vascular disease. It was found that the bifurcation angle and the out-of-plane angle of the internal carotid artery affect the formation of low stress regions on the carotid walls. The main conclusions are: (a) larger internal carotid artery angles (theta(IC)) generally increase the frequency and the area of blood recirculation and lower the WSS on the sinus wall, hence increasing the risk of plaque build-up; (b) off-plane angles were found to lower the WSS on the sinus for geometries with theta(IC)25 degrees . Larger off-plane angles generally increase the danger of plague build-up; (c) for theta(IC) < 25 degrees , the off-plane angle does not have an obvious effect on the hemodynamic WSS; (d) symmetric bifurcations were found to increase the WSS on the sinus wall and ease the risk of vascular disease.     

Hemodynamics analysis of a stenosed carotid bifurcation and its plaque-mitigating design

Considering transient two-dimensional laminar flow in a diseased carotid artery segment with realistic inlet and outflow conditions, detailed velocity profiles, pressure fields, wall shear stress distributions and coupled, localized plaque formations have been simulated. The type of outflow boundary condition influences to a certain degree the extent of plaque build-up, which in turn reduces "disturbed flow" phenomena such as flow separations, recirculation zones, and wavy flow patterns in the artery branches during portions of the pulse. Based on computer experiments varying key geometric factors, a plaque-mitigating design of a carotid artery bifurcation has been proposed. Elimination of the carotid bulb, a smaller bifurcation angle, lower area ratios, and smooth wall curvatures generated a design with favorable hemodynamics parameters, leading to reduced plaque build-up by factors of 10 and 2 in the internal carotid and in the external carotid, respectively.     

Adaptive regulation of wall shear stress optimizing vascular tree function

The branching structure of the mammalian arterial tree has been known to be close to that of an optimal conduit system of the minimum work model characterized as the branch system of constant wall shear rate. The physiological mechanism producing such construction was considered to be based on the local response of arterial caliber induced by the wall shear stress (shear rate × blood viscosity) and thereby maintaining this stress constant, which was previously observed at the canine common carotid artery shunted to the external jugular vein. The stress levels at various parts of the arterial system estimated from available data fell within ±50% of the mean (15 dyn/cm²), which was consistent with the value predicted from the model. Theoretical analyses on the cost function of the model indicated that the suspected variation of shear rate levels in the arterial tree due to the anomalous changes in blood viscosity which might bring about 3- to 4-fold differences between the minimum and maximum shear rates would cause less than 10% increase in the total energy cost. It was concluded that a local adaptive response to wall shear stress is the mechanism which effectively optimizes the design of the arterial tree.     

Computational study of the effect of geometric and flow parameters on the steady flow field at the rabbit aorto-celiac bifurcation

Arterial hemodynamic forces may play a role in the localization of early atherosclerotic lesions. We have been developing numerical techniques based on overset or "Chimera" type formulations to solve the Navier-Stokes equations in complex geometries simulating arterial bifurcations. This paper presents three-dimensional steady flow computations in a model of the rabbit aorto-celiac bifurcation. The computational methods were validated by comparing the numerical results to previously-obtained flow visualization data. Once validated, the numerical algorithms were used to investigate the sensitivity of the computed flow field and resulting wall shear stress distribution to various geometric and hemodynamic parameters. The results demonstrated that a decrease in the extent of aortic taper downstream of the celiac artery induced looping fluid motion along the lateral walls of the aorta and shifted the peak wall shear stress from downstream of the celiac artery to upstream. Increasing the flow Reynolds number led to a sharp increase in spatial gradients of wall shear stress. The flow field was highly sensitive to the flow division ratio, i.e., the fraction of total flow rate that enters the celiac artery, with larger values of this ratio leading to the occurrence of flow separation along the dorsal wall of the aorta. Finally, skewness of the inlet velocity profile had a profound impact on the wall shear stress distribution near the celiac artery. While not physiological due to the assumption of steady flow, these results provide valuable insight into the fluid physics at geometries simulating arterial bifurcations.     

A New Near-wall Residence Time Model Applied to Three Arterio-venous Graft End-to-side Anastomoses

As a representative example of an end-to-side anastomosis, the distal portion of an arterio-venous hemodialysis graft with three graft-end designs and two outflow conditions has been considered. Arterio-venous graft failure for hemodialysis patients can be frequently related to stenotic developments, especially in the toe region. With critical blood particles such as LDL, platelets, and monocytes, being considered as a first-order approximation of; blood elements pathlines, near-wall residence times and wall stagnation points have been simulated to identify, in conjunction with the wall shear stress gradient, susceptible sites of stenotic developments. Assuming transient laminar three-dimensional non-Newtonian fluid flow, the transport equations were solved with validated finite-volume based CFD software and user-Fortran programs for the computation of fluid element pathlines and hemodynamic parameters. We conclude from this study that for the application of looped arterio-venous grafts, the graft-end geometry and the presence of retrograde outflow significantly influence the magnitude and location of the hemodynamic wall parameters considered. The new concept of near-wall blood “particle” behaviour, in conjunction with a wall shear stress based hemodynamic parameter, can be compared to similar histopathologic studies of intimal hyperplasia formation to understand better the role of hemodynamic factors in the biogenesis of the disease.     

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.     

Numerical simulation of sinusoidal flow in a straight elastic tube: effects of phase angles

Numerical simulations of flow in straight elastic (moving wall) tubes subjected to a sinusoidal pressure gradient were performed for conditions prevailing in large and medium sized arteries. The effects of varying the phase angle between the pressure gradient and the tube radius, the amplitude of wall motion, and the unsteadiness parameter (alpha) on flow rate and wall shear stress were investigated. Mean and peak flow rates and shear stresses were found to be strongly affected by the phase angle between the pressure gradient and the tube radius with greater sensitivity at higher diameter variation and higher alpha. In large artery simulations (alpha = 12), means flow rate was found to be 60% higher and peak flow rate to be 73% higher than corresponding rigid tube values for certain phase angles, while a threefold increase in mean wall shear stress and sevenfold increase in peak wall shear stress were observed in a sensitive phase angle range. Significant reversal in the wall shear stress direction occurred in the sensitive phase angle range even when there was negligible flow rate reversal. All effects were greatly diminished in simulations of medium sized vessels (alpha = 4). Some experimental evidence to support the predictions of a strong effect of phase angle on wall shear stress in large vessels is presented. Finally, physiological implications of the present work are discussed from a basis of aortic input impedance data, and a physical explanation for the extreme sensitivity of the flow field to small amplitude wall motion at high alpha is given.     

Effect of blood pressure on vascular hemodynamics in acute tachycardia

Paroxysmal supraventricular tachycardia is accompanied by hypotension, which can affect vascular hemodynamics. Here, we hypothesized that a fall in blood flow as a result of hypotension has a larger effect on hemodynamics in medium-sized peripheral arteries compared with increased pulsatility in rapid pacing. To test this hypothesis, we experimentally and theoretically investigated hemodynamic changes in femoral, carotid, and subclavian arteries at heart rates of 95-170 beats/min after acute pacing. The arterial pressure, blood flow, and other hemodynamic parameters remained statistically unchanged for heart rates ≤ 135 beats/min. Systemic pressure and flow velocities, however, showed an abrupt decrease, resulting in larger alteration of hemodynamic parameters for heart rates ≥ 155 beats/min after pacing (initial period) and then recovered close to baseline after several minutes of pacing (recovery period). During the initial period, the pressure dropped from 88 mmHg (baseline) to 44 mmHg, and the flow velocity decreased to about one-third of baseline at heart rate of 170 beats/min. A hemodynamic analysis showed a velocity profile with a near-wall retrograde flow or a fully reversed flow during the initial period, which vanished at the recovery period. It was concluded that the initial fall of blood flow due to pressure drop led to transient flow reversal and negative wall shear stress because this phenomena was not observed at the recovery period. This study underscores the significant effects of hypotension on vascular hemodynamics, which may have relevance to physiology and chronic pathophysiology in paroxysmal supraventricular tachycardia.     

Fluid shear stress and the vascular endothelium: for better and for worse

As blood flows, the vascular wall is constantly subjected to physical forces, which regulate important physiological blood vessel responses, as well as being implicated in the development of arterial wall pathologies. Changes in blood flow, thus generating altered hemodynamic forces are responsible for acute vessel tone regulation, the development of blood vessel structure during embryogenesis and early growth, as well as chronic remodeling and generation of adult blood vessels. The complex interaction of biomechanical forces, and more specifically shear stress, derived by the flow of blood and the vascular endothelium raise many yet to be answered questions:How are mechanical forces transduced by endothelial cells into a biological response, and is there a "shear stress receptor"?Are "mechanical receptors" and the final signaling pathways they evoke similar to other stimulus-response transduction systems?How do vascular endothelial cells differ in their response to physiological or pathological shear stresses?Can shear stress receptors or shear stress responsive genes serve as novel targets for the design of diagnostic and therapeutic modalities for cardiovascular pathologies?The current review attempts to bring together recent findings on the in vivo and in vitro responses of the vascular endothelium to shear stress and to address some of the questions raised above.     

Flow and wall shear stress in end-to-side and side-to-side anastomosis of venous coronary artery bypass grafts

Purpose  

Coronary artery bypass graft (CABG) surgery represents the standard treatment of advanced coronary artery disease. Two major types of anastomosis exist to connect the graft to the coronary artery, i.e., by using an end-to-side or a side-to-side anastomosis. There is still controversy because of the differences in the patency rates of the two types of anastomosis. The purpose of this paper is to non-invasively quantify hemodynamic parameters, such as mass flow and wall shear stress (WSS), in end-to-side and side-to-side anastomoses of patients with CABG using computational fluid dynamics (CFD).     

Effect of hematocrit on wall shear rate in oscillatory flow: do the elastic properties of blood play a role?

Porcine blood was used to examine the relationship between hematocrit levels and wall shear rate patterns in straight and curved artery models under fixed oscillatory flow conditions characteristic of larger arteries. It is demonstrated that porcine blood models both the viscous and elastic components of the 2 Hz complex viscosity of human blood quite accurately over a broad range of shear rates (1-1000 s-1) and hematocrits (20%-80%). For a fixed oscillatory flow waveform (Poiseuille peak shear rate = 168 s-1; mean shear rate 84 s-1), increases in hematocrit produced a decrease in the peak wall shear rate in both the straight and curved artery models and a corresponding decrease in wall shear rate reversal on the inside wall of the curved artery model. The same trends were also observed for oscillatory flows of aqueous glycerin solutions of increasing viscosity in the range of viscosity of the blood samples tested. Aqueous glycerin solutions produced wall shear rate waveforms of the same magnitude and shape as the porcine blood. This indicates that variations in the shear rate, and therefore the shear stress, were caused primarily by changes in the viscous and not the elastic properties of blood. The results suggest that simple Newtonian fluids may be sufficient for in vitro determination of the first order effects to be expected of human blood flow in large vessels having complex geometries and shear rates in or above the range of the present study.     

Biomechanical, morphological and zero-stress state characterization of jugular vein remodeling in arteriovenous fistulas for hemodialysis

While the role of hemodynamic variables on the development of intimal hyperplasia in arteriovenous fistulas for hemodialysis has been examined, less is known about the intramural biomechanical factors. In this study, arteriovenous fistulas were created by implantation of e-PTFE grafts between carotid artery and jugular vein in healthy pigs. In vivo recordings exhibited a three-fold pressure and flow elevation in grafted veins after fistula creation, remaining so until sacrifice. The chief morphological observation in grafted vessels was wall thickening at two weeks, serving to restore intramural stresses to homeostatic levels, and a less marked internal diameter enlargement, gradually normalizing intimal shear after four weeks. The residual strains and opening angle, specifying the zero-stress configuration, increased with differences reaching significance at twelve weeks. Association with histomorphological findings on intima, media and adventitia growth disclosed a correlation between intimal hyperplasia and opening angle increase. Elastin and cellular contents diminished opposite to collagen content, most differences occurring within the first four weeks after grafting. Inflation/extension testing showed that post-fistula the vein wall became progressively thicker and stiffer, lacking restoration of compliance to baseline levels. The present data may further our understanding of the dynamics of venous biomechanical remodeling under pressure and flow-overload conditions.     

Parametric geometry exploration of the human carotid artery bifurcation

A parametric computational model of the human carotid artery bifurcation is employed to demonstrate that it is only necessary to simulate approximately one-half of a single heart pulse when performing a global exploration of the relationships between shear stress and changes in geometry. Using design of experiments and surface fitting techniques, a landscape is generated that graphically depicts these multi-dimensional relationships. Consequently, whilst finely resolved, grid and pulse independent results are traditionally demanded by the computational fluid dynamics (CFD) community, this strategy demonstrates that it is possible to efficiently detect the relative impact of different geometry parameters, and to identify good and bad regions of the landscape by only simulating a fraction of a single pulse. Also, whereas in the past comparisons have been made between the distributions of appropriate shear stress metrics, such as average wall shear stress and oscillatory shear index, this strategy requires a figure of merit to compare different geometries. Here, an area-weighted integral of negative time-averaged shear stress, tau , is used as the principal objective function, although the discussion reveals that the extent as well as the intensity of reverse flow may be important. Five geometry parameters are considered: the sinus bulb width, the angles and the outflow diameters of the internal carotid artery (ICA) and external carotid artery (ECA). A survey of the landscape confirms that bulb shape has the dominant effect on tau with maximum tau occurring for large bulb widths. Also, it is shown that different sets of geometric parameters can produce low values of tau by either relatively small intense areas, or by larger areas of less intense reverse flow.     

Coupled fluid–structure interaction hemodynamics in a zero-pressure state corrected arterial geometry

Hemodynamic conditions in large arteries are significantly affected by the interaction of the pulsatile blood flow with the distensible arterial wall. A numerical procedure for solving the fluid–structure interaction problem encountered in cardiovascular flows is presented. We consider a patient-specific carotid bifurcation geometry, obtained from 3D reconstruction of in vivo acquired tomography images, which yields a geometrical representation of the artery corresponding to its pressurized state. To recover the geometry of the artery in its zero-pressure state which is required for a fluid–structure interaction simulation we utilize inverse finite elastostatics. Time-dependent flow simulations with in vivo measured inflow volume flow rate in the 3D undeformed artery are performed through the finite element method. The coupled-momentum method for fluid–structure interaction is adopted to incorporate the influence of wall compliance in the numerical computation of the time varying flow domain. To demonstrate the importance in recovering the zero-pressure state of the artery in hemodynamic simulations we compute the time varying flow field with compliant walls for the original and the zero-pressure state corrected geometric configurations of the carotid bifurcation. The most important resulting effects in the hemodynamic environment are evaluated. Our results show a significant change in the wall shear stress distribution and the spatiotemporal extent of the recirculation regions.     

Sequential venous anastomosis design to enhance patency of arterio-venous grafts for hemodialysis

Arterio-venous grafts (AVGs), the second best option as long-term vascular access for hemodialysis, face major issues of stenosis mainly due to development of intimal hyperplasia at the venous anastomosis which is linked to unfavorable hemodynamic conditions. We have investigated computationally the utility of a coupled sequential venous anastomotic design to replace conventional end-to-side (ETS) venous anastomosis, in order to improve the hemodynamic environment and consequently enhance the patency of AVGs. Two complete vascular access models with the conventional and the proposed venous anastomosis configurations were constructed. Three-dimensional, pulsatile blood flow through the models was simulated, and wall shear stress (WSS)-based hemodynamic parameters were calculated and compared between the two models. Simulation results demonstrated that the proposed anastomotic design provides: (i) a more uniform and smooth flow at the ETS anastomosis, without flow impingement and stagnation point on the artery bed and vortex formation in the heel region of the ETS anastomosis; (ii) more uniform distribution of WSS and substantially lower WSS gradients on the venous wall; and (iii) a spare route for the blood flow to the vein, to avoid re-operation in case of stenosis. The distinctive hemodynamic advantages observed in the proposed anastomotic design can enhance the patency of AVGs.     

Which diameter and angle rule provides optimal flow patterns in a coronary bifurcation?

The branching angle and diameter ratio in epicardial coronary artery bifurcations are two important determinants of atherogenesis. Murray's cubed diameter law and bifurcation angle have been assumed to yield optimal flows through a bifurcation. In contrast, we have recently shown a 7/3 diameter law (HK diameter model), based on minimum energy hypothesis in an entire tree structure. Here, we derive a bifurcation angle rule corresponding to the HK diameter model and critically evaluate the streamline flow through HK and Murray-type bifurcations. The bifurcations from coronary casts were found to obey the HK diameter model and angle rule much more than Murray's model. A finite element model was used to investigate flow patterns for coronary artery bifurcations of various types. The inlet velocity and pressure boundary conditions were measured by ComboWire. Y-bifurcation of Murray type decreased wall shear stress-WSS (10%-40%) and created an increased oscillatory shear index-OSI in atherosclerosis-prone regions as compared with HK-type bifurcations. The HK-type bifurcations were found to have more optimal flow patterns (i.e., higher WSS and lower OSI) than Murray-type bifurcations which have been traditionally believed to be optimized. This study has implications for changes in bifurcation angles and diameters in percutaneous coronary intervention.