Secondary flow in the human common carotid artery imaged by MR angiography

Spatiotemporal Hemodynamic Complexity in Carotid Arteries: An Integrated Computational Hemodynamics and Complex Networks-Based Approach

OBJECTIVE

The study of the arterial hemodynamics is essential for a better understanding of the risks associated with the onset/progression of vascular disease. However, conventional quantification and visualization paradigms are not sufficient to fully capture the spatiotemporal evolution of correlated blood flow patterns and their "sphere of influence" in complex vascular geometries. In the attempt to bridge this knowledge gap, an integrated computational hemodynamics and complex networks-based approach is proposed to unveil organization principles of cardiovascular flows.

METHODS

The approach is applied to ten patient-specific hemodynamic models of carotid bifurcation, a vascular bed characterized by a complex hemodynamics and clinically-relevant disease. Correlation-based networks are built starting from time-histories of two fluid mechanics quantities of physiological significance, respectively (1) the blood velocity vector axial component locally aligned with the main flow direction, and (2) the kinetic helicity density.

RESULTS

Unlike conventional hemodynamic analyses, here the spatiotemporal similarity of dynamic intravascular flow structures is encoded in a distance function. In the case of the carotid bifurcation, this study measures for the first time to what extent flow similarity is disrupted by vascular geometric features.

CONCLUSION

It emerges that a larger bifurcation expansion, a hallmark of vascular disease, significantly disrupts the network topological connections between axial flow structures, reducing also their anatomical persistence length. On the contrary, connections in helical flow patterns are overall less geometry-sensitive.

SIGNIFICANCE

The integrated approach proposed here, by exploiting the connections of hemodynamic patterns undergoing similar dynamical evolution, opens avenues for further comprehension of vascular physiopathology.

On the shape of the common carotid artery with implications for blood velocity profiles

Clinical and engineering studies typically assume that the common carotid artery (CCA) is straight enough to assume fully developed flow, yet recent studies have demonstrated the presence of skewed velocity profiles. Toward elucidating the influence of mild vascular curvatures on blood flow patterns and atherosclerosis, this study aimed to characterize the three-dimensional shape of the human CCA. The left and right carotid arteries of 28 participants (63 ± 12 years) in the VALIDATE (Vascular Aging--The Link that Bridges Age to Atherosclerosis) study were digitally segmented from 3D contrast-enhanced magnetic resonance angiograms, from the aortic arch to the carotid bifurcation. Each CCA was divided into nominal cervical and thoracic segments, for which curvatures were estimated by least-squares fitting of the respective centerlines to planar arcs. The cervical CCA had a mean radius of curvature of 127 mm, corresponding to a mean lumen:curvature radius ratio of 1:50. The thoracic CCA was significantly more curved at 1:16, with the plane of curvature tilted by a mean angle of 25° and rotated close to 90° with respect to that of the cervical CCA. The left CCA was significantly longer and slightly more curved than the right CCA, and there was a weak but significant increase in CCA curvature with age. Computational fluid dynamic simulations carried out for idealized CCA geometries derived from these and other measured geometric parameters demonstrated that mild cervical curvature is sufficient to prevent flow from fully-developing to axisymmetry, independent of the degree of thoracic curvature. These findings reinforce the idea that fully developed flow may be the exception rather than the rule for the CCA, and perhaps other nominally long and straight vessels.

Choice of in vivo versus idealized velocity boundary conditions influences physiologically relevant flow patterns in a subject-specific simulation of flow in the human carotid bifurcation

Accurate fluid mechanics models are important tools for predicting the flow field in the carotid artery bifurcation and for understanding the relationship between hemodynamics and the initiation and progression of atherosclerosis. Clinical imaging modalities can be used to obtain geometry and blood flow data for developing subject-specific human carotid artery bifurcation models. We developed subject-specific computational fluid dynamics models of the human carotid bifurcation from magnetic resonance (MR) geometry data and phase contrast MR velocity data measured in vivo. Two simulations were conducted with identical geometry, flow rates, and fluid parameters: (1) Simulation 1 used in vivo measured velocity distributions as time-varying boundary conditions and (2) Simulation 2 used idealized fully-developed velocity profiles as boundary conditions. The position and extent of negative axial velocity regions (NAVRs) vary between the two simulations at any given point in time, and these regions vary temporally within each simulation. The combination of inlet velocity boundary conditions, geometry, and flow waveforms influences NAVRs. In particular, the combination of flow division and the location of the velocity peak with respect to individual carotid geometry landmarks (bifurcation apex position and the departure angle of the internal carotid) influences the size and location of these reversed flow zones. Average axial wall shear stress (WSS) distributions are qualitatively similar for the two simulations; however, instantaneous WSS values vary with the choice of velocity boundary conditions. By developing subject-specific simulations from in vivo measured geometry and flow data and varying the velocity boundary conditions in otherwise identical models, we isolated the effects of measured versus idealized velocity distributions on blood flow patterns. Choice of velocity distributions at boundary conditions is shown to influence pathophysiologically relevant flow patterns in the human carotid bifurcation. Although mean WSS distributions are qualitatively similar for measured and idealized inlet boundary conditions, instantaneous NAVRs differ and warrant imposing in vivo velocity boundary conditions in computational simulations. A simulation based on in vivo measured velocity distributions is preferred for modeling hemodynamics in subject-specific carotid artery bifurcation models when studying atherosclerosis initiation and development.

Inlet Conditions for Image-Based CFD Models of the Carotid Bifurcation: Is it Reasonable to Assume Fully Developed Flow?

Background: Computational fluid dynamics tools are useful for their ability to model patient specific data relevant to the genesis and progression of atherosclerosis, but unavailable to measurement tools. The sensitivity of the physiologically relevant parameters of wall shear stress (WSS) and the oscillatory shear index (OSI) to secondary flow in the inlet velocity profiles was investigated in three realistic models of the carotid bifurcation. Method of Approach: Secondary flow profiles were generated using sufficiently long entrance lengths, to which curvature and helical pitch were added. The differences observed were contextualized with respect to effect of the uncertainty of the models’ geometry on the same parameters. Results: The effects of secondary velocities in the inlet profile on WSS and OSI break down within a few diameters of the inlet. Overall, the effect of secondary inlet flow on these models was on average more than 3.5 times smaller than the effect of geometric variability, with 13% and 48% WSS variability induced by inlet secondary flow and geometric differences, respectively. Conclusions: The degree of variation is demonstrated to be within the range of the other computational assumptions, and we conclude that given a sufficient entrance length of realistic geometry, simplification to fully developed axial (i.e., Womersley) flow may be made without penalty. Thus, given a choice between measuring three components of inlet velocity or a greater geometric extent, we recommend effort be given to more accurate and detailed geometric reconstructions, as being of primary influence on physiologically significant indicators.

Interaction between secondary velocities, flow pulsation and vessel morphology in the common carotid artery

The common carotid artery (CCA), one of the vessels more frequently investigated by ultrasound (US), is often modeled as a straight tube in quasi-laminar flow regimens. Experimental investigations based on a prototype multigate system show that blood velocity profiles are parabolic during diastole and early systole, and flat during the systolic peak. However, during late systole/beginning of diastole, they have an "M" shape, where the velocity near the walls is higher than in the vessel center. Moreover, the profile shape changes when the sound beam direction is moved over a given cross-section; thus, suggesting a nonaxisymmetrical velocity distribution, which contradicts the straight tube assumption. The purpose of this paper was twofold. First, the actual velocity distribution in "normal" CCAs was reconstructed. The analysis of several velocity profiles confirms that the velocity distribution is markedly asymmetrical, especially during the deceleration phase following the systolic peak. Second, a tentative explanation for such behavior is given by correlating it with the growth of secondary flows caused by the slight vessel curvature and viscous effects. This explanation is supported by the comparison between in vitro results and numerical solution of the Navier-Stokes equations in laminar pulsed-flow regimens.

Reconstruction of blood flow patterns in a human carotid bifurcation: a combined CFD and MRI study

The carotid bifurcation is a common site for clinically significant atherosclerosis, and the development of this disease may be influenced by the local hemodynamic environment. It has been shown that vessel geometry and pulsatile flow conditions are the predominant factors that determine the detailed blood flow patterns at the carotid bifurcation. This study was initiated to quantify the velocity profiles and wall shear stress (WSS) distributions in an anatomically true model of the human carotid bifurcation using data acquired from magnetic resonance (MR) imaging scans of an individual subject. A numerical simulation approach combining the image processing and computational fluid dynamics (CFD) techniques was developed. Individual vascular anatomy and pulsatile flow conditions were all incorporated into the computer model. It was found that the geometry of the carotid bifurcation was highly complex, involving helical curvature and out-of-plane branching. These geometrical features resulted in patterns of flow and wall shear stress significantly different from those found in simplified planar carotid bifurcation models. Comparisons between the predicted flow patterns and MR measurement demonstrated good quantitative agreement.

Spatial and temporal regulation of gap junction connexin43 in vascular endothelial cells exposed to controlled disturbed flows in vitro

Hemodynamic regulation of the endothelial gap junction protein connexin43 (Cx43) was studied in a model of controlled disturbed flows in vitro. Cx43 mRNA, protein expression, and intercellular communication were mapped to spatial variations in fluid forces. Hemodynamic features of atherosclerotic lesion-prone regions of the vasculature (flow separation and recirculation) were created for periods of 5, 16, and 30 h, with laminar shear stresses ranging between 0 and 13.5 dynes/cm2. Within 5 h, endothelial Cx43 mRNA expression was increased in all cells when compared with no-flow controls, with highest levels (up to 6- to 8-fold) expressed in regions of flow recirculation corresponding to high shear stress gradients. At 16 h, Cx43 mRNA expression remained elevated in regions of flow disturbance, whereas in areas of fully developed, undisturbed laminar flow, Cx43 expression returned to control levels. In all flow regions, typical punctate Cx43 immunofluorescence at cell borders was disrupted by 5 h. After 30 h of flow, disruption of gap junctions persisted in cells subjected to flow separation and recirculation, whereas regions of undisturbed flow were substantially restored to normal. These expression differences were reflected in sustained inhibition of intercellular communication (dye transfer) throughout the zone of disturbed flow (84.2 and 68.4% inhibition at 5 and 30 h, respectively); in contrast, communication was fully reestablished by 30 h in cells exposed to undisturbed flow. Up-regulation of Cx43 transcripts, sustained disorganization of Cx43 protein, and impaired communication suggest that shear stress gradients in regions of disturbed flow regulate intercellular communication through the expression and function of Cx43.

Hemodynamics of human carotid artery bifurcations: computational studies with models reconstructed from magnetic resonance imaging of normal subjects

PURPOSE

The precise role played by hemodynamics, particularly wall shear stress, in the development and progression of vascular disease remains unclear, in large part because of a lack of in vivo studies with humans. Although technical challenges remain for noninvasively imaging wall shear stresses in humans, vascular anatomy can be imaged with sufficiently high resolution to allow reconstruction of three-dimensional models for computational hemodynamic studies. In this paper we present an entirely noninvasive magnetic resonance imaging (MRI) protocol that provides carotid bifurcation geometry and flow rates from which the in vivo hemodynamics can be computed. Maps of average, oscillatory, and gradients of wall shear stress are presented for two normal human subjects, and their data are compared with those computed for an idealized carotid bifurcation model.

METHODS

An MRI protocol was developed to acquire all necessary image data in scan times suitable for patient studies. Three-dimensional models of the carotid bifurcation lumen were reconstructed from serial black blood MR images of two normal volunteers. Common and internal carotid artery flow rate waveforms were determined from MRI phase-contrast velocity imaging in the same subjects and were used to impose fully developed velocity boundary conditions for the computational model. Subject-specific time-resolved velocities and wall shear stresses were then computed with a finite element-based Navier-Stokes equation solver.

RESULTS

Models reconstructed from in vivo MRI of two subjects showed obvious differences in branch angle, bulb size and extent, and three-dimensional curvature. Maps of a variety of wall shear stress indices showed obvious qualitative differences in patterns between the in vivo models and between the in vivo models and the idealized model. Secondary, helical flow patterns, induced primarily by the asymmetric and curved in vivo geometries, were found to play a key role in determining the resulting wall shear stress patterns. The use of in vivo flow rate waveforms was found to play a minor but noticeable role in some of the wall shear stress behavior observed.

CONCLUSIONS

Conventional "averaged" carotid bifurcation models mask interesting hemodynamic features observed in realistic models derived from noninvasive imaging of normal human subjects. Observation of intersubject variations in the in vivo wall shear stress patterns supports the notion that more conclusive evidence regarding the role of hemodynamics in vascular disease may be derived from such individual studies. The techniques presented here, when combined with subject-specific MRI measurements of carotid artery plaque thickness and composition, provide the tools necessary for entirely noninvasive, prospective, in vivo human studies of hemodynamics and the relationship of hemodynamics to vascular disease.

Reproducibility of shear rate and shear stress assessment by means of ultrasound in the common carotid artery of young human males and females

In the present study, the reliability of an ultrasonic shear rate estimating system, in terms of intrasubject intrasession, intersubject intrasession and intersubject intersession variability coefficients for the assessment of wall shear rate (WSR) in the common carotid artery (CCA) was determined in eight presumed healthy volunteers. Measurements were performed on consecutive days (day 1, day 2 and day 7). To investigate whether there were differences in WSR due to gender, dynamic WSR in the CCA was assessed in 11 presumed healthy males (mean age 24 y) and 11 presumed healthy females (mean age 25 y). Wall shear stress (WSS) was estimated from WSR and calculated whole blood viscosity. The average intrasubject intrasession variability was about 15% for peak WSR and about 12% for mean WSR. The intersubject intrasession variability for peak WSR decreased from 19% on day 1 to 16% on day 7 and for mean WSR from 17% on day 1 to 11% on day 7. The intersubject intersession variability is on the order of 5% for peak WSR and about 4% for mean WSR. No significant differences could be detected between peak and mean WSR values on day 1, day 2 and day 7, indicating good short- and medium-term intersubject intersession reproducibilities. No differences in peak and mean WSR were found between the left and the right CCA in the male group as well as in the female group. Mean WSS was similar in males (1.3 +/- 0.3 Pa) and in females (1.2 +/- 0.2 Pa), but peak WSS was slightly, but significantly, higher in males (4.3 +/- 1.3 Pa) than in females (3.3 +/- 0.7 Pa). It can be concluded that peak and mean WSR can be reliably determined noninvasively using ultrasound.

The influence of the angle of confluence on the flow in a vertebro-basilar junction model

In earlier work, it was demonstrated that the flow in models of the vertebro-basilar junction is highly three-dimensional and the geometry exerts a strong influence on the hemodynamics. The morphology of the vertebro-basilar junction is very variable amongst individuals. In a study of 85 human vertebro-basilar junctions, the angle between the vertebral arteries varied between 10 and 160 degrees. To determine how the flow is influenced by this geometrical parameter, the flow is studied both experimentally, with laser Doppler velocimetry, and numerically, with a finite element package. A series of junction models is used with a range of confluence angles (45, 85 and 125 degrees). It appears that the angle of confluence has a strong influence on the structure and strength of the secondary flow field. The secondary velocities persist far downstream. Furthermore, near the apex, a region with low velocities is present. The larger the confluence angle is, the larger this region is, and even backflow may occur. In addition, the occurrence of atherosclerotic plaques in 85 human vertebro-basilar junctions is studied. Only one preferential location was found: the apex, the other plaques seem to be randomly distributed. The magnitude of the confluence angle of junctions with sharp-edged apices has a significant influence (p = 0.006) on the occurrence of a plaque at the apex. Apparently, a large confluence angle is a geometrical risk factor for atherosclerosis.

Hemodynamics and wall shear rate in the abdominal aorta of dogs. Effects of vasoactive agents

Vasoactive drugs are known to affect impedance (pressure/flow) and vessel wall motion in arteries. The nonlinear theory of oscillatory flow in straight elastic vessels indicates that wall shear rate is affected by changes in impedance phase angle and wall motion. To test whether wall shear rate depends on impedance phase angle and wall motion in vivo, wall shear rate was measured in the abdominal aorta of anesthetized dogs by using a flush-mounted hot-film anemometer, and the hemodynamic state was characterized by pressure, flow, and vessel dimension measurements. Vasodilators (nitroprusside and isoproterenol) and vasoconstrictors (angiotensin II and norepinephrine) were administered acutely, and the responses of wall shear rate and hemodynamics were determined. In the control state (no drugs), peak wall shear rate was 1835 +/- 153 s-1 (mean +/- SEM). The vasodilators induced large increases in impedance phase angle and wall motion concomitant with large increases in peak wall shear rate (62.4 +/- 20.4% for nitroprusside and 68.9 +/- 28.3% for isoproterenol), which were not predicted accurately by Womersley's theory of oscillatory flow in a rigid vessel or the nonlinear theory of oscillatory flow in an elastic vessel, with measured flow and vessel dimension used as inputs. The vasoconstrictors induced small decreases in impedance phase angle and wall motion and small changes in peak wall shear rate (increase, 30.5 +/- 8.0% for norepinephrine; decrease, 18.2 +/- 7.1% for angiotensin II), which were predicted accurately by Womersley's theory. The present study shows that vasoactive drugs, particularly vasodilators, can have significant effects on wall shear rate (stress) in the abdominal aorta that appear to be related to changes in impedance phase angle and vessel wall motion. However, the effects on wall shear rate are not predicted accurately by straight-tube theory.