MRI and CFD studies of pulsatile flow in healthy and stenosed carotid bifurcation models

Pulsatile flow was studied in physiologically realistic models of a normal and a moderately stenosed (30% diameter reduction) human carotid bifurcation. Time-resolved velocity measurements were made using magnetic resonance imaging, from which wall shear stress (WSS) vectors were calculated. Velocity measurements in the inflow and outflow regions were also used as boundary conditions for a computational fluid dynamics (CFD) model. Experimental flow patterns and derived WSS vectors were compared qualitatively with the corresponding CFD predictions. In the stenosed phantom, flow in the bulb region of the "internal carotid artery" was concentrated along the outer wall, with a region of low and recirculating flow near the inner wall. In the normal phantom, the converse was found, with a low flow region near the outer wall of the bulb. Time-averaged WSS and oscillatory shear index were also markedly different for the two phantoms.     

Hemodynamics in the carotid artery bifurcation: a comparison between numerical simulations and in vitro MRI measurements

The presence of atherosclerotic plaques has been shown to be closely related to the vessel geometry. Studies on postmortem human arteries and on the experimental animal show positive correlation between the presence of plaque thickness and low shear stress, departure of unidirectional flow and regions of flow separation and recirculation. Numerical simulations of arterial blood flow and direct blood flow velocity measurements by magnetic resonance imaging (MRI) are two approaches for the assessment of arterial blood flow patterns. In order to verify that both approaches give equivalent results magnetic resonance velocity data measured in a compliant anatomical carotid bifurcation model were compared to the results of numerical simulations performed for a corresponding computational vessel model. Cross sectional axial velocity profiles were calculated and measured for the midsinus and endsinus internal carotid artery. At both locations a skewed velocity profile with slow velocities at the outer vessel wall, medium velocities at the side walls and high velocities at the flow divider (inner) wall were observed. Qualitative comparison of the axial velocity patterns revealed no significant differences between simulations and in vitro measurements. Even quantitative differences such as for axial peak flow velocities were less than 10%. Secondary flow patterns revealed some minor differences concerning the form of the vortices but maximum circumferential velocities were in the same range for both methods.     

On the relative importance of rheology for image-based CFD models of the carotid bifurcation

BACKGROUND: Patient-specific computational fluid dynamics (CFD) models derived from medical images often require simplifying assumptions to render the simulations conceptually or computationally tractable. In this study, we investigated the sensitivity of image-based CFD models of the carotid bifurcation to assumptions regarding the blood rheology. METHOD OF APPROACH: CFD simulations of three different patient-specific models were carried out assuming: a reference high-shear Newtonian viscosity, two different non-Newtonian (shear-thinning) rheology models, and Newtonian viscosities based on characteristic shear rates or, equivalently, assumed hematocrits. Sensitivity of wall shear stress (WSS) and oscillatory shear index (OSI) were contextualized with respect to the reproducibility of the reconstructed geometry, and to assumptions regarding the inlet boundary conditions. RESULTS: Sensitivity of WSS to the various rheological assumptions was roughly 1.0 dyn/cm(2) or 8%, nearly seven times less than that due to geometric uncertainty (6.7 dyn/cm(2) or 47%), and on the order of that due to inlet boundary condition assumptions. Similar trends were observed regarding OSI sensitivity. Rescaling the Newtonian viscosity based on time-averaged inlet shear rate served to approximate reasonably, if overestimate slightly, non-Newtonian behavior. CONCLUSIONS: For image-based CFD simulations of the normal carotid bifurcation, the assumption of constant viscosity at a nominal hematocrit is reasonable in light of currently available levels of geometric precision, thus serving to obviate the need to acquire patient-specific rheological data.     

Effect of inlet velocity profiles on patient-specific computational fluid dynamics simulations of the carotid bifurcation

Patient-specific computational fluid dynamics (CFD) is a powerful tool for researching the role of blood flow in disease processes. Modern clinical imaging technology such as MRI and CT can provide high resolution information about vessel geometry, but in many situations, patient-specific inlet velocity information is not available. In these situations, a simplified velocity profile must be selected. We studied how idealized inlet velocity profiles (blunt, parabolic, and Womersley flow) affect patient-specific CFD results when compared to simulations employing a "reference standard" of the patient's own measured velocity profile in the carotid bifurcation. To place the magnitude of these effects in context, we also investigated the effect of geometry and the use of subject-specific flow waveform on the CFD results. We quantified these differences by examining the pointwise percent error of the mean wall shear stress (WSS) and the oscillatory shear index (OSI) and by computing the intra-class correlation coefficient (ICC) between axial profiles of the mean WSS and OSI in the internal carotid artery bulb. The parabolic inlet velocity profile produced the most similar mean WSS and OSI to simulations employing the real patient-specific inlet velocity profile. However, anatomic variation in vessel geometry and the use of a nonpatient-specific flow waveform both affected the WSS and OSI results more than did the choice of inlet velocity profile. Although careful selection of boundary conditions is essential for all CFD analysis, accurate patient-specific geometry reconstruction and measurement of vessel flow rate waveform are more important than the choice of velocity profile. A parabolic velocity profile provided results most similar to the patient-specific velocity profile.     

Stress-modulated collagen fiber remodeling in a human carotid bifurcation

This work concerns with the implementation of a new stress-driven remodeling model for simulating the overall structure and mechanical behavior of a human carotid bifurcation. By means of an iterative finite element based procedure collagen fiber direction and maximal principal stresses are computed. We find that the predicted fibers' architecture at the cylindrical branches and at the apex of the bifurcation correlates well with histological observations. Some insights about the mechanical response of the sinus bulb and the bifurcation apex are revealed and discussed. The results are compared with other, isotropic and orthotropic, models available in the literature.     

Pulsatile two-dimensional flow and plaque formation in a carotid artery bifurcation

Velocity and pressure fields, streamlines and wall shear stress distributions were numerically obtained for two-dimensional, steady and pulsatile flow in a carotid artery segment. Distinct regions of reverse flow near the bifurcation and wavy flow patterns in the branching channels were observed during portions of the pulse. These phenomena disappear at the end of the systolic phase of the cardiac cycle. A previously validated plaque formation model predicts that plaque sites and the local extent of atherosclerotic lesions are similar for those present on human angiograms.     

Chemically accurate protein structures: Validation of protein NMR structures by comparison of measured and predicted pK a values

A new method is presented for evaluating the quality of protein structures obtained by NMR. This method exploits the dependence between measurable chemical properties of a protein, namely pK _a values of acidic residues, and protein structure. The accurate and fast empirical computational method employed by the PROPKA program () allows the user to test the ability of a given structure to reproduce known pK _a values, which in turn can be used as a criterion for the selection of more accurate structures. We demonstrate the feasibility of this novel idea for a series of proteins for which both␣NMR and X-ray structures, as well as pK _a values of all ionizable residues, have been determined. For the 17 NMR ensembles used in this study, this criterion is shown effective in the elimination of a large number of NMR structure ensemble members.     

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.     

Electric fields induced in rat and human models by 60-Hz magnetic fields: comparison of calculated and measured values.

The calculated distribution of electric fields induced in homogeneous human and rat models by a 60-Hz magnetic field is compared with values measured in instrumented mannequins. The calculated values agree well with measured values.     

Numerical analysis of flow through a severely stenotic carotid artery bifurcation

The results of computational simulations may supplement MR and other in vivo diagnostic techniques to provide an accurate picture of the hemodynamics in particular vessels, which may help demonstrate the risks of embolism or plaque rupture posed by particular plaque deposits. In this study, a model based on an endarterectomy specimen of the plaque in a carotid bifurcation was examined. The flow conditions include steady flow at Reynolds numbers of 300, 600, and 900 as well as unsteady pulsatile flow. Both dynamic pressure and wall shear stress are very high, with shear values up to 70 N/m2, proximal to the stenosis throat in the internal carotid artery, and both vary significantly through the flow cycle. The wall shear stress gradient is also strong along the throat. Vortex shedding is observed downstream of the most severe occlusion. Two turbulence models, the Chien and Goldberg varieties of k-epsilon, are tested and evaluated for their relevance in this geometry. The Chien model better captures phenomena such as vortex shedding. The flow distal to stenosis is likely transitional, so a model that captures both laminar and turbulent behavior is needed.     

Changes in erythrocyte velocity in microvessels measured with a microprismatic grating

Using an instrument designed by the Ernst Leitz Wetzlar Company (FRG) red blood cell velocity was evaluated in model and intravital experiments. The instrument provides for an accurate quantitative determination of blood microflow velocity, enables the measurements within a wide range of velocities and diameters of microvessels. It is more unsophisticated as regards the design and operation than other instruments intended for similar purposes.     

Sympathetic innervation of the carotid bifurcation in the rabbit and cat: Blood vessels,carotid body and carotid sinus

Summary Two postganglionic branches of the superior cervical ganglion enter the area of the carotid bifurcation in the rabbit and the cat. The common and external carotid arteries receive a rich adrenergic nerve supply, which can be demonstrated by fluorophores of biogenic amines appearing after formaldehyde treatment. The internal carotid artery is only sparsely innervated; however, it shows a dense sympathetic supply at the site of pressor receptors. Following removal of the superior cervical ganglion, a total loss of fluorescent adrenergic nerves occurs and degeneration of nerve endings possessing dense core vesicles is conspicuous. These nerve terminals are situated mainly subendothelially in the carotid body sinusoids; they only rarely terminate on type I cells.     

EGS_cbct: Simulation of a fan beam CT and RMI phantom for measured HU verification

IntroductionA mathematical 3D model of an existing computed tomography (CT) scanner was created and used in the EGSnrc-based BEAMnrc and egs_cbct Monte Carlo codes. Simulated transmission dose profiles of a RMI-465 phantom were analysed to verify Hounsfield numbers against measured data obtained from the CT scanner.Methods and materialsThe modelled CT unit is based on the design of a Toshiba Aquilion 16 LB CT scanner. As a first step, BEAMnrc simulated the X-ray tube, filters, and secondary collimation to obtain phase space data of the X-ray beam. A bowtie filter was included to create a more uniform beam intensity and to remove the beam hardening effects. In a second step the Interactive Data Language (IDL) code was used to build an EGSPHANT file that contained the RMI phantom which was used in egs_cbct simulations. After simulation a series of profiles were sampled from the detector model and the Feldkamp-Davis-Kress (FDK) algorithm was used to reconstruct transversal images. The results were tested against measured data obtained from CT scans.ResultsThe egs_cbct code can be used for the simulation of a fan beam CT unit. The calculated bowtie filter ensured a uniform flux on the detectors. Good correlation between measured and simulated CT numbers was obtained.ConclusionsIn principle, Monte Carlo codes such as egs_cbct can model a fan beam CT unit. After reconstruction, the images contained Hounsfield values comparable to measured data.     

Quantitative comparison of errors in 15N transverse relaxation rates measured using various CPMG phasing schemes

Nitrogen-15 Carr-Purcell-Meiboom-Gill (CPMG) transverse relaxation experiment are widely used to characterize protein backbone dynamics and chemical exchange parameters. Although an accurate value of the transverse relaxation rate, R(2), is needed for accurate characterization of dynamics, the uncertainty in the R(2) value depends on the experimental settings and the details of the data analysis itself. Here, we present an analysis of the impact of CPMG pulse phase alternation on the accuracy of the (15)N CPMG R(2). Our simulations show that R(2) can be obtained accurately for a relatively wide spectral width, either using the conventional phase cycle or using phase alternation when the r.f. pulse power is accurately calibrated. However, when the r.f. pulse is miscalibrated, the conventional CPMG experiment exhibits more significant uncertainties in R(2) caused by the off-resonance effect than does the phase alternation experiment. Our experiments show that this effect becomes manifest under the circumstance that the systematic error exceeds that arising from experimental noise. Furthermore, our results provide the means to estimate practical parameter settings that yield accurate values of (15)N transverse relaxation rates in the both CPMG experiments.     

Flow field and oscillatory shear stress in a tuning-fork-shaped model of the average human carotid bifurcation

The oscillatory shear index (OSI) was developed based on the hypothesis that intimal hyperplasia was correlated with oscillatory shear stresses. However, the validity of the OSI was in question since the correlation between intimal thickness and the OSI at the side walls of the sinus in the Y-shaped model of the average human carotid bifurcation (Y-AHCB) was weak. The objectives of this paper are to examine whether the reason for the weak correlation lies in the deviation in geometry of Y-AHCB from real human carotid bifurcation, and whether this correlation is clearly improved in the tuning-fork-shaped model of the average human carotid bifurcation (TF-AHCB). The geometry of the TF-AHCB model was based on observation and statistical analysis of specimens from 74 cadavers. The flow fields in both models were studied and compared by using flow visualization methods under steady flow conditions and by using laser Doppler anemometer (LDA) under pulsatile flow conditions. The TF-shaped geometry leads to a more complex flow field than the Y-shaped geometry. This added complexity includes strengthened helical movements in the sinus, new flow separation zone, and directional changes in the secondary flow patterns. The results show that the OSI-values at the side walls of the sinus in the TF-shaped model were more than two times as large as those in the Y-shaped model. This study confirmed the stronger correlation between the OSI and intimal thickness in the tuning-fork geometry of human carotid bifurcation, and the TF-AHCB model is a significant improvement over the traditional Y-shaped model.     

Comparison of measured and calculated doses in a Rando phantom with a realistic lung radiotherapy treatment plan including heterogeneities

In this work, dose measurements were performed to evaluate an external radiotherapy treatment plan and, particularly, to validate dose calculations for a lung lesion case. Doses were calculated by the Varian Eclipse treatment planning system using the AAA anisotropic analytical algorithm. The measurements were performed using a Rando anthropomorphic phantom and TLD700 thermoluminescent dosimeters. The comparison between doses calculated and doses measured by means of thermoluminescence (TL) shows compatibility except for a few points, due to the limitations in the heterogeneity correction used for the case studied here. The deviation between the calculated and measured doses is about 6.5% for low (<?0.5 Gy) doses and about 1% for higher doses (>?0.5 Gy).The deviation between AAA-calculated and TL-measured doses was also found to be higher in proximity to heterogeneous tissue interfaces.     

A numerical analysis of steady flow in a three-dimensional model of the carotid artery bifurcation

A finite element approximation of steady flow in a rigid three-dimensional model of the carotid artery bifurcation is presented. A Reynolds number of 640 and a flow division ratio of about 50/50, simulating systolic flow, was used. To limit the CPU- and I/O-times needed for solving the systems of equations, a mesh-generator was developed, which gives full control over the number of elements into which the bifurcation is divided. A mini-supercomputer, based on parallel and vector processing techniques, was used to solve the system of equations. The numerical results of axial and secondary flow compare favorably with those obtained from previously performed laser-Doppler velocity measurements. Also, the influence of the Reynolds number, the flow division ratio, and the bifurcation angle on axial and secondary flow in the carotid sinus were studied in the three-dimensional model. The influence of the interventions is limited to a relatively small variation in the region with reversed axial flow, more or less pronounced C-shaped axial velocity contours, and increasing or decreasing axial velocity maxima.     

Carotid bifurcation position and branching angle in patients with atherosclerotic carotid disease

Carotid artery bifurcation (CB) is the preferred site for development of atherosclerosis (AS) in extracranial cerebral arteries; internal carotid artery stenosis is the most common cause of ischemic stroke. The frequent atherosclerotic disease of CB may best be explained by the hemodynamic influence of complex blood flow that results from the unique geometry of the bifurcation. Few papers analyze all possible geometric structural characteristics of this bifurcation. While performing many carotid endarterectomies, we noticed that a certain correlation between CB height in the neck and its angle existed, that a larger angle is accompanied with increased frequency of elongation and kinking and that CB shape influences distribution of atherosclerosis. The purpose of this paper is to quantify and evaluate these clinical observations. Radiogrametric analysis of 154 bi-plane orthogonal aortic arch arteriograms of patients with symptomatic atherosclerotic carotid artery disease was performed and a total of 289 CBs were analyzed. The CB height in relation to cervical spine segments was measured and real angles of each bifurcation were calculated. A positive linear correlation between CB height and angle exists: the CB angle increases /decreases 3.34 degrees for each third of the cervical vertebral body height or intervertebral space height. The CB is positioned a little higher on the left side. The proximal border of the atherosclerotic process is found at the level of intersection of the axes of the common carotid artery branches in 92.6% of examined CBs. In lower CBs (with smaller angles) the proximal border was located in the last segment of the common carotid artery, while in high bifurcations (wider angles) the proximal border of the AS process is more distally in the blood flow, in the beginning of the internal carotid artery, and the process was more extensive. High CBs are more suitable for eversion endarterectomy while normal and low CBs are more suitable for open (classic) carotid endarterectomy. The influence of the geometric risk factor demands further investigation.