Geometric characterization of stenosed human carotid arteries

Development of an in vitro setup for flow studies in a stented carotid artery bifurcation

To investigate flow conditions in a double-layered carotid artery stent, a bench-top in vitro flow setup including a bifurcation phantom was designed and fabricated. The geometry of the tissue-mimicking phantom was based on healthy individuals. Two identical phantoms were created using 3D-printing techniques and molding with PVA-gel. In one of them, a clinically available CGuard double-layer stent was inserted. Measurements were performed using both continuous and pulsatile flow conditions. Blood flow studies were performed using echoPIV: a novel ultrasound-based technique combined with particle image velocimetry. A maximum deviation of 3% was visible between desired and measured flow patterns. The echoPIV measurements showed promising results on visualization and quantification of blood flow in and downstream the stent. Further research could demonstrate the effects of a double-layered stent on blood flow patterns in a carotid bifurcation in detail.

Atherosclerosis risk assessment in human carotid artery with variation in sinus length: a numerical approach

The mortality rates due to cardiovascular diseases are on a rise globally. One of the major cardiovascular diseases is stroke which occurs due to atherosclerotic plaques build-up in the carotid artery. The common carotid artery (CCA) bifurcates into the internal carotid artery (ICA) and external carotid artery (ECA). Sinus present at ICA is an ellipsoidal-shaped dilated region acting as a pressure receptor and blood flow regulator. Dimensions of the sinus vary from person to person, affecting the hemodynamics of the carotid artery. The current numerical study manifests a 3D flow analysis by varying the sinus length to investigate its local and global effects on the hemodynamics of the carotid artery using various biomechanical risk analysis parameters of atherosclerosis. User-defined function (UDF) dictates the pulsatile flow velocity profile imposed at the inlet. Near the outer wall (OW) of the sinus, the blood flow velocities are lower and recirculation zones are more. Though the recirculation zones for shorter sinus will be close to the inner wall (IW), interestingly, with an increase in the sinus length, the recirculation zones shift toward the OW with higher strength. These significantly decrease the x-wall shear stress (x-WSS) and time-averaged wall shear stress (TAWSS) values on the OW of the longer sinus. The other risk analysis parameters, like oscillatory shear index (OSI) and relative residence time (RRT), support the described consequences. These results reveal that sinus of increased length is more prone to developing atherosclerotic plaque.

Deep learning-based hemodynamic prediction of carotid artery stenosis before and after surgical treatments

Hemodynamic prediction of carotid artery stenosis (CAS) is of great clinical significance in the diagnosis, prevention, and treatment prognosis of ischemic strokes. While computational fluid dynamics (CFD) is recognized as a useful tool, it shows a crucial issue that the high computational costs are usually required for real-time simulations of complex blood flows. Given the powerful feature-extraction capabilities, the deep learning (DL) methodology has a high potential to implement the mapping of anatomic geometries and CFD-driven flow fields, which enables accomplishing fast and accurate hemodynamic prediction for clinical applications. Based on a brain/neck CT angiography database of 280 subjects, image based three-dimensional CFD models of CAS were constructed through blood vessel extraction, computational domain meshing and setting of the pulsatile flow boundary conditions; a series of CFD simulations were undertaken. A DL strategy was proposed and accomplished in terms of point cloud datasets and a DL network with dual sampling-analysis channels. This enables multimode mapping to construct the image-based geometries of CAS while predicting CFD-based hemodynamics based on training and testing datasets. The CFD simulation was validated with the mass flow rates at two outlets reasonably agreed with the published results. Comprehensive analysis and error evaluation revealed that the DL strategy enables uncovering the association between transient blood flow characteristics and artery cavity geometric information before and after surgical treatments of CAS. Compared with other methods, our DL-based model trained with more clinical data can reduce the computational cost by 7,200 times, while still demonstrating good accuracy (error<12.5%) and flow visualization in predicting the two hemodynamic parameters. In addition, the DL-based predictions were in good agreement with CFD simulations in terms of mean velocity in the stenotic region for both the preoperative and postoperative datasets. This study points to the capability and significance of the DL-based fast and accurate hemodynamic prediction of preoperative and postoperative CAS. For accomplishing real-time monitoring of surgical treatments, further improvements in the prediction accuracy and flexibility may be conducted by utilizing larger datasets with specific real surgical events such as stent intervention, adopting personalized boundary conditions, and optimizing the DL network.

A Review of Carotid Artery Phantoms for Doppler Ultrasound Applications

Ultrasound imaging systems need tissue-mimicking phantoms with a good range of acoustic properties. Many studies on carotid artery phantoms have been carried out using ultrasound; hence this study presents a review of the different forms of carotid artery phantoms used to examine blood hemodynamics by Doppler ultrasound (DU) methods and explains the ingredients that constitute every phantom with their advantages and disadvantages. Different research databases were consulted to access relevant information on carotid artery phantoms used for DU measurements after which the information were presented systematically spanning from walled phantoms to wall-less phantoms. This review points out the fact that carotid artery phantoms are made up of tissue mimicking materials, vessel mimicking materials, and blood mimicking fluid whose properties matched those of real human tissues and vessels. These materials are a combination of substances such as water, gelatin, glycerol, scatterers, and other powders in their right proportions.

Computational Modeling of Carotid Bruits

The sound generated by diseased carotid arteries was investigated through computational means using three-dimensional, idealized, stenosed carotid bifurcation models. Stenosis levels of 50% and 70% with axi-symmetric and asymmetric stenosis shapes were considered. The hemodynamic flow field was obtained by solving the incompressible, Navier-Stokes equations. The resulting pressure fluctuations at the vessel walls were then used as input for a linearized wave equation for the propagation of vibrations through the modeled surrounding tissue. As observed in prior studies, the sound spectra obtained at the tissue surface indicate a 'break frequency', i.e. a frequency beyond which there is a drop-off in sound spectra intensity. This frequency was found to scale with stenosis diameter and average velocity at the stenosis throat, provided the stenosis shape remained the same. This has important implications on past attempts to estimate stenosis diameter from the break frequency.

Transport of blood particles: Chaotic advection even in a healthy scenario

We study the advection of blood particles in the carotid bifurcation, a site that is prone to plaque development. Previously, it has been shown that chaotic advection can take place in blood flows with diseases. Here, we show that even in a healthy scenario, chaotic advection can take place. To understand how the particle dynamics is affected by the emergence and growth of a plaque, we study the carotid bifurcation in three cases: a healthy bifurcation, a bifurcation with a mild stenosis, and the another with a severe stenosis. The result is non-intuitive: there is less chaos for the mild stenosis case even when compared to the healthy, non-stenosed, bifurcation. This happens because the partial obstruction of the mild stenosis generates a symmetry in the flow that does not exist for the healthy condition. For the severe stenosis, there is more irregular motion and more particle trapping as expected.

Arterial Phantoms with Regional Variations in Wall Stiffness and Thickness

Regional wall stiffening and thickening are two common pathological features of arteries. To account for these two features, we developed a new arterial phantom design framework to facilitate the development of vessel models that contain a lesion segment whose wall stiffness and thickness differ from those of other segments. This new framework is based on multi-part injection molding principles that sequentially casted the lesion segment and the flank segments of the vessel model using molding parts devised with computer-aided design tools. The vessel-mimicking material is created from polyvinyl alcohol cryogel, and its acoustic properties are similar to those of arteries. As a case demonstration, we fabricated a stenosed three-segment phantom composed of a central lesion segment (5.1-mm diameter, 1.95-mm wall thickness, 212.6-kPa elastic modulus) and two flank segments (6.0-mm diameter, 1.5-mm wall thickness, 133.7-kPa elastic modulus). B-mode imaging confirmed the difference in thickness between the lesion segment and flank segments of the phantom. Also, Doppler-based vessel wall displacement analysis revealed that when pulsatile flow was fed through the phantom (carotid pulse; 27 mL/s peak flow rate), the lesion segment distended less compared with the flank segments. Specifically, the three-beat averaged peak wall displacement in the lesion segment was measured as 0.28 mm, and it was significantly smaller than that of the flank segments (0.60 mm). It is anticipated that this new multi-segment arterial phantom can serve as a performance testbed for the evaluation of local arterial stiffness estimation algorithms.

Walled Carotid Bifurcation Phantoms for Imaging Investigations of Vessel Wall Motion and Blood Flow Dynamics

As a major application domain of vascular ultrasound, the carotid artery has long been the subject of anthropomorphic phantom design. It is nevertheless not trivial to develop walled carotid phantoms that are compatible for use in integrative imaging of carotid wall motion and flow dynamics. In this paper, we present a novel phantom design protocol that can enable efficient fabrication of walled carotid bifurcation phantoms with: (i) high acoustic compatibility, (ii) artery-like vessel elasticity, and (iii) stenotic narrowing feature. Our protocol first involved direct fabrication of the vessel core and an outer mold using computer-aided design tools and 3-D printing technology; these built parts were then used to construct an elastic vessel tube through investment casting of a polyvinyl alcohol containing mixture, and an agar-gelatin tissue mimicking slab was formed around the vessel tube. For demonstration, we applied our protocol to develop a set of healthy and stenosed (25%, 50%, 75%) carotid bifurcation phantoms. Plane wave imaging experiments were performed on these phantoms using an ultrasound scanner with channel-level configurability. Results show that the wall motion dynamics of our phantoms agreed with pulse wave propagation in an elastic vessel (pulse wave velocity of 4.67±0.71 m/s measured at the common carotid artery), and their flow dynamics matched the expected ones in healthy and stenosed bifurcation (recirculation and flow jet formation observed). Integrative imaging of vessel wall motion and blood flow dynamics in our phantoms was also demonstrated, from which we observed fluid-structure interaction differences between healthy and diseased bifurcation phantoms. These findings show that the walled bifurcation phantoms developed with our new protocol are useful in vascular imaging studies that individually or jointly assess wall motion and flow dynamics.

Characterization of atherosclerotic plaque: a contrast-detail study using multidetector and cone-beam computed tomography

A Hindmarsh-Rose model perceptibility phantom containing inserts with various in vitro atherosclerotic plaque compositions was constructed and imaged on a clinical 64 slice multidetector (MDCT) system using 80 and 120 kVp settings and two other cone-beam (CBCT) systems at 80 kVp. Perceptibility of the simulated lipid-fibrotic plaque solutions in the images was evaluated by six observers. The effective doses of the protocols employed were estimated using phantom CTDI-vol measurements placed at identical settings. The CBCT system allowed reduction in effective dose in comparison with the conventional MDCT system for imaging of the carotid plaque phantoms without degrading image quality. The CBCT dose was less than MDCT, with a mean dose of 1.14 ± 0.01 mSv and 1.11 ± 0.02 mSv for MDCT using two measuring techniques vs. 0.35 ± 0.01 mSv for CBCT. The image quality analysis showed no significant differences in the contrast-detail (C-D) curves of the best performing CBCT vs. clinical MDCT (p &gt; 0.05) using a Mann-Whitney U test. Results indicate that low-tube-potential CBCT may produce comparable C-D resolution for phantom-based representations of soft plaque types with respect to MDCT systems. This study suggests that the utility of low kVp CT techniques for evaluating carotid vulnerable atherosclerotic plaque merits further study.

Turbulence intensity measurements using particle image velocimetry in diseased carotid artery models: effect of stenosis severity, plaque eccentricity, and ulceration

Clinical decision-making for the treatment of patients with diseased carotid artery is mainly based on the severity of the stenosis. However, stenosis severity alone is not a sensitive indicator, and other local factors for the assessment of stroke risk are required. Flow disturbance is of particular interest due to its proven association with increased thromboembolic activities. The objective of this study was to investigate the level of turbulence intensity (TI) with regards to certain geometrical features of the plaque - namely stenosis severity, eccentricity, and ulceration. A family of eight carotid-artery bifurcation models was examined using particle image velocimetry. Results showed a marked difference in turbulence intensity among these models; increasing degree of stenosis severity resulted in increased turbulence intensity, going from 0.12 m/s for mild stenosis to 0.37 m/s for severe stenosis (with concentric geometry). Moreover, independent of stenosis severity, eccentricity led to further elevations in turbulence intensity, increasing TI by 0.05-0.10 m/s over the counterpart concentric plaque. The presence of ulceration (in a 50% eccentric plaque) produced a larger portion of moderate turbulence intensity (~0.10 m/s) compared to the non-ulcerated model, more proximal to the bifurcation apex in the post-stenotic recirculation zone. The effect of plaque eccentricity and ulceration in enhancing the downstream turbulence has potential clinical implications for a more sensitive assessment of stroke risk beyond stenosis severity alone.

Design of anthropomorphic flow phantoms based on rapid prototyping of compliant vessel geometries

Anatomically realistic flow phantoms are essential experimental tools for vascular ultrasound. Here we describe how these flow phantoms can be efficiently developed via a rapid prototyping (RP) framework that involves direct fabrication of compliant vessel geometries. In this framework, anthropomorphic vessel models were drafted in computer-aided design software, and they were fabricated using stereolithography (one type of RP). To produce elastic vessels, a compliant photopolymer was used for stereolithography. We fabricated a series of compliant, diseased carotid bifurcation models with eccentric stenosis (50%) and plaque ulceration (types I and III), and they were used to form thin-walled flow phantoms by coupling the vessels to an agar-based tissue-mimicking material. These phantoms were found to yield Doppler spectrograms with significant spectral broadening and color flow images with mosaic patterns, as typical of disturbed flow under stenosed and ulcerated disease conditions. Also, their wall distension behavior was found to be similar to that observed in vivo, and this corresponded with the vessel wall's average elastic modulus (391 kPa), which was within the nominal range for human arteries. The vessel material's acoustic properties were found to be sub-optimal: the estimated average acoustic speed was 1801 m/s, and the attenuation coefficient was 1.58 dB/(mm·MHz(n)) with a power-law coefficient of 0.97. Such an acoustic mismatch nevertheless did not notably affect our Doppler spectrograms and color flow image results. These findings suggest that phantoms produced from our design framework have the potential to serve as ultrasound-compatible test beds that can simulate complex flow dynamics similar to those observed in real vasculature.

High-frame-rate ultrasound color-encoded speckle imaging of complex flow dynamics

Realization of flow imaging at high frame rates is essential to the visualization of complex flow patterns with fast-changing spatiotemporal dynamics. In this study, we present an experimental demonstration of a novel ultrasound-based high-frame-rate flow visualization technique called color-encoded speckle imaging (CESI), which depicts flow information in a hybrid form comprising flow speckle pattern and color-encoded velocity mapping. This technique works by integrating two key principles: (i) using broad-view data acquisition schemes like plane wave compounding to obtain image data at frame rates well beyond the video display range and (ii) deriving and displaying both flow speckles and velocity estimates from the acquired broad-view image data. CESI was realized on a channel-domain ultrasound imaging research platform, and its performance was evaluated in the context of monitoring complex flow dynamics inside a carotid bifurcation flow phantom with 25% eccentric stenosis at the inlet of the internal carotid artery. Results show that, using an imaging frame rate of 2000 frames per second (based on plane wave compounding with five steering angles), CESI can effectively render flow acceleration and deceleration with visual continuity. It is also effective in depicting how stenosis-related flow disturbance events, such as flow jet formation and post-stenotic flow recirculation, evolve spatiotemporally over a pulse cycle. We anticipate that CESI can represent a rational approach to rendering flow information in ultrasound-based vascular diagnoses.

Three-dimensional geometry of the human carotid artery

Accurate characterization of carotid artery geometry is vital to our understanding of the pathogenesis of atherosclerosis. Three-dimensional computer reconstructions based on medical imaging are now ubiquitous; however, mean carotid artery geometry has not yet been comprehensively characterized. The goal of this work was to build and study such geometry based on data from 16 male patients with severe carotid artery disease. Results of computerized tomography angiography were used to analyze the cross-sectional images implementing a semiautomated segmentation algorithm. Extracted data were used to reconstruct the mean three-dimensional geometry and to determine average values and variability of bifurcation and planarity angles, diameters and cross-sectional areas. Contrary to simplified carotid geometry typically depicted and used, our mean artery was tortuous exhibiting nonplanarity and complex curvature and torsion variations. The bifurcation angle was 36 deg ± 11 deg if measured using arterial centerlines and 15 deg ± 14 deg if measured between the walls of the carotid bifurcation branches. The average planarity angle was 11 deg ± 10 deg. Both bifurcation and planarity angles were substantially smaller than values reported in most studies. Cross sections were elliptical, with an average ratio of semimajor to semiminor axes of 1.2. The cross-sectional area increased twofold in the bulb compared to the proximal common, but then decreased 1.5-fold for the combined area of distal internal and external carotid artery. Inter-patient variability was substantial, especially in the bulb region; however, some common geometrical features were observed in most patients. Obtained quantitative data on the mean carotid artery geometry and its variability among patients with severe carotid artery disease can be used by biomedical engineers and biomechanics vascular modelers in their studies of carotid pathophysiology, and by endovascular device and materials manufacturers interested in the mean geometrical features of the artery to target the broad patient population.

Evaluation of distal turbulence intensity for the detection of both plaque ulceration and stenosis grade in the carotid bifurcation using clinical Doppler ultrasound

OBJECTIVES

To determine the interrelationship of stenosis grade and ulceration with distal turbulence intensity (TI) in the carotid bifurcation measured using conventional clinical Doppler ultrasound (DUS) in vitro, in order to establish the feasibility of TI as a diagnostic parameter for plaque ulceration.

METHODS

DUS TI was evaluated in a matched set of ulcerated and smooth-walled carotid bifurcation phantoms with various stenosis severities (30, 50, 60 and 70 %), where the ulcerated models incorporated a type 3 ulceration.

RESULTS

Post-stenotic TI was significantly elevated owing to ulceration in the mild and moderate stenoses (P < 0.001). TI increased with stenosis severity in both the ulcerated and non-ulcerated series, with a statistically significant effect of increasing stenosis severity (P < 0.001). Whereas TI in the mild and non-ulcerated moderate stenoses was less than 20.4 ± 1.3 cm s(-1), TI in the ulcerated moderate and severe models was higher than 25.6 ± 1.3 cm s(-1), indicating a potential diagnostic threshold.

CONCLUSION

We report a two-curve relationship of stenosis grade and ulceration to distal TI measured using clinical DUS in vitro. Clinical DUS measurement of distal TI may be a diagnostic approach to detecting ulceration in the mild and moderately stenosed carotid artery.

KEY POINTS

• Patients with carotid artery plaque ulcerations are at higher risk of stroke. • Clinical Doppler ultrasound is routinely used to detect carotid artery stenosis. • Doppler ultrasound turbulence intensity can detect ulceration in realistic flow models. • Turbulence intensity also increases with stenosis severity independent of ulceration. • Doppler ultrasound should help in assessing both stenosis severity and ulceration.

Transitional flow analysis in the carotid artery bifurcation by proper orthogonal decomposition and particle image velocimetry

Blood flow instabilities in the carotid artery bifurcation have been highly correlated to clot formation and mobilization resulting in ischemic stroke. In this work, PIV-measured flow velocities in normal and stenosed carotid artery bifurcation models were analyzed by means of proper orthogonal decomposition (POD). Through POD analysis, transition to more complex flow was visualized and quantified for increasing stenosis severity. While no evidence of transitional flow was seen in the normal model, the 50%-stenosed model started to show characteristics of transitional flow, which became highly evident in the 70% model, with greatest manifestation during the systolic phase of the cardiac cycle. By means of a model comparison, we demonstrate two quantitative measures of the flow complexity through the power-law decay slope of the energy spectrum and the global entropy. The more complex flow in the 70%-stenosed model showed a flatter slope of energy decay (-0.91 compared to -1.34 for 50% stenosis) and higher entropy values (0.26 compared to 0.17). Finally, the minimum temporal resolution required for POD analysis of carotid artery flow was found to be 100 Hz when determined through a more typical energy-mode convergence test, as compared to 400 Hz based on global entropy values.

Targeted particle tracking in computational models of human carotid bifurcations

A significant and largely unsolved problem of computational fluid dynamics (CFD) simulation of flow in anatomically relevant geometries is that very few calculated pathlines pass through regions of complex flow. This in turn limits the ability of CFD-based simulations of imaging techniques (such as MRI) to correctly predict in vivo performance. In this work, I present two methods designed to overcome this filling problem, firstly, by releasing additional particles from areas of the flow inlet that lead directly to the complex flow region ("preferential seeding") and, secondly, by tracking particles both "downstream" and "upstream" from seed points within the complex flow region itself. I use the human carotid bifurcation as an example of complex blood flow that is of great clinical interest. Both idealized and healthy volunteer geometries are investigated. With uniform seeding in the inlet plane (in the common carotid artery (CCA)) of an idealized bifurcation geometry, approximately half the particles passed through the internal carotid artery (ICA) and half through the external carotid artery. However, of those particles entering the ICA, only 16% passed directly through the carotid bulb region. Preferential seeding from selected regions of the CCA was able to increase this figure to 47%. In the second method, seeding of particles within the carotid bulb region itself led to a very high proportion (97%) of pathlines running from CCA to ICA. Seeding of particles in the bulb plane of three healthy volunteer carotid bifurcation geometries led to much better filling of the bulb regions than by particles seeded at the inlet alone. In all cases, visualization of the origin and behavior of recirculating particles led to useful insights into the complex flow patterns. Both seeding methods produced significant improvements in filling the carotid bulb region with particle tracks compared with uniform seeding at the inlet and led to an improved understanding of the complex flow patterns. The methods described may be combined and are generally applicable to CFD studies of fluid and gas flow and are, therefore, of relevance in hemodynamics, respiratory mechanics, and medical imaging science.

3-D flow characterization and shear stress in a stenosed carotid artery bifurcation model using stereoscopic PIV technique

The carotid artery bifurcation is a common site of atherosclerosis which is a major leading cause of ischemic stroke. The impact of stenosis in the atherosclerotic carotid artery is to disturb the flow pattern and produce regions with high shear rate, turbulence, and recirculation, which are key hemodynamic factors associated with plaque rupture, clot formation, and embolism. In order to characterize the disturbed flow in the stenosed carotid artery, stereoscopic PIV measurements were performed in a transparent model with 50% stenosis under pulsatile flow conditions. Simulated ECG gating of the flowrate waveform provides external triggering required for volumetric reconstruction of the complex flow patterns. Based on the three-component velocity data in the lumen region, volumetric shear-stress patterns were derived.

Computational simulations and experimental studies of 3D phase-contrast imaging of fluid flow in carotid bifurcation geometries

PURPOSE

To evaluate the use of computational fluid dynamic (CFD)-based magnetic resonance imaging (MRI) simulations to predict the image appearance and velocity measurement of fluid flow in human carotid bifurcation geometries, and to compare the results with images from experimental MRI studies.

MATERIALS AND METHODS

Simulated particle paths were calculated from available CFD datasets of normal and moderately stenosed carotid bifurcation geometries. An MRI simulator based on the spin isochromat method was used to generate images corresponding to a 3D phase-contrast sequence with velocity encoding in three orthogonal directions. The resulting images were compared qualitatively with experimental MRI scans of the corresponding physical models.

RESULTS

The simulations predicted the main features observed in experimental studies, such as the low image intensity in regions of complex flow and the position and bright appearance of the jet in the stenosed bifurcation. Simulated velocity images also agreed well with experimental results. The effects of sequence parameters such as repetition time (TR) and echo time (TE) were readily demonstrated by the simulations.

CONCLUSION

CFD-based MRI simulations can be used to predict the appearance of MRI images of regions of physiological flow, and may be useful in the development of improved pulse sequences for flow measurement.

Flow patterns in carotid bifurcation models using pulsed Doppler ultrasound: effect of concentric vs. eccentric stenosis on turbulence and recirculation

Hemodynamics play a significant role in stroke risk, where thrombus formation may be accelerated in regions of slow or recirculating flow, high shear and increased turbulence. An in vitro investigation was performed with pulsed Doppler ultrasound (DUS) using the complete spectral data to investigate the three-dimensional (3-D) distribution of advanced parameters that may have potential for making a more specific in vivo diagnosis of carotid disease and stroke risk. The effect of stenosis symmetry and the potential of DUS spectral parameters for visualizing regions of recirculation or turbulence were explored. DUS was used to map pulsatile flow in four model geometries representing two different plaque symmetries (eccentricity) and two stenosis severities (mild, severe). Qualitative comparisons were made with flow patterns visualized using digital particle imaging. Color-encoded maps of DUS spectral parameters (mean velocity, spectral-broadening index and turbulence intensity) clearly distinguished regions of slow or recirculating flow and disturbed or turbulent flow. Distinctly different flow patterns resulted from stenoses of equal severity but different eccentricity. Noticeable differences were seen in both the size and location of recirculation zones and in the paths of high-velocity jets. Highly elevated levels of turbulence intensity were seen distal to severe stenosis. Results demonstrated the importance of plaque shape, which is typically not considered in standard diagnosis, in addition to stenosis severity.

In vivo Doppler ultrasound quantification of turbulence intensity using a high-pass frequency filter method

The objective of this investigation was to implement a high-pass frequency filter method to analyze Doppler ultrasound velocity waveforms and quantify turbulence intensity (TI) in vivo. Doppler velocity data were analyzed using two techniques, based on either ensemble averaging or high-pass frequency domain filtering of the periodic waveforms. The accuracy and precision of TI measurements were determined with controlled in vitro experiments, using a pulsatile-flow model of a stenosed carotid bifurcation. The high-pass filter technique was also applied in vivo to determine whether this technique could successfully distinguish between pertinent hemodynamic sites within the carotid artery bifurcation. Twenty-five seconds of Doppler audio data were acquired at three sites (common carotid artery [CCA], internal carotid artery [ICA] stenosis and distal ICA) within 10 human carotid arteries, and repeated three times. Doppler velocity data were analyzed using a ninth-order high-pass Butterworth filter with a 12-Hz inflection point. TI measured within the CCA and distal ICA was found to be significantly different (p < 0.0001) for moderate to nearly occluded carotid artery classifications. Also, TI measured within the distal ICA increased with stenosis severity, with the ability to distinguish between each stenosis class (p < 0.05). This investigation demonstrated the ability to precisely quantify TI using a conventional Doppler ultrasound machine in human subjects, without interfering with normal clinical protocols.

In vitro performance assessment of distal protection filters: pulsatile flow conditions

PURPOSE

To evaluate in vitro the capture efficiency of a distal protection filter (DPF) used during carotid artery stenting and examine the longitudinal vascular impedance in the presence of a DPF.

METHODS

Four approved DPFs (Spider RX, FilterWire EZ, RX Accunet, and FiberNet) were evaluated in a physiologically realistic in vitro setup. A pulsatile programmable piston pump circulated a blood analog at a time-varying flow rate representative of the human common carotid artery. A silicone carotid bifurcation having average human dimensions was used for the carotid flow model. Microspheres ranging from 40 to 900 microm were injected to simulate embolization. The longitudinal vascular impedance was calculated as the ratio of the time-varying pressure gradient across the DPF to the time-varying flow rate in the internal carotid artery.

RESULTS

RX Accunet had the highest capture efficiency (99.4%) and Spider RX the lowest (78.1%). Spider RX increased the longitudinal vascular impedance the least after deployment (+23%), while FilterWire EZ increased the longitudinal vascular impedance the least after particles were injected (+29%). FiberNet increased longitudinal vascular impedance the most (+84%).

CONCLUSION

This investigation, unique for examining the effects of physiologically realistic pulsatile flow on DPF performance, can aid in the development of future generations of novel DPFs.

In vitro Doppler ultrasound investigation of turbulence intensity in pulsatile flow with simulated cardiac variability

An in vitro investigation of turbulence intensity (TI) associated with a severe carotid stenosis in the presence of physiological cardiac variability is described. The objective of this investigation was to determine if fluctuations due to turbulence could be quantified with conventional Doppler ultrasound (DUS) in the presence of normal physiological cycle-to-cycle cardiac variability. An anthropomorphic model of a 70% stenosed carotid bifurcation was used in combination with a programmable flow pump to generate pulsatile flow with a mean flow rate of 6 mL/s. Utilizing the pump, we studied normal, nonrepetitive cycle-to-cycle cardiac variability (+/-3.9%) in flow, as well as waveform shapes with standard deviations equal to 0, 2 and 3 times the normal variation. Eighty cardiac cycles of Doppler data were acquired at two regions within the model, representing either laminar or turbulent flow; each measurement was repeated six times. Turbulence intensity values were found to be 11 times higher (p < 0.001), on average, in the turbulent region than in the laminar region, with a mean difference of 24 cm/s. Twenty cardiac cycles were required for confidence in TI values. In conclusion, these results indicate that it is possible to quantify TI in vitro, even in the presence of normal and exaggerated cycle-to-cycle cardiac variability.

Quantification of carotid vessel wall and plaque thickness change using 3D ultrasound images

Quantitative measurements of carotid plaque burden progression or regression are important in monitoring patients and in evaluation of new treatment options. 3D ultrasound (US) has been used to monitor the progression or regression of carotid artery plaques. This paper reports on the development and application of a method used to analyze changes in carotid plaque morphology from 3D US. The technique used is evaluated using manual segmentations of the arterial wall and lumen from 3D US images acquired in two imaging sessions. To reduce the effect of segmentation variability, segmentation was performed five times each for the wall and lumen. The mean wall and lumen surfaces, computed from this set of five segmentations, were matched on a point-by-point basis, and the distance between each pair of corresponding points served as an estimate of the combined thickness of the plaque, intima, and media (vessel-wall-plus-plaque thickness or VWT). The VWT maps associated with the first and the second US images were compared and the differences of VWT were obtained at each vertex. The 3D VWT and VWT-Change maps may provide important information for evaluating the location of plaque progression in relation to the localized disturbances of flow pattern, such as oscillatory shear, and regression in response to medical treatments.

Doppler ultrasound compatible plastic material for use in rigid flow models

A technique for the rapid but accurate fabrication of multiple flow phantoms with variations in vascular geometry would be desirable in the investigation of carotid atherosclerosis. This study demonstrates the feasibility and efficacy of implementing numerically controlled direct-machining of vascular geometries into Doppler ultrasound (DUS)-compatible plastic for the easy fabrication of DUS flow phantoms. Candidate plastics were tested for longitudinal speed of sound (SoS) and acoustic attenuation at the diagnostic frequency of 5 MHz. Teflon was found to have the most appropriate SoS (1376 +/- 40 m s(-1) compared with 1540 m s(-1) in soft tissue) and thus was selected to construct a carotid bifurcation flow model with moderate eccentric stenosis. The vessel geometry was machined directly into Teflon using a numerically controlled milling technique. Geometric accuracy of the phantom lumen was verified using nondestructive micro-computed tomography. Although Teflon displayed a higher attenuation coefficient than other tested materials, Doppler data acquired in the Teflon flow model indicated that sufficient signal power was delivered throughout the depth of the vessel and provided comparable velocity profiles to that obtained in the tissue-mimicking phantom. Our results indicate that Teflon provides the best combination of machinability and DUS compatibility, making it an appropriate choice for the fabrication of rigid DUS flow models using a direct-machining method.

Vascular resistance in the carotid artery: an in vitro investigation of embolic protection filters

PURPOSE

To assess in vitro performance of four embolic protection filters (EPFs) with a varying mass of injected particles. Evaluation is based on capture efficiency, pressure gradient, flow rate, and vascular resistance.

MATERIALS AND METHODS

A bench-top flow apparatus was used for in vitro testing of four devices (Spider RX, FilterWire EZ, RX Accunet, and Emboshield). A silicone phantom with average human carotid artery dimensions and a 70% symmetric internal carotid artery (ICA) stenosis was used to model the carotid bifurcation. A blood-mimicking solution (glycerol/deionized water) was circulated at the time-averaged mean peak velocity for the common carotid artery. Five and 10 mg of 200- or 300-mum-diameter microspheres were injected into the ICA to evaluate the capture efficiency of the devices. The normalized pressure gradient, flow rate, and vascular resistance in the ICA were calculated from measured values of pressure and flow rate.

RESULTS

The Spider RX captured the most particles (99.9% for 5 mg, 98.4% for 10 mg) and was associated with the slightest increase in pressure gradient (+8%, +15%) for both masses of microspheres injected. The Spider RX and FilterWire EZ were associated with the slightest decreases in flow rate (Spider RX, -1.9% and -12.1%; FilterWire EZ, -3.5% and -8.2%) and the slightest increases in vascular resistance (Spider RX, +10.1% and +33.0%; FilterWire EZ, +20.5% and +32.7%). The device-specific porosity was calculated, and the Spider RX was found to have the greatest at 50.4%; the Emboshield had the lowest at 2.2%.

CONCLUSIONS

The Spider RX and FilterWire EZ had the best overall performances. Design features such as porosity and pore density are important parameters for improving the effectiveness of EPFs. Vascular resistance in the ICA is a flow-derived variable indicative of device performance and affected by the filter design features.

Use of an ultrasound blood-mimicking fluid for Doppler investigations of turbulence in vitro

Turbulence is an important factor in the assessment of stenotic disease and a possible causative mechanism for thromboembolism. Previous Doppler studies of turbulence have typically used whole-blood preparations or suspensions of erythrocytes. Recently, a water-glycerol based blood-mimicking fluid (BMF) has been developed for use in Doppler ultrasound studies. This fluid has desirable ultrasound properties but it has not previously been described during in vitro investigations of turbulence intensity. We report on investigations of grid-generated and constrained-jet turbulence in an in vitro test system. The BMF was found to generate significant levels of turbulence during steady flow at physiological flow rates, producing turbulent patterns in the distal region that were consistent with previous studies. Turbulence intensity increased significantly with flow rate (p < 0.005) for both the constrained jet and the constrained grid. Based on our observations, we conclude that a water-glycerol based BMF provides a suitable working fluid during in vitro investigations of turbulence using Doppler ultrasound.

Simulation and validation of arterial ultrasound imaging and blood flow

We reviewed the simulation and validation of arterial ultrasound imaging and blood flow assessment. The physical process of ultrasound imaging and measurement is complex, especially in disease. Simulation of physiological flow in a phantom with tissue equivalence of soft tissue, vessel wall and blood is now achievable. Outstanding issues are concerned with production of anatomical models, simulation of arterial disease, refinement of blood mimics to account for non-Newtonian behavior and validation of velocity measurements against an independent technique such as particle image velocimetry. String and belt phantoms offer simplicity of design, especially for evaluation of velocity estimators, and have a role as portable test objects. Electronic injection and vibrating test objects produce nonphysiologic Doppler signals, and their role is limited. Computational models of the ultrasound imaging and measurement process offer considerable flexibility in their ability to alter multiple parameters of both the propagation medium and ultrasound instrument. For these models, outstanding issues are concerned with the inclusion of different tissue types, multilayer arteries, inhomogeneous tissues and diseased tissues.

In vitro performance assessment of distal protection devices for carotid artery stenting: effect of physiological anatomy on vascular resistance

PURPOSE

To assess in vitro the performance of 5 distal protection devices (DPDs) by evaluating the capture efficiency, pressure gradient, volume flow rate, and vascular resistance in the internal carotid artery (ICA).

METHODS

The time-averaged mean peak velocity in the common carotid artery and a blood-mimicking solution were used to simulate physiologICAl conditions in a silicone carotid phantom representing average human carotid artery geometry with a 70% symmetrICAl ICA stenosis. Five milligrams of dyed 200-microm nominal diameter polymer microspheres (larger than the pore size of the devices, except Spider RX, which was tested with 300-microm-diameter particles) were injected into the ICA. The percentages of particles missed after injection and lost during device retrieval were measured for the 5 devices (Spider RX, FilterWire EZ, RX Accunet, Angioguard XP, and Emboshield). The normalized pressure gradient, fraction of the volume flow rate, and vascular resistance in the ICA were calculated.

RESULTS

Spider RX captured the most particles (missing 0.06%, p<0.05) and yielded the smallest normalized pressure gradient increase (4.2%), the largest volume flow rate fraction (0.40), and the smallest vascular resistance in the ICA (272 mmHg/L x min(-1), a 5.4% increase with respect to initial conditions). Angioguard XP captured the fewest particles (missing 36.3%, p<0.05 except Emboshield) and resulted in the largest normalized pressure gradient increase (37%) in the ICA. RX Accunet produced the smallest volume flow rate fraction in the ICA (0.30) and the largest vascular resistance in the ICA (470 mmHg/ L x min(-1), an 82.2% increase). Emboshield migrated approximately 6 cm distal to the original position after particle injection. FilterWire EZ lost the fewest particles during retrieval (0.45%, p<0.05 except Accunet RX and Spider RX) and had the best overall performance with 200-microm emboli (p<0.05 except Accunet RX).

CONCLUSION

None of the devices tested completely prevented embolization. Overall, Spider RX had the best performance and is conjectured to have the best wall apposition of the devices tested. Vascular resistance should be considered a key filter design parameter for performance testing since it represents a quantitative estimation of the "slow-flow phenomenon." Our findings should be extrapolated cautiously to help interventionists choose the best device.

Methods for Three-Dimensional Geometric Characterization of the Arterial Vasculature

Complex vascular anatomy often affects endovascular procedural outcome. Accurate quantitative assessment of three-dimensional (3D) in-vivo arterial morphology is therefore vital for endovascular device design, and preoperative planning of percutaneous interventions. The aim of this work was to establish geometric parameters describing arterial branch origin, trajectory, and vessel curvature in 3D space that eliminate the errors implicit in planar measurements. 3D branching parameters at visceral and aortic bifurcation sites, as well as arterial tortuosity were determined from vessel centerlines derived from magnetic resonance angiography data for three subjects. Errors in coronal measurements of 3D branching angles for the right and left renal arteries were 3.1 +/- 3.4 degrees and 7.5 +/- 3.7 degrees , respectively. Distortion of the anterior visceral branching angles from sagittal measurements was less pronounced. Asymmetry in branching and planarity of the common iliac arteries was observed at aortic bifurcations. The renal arteries possessed considerably greater 3D curvature than the abdominal aorta and common iliac vessels with mean average values of 0.114 +/- 0.015 and 0.070 +/- 0.019 mm(-1) for the left and right, respectively. In conclusion, planar projections misrepresented branch trajectory, vessel length, and tortuosity proving the importance of 3D geometric characterization for possible applications in planning of endovascular interventional procedures and providing parameters for endovascular device design.

Generating an ex vivo vascular model

Realistic ex vivo anthropometric vascular environments are required for endovascular device optimization and for preclinical evaluation of interventional procedures. The objective of this research is to build an anthropomorphic model of the human carotid artery. The combination of magnetic resonance angiography image processing and computer-aided design and manufacturing techniques allowed fabrication of multicomponent morphologically precise casts of the carotid artery. The lost core technique was used to produce a hollow vessel prototype incorporating polyvinyl alcohol cryogel (PVA-C) as a tissue-mimicking vessel wall material. PVA-C was mechanically characterized by uniaxial tensile testing after different numbers of freeze/thaw cycles. The novel model construction approach outlined in this study accounts for the morphologic complexities of the human vasculature, and proved successful for the production of realistic compliant ex vivo arterial model.

Operator dependence of 3-D ultrasound-based computational fluid dynamics for the carotid bifurcation

The association between vascular wall shear stress (WSS) and the local development of atherosclerotic plaque makes estimation of in vivo WSS of considerable interest. Three-dimensional ultrasound (3DUS) combined with computational fluid dynamics (CFD) provides a potentially valuable tool for acquiring subject-specific WSS, but the interoperator and intraoperator variability associated with WSS calculations using this method is not known. Here, the accuracy, reproducibility and operator dependence of 3DUS-based computational fluid dynamics were examined through a phantom and in vivo studies. A carotid phantom was scanned and reconstructed by two operators. In the in vivo study, four operators scanned a healthy subject a total of 11 times, and their scan data were processed by three individuals. The study showed that with some basic training, operators could acquire accurate carotid geometry for flow reconstructions. The variability of measured cross-sectional area and predicted shear stress was 8.17% and 0.193 N/m2 respectively for the in vivo study. It was shown that the variability of the examined parameters was more dependent on the scan operators than the image processing operator. The range of variability of geometrical and flow parameters reported here can be used as a reference for future in vivo studies using the 3DUS-based CFD approach.

Real-time numerical simulation of Doppler ultrasound in the presence of nonaxial flow

Numerical simulations of Doppler ultrasound (DUS) relying on computational fluid dynamics (CFD) models of nonaxial flow have traditionally employed detailed (but computationally intensive) models of the DUS physics, or have sacrificed much of the physics in the interest of computational or conceptual simplicity. In this paper, we present a compromise between these extremes, with the objective of simulating the essential characteristics of DUS spectrograms in a real-time manner. Specifically, a precomputed pulsatile CFD velocity field is interrogated at some number, N, of discrete points distributed spatially within a sample volume of prescribed geometry and power distribution and temporally within a prescribed sampling window. Intrinsic spectral broadening is accounted for by convolving each of the point velocities with a semiempirical broadening function. Real-time performance is facilitated through the use of an efficient algorithm for interpolating the unstructured CFD data. A spherical sample volume with Gaussian power distribution, N = 1000 sampling points, and quadratic broadening function are shown to be adequate for simulating, at frame rates of 86 Hz on a 1.5 GHz desktop workstation, realistic-looking spectrograms at representative locations within a stenosed carotid bifurcation model. Via qualitative comparisons with matched in vitro data, these simulated spectrograms are shown to mimic the distinctive spectral envelopes, broadening and power characteristics associated with common carotid, stenotic jet and poststenotic recirculating flows. We conclude that the complex interaction between Doppler ultrasound and complicated clinically relevant blood flow dynamics can be simulated in real time via this relatively straightforward semiempirical approach.

A thin-walled carotid vessel phantom for Doppler ultrasound flow studies

A technique is discussed for producing a robust ultrasound (US)-compatible flow phantom that consists of a thin-walled silicone-elastomer vessel with a lumen of arbitrary geometry, embedded in an agar-based tissue-mimicking material (TMM). The TMM has an acoustic attenuation of 0.56 dB cm(-1) MHz(-1) at 5 MHz, with nearly linear frequency-dependence and acoustic velocity of 1539 +/- 4 m s(-1). The vessel-mimicking material (VMM) has an acoustic attenuation of 3.5 dB cm(-1) MHz(-1) with linear frequency-dependence and an acoustic velocity of 1020 +/- 20 m s(-1). Scattering particles, which are added to the VMM to increase echogenicity and add speckle texture, lead to higher attenuation, depending on particle concentration and frequency. The VMM is stable over time, with a Young's elastic modulus of 1.3 to 1.7 MPa for strains of up to 10%, which mimics human arteries under typical physiological conditions. The phantom is sealed to prevent TMM exposure to air or water, to avoid changes to the acoustic velocity.

Robust and objective decomposition and mapping of bifurcating vessels

Computational modeling of human arteries has been broadly employed to investigate the relationships between geometry, hemodynamics and vascular disease. Recent developments in modeling techniques have made it possible to perform such analyses on realistic geometries acquired noninvasively and, thus, have opened up the possibility to extend the investigation to populations of subjects. However, for this to be feasible, novel methods for the comparison of the data obtained from large numbers of realistic models in the presence of anatomic variability must be developed. In this paper, we present an automatic technique for the objective comparison of distributions of geometric and hemodynamic quantities over the surface of bifurcating vessels. The method is based on centerlines and consists of robustly decomposing the surface into its constituent branches and mapping each branch onto a template parametric plane. The application of the technique to realistic data demonstrates how similar results are obtained over similar geometries, allowing for proper model-to-model comparison. Thanks to the computational and differential geometry criteria adopted, the method does not depend on user-defined parameters or user interaction, it is flexible with respect to the bifurcation geometry and it is readily extendible to more complex configurations of interconnecting vessels.

Reconstruction and quantification of the carotid artery bifurcation from 3-D ultrasound images

Three-dimensional (3-D) ultrasound is a relatively new technique, which is well suited to imaging superficial blood vessels, and potentially provides a useful, noninvasive method for generating anatomically realistic 3-D models of the peripheral vasculature. Such models are essential for accurate simulation of blood flow using computational fluid dynamics (CFD), but may also be used to quantify atherosclerotic plaque more comprehensively than routine clinical methods. In this paper, we present a spline-based method for reconstructing the normal and diseased carotid artery bifurcation from images acquired using a freehand 3-D ultrasound system. The vessel wall (intima-media interface) and lumen surfaces are represented by a geometric model defined using smoothing splines. Using this coupled wall-lumen model, we demonstrate how plaque may be analyzed automatically to provide a comprehensive set of quantitative measures of size and shape, including established clinical measures, such as degree of (diameter) stenosis. The geometric accuracy of 3-D ultrasound reconstruction is assessed using pulsatile phantoms of the carotid bifurcation, and we conclude by demonstrating the in vivo application of the algorithms outlined to 3-D ultrasound scans from a series of patient carotid arteries.

Accuracy and reproducibility of CFD predicted wall shear stress using 3D ultrasound images

Computational fluid dynamics (CFD) flow simulation techniques have the potential to enhance our understanding of how haemodynamic factors are involved in atherosclerosis. Recently, 3D ultrasound has emerged as an alternative to other 3D imaging techniques, such as magnetic resonance angiography (MRA). The method can be used to generate realistic vascular geometry suitable for CFD simulations. In order to assess accuracy and reproducibility of the procedure from image acquisition to reconstruction to CFD simulation, a human carotid artery bifurcation phantom was scanned three times using 3D ultrasound. The geometry was reconstructed and flow simulations were carried out on the three sets as well as on a model generated using computer aided design (CAD) from the geometric information given by the manufacturer. It was found that the three reconstructed sets showed good reproducibility as well as satisfactory quantitative agreement with the CAD model. Analyzing two selected locations probably representing the 'worst cases,' accuracy comparing ultrasound and CAD reconstructed models was estimated to be between 7.2% and 7.7% of the maximum instantaneous WSS and reproducibility comparing the three scans to be between 8.2% and 10.7% of their average maximum.

MP3 compression of Doppler ultrasound signals

The effect of lossy, MP3 compression on spectral parameters derived from Doppler ultrasound (US) signals was investigated. Compression was tested on signals acquired from two sources: 1. phase quadrature and 2. stereo audio directional output. A total of 11, 10-s acquisitions of Doppler US signal were collected from each source at three sites in a flow phantom. Doppler signals were digitized at 44.1 kHz and compressed using four grades of MP3 compression (in kilobits per second, kbps; compression ratios in brackets): 1400 kbps (uncompressed), 128 kbps (11:1), 64 kbps (22:1) and 32 kbps (44:1). Doppler spectra were characterized by peak velocity, mean velocity, spectral width, integrated power and ratio of spectral power between negative and positive velocities. The results suggest that MP3 compression on digital Doppler US signals is feasible at 128 kbps, with a resulting 11:1 compression ratio, without compromising clinically relevant information. Higher compression ratios led to significant differences for both signal sources when compared with the uncompressed signals.

A dual-pressure boundary condition for use in simulations of bifurcating conduits

A dual-pressure boundary condition has been developed for computational modelling of bifurcating conduits. The condition involves the imposition of a constant pressure on one branch while adjusting iteratively the pressure on the other branch until the desired flow division is obtained. The dual-pressure condition eliminates the need for specifying fully-developed flow conditions, which thereby enables significant reduction of the outlet branch lengths. The dual-pressure condition is suitable for both steady and time-periodic simulations of laminar or turbulent flows.

Diffusion-enhanced visualization and quantification of vascular anomalies in three-dimensional rotational angiography: Results of an in-vitro evaluation

Three-dimensional rotational angiography (3DRA) is a new and promising technique for obtaining high-resolution isotropic 3D images of vascular structures. However, due to the relatively high noise level and the presence of other background structures in clinical 3DRA images, noise reduction is inevitable. In this paper, we evaluate a number of linear and nonlinear diffusion techniques for this purpose. Specifically, we analyze the effects of these techniques on the threshold-based visualization and quantification of vascular anomalies in 3DRA images. The results of in-vitro experiments indicate that edge-enhancing anisotropic diffusion filtering is most suitable: the increase in the user-dependency of visualizations and quantifications is considerably less with this technique compared to linear filtering techniques, and it is better at reducing noise near edges than isotropic nonlinear diffusion. However, in view of the memory and computation-time requirements of this technique, the latter scheme may be considered a useful alternative.

Peak velocity determination using fast Fourier velocity encoding with minimal spatial encoding

For quantitative peak velocity determination, a technique was developed that uses Fourier velocity encoding (FVE) for the fast acquisition of images of velocity with no spatial encoding other than slice selection. The technique produces images of velocity versus temporal frequency. In applications where the quantity of interest is the peak velocity and in-plane spatial localization is not required, high SNR images are produced with reduced sensitivity to errors due to slice thickness and motion. The technique was validated using steady and pulsatile flow in a straight tube, and compared to both phase contrast measurements and numerical models using steady flow in a 50% and a 75% cosinusoidal stenosis phantom. Results show that for slices as large as 2 cm and/or undergoing periodic motion, FVE can accurately measure the peak velocity in cases where a distribution of velocities exist.

An in vitro system for Doppler ultrasound flow studies in the stenosed carotid artery bifurcation

To investigate the correlation between disease severity and Doppler spectral measurements in the carotid artery bifurcation, a unique in vitro system has been developed that mimics the human vasculature with respect to both anatomy and flow perfusion. Agar-based carotid phantoms are perfused with a blood-mimicking fluid using a computer-controlled pump and realistic pulsatile flow waveform. A three-axis translational stage allows the lumen to be interrogated with a 0.6-microL Doppler sample volume at the desired spatial intervals using a semiautomated acquisition system, to collect 10 cardiac cycles of gated quadrature data at each site. Off-line analysis, including a 1024-point FFT, produces a 4-D (i.e., time-varying 3-D) Doppler velocity data set with 1.3-cm/s velocity resolution and 12-ms temporal resolution. Using this system, in vitro flow in bifurcations with both normal and stenosed lumen geometry (from 30% to 80% stenosis by NASCET criteria) can be studied, along with the effect of factors, such as stenosis geometry (concentric vs. eccentric) and flow rate, on the observed Doppler ultrasound (US) spectra and haemodynamic patterns.

On assessing the quality of particle tracking through computational fluid dynamic models

Quantification of particle deposition patterns, transit times, and shear exposure is important for computational fluid dynamic (CFD) studies involving respiratory and arterial models. To numerically compute such path-dependent quantities, it is necessary to employ a Lagrangian approach where particles are tracked through a pre-computed velocity field. However, it is difficult to determine in advance whether a particular velocity field is sufficiently resolved for the purposes of tracking particles accurately. Towards this end, we propose the use of volumetric residence time (VRT)--previously defined for 2-D studies of platelet activation and here extended to more physiologically relevant 3-D models--as a means of quantifying whether a volume of Lagrangian fluid elements (LFE's) seeded uniformly and contiguously at the model inlet remains uniform throughout the flow domain. Such "Lagrangian mass conservation" is shown to be satisfied when VRT=1 throughout the model domain. To demonstrate this novel concept, we computed maps of VRT and particle deposition in 3-D steady flow models of a stenosed carotid bifurcation constructed with one adaptively refined and three nominally uniform finite element meshes of increasing element density. A key finding was that uniform VRT could not be achieved for even the most resolved meshes and densest LFE seeding, suggesting that care should be taken when extracting quantitative information about path-dependent quantities. The VRT maps were found to be useful for identifying regions of a mesh that were under-resolved for such Lagrangian studies, and for guiding the construction of more adequately resolved meshes.

Vessel surface reconstruction with a tubular deformable model

Three-dimensional (3-D) angiographic methods are gaining acceptance for evaluation of atherosclerotic disease. However, measurement of vessel stenosis from 3-D angiographic methods can be problematic due to limited image resolution and contrast. We present a method for reconstructing vessel surfaces from 3-D angiographic methods that allows for objective measurement of vessel stenosis. The method is a deformable model that employs a tubular coordinate system. Vertex merging is incorporated into the coordinate system to maintain even vertex spacing and to avoid problems of self-intersection of the surface. The deformable model was evaluated on clinical magnetic resonance (MR) images of the carotid (n = 6) and renal (n = 2) arteries, on an MR image of a physical vascular phantom and on a digital vascular phantom. Only one gross error occurred for all clinical images. All reconstructed surfaces had a realistic, smooth appearance. For all segments of the physical vascular phantom, vessel radii from the surface reconstruction had an error of less than 0.2 of the average voxel dimension. Variability of manual initialization of the deformable model had negligible effect on the measurement of the degree of stenosis of the digital vascular phantom.