Towards a multi-physics modelling framework for thrombolysis under the influence of blood flow.

Thrombolytic therapy is an effective means of treating thromboembolic diseases but can also give rise to life-threatening side effects. The infusion of a high drug concentration can provoke internal bleeding while an insufficient dose can lead to artery reocclusion. It is hoped that mathematical modelling of the process of clot lysis can lead to a better understanding and improvement of thrombolytic therapy. To this end, a multi-physics continuum model has been developed to simulate the dissolution of clot over time upon the addition of tissue plasminogen activator (tPA). The transport of tPA and other lytic proteins is modelled by a set of reaction-diffusion-convection equations, while blood flow is described by volume-averaged continuity and momentum equations. The clot is modelled as a fibrous porous medium with its properties being determined as a function of the fibrin fibre radius and voidage of the clot. A unique feature of the model is that it is capable of simulating the entire lytic process from the initial phase of lysis of an occlusive thrombus (diffusion-limited transport), the process of recanalization, to post-canalization thrombolysis under the influence of convective blood flow. The model has been used to examine the dissolution of a fully occluding clot in a simplified artery at different pressure drops. Our predicted lytic front velocities during the initial stage of lysis agree well with experimental and computational results reported by others. Following canalization, clot lysis patterns are strongly influenced by local flow patterns, which are symmetric at low pressure drops, but asymmetric at higher pressure drops, which give rise to larger recirculation regions and extended areas of intense drug accumulation.

Hemodynamic changes in the femoral vein with increasing outflow resistance.

INTRODUCTION: In post-thrombotic and May-Thurner syndromes, the iliac veins may be scarred, compressed, or obstructed. Obesity and increased intra-abdominal pressure may also hamper the venous return. Therefore, measurements of outflow resistance (OR) impeding venous return may be helpful to select patients for intervention and to assess the impact of intervention. A proof-of-concept study is presented in healthy volunteers where OR is quantified using duplex assessment of the femoral vein (FV) at mid-thigh following predetermined inflation pressures with a high thigh tourniquet. METHODS: Twenty-two consecutive subjects (15 male) without evidence of venous disease by clinical and duplex examination were studied. Two male exclusions were due to bifid FVs. Median (range) baseline characteristics were age 30 years (24-57 years), height 173 cm (158-197 cm), weight 72 kg (50-97 kg), leg length 80 cm (74-94 cm), and FV diameter 11.2 mm (6.8-14.8 mm). Subjects were examined standing with the test leg nonweight-bearing, resting gently on the floor. A 26-cm-wide calf cuff was attached to an intermittent pneumatic compression device that delivered three compressions per minute at 120 mm Hg. A high thigh cuff, 12 cm wide, was inflated just before each calf compression in multiples of 20 mm Hg, from 0 to 120 mm Hg, to provide a standard OR. FV waveform parameters were recorded using duplex beneath each thigh-cuff inflation pressure and repeated three times. OR was calculated using change in pressure (P2-P1)/Flow (Q). Pressure P2 was 120 mm Hg minus the additional height to the duplex transducer. P1 was assumed to be zero. Flow was cross-sectional area (π × diameter [d](2)/4) × velocity. The velocity parameters chosen were peak velocity (PV), time-averaged mean velocity (TAMV), and TAMV from start to peak. RESULTS: Peak velocity, TAMV, and TAMV to peak all decreased significantly (P < .0005; Friedman) with increasing thigh cuff pressure with P < .0005 correlations (Spearman) of r = .842, r = .488, and r = .744, respectively. Furthermore, increasing thigh cuff pressure at 0, 20, 40, 60, 80, 100, and 120 mm Hg also caused a gradual and significant increase in median (interquartile range) OR at 27 (19-34), 30 (21-42), 30 (23-44), 40 (26-47), 46 (32-51), 61 (38-71), and 79 (45-134) resistance units, respectively (P < .0005; Friedman, and r = .516; Spearman). Higher baseline (innate) OR values were found in taller (P = .002) and heavier (P = .043) subjects. CONCLUSIONS: Hemodynamic velocity parameters in the femoral vein attenuate progressively with increasing venous obstruction. Outflow resistance (OR) can be quantified using duplex measurements when they are substituted into equations of fluid mechanics. Optimization of this novel technique, which requires an IPC outflow challenge test, may provide useful information in the assessment and treatment of patients.

Nitric oxide transport in an axisymmetric stenosis.

To test the hypothesis that disturbed flow can impede the transport of nitric oxide (NO) in the artery and hence induce atherogenesis, we used a lumen-wall model of an idealized arterial stenosis with NO produced at the blood vessel-wall interface to study the transport of NO in the stenosis. Blood flows in the lumen and through the arterial wall were simulated by Navier-Stokes equations and Darcy's Law, respectively. Meanwhile, the transport of NO in the lumen and the transport of NO within the arterial wall were modelled by advection-diffusion reaction equations. Coupling of fluid dynamics at the endothelium was achieved by the Kedem-Katchalsky equations. The results showed that both the hydraulic conductivity of the endothelium and the non-Newtonian viscous behaviour of blood had little effect on the distribution of NO. However, the blood flow rate, stenosis severity, red blood cells (RBCs), RBC-free layer and NO production rate at the blood vessel-wall interface could significantly affect the transport of NO. The theoretical study revealed that the transport of NO was significantly hindered in the disturbed flow region distal to the stenosis. The reduced NO concentration in the disturbed flow region might play an important role in the localized genesis and development of atherosclerosis.

MR phase-contrast velocity mapping methods for measuring venous blood velocity in the deep veins of the calf.

PURPOSE: To evaluate the feasibility of using un-gated, real-time MRI for venous blood velocity mapping in the calf, comparing an interleaved spiral k-space sequence (ISP) against a standard segmented gradient echo sequence (GRE). MATERIALS AND METHODS: A flow phantom with a variable flow-rate was scanned using both GRE and ISP sequences for an in vitro comparison. Seven subjects were scanned prone, performing metronome guided breathing, using the (externally triggered) segmented GRE and real-time ISP sequences. The segmented GRE acquisition duration was 2.5 mins (22 guided respiratory cycles) and the ISP sequence ran continuously for 35 s, 4 full guided respiratory cycles. Mean velocity from each of the deep veins was measured and peak mean velocity, peak flow rate and cumulative volume flow over a respiratory cycle compared between sequences. RESULTS: The two sequences compared well both in vitro and in vivo. The real-time ISP sequence showed short-term variations in mean velocity superimposed on the respiratory induced flow, which were averaged out using the segmented GRE sequence. CONCLUSION: Real-time ISP provides comparable time-averaged flow results to the standard sequence with additional information on real-time flow variations and so could be used for further investigation into venous blood flow in the lower leg.

MR image-based geometric and hemodynamic investigation of the right coronary artery with dynamic vessel motion.

The aim of this study was to develop a fully subject-specific model of the right coronary artery (RCA), including dynamic vessel motion, for computational analysis to assess the effects of cardiac-induced motion on hemodynamics and resulting wall shear stress (WSS). Vascular geometries were acquired in the right coronary artery (RCA) of a healthy volunteer using a navigator-gated interleaved spiral sequence at 14 time points during the cardiac cycle. A high temporal resolution velocity waveform was also acquired in the proximal region. Cardiac-induced dynamic vessel motion was calculated by interpolating the geometries with an active contour model and a computational fluid dynamic (CFD) simulation with fully subject-specific information was carried out using this model. The results showed the expected variation of vessel radius and curvature throughout the cardiac cycle, and also revealed that dynamic motion of the right coronary artery consequent to cardiac motion had significant effects on instantaneous WSS and oscillatory shear index. Subject-specific MRI-based CFD is feasible and, if scan duration could be shortened, this method may have potential as a non-invasive tool to investigate the physiological and pathological role of hemodynamics in human coronary arteries.

Stress phase angle depicts differences in coronary artery hemodynamics due to changes in flow and geometry after percutaneous coronary intervention.

The effects of changes in flow velocity waveform and arterial geometry before and after percutaneous coronary intervention (PCI) in the right coronary artery (RCA) were investigated using computational fluid dynamics. An RCA from a patient with a stenosis was reconstructed based on multislice computerized tomography images. A nonstenosed model, simulating the same RCA after PCI, was also constructed. The blood flows in the RCA models were simulated using pulsatile flow waveforms acquired with an intravascular ultrasound-Doppler probe in the RCA of a patient undergoing PCI. It was found that differences in the waveforms before and after PCI did not affect the time-averaged wall shear stress and oscillatory shear index, but the phase angle between pressure and wall shear stress on the endothelium, stress phase angle (SPA), differed markedly. The median SPA was -63.9 degrees (range, -204 degrees to -10.0 degrees ) for the pre-PCI state, whereas it was 10.4 degrees (range, -71.1 degrees to 25.4 degrees ) in the post-PCI state, i.e., more asynchronous in the pre-PCI state. SPA has been reported to influence the secretion of vasoactive molecules (e.g., nitric oxide, PGI(2), and endothelin-1), and asynchronous SPA ( approximately -180 degrees ) is proposed to be proatherogenic. Our results suggest that differences in the pulsatile flow waveform may have an important influence on atherogenesis, although associated with only minor changes in the time-averaged wall shear stress and oscillatory shear index. SPA may be a useful indicator in predicting sites prone to atherosclerosis.

Modelling in congenital heart disease. Art or science?

Despite the advances in imaging modalities and surgical techniques, the management of adults with congenital heart disease (ACHD) over the years has remained largely empirical rather than evidence-based. Animal models have been difficult to develop and very costly, while clinical trials are difficult to design and perform in ACHD, leaving gaps in our understanding of the pathophysiology and treatment of congenital heart disease. Disease modelling, both hypothetical and patient-specific, provides an alternative solution to many of these problems. Advances in cardiovascular imaging and diagnostics have led to the easy acquisition of large quantities of structural and functional information, which cannot be handled "intuitively". Computational modelling introduces mathematical rigour in the analysis and utilisation of these data by quantitative simulation and testing of clinically relevant hypotheses through experimentally validated models. Close multidisciplinary collaboration between bioengineers and clinicians is essential for transforming data and images derived from models of disease into clinically useful information.

Computational modeling of LDL and albumin transport in an in vivo CT image-based human right coronary artery.

Low wall shear stress (WSS) is implicated in endothelial dysfunction and atherogenesis. The accumulation of macromolecules is also considered as an important factor contributing to the development of atherosclerosis. In the present study, a fluid-wall single-layered model incorporated with shear-dependent transport parameters was used to investigate albumin and low-density lipoprotein (LDL) transport in an in vivo computed tomographic image-based human right coronary artery (RCA). In the fluid-wall model, the bulk blood flow was modeled by the Navier-Stokes equations, Darcy's law was employed to model the transmural flow in the arterial wall, mass balance of albumin and LDL was governed by the convection-diffusion mechanism with an additional reaction term in the wall, and the Kedem-Katchalsky equations were applied at the endothelium as the interface condition between the lumen and wall. Shear-dependent models for hydraulic conductivity and albumin permeability were derived from experimental data in literature to investigate the influence of WSS on macromolecular accumulation in the arterial wall. A previously developed so-called lumen-free time-averaged scheme was used to approximate macromolecular transport under pulsatile flow conditions. LDL and albumin accumulations in the subendothelial layer were found to be colocalized with low WSS. Two distinct mechanisms responsible for the localized accumulation were identified: one was insufficient efflux from the subendothelial layer to outer wall layers caused by a weaker transmural flow; the other was excessive influx to the subendothelial layer from the lumen caused by a higher permeability of the endothelium. The comparison between steady flow and pulsatile flow results showed that the dynamic behavior of the pulsatile flow could induce a wider and more diffuse macromolecular accumulation pattern through the nonlinear shear-dependent transport properties. Therefore, it is vital to consider blood pulsatility when modeling the shear-dependent macromolecular transport in large arteries. In the present study, LDL and albumin accumulations were observed in the low WSS regions of a human RCA using a fluid-wall mass transport model. It was also found that steady flow simulation could overestimate the magnitude and underestimate the area of accumulations. The association between low WSS and accumulation of macromolecules leading to atherosclerosis may be mediated through effects on transport properties and mass transport and is also influenced by flow pulsatility.

Effects of elastic compression stockings on wall shear stress in deep and superficial veins of the calf.

The purpose of this study was to estimate wall shear stress (WSS) in individual vessels of the venous circulation of the calf and quantify the effects of elastic compression based on change of vessel geometry and velocity waveform. The great saphenous vein and either a peroneal or posterior tibial vein have been imaged in four healthy subjects using magnetic resonance imaging, with and without the presence of a grade 1 medical stocking. Flow through image-based reconstructed geometries was numerically simulated for both a range of steady flow rates and ultrasound-derived transient velocity waveforms, scaled to give a standardized time averaged flow rate. For steady flow, the stocking produced an average percentage increase in mean WSS of approximately 100% in the great saphenous vein across a range of 0.125-1.25 ml/s. The percentage increase in the peroneal/posterior tibial veins varied from 490 to 650% across a range of 0.5-5 ml/s. In addition, application of the stocking eliminated periods of very low or zero flow from the transient waveforms. The average minimum value of WSS in all vessels without the stocking was <0.1 Pa. With the stocking, this was increased to 0.7 Pa in the great saphenous and 0.9 Pa in the peroneal/posterior tibial veins. The pathophysiological effects of these changes are discussed. In conclusion, the flight stocking was effective in raising venous WSS levels in prone subjects, and this effect was much more pronounced in the deep vessels. The stocking also tended to prevent cessation of flow during periods of increased downstream pressure produced by respiration.

Influence of pulsatile flow on LDL transport in the arterial wall.

The accumulation of low-density lipoprotein (LDL) is one of the important factors in atherogenesis. Two different time scales may influence LDL transport in vivo: (1) LDL transport is coupled to blood flow with a pulse cycle of around 1 s in humans; (2) LDL transport within the arterial wall is mediated by transmural flow in the order of 10(-8) m/s. Most existing models have assumed steady flow conditions and overlooked the interactions between physical phenomena with different time scales. The objective of this study was to investigate the influence of pulsatile flow on LDL transport and examine the validity of steady flow assumption. The effect of pulsatile flow on transmural transport was incorporated by using a lumen-free cyclic (LFC) and a lumen-free time-averaged (LFTA) procedures. It is found that the steady flow simulation predicted a focal distribution in the post-stenotic region, differing from the diffuse distribution pattern produced by the pulsatile flow simulation. The LFTA procedure, in which time-averaged shear-dependent transport properties calculated from instantaneous wall shear stress (WSS) were used, predicted a similar distribution pattern to the LFC simulations. We conclude that the steady flow assumption is inadequate and instantaneous hemodynamic conditions have important influence on LDL transmural transport in arterial geometries with disturbed and complicated flow patterns.

Role of MRI in investigating the effects of elastic compression stockings on the deformation of the superficial and deep veins in the lower leg.

PURPOSE: To evaluate the potential of MRI to investigate the mechanical effects of compression stockings on the veins of the lower limb. MATERIALS AND METHODS: The right calves of eight healthy volunteers were imaged in the prone position, with and without the presence of a compression stocking. Cross-sectional areas of all peroneal and posterior tibial veins, both saphenous veins, and any sufficiently large superficial veins were segmented in all subjects at mid-calf level in both cases. Variation in cross-sectional area along the axis of the great saphenous vein and a peroneal vein was also examined in three subjects. RESULTS: The mean cross-sectional area reduction was found to be greater in the deep veins (64%) than in the superficial veins (39%). Deep-vein cross-sections were generally elliptical, while superficial veins were approximately circular. Significant axial fluctuations were found in the cross-sectional areas. CONCLUSION: MRI offers a precise source of data on the mechanical effects of lower-limb compression. Ultrasound (US) may be more cost-effective, but the data acquired are less comprehensive. Future biomechanical studies of lower-limb compression should make use of MRI.

A computational study on the influence of catheter-delivered intravascular probes on blood flow in a coronary artery model.

Catheter-delivered intravascular probes are widely used in clinical practice to measure coronary arterial velocity and pressure, but the artefactual effect of the probe on the variables being measured is not well characterised. A coronary artery was simulated with a 180 degrees curved tube 3mm in diameter and the effect of catheters of different diameters was modelled numerically under pulsatile flow conditions. The presence of a catheter increased pressure by 1.3-4.3 mmHg depending on its diameter, and reduced velocity-pressure phase-lag. For an ultrasound sample volume 5mm downstream from the probe tip, the underestimation in velocity measurement attributed to catheter blockage is approximately 15-21% for an average inlet velocity of 0.1m/s. The velocity measurement error is lower at higher mean flow velocity. Accuracy of clinical velocity measurements could be improved by moving the sample volume farther downstream from the probe tip, because the centrifugal pressure gradient intrinsic to the curvature promotes re-development of flow.

3D geometric reconstruction of thoracic aortic aneurysms.

BACKGROUND: The thoracic aortic aneurysm (TAA) is a pathology that involves an expansion of the aortic diameter in the thoracic aorta, leading to risk of rupture. Recent studies have suggested that internal wall stress, which is affected by TAA geometry and the presence or absence of thrombus, is a more reliable predictor of rupture than the maximum diameter, the current clinical criterion. Accurate reconstruction of TAA geometry is a crucial step in patient-specific stress calculations. METHODS: In this work, a novel methodology was developed, which combines data from several sets of magnetic resonance (MR) images with different levels of detail and different resolutions. Two sets of images were employed to create the final model, which has the highest level of detail for each component of the aneurysm (lumen, thrombus, and wall). A reference model was built by using a single set of images for comparison. This approach was applied to two patient-specific TAAs in the descending thoracic aorta. RESULTS: The results of finite element simulations showed differences in stress pattern between the coarse and fine models: higher stress values were found with the coarse model and the differences in predicted maximum wall stress were 30% for patient A and 11% for patient B. CONCLUSION: This paper presents a new approach to the reconstruction of an aneurysm model based on the use of several sets of MR images. This enables more accurate representation of not only the lumen but also the wall surface of a TAA taking account of intraluminal thrombus.

Fluid-wall modelling of mass transfer in an axisymmetric stenosis: effects of shear-dependent transport properties.

Mechanical forces, such as low wall shear stress (WSS), are implicated in endothelial dysfunction and atherogenesis. The accumulation of low density lipoprotein (LDL) and hypoxia are also considered as main contributing factors in the development of atherosclerosis. The objective of this study was to investigate the influences of WSS on arterial mass transport by modelling the flow of blood and solute transport in the lumen and arterial wall. The Navier-Stokes equations and Darcy's Law were used to describe the fluid dynamics of the blood in the lumen and wall respectively. Convection-diffusion-reaction equations were used to model LDL and oxygen transport. The coupling of fluid dynamics and solute dynamics at the endothelium was achieved by the Kedem-Katchalsky equations. A shear-dependent hydraulic conductivity relation extracted from experimental data in the literature was employed for the transport of LDL and a shear-dependent permeability was used for oxygen. The integrated fluid-wall model was implemented in Comsol Multiphysics 3.2 and applied to an axisymmetric stenosis. The results showed elevated LDL concentration and reduced oxygen concentration in the subendothelial layer of the arterial wall in areas where WSS is low, suggesting that low WSS might be responsible for lipid accumulation and hypoxia in the arterial wall.

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.

Influence of head position on carotid hemodynamics in young adults.

Studies in adults have shown marked changes in geometry and relative positions of the carotid arteries when rotating the head. The aim of this study was to quantify the change in geometry and analyze its effect on carotid hemodynamics as a result of head rotation. The right carotid arteries of nine young adult subjects were investigated in supine position with straight and left turned head positions, respectively. The three-dimensional (3D) carotid geometry was reconstructed by using 3D ultrasound (3D US), and the carotid hemodynamics were calculated by combining 3D US with computational fluid dynamics. It was observed that cross-sectional areas and shapes did not change markedly with head rotation, but carotid vessel center lines altered with planarification of the common carotid artery as a main feature (P < 0.05). Measured common carotid flow rates changed significantly at the individual level when the head was turned, but on the average, the change in mean common carotid flow rate was relatively small (0.37 +/- 1.11 ml/s). The effect of the altered center lines and flow rates on the atherogenic nature of the carotid bifurcation was evaluated by using calculated hemodynamic wall parameters, such as wall shear stress (WSS) and oscillatory shear index (OSI). It was found that WSS and OSI patterns changed significantly with head rotation, but the variations were very subject dependent and could not have been predicted without assessing the altered geometry and flow of the carotid bifurcation for individual cases. This study suggests that there is a need for standardization of the choice of head position in the 3D US scan protocol, and that carotid stents and emboli diverters should be studied in different head positions.

MRI measurement of time-resolved wall shear stress vectors in a carotid bifurcation model, and comparison with CFD predictions.

PURPOSE: To study pulsatile fluid flow in a physiologically realistic model of the human carotid bifurcation, and to derive wall shear stress (WSS) vectors. MATERIALS AND METHODS: WSS vectors were calculated from time-resolved 3D phase-contrast (PC) MRI measurements of the velocity field. The technique was first validated with sinusoidal flow in a straight tube, and then used in a model of a healthy human carotid bifurcation. Velocity measurements in the inflow and outflow regions were also used as boundary conditions for computational fluid dynamics (CFD) calculations of WSS, which were compared with those derived from MRI alone. RESULTS: The straight tube measurements gave WSS results that were within 15% of the theoretical value. WSS results for the phantom showed the main features expected from fluid dynamics, notably the low values in the bulb region of the internal carotid artery, with a return to ordered flow further downstream. MRI was not able to detect the high WSS values along the divider wall that were predicted by the CFD model. Otherwise, there was good general agreement between MRI and CFD. CONCLUSION: This is the first report of time-resolved WSS vectors estimated from 3D-MRI data. The technique worked well except in regions of disturbed flow, where the combination with CFD modeling is clearly advantageous.

Quantitative comparison of CFD predicted and MRI measured velocity fields in a carotid bifurcation phantom.

Steady flow of a blood mimicking fluid in a physiologically realistic model of the human carotid bifurcation was studied using both magnetic resonance imaging (MRI) and computational fluid dynamics (CFD) modelling techniques. Quantitative comparisons of the 3D velocity field in the bifurcation phantom were made between phase contrast MRI measurements and CFD predictions. The geometry for the CFD model was reconstructed from T(1) weighted MR imaging of the test phantom. It was found that the predicted velocity fields were in fair agreement with MR measured velocities. In both the internal and external carotid arteries, the agreement between CFD predictions and MRI measurements was better along the inner-outer wall axis with a correlation factor C>0.897 (average 0.939) where the velocity profiles were skewed, than along the anterior-posterior axis (average correlation factor 0.876) where the velocity profiles were in M-shape.

Measurement of hemodynamics in human carotid artery using ultrasound and computational fluid dynamics.

The objective of the study was to investigate the feasibility of using computational fluid dynamic modeling (CFD) with noninvasive ultrasound measurements to determine time-variant three-dimensional (3D) carotid arterial hemodynamics in humans in vivo. The effects of hyperoxia and hypoxic hypercapnia on carotid artery local hemodynamics were examined by use of this approach. Six normotensive volunteers followed a double-blind randomized crossover design. Blood pressure, heart rate, and carotid blood flow were measured while subjects breathed normal air, a mixture of 5% CO(2) and 15% O(2) (hypoxic hypercapnia), and 100% O(2) (hyperoxia). Carotid artery geometry was reconstructed on the basis of B-mode ultrasound images by using purpose-built image processing software. Time-variant 3D carotid hemodynamics were estimated by using finite volume-based CFD. Systemic blood pressure was not significantly affected by hyperoxia or hypoxic hypercapnia, but heart rate decreased significantly with hyperoxia. There was an increase in diastolic flow velocity in the external carotid artery after hypoxic hypercapnia, but otherwise carotid blood flow velocities did not change significantly. Compared with normal air, hyperoxic conditions were associated with a decrease in the width of the region of flow separation in the external carotid artery. During hyperoxia, there was also an increase in the minimum and a decrease in maximum shear stress in the bifurcation and hence a reduction in cyclic variation in shear stress. Hypoxic hypercapnia was associated with a reduced duration of flow separation in the external carotid artery and an increase in the minimum shear stress without affecting the cyclic variation in shear stress. This study demonstrates the feasibility of using noninvasive ultrasound techniques in conjunction with CFD to describe time-variant 3D hemodynamics in the human carotid arterial bifurcation in vivo.