Womersley number-based estimates of blood flow rate in Doppler analysis: in vivo validation by means of phase-contrast MRI

Quantifying CSF Dynamics disruption in idiopathic normal pressure hydrocephalus using phase lag between transmantle pressure and volumetric flow rate

Background and purpose

Idiopathic normal pressure hydrocephalus (iNPH) is a cerebrospinal fluid (CSF) dynamics disorder as evidenced by the delayed ascent of radiotracers over the cerebral convexity on radionuclide cisternography. However, the exact mechanism causing this disruption remains unclear. Elucidating the pathophysiology of iNPH is crucial, as it is a treatable cause of dementia. Improving the diagnosis and treatment prognosis rely on the better understanding of this disease. In this study, we calculated the pulsatile transmantle pressure and investigated the phase lag between this pressure and the volumetric CSF flow rate as a novel biomarker of CSF dynamics disruption in iNPH.

Methods

44 iNPH patients and 44 age- and sex-matched cognitively unimpaired (CU) control participants underwent MRI scans on a 3T Siemens scanner. Pulsatile transmantle pressure was calculated analytically and computationally using volumetric CSF flow rate, cardiac frequency, and aqueduct dimensions as inputs. CSF flow rate through the aqueduct was acquired using phase-contrast MRI. The aqueduct length and radius were measured using 3D T1-weighted anatomical images.

Results

Peak pressure amplitudes and the pressure load (integrated pressure exerted over a cardiac cycle) were similar between the groups, but the non-dimensionalized pressure load (adjusted for anatomical factors) was significantly lower in the iNPH group ( p < 0.001 , Welch's t-test). The phase lag between the pressure and the flow rate, arising due to viscous drag, was significantly higher in the iNPH group ( p < 0.001 ).

Conclusion

The increased phase lag is a promising new biomarker for quantifying CSF dynamics dysfunction in iNPH.

Statement of Significance

The exact mechanism causing the disruption of CSF circulation in idiopathic normal pressure hydrocephalus (iNPH) remains unclear. Elucidating the pathophysiology of iNPH is crucial, as it is a treatable cause of dementia. In this study, we provided an analytical and a computational method to calculate the pulsatile transmantle pressure and the phase lag between the pressure and the volumetric CSF flow rate across the cerebral aqueduct. The phase lag was significantly higher in iNPH patients than in controls and may serve as a novel biomarker of CSF dynamics disruption in iNPH.

Time-dependent simulation of blood flow through an abdominal aorta with iliac arteries

Atherosclerosis is one of the important diseases of the circulatory system because atherosclerotic plaques cause significant disruption of blood flow. Therefore, it is very important to properly understand these processes and skillfully simulate blood flow. In our work, we consider blood flow through an abdominal aorta with iliac arteries, assuming that the right iliac artery is narrowed by an atherosclerotic lesion. Blood flow is simulated using the laminar, standard k - ω and standard k - ϵ models. The obtained results show that despite the use of identical initial conditions, the distribution of velocity flow and wall shear stress depends on the choice of flow simulation model. For the k - ϵ model, we obtain higher values of speed and wall shear stress on atherosclerotic plaque than in the other two models. The laminar and k - ω models predict larger areas where reverse blood flow occurs in the area behind the atherosclerotic lesion. This effect is associated with negative wall shear stress. These two models give very similar results. The results obtained by us, and those reported in the literature, indicate that k - ω model is the most suitable for blood flow analysis.

Particle Image Velocimetry Evaluation of Hemodynamics Proximal to the Kissing Stent Configuration in the Aorto-Iliac Bifurcation

PURPOSE

The kissing stent (KS) method is low-risk compared with open surgery techniques. It is often used to treat aorto-iliac occlusive disease (AIOD). Deployment of the KS geometry has a high technical success rate. However, stent patency reduces in the first 5 years potentially due to deleterious flow behavior. Potentially harmful hemodynamics due to the KS were investigated in vitro.

METHODOLOGY

A compliant phantom of the aorto-iliac bifurcation was manufactured. Two surrogate stent-grafts were deployed into the phantom in the KS configuration to investigate effects of the presence of the stents, including the compliance mismatch they cause, on the hemodynamics proximal and distal to the KS. The investigation used pulsatile flow through a flow circuit to simulate abdominal aortic flow. Particle image velocimetry (PIV) was used to quantify the hemodynamics.

RESULTS

PIV identified peak proximal and distal velocity in vitro was 0.71 and 1.40m·s-1, respectively, which were within physiological ranges. Throughout systole, flow appeared normal and undisturbed. A lumen wall collapse in the sagittal plane formed during late systole and continued to early diastole proximal to the aorto-iliac bifurcation, distal to the inlet stent position. The wall collapse led to disturbed flow proximal to the stented region in early diastole producing potential recirculation zones and abnormal flow patterns.

CONCLUSION

The normal systolic flow behavior indicates the KS configuration is unlikely to cause an inflammatory response of the arterial walls. The collapse has not been previously identified and may potentially cause long-term patency reduction. It requires further investigation.

CLINICAL IMPACT

The role of this article is to provide further insight into the haemodynamic behavior through a stented aorto-iliac artery. The results of this investigation will improve the understanding of the effects that using the kissing stent method may have on a patient and help to identify high risk regions that may require more detailed monitoring. This paper also develops the in vitro modelling techniques that will enable further research that cannot be carried out within patients.

Hemolysis of red blood cells in blood vessels modeled via computational fluid dynamics

The research aims to verify the universal relationship between vessel shape and the risk of hemolysis using a rheological model of blood reflecting the physiological processes related to blood for any blood vessel. Blood is a multi-component fluid, the rheology of which depends on many factors, such as the concentration of red blood cells and local shear stress, which significantly affect the process of hemolysis. Blood rheology models used so far cannot be used for all flows and geometries. Therefore, a new rheology model has been introduced suitable for modeling hemolytic flows observed in arteries with atherosclerotic lesions in the in vivo environment. The previously presented model also has advantages in modeling local viscosity in stenosis. Geometries of the blood vessels from computed tomography scans and simplified models of the actual arteries observed during medical procedures were used in the calculations. Population Balance Based Rheology model predicts the concentration of single, deagglomerated red blood cells and the concentration and size of red blood cell agglomerates, which affect blood rheology and hemolysis. Based on the simulations carried out, a correlation was found between the shape of the vessel cavity and the risk of hemolysis. Presented results can be used in the future to create a correlation between the shape of the atherosclerotic lesions and the risk of hemolysis in the blood to make an initial risk assessment for a given patient.

Building Valveless Impedance Pumps From Biological Components: Progress and Challenges

Valveless pumping based on Liebau mechanism entails asymmetrical positioning of the compression site relative to the attachment sites of the pump's elastic segment to the rest of the circuit. Liebau pumping is believed to play a key role during heart development and be involved in several other physiological processes. Until now studies of Liebau pump have been limited to numerical analyses, in silico modeling, experiments using non-biological elements, and a few indirect in vivo measurements. This review aims to stimulate experimental efforts to build Liebau pumps using biologically compatible materials in order to encourage further exploration of the fundamental mechanisms behind valveless pumping and its role in organ physiology. The covered topics include the biological occurrence of Liebau pumps, the main differences between them and the peristaltic flow, and the potential uses and body sites that can benefit from implantable valveless pumps based on Liebau principle. We then provide an overview of currently available tools to build such pumps and touch upon limitations imposed by the use of biological components. We also talk about the many variables that can impact Liebau pump performance, including the concept of resonant frequencies, the shape of the flowrate-frequency relationship, the flow velocity profiles, and the Womersley numbers. Lastly, the choices of materials to build valveless impedance pumps and possible modifications to increase their flow output are briefly discussed.

Smart Blood Vessel Detection System for Laparoscopic Surgery

Objective: Compared with traditional surgery, laparoscopic surgery offers the advantages of smaller scars and rapid recovery and has gradually become popular. However, laparoscopic surgery has the limitation of low visibility and a lack of touch sense. As such, a physician may unexpectedly damage blood vessels, causing massive bleeding. In clinical settings, Doppler ultrasound is commonly used to detect vascular locations, but this approach is affected by the measuring angle and bone shadow and has poor ability to distinguish arteries from veins. To tackle these problems, a smart blood vessel detection system for laparoscopic surgery is proposed. Methods: Based on the principle of near-infrared spectroscopy, the proposed instrument can access hemoglobin (HbT) parameters at several depths simultaneously and recognize human tissue type by using a neural network. Results: Using the differences in HbT and StO₂ between different tissues, vascular and avascular locations can be recognized. Moreover, a mechanically rotatable stick enables the physician to easily operate in body cavities. Phantom and animal experiments were performed to validate the system’s performance. Conclusion: The proposed system has high ability to distinguish vascular from avascular locations at various depths.

Turbulent finite element model applied for blood flow calculation in arterial bifurcation

BACKGROUND AND OBJECTIVE

Due to the relatively low fluid velocities in major arteries and veins, blood flow is by default laminar, however, turbulence can occur as a result of stenosis or other obstacles. Hemodynamic parameters like Wall Shear Stress or Oscillatory Shear Index can be used for plaque formation prediction, and these parameters are depended on the nature of the flow. Implementation of the k-ω turbulent flow in the Finite Element solver aims to improve numerical analysis of cardio-vascular condition development and progression. Calculation of turbulent fluid flow in this paper is performed using a two-equation turbulent finite element model that can calculate values in the viscous sublayer.

METHODS

Implicit integration of the equations is used for determining the fluid velocity, turbulent kinetic energy and dissipation of turbulent kinetic energy. These values are calculated in the finite element nodes for each step of the incremental-iterative procedure. Developed turbulent finite element model with the customized generation of finite element meshes is used for calculating complex blood flow problems.

RESULTS

Turbulent model is verified on an example of fluid flow in the backward-facing step channel and analysis results correspond well with the experimental ones from the literature. Further, a turbulent model is applied for the simulation of blood flow through artery bifurcation. Verification of numerical examples obtained using different commercial software packages (Ansys, COMSOL Multiphysics) ensuring usage and accuracy of PAK in-house solver.

CONCLUSIONS

Analysis results show that turbulence cannot be neglected in the modelling of cardio-vascular conditions and that cardiologists can use the proposed tools and methods for investigating the hemodynamic conditions inside the bifurcation of arteries. Appropriate agreement between experimental results, and results obtained using commercial solutions and the k-ω turbulent flow in the Finite Element solver PAK, validate methodology presented in this paper. However, small deviations between the results underline the importance of the proper boundary condition prescription and mesh size and node distribution, which is also discussed in this paper. Due to the implicit integration implemented in PAK solver, time step size has an insignificant influence on the analysis results, assuming the initial time increments are sufficiently small to ensure proper discretization of velocity and pressure pulsatile functions.

Output of a valveless Liebau pump with biologically relevant vessel properties and compression frequencies

Liebau pump is a tubular, non-peristaltic, pulsatile pump capable of creating unidirectional flow in the absence of valves. It requires asymmetrical positioning of the pincher relative to the attachment sites of its elastic segment to the rest of the circuit. Biological feasibility of such valveless pumps remains a hotly debated topic. To test the feasibility of the Liebau-based pumping in vessels with biologically relevant properties we quantified the output of Liebau pumps with their  compliant segments made of a silicone rubber that mimicked the Young modulus of soft tissues. The lengths, the inner diameters, thicknesses of the tested compliant segments ranged from 1 to 5 cm, 3 to 8 mm and 0.3 to 1 mm, respectively. The compliant segment of the setup was compressed at 0.5–2.5 Hz frequencies using a 3.5-mm-wide rectangular piston. A nearest-neighbor tracking algorithm was used to track movements of 0.5-mm carbon particles within the system. The viscosity of the aqueous solution was varied by increased percentage of glycerin. Measurements yielded quantitative relationships between viscosity, frequency of compression and the net flowrate. The use of the Liebau principle of valveless pumping in conjunction with physiologically sized vessel and contraction frequencies yields flowrates comparable to peristaltic pumps of the same dimensions. We conclude that the data confirm physiological feasibility of Liebau-based pumping and warrant further testing of its mechanism using excised biological conduits or tissue engineered components. Such biomimetic pumps can serve as energy-efficient flow generators in microdevices or to study the function of embryonic heart during its normal development or in diseased states.

Hemodynamic Abnormalities in the Aorta of Turner Syndrome Girls

Congenital abnormalities in girls and women with Turner syndrome (TS), alongside an underlying predisposition to obesity and hypertension, contribute to an increased risk of cardiovascular disease and ultimately reduced life expectancy. We observe that children with TS present a greater variance in aortic arch morphology than their healthy counterparts, and hypothesize that their hemodynamics is also different. In this study, computational fluid dynamic (CFD) simulations were performed for four TS girls, and three age-matched healthy girls, using patient-specific inlet boundary conditions, obtained from phase-contrast MRI data. The visualization of multidirectional blood flow revealed an increase in vortical flow in the arch, supra-aortic vessels, and descending aorta, and a correlation between the presence of aortic abnormalities and disturbed flow. Compared to the relatively homogeneous pattern of time-averaged wall shear stress (TAWSS) on the healthy aortae, a highly heterogeneous distribution with elevated TAWSS values was observed in the TS geometries. Visualization of further shear stress parameters, such as oscillatory shear index (OSI), normalized relative residence time (RRTn), and transverse WSS (transWSS), revealed dissimilar heterogeneity in the oscillatory and multidirectional nature of the aortic flow. Taking into account the young age of our TS cohort (average age 13 ± 2 years) and their obesity level (75% were obese or overweight), which is believed to accelerate the initiation and progression of endothelial dysfunction, these findings may be an indication of atherosclerotic disease manifesting earlier in life in TS patients. Age, obesity and aortic morphology may, therefore, play a key role in assessing cardiovascular risk in TS children.

A surrogate model for plaque modeling in carotids based on Robin conditions calibrated by cine MRI data

We propose a surrogate model for the fluid-structure interaction (FSI) problem for the study of blood dynamics in carotid arteries in presence of plaque. This is based on the integration of a numerical model with subject-specific data and clinical imaging. We propose to model the plaque as part of the tissues surrounding the vessel wall through the application of an elastic support boundary condition. In order to characterize the plaque and other surrounding tissues, such as the close-by jugular vein, the elastic parameters of the boundary condition were spatially differentiated and their values were estimated by minimizing the discrepancies between computed vessel displacements and reference values obtained from CINE Magnetic Resonance Imaging data. We applied the model to three subjects with a degree of stenosis greater than 70%. We found that accounting for both plaque and jugular vein in the estimation of the elastic parameters increases the accuracy. In particular, in all patients, mismatches between computed and in vivo measured wall displacements were one to two orders of magnitude lower than the spatial resolution of the original MRI data. These results confirmed the validity of the proposed surrogate plaque model. We also compared fluid-dynamics results with those obtained in a fixed wall setting and in a full FSI model, used as gold standard, highlighting the better accordance of our results in comparison to the rigid ones.

Verification of the coupled-momentum method with Womersley's Deformable Wall analytical solution

In this paper, we perform a verification study of the Coupled-Momentum Method (CMM), a 3D fluid-structure interaction (FSI) model which uses a thin linear elastic membrane and linear kinematics to describe the mechanical behavior of the vessel wall. The verification of this model is done using Womersley's deformable wall analytical solution for pulsatile flow in a semi-infinite cylindrical vessel. This solution is, under certain premises, the analytical solution of the CMM and can thus be used for model verification. For the numerical solution, we employ an impedance boundary condition to define a reflection-free outflow boundary condition and thus mimic the physics of the analytical solution, which is defined on a semi-infinite domain. We first provide a rigorous derivation of Womersley's deformable wall theory via scale analysis. We then illustrate different characteristics of the analytical solution such as space-time wave periodicity and attenuation. Finally, we present the verification tests comparing the CMM with Womersley's theory.

Measurement of Wall Shear Stress Exerted by Flowing Blood in the Human Carotid Artery: Ultrasound Doppler Velocimetry and Echo Particle Image Velocimetry

Vascular endothelial cells lining the arteries are sensitive to wall shear stress (WSS) exerted by flowing blood. An important component of the pathophysiology of vascular diseases, WSS is commonly estimated by centerline ultrasound Doppler velocimetry (UDV). However, the accuracy of this method is uncertain. We have previously validated the use of a novel, ultrasound-based, particle image velocimetry technique (echo PIV) to compute 2-D velocity vector fields, which can easily be converted into WSS data. We compared WSS data derived from UDV and echo PIV in the common carotid artery of 27 healthy participants. Compared with echo PIV, time-averaged WSS was lower using UDV (28 ± 35%). Echo PIV revealed that this was due to considerable spatiotemporal variation in the flow velocity profile, contrary to the assumption that flow is steady and the velocity profile is parabolic throughout the cardiac cycle. The largest WSS underestimation by UDV was found during peak systole (118 ± 16%) and the smallest during mid-diastole (4.3± 46%). The UDV method underestimated WSS for the accelerating and decelerating systolic measurements (68 ± 30% and 24 ± 51%), whereas WSS was overestimated for end-diastolic measurements (-44 ± 55%). Our data indicate that UDV estimates of WSS provided limited and largely inaccurate information about WSS and that the complex spatiotemporal flow patterns do not fit well with traditional assumptions about blood flow in arteries. Echo PIV-derived WSS provides detailed information about this important but poorly understood stimulus that influences vascular endothelial pathophysiology.

Effect of organic and inorganic nitrates on cerebrovascular pulsatile power transmission in patients with heart failure and preserved ejection fraction

OBJECTIVE

Increased penetration of pulsatile power to the brain has been implicated in the pathogenesis of age-related cognitive dysfunction and dementia, a common comorbidity in patients with heart failure and preserved ejection fraction (HFpEF). However, there is a lack of knowledge on the effects of organic and inorganic nitrates administration in this population on the power carried by pressure and flow waves traveling through the proximal aorta and penetrating the carotid artery into the brain microvasculature.

APPROACH

We assessed aortic and carotid hemodynamics non-invasively in two sub-studies: (1) at baseline and after administration of 0.4 mg of sublingual nitroglycerine (an organic nitrate; n  =  26); and (2) in a randomized controlled trial of placebo (PB) versus inorganic nitrate administration (beetroot-juice (BR), 12.9 mmol NO₃; n  =  16).

MAIN RESULTS

Wave and hydraulic power analysis demonstrated that NTG increased total hydraulic power (from 5.68% at baseline to 8.62%, P  =  0.001) and energy penetration (from 8.69% to 11.63%; P  =  0.01) from the aorta to the carotid, while inorganic nitrate administration did not induce significant changes in aortic and carotid wave power (power: 5.49%PB versus 6.25%BR, P  =  0.49; energy: 8.89%PB versus 10.65%BR, P  =  0.27).

SIGNIFICANCE

Organic nitrates, but not inorganic nitrates, increase the amount of hydraulic energy transmitted into the carotid artery in subjects with HFpEF. These findings may have implications for the adverse effect profiles of these agents (such as the differential incidence of headaches) and for the pulsatile hemodynamic stress of the brain microvasculature in this patient population.

Effects of organic and inorganic nitrate on aortic and carotid haemodynamics in heart failure with preserved ejection fraction

AIMS

To assess the haemodynamic effects of organic vs. inorganic nitrate administration among patients with heart failure with preserved ejection fraction (HFpEF).

METHODS AND RESULTS

We assessed carotid and aortic pressure-flow relations non-invasively before and after the administration of 0.4 mg of sublingual nitroglycerin (n = 26), and in a separate sub-study, in response to 12.9 mmoL of inorganic nitrate (n = 16). Nitroglycerin did not consistently reduce wave reflections arriving at the proximal aorta (change in real part of reflection coefficient, 1st harmonic: -0.09; P = 0.01; 2nd harmonic: -0.045, P = 0.16; 3rd harmonic: +0.087; P = 0.05), but produced profound vasodilatation in the carotid territory, with a significant reduction in systolic blood pressure (133.6 vs. 120.5 mmHg; P = 0.011) and a marked reduction in carotid bed vascular resistance (19 580 vs. 13 078 dynes · s/cm⁵ ; P = 0.001) and carotid characteristic impedance (3440 vs. 1923 dynes · s/cm⁵ ; P = 0.002). Inorganic nitrate, in contrast, consistently reduced wave reflections across the first three harmonics (change in real part of reflection coefficient, 1st harmonic: -0.12; P = 0.03; 2nd harmonic: -0.11, P = 0.01; 3rd harmonic: -0.087; P = 0.09) and did not reduce blood pressure, carotid bed vascular resistance, or carotid characteristic impedance (P = NS).

CONCLUSIONS

Nitroglycerin produces marked vasodilatation in the carotid circulation, with a pronounced reduction in blood pressure and inconsistent effects on central wave reflections. Inorganic nitrate, in contrast, produces consistent reductions in wave reflections, and unlike nitroglycerin, it does so without significant hypotension or cerebrovascular dilatation. These haemodynamic differences may underlie the different effects on exercise capacity and side effect profile of inorganic vs. organic nitrate in HFpEF.

Investigation of Ultrasound-Measured Flow Velocity, Flow Rate and Wall Shear Rate in Radial and Ulnar Arteries Using Simulation

Parameters of blood flow measured by ultrasound in radial and ulnar arteries, such as flow velocity, flow rate and wall shear rate, are widely used in clinical practice and clinical research. Investigation of these measurements is useful for evaluating accuracy and providing knowledge of error sources. A method for simulating the spectral Doppler ultrasound measurement process was developed with computational fluid dynamics providing flow-field data. Specific scanning factors were adjusted to investigate their influence on estimation of the maximum velocity waveform, and flow rate and wall shear rate were derived using the Womersley equation. The overestimation in maximum velocity increases greatly (peak systolic from about 10% to 30%, time-averaged from about 30% to 50%) when the beam-vessel angle is changed from 30° to 70°. The Womersley equation was able to estimate flow rate in both arteries with less than 3% error, but performed better in the radial artery (2.3% overestimation) than the ulnar artery (15.4% underestimation) in estimating wall shear rate. It is concluded that measurements of flow parameters in the radial and ulnar arteries with clinical ultrasound scanners are prone to clinically significant errors.

Investigation of Ultrasound-Measured Flow Rate and Wall Shear Rate in Wrist Arteries Using Flow Phantoms

The aim of this study was to evaluate the errors in measurement of volumetric flow rate and wall shear rate measured in radial and ulnar arteries using a commercial ultrasound scanning system. The Womersley equations were used to estimate the flow rate and wall shear rate waveforms, based on the measured vessel diameter and centerline velocity waveform. In the experiments, each variable (vessel depth, diameter, flow rate, beam-vessel angle and different waveform) in the phantom was investigated in turn, and its value was varied within a normal range while others were fixed at their typical values. The outcomes revealed that flow rate and wall shear rate were overestimated in all cases, from around 13% to nearly 50%. It is concluded that measurements of flow rate and wall shear rate in radial and ulnar arteries with a clinical ultrasound scanner are vulnerable to overestimation.

The 'Sphere': A Dedicated Bifurcation Aneurysm Flow-Diverter Device

We present flow-based results from the early stage design cycle, based on computational modeling, of a prototype flow-diverter device, known as the 'Sphere', intended to treat bifurcation aneurysms of the cerebral vasculature. The device is available in a range of diameters and geometries and is constructed from a single loop of NITINOL^® wire. The 'Sphere' reduces aneurysm inflow by means of a high-density, patterned, elliptical surface that partially occludes the aneurysm neck. The device is secured in the healthy parent vessel by two armatures in the shape of open loops, resulting in negligible disruption of parent or daughter vessel flow. The device is virtually deployed in six anatomically accurate bifurcation aneurysms: three located at the Basilar tip and three located at the terminus bifurcation of the Internal Carotid artery (at the meeting of the middle cerebral and anterior cerebral arteries). Both steady state and transient flow simulations reveal that the device presents with a range of aneurysm inflow reductions, with mean flow reductions falling in the range of 30.6-71.8% across the different geometries. A significant difference is noted between steady state and transient simulations in one geometry, where a zone of flow recirculation is not captured in the steady state simulation. Across all six aneurysms, the device reduces the WSS magnitude within the aneurysm sac, resulting in a hemodynamic environment closer to that of a healthy vessel. We conclude from extensive CFD analysis that the 'Sphere' device offers very significant levels of flow reduction in a number of anatomically accurate aneurysm sizes and locations, with many advantages compared to current clinical cylindrical flow-diverter designs. Analysis of the device's mechanical properties and deployability will follow in future publications.

An ultrasound model to calculate the brain blood outflow through collateral vessels: a pilot study

Background

The quantification of the flow returning from the head through the cervical veins and the collaterals of the internal jugular vein (IJV), is becoming of prominent interest in clinical practice. We developed a novel model to calculate the cerebral venous return, normalized to the arterial inflow, in the different segments of the IJV.

Methods

We assessed, by established Echo Colour Doppler (ECD) methodology, the head inflow (HBinF) defined as the sum of common carotids and vertebral arteries, as well as the cerebral flow (CBF) defined as the sum of internal carotid and vertebral arteries. We also assessed the head outflow (HBoutF) defined as the sum of the measurements at the junction of the IJV and the vertebral veins. In addition, we also calculated the collateral flow index (CFI) by estimating the flow which re-enters directly into the superior vena cava as the amount of blood extrapolated by the difference between the HBinF and the HBoutF. We preliminarily tested the model by comparing ten healthy controls (HC) with ten patients affected by chronic cerebral spinal venous insufficiency (CCSVI), a condition characterized by some blockages in the IJV which are bypassed by collateral circulation.

Results

In HC the HBinF was 956+-105ml/min, whereas the HBoutF was > 90% of the HBinF, leading to a final CFI value of 1%. The last result shows that a very small amount of blood is drained by the collaterals. In upright we confirmed a reduction of the outflow through the IJV which increased CFI to 9%. When we applied the model to CCSVI, the HBinF was not significantly different from controls. In supine, the flow of CCSVI patients in the IJV junction was significantly lower (p < 0.001) while the correspondent CFI value significantly increased (61%, p < 0.0002).

Conclusions

Our preliminary application of the novel model in the clinical setting suggests the pivotal role of the collateral network in draining the blood into the superior vena cava under CCSVI condition.

Effect of velocity profile skewing on blood velocity and volume flow waveforms derived from maximum Doppler spectral velocity

Given evidence that fully developed axisymmetric flow may be the exception rather than the rule, even in nominally straight arteries, maximum velocity (V(max)) can lie outside the Doppler sample volume (SV). The link between V(max) and derived quantities, such as volume flow (Q), may therefore be more complex than commonly thought. We performed idealized virtual Doppler ultrasound on data from image-based computational fluid dynamics (CFD) models of the normal human carotid artery and investigated how velocity profile skewing and choice of sample volume affected V(max) waveforms and derived Q variables, considering common assumptions about velocity profile shape (i.e., Poiseuille or Womersley). Severe velocity profile skewing caused substantial errors in V(max) waveforms when using a small, centered SV, although peak V(max) was reliably detected; errors with a long SV covering the vessel diameter were orientation dependent but lower overall. Cycle-averaged Q calculated from V(max) was typically within ±15%, although substantial skewing and use of a small SV caused 10%-25% underestimation. Peak Q derived from Womersley's theory was generally accurate to within ±10%. V(max) pulsatility and resistance indexes differed from Q-based values, although the Q-based resistance index could be predicted reliably. Skewing introduced significant error into V(max)-derived Q waveforms, particularly during mid-to-late systole. Our findings suggest that errors in the V(max) and Q waveforms related to velocity profile skewing and use of a small SV, or orientation-dependent errors for a long SV, could limit their use in wave analysis or for constructing characteristic or patient-specific flow boundary conditions for model studies.