Haemodynamics and blood flow measured using ultrasound imaging.

Visualization of, and measurements related to, haemodynamic phenomena in arteries may be made using ultrasound systems. Most ultrasound technology relies on simple measurements of blood velocity taken from a single site, such as the peak systolic velocity for assessment of the degree of lumen reduction caused by an arterial stenosis. Real-time two-dimensional (2D) flow field visualization is possible using several methods, such as colour flow, blood flow imaging, and echo particle image velocimetry; these have applications in the examination of the flow field in diseased arteries and in heart chambers. Three-dimensional (3D) and four-dimensional ultrasound systems have been described. These have been used to provide 2D velocity profile data for the estimation of volumetric flow. However, they are limited for haemodynamic evaluation in that they provide only one component of the velocity. The provision of all seven components (three space, three velocity, and one time) is possible using image-guided modelling, in which 3D ultrasound is combined with computational fluid dynamics. This method also allows estimation of turbulence data and of relevant quantities such as the wall shear stress.

Fluid-structure interaction in axially symmetric models of abdominal aortic aneurysms.

Abdominal aortic aneurysm disease progression is probably influenced by tissue stresses and blood flow conditions and so accurate estimation of these will increase understanding of the disease and may lead to improved clinical practice. In this work the blood flow and tissue stresses in axially symmetric aneurysms are calculated using a complete fluid-structure interaction as a benchmark for calculating the error introduced by simpler calculations: rigid walled for the blood flow, homogeneous pressure for the tissue stress, as well as one-way-coupled interactions. The error in the peak von Mises stress in a homogeneous pressure calculation compared with a fluid-structure interaction calculation was less than 3.5 per cent for aneurysm diameters up to 7 cm. The error in the mean wall shear stress, in a rigid-walled calculation compared with a fluid-structure interaction calculation, varied from 30 per cent to 60 per cent with increasing aneurysm diameter. These results suggest that incorporation of the fluid-structure interaction is unnecessary for purely mechanical modelling, with the aim of evaluating the current rupture probability. However, for more complex biological modelling, perhaps with the aim of predicting the progress of the disease, where accurate estimation of the wall shear stress is essential, some form of fluid-structure interaction is necessary.

Numerical analysis of pulsatile blood flow and vessel wall mechanics in different degrees of stenoses.

Hemodynamics factors and biomechanical forces play key roles in atherogenesis, plaque development and final rupture. In this paper, we investigated the flow field and stress field for different degrees of stenoses under physiological conditions. Disease is modelled as axisymmetric cosine shape stenoses with varying diameter reductions of 30%, 50% and 70%, respectively. A simulation model which incorporates fluid-structure interaction, a turbulence model and realistic boundary conditions has been developed. The results show that wall motion is constrained at the throat by 60% for the 30% stenosis and 85% for the 50% stenosis; while for the 70% stenosis, wall motion at the throat is negligible through the whole cycle. Peak velocity at the throat varies from 1.47 m/s in the 30% stenosis to 3.2m/s in the 70% stenosis against a value of 0.78 m/s in healthy arteries. Peak wall shear stress values greater than 100 Pa were found for > or =50% stenoses, which in vivo could lead to endothelial stripping. Maximum circumferential stress was found at the shoulders of plaques. The results from this investigation suggest that severe stenoses inhibit wall motion, resulting in higher blood velocities and higher peak wall shear stress, and localization of hoop stress. These factors may contribute to further development and rupture of plaques.

Anatomical flow phantoms of the nonplanar carotid bifurcation, part II: experimental validation with Doppler ultrasound.

A nonplanar wall-less anatomical flow phantom of a healthy human carotid artery is described, the construction of which is based on a lost-core technique described in the companion paper (Part I) by . The core was made by rapid prototyping of an idealized three-dimensional computer model of the carotid artery. Flow phantoms were built using these idealized non planar carotid artery bifurcations. Physiologically realistic flow waveforms were produced with resistance index values of 0.75, 0.72 and 0.63 in the common, external and internal carotid artery branches, respectively. Distension of the common carotid using M-mode imaging was found to be at 10% of diameter. Although differences in vessel diameter between the phantom and that of the original computer model were statistically significant (p < 0.05), there was no difference (p > 0.05) in measurements made on the lost-cores and those obtained by B-mode ultrasound on the resulting flow phantoms. In conclusion, it was possible to reliably reproduce geometrically similar anatomical flow phantoms that are capable of producing realistic physiological flow patterns and distensions.

Anatomical flow phantoms of the nonplanar carotid bifurcation, part I: computer-aided design and fabrication.

Doppler ultrasound is widely used in the diagnosis and monitoring of arterial disease. Current clinical measurement systems make use of continuous and pulsed ultrasound to measure blood flow velocity; however, the uncertainty associated with these measurements is great, which has serious implications for the screening of patients for treatment. Because local blood flow dynamics depend to a great extent on the geometry of the affected vessels, there is a need to develop anatomically accurate arterial flow phantoms with which to assess the accuracy of Doppler blood flow measurements made in diseased vessels. In this paper, we describe the computer-aided design and manufacturing (CAD-CAM) techniques that we used to fabricate anatomical flow phantoms based on images acquired by time-of-flight magnetic resonance imaging (TOF-MRI). Three-dimensional CAD models of the carotid bifurcation were generated from data acquired from sequential MRI slice scans, from which solid master patterns were made by means of stereolithography. Thereafter, an investment casting procedure was used to fabricate identical flow phantoms for use in parallel experiments involving both laser and Doppler ultrasound measurement techniques.

Finite element analysis to investigate variability of MR elastography in the human thigh.

PURPOSE: To develop finite element analysis (FEA) of magnetic resonance elastography (MRE) in the human thigh and investigate inter-individual variability of measurement of muscle mechanical properties. METHODS: Segmentation was performed on MRI datasets of the human thigh from 5 individuals and FEA models consisting of 12 muscles and surrounding tissue created. The same material properties were applied to each tissue type and a previously developed transient FEA method of simulating MRE using Abaqus was performed at 4 frequencies. Synthetic noise was applied to the simulated data at various levels before inversion was performed using the Elastography Software Pipeline. Maps of material properties were created and visually assessed to determine key features. The coefficient of variation (CoV) was used to assess the variability of measurements in each individual muscle and in the groups of muscles across the subjects. Mean measurements for the set of muscles were ranked in size order and compared with the expected ranking. RESULTS: At noise levels of 2% the CoV in measurements of |G*| ranged from 5.3 to 21.9% and from 7.1 to 36.1% for measurements of ϕ in the individual muscles. A positive correlation (R2 value 0.80) was attained when the expected and measured |G*| ranking were compared, whilst a negative correlation (R2 value 0.43) was found for ϕ. CONCLUSIONS: Created elastograms demonstrated good definition of muscle structure and were robust to noise. Variability of measurements across the 5 subjects was dramatically lower for |G*| than it was for ϕ. This large variability in ϕ measurements was attributed to artefacts.

Design and characterisation of a wall motion phantom.

Arterial wall motion is an essential feature of a healthy cardiovascular system and it is known that wall motion is affected by age and disease. In recent years, methods have been developed for measurement of wall motion with the intention of providing diagnostically useful information. An issue with all of these techniques is the accuracy and variability of both wall motion and derived quantities such as elasticity, which requires the development of suitable test tools. In this paper, a vessel wall phantom is described for use in ultrasound studies of wall motion. The vessel was made from polyvinyl alcohol (PVA) subjected to a freeze-thaw process to form a cryogel (PVA-C). The elastic modulus, acoustic velocity and attenuation coefficient varied from 57 kPa, 1543 m s(-1) and 0.18 dB cm(-1) MHz(-1) for one freeze-thaw cycle to 330 kPa, 1583 m s(-1) and 0.42 dB cm(-1) MHz(-1) for 10 freeze-thaw cycles. Wall motion was effected by the use of pulsatile flow produced from a gear pump. The use of a downstream flow resistor removed gross distortions in the wall motion waveform, possibly by removal of reflected pressure waves. However, a low amplitude 20 Hz oscillation remained, which is unphysiologic and thought to be caused by the vibration of the distended PVA-C vessel.

The simulation of magnetic resonance elastography through atherosclerosis.

The clinical diagnosis of atherosclerosis via the measurement of stenosis size is widely acknowledged as an imperfect criterion. The vulnerability of an atherosclerotic plaque to rupture is associated with its mechanical properties. The potential to image these mechanical properties using magnetic resonance elastography (MRE) was investigated through synthetic datasets. An image of the steady state wave propagation, equivalent to the first harmonic, can be extracted directly from finite element analysis. Inversion of this displacement data yields a map of the shear modulus, known as an elastogram. The variation of plaque composition, stenosis size, Gaussian noise, filter thresholds and excitation frequency were explored. A decreasing mean shear modulus with an increasing lipid composition was identified through all stenosis sizes. However the inversion algorithm showed sensitivity to parameter variation leading to artefacts which disrupted both the elastograms and quantitative trends. As noise was increased up to a realistic level, the contrast was maintained between the fully fibrous and lipid plaques but lost between the interim compositions. Although incorporating a Butterworth filter improved the performance of the algorithm, restrictive filter thresholds resulted in a reduction of the sensitivity of the algorithm to composition and noise variation. Increasing the excitation frequency improved the techniques ability to image the magnitude of the shear modulus and identify a contrast between compositions. In conclusion, whilst the technique has the potential to image the shear modulus of atherosclerotic plaques, future research will require the integration of a heterogeneous inversion algorithm.

Recent developments in vascular ultrasound technology.

This article describes four technologies relevant to vascular ultrasound which are available commercially in 2015, and traces their origin back through the research literature. The technologies are 3D ultrasound and its use in plaque volume estimation (first described in 1994), colour vector Doppler for flow visualisation (1994), wall motion for estimation of arterial stiffness (1968), and shear wave elastography imaging of the arterial wall (2010). Overall these technologies have contributed to the understanding of vascular disease but have had little impact on clinical practice. The basic toolkit for vascular ultrasound has for the last 25 years been real-time B-mode, colour flow and spectral Doppler. What has changed over this time is improvement in image quality. Looking ahead it is noted that 2D array transducers and high frame rate imaging continue to spread through the commercial vascular ultrasound sector and both have the potential to impact on clinical practice.

A Protocol for Improved Measurement of Arterial Flow Rate in Preclinical Ultrasound.

PURPOSE: To describe a protocol for the measurement of blood flow rate in small animals and to compare flow rate measurements against measurements made using a transit time flowmeter. MATERIALS AND METHODS: Measurements were made in rat and mice using a Visualsonics Vevo 770 scanner. The flow rate in carotid and femoral arteries was calculated from the time-average maximum velocity and vessel diameter. A correction factor was applied to correct for the overestimation of velocity arising from geometric spectral broadening. Invasive flow rate measurements were made using a Transonics system. RESULTS: Measurements were achieved in rat carotid and femoral arteries and in mouse carotid arteries. Image quality in the mouse femoral artery was too poor to obtain diameter measurements. The applied correction factor in practice was 0.71-0.77. The diameter varied by 6-18% during the cardiac cycle. There was no overall difference in the flow rate measured using ultrasound and using transit-time flowmeters. The flow rates were comparable with those previously reported in the literature. There was wide variation in flow rates in the same artery in individual animals. Transit-time measurements were associated with changes of a factor of 10 during the typical 40 min measurement period, associated with probe movement, vessel spasm, vessel kinking and other effects. CONCLUSION: A protocol for the measurement of flow rate in arteries in small animals has been described and successfully used in rat carotid and femoral arteries and in mouse carotid arteries. The availability of a noninvasive procedure for flow rate measurement avoids the problems with changes in flow associated with an invasive procedure.

A computer controlled flow phantom for generation of physiological Doppler waveforms.

A flow phantom for the generation of physiological Doppler waveforms is described. The suspension of scattering particles is driven by a gear pump powered by a stepping motor. The speed of the stepping motor is controlled by a BBC microcomputer. The waveform shape is selected from a library of waveforms from disc. Use of the microcomputer allows the waveform shape and mean flow to be easily changed. Sephadex particles suspended in a solution of glycerol were used as artificial blood. Thin walled heat shrink tubing which had been moulded around metal rods was used. Distortions in the waveforms caused by reflections from the end of the tubing were largely removed by reducing the pipe diameter to half of its value for 30 cm from the end of the pipe. There was good agreement between the control waveforms and the Doppler waveforms over a wide range of waveform pulsatility.

Quantitative analysis of PC MRI velocity maps: pulsatile flow in cylindrical vessels.

The accuracy of MR phase contrast (PC) velocity mapping, and the subsequent derivation of wall shear stress (WSS) values, has been quantitatively assessed. Using a retrospectively gated PC gradient-echo technique, the temporal-spatial velocity fields were measured for pulsatile flow in a rigid cylindrical vessel. The experimental data were compared with values derived from the Womersley solution of the Navier-Stokes equations. For a sinusoidal waveform, the overall root-mean-square (rms) difference between the measured and analytical velocities corresponded to 13% of the peak fluid velocity. The WSS derived from the data displayed a 14% rms difference with the analytical model. As an example of a more complicated flow, a triangular saw-tooth waveform was deconstructed into its Fourier components. Velocity maps and the WSS were calculated by the superposition of the individual solutions, weighted by the Fourier series coefficient, for each harmonic. The velocity and experimentally derived WSS agreed with the analytical results (4% and 12% rms difference, respectively). Evaluation of the analytical models allowed an estimate of the inherent accuracy in the measurement of velocity maps and WSS values.

Clinical trial of umbilical artery Doppler waveform quality indices.

The ability of two Doppler waveform quality indices to discriminate between high- and low-quality waveforms was tested using 427 sets of umbilical artery Doppler waveforms from patients. The waveforms had been acquired using a 4-MHz continuous-wave Doppler unit. The quality indices (QI) were based on an assessment of the degree of noise of the maximum frequency envelope of the waveforms, and were first a correlation between successive waveform envelopes (QI1), and, second, a sum of local linearity measures (QI2). The sets of waveforms were graded subjectively according to the clarity of the outline of the waveforms, the degree of interference in the region of the spectrum above the outline, and in terms of the degree of variability caused by fetal breathing. At 90% sensitivity for detection of low-quality waveforms according to a high envelope clarity score, the specificities were 68.2% and 52.7%, respectively, for QI1 and QI2. QI1 was independent from pulsatility index and waveform length, but showed strong dependence on fetal breathing. QI2 showed strong independence from pulsatility and fetal breathing and reasonable independence from waveform length. Both QI1 and QI2 performed poorly when there was a large degree of noise in the region of the spectrum above the envelope; however, this poor performance was often related to the inability of the maximum frequency follower to estimate correctly the maximum frequency envelope in those conditions so that the high waveform quality values reflected the erroneous calculation of pulsatility index in those cases.

An investigation of simulated umbilical artery Doppler waveforms. II. A comparison of three Doppler waveform quality indices.

Three Doppler waveform quality indices based upon assessment of the noise of the maximum frequency envelope of simulated umbilical artery waveforms were investigated. These indices were: an estimate of the correlation between successive waveforms (QI1), a local linearity measure (QI2) and a ratio of two regions of the Fourier transform amplitude spectrum of the maximum frequency envelope (QI3). Simulated umbilical artery waveforms were acquired from a physiological flow phantom. A test population was used consisting of a large number of waveforms where one of three physical variables had been adjusted to produce waveforms of varying quality. These three physical variables were: beam-vessel angle, beam-vessel axial misalignment and attenuator thickness. For this group of waveforms the accuracy of estimation of the maximum frequency envelope and pulsatility index (PI) were known. All three quality indices gave good separation of high- and low-quality waveforms based upon threshold values of the accuracy of PI and maximum frequency envelope. The dependence of each quality index on fetal breathing, waveform length and waveform pulsatility was investigated. QI2, the local linearity measure, showed most promise in its independence from these variables.

Choice of moving target for a string phantom: I. Measurement of filament backscatter characteristics.

Detected back-scattered Doppler signal level was measured from the following filaments: braided silk filaments, nylon and O-ring rubber. The detected signal level fell with time from the point of immersion by 45-85% for the silk filaments and by 50% for the nylon, but did not change for the O-ring rubber. For all of the silk filaments there were strong backscatter peaks at Doppler angles varying from 55-80 degrees for a transmit frequency of 4 MHz. Nylon demonstrated a large peak at 90 degrees, whereas there was no large backscatter peak present for O-ring rubber. The paper concludes that the use of braided filaments for the assessment of the accuracy of Doppler estimated velocity may lead to errors if the angular backscattered peak is very strong. O-ring rubber may be suitable for the testing of Doppler-estimated velocity.

Choice of moving target for a string phantom: II. On the performance testing of Doppler ultrasound systems.

A string phantom was used to test a duplex system using several filaments: braided silk, nylon and O-ring rubber. The estimated pulsatility index was identical for all filaments tested. Range gate registration measurements were identical for all filaments tested. Maximum velocity was underestimated in the region of a strong angular backscatter peak; this was the case for several of the braided silk filaments. This effect was not observed for O-ring rubber. The paper concluded that O-ring rubber is a suitable filament for the testing of several key Doppler quantities. Recalibration of the string phantom velocity indicator is necessary due to the large diameter of the O-ring rubber.

An investigation of simulated umbilical artery Doppler waveforms. III. The effect of noise reduction algorithms on the maximum frequency envelope and on the pulsatility index.

The effect of two noise reduction algorithms on the accuracy of estimation of the maximum frequency envelope and pulsatility index (PI) of simulated umbilical artery Doppler waveforms was investigated. The algorithms were: first, smoothing of the envelope from unfiltered Doppler spectra using a double window modified trimmed mean (DWMTM) filter and second, speckle and noise reduction of the Doppler spectrum using an image processing method. The test population consisted of waveforms were the degree of beam-vessel misalignment had been varied. The accuracy of estimation of the maximum frequency envelope and the PI was calculated by comparing each set of waveforms with the gold-standard maximum frequency envelope from the ensemble averaged waveform obtained with no misalignment. Speckle reduction gave rise to PI values that were low by approximately 0.1 (3%-4%). When there was no background noise present the improvements in envelope estimation were factors of 1.27 and 1.24, respectively, for the DWMTM method and the spectral filter, whereas the factors were 1.56 and 2.07 when background noise was present. For estimation of PI the DWMTM filter was superior. For no background noise the DWMTM filter gave a factor of 3.36 improvement whereas there was no improvement with the spectral filter. When background noise was present the factors for improvement in PI estimation were 2.39 and 4.16.

A comparison of single- and dual-beam methods for maximum velocity estimation.

The purpose of this study was to compare the precision and accuracy of maximum velocity estimation when the target direction is known (a string phantom), and when the target direction is unknown (a flow model of arterial stenosis with stenoses of 0-80% by area). Maximum velocity was estimated using single- and dual-beam methods. A linear-array system was used to acquire Doppler spectra from a single-beam direction. The same array was used for sequential acquisition of Doppler spectra from 2 beam directions; the velocity estimates from these were then compounded in a vector manner. The variation of estimated maximum velocity with beam-string angle over the range 40-80 degrees was 27% for conventional Doppler, 2.6% for angle correction from the edge of the array and 1.6% for the vector Doppler. In the stenosis model, for the single-beam methods, the highest frequency shift was obtained just prior to the point of minimum lumen. At this location, the variation with beam-vessel angle over the range 40-80 degrees was 35% for conventional Doppler, 7.4% for the correction factor method and 6.9% for correction from the edge of the array. For the vector method, the maximum velocity is obtained from within the poststenotic jet, the variation was 2% over the range 40-80 degrees. It is recommended that existing Doppler systems use the correction-factor method to reduce variation in measured maximum velocity. The use of the vector technique by future generations of Doppler systems may lead to angle-independent velocity estimation.

Peak velocity estimation in arterial stenosis models using colour vector Doppler.

Maximum velocity as measured from spectral Doppler is dependent on the angle theta between the bean and the direction of motion of blood. The Doppler shift is dependent on the velocity component in the direction of the ultrasound beam, hence theta cannot be determined accurately. These factors produce errors in the estimation of arterial stenosis from velocity. In this study, a 2D colour vector Doppler technique was tested using a flow model with simulated arterial stenoses. Colour-flow images obtained from different bean directions were compounded, giving estimates of velocity magnitude and angle. The maximum velocity magnitude increased with the degree of stenosis, and there was no dependence on the beam-vessel angle. This technique does not require manual entry of beam-vessel angle, nor does it have the angle dependence associated with spectral estimation of maximum velocity. This may help reduce the errors in assessment of arterial stenosis.

An investigation of simulated umbilical artery Doppler waveforms. I. The effect of three physical parameters on the maximum frequency envelope and on pulsatility index.

The effect of three physical parameters on the accuracy of estimation of the maximum frequency envelope and pulsatility index (PI) of simulated umbilical artery Doppler waveforms was investigated. The physical parameters were beam-vessel angle, the offset between the beam axis and vessel axis, and the thickness of overlying attenuating material. Waveforms were acquired using a physiological flow phantom. The maximum frequency envelope was calculated using a threshold maximum frequency follower which was adaptive to the level of background noise. A gold standard maximum frequency envelope was obtained from the ensemble averaged waveform when there was alignment of beam and vessel axis, a 50 degrees beam-vessel angle and 2 cm of attenuating material. Indices of bias, variability and accuracy of estimation of the maximum frequency envelope and PI were calculated by comparing subsequent maximum frequency envelopes with the gold standard maximum frequency envelope. Both the maximum frequency envelope and PI were estimated to a similar degree of accuracy over a wide range of physical conditions. In this study, the error in PI was less than 0.15 for beam-vessel angles less than 80 degrees, for beam-vessel axis offset distances less than 7.5 mm, at a transducer-vessel distance of 5 cm, and for attenuator thicknesses less than 4.5 cm. The percentage root-mean square error for estimation of the maximum frequency envelope was approximately 10% or less for beam-vessel angles less than 75 degrees, for beam-vessel axis offset distances less than 7.5 mm, and for attenuator thicknesses less than 4 cm.