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.

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.

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.

Measurement of arterial stiffness in subjects with vascular disease: Are vessel wall changes more sensitive than increase in intima-media thickness?

BACKGROUND AND AIMS: It is widely accepted that subjects with vascular disease have increased arterial stiffness and intima-media thickness (IMT) when compared with healthy controls. The aim of this study was to investigate indices of arterial stiffness and IMT in the common carotid arteries (CCAs) of subjects with and without peripheral arterial disease (PAD), in order to look for evidence of change in wall quality and quantity to explain increased stiffness that has been found in the arteries of subjects with vascular disease. METHODS AND RESULTS: The arterial distension waveform (ADW), IMT, diameter and brachial blood pressure were measured to calculate Young's Modulus (E) and elastic modulus (Ep) in the common carotid arteries of subjects with and without PAD. 38 subjects with confirmed PAD were compared with 43 normal controls matched for age, sex, smoking and hypertension. The mean diameter (8.35mm [95% CI 7.93-8.77] vs. 6.93mm [6.65-7.20] P<0.001, increase 20%), IMT (0.99mm [0.92-1.07] vs. 0.88mm [0.82-0.93] P=0.020, increase 12.5%), Ep (315kPa [185-444] vs. 190kPa [164-216] P=0.034, increase 66%) and E (1383kPa [836-1930] vs. 744kPa [641-846] P=0.006, increase 86%) were all significantly higher in subjects with PAD. CONCLUSIONS: This study suggests that increased stiffness observed in subjects with peripheral vascular disease is a result of change in both quantity and quality of the arterial wall. Changes in indices of arterial stiffness were much higher than changes in IMT and diameter. These preliminary observations may be an indication that indices of arterial stiffness are a sensitive early marker of atherosclerosis.

Three-dimensional imaging and computational modelling for estimation of wall stresses in arteries.

The paper reviews techniques for the estimation of wall stresses in arterial disease. Wall stresses are important as arterial disease progresses through a complex interplay between local biology and local mechanical stresses. The possibility then arises of using wall stresses as new diagnostic indicators in patients with arterial disease. Estimation of wall stresses using imaging systems is problematic. Developments in the last 10 years have been aimed at providing tools for estimation of wall stresses within individual patients, using a combination of three-dimensional (3D) imaging and computational modelling. For blood flow, 3D arterial lumen information is obtained from 3D imaging. Computational fluid dynamics is then used to estimate the 3D velocity field within the lumen, from which wall shear stress may be calculated. For arterial mechanics, the 3D arterial wall geometry is integrated with solid modelling to provide estimates of the strain field and stress field within the artery wall. For intraplaque stresses, this has been achieved through the use of detailed two-dimensional (2D) intraplaque geometry from MRI. Inverse techniques have been used to provide images of Young's modulus in atherosclerotic plaque using intravascular ultrasound and solid modelling. Several research centres now have processing chains to allow this technology to be used in clinical studies. In time, possibly over the next 10 years or so, robust protocols with proven clinical utility will arise which, when combined with high-performance computing, will allow image-guided modelling to be used as an adjunct to modern radiology in the same way that image-processing tools are used today.

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 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.

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.

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.

Angle-dependence and reproducibility of dual-beam vector doppler ultrasound in the common carotid arteries of normal volunteers.

Dual-beam vector Doppler has the potential to improve peak systolic blood velocity measurement accuracy by automatically correcting for the beam-flow Doppler angle. Using a modified linear-array system with a split receive aperture, we have assessed the angle-dependence over Doppler angles of 40 degrees -70 degrees and the reproducibility of the dual-beam blood maximum velocity estimate measured in the common carotid arteries (CCA) 1 to 2 cm prior to the bifurcation of 9 presumed-healthy volunteers. The velocity magnitude estimate was reduced by approximately 7.9% as the angle between the transmit beam and the vessel axis was increased from 40 degrees to 70 degrees. With repeat measurements made, on average, approximately 6 weeks apart, the 95% velocity magnitude limits of agreement were as follows: Intraobserver -41.3 to +45.2 cm/s; interobserver -29.6 to +46.8 cm/s. There was an 8.6 cm/s interobserver bias in velocity magnitude. We conclude that the dual-beam vector Doppler system can measure blood velocity within its scan plane with low dependence on angle and with similar reproducibility to that of single-beam systems.

Assessment of the acoustic properties of common tissue-mimicking test phantoms.

Ultrasound (US) test phantoms incorporating tissue-mimicking materials (TMMs) play an important role in the quality control (QC) and performance testing of US equipment. Three commercially available TMMs (Zerdine from CIRS Inc.; condensed-milk-based gel from Gammex RMI; urethane-rubber-based from ATS Labs) and a noncommercial agar-based TMM, were investigated. Acoustic properties were measured over the frequency range 2.25 to 15 MHz at a range of ambient temperatures (10 to 35 degrees C). The acoustic velocity of the TMMs remained relatively constant with increasing frequency. Only the agar-based TMM had a linear increase of attenuation with frequency, with the other materials exhibiting nonlinear responses to varying degrees (f(1.08) to f(1.83)). The acoustic velocity and attenuation coefficient of all the TMMs varied with temperature, with the urethane-rubber TMM showing the greatest variation of +/- 1.2% for acoustic velocity and +/- 12% for attenuation coefficient. The data obtained in this study highlight the importance of greater knowledge of the acoustic behavior of TMMs to variations in both frequency and temperature, to ensure that accurate and precise measurements are obtained during QC and performance testing.

Ultrasound techniques for measurement of blood flow and tissue motion.

This article will review the ability of ultrasound techniques to provide 3D information on arterial geometry, blood flow and tissue motion.3D systems. 3D datasets can be obtained by sequential acquisition of 2D slices. Ideally a transducer is required in which there is full control of beam steering within a 3D volume. This requires a 2D array consisting of several thousand elements. Prototype 2D arrays have been built which provide several 3D datasets per second. Blood velocity measurement. Current Doppler systems estimate only the component of velocity in the direction of the Doppler beam. Lack of knowledge of the direction of blood motion and also other effects associated with 'spectral broadening' limit the accuracy of velocity measurement. Improved accuracy can be obtained using vector Doppler systems using 2 or 3 beam directions; this approach is referred to as 'vector Doppler'. Tissue motion. Doppler techniques can also be used to detect tissue motion (Tissue Doppler Imaging or TDI). Motion of the artery wall can be calculated from the TDI images. It is possible to estimate simultaneously motion for adjacent diameters within the longitudinal plane, and to visualise the relative motion at different parts of the wall.

MRI measurement of wall shear stress vectors in bifurcation models and comparison with CFD predictions.

Steady fluid flow was studied in a simple bifurcation model and in a physiologically realistic model of the human carotid bifurcation. Wall shear stress (WSS) vectors were calculated from phase-contrast (PC) magnetic resonance imaging (MRI) measurements of the velocity field. Velocity measurements in the inflow regions were also used as boundary conditions for computational fluid dynamics (CFD) calculations of WSS, which were compared with those derived from MRI alone. In regions of well-behaved flow, MRI and CFD estimates of WSS were in good general agreement. In regions of disturbed flow, for example near the bifurcation, the quality of the MRI measurements was sufficient for reliable calculation of WSS vectors when a sensitive surface coil was used. The combination of MRI and CFD would seem to be a powerful technique for the investigation of flow phenomena.

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.

Comparison of brachial artery pressure and derived central pressure in the measurement of abdominal aortic aneurysm distensibility.

OBJECTIVE: AAA distensibility (Ep, beta) may predict growth and risk of rupture. However, distensibility measurements based on brachial rather than central pressure may be inaccurate. Our aim was to compare AAA distensibility using non-invasive brachial and derived central aortic pressure. DESIGN: brachial and central pressures were measured prospectively by automated sphygmomanometry (Omron) and pulse wave analysis (SphygmoCor) respectively. AAA distensibility was calculated using brachial (Ep(b), beta(b)) and central (Ep(c), beta(c)) pressures by ultrasonic echo-tracking (Diamove). Twenty-eight patients (18 males) were selected on a first come basis from a larger study of AAA patients. There were no exclusion criteria, so 54% had cardiac dysfunction (MI, angina) and 14% were hypertensive (BP >140/90 mmHg). RESULTS: median (IQR) age was 74 (70-77) years, median AAA (IQR) diameter was 44 (40-51) mm. Central and brachial systolic pressures were significantly different, [140 (121-153) vs 144 (130-164) mmHg respectively, p < or =0.01]. Central and brachial diastolic pressures were not significantly different [76 (72-86) vs 76 (71-86) mmHg respectively, p=0.5]. Ep(c)(3.0, [2.2-4.9]) and beta(c)(22.2 [15.5-33.2]) were significantly lower than Ep(b)(3.6, [2.4-5.1] 10(5)Nm(-2)) and beta(b)(24.7 [17.1-33.0] a.u., all p < 0.001. Brachial and central derived distensibility remained significantly different after adjusting for age and diameter (p<0.001). CONCLUSION: the use of brachial pressure leads to a small, systematic overestimate of Ep (18%) and beta (11%) independent of age and AAA diameter. This systematic error will not bias follow-up of changes in distensibility.

Construction and geometric stability of physiological flow rate wall-less stenosis phantoms.

Wall-less flow phantoms are preferred for ultrasound (US) because tissue-mimicking material (TMM) with good acoustical properties can be made and cast to form anatomical models. The construction and geometrical stability of wall-less TMM flow phantoms is described using a novel method of sealing to prevent leakage of the blood-mimicking fluid (BMF). Wall-less stenosis flow models were constructed using a robust agar-based TMM and sealed using reticulated foam at the inlet and outlet tubes. There was no BMF leakage at the highest flow rate of 2.8 L/min in 0%, 35% and 57% diameter reduction stenoses models. Failure of the 75% stenosis model, due to TMM fracture, occurred at maximum flow rate of 2 L/min (mean velocity 10 m/s within the stenosis). No change of stenosis geometry was measured over 4 days. The construction is simple and effective and extends the possibility for high flow rate studies using robust TMM wall-less phantoms.

The relationship between abdominal aortic aneurysm distensibility and serum markers of elastin and collagen metabolism.

BACKGROUND: abdominal aortic aneurysm (AAA) distensibility may be an independent predictor of growth and rupture, possibly because it reflects changes in aortic wall structure and composition. AIM: to determine whether AAA distensibility is related to circulating markers of elastin and collagen metabolism. METHODS: sixty-two male patients of median age (IQR) 68 (65-72) years with asymptomatic AAA of median (IQR) diameter 42 (37-45) mm were prospectively studied. Pressure-strain elastic modulus (Ep) and stiffness (beta) were measured using an ultrasonic echo-tracker (Diamove). Serum elastin peptides (SEP), plasma elastin-alpha1-antitrypsin complex (E-AT), procollagen III-N-terminal propeptide (PIIINP) were measured by enzyme-linked immunoassay. RESULTS: age and smoking adjusted Ep and beta were significantly inversely related to SEP (r=-0.33 and r=-0.31 respectively, both p<0.02) and E-AT (r=-0.27 and r=-0.27 respectively, both p<0.05) both of which indicate elastolysis. By contrast, there was a significant positive correlation between PIIINP, indicative of increased collagen turn-over, and both Ep and beta (both r=0.45, p<0.01 unadjusted correlations). CONCLUSION: increased elastolysis is associated with increased AAA wall distensibility; whereas increased collagen turn-over is associated with reduced distensibility.