Search PubMed⌕ Search

Biomedical subjects

A P Hoeks

Publications and source records attributed to A P Hoeks.

At least 37 records · Page 2Linked to original sources

Non-invasive measurement of mechanical properties of arteries in health and disease.

Major conduit arteries should, by their elastic nature, be able to store blood volume temporarily during systole and release it during diastole. This reduces the systolic blood pressure required for the flow of a given volume quantity and gradually suppresses the pulsatile flow pattern. The haemodynamic characteristics of arteries have consequences for the load of the heart but also for the mechanical load of the arterial wall. The repetitive stretching of the wall (strains of up to 10 per cent) may cause fragmentation of the elastic fibres in the wall, modifying wall elasticity. To maintain wall stress the elastic arteries respond with a diameter increase in combination with an increase of arterial wall thickness. A larger diameter for a smaller distension (change in artery diameter from diastole to systole) will restrict the reduction in storage capacity. Alternatively, pulse pressure may go up increasing the mechanical load on the wall. In recent years various methods have been developed to assess and monitor the above interaction. Most of these methods are based on ultrasound techniques because of its wide availability and its non-invasive and non-traumatic nature. Presently these techniques enable the assessment of wall thickness, diastolic diameter, distension waveform, i.e., the tie-dependent change in diameter, the relative pulsatile increase in diameter, and pulse wave velocity, for elastic and muscular arteries in humans but also in small animals such as rats and mice. The present paper discusses the techniques in more detail.

Arteries↗

Wall shear stress in the human common carotid artery as function of age and gender.

OBJECTIVES: It has been postulated that in the arterial system mean wall shear stress is maintained at a constant value. The present study was performed to investigate the level of wall shear stress in the common carotid artery (CCA) as function of age and possible interactions between diameter and storage capacity, defined as the absolute area change per heart beat, with mean wall shear stress. METHODS: Wall shear stress (wall shear rate multiplied by whole blood viscosity) was assessed in the right CCA of 111 presumed healthy male (n = 56) and female (n = 55) volunteers, varying in age between 10 and 60 years. Wall shear rate was measured with a high resolution ultrasound system. Simultaneously, arterial diameter and storage capacity were determined. Whole blood viscosity was calculated from haematocrit, plasma viscosity and shear rate. RESULTS: From the second to the sixth age decade peak wall shear stress was significantly higher in males than in females and decreased from 4.3 Pa to 2.6 Pa (r = -0.56, p < 0.001) in males and from 3.3 Pa to 2.5 Pa (r = -0.54, p < 0.001) in females. Mean wall shear stress tended to decrease from 1.5 Pa to 1.2 Pa (r = -0.26, p = 0.057) in males and decreased significantly from 1.3 Pa to 1.1 Pa (r = -0.30, p = 0.021) in females. No significant difference in mean wall shear stress was found between males and females in any age decade. The diameter of the CCA increased significantly in both males (r = 0.26, p < 0.05) and females (r = 0.40, p < 0.003). Storage capacity decreased significantly in both sexes (males: r = -0.63, p < 0.001; females: r = -0.68, p < 0.001). CONCLUSIONS: These observations suggest that the reduction in mean wall shear stress with age results from the concomitant increase in diameter in an attempt of the arterial system to limit the reduction in storage capacity of the arterial system with increasing age.

Adolescent↗

Bladder filling reduces femoral artery wall distension and strain: beware of a full bladder!

During a previous study, we noted that the distension and strain of the femoral artery were relatively low when the bladder was full, a situation normally necessary for transabdominal echography. Therefore, in the present study we investigated the influence of bladder filling, if any, on wall properties of the common femoral artery. The results obtained were compared with those obtained in the common carotid artery. The study was performed on the right common carotid and right common femoral arteries of normotensive young (18-35 y) female volunteers (n = 24). Using a specially designed ultrasonic wall-tracking device and automatic brachial artery cuff blood pressure measurements, arterial distension (absolute change in diameter during the cardiac cycle; deltaD), strain (deltaD/D), and cross-sectional distensibility (DC) and compliance (CC) were determined before and after voiding. Distension and strain of the common femoral artery were significantly lower for a full than for an empty bladder. DC and CC were lower when the bladder was filled, but these differences did not reach the level of significance. Blood pressure as measured at the level of the brachial artery and heart rate were not statistically significantly different during a full or an empty bladder. It is concluded that bladder filling affects femoral artery wall properties, an observation that should be kept in mind when performing studies on artery wall properties at this level of the circulation.

Adolescent↗

Experimental verification of the correlation behavior of analytic ultrasound radiofrequency signals received from moving structures.

Conventional pulsed ultrasound systems are only able to detect motion along the ultrasound beam (i.e., axial motion). If the angle between the actual motion direction and the ultrasound beam is known, then the magnitude of the actual motion can be derived. This technique can be applied for laminar blood-flow measurements in straight vessels, but for tissue motion it is inadequate because the local tissue motion direction is unknown and may be position-dependent. Assessment of both the axial motion and the lateral motion (i.e., in the direction perpendicular to the ultrasound beam) makes angle-independent assessment of the magnitude of the actual motion feasible. Information about the axial and lateral motion is available in a set of radiofrequency (RF) signals obtained along the same line of observation (M-mode). The experiments described in the present paper show that axial and lateral motion can be estimated from the shape of the envelope of the 2-D (spatial and temporal) correlation function of analytic M-mode RF signals. Furthermore, it is demonstrated that the shape is also affected by the Band width of the received RF signals, signal-to-noise ratio, and local amplitude and phase characteristics of the ultrasound beam.

Humans↗

A noninvasive method to estimate pulse wave velocity in arteries locally by means of ultrasound.

Noninvasive evaluation of vessel wall properties in humans is hampered by the absence of methods to assess directly local distensibility, compliance, and Young's modulus. Contemporary ultrasound methods are capable of assessing end-diastolic artery diameter, the local change in artery diameter as a function of time, and local wall thickness. However, to assess vessel wall properties of the carotid artery, for example, the pulse pressure in the brachial artery still must be used as a substitute for local pulse pressure. The assessment of local pulse wave velocity as described in the present article provides a direct estimate of local vessel wall properties (distensibility, compliance, and Young's modulus) and, in combination with the relative change in artery cross-sectional area, an estimate of the local pulse pressure. The local pulse wave velocity is obtained by processing radio frequency ultrasound signals acquired simultaneously along two M-lines spaced at a known distance along the artery. A full derivation and mathematical description of the method to assess local pulse wave velocity, using the temporal and longitudinal gradients of the change in diameter, are presented. A performance evaluation of the method was carried out by means of experiments in an elastic tube under pulsatile pressure conditions. It is concluded that, in a phantom set-up, the assessed local pulse wave velocity provides reliable estimates for local distensibility.

Arteries↗

A longitudinal study of vessel wall properties in normotensive and hypertensive renal transplant recipients.

The mechanisms responsible for reduced arterial distensibility in renal transplant recipients remain to be evaluated. The present longitudinal study was aimed to evaluate the effect of hypertension on the evolution of vessel wall properties in renal transplant recipients. The mechanical properties of the common carotid artery were determined in 24 normotensive and 24 treated hypertensive renal transplant recipients 6-12 weeks after transplantation. The measurements were repeated after 2 years. Arterial distension was determined by using a multigate pulsed Doppler system, blood pressure (BP) was measured by a mercury sphygmomanometer. BP was 127 +/- 3/80 +/- 2 mm Hg at entry and 133 +/- 3/82 +/- 2 mm Hg after 2 years in the normotensive group, 146 +/- 4/90 +/- 3 mm Hg at entry and 145 +/- 3/87 +/- 2 mm Hg after 2 years in the hypertensive group (P < 0.01, normotensives vs hypertensives). The distensibility coefficient (DC) decreased significantly after 2 years in the hypertensive group (DC 18.3 +/- 1.3 10(-3)/kPa before, 15.1 +/- 1.2 10(-3)/kPa after 2 years, P < 0.05) whereas no significant change was observed in the normotensive group (DC 19.0 +/- 1.4 10(-3)/kPa before, DC 17.8 +/- 1.3 10(-3)/kPa after 2 years, NS). There was a significant correlation between the change of the distensibility coefficient after 2 years and mean arterial pressure (n = 48, r = 0.42, P < 0.01). The results show that the decrease of arterial distensibility after 2 years is accelerated in hypertensive renal transplant recipients despite effective anti-hypertensive treatment. Since BP levels were not different at entry into the study and after 2 years, differences in distending pressure along cannot explain the more pronounced decrease of arterial distensibility over time in hypertensive renal transplant recipients.

Adult↗

Effect of hyperparathyroidism on arterial distensibility in renal transplant recipients.

BACKGROUND: The cushioning function of the arterial system is altered in patients with end-stage renal failure. The role of hyperparathyroidism for the altered vessel wall properties of large arteries not known. METHODS: To exclude the confounding effects of fluid volume changes and hypercirculation as well as uremic toxicity on vessel wall properties from those of hyperparathyroidism, the present study was conducted in 54 normotensive renal transplant recipients with good graft function, three to six months after transplantation. The vessel wall properties of the common carotid artery were investigated in 32 of them, who had increased plasma intact parathyroid hormone (iPTH) levels (136 +/- 12 ng/liter, SEM), and compared to those of 22 control recipients of same age with normal plasma iPTH levels (34 +/- 4 ng/liter). Arterial distension was measured by Doppler analysis of the vessel wall movements, blood pressure was determined by sphygmomanometry. RESULTS: Blood pressure was 140 +/- 3/85 +/- 2 mm Hg in renal transplant recipients with hyperparathyroidism, 135 +/- 3/83 +/- 1 mm Hg in patients with normal plasma iPTH levels (NS). There was no difference in enddiastolic diameter of the common carotid artery (7.4 +/- 0.2 mm) in renal transplant recipients with hyperparathyroidism as compared with the control patients (7.3 +/- 0.2 mm; NS). Renal transplant recipients with hyperparathyroidism had a lower distension (389 +/- 27 microns vs. 486 +/- 28 microns, P < 0.05) and distensibility coefficient of the common carotid artery (15.1 +/- 1.1 10(-3)/kPa vs. DC 19.0 +/- 1.0 10(-3)/kPa, P < 0.001) when compared with the control patients. Multiple regression analysis showed that the distensibility coefficient of the common carotid artery was negatively correlated with age (P < 0.001), mean arterial blood pressure (P < 0.05) and plasma iPTH levels (P < 0.05). The effects of plasma iPTH levels were not related to serum calcium concentrations or to differences in the enddiastolic diameter of the common carotid artery. CONCLUSIONS: The data suggest that secondary hyperparathyroidism can affect the cushioning function of larger arteries in patients with end-stage renal failure independently of high blood pressure.

Adult↗

Baseband velocity estimation for second-harmonic signals exploiting the invariance of the Doppler equation.

All Doppler systems, whether conventional Doppler domain or radio frequency (RF) processing is employed, relate the temporal frequency characteristics of the signal at a certain point in depth as function of time to the spatial frequency characteristics of the received signal as function of depth. The mean frequency of the latter may change as a result of depth-dependent attenuation, nonlinear scattering mechanisms, as in harmonic imaging of ultrasound contrast agents, or RF signal demodulation. For all these cases, the relationship between spatial and temporal mean frequency and target velocity is still governed by the familiar Doppler expression if the signal modifications have been properly accounted for. A major drawback of RF signal processing to extract the target velocity is the large number of data points to consider. The computational complexity increases further for harmonic imaging. It is shown conceptually, and demonstrated by signal simulations, that prior to velocity estimation RF demodulation followed by decimation 1) does not affect the Doppler equation, 2) enhances the information content of the samples, 3) reduces the computational load by a factor of four and for harmonic signals by a higher factor, and 4) while demodulation does not have to be actually performed, but can be accounted for by a scaling factor in the cross-correlation function. It is concluded that decimation hardly affects the precision of the velocity estimate if possible frequency aliasing is maintained within bounds, suggesting that the decimation factor is not critical.

Computer Simulation↗

Differences in near-wall shear rate in the carotid artery within subjects are associated with different intima-media thicknesses.

In the common carotid artery, reflections originating from the periphery and the flow divider may affect the shape of the flow velocity profile and, hence, near-wall shear rate (WSR) differently just before the bifurcation (location B) than 20 to 30 mm farther upstream (location A). Recent developments in ultrasound technology allow the assessment of WSR and intima-media thickness (IMT) at the same site in the carotid artery in vivo. We therefore determined WSR at locations A and B and investigated whether the differences between both sites, if any, were associated with different IMTs and different mechanical properties of the arterial wall. The effect of age on the possible differences was assessed as well. The study was performed on presumably healthy volunteers (n=53). In all individuals, IMT was larger at location B than at location A. The relative difference in IMT between both locations was not affected by age. No significant differences in diameter and distension were found between locations. Near peak systolic and near mean WSR at the posterior wall (PWSRp and MWSRp, respectively) were significantly lower at location B than at location A. The relative differences in PWSRp and MWSRp between both locations within subjects were independent of age. The velocity profiles were more blunted at location A than at location B. PWSRp and MWSRp significantly decreased and IMT significantly increased with age at both locations. IMT was negatively correlated with PWSRP and MWSRP at location B, but this correlation was not significant at location A. In summary, in the common carotid artery, the lower WSR near the bifurcation, as compared with 20 to 30 mm upstream, is associated with a larger IMT than at the more proximal site. The relative difference between both locations within subjects is independent of age.

Adolescent↗

Modeling of the correlation of analytic ultrasound radiofrequency signals for angle-independent motion detection.

Conventional pulsed ultrasound systems are able to assess motion of scatterers in the direction of the ultrasound beam, i.e., axial motion, by determining the lag at which the maximum correlation occurs between consecutively-received radiofrequency (rf) signals. The accuracy, resolution, and processing time of this technique is improved by making use of a model for the correlation of rf signals. All previously-described correlation models only include axial motion, but it is common knowledge that lateral motion, i.e., motion in the plane perpendicular to the beam axis, reduces the correlation of rf signals in time. In the present paper, a model for the correlation of analytic rf signals in depth and time is derived and verified. It also includes, aside of some signal and transducer parameters, both axial and lateral motion. The influence of lateral motion on the correlation of (analytic) rf signals is strongly related to local phase and amplitude characteristics of the ultrasound beam. It is shown how the correlation model, making use of an ultrasound transducer with a circular beam shape, can be applied to estimate, independent of angle, the magnitude of the actual motion. Furthermore, it is shown that the model can be applied to estimate the local signal-to-noise ratio and rf bandwidth.

Blood Flow Velocity↗

A radio frequency domain complex cross-correlation model to estimate blood flow velocity and tissue motion by means of ultrasound.

This article introduces a mean frequency estimator based on a radio frequency (RF) domain complex cross-correlation model (C3M). The C3M estimator differs from the real cross-correlation model (CCM) estimator in two respects; it is an unbiased estimator of blood flow velocity and/or tissue motion independent of the bandwidth of the RF ultrasound signals, and it provides an estimate of the spatial bandwidth of the RF-signal. The estimators derived from the complex cross-correlation model (mean spatial frequency, mean temporal frequency, spatial bandwidth and signal-to-noise ratio) are based on three complex cross-correlation coefficients. A full derivation and mathematical description of both estimators (C3M and CCM), starting from a Gaussian model of the complex power spectral density distribution of sampled RF signals, are presented. In addition, a thorough performance evaluation of the C3M estimator in comparison with the CCM estimator is carried out by means of simulations to document the effect of signal-to-noise ratio, bandwidth and sample frequency. In the context of the specific simulation conditions considered, the quality of the C3M estimator is shown to offer the best performance (no bias, low standard deviation of the estimate). Taking into account the computational load and the robustness of the C3M estimator, it may be concluded that the C3M estimator combines high quality and modest complexity.

Blood Flow Velocity↗

Reproducibility of shear rate and shear stress assessment by means of ultrasound in the common carotid artery of young human males and females.

In the present study, the reliability of an ultrasonic shear rate estimating system, in terms of intrasubject intrasession, intersubject intrasession and intersubject intersession variability coefficients for the assessment of wall shear rate (WSR) in the common carotid artery (CCA) was determined in eight presumed healthy volunteers. Measurements were performed on consecutive days (day 1, day 2 and day 7). To investigate whether there were differences in WSR due to gender, dynamic WSR in the CCA was assessed in 11 presumed healthy males (mean age 24 y) and 11 presumed healthy females (mean age 25 y). Wall shear stress (WSS) was estimated from WSR and calculated whole blood viscosity. The average intrasubject intrasession variability was about 15% for peak WSR and about 12% for mean WSR. The intersubject intrasession variability for peak WSR decreased from 19% on day 1 to 16% on day 7 and for mean WSR from 17% on day 1 to 11% on day 7. The intersubject intersession variability is on the order of 5% for peak WSR and about 4% for mean WSR. No significant differences could be detected between peak and mean WSR values on day 1, day 2 and day 7, indicating good short- and medium-term intersubject intersession reproducibilities. No differences in peak and mean WSR were found between the left and the right CCA in the male group as well as in the female group. Mean WSS was similar in males (1.3 +/- 0.3 Pa) and in females (1.2 +/- 0.2 Pa), but peak WSS was slightly, but significantly, higher in males (4.3 +/- 1.3 Pa) than in females (3.3 +/- 0.7 Pa). It can be concluded that peak and mean WSR can be reliably determined noninvasively using ultrasound.

Adult↗

Automated detection of local artery wall thickness based on M-line signal processing.

The Young's modulus of an arterial segment, a measure of the elastic properties of the arterial wall, requires the simultaneous and local assessment of pulse pressure, wall thickness, diameter, and distensibility (relative increase in cross-sectional area per change in blood pressure). The diameter and relative increase in cross-sectional area can be obtained with a wall track system, processing the radiofrequency (r.f.) ultrasound signals received along a single line of observation (M-line processing). It will be demonstrated that it is feasible to combine, in a single measurement, the assessment of wall thickness and the (relative change in) diameter involving a minimum of user interaction. Phantom tests show a standard error of the estimate for intima-media thickness measurements of less than 20 microns; in vivo registrations exhibit a variation on the order of 45 microns. It is concluded that processing of the radiofrequency ultrasound signal, acquired along an M-line, provides an accurate and time-efficient alternative for videoprocessing of 2-dimensional B-mode ultrasound images to estimate artery wall thickness.

Adult↗

Female sex hormones do not influence arterial wall properties during the normal menstrual cycle.

1. In previous studies, the elastic properties of the common carotid artery were found to differ between men and women. In these studies, however, the phase of the menstrual cycle was not taken into consideration. It was the aim of the present study to investigate the effect of changing ovarian hormone levels during the normal menstrual cycle on the arterial wall properties of female large arteries. 2. We investigated the elastic right common carotid artery and the muscular right common femoral artery of normotensive young (18-35 years) female subjects (n = 12). The arterial distensibility and cross-sectional compliance coefficients were determined by the use of a specially designed ultrasonic wall-tracking device and measurements of automatic brachial artery cuff blood pressure. The phase of the menstrual cycle was assessed by ultrasonographic evaluation and measurement of 17 beta-oestradiol and progesterone blood plasma levels. 3. The distensibility coefficient and the cross-sectional compliance coefficient of both the common carotid and the common femoral artery did not change significantly during the normal menstrual cycle despite evidently changing ovarian hormone levels. 4. We conclude that the menstrual cycle does not influence the arterial wall properties of either the elastic common carotid artery or the muscular common femoral artery.

Adolescent↗

Reduction of the clutter component in Doppler ultrasound signals based on singular value decomposition: a simulation study.

In pulsed Doppler ultrasound systems, the ultrasound radiofrequency (RF) signals received can be employed to estimate noninvasively the time-dependent blood velocity distribution within and artery. The RF signals are composed of signals originating from clutter (e.g., vessel walls) and scatterers (e.g., red blood cells). The clutter, which is induced by stationary or slowly-moving structure interfaces, must be suppressed to get reliable estimates of the mean blood flow velocities. In conventional pulsed Doppler systems, this is achieved with a static temporal high-pass filter. The static cut-off frequency and the roll-off of these filters cause the culture not always to be optimally suppressed. This paper introduces a clutter removal filter that is based on Singular Value Decomposition (SVD). Unlike conventional high-pass filters, which take into account only the information of the temporal direction, the SVD filter makes use of the information of the temporal and spatial directions. The advantage of this approach is that it does not matter where the clutter is located in the RF signal. The performance of the SVD filter is examined with computer-generated Doppler RF signals. The results are compared with those of standard linear regression (SLR) filter. The performance of the SVD filter is good, especially if a large temporal window (i.e., approximately 100 RF signals) is applied, which improves the performance for low blood flow velocities, A major disadvantage of the SVD filter is its computational complexity, which increases considerably for larger temporal windows.

Blood Flow Velocity↗

A single bit RF domain complex cross-correlation velocity estimator for color flow mapping.

This paper evaluates the performance of a one bit mean frequency estimator to estimate blood flow velocity for ultrasound color flow mapping. This one bit mean frequency estimator, referred to as BC3 estimator, is derived from the recently introduced complex cross-correlation model (C3M) employing the full dynamic data range. The C3M velocity estimator is not suitable for application in color flow mapping because of its high hardware complexity and associated computational load. The BC3 estimator estimates the mean blood flow velocity using only two complex cross-correlation coefficients. For this purpose the latter are computed by means of a complex one bit cross-correlation operation. Each sample of the RF signals is converted into an one bit representation based on the sign of the real and imaginary part of the RF samples. A full derivation and mathematical description of the BC3 estimator is presented. In addition, a thorough performance evaluation of the BC3 estimator in comparison with the full dynamic range C3M velocity estimator is carried out by means of signal simulations to document the effect of signal to noise ratio, sample frequency and bandwidth. For the specific simulation conditions considered the standard deviation of both estimators (C3M and BC3) is comparable. The bias of the BC3 estimator appears to be a function of velocity, while the full dynamic range C3M velocity estimator exhibits no bias. The simulation results are confirmed by evaluation of data from an in vivo measurement. Taking into account the low hardware complexity and computational load in combination with the achieved precision, it may be concluded that the BC3 estimator is well suited for implementation in color flow mapping.

Blood Flow Velocity↗

Enhanced cellular proliferation in intact stenotic lesions derived from human arteriovenous fistulas and peripheral bypass grafts. Does it correlate with flow parameters?

BACKGROUND: Vascular interventions are often complicated by the development of intimal thickening, leading to stenosis. Cellular proliferation is a key event in stenosis formation in animals, but the role of cell proliferation in intimal thickening in humans is still unclear. Furthermore, the relation between proliferation in human stenotic lesions and flow parameters has not been established. METHODS AND RESULTS: We studied the proliferation patterns of 35 anatomically intact human stenotic lesions derived from either peripheral bypasses (normal flow) or hemodialysis AV fistulas (high flow) with the use of Ki-67, a cell proliferation marker. Local flow parameters were assessed with ultrasound. Proliferation patterns were similar in AV fistula and bypass stenoses. In the intima, proliferation was highest in the area just below the endothelium (AV fistulas, 3.6%; bypasses, 3.5%; P = NS). In adjacent nonstenotic vessel segments that were used as controls, proliferation rate in the intima was 0.3%. Double-labeling studies revealed that subendothelial-intimal proliferation consisted mainly (90%) of vascular smooth muscle cells, whereas proliferation in the other layers of the vessel wall also consisted of endothelial cells and macrophages. Blood flow velocity was negatively correlated with subendothelial-intimal proliferation (r = -.61, P < .05). The endothelial cell coverage of the lumen was positively correlated with proliferation (r = .85, P < .01). CONCLUSIONS: These data suggest enhanced cellular proliferation in human stenotic tissue derived from AV fistulas and peripheral bypass grafts. Furthermore, high proliferation rates seem to be associated with endothelial cell coverage of the lumen and low local flow velocities.

Adult↗

A noninvasive method to estimate arterial impedance by means of assessment of local diameter change and the local center-line blood flow velocity using ultrasound.

Vascular impedance is defined as the ratio between the frequency components of the local blood pressure waveform and those of the local blood volume flow waveform. Assessment of vascular impedance is, for example, important to study heart load and distal vascular bed vasomotricity. However, only a few studies on vascular impedance have been performed in humans because pulsatile pressure and volume flow waveforms, simultaneously recorded at the same location, are difficult to obtain noninvasively. The noninvasive assessment of arterial impedance as described in this study is based on the replacement of the pressure waveform by the distension (change in diameter) waveform and the volume flow waveform by the center-line blood flow velocity waveform. Both waveforms can simultaneously and accurately be assessed by means of pulsed ultrasound. It will be shown that, depending on the Womersley number, the volume flow waveform may be replaced by the center-line blood flow velocity waveform for a given frequency range and that the pressure waveform may be replaced by the distension waveform for a wide frequency range. The validation of the proposed ultrasound method was performed through an in vitro study in a flow model with a distensible tube terminated with a hydraulic load (modified windkessel model). It is shown that, in vitro, the proposed method gives the same results as the local spectral pressure-flow relationship.

Arteries↗