In Vivo flow and wall shear stress assessment in the carotid artery with MRI Box, F.M.A.

Box, F.M.A.

Citation

Box, F. M. A. (2007, September 13). In Vivo flow and wall shear stress assessment in the carotid artery with MRI. Retrieved from

https://hdl.handle.net/1887/12558

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Chapter 2

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Automatic Model-Based Contour

Detection and Blood Flow

Quantification in Small Vessels with

Velocity Encoded MRI

Frieke MA Box, Aart Spilt, Mark A van Buchem, Rob J

van der Geest, Johan HC Reiber

From the Division of Image Processing (F.M.A.B., R.J.vd G., J.H.C.R.) of the Department of Radiology (A.S., M.A.v B.), Leiden University Medical Center, Leiden, the Netherlands

Invest Radiol 2003:38;567-577

Abstract

Rational and Objectives The quantitative assessment of blood flow in peripheral vessels from phase-contrast MR imaging studies requires the accurate delineation of vessel contours in cross-sectional magnetic resonance images. The

conventional manual segmentation approach is tedious, time-consuming and leads to significant inter- and intra-observer variabilities. The aim of this study was to verify whether automatic model-based segmentation decreases these problems, by fitting a model to the actual blood velocity profile.

Methods In this study two new fully automatic methods (a static and a dynamic approach) were developed and compared with manual analyses using phantom and in vivo studies of internal carotid and vertebral arteries in healthy volunteers. The automatic segmentation approaches were based on fitting a 3D parabolic velocity model to the actual velocity profiles. In the static method, the velocity profiles were averaged over the complete cardiac cycle, whereas the dynamic method takes into account the velocity data of each cardiac time bin individually. Materials consisted of the MRI data from three straight phantom tubes and the blood velocity profiles of eight volunteers.

Results For the phantom studies, the automatic dynamic approach performed significantly better than the manual analysis (intra-class correlations (ICC) of 0.62-0.98 and 0.30-0.86, respectively). For the assessment of the total cerebral blood flow (TCBF) in the in-vivo studies, the automatic static method performed significantly better than the manual one (intra-class correlations (ICC) of 0.98- 0.98 and 0.93-0.95, respectively). On the other hand, the automatic dynamic method was not significantly better than the manual one (ICC = 0.92-0.96), but had the advantage of providing additional parameters.

Conclusion Blood flow in MR images of small vessels can be assessed accurately, rapidly and fully automatically using model-based postprocessing by fitting a first approximation of the velocity profile to the actual flow data.

2.1 Introduction

Under physiological circumstances, blood flow to the brain is secured by auto regulation mechanisms. Pathologic conditions, such as an internal carotid artery stenosis, may give rise to diminished cerebral blood flow, which may cause neurologic symptoms.

Furthermore, it has recently been demonstrated that age-related white matter lesions are associated with decreased total cerebral blood flow (TCBF). TCBF can be assessed by summation of the individual flows in the four arteries supplying the brain: the left and right internal carotid arteries and the left and right vertebral arteries. Buis et al. have shown that these individual flow measurements can be determined by cine phase-contrast MR flow velocity mapping¹. This non-invasive imaging technique allows the assessment of flow in vessels over a full cardiac cycle.

Quantification of flow from such MR examinations requires a post processing step to segment the pixels within a vessel’s cross section from the surrounding background tissue.

The most commonly applied post processing method is manual segmentation, which is time-consuming and has limited reproducibility. Given the small size of the arteries supplying the brain the accuracy is also restricted by the image resolution. For studies aiming at detecting small changes in flow, manual image analysis will be inadequate and more accurate and reproducible computer assisted automatic methods are needed². In previous literature various automatic segmentation methods have been proposed for more accurate and reproducible measurement of flow from phase contrast MR imaging studies. Burkart et al. describe a thresholding-based technique that is automatic, but still suffers from considerable variability caused by limited image resolution and inter-user variabilities³. Oyre et al. proposed a method of fitting parabolic velocity profiles to the MR velocity data in multiple sectors on the pixels inside the vessel and close to the vessel boundary⁴. This method requires extremely high spatial resolution information, which is associated with time-consuming MR acquisition techniques. These long acquisition times may render incorporation of such techniques in patient protocols less attractive. The method presented by Hoogenveen et al. is also based on fitting a parabolic velocity profile on measured MR data⁵. The authors propose an automatic correction of errors in the velocity data based on the matrix format. A disadvantage of this method is that the applied filter has to be inverted. This is solved by simulation of the MRI acquisition. A

convolution with the result of the simulation and the assumed velocity profile is carried out. However, the MR-simulation is not standardly available and it requires much programming, expertise and effort to implement it. The difference with our work is that Hoogeveen assumes the underlying velocity profile to be parabolic, while we assume that the MR measures the parabolic velocity profile without errors.

The purpose of the current study, therefore, was to develop and validate a fast, user- independent automatic segmentation approach, which is relatively simple to implement on each MR-machine and flow-protocol. It is based on a pragmatic MR TCBF acquisition protocol, yielding accurate and reproducible flow data.

It was assumed that a parabolic flow velocity profile is a valid model for the blood flow in the intra-cranial vessels given its small diameter and the relatively constant flow rate over the cardiac cycle. The proposed automatic segmentation approach, therefore, is based on the fitting of a three-dimensional parabolic velocity profile to the actual velocity data, thus providing boundary positions of the vessel of interest.

Two different methods were investigated: the first, static method, takes the average velocity profile over the complete cardiac cycle into consideration. The flow values are then calculated by the multiplication of the actual velocity values and the area of the automatically segmented region-of-interest (ROI). The second, dynamic, method performs a fitting for each individual phase in the cardiac cycle and calculates the flow volume by the analytical integration of the individual paraboloids. The accuracy and reproducibility of these new automatic segmentation approaches were evaluated and compared to the

conventional manual analyses using phantom and in-vivo studies.

2.2 Materials and Methods 2.2.1 Study design

A method to assess the Total Cerebral Blood Flow (TCBF) in an accurate and fast manner without inter- or intra-user variability has been developed and tested. The method is based on a first approximation of the blood flow properties. This means that this method is based on the assumptions that these vessels are round in shape, and that the flow in these vessels is characterized by a fully developed steady laminar flow profile, so that a parabolic velocity profile is valid. These assumptions are supported by the following observations in the existing literature: 1) for small vessels outside of the thorax the velocity profile in a vessel can be described by a paraboloid ^6,7; and 2) most arteries and in particular small arteries are circular in shape ^4,5,6. The blood flow volumes of three straight phantom tubes and 8 volunteers were assessed by the conventional (manual) analysis and by two automatic approaches, a dynamic and a static method. The dynamic method makes use of the variation of the flow during the cardiac cycle, while the static method uses the average of this flow-volume. Since the systematic error for in vivo studies could not be assessed, the Intra Class Correlation (ICC) was used to describe the reproducibility of the methods.

The three methods were tested for individual vessels, the internal carotid arteries and the vertebral arteries, and on the sum of the flows through these vessels, the TCBF.

Furthermore, the inter- and intra-user variability for the manual methods were evaluated.

2.2.2 Phantom study

To compare the results of the manual and automatic contour detection procedures in an objective manner, twelve acquisitions -three for each FOV- with pulsatile flow were obtained in a phantom using Field of Views (FOV) varying from 150 to 300 mm. Variation of the FOV simulates flow measurements in vessels with different diameters, because the number of pixels per diameter was varied in this way, respectively from 4.3 to 15.4 pixels over the diameter of the phantom. The flow phantom consisted of three straight tubes made of glass with an inner diameter of 5, 8 and 9 mm and a length of 20 cm connected to a programmable pulsatile pump which delivered a physiological waveform (Shelley Medical Imaging Technologies, London, Ontario, Canada). The flow volume delivered by the pump was set at 551.76 ml/min (9.196 ml/s). The flow curve as a function of time (flow(t)) was typical for a carotid artery with an amplitude of 30 ml/s. The liquid consisted of a mixture of water (60%) and glycerol (40%), so that the viscosity was comparable to that of blood (4.3 mPas).

2.2.3 Study population

The study population consisted of 8 healthy volunteers (aged 20-30 years, 3 women and 5 men). Flow velocities in the vertebral and internal carotid arteries were assessed in a plane perpendicular to these arteries at different positions in the neck. For the internal carotid artery a slice location 2 cm distal of the bifurcation was selected, and for the vertebral artery 2 cm proximal to the pars atlantica. For each vessel the acquisition procedure was repeated three times. To assess the stability of flow measurements (re-examination) on a given MR system, a second scan was performed directly after the first one, while the volunteer stayed inside the MR scanner. To assess the influence of repositioning a patient in our MR system, which may give rise to variation in location and angle of the flow measurement, a third acquisition procedure was performed after the volunteer came out of the machine and was repositioned inside the scanner. For the third scan, new plan scans were set and the flow measurement was based on these new plan scans. The total cerebral blood flow (TCBF) is calculated by the summation of the derived flow values through the four vessels.

2.2.4 Acquisition procedures

MR examinations were performed on a 1.5 T scanner (Gyroscan NT; Philips Medical Systems, Best, the Netherlands) using a standard head coil. A gradient echo phase contrast imaging sequence was applied using retrospective cardiac gating by means of a peripheral pulse unit, resulting in 16 phases over the cardiac cycle. The imaging parameters were: TE 9 ms, TR 16 ms, 7.5° flip angle, 5 mm slice thickness, 150-300 mm field of view for the phantom studies and 250 mm for the in-vivo studies, scan matrix 256 × 256 pixels and a velocity sensitivity of 100 cm/s. The scan time was dependent on the heart rate being 3 minutes at 60 beats/min.

2.2.5 Quantitative analysis approach

During a velocity-encoded MR study, phase difference and standard gradient echo images are acquired at multiple points in the cardiac cycle. Since the gradient images show good contrast, even in the absence of flow, the analysis algorithm was developed to operate on phase images. The basic steps in the quantitative analysis of the velocity encoded cine MR imaging studies was carried out with the analytical software package MRI-FLOW^® (MEDIS medical imaging systems, Leiden, the Netherlands) that was described in detail elsewhere⁸. MRI-FLOW provides an intuitive user-interface for viewing and interaction with all images, which are acquired during a velocity-encoded study (Fig. 1).

2.2.6 Automatic contour detection procedure for small vessels

To assess the flow through these small cranial vessels, we have assumed the cross section of the vessel to be circular and the velocity profile to be parabolic.

The velocity profile u(x,y) is shown in Figures 2a and 2b and is described by:

u(x,y) = A*(x² + y²) +Bx +Cy +D (1) ,

where x and y represent the distances to the initial point in number of pixels, while B and C are used to be able to shift the paraboloid a little. If (B²+C²)/A << 1, D is the amplitude

of the paraboloid and A describes the steepness of the velocity profile.

To fit the paraboloid to the actual velocity profile a Levenberg-Marquardt algorithm was used,

which minimizes the chi-squared error (χ²):

∑ ⁻

=

i i

i

i

u

v

2

2

( )

χ σ

for non-linear functions⁹, where ν_i is the measured velocity for a particular pixel and ui is the fitted velocity. The error σi for each data-point was defined as,

i

i

= 1 / v

σ

This can also be understood as giving a certain weight to each data point. The weight was the inverse of the error squared so that data points with a large error are assigned little weight¹⁰. As

a result, Eq. (2) can be written as:

∑

∑ ^{− = −}

=

i

i i i i

i i

i

v u v v u

W

2

( ) ( )

χ

The basic assumption was that the error was largest for low velocities. Experimentally it was found that this error estimation gave good stability.

The fitting procedure for the paraboloid was carried out as follows: This procedure was initialized manually by providing a seed point inside the vessel. The signal in the

neighborhood (5 pixels in x and y direction) of this point was averaged over the 16 cardiac time phases. The highest velocity in this region was taken as the initial top of the

paraboloid. Next, a threshold was applied so that all pixels with a velocity value above the threshold would be used in the fitting procedure. As a consequence of this threshold, errors due to slow flow, phase noise and partial volume effects were removed. The paraboloid was fitted by the Levenberg Marquardt algorithm. This fitting procedure was carried out iteratively until the chi-squared error did not decrease anymore; at that time the final solution was obtained⁹. Based on the results from this parabolic fitting procedure, the contour of the vessel of interest was defined; The threshold level was determined by minimalization of the random error in the ICC (see statistical analysis). This means that the ICC was maximized.

A quality parameter was defined by the sum of the squared differences between the fitted values and the measurement values divided by the number of pixels inside the mask. The fittings were designated ‘inadequate’ when the difference between the measurements and the fitting was above a certain threshold in one or more time bins. The threshold was determined by optimization of the ICC for each of the vessel types. Vessels can also be detected as ‘inadequate’ when the shape does not appear to be circular. This

was the case when the component of the flow parallel to the image plane was not negligible. The data was processed in two iterations: for the automatic static method only iteration one was used, while for the automatic dynamic method two iterations were used.

Figure 1. An example of an MR image presented with the package FLOW^®.

2.2.7 Automatic static method

An average velocity image was derived from all the individual image data collected over the cardiac cycle. The velocities were thresholded, pixels with velocities under this threshold were rejected and the paraboloid was fitted on the remaining data. For the static method the threshold was set at 0.42 times the maximum measured velocity (Amax).

Based on the results from this parabolic fitting procedure, the contour of the vessel of interest was defined; it is the circle for which the paraboloid equals zero. Finally, the flow was calculated by averaging the velocity values from the individual pixels in the

segmented area. This number was multiplied with the size of the enclosed area. The advantage of this method is a good reproducibility. The quality parameter was found to be 6.0 for the carotid arteries and 0.9 for the vertebral arteries. For example, assuming 15 pixels for a carotid artery, the average difference between model and measurement per pixel had to stay below 0.77 cm/s and for a vertebral artery assuming 4 pixels, below 0.47

cm/s, to be valid. The procedure used in the automatic static method is also explained in Figure 2a.

2.2.8 Automatic dynamic method

In the automatic dynamic method each phase in the cardiac cycle was fitted separately.

This method requires two iterations. The central pixel for the second iteration was determined by the first iteration discussed above under the automatic static method. In other words, the analysis dynamic method was different for the internal carotids and the vertebrals and was equal to 0.43*Amax and 0.29*Amax, respectively. After the second fit, the boundary of the vessel was taken as the circle for which the paraboloid equals zero and the velocity profile was assumed to be formed by the fitted paraboloid. The flow-volumes were assessed by calculation of the integrals of the paraboloids. If the value of the quality parameter exceeded a fixed value in one or more time bins, the fit was rejected. The quality parameter was found to be 0.63 for the carotid arteries and 0.79 for the vertebral arteries. For example, assuming 15 pixels for a carotid artery, the average difference between model and measurement per pixel had to stay below 0.04 cm/s and for a vertebral artery assuming 4 pixels, below 0.20 cm/s, to be valid. The procedure used in the dynamic method is also explained in Figure 2b.

2.2.9 Manual contour definition procedure

For this type of study the manual contour definition is known as the conventional method.

Each acquisition run was analyzed manually in an independent manner by 7 experienced observers. The group of observers consisted of a radiologist and six image processing scientists. They were instructed to segment the image in the following manner: The delineation of the vessel contour was carried out on an enlarged image of one time bin (one phase in the cardiac cycle). First, the observer selected the phase within the cardiac cycle characterized visually by the highest contrast in the image. The observers were advised to take a slice during systole. Next, the observer defined manually a region of interest (ROI) in the vessel. Finally, this ROI was subsequently copied to the 15 remaining phases within the cardiac cycle. The instantaneous flow values were calculated by

multiplication of the measured velocities inside the ROI times the area of the ROI.

2.2.10 Intra- and inter-observer variability

Because there was no inter- or intra-observer variability associated with the automatic method these sources of error were only analyzed for the manual method. To determine the inter-observer variability seven experts traced the contours of the four vessels in the images of eight healthy volunteers. The intra-observer variability was assessed, by having each image traced twice. Therefore the images were distributed to the experts and the results of the second drawings were compared to the first ones of the same expert. The time between the two drawing sessions varied between 2 and 5 weeks.

Figure 2. A, The automatic static method. I: All time phases were averaged and the pixel with the highest average velocity (Vmaxav) is selected. The average velocity values in the neighborhood of this pixel are read. II: A threshold of 0.42 times Vmaxav is applied to the carotid data and a threshold of 0.45 times Vmaxav is applied to the vertebral data. III: A paraboloid was fitted to the velocity data above the threshold and the edge of the vessel was assumed to be where this paraboloid equals zero.

IV: This mask was used to segment the image. To assess the flow rate, all velocities inside this mask were averaged and multiplied with the vessel area. B, The automatic dynamic method. I: All time phases were averaged and the pixel with the highest average velocity (Vmaxav) was searched for. II:

For each time slice the data within a window of 10 by 10 pixels was read and the pixel with Vmaxav was positioned in the be formed by the fitted paraboloid. The flow-volumes were assessed by calculation of the middle. In starts with the calculation of the image summed over the cardiac cycle.

The threshold for the each time slice the highest velocity (Vmax) was determined. A threshold of 0.43 times Vmax for the carotid and 0.29 times Vmax for the vertebrals was applied in each time slice. III: A paraboloid was fitted to the velocity data above the threshold and the paraboloid was assumed to be the real velocity profile.

2.2.11 Statistical analysis

Differences in outcomes between the various approaches were expressed in terms of mean flow and standard deviations, the coefficient of variation (CV), the inter-class correlation (ICC), the systematic difference and the P-values. For the phantom studies the systematic errors (between the measured and true flow volumes) were calculated. For the in vivo studies the total flow volume in ml/min was used as the parameter to compare the three flow quantification approaches. For each method and vessel a coefficient of variation (CV) defined by the standard deviation divided by the mean value, was calculated to assess the reproducibility of the method in the following manner: First, a CV was determined for the two acquisitions (re-examination or reposition) of each vessel under study. Then these CV’s were averaged to obtain the total CV, which will be presented under “Results”.

A T-test is normally used to calculate the difference or correspondence between two data sets. On the contrary the vessels under study were the same for all the methods. Therefore another test was needed, one which can give a measure for the reproducibility of a method.

The Intra (or Inter) Class Correlation (ICC) analysis was used for that purpose. The ICC is defined as: (ST2 / (ST2 + Se2)), were S²T is the component of variance due to error free variability among subjects and Se2 is the component of variance due to the random measurement error¹¹. Also the 95% reliability interval of the ICC is determined. Finally, for the manual method only, the inter-observer variability was calculated to assess the variation in flow volume caused by segmentation done by different users. The intra- observer variability was calculated to compare the errors produced by one observer. The automatic methods had no inter- or intra- observer variability associated with it.

The statistical analysis was carried out for measurements taken directly after each other (re-examination variability). To assess the reposition variability, each volunteer was scanned once, was repositioned and than scanned for the second time. The re-examination and reposition variability were calculated both for individual vessels and for the TCBF. P- values express in this study the differences between the methods. P-values are given in the tables.

2.3 Results 2.3.1 Validation

The amount of non-pulsatile flow selected in the phantom study was comparable to the flow volume in the carotid arteries. The results of the phantom studies are given in Table 1 for the range of FOV’s (150, 200, 250 and 300). A FOV of 300 resulted in a larger standard deviation in the derived flow volumes. The automatic dynamic method was unable to calculate flow volumes for most cases at a FOV of 150. For an average field of view (200 and 250) the automated dynamic method performed best. It had the lowest systematic error (average 7.92 ml/min, this is 1,4%) and coefficient of variation (2.86%).

The ICC indicates that the reproducibility was significantly better compared to manual analysis for this method. The automated static method produced a larger systematic error than the manual analysis approach, but -when FOV 300 was not taken into account- has a smaller CV. Also the ICC gave a better reproducibility for the automatic static method compared to the manual one, but that was not statistically significant.

Method;

FOV Flow volume

(ml/min) Coefficient of

variation (%) Systematic Error

(ml/min) ICC (95% rel)

MM; 150 MM; 200 MM; 250 MM; 300 Mean MM ASM; 150 ASM; 200 ASM; 250 ASM; 300 Mean ASM ADM; 150 ADM; 200 ADM; 250 ADM; 300 Mean ADM

513.85 504.10 512.93 509.59 488.85 496.70 478.87 486.05 540.60*

541.86 545.82 474.85 520.84**

4.43 2.75 4.22 3.26

2.47 2.73 7.52 3.86

- 1.23 4.48 6.44 4.05**

-44.25 -37.91 -47.66 -38.83 -42.17

-71.96 -62.91 -55.06 -72.89 -65.71

- -9.90 -5.94 -76.91 -30.92

- - - -

0.62 (0.30-0.86) -

- - -

0.78 (0.53-0.92) -

- - -

0.85 (0.62-0.96)*

Table 1. The random and systematic errors for the pulsatile flow phantom

The phantom consisted of three straight tubes with a diameter of 5, 8 and 9 mm. Total flow amount is 551.76 ml/min. Each FOV and tube is scanned three times. MM stands for Manual Method; ASM is Automatic Static Method and ADM is Automatic Dynamic Method.* Note that the tubes with diameters of 5 and 8 mm gave NaN. The flow volume given is three times the flow volume assessed by the tube with 9 mm diameter. This has some effect on the reliability of the data because the amount of data used in the statistical analyses is not everywhere exactly the same.** Based on FOV 200, 250 and 300

2.3.2 Reproducibility for re-examination and for reposition of individual vessels To determine the stability of the method in time, two repeated measurements one directly after the other, were carried out (re-examination). To determine the stability of the method for repositioning, the volunteer was scanned, repositioned and scanned again. The study was performed on 8 subjects. Since separate scans were performed for the internal carotid and vertebral arteries, a total of 16 scan series was acquired. This gives 32 individual vessels, 16 internal carotids and 16 vertebrals. Some scan series could not be used: 3 vertebral arteries had little flow and were not clearly visible; furthermore, one internal carotid artery was found to be non-circular in shape. This left a total of 15 internal carotids and 13 vertebrals for further analysis.

Automatic static method Manual Method Sys diff p-value Mean (stdev) CV (%) ICC (95% rel) Mean (stdev) CV (%) ICC (95% rel)

RE ICA RP ICA RE VA RP VA

289.8 (7.5) 278.1 (12.9)

109.0 (5.4) 108.0 (6.6)

2.7 4.3 4.7 5.7

0.97**(0.91-0.99) 0.93* (0.82-0.88) 0.96* (0.87-0.99) 0.95* (0.86-0.99)

257.8 (27.2) 250.8 (27.7) 101.0 (12.5) 97.3 (12.4)

11.0 11.1 13.2 14.0

0.90 (0.82-0.96) 0.84 (0.73-0.93) 0.94 (0.89-0.98) 0.94 (0.89-0.98)

32.0 27.4 8.0 10.7

8.27.10^-5 0.0015

0.352 0.189 Table 2a. The automatic static method compared to the manual method for re-examination (RE) and the repositioning (RP) of individual vessels. The number of vessels with valid fit-quality was 15 for the carotids and 13 for the vertebrals.

Automatic dynamic method Manual Method Sys diff p-value

Mean (stdev) CV (%) ICC (95% rel) Mean (stdev) CV(%) ICC (95% rel) RE ICA

RP ICA RE VA RP VA

285.2(13.7) 278.6(14.0) 114.4 (9.9) 111.6 (8.5)

5.6 4.4 8.2 6.5

0.93* (0.82-0.88) 0.94* (0.83-0.98) 0.86 (0.58-0.96) 0.96* (0.86-0.99)

257.5(25.9) 251.5(27.8) 107.3(12.8) 105.5(13.0)

10.6 11.2 9.7 12.3

0.92 (0.86-0.91) 0.87 (0.76-0.95) 0.94 (0.88-0.98) 0.94 (0.88-0.98)

27.7 27.1 7.1 6.1

0.0028 0.0036 0.0062 0.0002 Table 2b. The automatic dynamic method compared to the manual method for re-examination (RE) and the repositioning (RP) of individual vessels. The number of vessels with valid fit-quality was 13 for the carotids and 11 for the vertebrals.

The mean flow and standard deviation, the coefficient of variation (CV) and the intra-class correlation (ICC) with 95% reliability and the number of used vessels for the three methods for in vivo flow determination in individual vessels. ICA means internal carotid artery, VA is vertebral artery. When the automatic method performs better than the conventional manual analysis it is indicated by *, when it performs significantly better (2 std. dev.) it is indicated by **

Automatic static method Manual Method Syst diff p-value Mean (stdev) CV (%) ICC (95% rel ) Mean (stdev) CV(%) ICC (95% rel)

RE 720.6 (15.3) 2.1 0.98**(0.95-1.0) 646.9 (62.3) 9.7 0.95 (0.89-0.99) 73.7 0.0085 RP 698.5 (27.0) 4.2 0.98* (0.89-1.0) 629.9 (63.4) 10.2 0.93 (0.85-0.98) 68.6 0.0194 Table 3a. The automatic static method for re-examination (RE) and repositioning (RP) of TCBF. The number of vessels with valid fit-quality was 15 for the carotids and 13 for the vertebrals.

Automatic dynamic method Manual Method Sys diff p-value

Mean (stdev) CV (%) ICC (95% rel) Mean (stdev) CV (%) ICC (95% rel) RE

RP 620.8 (34.1)

597.6 (29.0) 5.5

4.6 0.92 (0.66-0.98)

0.96* (0.83-0.99) 577.4 (55.1)

565.5 (58.9) 9.7

10.3 0.95 (0.88-0.99)

0.92 (0.83-0.98) 43.4

32.1 0.059 0.047

Table 3b. The automatic dynamic method versus the manual method for re-examination (RE) and repositioning (RP) of TCBF. The number of vessels with valid fit-quality was 13 for the carotids and 11 for the vertebrals.

The mean flow and standard deviation, the coefficient of variation (CV) and the intra-class correlation (ICC) with 95% reliability and the number of used vessel (number of internal carotids + number of vertebrals) for the three methods for TCBF determination. When the automatic method performs better than the conventional manual analysis it is indicated by *, when it performs significantly better (2 std. dev.) it is indicated by **.

Inter-observer variability Intra-observer variability

CV (%) ICC (95%) CV (%) ICC (95%)

TCBF 9.5 0.97 (0.95-0.99) 3.9 0.96 (0.91-0.98)

Table 4. The inter- and intra-observer variability is only applicable for the manual method.

Based on the value of the fit-quality parameter in the automatic dynamic method, two series of a vertebral artery were designated as inadequate data points because of insufficient quality in one or more time slices. Also two internal carotids had an

unsatisfactory fit quality. These measurements were excluded from further analysis. The mean flow volumes, standard deviations CV’s, ICC’s, systematic differences and P_values for the three methods are presented in Table 2a and 2b. The CV’s for the automatic static method were 35 per cent of the CV values for the manual method. The ICC data made clear that the automatic static method performed better (but not always statistically significant) than the manual analysis approach. The automatic static method also

performed also better than the automatic dynamic method. The number of iterations for the automatic static method was 21 (± 5) and for the automatic dynamic method 306 (± 37).

The computation time (on a 440 MHz SUN SPARC, Solaris) to fit 1 to 16 paraboloids equals a few seconds per vessel.

It has to be noted that for these measurements the head-coil was used because this study was part of a larger clinical trail aiming at the brain^12,13. When carotid- and vertebral arteries are measured, results can be improved by using the head-neck coil.

IC C r e - e x a m in a t io n

0 .6 5 0 .7 0 .7 5 0 .8 0 .8 5 0 .9 0 .9 5 1 1 .0 5

# 1 5 + 1 3 1 3 + 1 1 1 5 + 1 3 .

T C B F a u to s ta tic T C B F a u to d y n . T C B F m a n u a l

Figure 3. Graphical illustration of the inter-class-correlation with 95% reliability intervals for the TCBF for re-examination.

2.3.3 Re-examination and reposition variability for TCBF

The mean flow volumes, standard deviations, CV’s, ICC’s , systematic differences and P- values are presented in Table 3a and 3b. The ICC data of the TCBF are presented in Figure 3 for the re-examination procedure and in Figure 4 for the repositioning procedure. The CV for the automatic dynamic method was 51 per cent of the CV for the manual method.

For the automatic static approach the CV was 32 per cent when compared with manual.

For the re-examination it is even 22 per cent compared to the CV for manual analysis. The ICC data shows that for re-examination the automatic static method performed

significantly better than the manual method. Note that the dynamic method excludes more vessels, because the fit-quality had to be good in all the individual time bins.

2.3.4 Intra- and inter-observer variability for manual analysis

The results for the intra- and inter-observer variabilities are presented in Table 4.

This table shows that the CV for the intra-observer variability was much smaller than the one for the inter-observer variability. The ICC values are nearly identical.

IC C re p o s itio n in g

0 .6 5 0 .7 0 .7 5 0 .8 0 .8 5 0 .9 0 .9 5 1 1 .0 5

# 1 5 + 1 3 1 3 + 1 1 1 5 + 1 3 .

T C B F a u to sta tic T C B F a u to d yn . T C B F m a n u a l

Figure 4. Graphical illustration of the inter-class-correlation with 95% reliability intervals for the TCBF for re-positioning.

2.4 Discussion

2.4.1 Validity of parabolic velocity profiles

In this paper we present the development and validation of a new automatic method for the assessment of flow in small arteries by MRI. In Figure 2a en 2b a typical velocity profile for an internal carotid artery and the fitted paraboloid are presented.

For the in-vivo situation the measured signal was a summation of non-parabolic shapes¹⁴. Deviations from the paraboloid were visible on the MR images, but the fitting of a parabolic profile shape has proven to give good results for the flow determination and is a precise method for segmenting small vessels. For larger vessels, vessels with plaques, vessels with significant motion as for instance the coronary arteries, and vessels with branches this method can only be useful if the parabolic shape of the velocity profile a is reasonable approximation in all cardiac phases. This is the case when the vessel is small enough, the motion correction is sufficient and the measuring plane is far enough from the branching.

PC-velocity images can be carried out on clinical applications of flow measurements in the renal arteries ¹⁵, portal vein ¹⁶, mesenteric vein ^16,17 and the coronaries¹⁸. This method can be applied on these measurements but adaptations as tracking of movements and

corrections for variation in the angle between the cross section and the measuring plane, will be needed. Thresholds are used to eliminate phase errors resulting from partial volume effects, noise and slow flow. Therefore, the thresholds require adaptation in other cases.

But when repetitive measurements of the vessels in a small group of volunteers or patients are available, the threshold can be set by optimization of the ICC value. This was

described in the section: "Automatic contour detection procedure for small vessels" in

"Materials and Methods".

2.4.2 Errors sources for the various methods

For the manual method the random and systematic errors were due to a combination of the intrinsic errors associated with the manual drawing of the contours by the different observers, plus the changes in flow volumes associated with measurements taken at various time points of the same vessel. For the automatic methods (both the static and the dynamic method) the inter- and intra-observer variability was equal to zero. The variability is caused by errors in the calculation of the flow rate, and truly existing changes in flow volumes in volunteers. Our findings demonstrate that the automatic static contour detection procedure was significantly more accurate than the manual contour detection procedure.

The greater reliability for the automatic methods was probably partly due to the way of dealing with the individual pixels. In small vessels, such as the carotid and vertebral arteries, and scans with a limited resolution, most of the pixels are edge-pixels. This is illustrated in Figure 5, demonstrating a typical example of an internal carotid artery in relation to the pixel size. When contours of vessels were defined manually, individual pixels need to be selected. The automatic methods fit a paraboloid first and then determine whether the middle of a pixel is inside or outside of the vessel.

When comparing our method with the method of Hoogeveen⁵, the most striking difference is that Hoogeveen’s manual drawings method is overestimating the flow rate while our method is underestimating the flow rate. Hoogeveen, however, is working with non- triggered pcMRI, while our data had 16 time slices during the cardiac cycle. Spilt¹⁹ has shown that triggered pc MRI results in lower flow values than non-triggered pcMRI, but this can only explain part of the difference, since our phantom data show always

underestimation of the real flow. When comparing Hoogeveen’s method with our method, it is apparent that the variation in the non-triggered in vivo data of Hoogeveen is about 10

% and our triggered measurements give a variability between 2.7 % and 5.7 % for the automatic static method and between 4.4 % and 8.2 % for the automatic dynamic method.

Spilt has demonstrated that the reproducibility of triggered measurements is better than for non-triggered pcMRI, and Hoogeveen uses another method to determine the error.

Therefore the methods cannot directly be compared.

Figure 5. Example of vessel segmentation for a small vessel on the basis of pixel settings when more than half of the pixel is inside the vessel. Note that the segmented vessel does not preserve the vessel shape.

2.4.3 Used corrections

A threshold was needed to stabilize the fitting procedure. The threshold was set at a percentage of the maximal value of the paraboloid fitted on the time-averaged flow profile.

It was different for steady and pulsatile flow and for the carotids and vertebrals. The threshold can be related to systematic deviations from a parabolic velocity profile. For pulsating flow these deviations are expected to increase with the diameter of the artery.

When the vessels do not appear to be circular or are not clearly visible during all cardiac phases, χ² [Eq. 2] is too large. Vessels appeared circular on visual inspection and clearly visible during all cardiac phases; only one out of the total of 81 vessels in this data set was rejected. The TCBF in this paper may seem to be low. However, this was a result of the rejection of some flow values needed for the statistics. When one acquisition had a quality parameter, which was too high, the whole series of that particular vessel had to be rejected.

2.4.4 Summary

In summary, the validation results demonstrate that the automated method gave better results than the manual method. For the phantom studies, with the exception of FOV 300, the CV of the automatic methods was comparable to the manual method. For the in-vivo studies the CV was approximately four times smaller for the automatic static method and two times smaller for the automatic dynamic method. The reproducibility (expressed in the ICC) was always better for the automated methods. For the automated dynamic method in the phantom and for the static method in the vivo studies the difference was significant.

2.5 Conclusions

In conclusion, the method proposed in this study allows the rapid, fully automatic and accurate assessment of flow values in carotid and vertebral arteries. This method permits

incorporated in clinical MRI protocols. This method can be applied to static as well as dynamic data. The advantages of this automatic method over manual methods were shorter analysis time, the absence of inter- and intra- observer variability and a better

reproducibility.

Acknowledgements

The authors are grateful to Koos Zwinderman, PhD, for his statistical advices. They are also grateful to the experts Hans van Assen, MSc., Michael Egmont Petersen, PhD, Jorrit Schaap, MSc, and Berend Stoel, PhD, for the accurate drawing of the vessel contours.

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