Spilt, A.
Citation
Spilt, A. (2006, March 9). Changes in total cerebral blood flow and morphology in aging.
Retrieved from https://hdl.handle.net/1887/4342
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Corrected Publisher’s Version
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Licence agreement concerning inclusion of doctoral thesis in the
Institutional Repository of the University of Leiden
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Autom ati
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vessel
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blood fl ow quantifi cation in small vessels with
velocity encoded magnetic resonance imaging
Frieke M.A. Box Aart Spilt
Mark A. van Buchem Rob J. van der G eest Johan H.C. Reiber
Investigative Radiology 2003; 38:567-577
Rationale and Objectives
The quantitative assessment of blood fl ow in peripheral vessels from phase-contrast magnetic resonance 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 signifi cant inter- and intraobserver variabilities. The aim of this study was to verify whether automatic model-based segmentation decreases these problems by fi tting a model to the actual blood velocity profi le.
M ethods
In this study two new fully automatic methods (a static and a dynamic approach) were developed and compared with manual analyzes using phantom and in vivo studies of internal carotid and vertebral arteries in healthy volunteers. The automatic segmentation approaches were based on fi tting a 3D parabolic velocity model to the actual velocity profi les. In the static method, the velocity profi les were averaged over the complete cardiac cycle, whereas the dynamic method takes into account the velocity data of each cardiac time bin individually. M aterials consisted of the magnetic resonance imaging data from three straight phantom tubes and the blood velocity profi les of eight volunteers.
Results
For the phantom studies, the automatic dynamic approach performed signifi cantly better than the manual analysis (intraclass correlations [ICC] of 0.62-0.98 and 0.30-0.86, respectively). For the assessment of the total cerebral blood fl ow in the in vivo studies, the automatic static method performed signifi cantly better than the manual one (ICC of 0.98-0.98 and 0.93-0.95, respectively). However, the automatic dynamic method was not signifi cantly better than the manual one (ICC = 0.92-0.96) but had the advantage of providing additional parameters.
Conclusion
Introduction
Under physiological circumstances, blood fl ow to the brain is secured by autoregulation mechanisms. Pathologic conditions, such as an internal carotid artery stenosis, may give rise to diminished cerebral blood fl ow, which may cause neurologic symptoms. Furthermore, it has recently been demonstrated that age-related white matter lesions are associated with decreased total cerebral blood fl ow (TCBF). TCBF can be assessed by summation of the individual fl ows 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 fl ow measurements can be determined by cine phase-contrast magnetic resonance (MR) fl ow velocity mapping26. This noninvasive
imaging technique allows the assessment of fl ow in vessels over a full cardiac cycle.
Q uantifi cation of fl ow from such MR examinations requires a postprocessing 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. G iven the small size of the arteries supplying the brain, accuracy also is restricted by the image resolution. For studies aiming at detecting small changes in fl ow, manual image analysis will be inadequate and more accurate and reproducible computer assisted automatic methods are needed33.
In previous literature, various automatic segmentation methods have been proposed for more accurate and reproducible measurement of fl ow 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 interuser variabilities34. O yre et al
proposed a method of fi tting parabolic velocity profi les to the MR velocity data in multiple sectors on the pixels inside the vessel and close to the vessel boundary35. 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 Hoogeveen et al is also based on fi tting a parabolic velocity profi le on measured MR data36. The
difference with our work is that Hoogeveen assumes the underlying velocity profi le to be parabolic, whereas we assume that the MR measures the parabolic velocity profi le without errors.
The purpose of the current study, therefore, was to develop and validate a fast, user-independent automatic segmentation approach that is relatively simple to implement on each MR machine and fl ow protocol. It is based on a pragmatic MR TCBF acquisition protocol that yields accurate and reproducible fl ow data.
It was assumed that a parabolic fl ow velocity profi le is a valid model for the blood fl ow in the intracranial vessels given its small diameter and the relatively constant fl ow rate over the cardiac cycle. The proposed automatic segmentation approach, therefore, is based on the fi tting of a three-dimensional parabolic velocity profi le to the actual velocity data, thus providing boundary positions of the vessel of interest.
Two different methods were investigated: the fi rst, static method, takes the average velocity profi le over the complete cardiac cycle into consideration. The fl ow 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 fi tting for each individual phase in the cardiac cycle and calculates the fl ow volume by the analytical integration of the individual paraboloids. The accuracy and reproducibility of these new automatic segmentation approaches were evaluated and compared with the conventional manual analysis using phantom and in vivo studies.
Materials and methods Study Design
A method to assess the TCBF in an accurate and fast manner without inter- or intrauser variability has been developed and tested. The method is based on a fi rst approximation of the blood fl ow properties. This means that this method is based on the assumptions that these vessels are round in shape and that the fl ow in these vessels is characterized by a fully developed steady laminar fl ow profi le so that a parabolic velocity profi le is valid. These assumptions are supported by the following observations in the existing literature: 1) for small vessels outside of the thorax, the velocity profi le in a vessel can be described by a paraboloid37,38; and 2) most arteries and in particular small arteries are
circular in shape35-37. The blood fl ow volumes of three straight phantom tubes
cycle, whereas the static method uses the average of this fl ow volume. Because 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 fl ows through these vessels, the TCBF. Furthermore, the inter- and intrauser variability for the manual methods were evaluated.
Phantom Study
To compare the results of the manual and automatic contour detection procedures in an objective manner, twelve acquisitions— three for each fi eld of view (FOV)— with pulsatile fl ow were obtained in a phantom using FOVs varying from 150 to 300 mm. Variation of the FOV simulates fl ow 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 fl ow phantom consisted of 3 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 fl ow volume delivered by the pump was set at 551.76 ml/min (9.196 ml/s). The fl ow curve as a function of time (fl ow(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).
Study Population
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 as follows: TE 9 milliseconds, TR 16 milliseconds, 7.5° fl ip angle, 5-mm slice thickness, 150-300 mm FOV 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.
Quantitative Analysis Approach
described in detail elsewhere29. MRI-FLOW provides an intuitive user-interface
for viewing and interaction with all images, which are acquired during a velocity-encoded study (Figure 1).
Automatic Contour Detection Procedure for Small Vessels
To assess the fl ow through these small cranial vessels, we have assumed the cross section of the vessel to be circular and the velocity profi le to be parabolic.
The velocity profi le u(x,y) is shown in Figure 2a and b and is described by the following:
(equation 1)
where x and y represent the distances to the initial point in number of pixels, whereas 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 profi le.
To fi t the paraboloid to the actual velocity profi le a Levenberg–Marquardt algorithm was used, which minimizes the X2 error (Ƹ2):
(equation 2)
for nonlinear functions39, where ǎ
i is the measured velocity for a particular pixel
and ui is the fi tted velocity. The error ǔi for each data-point ǎi was defi ned as
follows:
(equation 3)
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 weight40. As a result, equation 2 can be written
as follows:
(equation 4)
The basic assumption was that the error was largest for low velocities. Experimentally it was found that this error estimation gave good stability. The fi tting 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 (fi ve 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 fi tting procedure. As a consequence of this threshold, errors resulting from slow fl ow, phase noise, and partial volume effects were removed. The paraboloid
was fi tted by the Levenberg Marquardt algorithm. This fi tting procedure was conducted iteratively until the X2 error did not decrease anymore; at that time
the fi nal solution was obtained. Based on the results from this parabolic fi tting procedure, the contour of the vessel of interest was defi ned; The threshold level was determined by minimalization of the random error in the ICC (see statistical analysis section). This means that the ICC was maximized.
A quality parameter was defi ned by the sum of the squared differences between the fi tted values and the measurement values divided by the number of pixels inside the mask. The fi ttings were designated ‘inadequate’ when the difference between the measurements and the fi tting 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 fl ow parallel to the image plane was not negligible. The data was processed in one or two iterations: for the automatic static method only iteration one was used, while for the automatic dynamic method two iterations were used.
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 fi tted on the remaining data. For the static method the threshold was set at 0.4 times the maximum measured velocity (Amax). Based on the results from this parabolic fi tting procedure, the contour of the vessel of interest was defi ned; it is the circle for which the paraboloid equals zero. Finally, the fl ow 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 0.40 cm/s and for a vertebral artery assuming four pixels, below 0.23 cm/s, to be valid. The procedure used in the automatic static method is also explained in Figure 2a.
Automatic Dynamic Method
fi xed value in one or more time bins, the fi t 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 four pixels, below 0.20 cm/s, to be valid. The procedure used in the dynamic method is also explained in Figure 2b.
Manual Contour Defi nition Procedure
For this type of study the manual contour defi nition is known as the conventional method. Each acquisition run was analyzed manually in an independent manner by seven 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 conducted 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 defi ned 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 fl ow values were calculated by multiplication of the measured velocities inside the ROI times the area of the ROI.
Intra- and Interobserver Variability
Because there was no inter- or intraobserver variability associated with the automatic method these sources of error were only analyzed for the manual method. To determine the interobserver variability seven experts traced the contours of the four vessels in the images of eight healthy volunteers. The intraobserver 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 with the fi rst ones of the same expert. The time between the two drawing sessions varied between two and fi ve weeks.
Statistical Analysis
(re-examination or reposition) of each vessel under study. Then these CVs were averaged to obtain the total CV, which will be presented under the Results section.
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 ICC analysis was used for that purpose. The ICC is defi ned as: (ST2 / (ST2 + Se2)), were ST2 is the component
of variance as the result of error free variability among subjects and Se2 is the component of variance due to the random measurement error41. Also the
95% reliability interval of the ICC is determined. Finally, for the manual method only, the interobserver variability was calculated to assess the variation in fl ow volume caused by segmentation conducted by different users. The intraobserver variability was calculated to compare the errors produced by one observer. The automatic methods had no inter- or intraobserver variability associated with it.
Method; FOV Flow volume (ml/min) Coeffi cient of variation (%) Systematic Error (ml/min) ICC (95% rel) MM; 150 502.51 3.09 -44.25 -MM; 200 513.85 4.43 -37.91 -MM; 250 504.10 2.75 -47.66 -MM; 300 512.93 4.22 -38.83 -Mean MM 509.59 3.26 -42.17 0.62 (0.30-0.86) ASM; 150 479.80 2.73 -71.96 -ASM; 200 488.85 2.47 -62.91 -ASM; 250 496.70 2.73 -55.06 -ASM; 300 478.87 7.52 -72.89 -Mean ASM 486.05 3.86 -65.71 0.78 (0.53-0.92) ADM; 150 540.60* - - -ADM; 200 541.86 1.23 -9.90 -ADM; 250 545.82 4.48 -5.94 -ADM; 300 474.85 6.44 -76.91 -Mean ADM 520.84† 4.05† -30.92 0.85 (0.62-0.96)* Table 1 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 fl ow amount is 551.76 ml/min. Each FOV is scanned 3 times. MM stands for manual method; ASM is Automatic Static Method, and ADM is Automatic Dynamic Method.
* Note that the tubes with diameters 5 and 8 mm gave NaN. The fl ow volume given is three times the fl ow 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 analysis is not everywhere exactly the same.
†Based on FOV 200, 250, and 300.
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.
Results Validation
The amount of nonpulsatile fl ow selected in the phantom study was comparable to the fl ow volume in the carotid arteries. The results of the phantom studies are given in Table 1 for the range of FOVs (150, 200, 250, and 300). An FOV of 300 resulted in a larger standard deviation in the derived fl ow volumes. The automatic dynamic method was unable to calculate fl ow volumes for most cases at a FOV of 150. For an average FOV (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 coeffi cient of variation (2.86%). The ICC indicates that the reproducibility was signifi cantly better compared with 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
Table 2a Automatic Static Method Compared With the Manual Method for Re-examination (RE) and the Repositioning (RP) of Individual Vessel
The number of vessels with valid fi t-quality was 15 for the carotids and 13 for the vertebralis Automatic Dynamic Method Manual Method
Mean (SD) CV (%) ICC (95% rel) Mean (SD) CV (%) ICC (95% rel) Sys Diff P value RE ICA 289.8 (7.5) 2.7 0.97 (0.91-0.99)† 257.8 (27.2) 11.0 0.90 (0.82-0.96) 32.0 8.27.10-5 RP ICA 278.1 (12.9) 4.3 0.93 (0.82-0.88)* 250.8 (27.7) 11.1 0.84 (0.73-0.93) 27.4 0.0015
RE VA 109.0 (5.4) 4.7 0.96 (0.87-0.99)* 101.0 (12.5) 13.2 0.94 (0.89-0.98) 8.0 0.352 RP VA 108.0 (6.6) 5.7 0.95 (0.86-0.99)* 97.3 (12.4) 14.0 0.94 (0.89-0.98) 10.7 0.189
Automatic Dynamic Method Manual Method
Mean (SD) CV (%) ICC (95% rel) Mean (SD) CV (%) ICC (95% rel) Sys Diff P value RE ICA 285.2 (13.7) 5.6 0.93 (0.82-0.88)* 257.5 (25.9) 10.6 0.92 (0.86-0.91) 27.7 0.0028 RP ICA 278.6 (14.0) 4.4 0.94 (0.83-0.98)* 251.5 (27.8) 11.2 0.87 (0.76-0.95) 27.1 0.0036 RE VA 114.4 (9.9) 8.2 0.86 (0.58-0.96) 107.3 (12.8) 9.7 0.94 (0.88-0.98) 7.1 0.0062 RP VA 111.6 (8.5) 6.5 0.96 (0.86-0.99)* 105.5 (13.0) 12.3 0.94 (0.88-0.98) 6.1 0.0002 Table 2b Automatic Dynamic Method Compared with the Manual Method for Re-examination (RE) and the Repositioning (RP) of Individual Vessels
The number of vessels with valid fi t-quality was 13 for the carotids and 11 for the vertebralis.
into account—has a smaller CV. Also the ICC gave a better reproducibility for the automatic static method compared with the manual one, but that was not statistically signifi cant.
Reproducibility for Re-examination and for Reposition of Individual Vessels To determine the stability of the method in time, two repeated measurements 1 directly after the other, were conducted (re-examination). To determine the stability of the method for repositioning, the volunteer was scanned, repositioned, and scanned again. The study was performed on eight subjects. Because 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 carotid arteries and 16 vertebral arteries. Some scan series could not be used: three vertebral arteries had little fl ow and were not clearly visible; furthermore, one internal carotid artery was found to be noncircular in shape. This left a total of 15 internal carotid arteries and 13 vertebral arteries for further analysis. Based on the value of the fi t-quality parameter in the automatic dynamic method, two series of a vertebral artery were designated as inadequate data points because of insuffi cient quality in one or more time slices. Also two internal carotid arteries had an unsatisfactory fi t quality. These measurements were excluded from further analysis. The mean fl ow volumes, standard deviations CVs, ICCs, systematic differences, and P values for the three methods are presented in Table 2a and b. The CVs for the automatic static method were 35% of the CV values for the manual method. The ICC data made clear that the automatic static method performed better (but not always statistically signifi cant) than the manual analysis approach. The automatic static method 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 fi t one 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 brain42,43.
When carotid and vertebral arteries are measured, results can be improved by using the head-neck coil.
Re-examination and Reposition Variability for TCBF
Figure 3 Graphical illustration of the ICC with 95% reliability intervals for the TCBF for re-examination.
ICC re-examinat ion
0.65 0.7 0.75 0.8 0.85 0.9 0.95 1
Automatic static method Automatic dynamic method Manual method
Automatic Static Method Manual Method
Mean (SD) CV (%) ICC (95% rel) Mean (SD) CV (%) ICC (95% rel) Sys Diff P value 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 Automatic Static Method for re-examination (RE) and Repositioning (RP) of TCBF
Automatic Dynamic Method Manual Method
Mean (SD) CV (%) ICC (95% rel) Mean (SD) CV (%) ICC (95% rel) Sys Diff P value RE 620.8 (34.1) 5.5 0.92 (0.66-0.98) 577.4 (55.1) 9.7 0.95 (0.88-0.99) 43.4 0.059 RP 597.6 (29.0) 4.6 0.96 (0.83-0.99)* 565.5 (58.9) 10.3 0.92 (0.83-0.98) 32.1 0.047 The number of vessels with valid fi t-quality was 15 for the carotid arteries and 13 for the vertebral arteries.
Table 3b Automatic Dynamic Method Versus the Manual Method for Re-examination (RE) and Repositioning (RP) of TCBF
The number of vessels with valid fi t-quality was 13 for the carotid arteries and 11 for the vertebral arteries.
The mean fl ow and standard deviation, the coeffi cient of variation (CV) and the intra-class correlation (ICC) with 95% reliability and the number of used vessels (number of internal carotid arteries + number of vertebral arteries) for the three methods for TCBF determination. When the automatic method performs better than the conventional manual analysis it is indicated by *, and when it performs signifi cantly better (2SD) it is indicated by †.
was 32% when compared with manual. For the re-examination it is even 22% compared with the CV for manual analysis. The ICC data shows that for re-examination the automatic static method performed signifi cantly better than the manual method. Note that the dynamic method excludes more vessels, because the fi t-quality had to be good in all the individual time bins.
Intra- and Interobserver Variability for Manual Analysis
Discussion
Validity of Parabolic Velocity Profi les
In this work, we presented the development and validation of a new automatic method for the assessment of fl ow in small arteries by MRI. In Figure 2a and b, a typical velocity profi le for an internal carotid artery and the fi tted paraboloid are presented.
For the in vivo situation, the measured signal was a summation of nonparabolic shapes44. Deviations from the paraboloid were visible on the MR images, but
the fi tting of a parabolic profi le shape has proven to give good results for the fl ow determination and is a precise method for segmenting small vessels. For larger vessels, vessels with plaques, vessels with signifi cant motion as for instance the coronary arteries, and vessels with branches this method can only be useful if the parabolic shape of the velocity profi le a is reasonable approximation in all cardiac phases. This is the case when the vessel is small enough, the motion correction is suffi cient and the measuring plane is far enough from the branching.
Figure 4 Graphical illustration of the ICC with 95% reliability intervals for the TCBF for repositioning.
ICC reposit ioning
0.65 0.7 0.75 0.8 0.85 0.9 0.95 1
Automatic static method Automatic dynamic method Manual method
Interobserver Variability Intraobserver Variability CV (%) ICC (95%) CV (%) ICC (95%) TCBF 9.5 0.97(0.95-0.99) 3.9 0.96(0.91-0.98)
PC velocity images can be conducted on clinical applications of fl ow measurements in the renal arteries45, portal vein46, mesenteric vein46,47 and
the coronaries48. 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 fl ow. 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 the Materials and Methods.
Error Sources for the Various Methods
For the manual method, the random and systematic errors were caused by a combination of the intrinsic errors associated with the manual drawing of the contours by the different observers, plus the changes in fl ow 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 intraobserver variability was equal to zero. The variability is caused by errors in the calculation of the fl ow rate and truly existing changes in fl ow volumes in volunteers. Our fi ndings demonstrate that the automatic static contour detection procedure was signifi cantly more accurate than the manual contour detection procedure. The greater reliability for the automatic methods was probably partly caused by 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 defi ned manually, individual pixels need to be selected. The automatic methods fi t a paraboloid fi rst and then determine whether the middle of a pixel is inside or outside of the vessel.
When comparing our method with the method of Hoogeveen36,the most striking
difference is that Hoogeveen’s manual drawings method is overestimating the fl ow rate whereas our method is underestimating the fl ow rate. Hoogeveen, however, is working with non triggered pcMRI, whereas our data had 16 time slices during the cardiac cycle. Spilt et al49 have shown that triggered pc MRI
results in lower fl ow values than non triggered pcMRI, but this can only explain part of the difference, since our phantom data show always underestimation of the real fl ow. 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– 5.7% for the automatic static method and between 4.4–8.2% 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.
Used Corrections
A threshold was needed to stabilize the fi tting procedure. The threshold was set at a percentage of the maximal value of the paraboloid fi tted on the time-averaged fl ow profi le. It was different for steady and pulsatile fl ow and for the carotid and vertebral arteries. The threshold can be related to systematic deviations from a parabolic velocity profi le. For pulsating fl ow 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, X2 (equation 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 work may seem to be low. However, this was a result of the rejection of some fl ow 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.
Summary
