Eur J Vasc Endovasc Surg 16, 517-524 (1998)

Automatic Accurate Non-invasive Quantitation of Blood Flow, Cross- sectional Vessel Area, and Wall Shear Stress by Modelling of Magnetic

Resonance Velocity Data*

S. Oyre-i -~-3, W. P. Paaske ~, S. Ringgaard 2, S. Kozerke 3, M. Erlandsen 4, P. Boesiger ~ and E. M. Pedersen ~'2

1Department of Cardiothoraczc and Vascular Surgery T and 2MR Research Centre, Institute of Experimental Clinical Research, Aarhus Universzty Hospital, Skejby Sygehus, Aarhus, Denmark, 3Institute of Biomedical Engineering and

MedtcaI Informatics, Universzty of Zt~rich and Swiss Federal Institute of Technology, Z12rich, Switzerland, 4Department of Biostatzstics, Aarhus Umverszty, Denmark

Objectives: to apply a new, automatzc and non-mvasive method for quantzfication of blood flow, dynamic cross-sectional vessel area, and wall shear stress (WSS) by m wvo magnetic resonance veloczty mapping of normal subjects. Design: prospectzve, open study. Materials: six young volunteers. Methods: a three-dimenszonal parabolozd model enabhng automatzc determmatzon of blood flow, vessel distensibzhty and WSS was apphed to blood velocity determmatmns zn the common carotzd artery Blood flow was also determined by a manual edge detection method. Results: using the new method, the common carotzd mean blood flow was 7.28 (5 61-9 63) (mean (range)) ml/s By the manual method blood flow was 7.21 (5.55-9 60) ml/s. Mean luminal vessel area was 26% larger in peak systole than in diastole. Mean/peak WSS was 0 82/2.28 N/m 2. Manually and automatzcally determined flows correlated (r2=0.998, p<O.O001). WSS and peak centre velocity were associated (r2= 0 805, p<O.O001). Conclusions: blood flow, luminal vessel area ddatatzon, and WSS can be determined by the automatic three-dimens~onal parabolozd method. The hypotheszs of assoczatzon between peak centre veloczty and WSS was not contradicted by the results of the present study.

Key Words. Blood flow; Carotid artery; Haemodynamics, Magnetzc resonance zmagmg; Wall shear stress

Introduction method of volumetric analysis have been shown to have high inter-user variability in routine practice. 7's

MR phase contrast velocity mapping techniques with In addition, accurate detection of vessel wall position high temporal and spatial resolution have made it and blood flow velocity estimations are necessary for possible to determine, in vivo and in humans, blood determinations of WSS and vessel distension. It has flow velocity vectors during the entire heart cycle, been assumed that WSS could be estimated from volume blood flow in large 1 and smaller vessels, 2'3 velocity measurement of blood movements in the blood vessel distensibility (compliance), 4 and wall centre point of a vessel? '1° Recent measurements wi th shear stress (WSS). 5'6 Clinical applications of the tech- high spatial resolution techniques using ul t rasound niques are time consuming, but since essential in- Doppler have shown that this assumption is probably formation on haemodynamics can be obtained, the erroneous) 1'~2 need for accurate and automatic procedures is ap- We have previously presented a method for de- parent, termination of WSS based on subpixel edge detection?

Phase contrast flow measurements with a manual The present paper introduces a new MR based tech- nique with automatic acquisition of a large number of blood velocity data in connection with a priori

* Ttus paper was awarded the ESVS prize for the best experimental knowledge of the blood-vessel wall boundary layer paper, 1997 t Please address all correspondence to' S. Oyre, Department of and of the blood flow profile. The method relies on Cardlothoraclc and Vascular Surgery T, Aarhus Umversity Hospital, the assumptions that laminar conditions exist in a Skejby Sygehus, DK-8200 Aarhus N, Denmark. finite interface layer with zero velocity at the vessel

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518 S. Oyre et al.

u(x,y) ~ The data were collected automatically in two steps. First, a simple magnitude masking was applied as previously described# Second, only the pixels in the ROI with velocities in the area of 20-80% of the peak centre velocity (centre of ROI) were collected (Fig. 2). The first step eliminated noise outside the vessel, while the second step selected velocities in the middle of the boundary layer.

The pixels from this automatic selection were sub- sequently fitted by multiple linear regression (least

J.× square method) to the 3-DP equation.

Fig. 1. A three-dlmenmonal (3-D) surface plot of a 3-D parabolold This profile is vahd for Polseullle flow m rigid tubes u(x,y) is the velocity m the x,y coordinate system.

Automatic edge detectmn and blood flow calculatzons wall, and that the blood stream profile in the boundary layer can be described by a three-dimensional para- The circumferential vessel wall position was computed boloid (3-DP) as previously described (unpublished throughout the heart cycle assuming zero velocity at results 1997). the vessel wall, and the cross-sectional vessel area

The aims of the study were: (i) to apply the automatic was calculated. Volume blood flow was calculated by 3-DP technique to the common carotid arteries (CCA) summation of all pixel velocities within the vessel. of normal subjects, (ii) to compare automatic flow The peak central blood flow velocity was found as the determination using the automatic 3-DP method with average of the central nine pixels, i.e., nine pixels manually determined edge detection and blood flow, covering a 1.5 x 1.5 mm 2 square area in the centre of and (iii) to test the hypothesis that there is an as- the vessel. sociation between WSS and peak centre velocity meas- urements.

Materials and Methods Manual edge detectmn and blood flow calculations

Theory of three-dimensional paraboloid model A simple detection of the vessel wall was performed: a circle was fitted through two points placed manually

The method is based on the following assumptions: on the "top" (anterior) and "bottom" (posterior) of (i) the blood velocity at the vessel wall is zero, (ii) the the vessel by visual inspection of the cross-sectional blood flow in the boundary layer of the common magnitude image. Volume blood flow was calculated carotid artery is parabolic and has rotational symmetry, by summation of all pixel velocities within this circle. and (hi) arteries are circular in shape when cut per- pendicularly.

This gives the following equation describing the three-dimensional paraboloid (3-DP) blood flow ve- Wall shear stress calculatzons locity profile in the boundary layer close to the artery wall: Wall shear stress (WSS) is the term for the mechamcal

u(x,y) = a(x 2 + y2) + bx + cy + d stresses on the vessel wall exerted by the flowing blood.

where u(x,y) is blood velocity in the x,y coordinate Assuming Newtonianblood and non-slip conditions at system, and a, b, c and d are the parameters to be the vessel wall, WSS is the dynamic viscosity (4.3 cP 9) determined (see Fig. 1). multiphed with the velocity gradient at the vessel

wall. The gradient was calculated by differentiating the equation for the 3-DP model at the vessel wall.

Automatic selectzon of pzxels for 3-DP fitting The peak systolic, end diastolic, and average WSS in the cardiac cycle were calculated. The peak systole

The only user interaction was identification of the and end diastole heart phases were identified as the vessel of interest by selecting a circular region-of- heart phases with the highest and lowest flow, re- interest (ROI) on the peak systolic heart phase, spectively.

Eur J Vasc Endovasc Surg Vol 16, December 1998

Accurate Automatic Blood Flow 519

Peak systole profile Peak u (100%)

peak80% Ofu ! ~ .......... ! -~ .................................. r .....................

p~ai~//~ ~ ~ =

' 09 , : [~

20% of : -~ " " u~ ', ' 09

:: ; B o u n d a r y : , P o s i t i o n i n r a d m l i ' l a y e r d i m e n s i o n , r . i~ Radius

Fig. 2. The prmaple of the automahc three-&mensmnal paraboloid (3-DP) method A plot of flow velocity, u, as a funchon of length m radml &menmon, r, used for the automahc selechon of the plxels according to their velocity m relahon to the centre velocffy.

In vivo measurements Results

Six healthy young volunteers were studied (mean age Table 1 presents the in vivo results for peak systole, 25.8; range 20-36; three males) as approved by the end diastole, and mean of all heart phases. Mean institutional committee on human research, and in- luminal vessel area was 26% larger in peak systole dividual informed consent was obtained. Magnetic than in diastole. In Table 2 the statistics from the 3- resonance examinations were performed with a 1.5 T DP fits are summarised. whole body scanner (Philips Gyroscan-ACS-NT, Phil- Figure 3 shows the development of a representative ips Medical Systems, Best, The Netherlands). To op- velocity contour profile and surface plots from peak timise the signal-to-noise ratio, a standard 8cm systole to end diastole. In peak systole, the flow diameter circular surface coil was positioned over profiles were blunt in all six subjects and slightly the carotid artery. Perpendicular blood flow velocity skewed from the centre (Fig. 4). The parabolic form measurements in the common carotid artery (CCA) of the velocity profiles is clearly seen in the surface were performed 2 cm below the carotid bifurcation plots as well as in the contour plots (Figs 3 and 4). after initial visualisation of morphology by sagittal, We estimated the difference in elliptic component in transversal and coronal conventional images. A stand- peak systole by measuring the 0.1 m / s velocity ard ECG retrospectively triggered phase contrast contour diameter (the lowest velocity contour line sequence with bipolar velocity encoding gradients was shown in Fig. 4) in the long and in the short axis used. Velocity encoding was performed along the slice- using a ruler. We found 0% difference in two subjects, select direction. Thirty-two frames were recorded and between 5-11% difference in four volunteers throughout the cardiac cycle with an interval of 25 ms. (Figs 4b-e). In late systole, a small area of blood The thickness of the slice was 7mm, and in-plane flow separation was seen in six persons at the pixel resolution 0.5 x 0.5 mm 2 (data acquisition matrix posterior wall (Fig. 3b at 11 o'clock). During early 128 x 128 points, 64 mm field of view). Two signal diastole, the dicrotic notch was seen as a second averages, 8 ms echo time acquiring a full echo, and a peak in the velocity patterns of all subjects. At tl-us maximum velocity sensitivity of + 90 cm/s were used. time, all profiles were still blunt and slightly skewed.

During diastole, the velocity profiles became almost developed and parabolic, but still more or less skewed as demonstrated by the profile from end

Statzstics diastole in Fig. 3d (towards 5 o'clock). Figure 5 shows the automatically calculated blood

The 3-DP model statistics used were the root mean flow (a) and WSS (b) profiles for all subjects. square error (RMSE) and the adjusted r 2. Linear re- In Fig. 6 the automatically calculated blood flow vs. gression was used to test for correlation between auto- the manually determined flow is graphed, and their matically and manually determined flows as well as correlation is shown. In Fig. 7 the WSS as a function for association between WSS and peak centre velocity of peak centre velocity is shown, as well as the (stat- measurements, istically significant) result of the regression analysis.

Eur J Vasc Endovasc Surg Vol 16, December 1998

520 S. Oyre et al.

Table 1. ht vivo resul t s .

Mean (range)

Peak systole End diastole All heart frames

3-DP automahc flow, ml/s 20 27 (13 63-31.82) 3.69 (2 47-5 28) 7.28 (5 61-9 63) Manual flow, ml/s 20.18 (13 70-31 42) 3 70 (2 49-5 28) 7 21 (5.55-9 60) Vessel area, mm 2 44 01 (30 67-66 23) 34 91 (25 52-46 37) 42 91 (33.14-63 58) Vessel &ameter, mm 7 49 (6 25-9 18) 6 67 (5 70-7 68) 7 39 (6 50-9.00) WSS*, N / m 2 2.28 (1 76-2 67) 0 54 (0 38-0 74) 0 82 (0 59-1 07) Peak centre velocity, cm/s 71 7 (63 1-77 5) 20 6 (14 9-25.3) 31 6 (24.6-36 5)

* Wall shear stress (WSS) as calculated by the automatic three-dimensional parabolold (3-DP) method

T a b l e 2. In v w o s tat i s t ics .

Mean (range)

Peak systole End &astole All frames

Plxels m fit, n 64 (52-78) 51 (35-61) 59 (50-72) I~MSE ~, cm/s 4.1 (3 2-5 9) 1 1 (0 9-1 4) 2.0 (1 7-2 6) Adjusted r 2 0 87 (0 71-0 94) 0 85 (0 77-0 91) 0 82 (0 75-0 86)

* Root mean square error

~ l m/s

- 0 7

- - 0 . 6

l

Posterior

1 ! Anterior

Fig. 3. Grey-scale surface plots (top row) as well as contour plots of velocity prohles superimposed on magmtude images from (a) peak systole, Co) late systole, (c) early diastole, and (d) end diastole The surface plots are seen from a posterior point of view. The numerical values are flow veloclhes (m/s)

Eur J Vasc Endovasc Surg Vol 16, December 1998

Accurate Automatic Blood Flow 521

Y y = 1.009 x + 0.007 J

r 2 = 0.998 25 < o O O O l /

, i

, i

x dimension ~ lo Fig. 4. Contour plots of ve loo ty (m/s ) profiles from peak systole for all subjects (a through to f) are shown (from 0 1 m / s m steps of ~ 5 0.1 m/ s ) . A perfect parabolold wi th fully developed profile is shown m g Note the variation m location of centres and these blunt m ~ , , ~ j , v w o flow profiles 0 5 10 15 20 25 30 35

Manua l ly de t e rmined flow (ml/s) 35 30 (a) Fig. 6. The automatic blood flow vs the manually deterrmned flow

is shown for all heart phases from all subjects as well as the result 25 regression analysis. of the linear

20

15 3 10 Y = 0.080 x - 0.1_2

2.5 n = 192 5 ~ r 2 = 0.805 •. "

, , ~ p < 0.0001 • ' J 0 . . . . . 2 SEE = 0 20 N/m 2 3

~" (b) ~ ' 2 5 1.5

~ 2 ~ ..

"~ 1 5 ~ F . ' : : ! " " •

1 ~ : . . . . . . . " ' " 0.5

0.5

0 100 200 300 400 500 600 700 800 0 10 20 30 40 50 60 70 80 Time af ter R-wave of ECG (ms) Peak cent re velocity (m/s)

Fig. 5. (a) Volume blood flow and (b) wall shear stress (WSS) for Fig. 7. The wall shear stress as a f tmctmn of peak centre velocity is all subjects. ( 0 ) a, ( . ) b; (~) c, (V) d, (A) e; (A) f. shown as well as the result of the regression analysis

Discuss ion automated procedures solving the 3-DP model for u = 0 in the coordinate system, and WSS was calculated

The present paper describes a new automatic method by differentiating for u = 0. The assumption that the for non-invasive determination of blood flow, cross- blood velocity at the vessel wall is zero has never sectional luminal vessel area, and wall shear stress been definitely proven, but is a concept of general using standard MR acquisition techniques and ad- haemodynamic theory as well as the assumption of vanced, automatic postprocessing based on a recently parabolic flow in a thin boundary layer. ~3x4 developed three-dimensional paraboloid model for The large number of data points (nm~--59) and fitting of blood velocity data (unpublished results selective inclusion of data points from pixels within 1997). the blood stream only (avoiding edge pixels and pixels

Automatic acquisition of a large number of blood in the centre of the vessel), gave high precision of velocity data was obtained through a priori knowledge the fit (Table 2), thus supporting the assumption of of the blood-vessel wall boundary layer and the blood parabolic flow in the boundary layer. flow profile combined with simple noise reductional The common carotid artery is usually a relatively

Edge detection (circumferential vessel wall position) straight vessel, and the cross-section is approximately was made continuously throughout the heart cycle by circular (see Figs 3 and 4). These conditions favour

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522 S. Oyre et al.

developed and laminar flow profiles. In addition, flow previous values found by high resolution ultrasound in the common carotid artery was found to be ante- echo tracking techniques (9.6%, 12 9.6%, 22 9.4%). 23

grade (directed towards the brain) throughout the We have earlier introduced an MR method for WSS heart cycle. Nevertheless, the blood velocity profile estimation based on estimation of blood velocity m was blunt rather than fully developed (paraboloid) the edge pixel (partial volume pixel) and in the adjacent in peak systole and became increasingly developed pixel within the blood stream# Oshinski et al. have during diastole (Figs 3 and 4). Also, small flow sep- proposed a similar method. 6 These methods are not aration zones were seen in late systole resulting in optimal due to several limitations: (i) the methods are shght asymmetrical flow velocity profiles. This makes subjective, (ii) the methods are very time consuming, it evident that the model assumptions of perfect, ax- (iii) the partial volume pixel was used, (iv) a linear isymmetrical and fully developed blood flow are not curve fitting method was used, and finally, (v) a serious fulfilled in vivo. Despite these limitations, a high num- error will be introduced if the edge pixel is not chosen ber of data points (n . . . . =59) could be used for the 3- correctly. The 3-DP method overcomes all of these DP fit both during systole and diastole ensuring fine limitations. statistics of the fit (Table 2). We have previously (unpublished results 1997) de-

The mean (range) volume blood flow in the carotxd termined the error when assuming a parabolic velocity artery was 7.42 (5.58-9.58)ml/s (Table 2)which cor- profile and applying the Poiseuille concept in ac- responds to previous determinations with MR phase cordance with Gnasso et al. 9 for WSS estimation (peak contrast methods of (mean + S.D.) 7.6 +0.9 ml /s 15 and systole/mean WSS is underestimated 50/22%). The 6.5-t-0.9 ml / s J 6 A strong linear correlation was found present study showed a good linear correlation be- between the flow determined automatically using the tween WSS vs. peak centre velocity (r = 0.805, automatic method described in the present work and p<0.0001), indicating that peak centre velocity can be the traditional, manual volumetric blood flow de- used to estimate WSS if the correction factor is known termination (r = 0.998, p<0.0001). This suggests the (Fig. 7). However, since this study population is small feasibility of the automatic 3-DP method for volumetric (n = 6), a more extensive study is required to confirm flow analysis, these initial correlations in a larger cohort of healthy

Normal flow measurements as used in this study subjects. require a number of minutes (3-5) for the acquisition Peak centre velocity can be obtained from ultra- of the data, and the flow velocities displayed on the sound Doppler measurements 9 but this correlation phase velocity map represent a weighted average over factor could very well be variable according to vessel the time for acquisition. This averaging of velocities size, sex or age, and further investigations will be can be seen as an advantage, because any short-term needed before WSS can confidently be estimated in the variability of the flow does not introduce errors to the common carotid artery from only one centre velocity measurement. However, there are situations where measurement. short-term variations in flow, WSS and vessel luminal Some limitations of the method should be discussed; area are of interest, for example in the response to firstly, the assumptions of symmetry of the flow profile exercises short time acting pharmacological stress, or and circularity of the vessel - although acceptable in a number of other factors that have dynamic effects this study - are not applicable to most arterial vessel on the physiology of the body. 18'19 With MR, the flow segments. Further developments of the technique to acquisition can be speeded up using spiral scans 2° overcome this limitation are in progress. 24 or echo planer imaging. The final goal would be Secondly, the method only measures the axial WSS measurements in real time. This is not unrealistic m component. This is probably allowable in most cases, the near future, since real time blood flow imaging where this component may be completely dominant has already been performed. 2°'21 or, indeed, the only component present. MR is capable

The automatic 3-DP technique allows determination of measuring flow in all three space coordinate dir- of blood vessel cross-sectional area. This increases the ections, 25'26 and it would be possible to estimate the sensitivity for determination of dilation/contraction tangential WSS-force too, in areas with more complex during the heart cycle since radius enters with the flow, e.g., at the carotid bifurcation. second power in calculation of area. The diameter Finally, the method is limited to some extent by the of the common carotid artery as determined by our in-plane resolution and the signal-to-noise of the MR method was 7.49 (6.25-9.18)mm during peak systole velocity data. For this study, the use of standard MR and 6.67 (5.70-7.68) mm during end diastole giving a hard- and software was sufficient. For smaller vessels, diameter pulsation of 12.3%, which compared well to thinner boundary layers are to be expected and higher

Eur J Vasc Endovasc Surg Vol 16, December 1998

Accurate Automatic Blood Flow 523

A, BOESIGER P Renal artery velocity mapping with MR imaging r e so lu t ion wi l l be n e e d e d to ob t a in a suff ic ient ly h i g h ! Magn Reson Imaging 1995, 5 669-676 n u m b e r of da ta po in t s for the 3-DP fit. This cou ld be 4 URCHUK SN, PLEW~S DB A velocity correlation method for ob t a ined t h r o u g h use of h igh r e so lu t ion t echn iques measuring vascular compliance using MR Lmaging l Magn Reson such as FACE, 27 a n d b y u s i n g scanner h a r d w a r e w i t h Imaging 1995, 5: 628-634. i m p r o v e d g r a d i e n t p e r f o r m a n c e as wel l as ded ica ted 50YRE S, PEDERSEN EM, RINCGAARD S, BOESIGER P/ PAASKE ~NP.

in vwo wall shear stress measured by magnetic resonance velocity surface coi lsY mapping m the normal human abdominal aorta Eur J Vasc

The 3-DP m e t h o d i m p r o v e s the p rec i s ion of cir- Endovasc Surg 1997, 13 263-271 cumfe ren t i a l vessel wa l l detect ion. C o m b i n e d w i t h 60SHINSKI JR, K~ DN, MUKUNDAN S JR, LOTH F, PETTIGREW RI.

Determination of wall shear stress m the aorta with the use of h i g h r e so lu t ion MR i m a g i n g of p l a q u e morpho logy , 2° MR phase velocRy mapping J Magn Resort Imaging 1995; 5: the t echn ique cou ld b e c o m e a p o w e r f u l n o n - i n v a s i v e 640-647. tool w i t h suff icient accuracy for s t u d y i n g inter- a n d 7 BUONOCORE MH, BOG~N H Factors uffluencmg the accuracy

and precision of velocity-encoded phase imaging Magn Resort i n t r a - i n d i v i d u a l d e v e l o p m e n t of vascu la r d isease a n d Med 1992, 26 141-154 vascu la r r e sponses to in t e rven t ions . 8 BURY.ART DJ1 FELMLEE JP, JOHNSON CD, WOLF RL, WEAVER

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b e c o m e a use fu l a d d i t i o n to carot id MR a n g i o g r a p h y tection ] Comput Asszst Tomogr 1994, 18 469-475 p r o v i d i n g de ta i led a n d exact i n f o r m a t i o n a bou t the 9 GNASSO A, CARALLO C, IRACE C, SAPAGNUOLO V, NOVARA G, b iomechan i c s a n d h a e m o d y n a m i c s in atherosclerot ic MATTIOLI PL, PUJIA A Association between intn'na-media thick-

ness and wall shear stress m common carotid arteries m healthy arteries, male subjects Circulation 1996; 94 3257-3262

In conc lus ion , w e have descr ibed a new, au toma t i c 10 GNASSO A, IRACE C, CARALLO C1 FRANCESCHI MS, MOTTI C, n o n - i n v a s i v e m e t h o d for h igh ly accura te a n d robus t MATTIOLI PL, PUJIA A In wvo association between low wall

shear stress and plaque m subjects with asymmetrical carotid d e t e r m i n a t i o n of b lood flow, cross-sect ional vessel atheroscleros:s Stroke 1997, 28 993-998 area, a n d wal l shear stress in m e d i u m - s i z e d arteries. 11 I-IoEKS AP, S~IJO SK, BRANDS PJ, ILENEMAN RS Non-mvas:ve The first in vivo i m p l e m e n t a t i o n s u s i n g s t a n d a r d MR determmation of shear-rate distribution across the arterial lumen

Hypertension 1995; 26 26-33 h a r d - a n d sof tware h a v e s h o w n resul ts comparab l e to 12 HOEKS AP, SAMIJO SK, BRANDS PJ, RENEMAN RS. Assessment of those of the l i tera ture , a n d the stat is t ical ly s igni f icant wall shear rate m humans- an ultrasound study J Vasc Invest corre la t ion w i th the m a n u a l m e t h o d of vo lume t r i c 1995, 1 108-117 ana lys i s has d e m o n s t r a t e d the feasibi l i ty of the auto- 13 NICHOLS WW, O'RouI~KE MF The nature of flow of a fired In

McDonald's Blood Flow m Artemes. London. Lea & Febiger, 1990 mat ic f low de t e rmina t ions . The hypo thes i s of as- 14 Lou Z, YANG W, STEIN PD Errors m the estnnatlon of arterial soc ia t ion b e t w e e n peak centre veloci ty a n d WSS w a s wall shear rates that result from curve hthng of velocity profiles

] B~omech 1993, 26 383-390 no t con t rad ic t ed b y the resul ts of the p re sen t s tudy. 15 BOGREN HG, BUONOCORE MH, GU WZ Carotid and vertebral This n e w m e t h o d p rov ides a fast a n d accurate tech- artery blood flow m left- and right-handed healthy subjects n i q u e for d e t e r m i n a t i o n of d y n a m i c var iab les essent ia l measured with MR velocity mapping J Magn Reson Imaging

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26 KIM WY, WALKER PG, PEDERSEN EM, POULSEN JK, OYRE S, hemorrhagic, and thrombotic components of human athero- HOULIND K, YOGANATHAN AP Left ventncular blood flow pat- sclerosis m wvo Czrculaflon 1996; 94" 932-938 terns m normal subjects: a quantitative analysis by three-di- mensional magnetic resonance velocity mapping, l Am Coll Car&ol 1995, 26. 224-238. Accepted 11 August 1998

Eur J Vasc Endovasc Surg Vol 16, December 1998