Three-Dimensional Model-Based Stenosis Quantification of the Carotid Arteries from Contrast-Enhanced MR Angiography

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1 Three-Dimensional Model-Based Stenosis Quantification of the Carotid Arteries from Contrast-Enhanced MR Angiography Alejandro F. Frangi, Wiro J. Niessen, Paul J. Nederkoorn, Otto E.H. Elgersma, Max A. Viergever Image Sciences Institute, University Medical Center Utrecht Room E01.334, Heidelberglaan 100, 3584 CX Utrecht, The Netherlands Abstract A model-based technique for quantitative analysis of three-dimensional magnetic resonance angiography (MRA) is presented. The model consists of a deformable B-spline representation of the central vessel axis and the vessel wall. An efficient interaction mechanism to initialize the models in a three-dimensional setting is devised. Two novel image features are introduced in order to deform the central vessel axis and the vessel wall model respectively. A segmental optimization scheme for deforming the B-spline vessel wall model is introduced. Finally, the paper presents results on clinical contrast enhanced (CE) MRA of 19 carotid arteries. Percentages of stenosis obtained with our technique are compared to those of two experts using caliper measurements on Maximum Intensity Projection (MIP) CE MRA, and Digital Subtraction Angiography (DSA) as standard of reference. 1. Introduction Stroke is the third cause of death in the United States [1]. Most strokes result from atherosclerosis in the carotid arteries. Carotid endarterectomy is the recommended treatment for those patients with severe (> 70%) symptomatic stenosis in the carotids [2]. Patients with stenosis smaller than 30% are ruled out from this invasive treatment. Efficacy of surgical intervention in patients with stenoses between 30% and 70% is still under investigation. Several techniques have been used to examine the vasculature of patients suspected from carotid artery disease. Digital subtraction angiography (DSA) is the most widely used due to its high resolution and widespread availability. It is also regarded as the standard of reference to compare new acquisition techniques. Unfortunately, this technique suffers from several disadvantages. It is invasive, requiring patient catheterisation and injection of iodinated contrast agents. During image acquisition the patient is subjected to radiation. Finally, it is a projectional technique and vessel over-projection may hamper the visualization of the artery of interest. Since the estimation of the degree of stenosis is based on two-dimensional (projection) images, the measurements may not perfectly reflect the dimensions of the three-dimensional vasculature. Magnetic resonance angiography (MRA) is gaining popularity as a potential replacement of DSA for diagnostic imaging. It does not involve radiation and the contrast agents used have less side-effects than those used for DSA. Although it is possible to obtain three-dimensional reconstructions of the vasculature with MRA, the difficulty of handling and visualizing such images has been solved by retrospectively generating projection views. Popular techniques are the Maximum Intensity Projection (MIP) or Closest-Vessel Projection (CVP) visualization techniques. Although these projections resemble the DSA images familiar to radiologists, it has been recognized that such techniques introduce artifacts overestimating the degree of stenosis [3]. Some researchers have compared the use of MIPs and the three-dimensional source images for stenosis grading, and concluded that the latter method better correlates with DSA [4]. Unfortunately, grading of the threedimensional source images is more time-consuming and therefore has limited clinical implications. In previous work we presented an algorithm suitable for segmenting selected linear vessel segments from 3D MRA images [5]. The method is three-dimensional and thus uses all the information available after reconstruction. In this paper this methodology is extended. First, the feature to guide the evolution of the central vessel axis now incorporates directional information. Second, a segmental optimization scheme is proposed which improves the local fit. A clinical pilot validation of the method is performed by comparing the performance with two experts on 19 carotid arteries, with DSA as the gold standard. The paper is organized as follows. Section 2 overviews the original formulation of the method. Section 3 introduces two extensions to

2 the basic methodology. The set up and results of the clinical evaluation are presented in Section 4. Finally, the paper is closed with a discussion and conclusion in Sections 5 and 6, respectively. 2. Overview of the basic algorithm In this section an overview of our method for obtaining vessel diameter estimates [5] from three-dimensional MRA data is described. Extensions to this methodology will be discussed in the next section. The model-based vessel segmentation procedure consists of two main steps. First the central vessel axis is computed. Subsequently, a 3D boundary model is initialized which is fitted to the image data using a boundary criterion derived from knowledge of the image acquisition technique. The different steps in the algorithm can be summarized as follows (Figure 1) a) Using a rough iso-surface rendering of the vessel(s) of interest, the user selects a couple of points indicating the segment to be measured (Fig. 1(a)). These points are joined with a geodesic curve that runs on the iso-surface providing a coarse initialization of the central vessel axis (Fig. 1(b)). This initialization requires only a simple and intuitive interaction. b) The central vessel axis, C(v), is approximated using a B-spline curve of degree n with s +1control points. This representation enforces the lumen line to be connected C(v) = s N in (v)p i (1) i=0 Here P i are the control points, N in (v) denotes the i-th B-spline basis function of order n [6] and v [0, 1]. c) To fit the vessel axis to the image data, we developed a filter [5,7] based on a local operator that analyzes the eigenvalues of the Hessian matrix computed at each voxel of the image. The filter has the following properties: i. de-enhances non line-like structures, ii. is maximum at the center of the vessel. Moreover, since the filter is applied at multiple scales, with a subsequent scale selection procedure [8] effectively adapting the filter to the size of the vessel, the method is capable of handling varying vessel widths. In addition, it was shown by means of simulations that the response of the filter is rather insensitive to vessel curvature allowing to enhance even tortuous vessel paths [5]. In Section 3.1 we shall elaborate on this filter and discuss a further extension. d) The vessel wall, W(v, u), is modeled using a tensor product B-spline surface [6] W(v, u) = q j=0 k=0 r N jl (u)n km (v)p jk (2) where P jk are ((q +1) (r +1))control points, N jl (u) denotes the j-th B-spline periodic basis function of order l and u [0, 2π); N km (v) is the k-th B-spline non-periodic basis function of order m and v [0, 1]. The parameters u and v traverse the surface in the circumferential and longitudinal directions respectively. The model can be initialized using a standard Computer Assisted Design (CAD) technique known as swept surfaces [6]. A prototype cross-section is swept along the central vessel axis, and orthogonal to the curve at every point (Fig. 1(c)). This results in a deformable cylinder along the previously computed vessel axis. e) The vessel wall model is deformed to fit the boundaries of the underlying vessel (Fig. 1(d)). Here knowledge of the image acquisition is introduced. In an earlier study [9] it was shown that the full-width-half-maximum (FWHM) criterion is a reliable estimate of vessel width in Time-Of-Flight (TOF) and Contrast-Enhanced (CE) images. For Phase-Contrast (PC), however, the full-width- 10%-maximum (FWTM) is preferred. Therefore, we deform the vessel wall so that the luminance ratio between the voxels at the wall model and at the centerline model fulfils the FWHM or FWTM criterion, respectively. Mathematically, the model is deformed to minimize the function: E W = 1 S τ acq I(W(v, u)) I(C(v)) dvdu+r(w) (3) where I(x) denotes the image grey-level at position x, S is the total vessel wall area, and τ acq is a threshold that incorporates knowledge about the type of MRA imaging technique. This constant equals 0.5 for TOF and CE, and 0.1 for PC MR angiography. Finally, R(W) is a regularization term that imposes smoothness constraints on the vessel wall surface [5]. 3. Extensions to the basic approach 3.1. Central vessel axis image feature In the original formulation of our method a scalar potential map was used to deform the central vessel axis [5]. This potential map was derived from a multi-scale vessel enhancement filter [7]. The output of this filter is a measure of how likely a voxel is to be located on the center of a vessel. However, no directional information was used to infer the local orientation of the vessel. In Section 3.2 we 2

3 (a) (b) (c) (d) Figure 1. Algorithm overview. a) The user initializes two (or more) points on the surface. b) From these seeds, a geodesic path is computed. c) The geodesic path is deformed until the central vessel axis is determined. Using the distance between the newly obtained vessel axis and the original geodesic path, a circular cross-section is swept along the axis to generate an initialization of the vessel wall model. d) Vessel wall (after deformation) and central vessel axis. review the original formulation of our filter. Section 3.3 extends this idea to use local orientation information in the deformation of the central vessel axis Original (scalar) image feature Let I(x) be the intensity function (Fig. 2(a)) and H σ (x) the associated Hessian matrix at a given voxel x H σ (x) = I xx(x) I xy (x) I xz (x) I yx (x) I yy (x) I yz (x) I zx (x) I zy (x) I zz (x) where I ξ1ξ 2 (x) denote regularized derivatives of the image I(x), which are obtained by convolving the image with the derivatives of the Gaussian kernel at scale σ [10] I ξ1ξ 2 (x) σ 2 2 G(x,σ) I(x) ξ 1 ξ 2 1 x 2 G(x,σ) e 2σ 2 (2πσ2 ) 3 Here λ k will denote the eigenvalue with the k-th smallest magnitude ( λ 1 λ 2 λ 3 ). A voxel belonging to a vessel region will be signaled by λ 1 being small (ideally zero), and λ 2 and λ 3 being large and of equal sign (the sign is an indicator of brightness/darkness). The respective eigenvectors correspond to singular orientations: û 1 indicates the orientation of the vessel (minimum intensity variation) and û 2 and û 3 form a basis for the orthogonal plane. In previous work [5, 7] we have proposed a non-linear combination of the eigenvalues of the Hessian matrix that promotes the enhancement of linear structures while noise and non-line-like structures are smoothed out. At a single scale, σ, the output of the vessel enhancement filter is V(x,σ) [ 0, ( if λ 2 )] > 0 or ( λ 3 > 0 ( )] 1 exp R2 A 2α exp R2 2 B 2β )[1 exp S2 2 2c, 2 otherwise R A λ 2 λ 3, R B λ 1 λ2 λ 3 S H σ F = where R A, R B and S correspond to local measures of cross-sectional asymmetry, blobness and degree of image j λ 2 j (4) 3

4 structure [7]. The parameters α, β and c tune the sensitivity of the filter to deviations in R A, R B and S relative to the ideal behavior for a line structure. Equation (4) explicitly states that the filter response is a function of the scale at which the Gaussian derivatives are computed. Scale dependency, however, has been omitted in λ i, R A, R B and S for the sake of parsimony. The filter is applied at multiple scales that span the range of expected vessel widths according to the imaged anatomy. In order to provide a unique filter output for each voxel, the multiple scale outputs undergo a scale selection procedure [8]. This amounts to computing the maximum filter response across scales V (x) = max V(x,σ) (5) σ min σ σ max In this way, different vessel sizes will be detected at their corresponding scales and both small and large vessels will be captured with the same scheme (Fig. 2(b)) Extension to vector valued image feature In the original formulation, the image feature used to deform the centerline was the integral of the vessel enhancement filter output [Equation (5)] along the central vessel axis model. However, no information was used regarding the orientation of the vessel. The latter can also be inferred from the Hessian matrix. The orientation of the vessel at voxel x corresponds to that of the smallest-magnitude eigenvalue at that location, û 1 (x). This orientation is computed at the same scale at which the filter output yielded maximum response [Equation (5)]. In this way, if ˆt(v) is the tangent vector of the B-spline central vessel axis model at parameter value v, the centerline will be obtained by optimizing the following criterion E C = 1 l V (C(v)) ˆt(v), û 1 (C(v)) dv + Q(C) (6) where Q(C) is a regularization term only depending on the central vessel axis model [5], and, stands for the inner product. The extra factor, ˆt(v), û 1 (C(v)), enforces that the tangent to the central vessel axis model be parallel to the vessel as inferred from the image. 1 As a consequence of this term, the model will not only go through the voxels of maximum filter output but will smoothly vary in orientation according to the variation of the underlying vessel (Fig. 2(c)). In particular, we have observed that addition 1 Note that the eigenvectors of the Hessian matrix only provide an orientation but not a direction. Therefore, only the magnitude of the scalar product is useful. (a) (b) (c) Figure 2. Vessel enhancement filter. a) MIP of original CE MR dataset. b) MIP of intensity of vessel enhancement filter. c) Enlarged view of the local orientation provided by the vessel enhancement filter. of this factor improves the deformation of the ends of the model which will be enforced to end with the same orientation of the vessel Segmental vessel wall fitting In this section a segment-wise optimization scheme for the deformation of the vessel wall will be introduced. The basic idea is to subdivide the vessel wall model into vessel wall strips (or segments) that are optimized sequentially. We coin this method segment-wise optimization. Basically, the deformation is started from one end of the vessel wall and it proceeds segment-wise towards the other end. By taking advantage of the local support property of the B-splines, the deformation of the vessel wall can be broken into several independent optimization problems in a lower dimensional space. Although the overall computation load provided by this method is similar to the full-dimensional optimization (all control points simultaneously), this method is able to provide a better local fit. When optimizing all the control points simultaneously, the objective function averages the measure of fit over the whole surface (Equation 3). Therefore, the effect of small regions of the vessel wall model having a bad local fit would tend to be averaged out. Since in optimizing each vessel strip the objective function only gathers information of a portion of 4

5 (a) (b) (c) (d) (e) Figure 3. Segmental wall deformation. a-d) Four steps in optimizing the vessel wall model segmentwise (from proximal to distal). The surface is tessellated in B-spline patches as indicated by the chess-board pattern. Note how the segment-wise wall fitting progressively attaches to the wall. Therefore, each new optimization starts closer to the final solution than after the sweeping procedure. e) Final wall model after all control points have been optimized. the vessel wall, the segmental optimization yields a better fit along the whole model. In order to formulate this optimization strategy, let us start off by introducing the parameters that define a B- spline surface model. A B-spline surface of degree d u (d v ) and q +1(r +1) control points in the u (v) direction, is defined by a bidirectional net of control points, P jk, two knot vectors, U = {u j ; j = 0...q + d u +1} and V = {v k ; k =0...r+ d v +1}, and the product of univariate B-spline basis functions. This kind of surfaces are also known as tensor product surfaces (cf. Equation 2). To break the optimization problem of vessel wall model into wall strips optimized sequentially, the parameter space subdivision has to fullfil the following requirements. 2 Requirements. Let a B-spline vessel wall model be defined on the longitudinal parameter v [0, 1]. A partitioning of this space, V l [ˆv l, ˆv l+1 ), suitable for segmental optimization has to fulfil the following requirements 3 2 In the remainder of the discussion it is assumed that the model will only be chunked in the longitudinal direction, i.e., with respect to the parameter v. 3 Special care must be taken with the last V l to also include the value v =1. 1. l V l =[0, 1], 2. l V l =, 3. If P l is the subset of control points whose local support influences in V l, then P l Pl+1 = {P jl,j = 0...q}. Condition (1) and (2) simply state that our subdivision of the longitudinal parameter space is complete and nonoverlapping. Condition (3) states that after we have optimized the vessel wall in the l-th strip, we can leave q +1 control points fixed. This ensures that after we advance one strip in the segmental optimization, the position of some of the control points can be regarded as optimal. In fact, it is this last condition which ensures that the problem can be broken into small subproblems. Under clamp-end boundary conditions [6] the knot vector, V, of a B-spline surface has the following form V = {0,...,0,v }{{} dv+1,...,v r 1, 1,...,1} (7) }{{} d v +1 d v +1 If, additionally, multiple knots are not allowed, the following lemma follows from the local support properties of the B-splines [6] Lemma. A partition of the parameter space v that exactly fulfils all the abovementioned requirements is the partition generated by the knot vector V without repeating the 5

6 begin and end knots, i.e., ˆv l v dv+l with l =0...r d v. Finally, P l {P jk ; j =0...q,k= l...l+ d v }. In summary, optimizing the energy integral of Equation (3) entails solving an optimization problem with 3(q +1) (r +1)variables. The same problem can be broken into r d v +1 subsequent optimizations with 3(q +1) (d v +1) variables. After each subproblem is solved, one row of circumferential control points is frozen, since their values do not influence the subsequent optimization problems. The segmental approach obtains a substantial decrease in dimensionality and, moreover, the dimensionality of each subproblem is independent of the total vessel length. When solving the l-th optimization problem, the support of the double integral in Equation (3) can be reduced to the region that is influenced by P l. It is possible to show that this corresponds to a surface patch such that u [0, 2π) and v [v max (0,l dv),v l+1 ). 4. Clinical evaluation 4.1. Image acquisition and implementation Eleven patients suspected of carotid artery disease underwent a standard clinical MRA protocol including 3D CE MRA, in which the start of image acquisition was determined using BolusTrak, a technique to detect the arrival of the contrast bolus. Patients were scanned on a 1.5-Tesla MR imaging system (Philips Gyroscan ACS-NT, PowerTrak 6000 gradients, Philips Medical Systems, Best, The Netherlands). Scan parameters were: repetition time (TR) 4.4-ms, echo time (TE) 1.5-ms, flip angle (α) 40, slice thickness 1.2-mm with slice gap of -0.6-mm, matrix and 256-mm 140-mm rectangular field-of-view. In order to reduce partial volume effects, before applying the modelbased technique, all images were up-sampled to mm 3 isotropic voxels using sinc interpolation. Each patient also underwent a DSA examination. DSA was performed with a Philips Integris V3000 angiographic unit (Philips Medical Systems, Best, The Netherlands). Two or three projections (posteroanterior, oblique and possibly lateral) were acquired for each carotid bifurcation. From the eleven patients, three carotid arteries were not analyzed due to full occlusion. In the B-spline representation of the vessel model a few parameters have to be specified [cf. Equations (1) and (2)]. In our experiments third-order (cubic) B-spline curves and surfaces were used. The number of control points for the central vessel axis (s +1) and the vessel wall (r +1) models were determined from their length. A control point was placed every 5-mm in the central vessel axis. For the vessel wall model a ring of five control points was placed every mm. By means of preliminary experiments with different numbers of control points, it was observed that these densities yield a good trade-off between ability to capture the shape of the in vivo carotids and model complexity Results Figure 4 illustrates the results of the internal carotid artery (ICA) models that were fitted to data from several patients. Two observers scored the same carotid arteries using DSA and CE MR angiograms. Each observer scored the images of a given modality in separate sessions to avoid any inter-observer/inter-modality bias (blind scoring). DSA scores were obtained by averaging the stenosis indexes of standard projections (postero-anterior, leteral and oblique projections). Stenosis indexes in CE MRA images were measured on up to three MIP images (posteroanterior, leteral and oblique projections), and those averaged to obtain a final overall score. In both DSA and CE MRA, projection images with vessel overprojection were not used to compute the average. Manual measurements on MRA and DSA were performed on printed hard copies and using a caliper with a digital display (PAV Electronic, resolution 0.01-mm). Figures 4(a) and 4(b) exemplify the models of normal/mild ICAs. Figures 4(c) to 4(f) are examples of stenoted ICAs. Figures 4(e) and 4(f) show examples of models fitted in the presence of signal loss at the stenosis and distal to the stenosis respectively. In the latter case, signal voids are due to bad synchronization of the acquisition with respect to the arrival of the contrast bolus. Although we have included these examples in the evaluation of our method, we recognize that a large amount of prior knowledge about voids and artifacts is used by the experts to interpret these images. This prior knowledge may be hard to incorporate in an automatic algorithm. Figure 4.2 presents the results of this pilot evaluation. The angiograms were scored using the NASCET stenosis index (%D = 100% (1 stenosis / distal to stenosis )). Correlation between the DSA and CE MRA scores of the 19 carotid arteries included in this study was computed using linear regression. The scores obtained from the modelbased technique were compared against the average of the DSA scores of the two observers for the same artery. In the same figure, the 95% confidence intervals and 95% prediction intervals for the linear regressions are included. From this analysis it is concluded that the model-based technique presents tighter confidence bounds than those of the two observers. The slopes of the linear regressions (cf Table 1) indicate that the model-based technique consistently underestimates the degree of stenosis compared to DSA, although this is also the case for one of the observers. Table 1 shows the quantitative comparison between DSA and CE MRA for the two observers and the model-based technique. The Spearman coefficient indicates a good cor- 6

7 (a) (b) (c) (d) (e) (f) Figure 4. Examples of internal carotid artery (ICA) models. The top row shows maximum intensity projections of 3D CE MR angiograms of the ICA. The bottom row shows the three-dimensional models fitted to the source images. relation between the model-based technique and DSA. The Wilcoxon test indicates no statistically significant difference in the latter case, nor for the observers at 5% confidence level. We also computed the Bland and Altman [11] plots to establish the bias between the DSA and CE MRA scores and the 95% limits of agreement (LA) for the two observers and the model-based technique. The results are summarized in Table 1 and they are in agreement with the prediction intervals of the linear regression, namely, the model-based technique has a smaller dispersion compared to manual assessment. This means, that the model-based technique has, for a given individual, a larger predictive value for estimating the corresponding DSA scores (recall that the NASCET criterion [2] was developed for DSA). 5. Discussion Based on the pilot clinical evaluation of the model-based technique, some observations can be made with respect to the performance and possible solutions to improve the ap- DSA vs CE MRA Slope Bias (LA) Spearman s r s (p) Wilcoxon p Obs I (-22.8/+35.4) 0.80 (< 0.001) 0.13 Obs II (-24.5/+39.0) 0.84 (< 0.001) 0.09 MB (-20.8/+19.8) 0.91 (< 0.001) 0.97 Table 1. DSA vs CE MRA results for both observers (I and II) and the model-based (MB) technique. The bias and the 95% limits of agreement (LA) are computed according to Bland and Altman [11]. Spearman s correlation coefficient and the confidence level of the Wilcoxon test for differences are also provided. proach. Need for interaction in cases of severe stenosis. In three out of 19 carotid arteries, the central vessel determination failed in the stenotic region. In two of the cases, the diameter of the stenosis had a diameter smaller than three voxels and a length shorter than five voxels. Distal and proximal to the stenosis the diameter expanded very abruptly being aggravated by the fact that the stenoses were asymmetric. 7

8 %D (CE) %D (CE) %D (CE) %D (DSA) %D (DSA) %D (DSA) (a) (b) Figure 5. DSA vs CE MRA. Degree of stenosis measured in 19 carotid arteries. Measurements performed by (a-b) two observers on MIPs of the CE MRA angiograms, and (c) measurements obtained from the three-dimensional models fitted to the same angiograms. Scores from CE MRA are compared to those of DSA of the same observer. The model-based measurements were compared against the average DSA scores of the two observers for the same arteries. All scores were computed using the NASCET criterion [2] ( stenosis = 1 - stenosis diameter/distal diameter). The lines indicate the linear regression (solid line), 95% confidence interval (dashed line), and the 95% prediction intervals (dashed/dotted line). (c) Intensity in the stenotic region dropped to less than 50% of the normal lumen intensity. In the presence of this pathological geometry, the vessel enhancement filter had a low response at the stenosis. As a consequence, the central vessel axis model did not succeed in following the true central vessel axis. The third case, also a severe stenosis but with a slowly broadening distal lumen, failed due to stenotic and post-stenotic signal loss ( 50%) and the presence of adjacent high-contrast neighboring vessels which attracted the central vessel model. Determination of the vessel wall could be resumed in all three cases after manual correction of the vessel axis model. This was carried out by user-defined point constraints attracting the central vessel axis through the stenosis center. Adaptive model flexibility for the vessel wall. In the current implementation, the number of control points (CPs) of the vessel wall model in the longitudinal direction is determined from the length of the vessel and a pre-defined density (2.5-mm/CP). This imposes an approximately even distribution of the control points. An even distribution is quite convenient for vessels which do not contain abrupt changes in diameter. If this occurs, however, a higher density of control points usually solves the problem (in three carotids we have used a density of 2.0-mm/CP). Unfortunately, this increases the density everywhere with a consequent increase in computational load. Therefore, in regions with smoothly varying diameter, the model would be unnecessarily flexible. An alternative would be to unevenly distribute additional control points according to some measure of how the diameter varies over the vessel wall. This latter approach can be useful in order to introduce model flexibility where it is needed while speeding up the computations where the vessel has a smoothly varying diameter function. This alternative would be worthy of further investigation. There exist some techniques from CAD, namely, knot refinement, knot insertion and knot removal [6] that could be used to devise an adaptive model refinement in conjunction with a suitable measure of where extra flexibility is required. Boundary criterion adequacy. Figure 5(c) shows that all of the carotids graded as severe by DSA (%D >70%) were under-estimated with the model-based technique. From the experiments performed, we have seen that such underestimation arises mainly from an overestimation of the stenotic diameter. Two main reasons may explain this fact. On one side, the use of evenly distributed control points may impose a too stiff vessel wall model in this region which does not tend to nicely follow the narrowing lumen. This is particularly the case in rather short ( 4 voxels) stenoses with proximal and distal sudden broadenings. Use of an adaptive model as suggested above may partially solve this problem. The second reason is more fundamental. Stenotic regions are prone to have intensity artifacts due to flow (TOF/PC MRA) or to inhomogeneous concentration of the contrast agent (first-pass CE MRA with BolusTrak). All this non-idealities distort the luminal intensity profile for which the boundary criteria were derived. Unfortunately, a 8

9 small error in the diameter of the stenosis is magnified in the estimate of the degree of stenosis. Therefore, in order to make possible diameter quantification in small vessels, a more complex model of the acquisition is probably required which also incorporates tissue properties and parameters of the MR imaging sequence [12]. Quantitative comparison against reference technique. The results of Table 1 indicate that the model-based measurements correlate better (r s =0.91) with the standard of reference (DSA) than the measurements of each of the two observers (r s =0.80, 0.84). Moreover, the standard deviation of the differences between the DSA and CE measurements is smaller using the model-based technique (10.1%) than the standard deviation in the measurements of observer I (14.5%) and II (15.9%). This is also reflected in broader limits of agreement between the scores obtained with CE MRA vs DSA. Possibly, this smaller dispersion is related to the way the model-based measurements are performed. Diameter measurements are obtained using an objective criteria while manual scoring is still subjective and dependent on the interpretation of image artifacts, and the experience of the radiologist. In the case of the model-based technique, the slope of the linear regression indicates a consistent tendency to underestimate the degree of stenosis compared to DSA. This could be attributed to the different nature of the measurements (3D vs 2D) and/or to the model adequacy in the case of severe stenosis as discussed previously. On the other hand, a careful look at the linear regression plots, shows that the prediction interval is smaller in the case of the semi-automated method (cf Fig. 4.2). According to these plots, the ability of the model-based technique to predict the true (DSA) score for a given patient is better with our method than with the manual procedure. It is still needed to extend this pilot evaluation to a larger series of patients. In case that the underestimation can be regarded as systematic, a calibration could be applied to compensate for this effect. 6. Conclusion In this work we have presented a model-based technique extraction of vessel dimensions from three-dimensional MR angiograms. The first contribution of this work are methodological extensions; directional information is incorporated to improve central vessel axis fitting, and an segmental fit procedure improves the local fit. The second contribution is a pilot clinical evaluation on state-of-the-art images of the carotid arteries. The results are promising indicating that accurate measurements can be obtained in a semi-automatic fashion reducing the inter-observer variability. Further extensions are required to cope with certain geometries present in pathological arteries. Advances in image acquisition are needed to solve problems inherent to determining the arrival of the contrast bolus in CE MRA; early acquisition triggering which sometimes occurs leads to intensity artifacts in the lumen which render our boundary criterion non valid. 7. Acknowledgement This research was sponsored by the Dutch Ministry of Economic Affairs (Project IOP Beeldverwerking IBV97009) and EasyVision Advanced Development, Philips Medical Systems BV, Best, The Netherlands. References [1] American Heart Association, Dallas, Tex., American Heart Association 1998 Heart and Stroke Statistical Update, [2] North American Symptomatic Carotid Endarterectomy Trial (NASCET) Steering Committee, North American Symptomatic Carotid Endarterectomy Trial. Methods, patient characteristics, and progress, Stroke, vol. 22, no. 6, pp , June [3] C. M. Anderson, J. S. Saloner, D. Tsuruda, L. G. Shapeero, and R. E. 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