(Radiographics. 2002;22:421-436.)
© RSNA, 2002
Computer-assisted Analysis of Three-dimensional MR Angiograms1
Marcela Hernández-Hoyos, MS,
Maciej Orkisz, PhD,
Philippe Puech, MD,
Catherine Mansard-Desbleds, MS,
Philippe Douek, MD, PhD and
Isabelle E. Magnin, PhD
1 From the Centre de Recherche et d’Applications en Traitement de l’Image et du Signal, Institut National des Sciences Appliquées de Lyon, Bâtiment Blaise Pascal, 7 rue Capelle, F-69621 Villeurbanne, France. Presented as an infoRAD exhibit at the 2000 RSNA scientific assembly. Received March 1, 2001; revision requested May 1; final revision received November 8; accepted November 19. Supported by Carena S.A., Région Rhône-Alpes (ADéMo Project), and the French National Center for Scientific Research (GdR PRC ISIS). Address correspondence to M.H.H. (e-mail: marcela.hernandez@creatis.insa-lyon.fr).
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Abstract
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The software tools required for postprocessing of magnetic resonance (MR) angiograms include the following functions: data handling, image visualization, and vascular analysis. A custom postprocessing software called Magnetic Resonance Angiography Computer Assisted Analysis (MARACAS) has been developed. This software combines the most commonly used three-dimensional visualization techniques with image processing methods for analysis of vascular morphology on MR angiograms. The main contributions of MARACAS are (a) implementation of a fast method for stenosis quantification on three-dimensional MR angiograms, which is clinically applicable in a personal computer–based system; and (b) portability to the most widespread platforms. The quantification is performed in three steps: extraction of the vessel centerline, detection of vessel boundaries in planes locally orthogonal to the centerline, and calculation of stenosis parameters on the basis of the resulting contours. Qualitative results from application of the method to data from patients showed that the vessel centerline correctly tracked the vessel path and that contours were correctly estimated. Quantitative results obtained from images of phantoms showed that the computation of stenosis severity was accurate.
© RSNA, 2002
Index Terms: Arteries, stenosis or obstruction, 9*.7212 • Computers, diagnostic aid • Images, analysis • Magnetic resonance (MR), image processing Magnetic resonance (MR), three-dimensional • Magnetic resonance (MR), vascular studies, 9*.721
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Introduction
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Atherosclerosis, the principal acquired disease of the vascular wall, is one of the most important public health problems and is a leading cause of death among people older than 60 years in Western countries. Its major complications are arterial stenosis, which is characterized by thickening of the artery wall and narrowing of its lumen, and arterial aneurysms, which are characterized by an increase in the size of the vessel lumen.
Conventional or digital subtraction angiography (DSA), computed tomography (CT), and magnetic resonance (MR) angiography are the three most commonly used imaging techniques in diagnosis, treatment planning, and follow-up of this pathologic condition. A growing body of literature supports the accuracy of MR angiography compared with that of DSA (1), which remains the standard of reference for diagnosis of vascular diseases (2,3). MR angiography provides three-dimensional (3D) anatomic images of blood vessels. Moreover, it is noninvasive. In cases where DSA is too risky (excessive x-ray exposure for both the patient and the radiologist, patients with extensive vascular disease, patients with a risk of decreased renal function, or patients with difficult vascular access) or where two-dimensional (2D) information is not sufficient, MR angiography appears to be an effective alternative (4,5).
Despite the 3D nature of MR angiography, tools for diagnosis and treatment planning are commonly 2D. Most visualization consoles used in clinical practice for MR angiographic evaluation of vascular stenosis provide (a) simultaneous display of 2D maximum intensity projection (MIP) images and axial sections and (b) interactive measurement tools for "manual" evaluation of the diameters of pathologic and healthy vessels. Unfortunately, even if measurements are performed with precise interactive tools, user intervention may lead to subjective stenosis estimation associated with significant interobserver variability (6). First, selection of the reference healthy segment and of the tightest segment of a vessel is user dependent. Second, manual windowing may enlarge or narrow the apparent vessel diameter, resulting in possible over- or underestimation of stenosis severity. Furthermore, interactive evaluation of a stenosis on MIP images requires multiple projections. Indeed, it is very important to choose the projection with the shortest diameter, since elliptical, semilunar, or mild stenosis may be underestimated (7). This choice is also user dependent. A subjective estimate of stenosis severity is not accurate and reproducible enough to be considered a reliable criterion for determining the indications for pharmacologic, intravascular, or surgical treatment and for allowing precise postoperative follow-up with MR angiography. To achieve precise evaluation of stenosis severity and of the entire set of vessel parameters (eg, length, different diameters, and section areas of the diseased segment), the MR angiographic analysis should take full advantage of its intrinsic 3D information.
To meet these clinical requirements, a computer-assisted analysis system needs to be tailored for this specific application. We developed a postprocessing program called Magnetic Resonance Angiography Computer Assisted Analysis (MARACAS). MARACAS was designed for visualization and analysis of blood vessels based on dynamic contrast material–enhanced subtracted 3D MR angiograms and for automatic quantification of arterial stenosis. The originality of our work resides in the methods of automatic extraction of the vessel axis and boundaries. These methods are fast and require minimal user interaction at the initialization step.
The article is organized as follows: First, the computer tools required for postprocessing of MR angiograms are discussed. Second, the characteristics of MARACAS as a postprocessing system are described: how it works and what image processing algorithms are implemented in the software for vessel tracking and quantification. Qualitative and quantitative results obtained with MARACAS are then presented, followed by a discussion and conclusions.
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Tools for Postprocessing of MR Angiograms
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In vascular imaging, the term postprocessing stands for a vast number of image manipulation techniques performed with an independent console for assessment of arterial and venous structures. Postprocessing includes a variety of tools: from data transfer and image visualization to automatic quantification of vessel diseases. This section will focus on these three main functions of MR angiography postprocessing systems: data handling, image visualization, and vascular analysis (Fig 1).
Data Handling
Any postprocessing system for working with medical images should be compatible with the Digital Imaging and Communications in Medicine (DICOM) standard (8–12). This standard ensures that recent equipment is compatible. DICOM defines a complex communication protocol that requires that two connected stations agree on the exchanged services. The unit requesting a service is called a service class user; the unit supplying the requested service is called the service class provider. Typically, a service class user (a postprocessing workstation) performing a "query/retrieve" on a service class provider (an imaging unit) first asks for a list of patients; once the patient is locally selected, the service class user asks for a set of images (series). Afterward, the service class provider initiates the transfer through the network and the service class user locally stores the received files on a local hard disk. DICOM also defines the file format, in which the images are encoded, allowing local visualization and postprocessing of the data with no loss of quality. A DICOM file consists of two parts: (a) a header containing a set of data elements (eg, patient name, acquisition protocol, image matrix, pixel size) and (b) the original pixel or voxel data.
Initially, DICOM functions were limited to the exchange of data between proprietary workstations. Recently, some DICOM-compliant applications have become available on personal computers (PCs), and their easier diffusion allows medical institutions or laboratories to perform specific postprocessing tasks (measurements, multiplanar reformation [MPR], MIP, archiving) with a lower investment. Some of these applications can provide service class provider–service class user functions (13).
Image Visualization
Although exploration of the native sections that were acquired by the imaging unit gives access to precise local information (eg, vessel diameter, vessel area), mental reconstruction of the global morphology and spatial relationships is difficult. Moreover, this local information may not be exploitable when the sections are not perpendicular to the vessel of interest (14). Several postprocessing techniques are available for improved rendering of the overall morphology or the spatial relationships of the anatomic structures. Their purpose is to allow the user to simultaneously view the MR angiography data sets in different display formats such as MPR, MIP, surface rendering, volume rendering, and virtual intraluminal endoscopy. In this section, the principles of these techniques are briefly explained. Their main advantages and disadvantages are also discussed.
Multiplanar Reformation.—
MPR involves display of planar sections through the data volume. Some systems extract the sections only in the planes perpendicular to the native sections. This process allows the user to "slide" through the volume along the axial, coronal, or sagittal orientation. Others allow reconstruction of image planes according to any orientation in the space, making it possible to generate sections following an irregular orientation (curvilinear reformation). MPR is based on two operations: interpolation and resampling, so as to assign intensities to voxels located "somewhere between" the actual data points. With MPR images, the radiologist can simultaneously visualize the arterial lumen and the adjacent structures in a localized region and interactively view features that are not visible in native sections (15). However, MPR requires a trained operator, who mentally reconstructs a 3D picture from 2D sections.
Maximum Intensity Projection.—
To obtain the MIP, parallel rays are cast through the volume from each pixel of the projection image plane. Each pixel is assigned the maximum intensity encountered along the corresponding ray. MIP images have an aspect similar to that of conventional angiograms and are widely used in MR angiography analysis. They are often easier to interpret than native sections. However, this technique has some disadvantages. First, it tends to misrepresent anatomic spatial relationships because depth information is not displayed (16). Eccentrically located stenoses may remain undetected, and superimposition of structures may erroneously simulate a stenosis (17). Second, it tends to increase the mean intensity of the background (18,19). Consequently, some low-intensity vessels visible in individual sections may be partially or completely lost in the MIP image (20). To compensate for the loss of depth information in MIP images, postprocessing systems provide such solutions as (a) limiting the projection to a subvolume of interest, instead of projecting the whole volume, and (b) making the projection angle vary (interactive rotation).
Surface Rendering.—
Surface rendering uses the boundary voxels between the object to be displayed and the background to create a 3D surface. Hence, it requires a preliminary segmentation. The segmentation methods capable of precisely delineating the vascular structures and separating them from other tissues belong to the field of vascular analysis and are still under investigation. However, for an approximate visualization, the segmentation may be done by simple thresholding. Surface rendering is also called shaded surface display (SSD) because the intensity of each pixel in an SSD image is calculated by using the local orientation of the surface with respect to a virtual lighting source. In contrast to MPR and MIP, SSD better renders the 3D aspect of MR angiography data. The surface representation accurately captures and represents the positions and shapes of the relevant vascular structures and can be visualized and manipulated interactively. However, it requires a user intervention to select the appropriate thresholding value to extract the surface of the vessel of interest. This can sometimes be quite difficult, especially if boundaries are not well defined (eg, noisy or low-contrast data). Threshold-based SSD images should not be used for quantification, since vessel diameters are threshold dependent and thus can lead to under- or overestimation of the stenosis. In consequence, surface-rendered images should always be displayed simultaneously with at least one complementary visualization mode to assess the appropriateness of the threshold choice (16).
Volume Rendering.—
Volume rendering displays all of the 3D data at once. It works directly on the voxel intensities and creates translucent renderings of the full data set: objects with high signal intensity are opaque and objects with low signal intensity are transparent. As commonly implemented, volume rendering generates an image in the following way: First, it computes color and partial opacity for each voxel. Then, it blends contributions made by voxels projecting to the same pixel on the picture plane (along a line from the viewer’s eye through the data set). In most cases, the user manually sets color, opacity, and brightness corresponding to different voxel intensities. Some systems use standard presets (21). However, these presets are much more difficult to establish for MR angiograms than for CT images. The main advantage of this technique is the ability to generate images without explicitly defining surface geometry. It reveals internal structures that would normally be hidden or omitted when surface rendering techniques are used. Thus, volume rendering appears very interesting for the study of arterial plaque. However, its use requires a powerful computer configuration, and it has been demonstrated that the cost-to-performance ratios are not satisfactory (16).
Virtual Intraluminal Endoscopy.—
Virtual intraluminal endoscopy is a recently developed technique for assessing the inside of the vascular wall. It combines the features of endoscopic viewing and cross-sectional volumetric imaging and involves generation of a sequence of perspective views calculated from points (flight path) within the vascular lumen. These views can be computed by using both surface rendering and volume rendering algorithms. In the most recent systems, the flight path is automatically calculated. This process is based on a preliminary extraction of the vessel centerline, which constitutes a high-level method of image processing.
Vascular Analysis
The purpose of the vascular analysis is to allow the clinician to perform a quantitative assessment of the vessel morphology to decide on the appropriate treatment (surgical or pharmacologic) according to the degree of stenosis and to monitor the progress of the disease. It requires different vessel measurements. On the one hand, intraluminal diameters and cross-sectional areas are needed for quantifying the degree of stenosis. Traditionally, only diameters were used for stenosis estimation. The standard equation for calculating the percentage of stenosis is as follows:
where Ddistal is the diameter of the normal vessel beyond the diseased segment and Dmin is the smallest diameter within the stenosis. However, in the case of a nonelliptical or amorphous stenosis, estimation of the smallest (as well as of the largest) diameter is not clear. Moreover, some authors argue that, in this case, the reduction in cross-sectional area correlates better with the hemodynamic impact of the stenosis than does the reduction in diameter. For these reasons, the cross-sectional area has also been proposed as a measurement for stenosis calculation (22). On the other hand, curvilinear length measurements along the vessel axis are used in preoperative planning of endovascular therapy to determine the precise prosthesis size.
Most postprocessing systems provide interactive tools for manually performing these measurements. This approach considerably increases the accuracy of stenosis quantification compared with a purely visual evaluation. However, manual tracing of the lumen centerline and delineation of vessel boundaries are time-consuming tasks and are susceptible to variability between operators. These major drawbacks have motivated the development of new techniques for automatic quantification of vascular morphology.
In terms of image processing, the first step necessary for performing quantitative analysis of a vessel is to separate it from the surrounding structures to study its shape accurately. This procedure is called segmentation. Two main approaches to vessel segmentation can be distinguished in the literature. The first one relies on purely photometric criteria, mainly thresholding and region-growing techniques (23–26). Its major advantage is its generally simple implementation. However, a further modeling step is necessary to extract meaningful measurements from images segmented thus. The second approach exploits the geometric specificity of vessels, in particular the notions of orientation and tubular shape. Most of these approaches involve vessel tracking (27–31) and use (often implicitly) a generalized cylinder model, that is, an association between an axis (centerline) and a surface (vessel wall) (32,33). Consequently, the segmentation process involves two tasks: centerline extraction and vessel contour detection in the planes usually perpendicular to the axis. This procedure results in a stack of 2D contours along the vessel, allowing quantitative cross-sectional measurements and visualization by means of triangulation-based surface rendering. Other recent approaches use 3D models of the surface (34,35).
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Our Contribution: MARACAS
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Many general-purpose postprocessing systems are commercially available. Namely, there is a great diversity of programs called "DICOM viewers," which include the data handling and image visualization functions (eg, eFilm Workstation [eFilm Medical, Toronto, Canada] [13]; Dicom Eye [ETIAM, Rennes, France] [36]; Osiris [University Hospital, Geneva, Switzerland] [37]; Dicom Viewer [MediMatic, Genoa, Italy] [38]). However, although numerous approaches have been proposed in the literature for vessel segmentation and quantification, to our knowledge, there are few end-user software systems that include high-level vascular analysis methods. For approximately the past 2 years, these have been incorporated into commercially available general-purpose postprocessing software packages (eg, Vitrea [Vital Images, Plymouth, Minn] [21]). Most of them were developed by the major manufacturers of medical imaging systems and integrated into their proprietary workstations (eg, AW MRI Flex Trial [GE Medical Systems, Milwaukee, Wis] [39]; Leonardo [Siemens Medical Systems, Erlangen, Germany] [40]; EasyVision [Philips Medical Systems, Best, The Netherlands] [41]). None of them was specifically designed for small PC-based configurations.
In response to the specific medical need for MR angiography–targeted image analysis software, we developed a postprocessing program called MARACAS. The main features and contribution of this software are described in this section.
What Is MARACAS?
MARACAS is an interactive software for visualization and analysis of blood vessels in 3D MR angiography that provides automatic quantification of arterial stenosis. We emphasized three main aspects in the development of MARACAS: reliability of the results, minimization of postprocessing time, and portability of the software. Our main contribution resides in a novel method of vessel segmentation and quantification, which is fast enough for clinical application and is implemented in a graphical environment portable to multiple platforms. Compared with the above-mentioned postprocessing workstations, MARACAS is a small system that does not require a dedicated configuration (a simple PC is sufficient) and can be installed in almost every computer (PC or Unix workstation). The only additional requirement is the memory size: for full-speed execution, the use of 256 Mbytes of random-access memory is recommended. Installation of the software requires 17 Mbytes of disk space.
MARACAS includes almost all of the functions described in the previous section. First, as regards data handling, it supports the reading of DICOM image files previously transferred from the imaging device system. At present, we use the software eFilm (eFilm Medical) (13) as a DICOM client (service class user) to perform this transfer, that is, to import external DICOM files, to sort the incoming DICOM data by studies and series, and to hierarchically store them on the local hard disk. Second, as regards image visualization, MARACAS includes the following display modes: MPR, MIP, surface rendering (Fig 2), and virtual endoscopy (Fig 3). Third, to achieve vascular analysis, MARACAS provides both interactive tools for manual measurements and an automatic tool for vessel segmentation and stenosis quantification (42). There are three interactive tools: probe, statistics, and profile. These are to be used on the 2D images (sections or MIP images). The probe displays the intensity of the pixel selected by the cursor. The statistics tool displays the mean intensity and the standard deviation of a hand-drawn rectangular region. The profile tool displays the length and the intensity profile of a straight-line segment traced by the user (Fig 4). This tool can also display an estimate of the vessel width: If one supposes that the line is perpendicular to the vessel, the vessel width is calculated from the intensity profile as the width at middle height (full width at half maximum) of the highest peak of intensity.
The remainder of this section focuses on the automatic quantification tool.
How Does It Work?
The vessel extraction and quantification process is as follows (Fig 5): After manual determination of a volume of interest and of a point on the vessel surface, an initial point in the vessel is calculated and the vessel tracking process is started. First, extraction of the central axis of the vessel is performed with an expansible skeleton method. Contours are then detected in the planes locally orthogonal to the centerline by using an improved active contour. Finally, measurements based on the resulting contours allow calculation of the stenosis parameters.
The vessel tracking process is based on a generalized cylinder model. The main characteristics of our approach are the simplicity of the model initialization and the flexibility of its evolution (43). Thus, vessel tracking requires little user interaction and is accomplished in a very short time. In the following subsections, the most important steps of the method are described.
Selection of a Starting Point.—
The initialization is performed in the surface-rendered image of the volume of interest. The user defines the target segment (from which the centerline will be extracted) by marking one point on the vessel surface (the pick point). To extract the vessel axis, the algorithm needs a point within the vessel, which is automatically computed based on the position of the pick point (Fig 6).
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Figure 6. Interaction scenario for selection of a starting point. Left: The user-initialized pick point on the vessel surface (P1) is generated from the original image. Middle: Vessel surface points P2, P3, and P4 are automatically deduced from the pick point. Right: The starting point is calculated as the middle point of P1-P2.
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First, from the pick point (P1), a ray (pick ray) is cast into the vessel and intersects the opposite side of the vessel surface. The middle point of the segment P1–P2 is taken as the starting point for the algorithm. At the same time, MARACAS estimates the vessel width at this point by casting a ray perpendicular to the pick ray (P3–P4). The estimated vessel width corresponds to the average length of the segments P1–P2 and P3–P4. This measure is not used for quantification, but it is very useful for the tracking algorithm to automatically set its parameters. Indeed, different values of the parameters are required in the case of the aorta and of small peripheral arteries.
Extraction of the Vessel Axis.—
Vessel axis extraction is achieved with an expansible skeleton method. It is based on a tracking strategy, which begins from the computed starting point within the vessel and then iteratively estimates the subsequent axis points (at each iteration, a new point is added to the model). Point generation is a two-step procedure: First, a prediction of the new point position is obtained, based on the local vessel orientation at the current point. This position is then corrected under the influence of image forces and shape constraints.
The position of the next point is predicted by applying a "constant velocity" displacement of the current point along the local vessel orientation. The local vessel orientation is estimated by inertia moment minimization for a small volume (cell) centered on the current point (44). The size of the cell is automatically deduced from the vessel width estimated at the initialization step. The inertia-based approach provides a convenient way to automate axis extraction for most vascular structures. Moreover, it offers good noise robustness and gives satisfactory results even for small vessels. However, it has been shown that the inertia criterion alone may lead to an absurd axis in the case of a bifurcation (Fig 7) or significant curvature (Fig 8) (28). Hence, the predicted position of the new point sometimes needs to be corrected.
Correction results from submitting the point to two kinds of elementary forces: external and internal. The external forces are used to attract the point toward a position that has a high likelihood of being located on the vessel centerline. Assuming that the maximum of the MR signal is reached at the vessel axis, we propose two external forces, which attract the point toward a local maximum of intensity and toward the gravity center of the cell. The internal forces are used to impose smoothness and continuity constraints so as to limit oscillations and reduce the noise sensitivity. These forces are deduced from a deformable model that provides internal constraints on vessel axis elasticity and flexibility.
Manual corrections of the extracted vessel axis are allowed. This is particularly useful in the case of bifurcations. Although bifurcations are not incorporated into our local vessel model (a tubular structure), MARACAS succeeds in extracting the vessel centerline even at the branching points. However, it tracks only one branch at a time. Consequently, if the automatically extracted branch is not the desired one, the user can interactively force the tracking of another branch (Fig 9).
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Figure 9. Interaction scenario for user intervention in axis extraction of a femoral artery. In A, the centerline of the vessel is automatically extracted by the software. In B, the user marks one point just before the bifurcation. In C, the axis of the processed branch (the left branch) is removed. In D, the right branch is processed.
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In addition, different vessel axes can be saved when extracted. In this way, it is possible to process the whole image and extract the entire vascular tree.
Extraction of Vessel Contours in the Planes Orthogonal to the Vessel Axis.—
MARACAS automatically generates image planes orthogonal to the extracted vessel centerline (Figs 10, 11). For this purpose, the centerline is interpolated by using a B-spline curve and the image volume is resectioned. MARACAS displays the reformatted 2D image of the orthogonal plane in a separate window, where it can be interactively panned and zoomed. The location of the plane is displayed together with the surface-rendered image of the vessel. The user can slide the plane along the axis, thus obtaining a curvilinear MPR image along the automatically extracted centerline.
For detection of vessel lumen boundaries in the 2D images, MARACAS uses a deformable model: an active contour (45). An active contour, also called a "snake," is a planar elastic curve that can dynamically conform to a boundary. To do this, the active contour undergoes the action of fictitious external forces (mainly image forces) and the reaction of internal forces (elastic forces). The image forces are designed to attract the contour toward strong intensity gradients, whereas the internal forces encourage smooth curves. The contour is progressively displaced from its initial position toward an equilibrium position that corresponds to a minimum of potential energy. The active contour models combine detection of gray-level transitions within the image (local information) with obtainment of a closed smooth contour and thus constitute a suitable alternative to classic segmentation techniques based on edge detection. However, the very first versions (46) were strongly initialization dependent: To be attracted by the actual vessel boundaries, the initial curve had to be placed close to them. To overcome this problem, MARACAS uses an external force known as pressure or balloon force (47). Under its influence, the active contour is "inflated" like a balloon until it meets an edge strong enough to stop it (Fig 12).
Use of pressure force together with a new numeric implementation permits initialization with a single pixel, which is automatically defined by the intersection between the vessel axis and the orthogonal image plane. Vessel contour detection in the planes locally orthogonal to the centerline results in a stack of 2D contours along the vessel (Fig 13), allowing quantitative cross-sectional measurements. Furthermore, the generated outline can be visualized by means of a triangulation-based rendering technique.
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Figure 13. Vessel contour detection all along the vessel centerline. Left: Extraction of the vessel centerline. Middle: Extraction of the vessel contours. Right: Detection of vessel boundaries in the 2D images of the orthogonal cross sections.
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Sometimes, boundary detection fails when the initialization point for the active contour is on the true vessel boundary, since the deformation process is immediately stopped. This may happen in the case of a small cross section (2 or 3 pixels in diameter) in very thin or severely stenosed vessels. In cases where MARACAS cannot cope with vessel contour detection, the user can carry out corrections by retracing the contour manually (Fig 14) or by changing the starting point for the deformable model–based automatic detection of the vessel contour.
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Figure 14. Manual correction of a vessel contour. Left: Cross section of a severely stenosed region. Middle: Quantification curves obtained by automatic detection of the vessel contour. The area value equal to zero attracts attention to the section where the contour was not correctly detected. The contour remained a single point because the axis locally touched the actual vessel boundary. Right: Manual correction of the vessel contour and automatic updating of the curves.
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Automatic Quantification.—
MARACAS supplies automatic measurements for accurate quantitative analysis of vascular morphology. The quantification process is carried out simultaneously with extraction of the vessel boundaries. From the detected vessel lumen boundaries, several measurements are deduced: diameters (maximum, minimum, and average), perimeter, and area. The measurements are graphically displayed as curves. Corresponding numeric values can be read at any given point by moving a cursor line along the curves or by selecting a point directly on the vessel axis (Fig 15).
Once different measurements have been computed for the entire segment, quantification of the degree of stenosis can be performed. This step needs a user intervention to identify a normal (healthy) section, where the measurement Sdistal is taken as the reference value (the distal measurement). The local degree of stricture is computed in each section l by comparing the local measurement Sl with Sdistal (Fig 16):
Note that, in this formula, S stands for any of the measurements available for the purpose of quantification, not only for diameters as in Equation (1). The degree of stenosis is deduced from the most severe stricture, where Sl is minimum.
Tests and Results
Images.—
The precision of the methods described herein was assessed on images of two phantoms. Our computer-assisted design phantoms are cylinders whose internal surface represents the endoluminal shape of the vessel (48). Their internal reference diameter is 6 mm, and each of them comprises two stenoses (Fig 17). Phantom A was placed in a water tank. Phantom B was placed in the leg of a pig to simulate more realistic acquisition conditions. Both were centered in the magnet (Vision 1.5 T; Siemens Medical Systems) within a head coil.
After bolus injection of gadolinium contrast material, data sets were collected by using 3D fast imaging with steady-state precession sequences. The imaging parameters for phantom A were as follows: flip angle, 30°; repetition time, 4.4 msec; echo time, 1.4 msec; acquisition time, 22 seconds; section thickness, 0.76 mm; pixel size, 0.78 x 0.78 mm; pixel matrix, 256 x 256; and sagittal plane. The imaging parameters for phantom B were as follows: flip angle, 25°; repetition time, 5 msec; echo time, 2.1 msec; acquisition time, 40 seconds; section thickness, 1.0 mm; pixel size, 0.78 x 0.78 mm; pixel matrix, 256 x 256; and axial plane.
Qualitative Assessment.—
Because the precision of the vessel axis extraction method is difficult to estimate quantitatively, we carried out a qualitative evaluation. It was performed on data from 23 patients with stenoses located in different arteries: the carotid arteries (Fig 18), renal arteries, and arteries of the lower limbs (Fig 19). We also performed a visual evaluation of the extracted contours. The algorithm was tested on numerous contours with different shapes and sizes (Fig 20): circular, elliptical, semilunar, amorphous, and so on.
Quantitative Results on Images of Phantoms.—
We tackled the problem of area measurements for stenosis quantification. Cross-sectional areas Sl from the normal (healthy) parts of the vessel were used to calculate the average normal area Sn. The corresponding coefficients of variation were defined as follows:
and
where 
s is the standard deviation of the measured area. The degree of stenosis was computed as the ratio of the pathologic cross-sectional area Smin to Sn (Fig 16). The stenosis severity estimates were quantitatively evaluated by comparing them with the true (theoretical) stenosis values of the phantoms. A summary of the quantitative results for these data is given in Figure 21 and the Table.
The coefficients of variation (CV < 3.5%, CVmax < 7%) indicate good stability of the vessel contour extraction results. The fluctuations can be attributed to the partial volume effect. Indeed, let us consider the case of phantom B, which had the greatest coefficient of variation. The cross-sectional area of a normal (nonstenosed) section (diameter = 6 mm) is 28.27 mm2. The voxel size is 0.78 x 0.78 x 1.0 mm. Therefore, each missing or excessive pixel on the extracted surface represents an error of 2.15%. This outcome shows that our results contain no more than 3 misclassified pixels, which is a correct value if one takes into account the partial volume effect. Moreover, the absolute errors in stenosis quantification are not more significant than the variations and could be explained by the same reasons.
Discussion
Before discussing the accuracy of the extraction algorithms for the vessel axis and boundaries, let us note the efficiency of their implementation in terms of processing time. The processing time depends on the number of reconstructed cross sections. Indeed, computational cost is mainly determined by the extraction of image planes orthogonal to the axis, whereas extraction of the axis and of the boundaries is almost instantaneous. Typically, 1.4 seconds is needed to reconstruct one cross section on an 800-MHz PC. Consider a renal artery resectioned every 1 mm, which is a reasonably fine quantification step for typical MR angiographic image resolutions. The entire extraction and quantification process in this case takes 1 minute on average.
Precision of the Vessel Axis Extraction Method.—
According to a visual evaluation, the results were satisfactory for large vessels as well as for small and low-intensity ones. The vessel centerline correctly tracks the vessel path and lies inside it even in the presence of severe stenosis. However, one can argue that in some cases the axis should lie outside the actual lumen. Indeed, in MR angiography, only the vessel lumen is imaged. Therefore, the vessel axis extracted by our algorithm is in fact the centerline of the circulating blood lumen. This is not a problem in analysis of healthy vessels because the vessel centerline coincides with the lumen centerline. However, in the case of vessels with a severe or extremely eccentric stenosis, a question remains: What should be detected as the vessel centerline to generate the best perpendicular planes? Two answers are possible: The vessel axis can be centered in the lumen or it can be equidistant from the true vessel surface. We will discuss the pros and cons of each approach.
A vessel axis centered in the lumen indicates the true path of the blood flow. It can be used for guiding a virtual endoscopic exploration of the vessel. However, such an axis demonstrates significant curvatures in the regions adjacent to the stenosed segment. Consequently, cross sections in these regions may be erroneous (Fig 22a): They are not perpendicular to the vessel but oblique, and the corresponding lumen shape is elliptical. With a vessel axis equidistant from the true vessel surface (Fig 22b), the problem of oblique cross sections can be avoided. Such an axis also seems more appropriate for length measurements in preoperative planning of an endovascular prosthesis. However, it cannot be used for guiding a virtual endoscopic exploration of the vessel. In addition, it cannot be used to initialize the starting point for our contour extraction algorithm in the stenosed region because the point may be outside the vessel.
Our axis extraction method differs from other vascular network extraction techniques founded on second derivatives (29,49) or on curvatures (50), which have proved to be noise sensitive. Our objective was to reduce the noise sensitivity to be able to cope with even very small and low-contrast vessels. Owing to its expansible nature, the centerline extraction algorithm overcomes the initialization limitations of deformable models as well as some of the geometric flexibility constraints such as the adaptation to significant curvatures. Therefore, it gives satisfactory results in terms of vessel tracking even in situations with complex geometry: significant curvature (Figs 7, 13); a thin, severely stenosed vessel (Figs 11, 14, 15); and bifurcation (Figs 8, 9).
Accuracy of the Vessel Contour Detection Algorithm.—
We used two criteria to assess the precision of the vessel contour extraction method. The first was the final shape of the active contour used to extract the vessel boundary. Preliminary results on phantom images and on large vessels from patient data show precise estimation of the contour position. It is very difficult to judge the shape of the contours in the case of vessels as thin as 2 or 3 voxels. The second criterion was the area measurement, which can be compared with known theoretical values on images of phantoms. The reported quantitative results obtained in phantoms show the precision of our method.
The new numeric implementation of the active contour used by MARACAS to extract the vessel boundaries offers some advantages compared with the classic "snake" model. The contour deformation is independent of the contour size, and the final outline is not determined by the initialization. This allows (a) initialization with a single pixel and (b) growth in each direction with retention of a smooth outline.
As mentioned earlier, the main disadvantage of the model is that it cannot be initialized on the vessel boundary or very close to it. This happens in the case of small cross sections, in which the vessel centerline may touch the boundary. To overcome this problem, boundary detection should probably not be limited to 2D contours in the planes locally orthogonal to the axis but should be carried out in a 3D neighborhood.
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Conclusions
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We have described the software tools required for effective handling, visualization, and analysis of 3D images of blood vessels. This overview has been illustrated by MARACAS, software for blood vessel tracking applied to stenosis quantification in 3D MR angiography. Two image processing algorithms constitute the kernel of the software: vessel axis extraction and vessel boundary detection. These methods were evaluated qualitatively and quantitatively. Visual assessment of the automatically extracted axes and boundaries showed precise estimation of their positions and orientations. Quantitative results on images of phantoms showed that the degree of stenosis was estimated with good accuracy even for severe stenosis. User intervention is minimal, and the radiologist can supervise and interactively correct the vessel tracking procedure.
Additional work is necessary to improve the reliability of the contour detection in some situations with complex geometry, such as bifurcations or severe eccentric stenosis. A more extensive validation study is being performed, which incorporates additional phantoms as well as numerous images from patients. Use of the methods on CT angiographic data sets will also be evaluated.
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Acknowledgments
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We thank Alfred Anwander for his help in implementing the algorithm for vessel contour extraction, Bruno Marchand for providing the phantom data sets, and Leonardo Florez for his great contribution in programming. We also express our gratitude to Jean-Pierre Roux, Eric Boix, Fabrice Bellet, and Christophe Odet, members of the computer systems team of our laboratory, for their technical support.
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Footnotes
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9*. Vascular system, location unspecified 
Abbreviations: DICOM = Digital Imaging and Communications in Medicine,
MARACAS = Magnetic Resonance Angiography Computer Assisted Analysis,
MIP = maximum intensity projection,
MPR = multiplanar reformation,
PC = personal computer,
2D = two-dimensional,
3D = three-dimensional
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References
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Abstract
Introduction
