CHAPTER 84 Advanced Three-Dimensional Postprocessing in Computed Tomographic and Magnetic Resonance Angiography

Rob J. van der Geest, Pieter H. Kitslaar, Patrick J.H. de Koning, Ronald van ’t Klooster, J. Wouter Jukema, Gerhard Koning, Henk A. Marquering, Johan H.C. Reiber

INTRODUCTION

Over the past several years, the research and developments in visualization and quantitative analysis, as well as the clinical usage of cardiovascular MRI and, in particular, of multidetector computed tomography (MDCT) have made major progress. Both acquisition techniques have in common that enormous amounts of data are being generated that need to be visualized in a proper manner for interpretation purposes. It has been clear for many years that cardiovascular MRI has all the ingredients for the “one-stop-shop” approach, allowing the assessment of anatomy, function, perfusion, infarct imaging, flow, as well as spectroscopy, although imaging time has been a major limitation. These possibilities led to a data explosion, making it difficult to visualize, interpret all the data, and come to a diagnosis by the cardiologist/interpreting physician. Given these developments, it has been clear that quantitation of all these data sets becomes an imperative for various reasons. It has been documented that the variability in the quantitative analyses has been much smaller than by visual interpretation, leading to smaller population sizes in clinical trials with all the subsequent advantages, such as lower costs of the trials, results available earlier, and so on. In addition, quantitation will lead to an efficiency improvement in the clinical setting: less dependency on the experience of the interpreter, the analyses can be preprocessed for the final approval by the cardiologist/interpreting physician, and all the results can be stored right away in the hospital picture archiving and communication system (PACS) system. Given all the high expectations of molecular imaging and the hope to better understand the atherosclerotic process, MR vessel wall imaging appears to be an excellent means to study the changes in the vessel wall and the composition of the atheroma.

With the enormous technical developments in multislice CT now with 256 and 320 slice scanners, the depiction of anatomy in particular has become astonishing. An enormous advantage of CT is the very short acquisition times from one to a few cardiac cycles; greatest disadvantage is the radiation dose, although great efforts are underway to diminish that as much as possible. There has been a growing clinical interest in the use of the MDCT system for noninvasive coronary angiography. Visualization of the data sets is commonly done by 3D workstations, which increasingly provide some quantitation results as well, although the variabilities in the analyses have been enormous and clinically often not acceptable, even raising questions by the Food and Drug Administration (FDA). It has been evident that more complex segmentation techniques are necessary, and that validation of the results is a must. Also, MDCT is developing toward the assessment of function, perfusion, and viability, and the analysis of heart valves. In this chapter, we will describe and illustrate segmentation and quantitation approaches for both CT angiography (CTA) and MR angiography (MRA).

3D Postprocessing in Computed Tomographic Angiography

For the analysis of vessel structures in CTA data a number of postprocessing (image processing) steps are required. The first step is the (automated) extraction of the vessel centerline, which forms the foundation for a number of subsequent postprocessing steps. For stenosis quantification in the vessel, lumen contours are detected in a stretched vessel image based on the extracted centerline. In the next section these steps will be discussed in more detail.

Automated Vessel Extraction

Segmentation and analysis of vessels in 3D image data has been an area of research for many years. In general, the definition of the vessel centerline is a first major step in the process of segmentation and analysis of vessels. Existing methods for the determination of vessel centerlines can roughly be grouped into two categories: a minimal cost path calculation;¹ and methods based on first obtaining the whole set of image pixels containing the vessel (segmentation) and next gradually reducing these sets of pixels to a single centerline (skeletonization).² The first type is typically computationally faster and avoids the error-sensitive segmentation step. However, the minimal cost path may deviate from the true lumen center at strong curvatures of the vessels. Furthermore, the intermediate result of the second type does provide some advantages such as the visual evaluation of the presegmentation of the vessel (tree).

The presented method consists of the following steps: (1) the presegmentation of the coronary vessels; (2) the extraction of the vessel’s centerline; (3) a reformatting of the image volume to produce a stack of cross-sectional images perpendicular to the centerline; (4) a combination of longitudinal and transversal contour detection approaches; and (5) the quantification of vessel morphologic parameters. These five steps will be described in more detail in the following paragraphs.

Coronary Vessel Presegmentation

The first step in the segmentation and analysis process is a presegmentation step based on the so-called fast-marching level set method (called WaveProp for short).³ The WaveProp algorithm simulates the propagation of a wave through a medium starting from a user-selected source point, in this case the ostium of a vessel. The wave propagates through the volume set with a propagation speed given by the so-called speed function; this speed function can be designed based on image intensities in such a way that the wave propagates fast in the structures of interest (high intensities in a blood vessel) and slow in the remaining structures (low image intensities). By this image-based approach, the propagation automatically provides an initial segmentation of the vessel lumen.

For a complete analysis of a segment of a single vessel, the user places a proximal point at the beginning of the vessel and a distal point at the end of the vessel of interest. The expansion or propagation process stops when the wave propagation reaches the end point.

Centerline Detection

The fastest path, which is the path connecting the start and end point, can be obtained using a so-called steepest-descent approach by backtracking the path of an accepted voxel in the wave propagation to the source (starting point) following the minimal travel time (highest speed). However, the fastest path tends to deviate from the center of the lumen by taking the inside curve at bending vessels. To correct the fastest path such that it follows the center of the lumen, a modified distance transformation is used.⁴ This distance map defines for each voxel the minimal distance to a nonaccepted voxel, and as a result, the highest values represent the center of the segmented vessels. An example is given in Figure 84-1.

FIGURE 84-1 A, Volume rendering of CTA volume of the heart. B, Centerline obtained from the start (red) and end (blue) points. C, Centerline overlayed in the axial slice.

Curved Multiplanar Reformatting

Because of its tortuous course and the presence of other structures such as the heart chamber, the visual evaluation of the segmented vessels may still be cumbersome. When the vessel’s centerline is known, a curved multiplanar reformatted (CMPR) image along the vessel’s course can be constructed (Fig. 84-2). The goal of CMPR visualization is to make a vessel visible in one single image over its entire length. Traditionally, two separate approaches have been used in the construction: stretched CMPR or straightened CMPR. The stretched CMPR displays a tubular structure in one 2-D plane without overlap, whereas the straightened CMPR produces a linear representation of the vessel that simulates the vessel as if it has been pulled straight. To optimize the image for contour detection, we follow the latter approach. The reformatted image contains a stack of 2D images that are perpendicular to the centerline. The third dimension, Z, in this image represents the distance to the source point along the centerline, such that the centerline is transformed into a straight line running through the X-Y center of the stack of images.

FIGURE 84-2 CMPR images. A, Straight CMP image. B, CMPR slices in 3D. C, D, Stretched CMPR images.

Contour Detection

For the quantitative results to be insensitive to image noise, the contour detection needs to be relatively insensitive and robust to image distortions. Straight-forward contour detection methods based on thresholds of image intensities solely, second-order derivatives or the full-width half maximum method ⁵ are sensitive to image noise, and as a result limit the algorithm to adapt to variations in the dosage or distribution of contrast agent.⁵ Commonly, contour detection for the determination of vessel dimensions is carried out solely on the 2D cross-sectional planes perpendicular to the vessel’s centerline. To minimize the sensitivity to image noise, we use information of the complete 3D shape of the vessel. The reformatted CMPR image enables the use of multiple 2D contour detections. For that reason, we suggest the following approach, which has been successful in IVUS applications.⁶

Through the stack of images, a number of longitudinal cut planes (typically 4 to 6) can be defined, which are perpendicular to the transversal planes and pass through the center of the CMPR image, and thus through the centerline of the vessel (Fig. 84-3). These cut planes are subsequently used for the contour detection along the course of the vessel.⁷ Experiments have demonstrated that the construction of four cut planes is sufficient for the longitudinal contour detection.

FIGURE 84-3 A single longitudinal cut slice (left) and four transversal slices at the corresponding positions (right) in the CMPR image.

The longitudinal vessel borders are detected using the model-guided minimum cost approach (MCA)⁸. The cost function is based on a combination of spatial first-, and second-derivative gradient filters in combination with knowledge of the expected CT values, and curvature of the coronary vessels. Because the 3D shape of the vessel resembles a smoothly curved tube, the two vessel boundaries in a longitudinal cut plane are detected simultaneously.⁹ This means that a well-defined vessel border at one side can support the detection of the vessel border at the other side. This mutual guidance by the simultaneous detection of the vessel boundaries is especially helpful at locations with strong partial volume effects or close to bifurcations. In these cases, the shape of the opposite contour follows the shape of the well-defined edge.

Next, the four longitudinal cut planes displaying its associated contours are presented for visual inspection (Fig. 84-4A). In some cases, such as at the presence of strong calcifications or odd branchings, manual correction of the contours may be necessary, and can easily be carried out. The longitudinal detected vessel contours produce a series of intersection points with the transversal slices. These points have two functions: (1) they are used to specify the region of interest for the MCA contour detection in the transversal images; and (2) they function as attraction points with an adjustable strength to attract the contour detection to areas close to these points. The advantage of using attraction points instead of forcing contours to run through the intersection points is that small deviations in the longitudinal contours do not force the transversal contour to follow this point and makes the transversal contour detection less sensitive to small variations in the longitudinal contours. The contours in single transversal images can also be manually corrected by adjusting a part of the contour or by moving an attraction point (see Fig. 84-4B).