Level set based cerebral vasculature segmentation and diameter quantification in CT angiography

Abstract

A level set based method is presented for cerebral vascular tree segmentation from computed tomography angiography (CTA) data. The method starts with bone masking by registering a contrast enhanced scan with a low-dose mask scan in which the bone has been segmented. Then an estimate of the background and vessel intensity distributions is made based on the intensity histogram which is used to steer the level set to capture the vessel boundaries. The relevant parameters of the level set evolution are optimized using a training set. The method is validated by a diameter quantification study which is carried out on phantom data, representing ground truth, and 10 patient data sets. The results are compared to manually obtained measurements by two expert observers. In the phantom study, the method achieves similar accuracy as the observers, but is unbiased whereas the observers are biased, i.e., the results are 0.00 ± 0.23 vs. −0.32 ± 0.23 mm. Also, the method’s reproducibility is slightly better than the inter-and intra-observer variability. In the patient study, the method is in agreement with the observers and also, the method’s reproducibility −0.04 ± 0.17 mm is similar to the inter-observer variability 0.06 ± 0.17 mm. Since the method achieves comparable accuracy and reproducibility as the observers, and since the method achieves better performance than the observers with respect to ground truth, we conclude that the level set based vessel segmentation is a promising method for automated and accurate CTA diameter quantification.

Introduction

The dramatic increase of the number and sheer size of three dimensional (3D) angiographic data sets (magnetic resonance angiography – MRA and computed tomography angiography – CTA) has lead to an almost overwhelming amount of 3D information to be evaluated by clinicians. Since manual procedures to process these data are often tedious, time consuming and subject to inter- and intra-observer variability, there is a strong demand for segmentation methods that are (semi-) automatic. The methods for the specific task of vessel segmentation have received considerable interest in the last decade. They have been applied for improving visualization, therapy planning, detection of abnormalities (such as aneurysms), in quantification (e.g., of diameters or stenosis grade) and as preprocessing step for 3D vessel modeling, and in the design of computer aided diagnosis systems.

The focus of this work is on segmentation of the cerebral vasculature – in particular the Circle of Willis (CoW) – in CTA data sets, and on diameter quantification of parts of the vessel tree. Fig. 1 shows a maximum intensity projection (MIP) and a schematic drawing of the CoW together with the naming of its most important vessels. Segmentation of these vessels is clinically relevant since it allows for visualization of the vessel and inspection of vessel morphology, serves diagnostic purposes, provides the first step for quantification and can be used as input for haemodynamic studies. Accurate diameter measurements is clinically relevant since it allows for quantification of vessel widening or vessel spasm, which can be useful for e.g., spasm detection and stenosis quantification. Numerous methods for vessel segmentation have appeared in the literature; approaches based on front propagation or level set evolution (Osher and Sethian, 1988, Sethian, 1999, Osher and Paragios, 2003), model based approaches (Krissian et al., 2000, Frangi et al., 2001), (multi-scale) vessel tracking approaches such as Wink et al., 2000, Aylward and Bullit, 2002, Wink et al., 2004, region growing approaches such as Adams and Bischof, 1994, Wan and Higgins, 2003, Yi and Ra, 2003, Suryanarayanan et al., 2004, and hybrid combinations of these. To pursue the aforementioned goals of segmentation and diameter quantification, we will rely on a level set based approach (Osher and Sethian, 1988, Sethian, 1999, Osher and Paragios, 2003), which can be considered an implicit way of solving deformable models (McInerney and Terzopoulos, 1996, Montagnat and Delingette, 2001) such as the well known snakes (Kass et al., 1988). Level set evolution is a way of describing the movement of surfaces by embedding them as the zero level set of a higher dimensional function, thereby obtaining an intrinsic, i.e., parameter free representation, gaining topological flexibility, and allowing for a simple calculation of geometrical properties, such as curvature, of the moving surfaces. We believe that these properties make the level set framework an excellent choice for describing the varying and complex structures of vessel trees, as is also supported by a non-exhaustive list of examples from the literature (Leventon et al., 2000, Deschamps and Cohen, 2001, Lorigo et al., 2001, Quek, 2001, Vasilevskiy and Siddiqi, 2002, Pichon et al., 2003, van Bemmel et al., 2003, Manniesing et al., 2004, Manniesing and Niessen, 2004, Nain et al., 2004).

Several authors have used level set approaches for vascular segmentation. Most methods have focused on vessel segmentation from 3D MRA data. For example, in van Bemmel et al. (2003), a level set framework is proposed for the purpose of artery vein separation in blood pool agents contrast enhanced MRA data. Lorigo et al. (2001) aim at vessel segmentation by a co-dimension two level set evolution in 3D, i.e., evolving line structures in 3D, and the method is applied to cerebral MRA data. The latter is similar to our method, in which we evolve a level set which is constrained by curvature influence of the minimal principal component of the 3D curvature term. Compared to MRA, CTA has the additional problem of presence of bone structures in the image, whose intensity values, especially of the partial volume voxels, overlap with vessel intensities. Besides (Lorigo et al., 2001), the most closely related work is by Suryanarayanan et al. (2004). There a partitioning scheme is proposed which divides the CTA data set into three distinct regions (neck, skull base and skull). Subsequently, for each region a different type of segmentation method is applied based on a variant of a region growing algorithm. However, exact implementation details and details on how to deal with the bone structures, especially at the difficult part of the skull base, are missing. Furthermore, the work by Lorigo et al., 2001, Suryanarayanan et al., 2004 lack a proper validation. To our knowledge, there is no other work which targets both the segmentation of vessels from 3D CTA data and includes an extensive quantitative validation.

The main contribution of this work is the extensive validation of the results. Visual evaluation of the segmentation results is limited, as it is subject to inter- and intra-observer variability. Moreover, it is an extremely difficult task – especially in the case of the varying and complex morphology that large vessel structures exhibit. Therefore, we choose to validate based on diameter quantification of parts of the vessel tree. This choice is also motivated by the fact that diameter quantification is the first step in other clinical studies such as vasospasm detection or stenosis quantification in patients. Two large studies are conducted, a phantom study and a patient study, both including manual measurements obtained from two expert observers. The manually obtained results are compared to the method’s results.

This paper is organized as follows. In Section 2, the level set based method is explained in detail. We describe the data sets that are used for optimization and validation in Section 3. A major part of this work is devoted to evaluation and validation; Section 4 describes the applied evaluation criteria. Section 5 is on the experimental framework that includes the experiments designated for segmentation, parameter optimization and diameter quantification. Results are reported in Section 6 and discussed in Section 7.