Aortic Arch Quantification using Efficient Joint Segmentation and Registration

Abstract

Accurate aortic arch quantification is important for diagnosis and treatment of cardiovascular diseases. We introduce a new approach for the quantification of the aortic arch morphology with improved computational efficiency which combines 3D model-based segmentation with intensity-based image registration. The performance of the approach has been evaluated based on 3D synthetic images and clinically relevant 3D CTA images including pathologies. We also performed a quantitative comparison with a previous approach.

Introduction

Accurate segmentation of the aortic arch is crucial for diagnosis and treatment of cardiovascular diseases. Pathologies of the aortic arch may be treated by minimally-invasive placement using an endovascular graft, which should be chosen based on the anatomy of each patient. Therefore, individual morphological parameters such as the centerline position and the vessel diameters have to be quantified. The geometry of the aortic arch can be automatically determined from radiological images by segmentation approaches such as, for example, region growing, differential approaches, or deformable models.

Recently, increased attention has been paid to combined approaches that integrate segmentation and registration. These approaches can be classified as model-to-image registration (e.g., [ 1, 2, 3 ]) or as joint segmentation and registration approaches (e.g., [ 4, 5, 6 ]). While in model-to-image registration, segmentation is performed by image registration of a model, joint approaches combine segmentation and registration in a single functional. Joint approaches for the segmentation of human vessels have only recently been suggested [ 6 ].

In this contribution, we introduce a novel joint segmentation and registration approach for the quantification of the aortic arch morphology from 3D tomographic images.

Materials and Methods

Our approach for the segmentation of vessels in 3D tomographic images combines model-based segmentation with elastic image registration. The approach is based on an energy-minimizing functional Jk corresponding to a vessel segment k Jk(pk; uk) = JM (gM ; gIro;ki ; pk) + JR(gIro;ki ; gMroi;k; uk) (1) The first term JM denotes an intensity similarity measure between a 3D cylindrical intensity model gM with parameters pk and the intensities gIro;ki within a region-of-interest (ROI) of a 3D tomographic image gI . The second term JR denotes an energy-minimizing functional for elastic registration of gIro;ki with an image gMroi;k generated from the 3D intensity model gM .

The 3D parametric intensity model used in JM represents an ideal sharp 3D cylinder convolved with a 3D Gaussian [ 7 ]. The model includes parameters for the width R of the tubular structure and the image blur , and is well-suited to describe the plateau-like intensity structure of thick vessels. The complete 3D parametric intensity model gM also incorporates intensity levels a0 (surrounding tissue) and a1 (vessel) as well as a 3D rigid transform R with rotation = ( ; ; )T and translation x0 = (x0; y0; z0)T , which yields gM (x; p) = a0 + (a1 − a0) gCyl(R(x; ; x0); R; ) with parameters p = (R; a0; a1; ; ; ; ; x0; y0; z0)T .

The cylindrical model gM can accurately represent a vessel segment if the vessel has circular cross-sections. However, the model may be inaccurate in the case of non-circular cross-sections (e.g., Fig. 1a). To improve the accuracy between the model and the true vessel shape in this case, we suggest using elastic registration of an image gMroi;k generated from the 3D intensity model gM with the original image gIro;ki . The result of elastic registration is a deformation field uk which is used to compute a refined vessel contour and centerline position.

The functional in (1) is optimized by an iterative scheme which alternatingly minimizes JM and JR for each vessel segment k to obtain estimates for the model parameters pk and the deformation field uk. For a vessel segment k, we estimate pk by least-squares model fitting of gM to the image intensities gIro;ki . To compute uk, we generate an image gMroi;k using the fitted intensity model gM and perform intensity-based registration with gIro;ki by minimizing JR(uk) = JData;I (gIro;ki ; gMroi;k; uIk)+ I JI (uk; uIk)+ E JElastic(uk); where I and E are scalar weights. The first term JData;I describes the intensity-based similarity measure between gIro;ki and gMroi;k (sum-of-squared intensity differences). With the second term JI , the intensity-based deformation field uIk is coupled with the final deformation field uk using a weighted Euclidean distance. The third term JElastic represents the regularization of the deformation field according to the Navier equation of linear elasticity

The result of elastic registration is used to improve the result of model fitting by re-estimating the model parameters pk including the radius R, the orientation , as well as the translation x0. Based on the updated parameter vector pk and the deformation field uk, we again perform model-based segmentation with subsequent elastic registration for minimizing J . This alternating optimization is repeated until the results of model fitting and elastic registration converge for a vessel segment k. After convergence and having estimated the parameters for the current vessel segment, a new parameter vector pk+1 is predicted based on a Kalman filter and used as initialization for the next vessel segment.

We have developed two different variants of our approach to exploit the intensity information. The first variant performs model fitting within a 3D ROI and uses 3D image registration within the 3D ROI. The second variant uses 3D model fitting only for estimating the initial 3D orientation , while Jk is minimized based on model fitting and image registration of 2D image crosssections orthogonal to the vessel centerline.

To reduce the computational complexity of our approach, we introduce an automatic adaptive masking scheme. The idea is to perform intensity-based registration not for the whole ROI but only for those regions which contain relevant information. In our application, most information is contained in edge regions of a vessel. Hence, in each iteration k of the segmentation we generate a binary mask mrkoi(x) = { 1; if ∥∇gMroi;k(x)∥ > ct · xm2RaOxI(∥∇gMroi;k(x)∥) 0; otherwise (2) where ∥ · ∥ denotes the Euclidean norm, and xm2RaOxI(∥∇gMroi;k(x)∥) denotes the maximum magnitude of the gradient of gMroi;k within the ROI (we used ct = 0:1). Note that the gradient is computed based on the model, i.e., noise and neighboring structures in the original image do not disturb the result. 3

Results

We have applied our approach to 120 3D synthetic images and 15 clinically relevant 3D CTA images of the human thorax. To quantify the segmentation accuracy, we have computed mean errors for clinically relevant measures comprising the minimum, mean, and maximum vessel diameters, eD;min, eD;mean, and eD;max, respectively, and the mean error for the centerline position ex0 .

In a first experiment, we have generated 120 images of twisted tori with elliptical cross-sections that differ in radii and the level of Gaussian image noise (see (a) (b) (c) (d)

Fig. 1b). We have evaluated the segmentation accuracy of the new joint approach (2D and 3D variant) in comparison to a previous model-based approach [ 7 ]. The previous approach yields eD;min = 3:12 voxels, eD;mean = 0:11 voxels, and eD;max = 3:85 voxels. For the 2D joint approach we obtain eD;min = 1:05 voxels, eD;mean = 0:09 voxels, and eD;max = 1:52 voxels, which is a significant improvement for the minimum and maximum diameters, while for eD;mean we obtain a similar result. For the 3D joint approach, we obtain eD;min = 0:53 voxels, eD;mean = 0:16 voxels, and eD;max = 0:47 voxels, which is the best result for the minimum and maximum diameters. For ex0 , the previous approach yields ex0 = 0:16 voxels, while we obtain improved results for the new 2D and 3D approaches with ex0 = 0:11 voxels and ex0 = 0:09 voxels, respectively. It also turned out that the adaptive masking scheme reduces the computation time by 32% for the 3D approach and by 13% for the 2D approach.

In a second experiment, we applied our approach to two different sets of 3D CTA images of the thorax. The first set of images contains ten 3D CTA images of patients with only slight pathologies (see Fig. 1c,d). The second set of images contains five 3D CTA images of patients with severe pathologies (see Fig. 2). It turned out that for eD;min and eD;max the new 2D and 3D approaches yield more accurate results than the previous approach. For ex0 , the 2D approach yields the best result, while for eD;mean, the 3D approach yields the best result.

In addition, we applied our approach to pathological vessels in five different 3D CTA images. It turned out that the new approach significantly decreases the computation time by 41 % for the 3D variant and by 28% for the 2D variant (see Table 1). For eD;min and eD;max, the segmentation accuracy of the 2D approach is slightly reduced, while for the 3D approach, similar results are obtained. For eD;mean and ex0 both the new 2D and 3D approaches improve the segmentation accuracy in comparison to the unmasked approach. Moreover, for the clinically most relevant diameter measures the new approach consistently yields significant improvements compared to the previous pure model-based approach. (a) (b) (c) (d) Fig. 2. (a), (c) Segmentation results of the 3D joint approach for two 3D CTA images showing a pathology. (b), (d) Vessel contours using the model-based approach (black) and the 3D joint approach (white) for a section of the 3D CTA images. 2D joint approach 3D joint approach 4

Discussion

U eD;min

M

U

M 2.60 2.94 1.40 1.26 1.54 1.85 0.63 0.60 1.37 2.19 2.13 1.23 1.12 1.40 1.43 1.13 0.92 32.80 19.20 We have introduced a new joint approach for the quantification of the aortic arch from 3D CTA images that combines fitting of a parametric intensity model with intensity-based elastic image registration. We have demonstrated the applicability of our approach using 3D synthetic images and clinically relevant 3D CTA images. From the experiments it turned out that the new approach consistently yields more accurate segmentation results than a previous pure model-based approach for the minimum and maximum diameters. It also turned out that for the new approach significant improvements are obtained for difficult segmentation tasks, in particular, for pathologies. Furthermore, the new joint approach with the adaptive masking scheme leads to a significant reduction in computation time while the segmentation accuracy remains similar for the minimum and maximum diameters and the accuracy is even increased for the mean diameter.

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