3D geometric reconstruction of thoracic aortic aneurysms
© Borghi et al; licensee BioMed Central Ltd. 2006
Received: 28 July 2006
Accepted: 02 November 2006
Published: 02 November 2006
The thoracic aortic aneurysm (TAA) is a pathology that involves an expansion of the aortic diameter in the thoracic aorta, leading to risk of rupture. Recent studies have suggested that internal wall stress, which is affected by TAA geometry and the presence or absence of thrombus, is a more reliable predictor of rupture than the maximum diameter, the current clinical criterion. Accurate reconstruction of TAA geometry is a crucial step in patient-specific stress calculations.
In this work, a novel methodology was developed, which combines data from several sets of magnetic resonance (MR) images with different levels of detail and different resolutions. Two sets of images were employed to create the final model, which has the highest level of detail for each component of the aneurysm (lumen, thrombus, and wall). A reference model was built by using a single set of images for comparison. This approach was applied to two patient-specific TAAs in the descending thoracic aorta.
The results of finite element simulations showed differences in stress pattern between the coarse and fine models: higher stress values were found with the coarse model and the differences in predicted maximum wall stress were 30% for patient A and 11% for patient B.
This paper presents a new approach to the reconstruction of an aneurysm model based on the use of several sets of MR images. This enables more accurate representation of not only the lumen but also the wall surface of a TAA taking account of intraluminal thrombus.
An aortic aneurysm is an abnormal enlargement of a portion of the aorta, due to the progressive weakening of the aortic wall. TAAs, aneurysms involving the aorta in the thoracic area, are characterized by low frequency (0.006% in a given population) but very high mortality rate (39–62% of the diagnosed cases ). The only criterion for the selection of surgical patients is based on the maximum diameter of the aneurysm, which has been proved not to be completely reliable for the assessment of the rupture risk. Furthermore, recent studies focused on abdominal aortic aneurysms have shown that peak wall stress in the aortic wall, calculated by means of the finite element method, is a more reliable parameter .
The latest trend of the research in this field is to make use of image-based geometries in order to calculate patient-specific wall stress patterns [3–6]. The segmentation of the aortic lumen and wall is a crucial step for the creation of a finite element model. The reconstruction of arterial structures involves the use of sets of clinical data (MRI or CT, in general) that are processed to extract the vessel morphology. While the segmentation of the arterial lumen is a well established technique and has been performed with different modalities in living subjects [7–10], the segmentation of the wall and its connective components is still a challenge due to the low contrast between the wall and the surrounding tissues . The extraction of wall information has been attempted for the carotid and coronary arteries, using ex vivo imaging data [12–15]. As pointed out in these studies, the difficulty of achieving equivalent results with in vivo data is the frequent inability to acquire arterial wall images with a sufficient resolution . Good results were achieved by Thomas et al. , who applied the discrete dynamic contour algorithm to four subjects scanned at the left carotid artery using the black blood MRI technique. The results showed that while the SNR (signal to noise ratio) improved with the increase of the field of view (FOV), the SDNR (signal difference to noise ratio, a measure of the capability of a MR protocol to generate contrast between different tissues) is independent of the dimension of the FOV. Further work has been done using semi-automatic techniques applied to the segmentation of arterial structures, with good results for abdominal aortic aneurysms [11, 17, 18]. However, these methods are based on the use of CT images, where good differentiation between the thrombus and wall may be possible should there be calcifications inside the wall. Furthermore, all the studies on the application of these methods to the segmentation of thrombus show, with good agreement, that automatically segmented contours do not always match manual segmentation performed by experienced operators, and reducing the degree of user intervention does not necessarily correspond to a higher accuracy in contour depiction and volume measurement .
This paper presents a new approach to the reconstruction of patient-specific aneurysm models, based on the use of different MR imaging sequences. Two sets of images, with different specifics and resolutions, were used in order to create a model with the best level of anatomical details for both the wall and lumen. The 3D aneurysm model was then reconstructed using a CAD program and subsequently imported into a commercial finite element software for mesh generation and stress analysis. This method has been applied to two aneurysm models and the results have been compared with the less accurate models constructed from a single set of images.
Image summary. Summary of the images used for model creation
Slice thickness (mm)
Number of slices
Pixel resolution (mm)
Slice distance (mm)
For the acquisition of the second type of images contrast agent was injected intravenously in both subjects; oblique – sagittal planes encompassing the entire thoracic aorta were acquired. Maximum intensity projections and multi-planar reconstructions were performed on the acquired data. This technique eliminates the signal of the static tissues by means of a double sequence of acquisition before and after the injection of contrast agent . Table 1 summarizes the information about the patients and the images used for model reconstruction.
For the creation of the CAD models, the number of slices contained in cLM was reduced from 200 to 50 slices, while cLH and cW were interpolated from 20 to 50 contours in order to have the same vertical coordinates as cLM.
transformation of inner wall and lumen contours from Cartesian (xL-yL for the lumen and xT-yT inner wall) to polar coordinates (ρL-θL for the lumen and ρT-θT for the thrombus);
identification of the points of the lumen that are contained in the angular portion defined by
identification of the points that fail the minimum distance test
readjustment of the radial coordinate ρT of these points by adding to their original distance an adjustment distance c
transformation of the newly calculated points from polar coordinates (ρ'T-θT for the readjusted inner wall) to Cartesian coordinates (x'T-y'T).
Model creation summary. Summary of the contours used for the creation of the four models.
T = [2α W + 4β W (λ2 + 2λ-1 - 3)]·(λ2 - λ-1)
for the aortic aneurysm wall  and
T = [2α T + 4β T (2λ + λ-2 - 3)]·(λ - λ-2)
for the thrombus , where T is the stress and λ is the stretch ratio. For ascending TAA strips, Vorp et al.  found values for the constants as αW = 100 kPa and βW = 530 kPa while for intra-luminal thrombus Wang et al  found αT = 28 kPa and βT = 28.8 kPa.
Mesh generation for the thrombus and wall domains were carried out separately so it was necessary to define the interface as 'tied contact boundary' in order to hinder sliding and independent movement. Both ends of the models were constrained to avoid rigid translation.
A grid independence test was performed for each model and a maximum difference of 5% in displacement and stress between the adopted and a finer mesh was accepted.
The predicted stress patterns in aneurysm models are highly dependent on the reconstructed model geometry and in particular on the detailed shape of the lumen and outer wall. The segmentation of lumen contour is well established; however, the segmentation of the aortic wall and its components remains a problem to date for patient-specific model creation. Several attempts have been made to obtain wall thickness data from in vivo images, but few studies have focused on aneurysms, especially aneurysms with intraluminal thrombus. In this work, a novel method for the creation of an aneurysm model has been developed and applied to two subjects. The novelty of the method is the combination of two sets of MR images: the first set (HASTE images) allows segmentation of the arterial wall and thrombus but suffers from a low in-plane and vertical resolution so that the final result is a very coarse model of the aneurysm (see figure 2b). The second set (MR Angio sequence, acquired with subtraction technique) provides excellent details of the lumen of the aneurysm (see figure 2c) with high in-plane and vertical resolutions (see table 1 for detail); however, the use of contrast agent for the acquisition of these images makes only the lumen and other vascularised tissues visible, and the segmentation of wall and thrombus is not possible. Combining information from the two sets of images offers the opportunity to construct a model with the best resolution for both aortic wall and lumen. The procedure for incorporating the two sets of contours requires co-registration of the contours via smoothing and realignment of the centrelines of the lumen contours. Since the boundary between the aortic wall and the thrombus was not clearly visible everywhere in the image sets A1 and B1, the wall thickness has been measured where visible and then averaged for each patient. The aneurysm wall has been created as a layer with constant thickness with the segmented outer wall as external boundary. Because of the different levels of detail of the lumen segmented from the HASTE and MR Angio sequence sets, partial overlapping between the lumen surface and internal wall surface could occur in some sections especially where the circumferential distribution of the thrombus was non-uniform. Local readjustment of the contours was necessary and this led to local differences between the H and HM wall domains; however, for both patients the H and HM models gave the maximum stress at the same location and the thrombus thickness in that area was similar. The sensitivity of the predicted stress to the function parameters a, b, c used for the contour readjustment was assessed on one of the four models (model BH). The parameters for the readjustment of the thrombus contours were varied by at least 20% (a ranging from 60 degrees to 120 degrees, b ranging from 0.4 mm to 0.6 mm and c ranging from 0.6 mm to 1 mm) and the stress was calculated for each combination of values. The maximum difference between the stress of each combination and the initial case was 8.3%, which is lower than the maximum stress difference between the H and HM model for both patients. Furthermore, the average stress difference due to the parameter variation was 4.4% and the overall stress pattern does not change qualitatively; hence it is possible to confirm the validity of the comparison results. The proposed approach aimed at offering a better way to resolve the external wall and the aortic lumen boundary by merging the information from two sets of images, but an improved wall thickness measurement is needed.
The results of finite element stress analysis under a static loading condition showed differences in stress patterns between the two models due to differences in detailed geometrical features of the lumen surface. For both patients, the stress value of the coarse model was higher than that of the fine model created via two sets of images. The availability of a larger number of transverse slices and thinner slice thickness offers more details for the reconstruction of the lumen surface that captures the complicated realistic morphological features. The difference in lumen diameter between the H and HM model was examined and it was of the order of magnitude of the resolution of the HASTE images, so the difference in morphology can be attributed to the lower resolution of this image set, supporting the inferred higher reliability of the model created with both sets of images.
The resulting final shape for the wall model of the two aneurysms is fairly "smooth", due to the limited number of slices available for the creation of the external wall surface. It would be desirable to have a set of HASTE images with smaller inter-slice distance and larger number of slices, so that the outer wall surface could be reconstructed more realistically.
This paper presents a novel approach for the reconstruction of aneurysm models using two different sets of MRI data. The methodology has been applied to two patients and noticeable differences between the coarse and finer models have been found. The differences in predicted maximum wall stress were found to be 30% for patient A and 11% for patient B, suggesting that detailed lumen surface representation plays an important role in determining wall stress values.
This approach enables accurate representation of the lumen while making use of patient-specific information about the wall of a TAA. This is an important step towards the development of a reliable tool for patient-specific assessment of the risk of aneurysm rupture.
This project was funded by the British Heart foundation (grant no. FS/03/119/16285).
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