Elsevier

Medical Image Analysis

Volume 10, Issue 1, February 2006, Pages 2-18
Medical Image Analysis

Cerebrovascular segmentation from TOF using stochastic models

https://doi.org/10.1016/j.media.2004.11.009Get rights and content

Abstract

In this paper, we present an automatic statistical approach for extracting 3D blood vessels from time-of-flight (TOF) magnetic resonance angiography (MRA) data. The voxels of the dataset are classified as either blood vessels or background noise. The observed volume data is modeled by two stochastic processes. The low level process characterizes the intensity distribution of the data, while the high level process characterizes their statistical dependence among neighboring voxels. The low level process of the background signal is modeled by a finite mixture of one Rayleigh and two normal distributions, while the blood vessels are modeled by one normal distribution. The parameters of the low level process are estimated using the expectation maximization (EM) algorithm. Since the convergence of the EM is sensitive to the initial estimate of the model parameters, an automatic method for parameter initialization, based on histogram analysis, is provided. To improve the quality of segmentation achieved by the proposed low level model especially in the regions of significantly vascular signal loss, the high level process is modeled as a Markov random field (MRF). Since MRF is sensitive to edges and the intracranial vessels represent roughly 5% of the intracranial volume, 2D MRF will destroy most of the small and medium sized vessels. Therefore, to reduce this limitation, we employed 3D MRF, whose parameters are estimated using the maximum pseudo likelihood estimator (MPLE), which converges to the true likelihood under large lattice. Our proposed model exhibits a good fit to the clinical data and is extensively tested on different synthetic vessel phantoms and several 2D/3D TOF datasets acquired from two different MRI scanners. Experimental results showed that the proposed model provides good quality of segmentation and is capable of delineating vessels down to 3 voxel diameters.

Introduction

Large numbers of people suffer a major cerebrovascular event, usually a stroke, each year. Serious types of vascular diseases such as carotid stenosis, aneurysms, and arterio-venous malformations (AVM) may lead to brain stroke unless they are detected at early stages. Stenosis is a narrowing of the artery which results in a partial or complete blockage of blood supply. Aneurysm is a balloon of blood that occurs due to weakness in the arterial wall. The rupture of an aneurysm can cause severe headaches or even a life-threatening coma. AVM’s are abnormal connections of an artery, vein, or both, which deprive the tissue of its normal blood supply. Therefore, accurate cerebrovascular segmentation is the key to accurate diagnoses as well as endovascular treatment.

Magnetic resonance angiography (MRA) is a non-invasive MRI-based flow imaging technique. Its wide variety of acquisition sequences and techniques, beside its ability to provide detailed images of blood vessels, enabled its use in the diagnosis and surgical planning of the aforementioned diseases. There are three techniques commonly used in performing MRA; time-of-flight (TOF) angiography, phase contrast angiography (PCA), and contrast enhanced MRA (CE-MRA). Both TOF and PCA utilize the flowing blood as an inherent contrast medium, and as such, can be considered non-invasive techniques, while CE-MRA requires the injection of a paramagnetic substance (commonly gadolinium), which provides contrast upon the introduction into the circulatory system. PCA exploits the change in phase of the transverse magnetization as flowing spins move through a magnetic field gradient. It also provides good background signal suppression and can quantify the flow velocity vectors for each voxel. On the other hand, TOF relies on the difference in the amplitude of longitudinal magnetization between flowing and static spins. The TOF technique is not as quantitative but it is widely used clinically because it is fast and provides high contrast images, which is the main motivation behind our work.

A variety of techniques have been proposed for segmenting blood vessels from MRA. Most of the 2D approaches are not applicable to 3D images. 3D techniques can be classified under the following categories; scale space analysis, deformable models, statistical models, and Hybrid methods.

In multiscale filtering, each image is convolved with a series of Gaussian filters at different scales. The eigenvalues of the Hessian matrix at each voxel in the image is analyzed to determine whether it belongs to blood vessels or a background noise. The output of this filter is used to define an enhanced set of images in which blood vessels are brightened, while background noise and planar structures such as skin are darkened. Enhanced images are either visualized directly (Frangi et al., 1998), thresholded (Sato et al., 1998), or segmented using an active contour method (Lorenz et al., 1997). The eigenvalues are used to define a candidate set of voxels which could belong to the centerlines of the vessels (Krissian et al., 1999, Krissian et al., 1998). Multiscale response functions are evaluated at each of those voxels to determine the likelihood that the voxel is a vessel of various diameters. The maximal response over all choices of diameters is retained at each voxel. Finally, a surface model of the entire vascular structure is reconstructed from both the centerlines and diameters. As a different scale space approach, vessel centerlines are assumed to be very bright and are detected as intensity ridges (Aylward et al., 1996). The width of the vessel is then determined by a multiscale response function.

The main idea behind deformable model approaches is that an initial boundary estimate of the vessel is deformed iteratively to optimize an energy function which depends on the image gradient information and the smoothness of the surface (Caselles et al., 1997). Topologically adaptive surfaces (McInerney and Terzopoulos, 1997) are a variant of the classical deformable models but have an efficient topologically adaptable property for segmenting intracranial vasculature. Geodesic active contours were proposed to segment MRA speed images (Lorigo et al., 2001), where the contour is implemented using the level set methods to offer flexible topological adaptability, which has been extended to be locally more adaptable according to the properties of local geometrical structures such as the eigenvalues of the tensor (Wink et al., 2000). Deschamps and Cohen (2002) presented a fast approach for vessel surface segmentation by inflating a balloon from a user given single point utilizing fast marching methods.

Wilson and Noble (1999) developed a statistical model for extracting blood vessels from TOF data, based on the physical model of blood flow. Two different statistical models for segmenting PCA are suggested to provide a single global threshold (Chung and Noble, 1999) and an adaptive local threshold (Hassouna et al., 2002). Both speed and phase information provided by PCA are fused together to enhance the vessel segmentation (Chung et al., 2002) especially in the nearby of an aneurysm where the signal is very low.

Blood vessels are extracted iteratively from rotational angiography by combining a Gaussian statistical model with the maximum intensity projection (MIP) images acquired at three orthogonal directions (Gan et al., 2004). The MIP Z-buffer is segmented using a continuity criterion to generate candidate sets of seed voxels, which are then coupled with a global threshold to extract the whole tree using region growing (Parker et al., 2000). The accuracy of the MIP Z-buffer technique is later studied (Chapman et al., 2004). Vessels are detected by cylinder matching (Reuzé et al., 1993, Hernandez-Hoyos et al., 1999). The method is based on minimizing the inertia moments of a cylinder and a priori knowledge of the intensity profiles in and at the edge of a vessel. A more generalized technique approximating the vessel cross-section by a polygon has been suggested (Verdonck et al., 1995). Continuity and orientation between consecutive slices are used to calculate a locally optimal shape for the polygon with good accuracy. Summers et al. (1997) proposed an octree decomposition of a velocity field image of PCA in order to find an optimal tessellation. Each block of the octree contains at most one feature defined by a gray level function and orientation. Masutani et al. (1998) proposed another method, where the vessels initial shape is extracted by thresholding followed by a region growing to extract locally smooth surface by using binary mathematical morphological operations. As another level set approach, the speed function of the level set surface evolution is controlled by the intensity distribution of the data (Farag et al., 2004). A recursive hybrid segmentation framework has been proposed by Chen and Metaxas, 2000, Chen and Metaxas, 2003, that combines the Gibbs prior model, marching cubes, and deformable models. In the first step, the Gibbs model is used to estimate the object boundaries using region information from 2D image slices. The estimated boundaries are then used to construct a 3D mesh using marching cubes, which specifies the initial geometry of a deformable model. In the second step, the deformable model deforms and fits to the data under the influence of 3D image gradient forces. This recursive approach usually does not require more than two iterations to give a good estimate of the desired object’s surface.

Existing vascular segmentation methods have at least one of the following limitations:

  • 1.

    Rely on the intensity gradient field to estimate the vessel boundary, however, in practice, gradient values are not sufficiently high in the low or complex flow regions.

  • 2.

    The vessel cross-section is assumed to be circular, which is true for healthy arteries but not in the nearby of a stenosis or an aneurysm.

  • 3.

    Assume that the intensity distribution of each structure in the image has a Gaussian distribution, which is not necessarily true, resulting in an error between the proposed model and the clinical data.

  • 4.

    Suitable only for specific modality.

  • 5.

    Require user interaction to either insert a seed inside a vessel of interest or select its ending points.

  • 6.

    Have many tuning parameters whose estimation process is hard or not applicable.

  • 7.

    Computationally expensive.

In this paper, we present a new statistical approach for segmenting 3D cerebrovascular system from TOF-MRA data, which extends our prior work (Hassouna et al., 2003). The voxels of the observed dataset are classified as either background or blood vessels classes. Each class is modeled by a low level stochastic process that describes its intensity distribution across the volume and a high level stochastic process that describes its statistical dependence among neighboring voxels. The low level process of the background signal is modeled by a finite mixture of one Rayleigh and two normal distributions, while the blood vessels are modeled by one normal distribution. The parameters of the proposed mixture density model for the low level processes are estimated using the expectation maximization (EM) algorithm. The convergence of the EM algorithm is sensitive to the initial estimate of the parameters. Therefore, we present an automatic method based on histogram analysis to find a good initial estimate of them. To improve the quality of the statistical segmentation, spatial contextual information has been incorporated through 3D Markov random field (MRF), whose parameters are estimated using maximum pseudo likelihood method. The experimental results on different synthetic vessel phantoms and several 2D/3D TOF datasets acquired from two different MRI scanners showed that the proposed model provides good quality of segmentation and is capable of delineating vessels down to 3 voxel diameters.

This paper is organized as follows. In Section 2, we give a quick overview on the different TOF acquisition techniques, a derivation of the low level model for both blood vessels and background signal, and finally show how to estimate the parameters of that model. In Section 3, we give a brief introduction to MRF models and its usage in image segmentation, and then show how to combine it with our low level model to improve segmentation results. We validate our method using different synthetic phantoms in Section 4. In Section 5, we present our segmentation results on clinical datasets. In Section 6, we conclude with a discussion of the current and future work.

Section snippets

TOF statistical segmentation

In this section, we derive the low level model of both blood vessels and background signal and then estimate their parameters using the EM algorithm. First, we will give a quick overview on the different TOF acquisition techniques.

Enhancing segmentation

Although the low level model provides a good fit to the observed data, we may still have some misclassified voxels because classification is based only on voxel intensity. For example, some vessel voxels may be classified as non-vessel class. This happens in regions with significant vascular signal loss due to complicated flow conditions including slowly and turbulent blood flow, which is a typical problem with TOF acquisitions.

Also, some background voxels may be classified as blood vessels

Validation

We may find ground truth segmentation for carotid, aneurysm, or both but not for a complete vasculature because of its complexity and the more levels of details it involves. Therefore, in order to validate our method, we created several synthetic 3D phantoms that mimic bifurcation, zero, and high curvature vessels at different spatial resolution as well as a wooden tree phantom whose ground truth is acquired using CT scan.

Results

We have also tested our new segmentation method on several 2D/3D TOF clinical datasets that are acquired from two different 1.5 T (Picker Edge and GE) MRI scanners. The 3D datasets came in two different sizes, 512 × 512 × 93 and 512 × 512 × 63 with spatial resolution 0.43 × 0.43 × 1.0. The size of the 2D datasets is 256 × 256 × 60 with spatial resolution 0.78 × 0.78 × 1.0. In Fig. 10, we show how the proposed model provides high quality fit to the clinical data for both 2D and 3D acquisitions of different patients.

Discussion and conclusion

In this paper, we have presented an automated stochastic segmentation method for extracting cerebrovascular blood vessels from TOF-MRA data. The proposed method is based on two stochastic models for the observed data. The blood vessels are modeled by one normal distribution, while the background noise is modeled by a mixture of one Rayleigh and two normal distributions. To improve the quality of segmentation achieved by the proposed low level model, a MRF is used as a high level model to

Acknowledgments

This work has been supported by the US-Army Grant DABT60-02-P-0063 and Norton Health Care System Grants 97-33 and 97-72.

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