ECE 533: Report Vessel Branch Segmentation of Phase Contrast Vastly undersampled Isotropic PRojection Magnetic Resonance Imaging Kevin Johnson December 11, 2006§1 Purpose The purpose of this project will be to develop techniques to segment vascular and venous branches of state of the art phase contrast (PC) MRI exams. Specifically, 3D images obtained from a radial undersampling technique deemed Vastly undersampled Isotropic PRojection (VIPR) will be investigated. PC VIPR has the ability to provide a set of five corresponding 3D images showing the proton density, a vascular image, and three orthogonal velocity components as shown in figure 1. This project will focus on the segmentation of these image sets in order to separate various branches in the neuro-vasculature. Figure 1. Images obtained from a typical phase contrast sequence showing proton density, a vascular weighted image, and velocities in three directions. Segmentation is required to allow for visualization of the data as the velocity data is largely convoluted by the noise in background and tissue. Many authors have used other sources of data for segmentation which are more easily segmented. The data used in those studies has a more uniform contrast between the background and vasculature. Example segmented images show particle traces from such a study are shown in figure 2 [1]. The goal of this study is to explore the use of segmentation methods using phase contrast alone to perform the segmentation. Figure 2. Particle traces from phase contrast data that has been segmented using a separate high contrast exam. This data allows better visualization than standard source data. §2 Phase Coherence Theory Initially we had sought the use of a phase coherence model as an initial segmentation step as outlined by Chung et al [2]. This was initially implemented, but was found to have drastic errors associated with it. The paper defines local phase coherence as: ∑∈•=)(,)(cNssjilpcsjivvcCM Where N is a neighbor system of voxels, v is the velocity, and s is a voxel. The neighbor system is defined as the set of surrounding voxels with some maximal distance between them: }0|,{)(2cssWsscNjisjis<−<∈=Where W is some window set around the pixel of interest. The goes on to say this measure is associated with background, tissue, and vessels. A PDF is estimated from this measure and used in a mixture model to segment the data. Upon performing this operation, a large discrepancy between the data in the paper and that actual measured was realized. Shown in figure 3 are the PDF estimates for PC VIPR and as shown in the paper. Figure 4 shows the LPC maps obtained in the paper and those found in practice. Figure 3. PDF as found in the paper (left) and in practice (right), the large discrepancy in the PDF is expected from offsets in the author’s images. LPC values computed in practice were not normalized. Figure 4. Phase coherence maps from paper (left) and PC VIPR(right). Images shown in paper appear to be highly correlated to regions of higher magnitude while those from PC VIPR are not. This was immediately a concern, given that the two measures did not correlate at all, despite many attempts at altering the binning of the data. This may be due to a number of factors. First, comparisons were made concerning the acquisition method of the PC data it self. For the paper, data was acquired and reconstructed on GE and Phillips systems. This posses a problem likely unseen by the investigators. GE and Phillips systems do not save velocity images. Rather theysave images that are “magnitude masked” and are weighted by the magnitude (a non flow component) of the image. The other possible cause of this would be a phase offset of the images. PC VIPR images have corrections for acquisition errors which are not built into most 3D sequences. A phase shift in the image would offset the tissue data but not the background. To further understand these errors, the expected PDFs were investigated using previous investigators work. It has been shown by many investigators that the variance in the phase (velocity) information is inversely proportional to the magnitude of the data. Thus example phase PDFs for background and tissue can be shown in figure 5. Figure 5. Expected phase PDFs for tissue and background tissues. The PDF of the background is uniform over its range of [-π π] and the noise in the background is approximately a Gaussian over the same range. For any two points within the imaging volume the phase of the background or tissue should be drawn independently from its neighbors, unless it’s a velocity component. Thus the PDF of the local phase coherence should be the autocorrelation of the two functions. The background tissue should have a PDF in the approximate shape of a Gaussian, as the autocorrelation of a boxcar is an approximation of a normal distribution (as done in older random number generators). The PDF of the LPC-Gaussian function will be approximately a Gaussian. This discrepancy makes mixture model impossible as it requires the data have different means which is not true for properly corrected phase contrast data. In many ways, it is far effective to simple use the magnitude of the data as a second measure which would be a measure of the intra-voxel phase coherence. As the phase coherence model is ineffective, we instead used the complex-difference vascular data, and segmented in a more traditional fashion. Phase coherence was incorporated using thresholding at its expected value instead of a mixture model. §3 Methods All coding was implemented in C and run a high performance linux based reconstruction machine. Two goals were set for the project. The first was to develop a methodology to segment vessels from background, and divide those vessels into branching segments. The second was to develop a method to find a connected set of pixels values to describe the branching of the vessels. §3.1 Segmentation In stead of focusing on optimal thresholding, which is subjective due the undefined and variable PDF of velocities and magnitude, focus was placed on the morphological identification of vessels vs. background. A phase coherence map is initially created using a neighbor hood defined with reference to the pixel location. }0|,{)(200cssWsscNisis<−<∈=Where S0 is the pixel of interest. This is slightly different than that defined in the paper,
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