ac@sv1.smb.man.ac.uk

Many diseases of the brain, including schizophrenia and Alzheimer’s, are accompanied by structural, functional, and volumetric changes, both from the normal condition and over time. The aim of the work presented here is to develop a shape model of the cortex, specifically a Point Distribution Model (PDM) [6], which can incorporate knowledge of these changes and can aid in the automated interpretation of 3D head images by locating cortical landmarks in new examples. The model may be used not only in visualisation of the segmented structure, but also in detection of abnormality, monitoring the progress of a disease, and comparing characteristics within and between groups. The latter could aid in the diagnosis of a new patient by ascertaining the group model which best fits the subject. In addition the model can provide a means by which new examples can be co-registered for direct structural and functional comparisons.

Various approaches have already been used to segment 3D head images. Some authors use clustering techniques, which tend to be more effective with multi-sequence data[4][10], others have used image morphology [5][17]. However, although useful for visualisation of gross structure, the results of such methods provide no information about the location of particular areas. In general, the location and measurement of specific areas has required an expert user to label them manually [14][21]. In order to extract and label structures automatically the information must be incorporated into the model used. Several such anatomical atlases have been developed [19], but these tend to be developed from as little as one subject brain. Such atlases usually deform to the new example using intensity information or a combination of prescribed transformations [1][8], sometimes user driven [9]. These take little or no account of the natural variation of the subject and its possible configurations, the resulting labelling may therefore be unreliable. In contrast Hill et al. [11] developed a 3D PDM of structures in the head from a training set of examples which allowed knowledge of anatomical variation to be used when searching. However, the structures chosen were considerably simpler than the cortical surface, which meant that manual point correspondence was possible. Also the model was developed on a slice by slice basis and therefore takes no account of head rotation in 2 directions. Subsol et al. [23] developed a fully 3D model of skull ridges from a set of example CT scans. The ridges were detected and matched automatically to produce an atlas but, despite this, the authors still chose to model its variation using mathematical modal analysis based on physical structure [15] rather than statistical observation.

The work presented here is fully 3D and aims not only to extract the cortical surface in new MR images of the head, but to simultaneously label major landmarks, like the sulcal fissures, which are generally used as anatomical reference points [18] and as a diagnostic aid [21]. Sandor & Leahy [20] developed a model which could locate and label a small number of sulci, but again the model had no built in knowledge of their structural variations and configurations. To incorporate such knowledge into a shape model they need to be identified on every example and corresponded between examples. This poses a problem since the surface fissuring is complex in terms not only of density, but also configuration [16]. Most sulci exhibit breaking and branching, and can be duplicated in some individuals, and absent in others. It was necessary therefore to develop some way of automating the process. The first stage, that of locating the sulci, was achieved using some simple morphological processing to automatically place points over the mouths of the fissures on 3D MR images Szekely et al. [24] used a similar technique, except by working with the whole image instead of the hull they obtained points which were some distance above the cortical surface. The second stage, that of corresponding the points between sets was approached using seven different methods which are presented and compared here. The majority of these have been developed to tackle, specifically, the problems peculiar to the complex configuration of the cortex. All the methods are based on an iterative approach inspired by the work of Besl and McKay [3] and Zhang [25], and several are an extension of the curve matching idea presented by Subsol et al. [22]. Quantitative criteria were used to compare the quality of the models developed from each method. The most satisfactory has been used to identify and visualise major sources of variation between normal individuals.

PDMs have been used to model many classes of variable objects ranging from faces [13] to electrical components [7]. Full details of the PDM can be found in [6] but the following gives a brief description.

Given a set of example pattern vectors , where correspondence is established between the values at each index of , then each vector can be rewritten:

(1)

where is the mean pattern vector, E is the matrix whose columns are the eigenvectors of the co-variance matrix of the set, and is an n-dim vector of parameters describing the degree to which varies from in a way described by the corresponding eigenvectors. Each eigenvector describes the way in which linearly correlated x _ij move together over the set, referred to as a 'mode of variation'. New examples, not included in the training set, can be generated by manipulating the elements of p . To model objects in three-dimensions the are constructed using the co-ordinates of descriptive features of each example. The features must correspond to the same 'points' on each object. Given co-ordinates at each feature j of object i, the shape vector is:

Appropriate features may be corners, edges, borders, surface patterns, etc. These can often be identified and corresponded by hand, but for extremely complex subjects, like the cortical surface, an automated approach preferable.

The complex characteristics of the cortex provide a sizeable obstacle in the development of a PDM, where identical features must be labelled and corresponded in each example. An early attempt was made to build a small model of a portion of the cortex, placing points over the sulcal fissures by hand in 3D Magnetic Resonance images. The results indicated that such a model was viable but the matching process was extremely difficult and time-consuming. Therefore a method was developed to automatically locate the sulcal fissures for use in a model. All images used were T1 weighted with non-cubic voxels of 1 x 1 x 1.5 mm, and approximately 60 slices each. All had some upper slices missing. The new method capitalised on the high contrast in the images between the grey matter and the cerebro-spinal fluid (CSF). Each image was pre-processed by hand to remove the ‘skull’ and then thresholded. A closing operation was used to produce an approximation to the convex hull of the brain in a similar way to that of Sandor & Leahy [20]. The original (segmented) image was subtracted from the hull leaving a representation of the sulcal fissures. This was intersected with the surface of the hull to leave a collection of ribbons representing the mouths of the sulci. Finally these ribbons were thinned to give a set of lines following the medial axes of the sulci. These were converted to points at the intersection of each slice. Figure 1 illustrates this process. Due to the variation between subjects this generated point sets with numbers of points varying between 4000 and 6000 over 16 examples. No feature correspondences were established between points.

Figure 1. Left to right, top to bottom: segmented brain, hull, subtraction image (sulci), intersection with hull surface, thinned point set superimposed on the brain.