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Figure 1.20: Cross-sectional overlay of the detected focal cortical thickening locus. The colour scale increases with statistical significance. Significance is measures by comparison of feature measurements (cortical thickness over intensity gradient) to a control subject database (Color Slide).

1.7 Application to Schizophrenia

Several studies have reported morphological differences in the brains of schizophrenic patients when compared to normal controls [73], such as enlargement of the cerebral ventricles and decreased or reversed cerebral asymmetries. These findings suggest the presence of structural brain pathology in schizophrenia. Some hypotheses have been proposed about schizophrenia as a syndrome of anomalies in normal brain development [74] whose origin may be genetically determined. Characterization of the morphological processes in schizophrenia

may lead to new pharmacological treatments aimed at prevention and cure rather than suppression of symptoms. There is in addition a particular focus on asymmetry as the defining characteristic of the human brain and the correlate of language. Techniques are required for describing and quantifying cerebral asymmetries to determine where these are located, how variable they are between individuals, and how the distribution in individuals with schizophrenia differs from that in the general population.

As an application of the framework proposed in this chapter, we present here a method for fully automatic quantification of cerebral grey and white matter asymmetry from MR images. White and grey matter are segmented after bias correction by the intensity-based tissue classification algorithm presented in section 1.2. Separation of the computed white and grey matter probability maps into left and right halves is achieved by nonrigid registration of the study image to a template MR image in which left and right hemispheres have been carefully segmented. The delineations of left and right hemispheres in the template image were transformed into binary label images, which were subsequently edited by morphological operations to match the brain envelope rather than the individual gyri and sulci to be more robust against differences in local cortical topology. The template image is matched to the study image by a combination of affine [21] and locally nonrigid transformations [24]. The resulting deformation field is then applied to the label images, such that matched outlines of left and right hemispheres are obtained. These are used to separate left and right halves in the original grey and white matter segmentations and, at the same time, to remove nonrelevant structures such as the cerebellum and brain stem. Finally, volumes for grey and white matter for each half of the brain separately are computed by integrating the corresponding probability maps within the brain regions of interest defined by the matched template image. Figure 1.21 illustrates that the grey and white matter segmentation maps obtained from the original images are correctly split in separate maps for left and right hemispheres by nonrigid registration with the labelled template image.

Various authors have presented alternative techniques to separate the brain hemispheres by the so-called midsagittal plane, defined as the plane that best fits the interhemispheric fissure of the brain [76] or as the plane that maximizes similarity between the image and its reflection relative to this plane [77, 78]. The advantage of the approach of intensity-driven non-rigid registration to a labelled template image, as presented here, is that it does not assume the boundary

(a)

Figure 1.21: Left–right hemisphere grey matter and white matter separation on high quality high resolution data, consisting of a single sagittal T1-weighted image (Siemens Vision 1.5 T scanner, 3D MPRAGE, 256 256 matrix, 1.25 mm slice thickness, 128 slices, FOV = 256 mm, TR = 11.4 ms, TE = 4.4 ms) with good contrast between grey matter, white matter, and the tissues surrounding the brain. (a): Coronal sections through the grey matter segmentation map before (top row) and after left–right and cerebrum–cerebellum separation. (b) and (c): 3D Rendering of the segmented white and grey matter respectively. (Source: Ref. [75].)

between both hemispheres to be planar. We refer the reader to [75] for further details and discussion of the results obtained.

1.8 Conclusion

The model-based brain tissue classification framework presented here was setup to analyze MR signal abnormalities in neuropathological disorders in large sets of multispectral MR data in a reproducible and fully automatic way. The overall strategy adopted was to build statistical models for normal brain MR images, with emphasis on accurate intensity models. Signal abnormalities are detected as model outliers, i.e., voxels that cannot be well explained by the model. Special attention has been paid to automatically estimate all model parameters from the data itself to eliminate subjective manual tuning and training.

As discussed in section 1.1.1, geometry-driven and intensity-driven methods are the two main paradigms for model-based segmentation. In this chapter, both paradigms are used in a sequential order. Complex intensity models are developed that automatically fit to the data. As a result, multispectral MR data are segmented fully automatically without prior knowledge about the appearance of the different tissue types in the images. Bias fields are automatically corrected for, and the partial volume effect is explicitly taken into account. The intensity models are complemented with image-based brain atlas models of prior tissue probabilities. These atlases are first iconically matched to the images and subsequently used as constraints during the tissue classifications. The matching was originally limited to affine transformations between atlas and study image (see also [79], but was later extended to nonrigid transformations as well (see also [14, 50, 75, 80]).

These attempts to combine the ability of intensity-driven methods to capture local shape variations with the general description of global anatomy provided by geometry-driven methods have been limited to a sequential use of both methods in separate processing steps. Atlas maps of prior distributions of the different tissue classes are first geometrically aligned to the images to be segmented. These transformed maps provide an initial approximate segmentation to initialize the classification algorithm but also provide an estimate of the prior class probabilities for each voxel during further iterations.

In [13] an attempt was made to intertwine statistical intensity-based tissue classification and nonlinear registration of a digital anatomical template to segment both normal and abnormal anatomy. The algorithm iterates between a classification step to identify tissues and an elastic matching step to align a template of normal anatomy with the classified tissues. The alignment of the anatomical template is used to modify the classification to produce a spatially varying, rather than a global classification. The steps are iterated until the matched anatomy and the classification agree. However, this method currently needs manual supervision, and it still needs to be investigated how reliably this method can be automated. Moreover, the iterative procedure is not derived as the solution of an optimization problem. As a result, there is no guarantee that convergence, if at all, to a plausible solution can be obtained.

Wyatt and Noble [81], on the other hand, suggested a joint solution to the linked processes of segmentation and registration. They cast this as a maximum a posteriori (MAP) estimation of the segmentation labels and the geometric transformation parameters and pose the solution using MRF. Their results indicate that the addition of spatial priors (in the form of intermediate segmentation maps) leads to substantially greater robustness in rigid registration and the combination of data via registration improves the segmentation accuracy. However, their formulation is poorly suited for generalization to nonrigid registration.

D’Agostino et al. [82] explored the possibility of nonrigid image registration by maximizing an information theoretic measure of the similarity of voxel object labels directly, rather than of voxel intensities. Applied to intersubject MR brain image matching, such labels are obtained by the intensity-based tissue segmentation presented in this chapter, assigning each voxel a probability to belong to a particular tissue class. Using class labels as features for nonrigid image registration opens perspectives for integrating registration and segmentation as two cooperative processes in a single framework, by considering one of the images as an atlas that is nonrigidly warped onto the other and that provides a priori tissue distribution maps to guide the segmentation of the other image. The possibilities of such a method are enormous, since it would allow fully automated partial volume segmentation and bias correction of multispectral MR images with unknown tissue contrast, while deforming a label atlas at the same time. The quantification of intensity abnormalities could be confined to anatomical regions of interest. The brain could be automatically segmented into relevant substructures, allowing the quantification of changes in shape and volume, over

time in one individual patient, or between populations. Knowledge of the deformation of the label atlas would allow nonrigid multimodal registration of images of different patients and provide a common reference frame for population studies. Deriving realistic statistical models for the shape of the human brain is, therefore, a major challenge for further research.

Questions

1.What is the parametric model of the MR bias field proposed in this chapter?

2.How are the parameters of the MR bias field estimated?

3.What are alternative models for the MR bias field?

4.How is the atlas-based geometric prior constructed?

5.How is the atlas of priors integrated into the classification?

6.What are the drawbacks of using such an atlas of priors and how to deal with it?

7.What is the Markov random field model used in brain tissue classification?

8.How do we limit the overregularization of Markov random fields?

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