Structural Images

One of the most common kinds of analysis of structural images has been volumetric analysis. More specifically, a brain image is partitioned into a number of structures that are of interest to the investigator, and the volume of each structure is then measured and compared across subjects. Spatial normalization offers a highly automated and powerful way of performing volumetric analysis. We will follow our previous work on a method for regional volumetric analysis, referred to as Regional Analysis of Volumes Examined in Stereotaxic space (RAVENS) [35]. Consider a brain image, J, with sufficient contrast to allow segmentation into three major tissues: gray matter, white matter, and cerebrospinal fluid (CSF). This approach can be generalized to include an arbitrary number of tissue types. Apply a spatial transformation that morphs this brain to a template brain, such as an atlas. To each point in the atlas attach one counter for each tissue, whose purpose is to measure a small volume (in the continuum, an infinitesimal volume). Take each point in J and map it to some point in the template, according to this spatial transformation. According to the type of the tissue being mapped to the template, increment the corresponding counter in the arrival location by the volume of the tissue contained in a discrete image element. This procedure results in a number (three in our case) of spatial distributions in the stereotaxic space, one for each tissue. If the counters in each location in the stereotaxic space are put together to form three images, one for each tissue, then the intensity of each image is proportional to the amount of tissue present in that particular brain.

We will make this more specific through an example. Figures 9a and 9d show a representative magnetic resonance image for each of two individuals. Figures 9b and 9c show the corresponding spatial distributions of the ventricular CSF. Following the definition of these spatial maps, if we integrate the density of the images in Figs 9b and 9c within the ventricular region, we will obtain the volumes of the ventricles in the original images. This is in agreement with the fact that the image intensity of Fig. 9b is higher than that of Fig. 9c (more ventricular CSF was forced to fit into the same template for Fig. 9a than for Fig. 9d). The important issue is that these images can be compared pointwise, since the shapes of the ventricles of these two subjects are almost identical to the shape of the ventricles of the template. Therefore, highly localized differences can be detected and precisely quantified. For example, if in a small region the image intensity of Fig. 9d is 20% higher than that of Fig. 9c, this reflects a 20% percent difference in the volume of the ventricles in that region. Figure 9e shows a comparison of the spatial ventricular CSF maps of 10 relatively older individuals (average age: 75) with 10 relatively younger individuals (average age: 62). The red regions indicate relatively larger ventricles, obtained after subtracting the average CSF map of the younger group from the corresponding map of the older group, after spatial normalization to the same template.

Although the ventricles were used for illustration purposes, the primary interest of regional volumetric analyses is in measuring volumes of gray matter and of white matter, which might, for example, reflect neuronal or axonal loss with aging, disease, or other factors. In Fig. 10 we show the average distribution of gray matter obtained from 100 individuals [36]. Regions of local atrophy caused by aging, for example, can be identified by pointwise subtracting the corresponding volumetric maps of a relatively older population from a relatively younger population. A similar kind of analysis was adopted in [6] to point regions of local atrophy in Alzheimer's patients.

At this point we need to clarify an important issue. If the

FIGURE 9 A demonstration of volumetric measurements using the RAVENS approach. (a, d) Magnetic resonance images from two individuals that present different degrees of atrophy. The brain (a) has much higher ventricles (the dark regions in the middle) than the brain in (d). The corresponding distributions of ventricular cerebrospinal fluid (CSF) in a stereotaxic reference frame are shown in (b) and (c); the brighter the image, the more ventricular CSF is present. It is clear that the difference in these two subjects can be demonstrated simply by subtracting the two images (b) and (c). (e) A color-coded image of the difference between two groups, a relatively younger group and a relatively older group. The red corresponds to regions of relatively larger expansion of the ventricular cavities, resulting from the loss of brain tissue with aging. See also Plate 22.

FIGURE 9 A demonstration of volumetric measurements using the RAVENS approach. (a, d) Magnetic resonance images from two individuals that present different degrees of atrophy. The brain (a) has much higher ventricles (the dark regions in the middle) than the brain in (d). The corresponding distributions of ventricular cerebrospinal fluid (CSF) in a stereotaxic reference frame are shown in (b) and (c); the brighter the image, the more ventricular CSF is present. It is clear that the difference in these two subjects can be demonstrated simply by subtracting the two images (b) and (c). (e) A color-coded image of the difference between two groups, a relatively younger group and a relatively older group. The red corresponds to regions of relatively larger expansion of the ventricular cavities, resulting from the loss of brain tissue with aging. See also Plate 22.

Caudale Nucleus

Cortex

FIGURE 10 The average gray matter distribution of 100 healthy individuals is shown on the left. The atlas that was used as the template in the spatial normalization of these 100 images is shown on the right. A few representative structures that can be identified from the average gray matter distribution are labeled and are also identified on the atlas template. The reason why structures can be identified in the average image on the left is that all 100 brain images were morphed to the same target: the atlas on the right. See also Plate 23.

Cortex

FIGURE 10 The average gray matter distribution of 100 healthy individuals is shown on the left. The atlas that was used as the template in the spatial normalization of these 100 images is shown on the right. A few representative structures that can be identified from the average gray matter distribution are labeled and are also identified on the atlas template. The reason why structures can be identified in the average image on the left is that all 100 brain images were morphed to the same target: the atlas on the right. See also Plate 23.

spatial transformation that maps images from different individuals is "perfect," i.e., if it is capable of completely morphing each brain to the template, then the resulting transformed images will have the exact same shape, though the intensities of the corresponding volumetric maps will vary according to the original volumes. Under such a scenario, any kind of average, like the one of Fig. 10, will have exactly the shape of the template to which each image was spatially transformed. From Fig. 10 this is clearly not the case, especially in the cortical region. The fuzziness in Fig. 10 reflects the imperfection of the spatial transformation. We note, however, that volumetric measurements can still be obtained. For example, in Fig. 11 we have outlined the regions of two brain structures, the lenticular nucleus and the caudate nucleus, based on the average spatial distribution of the gray matter. Notice that although these structures are not in perfect registration (spatial coincidence) as revealed by the fuzzy boundary of the average gray matter distribution, the margins of the outlines counterbalance, to some extent, this problem, allowing volumetric measurements to be obtained. This is what makes the spatial normalization method described here more robust than the deformation analysis method described in Section 3: The inability to completely morph a brain to a template affects the accuracy of the deformation analysis much more than the accuracy of the regional volumetric measurements. We note, however, that the deformation analysis is far

FIGURE 11 The spatial normalization of images allows for the collection of statistics on the volume of a particular structure over a population. As it is demonstrated here for two structures, the caudate nucleus and the lenticular nucleus, a region that encompasses the structure of interest in the average map can be defined manually, and volumetric measurements for each subject can be subsequently obtained. This is possible because all images have been spatially normalized to the same template. See also Plate 24.

FIGURE 11 The spatial normalization of images allows for the collection of statistics on the volume of a particular structure over a population. As it is demonstrated here for two structures, the caudate nucleus and the lenticular nucleus, a region that encompasses the structure of interest in the average map can be defined manually, and volumetric measurements for each subject can be subsequently obtained. This is possible because all images have been spatially normalized to the same template. See also Plate 24.

more general than regional volumetrics, in that it not only measures volumes, but various shape parameters as well. Current work in our laboratory focuses on the more accurate registration of the relatively more variable cortical region [25].

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