On the modeling, construction, and evaluation of a probabilistic atlas of brain perfusion

Abstract

To detect subtle, abnormal perfusion patterns in brain single photon emission computer tomography (SPECT) images, it is necessary to develop quantitative methods in which computer-aided statistical analysis takes advantage of information present in databases of normal subjects. The purpose of this study was to evaluate and examine aspects of the creation and the modeling power of three statistical models for representing brain perfusion as observed in ECD-SPECT. The first model is a local model of voxel-by-voxel mean and variance. The second model is a PCA-based global model that accounts for covariance patterns in the images. The third model is an original model that is a non-linear extension to the second model. This model is based on robust statistics for modeling abnormalities. To evaluate the models, a leave-one-out procedure combined with simulations of abnormal perfusion patterns was adopted. Abnormal perfusion patterns were simulated at different locations in the brain, with different intensities and different sizes. The procedure yields receiver operator characteristics (ROC) that present a combined measure of model-fit and model-sensitivity at detecting abnormalities. The scheme can further be used to compare models as well as the influence of different preprocessing steps. In particular, the influence of different registration approaches is studied and analyzed. The results show that the original non-linear model always performed better than the other models. Finally, location-dependent detection performance was found. Most notably, a higher variation of perfusion was observed in the right frontal cortex than in the other locations studied.

Introduction

In clinical practice, single-photon emission computer tomography (SPECT) images of brain perfusion are mostly analyzed in a qualitative fashion. Less often, a semi-quantitative approach using an interactive region-of-interest (ROI) method is applied. Both approaches suffer from operator bias and are hence subjective. For the localization of seizure foci in epilepsy, a more objective method called SISCOM was developed (O'Brien et al., 1998, Zubal et al., 1995). An image acquired between seizures (interictal) is subtracted from an image acquired during seizure (ictal) after registration of the images with the patient's MRI image. The interictal image is thus used as a reference image for the ictal image. Such a reference image would also be desirable for the semi-quantitative analysis of SPECT exams in other pathologies such as dementia and depression, but are unfortunately not generally available for the same patient. This, beside the interest in understanding normal brain perfusion itself, motivates the efforts in creating normative data (Tanaka et al., 2000, Van Laere et al., 2001), mean images (Imran et al., 1998), and atlases that describe normal brain perfusion based on sample SPECT images of normal volunteers.

In particular, a computerized, voxel-based, probabilistic atlas of normal brain perfusion has the potential of improving the sensitivity and the objectivity in the evaluation of SPECT images. The objective of such an atlas is twofold: (1) the description of normal brain perfusion and (2) the design of statistical tests to detect significant abnormal perfusion patterns. However, the creation of such an atlas is complicated by several obstacles: (1) anatomical variability between subjects must be minimized by spatial normalization into a standard reference frame, (2) the issue of intensity normalization for semi-quantitative analysis needs to be solved, and (3), the validity of a statistical model must be assessed. The last point is particularly difficult since no ground truth information about the true activity distribution observed in a SPECT image exists.

Several approaches have been presented for quantitatively comparing images of brain perfusion with a normal population by means of a normal database. Existing methods are mostly based on automatic registration schemes for spatially normalizing the images before statistical analysis. A first group of approaches can be characterized as volume/region of interest (VOI/ROI) methods: after registration with an atlas, the average perfusion on predefined VOIs is automatically calculated and analyzed either for asymmetry (Kang et al., 2001) or for differences in mean (Greitz et al., 1991, Rizzo et al., 1995). Similar methods have been used to create normative data (Imran et al., 1998, Koyama et al., 1997) and to examine the effects of age and gender (Van Laere et al., 2001). In Pagani et al. (2002), the authors use principal component analysis (PCA) on the mean values of a set of VOIs to aid the interpretation.

A second approach consists in a voxel-by-voxel analysis after registration. In Chang et al. (2002), the authors compare the mean of differences in normal images with differences of ictal–interictal images of patients with temporal lobe epilepsy (TLE). Ictal images in TLE have also been compared in the same manner in (Lee et al., 2000). A similar study compared patients with head injury to normal subjects after correcting for age (Stamatakis et al., 2002). These kind of studies can conveniently be performed using statistical parametric mapping (SPM) (Acton and Friston, 1998).

A third approach, fundamentally different in nature, was presented in Minoshima et al. (1995) where the authors calculate a cortical surface from an atlas image and find the maximal intensity in the PET image on an inward perpendicular vector to the surface. Mean values across subjects are then calculated and a z score is estimated for images to evaluate. The utility of this approach was recently assessed in Honda et al. (2003).

A fourth and last approach, based on a multivariate analysis of voxel intensities has been proposed by Houston et al., 1994, Houston et al., 1998 where “building blocks” (eigenimages) of normal perfusion have been determined by PCA. The remaining residual, not explained by these eigenimages, was analyzed to find abnormal patterns of perfusion. The robust model presented in this work is an extension of this model.

The importance of validation of medical image analysis techniques has been emphasized in Jannin et al. (2002) and Bowyer (2000). Validation evaluates the performance and limitations of a method and can clarify the clinical potential of a method. Two objectives are central for the evaluation of a probabilistic brain atlas. These are issued by the following two questions: (1) how well does the model fit real data? and (2) how well are abnormalities detected for the pathologies of interest? Several factors contribute to complicate the evaluation: (1) the definition of normal data is subjective, (2) data is rare and expensive, (3) ground truth is not available and (4) a quality metric is difficult to define (what is a good detection?). We have combined the two objectives into a statistical evaluation framework that can give partial, joint answers to both. An advantage of the proposed methodology is that it permits the comparison of different atlas models and different strategies for atlas creation which are otherwise difficult to evaluate.

In this paper, we perform an evaluation study using a leave-one-out strategy combined with simulated abnormalities. First, the evaluation is used to compare three different models. We present a non-linear model that is original in this context. The first model evaluated is a model of the voxel-by-voxel type described above, the second is the PCA-based model presented in Houston et al., 1994, Houston et al., 1998 and the third, original model is based on a nonlinear extension of the second model. This non-linear model is robust to non-Gaussian perfusion patterns, which are likely in patients with different atrophies. Furthermore, we discuss and evaluate important aspects of the atlas construction: spatial and intensity normalization. Finally, the evaluation is used to analyze which brain regions are best modeled and hence where abnormalities are easier to detect.

Other simulation studies for assessing methods that characterize cerebral lesions in SPECT and PET images have been described, but none attempt to evaluate the model assumptions themselves. In (Stamatakis et al., 1999), the authors decrease and increase the perfusion on a sphere in the right frontal lobe of the mean image to evaluate the capacity of SPM to detect changes. We think this approach yields an optimistic estimate because an abnormality can vary in an additive manner around the variation of normal images, not only around their mean. Furthermore, the study is limited to only one location of the abnormality, whereas we show in this article that the detection sensitivity of the atlas is location-dependent. Another study (Van Laere et al., 2002) adds inclusions to a software phantom, thereby simulating a single-subject activation study, whereas we are more concerned with multiple individuals. In Missimer et al. (1999), the authors compare SPM and the computerized brain atlas (CBA) (Greitz et al., 1991) for PET activation studies using both human volunteers and simulations. The simulated images are also derived from a single (simulated) PET image. Our context is somewhat different from a standard activation study with multiple conditions/multiple subjects: we have several control images in rest state (learning set) and only one activation image of a subject that is not represented in the learning set. Another study (Davatzikos et al., 2001) also compares the effects of different registration and filtering algorithms on the detection capacity of SPM by simulating PET images. These are simulated from the MR images, but this time from 16 different persons. This way natural anatomical variance is present in the database, but the functional variance still lacks.