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. 2009 Sep;28(9):1473-87.
doi: 10.1109/TMI.2009.2017942. Epub 2009 Mar 24.

Image-driven population analysis through mixture modeling

Mert R Sabuncu  1 , Serdar K Balci, Martha E Shenton, Polina Golland
Affiliations

Image-driven population analysis through mixture modeling

Mert R Sabuncu et al. IEEE Trans Med Imaging. 2009 Sep.

Abstract

We present iCluster, a fast and efficient algorithm that clusters a set of images while co-registering them using a parameterized, nonlinear transformation model. The output of the algorithm is a small number of template images that represent different modes in a population. This is in contrast with traditional, hypothesis-driven computational anatomy approaches that assume a single template to construct an atlas. We derive the algorithm based on a generative model of an image population as a mixture of deformable template images. We validate and explore our method in four experiments. In the first experiment, we use synthetic data to explore the behavior of the algorithm and inform a design choice on parameter settings. In the second experiment, we demonstrate the utility of having multiple atlases for the application of localizing temporal lobe brain structures in a pool of subjects that contains healthy controls and schizophrenia patients. Next, we employ iCluster to partition a data set of 415 whole brain MR volumes of subjects aged 18 through 96 years into three anatomical subgroups. Our analysis suggests that these subgroups mainly correspond to age groups. The templates reveal significant structural differences across these age groups that confirm previous findings in aging research. In the final experiment, we run iCluster on a group of 15 patients with dementia and 15 age-matched healthy controls. The algorithm produces two modes, one of which contains dementia patients only. These results suggest that the algorithm can be used to discover subpopulations that correspond to interesting structural or functional "modes."

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Figures

Fig. 1
Fig. 1
Generative Model that assumes two templates.
Fig. 2
Fig. 2
iCluster: Pseudo-Code
Fig. 3
Fig. 3
Top row: Axial slices of the original subject MRI’s used to synthesize data. Middle row: Axial slices of representative synthetic images. Bottom row: Axial slices of the four templates computed by iCluster with K = 4 and 0:5% sampling percentage.
Fig. 4
Fig. 4
Output quality as a function of sampling percentage, i.e., the ratio of the size of stochastic set of voxels used at each iteration to the total number of voxels. Error bars indicate standard deviation.
Fig. 5
Fig. 5
BIC: Penalized negative log-likelihood values for a range of input K values. Error bars indicate standard error.
Fig. 6
Fig. 6
Consistency Criterion: The consistency of output membership probabilities for a range of input K values. Error bars indicate standard error.
Fig. 7
Fig. 7
Mean images for each clinical population after affine normalization.
Fig. 8
Fig. 8
Consistency Criterion for the schizophrenia data set: The consistency of output membership probabilities for input K = 2, 3, 4. Error bars indicate standard error.
Fig. 9
Fig. 9
Two Templates computed by iCluster. In the difference image, gray is zero, darker (lighter) values correspond to negative (positive) values.
Fig. 10
Fig. 10
Top row: Dice scores for each ROI. Bottom row: Haussdorff Distances in mm. Error bars indicate standard error.
Fig. 11
Fig. 11
Consistency Criterion for the Oasis data set: The consistency of output membership probabilities for a range of input K values. Error bars indicate standard error.
Fig. 12
Fig. 12
Two templates of the OASIS data. In the difference image, gray is zero, darker (lighter) values correspond to negative (positive) values.
Fig. 13
Fig. 13
Top Row: Three templates of the OASIS data. Bottom Row: Difference images. Gray is zero, darker (lighter) values correspond to negative (positive) values.
Fig. 14
Fig. 14
Typical Subjects: (a) Group 1: 24-year-old, healthy female, (b) Group 2: 52-year-old, healthy female, (c) Group 3: 76-year-old male with very mild dementia and probable AD.
Fig. 15
Fig. 15
Age distributions of the OASIS data. (a) Age distributions for K=2, (b) the relationship between the ages of subjects in clusters identified for K=2 and for K=3, (c) Age distributions for K=3.
Fig. 16
Fig. 16
Consistency Criterion for the 30 subject dementia data set: The consistency of output membership probabilities for a range of input K values. Error bars indicate standard error.
Fig. 17
Fig. 17
Two templates and their difference image for the 30 subject dementia data set.
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