Figure 1.
Procedure to identify discriminative voxels by the sparse representation method and t-test filter.
The sparse representation method and a t-test were applied to the original GM volume map. There are 2 steps in the sparse representation method: first, filtering of the original data by a t-test, where 20,000 voxels were retained; second, the sparse representation algorithm was performed on these voxels. Next, according to the age-related classification accuracy, we fix the number of remaining voxels as discriminative patterns of aging. As a comparison, the t-test selects the same amount of voxels as aging patterns for classification. The voxel selection and SVM training were both performed using a ten-fold cross validation on the first group of MRI images. The first 1,000 voxels of the intersection of rearranged voxels in the ten folds were defined as the final spatial patterns of aging. The final spatial patterns of aging according to sparse representation and the t-test were then applied on the second group of MRI images and tested by the LOOCV.
Figure 2.
Classification results of the sparse representation and t-test filter (group 1).
The voxels were ordered according to weight given by sparse representation and score of two-sample t-test. The x-axis is the number of voxels used for the classification, and the y-axis is the classification accuracy (GR).
Figure 3.
Full map of the sparse weightings and t-test values of all the 20,000 voxels used in Figure 2.
The sparse algorithm in a recursive procedure selects 200 voxels until all of the 20,000 voxels are selected. According to the selection order, the voxels were given weightings from 1.00, 0.99, 0.98, …, 0.01. The t-test score was generated by the same procedure. The voxel selection was implemented using the ten-fold cross-validation strategy, where ten groups of voxel weightings were generated. The mean of the ten groups of weightings was defined as the final weighting.
Figure 4.
Score of the SVM obtained in group 2 based on the spatial patterns of aging identified in group 1.
The results displayed in the left figure were obtained on the second group of MRI data by SVM. Voxels used for classification were the final spatial patterns of aging which were generated on the first group of MRI data; the right results are SVM score using voxels obtained by two-sample t-test.
Figure 5.
Locations of the representative brain regions of informative patterns identified by the sparse representation method.
The first 1000 voxels of spatial patterns identified by sparse representation were projected on the original human brain map. The sparse representation method selected human brain regions that included regions selected by a t-test filter, and were more widespread. The regions in the green circles were only identified by sparse representation.
Table 1.
The locations of the voxels that were selected by the sparse representation and statistical t-test.
Figure 6.
Locations of the representative brain regions of informative patterns identified by t-test filter.
The first 1000 voxels of brain regions identified by a t-test filter were projected on original brain map.
Figure 7.
Relationship between the mean volume of clusters and subject age (group 1).
The red circles represent the mean volume of all the voxels in one cluster for all of the subjects in the first group; the blue diamonds represent the mean volume of the entire brain (GM) for all of the subjects in the first group. The red and blue lines are the results of the linear curve fitting corresponding to the red circles and blue diamonds. The “b” represents the coefficient of linear regression of the mean cluster volume. The hypothesis t-test of the coefficients was implemented at a significance level of .
Figure 8.
Contribution of the correlation between a voxel in the precentral gyrus and voxels in the cerebellum, inferior frontal gyrus and thalamus.
The x-axis represents the gray value of a representative voxel in the precentral gyrus that corresponds with the 250 subjects used for classification, and the y-axis represents the gray value of a representative voxel in the left cerebellum (top-left), right cerebellum (top-right), right inferior frontal gyrus (down-left) and thalamus (down-right). The blue stars and red crosses represent the young cohort and old cohort samples in the first group of MRI images, respectively. The three gray lines in each subplot are discriminant boundaries estimated by the SVM which correspond with the x-axis, y-axis and combination of both. It is noteworthy that the voxel in the precentral gyrus is more discriminative (84.4%) than the voxels in the clusters described above (the left cerebellum 82.0%, right cerebellum 72.0%, inferior frontal gyrus 77.6%, and thalamus 80.4%), but the discrimination ability derived from combination of a voxel from the precentral gyrus and a voxel form the specific cluster is even higher (the left cerebellum 87.6%, right cerebellum 86.8%, inferior frontal gyrus 89.2%, and thalamus 89.2%).
Figure 9.
Brain regions extracted by the new method distributed over the sensorimotor and cognitive circuitry in the human brain.
The red font brain regions are identified in our study. The green arrows represent the sensorimotor functional circuitry, while the brown arrows represent the cognitive circuitry. The black dash arrow represents the newly found in [59]. BG: basal ganglia, GPi: internal globus pallidus, GPe: external globus pallidus.
Table 2.
Demographic characteristics of the subjects.