Combining boundary-based methods with tensor-based morphometry in the measurement of longitudinal brain change

Abstract

Tensor-based morphometry is a powerful tool for automatically computing longitudinal change in brain structure. Because of bias in images and in the algorithm itself, however, a penalty term and inverse consistency are needed to control the over-reporting of nonbiological change. These may force a tradeoff between the intrinsic sensitivity and specificity, potentially leading to an under-reporting of authentic biological change with time. We propose a new method incorporating prior information about tissue boundaries (where biological change is likely to exist) that aims to keep the robustness and specificity contributed by the penalty term and inverse consistency while maintaining localization and sensitivity. Results indicate that this method has improved sensitivity without increased noise. Thus it will have enhanced power to detect differences within normal aging and along the spectrum of cognitive impairment.

Fig. 1

(a) Synthetic “longitudinal” image pair in which the second “time point” has cortical atrophy of about 3%. Both synthetic images have additive Gaussian noise with magnitude 4.67% of underlying white matter intensity. The right panel shows the extent of “atrophy.” (b) Comparison of log-Jacobian fields computed by KL (right panel)—incorporating the R_KL penalty term, against our proposed method G-KL (left panel) incorporating R_KL plus prior boundary information. Log-Jacobian values are displayed in translucent color allowing underlying tissue structure to be visible. Same color scales apply to both images. Contractions (“atrophy”) are in cool colors (left color bar) and expansions in warm (right color bar). Jacobian values outside the image have been suppressed. Left panel: G-KL. Right: KL. (c) Cross section of log-Jacobian values along the horizontal line drawn in Fig. 1(b). Intensities for G-KL are in blue, those for KL in red. G-KL shows increased boundary discrimination and increased sensitivity to change over small structures.

Fig. 2

(a) Intensity PDF for log-Jacobians corresponding G-KL (blue), KL (red), and TBM (“NF” or no filter) having no penalty corrections (orange). G-KL and KL are symmetric about y-axis with G-KL showing slightly greater variance than KL. NF is very wide and asymmetric to the left, demonstrating the inherent bias in the uncorrected log-Jacobians as explained in the text. (b) Average log-Jacobian values for each method displayed in cool colors for contractions and warm colors for expansions. Most values are low in magnitude (in the range of 0.001–0.005 magnitude; 0.1%–0.5% change), but are higher at the edges for G-KL as would be expected through reduction of R_KL penalty at tissue boundaries. Left panel: G-KL. Right: KL.

Fig. 3

Average log-Jacobian values over 20 one-year AD “change” images. This figure shows that increased magnitude of brain change as evidenced by higher Jacobian values, particularly in the posterior temporal lobes, genu, splenium, as well as broader lower-level changes in subcortically. Left panel: G-KL. Right: KL.

Fig. 4

StatROIs for G-KL (left panel) and KL (right). Yellow areas show voxels with t-value p < 0.001 (uncorrected). These ROIs differ mainly with G-KL showing more extensive areas of significant change in the striatum and subcortical nuclei.

Fig. 5

Single-subject log-Jacobian image of an AD subject over (left to right) 6, 12, and 24 months scan intervals, showing patterns of increasing atrophy. This figure illustrates enhanced ability of G-KL to capture greater differences in regions expected to change with the disease. Top row: G-KL. Bottom row: KL.

Fig. 6

Change trajectories for each method, computed for three time intervals, averaged over 50 AD, 38 MCI, and 37 normals. Slope and intercept values of fitted trend lines are also displayed. Intercepts of fitted lines of the two methods are similar. Range of intercepts for both methods, from 0.15% to 0.28%, is also similar to the range of intercepts for statROIs reported by Hua et al., [14]. Top panel: G-KL. Bottom: KL.

Fig. 7

(a) Average patterns of change recorded by method for each diagnostic group, for 65 AD (left panels), 93 MCI (middle), and 106 CN subjects (right). Upper row: G-KL. Lower row: KL. (b) 3-D display of significant cortical atrophy by method over AD group of 65 subjects. Clusters aresignificant by size (p < 0.05, corrected) for log-Jacobian values less than −0.01. Left panel: G-KL. Right: KL. (c) Voxel locations of significant difference between AD and CN. Significant voxel differences (p < 0.05, corrected) for clinical diagnostic groups by method. Warm colors denote positive differences (greater expansion of group 1 compared to group 2); cold colors denote significant contractions. AD or MCI has significantly greater brain loss than CN, signified by cold colors, and greater CSF expansion, signified by warm colors. There were no significant voxel-based differences between AD and MCI. Left panel: G-KL. Right: KL. (d) Voxel locations of significant difference between MCI and CN. Same color scales as Fig. 7(c). Left panel: G-KL. Right: KL.

Fig. 8

(a) Mean Jacobian differences according to baseline clinical diagnosis. Using MANOVA, there was a significant main effect of diagnosis and method as well as a significant method by diagnosis interaction (see text for details). Paired t-tests identified significant differences between methods for each diagnostic category. The magnitude of the between-method differences increases with increasing cognitive severity (Normal = 5%, MCI =9% and AD= 11%). (b) Mean Jacobian differences according to conversion status (MCI to AD) among 88 MCI subjects during 24 months of the ADNI study. There was no significant difference by method for Jacobian rate of change measures among the nonconverters. Method related differences, however, were highly significant (p = 0.0004) among those converting to dementia within 24 months.

Fig. 9

Voxelwise significance images of correlation between one year change in MMSE versus log-Jacobian values. Cool colors (magenta, blue) indicate significant associations (p < 0.05, corrected) between brain atrophy and MMSE. Warm colors (yellows) indicate significant associations (p < 0.001, corrected) of CSF expansion and MMSE. Left panel: G-KL. Right: KL.

Fig. 10

Voxelwise cluster significance images for the association between baseline CSF A-β and log-Jacobian values by method. Individual clusters at thresholds of t = −3 (light blue), t = −4 (dark blue), and t = +4 (orange) are displayed. All clusters are significant to p < 0.05 (corrected). Cool colors indicate association of brain loss with levels of CSF A-β . Warm indicates association of CSF expansion versus CSF A-β . Left panel: G-KL. Right: KL.