Data-driven, voxel-based analysis of brain PET images: Application of PCA and LASSO methods to visualize and quantify patterns of neurodegeneration

Abstract

Spatial patterns of radiotracer binding in positron emission tomography (PET) images may convey information related to the disease topology. However, this information is not captured by the standard PET image analysis that quantifies the mean radiotracer uptake within a region of interest (ROI). On the other hand, spatial analyses that use more advanced radiomic features may be difficult to interpret. Here we propose an alternative data-driven, voxel-based approach to spatial pattern analysis in brain PET, which can be easily interpreted. We apply principal component analysis (PCA) to identify voxel covariance patterns, and optimally combine several patterns using the least absolute shrinkage and selection operator (LASSO). The resulting models predict clinical disease metrics from raw voxel values, allowing for inclusion of clinical covariates. The analysis is performed on high-resolution PET images from healthy controls and subjects affected by Parkinson's disease (PD), acquired with a pre-synaptic and a post-synaptic dopaminergic PET tracer. We demonstrate that PCA identifies robust and tracer-specific binding patterns in sub-cortical brain structures; the patterns evolve as a function of disease progression. Principal component LASSO (PC-LASSO) models of clinical disease metrics achieve higher predictive accuracy compared to the mean tracer binding ratio (BR) alone: the cross-validated test mean squared error of adjusted disease duration (motor impairment score) was 16.3 ± 0.17 years2 (9.7 ± 0.15) with mean BR, versus 14.4 ± 0.18 years2 (8.9 ± 0.16) with PC-LASSO. We interpret the best-performing PC-LASSO models in the spatial sense and discuss them with reference to the PD pathology and somatotopic organization of the striatum. PC-LASSO is thus shown to be a useful method to analyze clinically-relevant tracer binding patterns, and to construct interpretable, imaging-based predictive models of clinical metrics.

Fig 1. Schematic illustration of the image processing and analysis pipeline.

Parametric PET images of the left and right striatum were warped to a common space using an MR-derived striatal template. In the common space, the images were re-sorted according to the better (less clinically affected) and worse sides, and used in PCA to obtain side-specific PC loadings and PC scores. The PC loadings and scores in the putamen and caudate were analyzed separately. LASSO was used to obtain the fitting coefficients between the PC scores and clinical PD metrics—aDD and LMS. Using the fitting coefficients, the PC loadings were linearly combined to obtain the PC-LASSO estimators.

Fig 2. Examples of striatum images and segmentations in subject-native and common spaces.

A: Segmented MR image, DTBZ and RAC images in the native space for a PD subject. B: Rendering of the striatal template from two views. To generate the template, Freesurfer segmentations of the MR images of the putamen and caudate in the HC subjects were rigidly co-registered and averaged (N = 10, one side chosen randomly from each subject). C: Comparison of DTBZ and RAC BR images in the subject-native and common spaces (PD subject, same as A). AP = anteroposterior, LM = lateromedial, IS = inferosuperior.

Fig 3. Maximum intensity projections of the better- and worse-side PC loadings, obtained from PCA of all PD subjects.

Putamen and caudate loadings were computed separately, and ordered according to VAF expressed in percent. Positive and negative weights were projected separately and combined into a single composite image using different color scales. Color intensity reflects weight magnitude normalized to the maximum absolute value. Loadings with inverted color scales are equivalent. A: DTBZ PC loadings. B: RAC PC loadings.

Fig 4. Maximum intensity projections of the better-side DTBZ PC loadings, obtained from PCA of subject sub-groups at different stages of the disease.

The PCs are ordered according to VAF expressed in percent (shown in the corners). PC loadings in the putamen and caudate were computed separately. The first rows of the putamen and caudate loadings (mixed HC+PD) capture patterns associated with the initial onset of clinical PD symptoms. The second rows (early PD) represent stage of the disease shortly after symptom onset. The third rows (moderate PD) correspond to later stage of the disease.

Fig 5. Trace plots of the coefficients β_j and cross-validated MSE_test for the best three PC-LASSO models.

The coefficients β_j were fitted using the entire data. For comparison, the MSE_test produced by the mean BR and constant models are indicated by dashed horizontal lines. λ_min denotes the location of the global minimum in MSE_test (indicated by vertical lines).

Fig 6. Predicted clinical metrics plotted against the actual metrics.

The mean BR model predictions are shown on the top, and the PC-LASSO model predictions are shown on the bottom.

Fig 7. The mean values, standard deviations, and p-values of the fit coefficients β_j.

The means and standard deviations (error bars) were obtained from 500 training sets. The coefficients that were fitted on all available data are plotted for comparison. Values of p < 0.05 are highlighted with bold font.

Fig 8. Voxel weight distributions in the DTBZ-based PC-LASSO estimators of aDD and better-side LMS in the putamen.

Caudate is shown for spatial reference. The estimators were computed using β_j that were fitted on all data. Front view at the top, back view at the bottom. A = anterior; P = posterior.