Disease progression models are crucial to understanding degenerative diseases. Mixed-effects models have been consistently used to model clinical assessments or biomarkers extracted from medical images, allowing missing data imputation and prediction at any timepoint. However, such progression models have seldom been used for entire medical images. In this work, a Variational Auto Encoder is coupled with a temporal linear mixed-effect model to learn a latent representation of the data such that individual trajectories follow straight lines over time and are characterised by a few interpretable parameters. A Monte Carlo estimator is devised to iteratively optimize the networks and the statistical model. We apply this method on a synthetic data set to illustrate the disentanglement between time dependant changes and inter-subjects variability, as well as the predictive capabilities of the method. We then apply it to 3D MRI and FDG-PET data from the Alzheimer's Disease Neuroimaging Initiative (ADNI) to recover well documented patterns of structural and metabolic alterations of the brain.
Explicit descriptions of the progression of biomarkers across time usually involve priors on the shapes of the trajectories. To circumvent this limitation, we propose a geometric framework to learn a manifold representation of longitudinal data. Namely, we introduce a family of Riemannian metrics that span a set of curves defined as parallel variations around a main geodesic, and apply that framework to disease progression modeling with a mixed-effects model, where the main geodesic represents the average progression of biomarkers and parallel curves describe the individual trajectories. Learning the metric from the data allows to fit the model to longitudinal datasets and provides few interpretable parameters that characterize both the group-average trajectory and individual progression profiles. Our method outperforms the 56 methods benchmarked in the TADPOLE challenge for cognitive scores prediction.
Alzheimer's Disease (AD) is a heterogeneous disease that disproportionately affects women and people with the APOE-ε4 susceptibility gene. We aim to describe the not-well-understood influence of both risk factors on the dynamics of brain atrophy in AD and healthy aging. Regional cortical thinning and brain atrophy were modeled over time using non-linear mixed-effect models and the FreeSurfer software with t1-MRI scans from the Alzheimer's Disease Neuroimaging Initiative (N = 1,502 subjects, 6,728 images in total). Covariance analysis was used to disentangle the effect of sex and APOE genotype on the regional onset age and pace of atrophy, while correcting for educational level. A map of the regions mostly affected by neurodegeneration is provided. Results were confirmed on gray matter density data from the SPM software. Women experience faster atrophic rates in the temporal, frontal, parietal lobes and limbic system and earlier onset in the amygdalas, but slightly later onset in the postcentral and cingulate gyri as well as all regions of the basal ganglia and thalamus. APOE-ε4 genotypes leads to earlier and faster atrophy in the temporal, frontal, parietal lobes, and limbic system in AD patients, but not in healthy patients. Higher education was found to slightly delay atrophy in healthy patients, but not for AD patients. A cohort of amyloid positive patients with MCI showed a similar impact of sex as in the healthy cohort, while APOE-ε4 showed similar associations as in the AD cohort. Female sex is as strong a risk factor for AD as APOE−ε4 genotype regarding neurodegeneration. Women experience a sharper atrophy in the later stages of the disease, although not a significantly earlier onset. These findings may have important implications for the development of targeted intervention.
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