Geometric modes of the brain from MRI: predicting age through Laplace–Beltrami spectra

Aging is a complex natural process that also affects the brain with consequent structural and functional changes. To distinguish between healthy aging and the onset of neurodegenerative disorders, it is important to understand how the brain changes. Structural magnetic resonance imaging (MRI) provides a non-invasive technique for capturing the morphology of the brain and extracting discriminative features to study brain aging. In the present study, the analysis is carried out by spectral geometry, which through the Laplace-Beltrami operator (LBO) allowing the brain's geometry to be decomposed into eigenvectors and eigenvalues. The aim is to use these spectral characteristics to predict age by structural MRI. The BrainPrint tool extracts the eigenvalues and eigenvectors from cortical and subcortical meshes from FreeSurfer. They are ordered, comparable between subjects, and do not require point-to-point correspondence between surfaces. The level of information contained at different scales is examined, since the first eigenvalues contain global information while greater values contain fine details. The main results demonstrate that both cortical surfaces and subcortical structures yield informative spectra. The findings of this study are then compared to results based on simple traditional measurements. This comparative analysis resulted in greater or comparable predictive power for the spectra (left hemisphere pial MAE (mean absolute error) = 12.45 years, third ventricle MAE = 10.61 years), compared to measures such as cortical thickness (MAE = 11.38 years) and white matter volume (MAE = 13.41 years). The fractal dimension of grey matter was the only measure to show a lower value (MAE = 10.28 years). The Laplace-Beltrami spectrum is a condensed and comparable descriptor of brain morphology that maintains a good predictive ability of age and future potential in clinical applications and neuroscientific studies.