Laplace Beltrami Based Formulation of Corpus Callosum to Ventricle Ratio for the Analysis of Alzheimer's Condition in T1-Weighted MR Images

Alzheimer's Disease (AD) is a fatal neurological condition predominated by atrophic changes in brain sub-anatomic regions. Enlargement of lateral ventricle leads to deformations of corpus callosum in Mild Cognitive Impairment (MCI) and AD subjects. However, this phenomenon of shape change has not been comprehensively quantified. In this work, an attempt has been made to analyze the atrophy of corpus callosum (CC) due to the enlargement of lateral ventricles using Laplace Beltrami (LB) eigenvalue features. The images for this study are obtained from a public domain Open Access Series of Imaging Studies (OASIS) database. The lateral ventricles and CC are segmented using a reaction diffusion level set method. LB eigenvalue features are extracted from the segmented images and are statistically analyzed. The CC to Ventricle Ratio (CVR) has been formulated to quantify and differentiate the shape changes in normal, MCI and AD subjects. Results show that LB eigenvalues can capture the shape changes of ventricles and CC in normal, MCI and AD subjects. The newly formulated CVR using LB eigenvalues can quantify the shape changes of CC due to ventricle enlargement and statistically differentiates the normal, MCI and AD subjects (p < 0.001). Thus, this study seems to be clinically substantial.