Annals of Mathematical Sciences and Applications

Volume 9 (2024)

Number 2

QC-SPHARM: quasi-conformal spherical harmonics based geometric distortions on hippocampal surfaces for early detection of Alzheimer’s disease

Pages: 283 – 308

DOI: https://dx.doi.org/10.4310/AMSA.2024.v9.n2.a1

Authors

Anthony Hei-Long Chan (Hong Kong Centre for Cerebro-cardiovascular Health Engineering (COCHE), Hong Kong)

Yishan Luo (BrainNow Research Institute, Shenzhen, China)

Lin Shi (Department of Imaging and Interventional Radiology, Faculty of Medicine, The Chinese University of Hong Kong)

Ronald Lok Ming Lui (The Department of Mathematics, The Chinese University of Hong Kong)

Abstract

This paper examines the advantages of hippocampal surface geometry for the analysis of Alzheimer’s disease (AD). We propose a disease classification model, called the QC-SPHARM, for the early detection of AD. The proposed QC-SPHARM can distinguish between normal control (NC) subjects and AD patients, as well as between amnestic mild cognitive impairment (aMCI) patients having high possibility progressing into AD, and those who do not. Using the spherical harmonics (SPHARM) based registration, a template surface is constructed from the NC subjects. Each hippocampal surface segmented from the ADNI data are then individually registered to the template surface. Local geometric distortions of the deformation from the template surface to each subject are evaluated in terms of conformality distortions and curvatures distortions. These measurements are combined with the spherical harmonics coefficients and the hippocampal volume change to form the feature vector. Then, the bagging predictor incorporated t-test is applied to extract features having high discriminating power. The disease diagnosis machine can therefore be built using the discriminating feature vectors. The model is tested with two databases. The first database consists 110 NC-AD pairs, and the second database consists 20 aMCI patients who have advanced to AD during a two-year period, and 20 aMCI patients who remain non-AD for the next two years after the MRI scan. Using the SVM classification machine, the QC-SPHARM achieves 85.2% and 81.2% testing accuracy on 80 random samples and 10 random samples as testing subjects respectively. The QC-SPHARM has higher accuracy than other traditional classification models under experiments on the same database. The results demonstrate the advantages of using local geometric distortions as the discriminating criterion for early AD diagnosis.

Keywords

hippocampus, Alzheimer’s disease, amnestic mild cognitive impairment, disease classification, quasiconformal, spherical harmonics

Received 29 March 2023

Accepted 12 April 2023

Published 15 August 2024