A novel cortical thickness estimation method based on volumetric Laplace-Beltrami operator and heat kernel

Area of Science:

• Neuroimaging
• Computational Anatomy
• Medical Image Analysis

Background:

• Cortical thickness estimation is crucial for understanding brain development and neurodegenerative diseases.
• Existing methods may have limitations in accuracy and robustness.

Purpose of the Study:

• To present a novel heat kernel-based algorithm for cortical thickness estimation using magnetic resonance imaging (MRI).
• To validate the algorithm's ability to detect differences in cortical thickness associated with Alzheimer's disease (AD) and mild cognitive impairment (MCI).

Main Methods:

• Constructing a tetrahedral mesh from in vivo brain MRI data.
• Computing harmonic fields using the volumetric Laplace-Beltrami operator.
• Utilizing heat kernel diffusion to trace heat transfer probability for thickness calculation between pial and white matter surfaces.

Main Results:

• The algorithm demonstrated robustness and accuracy by relying on intrinsic brain geometry.
• Preliminary results on the Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset showed statistically significant differences in cortical thickness among AD, MCI, and control groups.
• The method successfully detected differences in 151 subjects (51 AD, 45 MCI, 55 controls).

Conclusions:

• The proposed heat kernel-based method provides an efficient and generalizable approach for cortical thickness estimation.
• The algorithm shows potential for clinical applications in diagnosing and monitoring neurodegenerative diseases.
• This framework can be adapted for thickness estimation in various biological structures with defined surfaces.