Quantifying Tensor Field Similarity With Global Distributions and Optimal Transport

Area of Science:

• Biomedical Engineering
• Medical Imaging Analysis
• Computational Mechanics

Background:

• Strain tensor fields are crucial for analyzing tissue deformation in organs like the heart and tongue.
• Quantifying similarity between complex, multidimensional strain datasets is challenging.
• Existing methods struggle with shape variations and require object registration.

Purpose of the Study:

• To develop a novel, geometry-independent method for quantifying similarity between tensorial strain fields.
• To enable accurate comparison of mechanical deformations across different object shapes.
• To correlate muscle activation with observed muscular contraction using medical imaging data.

Main Methods:

• Applied global distribution methods from pattern recognition to tensorial strain data.
• Approximated strain field properties using a 3D histogram.
• Utilized Wasserstein distance from optimal transport theory to compare histograms.
• Evaluated method consistency by sorting strain fields and comparing to existing techniques.

Main Results:

• The proposed method accurately matches tissue deformation regardless of object shape.
• Sorting accuracy of the new approach surpassed 1D shear distribution methods.
• Performance was comparable to tensor residual magnitude without needing registration.
• Successfully correlated muscle activation with muscular contraction from tagged MRI data.

Conclusions:

• The developed technique provides a robust and geometry-independent measure of strain field similarity.
• This method advances the functional analysis of moving organs and biomechanical studies.
• It offers a more accurate and less restrictive alternative to current strain quantification methods.