Moving frames for heart fiber geometry

Area of Science:

• Cardiovascular Science
• Biophysics
• Medical Imaging

Background:

• Cardiac muscle cells (cardiomyocytes) are arranged in a collagen matrix, forming helical fiber segments crucial for heart pumping.
• Understanding the geometrical variation of these cardiac fiber groupings is essential for comprehending normal heart function.

Purpose of the Study:

• To develop an extended mathematical framework for cardiac fiber architecture based on differential forms.
• To provide a new set of parameters complementary to existing models for studying cardiac fiber geometry.
• To enable direct computation of generalized helicoid parameters without optimization problems.

Main Methods:

• Utilized the Maurer-Cartan method of moving frames to analyze rotations of local fiber direction frame fields.
• Developed a novel framework based on differential forms to model cardiac fiber architecture.
• Applied Diffusion MRI to validate the framework and compare model fits across species.

Main Results:

• The differential forms framework allows direct computation of generalized helicoid parameters.
• A specialized model, the homeoid, constrains fibers to ellipsoidal shells.
• The homeoid model demonstrated improved fits compared to generalized helicoids in rat, dog, and human cardiac data.

Conclusions:

• The proposed differential forms framework offers a new approach to modeling cardiac fiber architecture.
• The homeoid specialization provides a more accurate representation of cardiac fiber geometry in various species.
• This work facilitates the development of new computational models for cardiac function and disease.