Discovery of Myocardial Tissue Fiber Dispersion: Fusion of Constitutive Neural Networks and Experimental Data

This article introduces a project that combines Constitutive Neural Networks (CANN) with experimental data to study myocardial tissue fiber dispersion, exploring the application of Physics-Informed Neural Networks (PINNs) in biomechanical modeling. The study aims to address issues such as difficult-to-measure parameters and insufficient interpretability in traditional biomechanical models. By embedding physical laws into the neural network architecture, it achieves the fusion of data-driven approaches and physical constraints, providing a new method for myocardial mechanics modeling.

Myocardial tissue is a complex biological material whose mechanical behavior is influenced by the arrangement of fiber structures, which is crucial for heart disease diagnosis, artificial valve design, etc. Traditional biomechanical modeling relies on physics-based constitutive equations, but parameters are difficult to measure directly. In recent years, Physics-Informed Neural Networks (PINNs) have embedded physical laws into neural networks, combining data-driven approaches with physical constraints to provide new ideas for solving this problem. This project is a practice of this trend: using CANN to study myocardial fiber dispersion.

Fiber Dispersion: Myocardial tissue is an anisotropic material with fibers arranged in a spiral pattern. Dispersion describes the degree of order in fiber arrangement: the higher the dispersion, the closer it is to isotropic; the lower the dispersion, the more obvious the anisotropy. Accurate measurement is crucial for modeling.

Constitutive Relationship: Describes the material's response to external forces. The stress-strain relationship of the myocardium is nonlinear, anisotropic, and viscoelastic. Parameters of traditional models lack physical meaning and vary greatly.

CANN: A special neural network that directly learns the constitutive relationship (input: deformation gradient tensor; output: strain energy density function; stress is obtained via automatic differentiation). Its advantages include automatically satisfying physical constraints, high data efficiency, and strong interpretability.

Experimental Data Acquisition: 3D fiber structures are obtained using two-photon microscopy, and direction vectors are extracted to calculate dispersion. Mechanical tests (e.g., biaxial stretching) provide stress-strain data to validate the model.

CANN Architecture Constraints: Must satisfy objectivity (results do not depend on the observer's reference frame), convexity (ensures material stability), and anisotropic modeling (captures different responses in fiber direction and perpendicular direction).

Training and Validation: Combines experimental data loss (difference between predicted and measured stress) and physical loss (penalty for violating constraints); uses leave-one-out cross-validation to ensure generalization ability.

Spatial Distribution of Dispersion: Myocardial fiber dispersion is non-uniformly distributed. The epicardial and endocardial regions have low dispersion (ordered arrangement), while the middle layer has higher dispersion, which may be related to the optimization of pumping function.

Changes in Disease States: Pathological samples (e.g., myocardial infarction scar tissue) have more disordered fiber arrangements and increased dispersion, affecting contraction efficiency and electrical conduction.

CANN vs. Traditional Models: CANN has higher prediction accuracy, more stable parameters, and stronger extrapolation ability (less likely to produce non-physical extreme values).

Personalized Cardiac Modeling: Combine patient medical images (e.g., MRI) with CANN models to establish personalized mechanical models, predict treatment responses, and guide surgical planning or drug selection.

Early Disease Diagnosis: Changes in fiber dispersion may be an early disease indicator. Non-invasive imaging measurements combined with machine learning can enable early screening.

Artificial Heart Design: Accurate constitutive relationships provide a foundation for numerical simulations of bionic artificial hearts and auxiliary devices.

Multi-scale Modeling: Current CANN focuses on the tissue scale and needs to be coupled with micro-scale (molecular) and macro-scale (organ) models.

Dynamic Response: Extend CANN to capture the dynamic mechanics of the heart (viscoelasticity, active contraction).

Electro-mechanical Coupling: Establish a CANN model coupling electrophysiology and mechanics to understand the mechanisms of arrhythmias.

Standardization of Data Sharing: Establish standardized experimental protocols and data formats to promote cross-group validation and comparison.

The Discovering-Dispersion-CANN project demonstrates the potential of physics-informed machine learning in biomechanics. It does not replace traditional models but deeply integrates physical laws with data-driven approaches, retaining physical intuition while gaining fitting flexibility. For biomedical researchers, it is a methodological demonstration; for machine learning practitioners, it is an interdisciplinary application case. In the future, with the advancement of computing power and imaging technology, PINNs will play a greater role in fields such as personalized medicine, and myocardial mechanics modeling will continue to push the boundaries of disciplines.