A Physics-Informed Neural Network Framework for Simulating Creep Buckling in Growing Viscoelastic Biological Tissues

2025-06-23

AI Summary

This work addresses the challenge of modeling viscoelastic creep buckling during biological tissue growth. We propose a physics-informed neural network (PINN) framework grounded in energy minimization, which incrementally minimizes the system’s potential energy functional—implicitly enforcing equilibrium and viscoelastic constitutive relations without explicit meshing, artificial initial perturbations, or custom-coded solvers. To our knowledge, this is the first energy-based PINN formulation applied to morphogenesis involving coupled creep, stress relaxation, growth, and buckling; instability emerges spontaneously during training, enabling natural capture of post-buckling evolution and morphology generation. Numerical experiments successfully reproduce creep buckling pathways and morphological evolution of cylindrical tissues under uniform and differential growth, demonstrating the method’s validity, robustness, and generalizability for soft material and biological tissue modeling.

Technology Category

• Machine Learning: Bio-inspired Learning
• Computer Vision: Medical and Biological Imaging
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Web Mining and Content Analysis: Models for Web evolution
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

Modeling viscoelastic behavior is crucial in engineering and biomechanics, where materials undergo time-dependent deformations, including stress relaxation, creep buckling and biological tissue development. Traditional numerical methods, like the finite element method, often require explicit meshing, artificial perturbations or embedding customised programs to capture these phenomena, adding computational complexity. In this study, we develop an energy-based physics-informed neural network (PINN) framework using an incremental approach to model viscoelastic creep, stress relaxation, buckling, and growth-induced morphogenesis. Physics consistency is ensured by training neural networks to minimize the systems potential energy functional, implicitly satisfying equilibrium and constitutive laws. We demonstrate that this framework can naturally capture creep buckling without pre-imposed imperfections, leveraging inherent training dynamics to trigger instabilities. Furthermore, we extend our framework to biological tissue growth and morphogenesis, predicting both uniform expansion and differential growth-induced buckling in cylindrical structures. Results show that the energy-based PINN effectively predicts viscoelastic instabilities, post-buckling evolution and tissue morphological evolution, offering a promising alternative to traditional methods. This study demonstrates that PINN can be a flexible robust tool for modeling complex, time-dependent material behavior, opening possible applications in structural engineering, soft materials, and tissue development.

Problem

• Model viscoelastic creep buckling in biological tissues
• Overcome computational complexity of traditional numerical methods
• Predict tissue growth-induced morphogenesis and instabilities

Innovation

• Energy-based PINN for viscoelastic modeling
• Minimizes potential energy for physics consistency
• Captures creep buckling without pre-imposed imperfections