Accurately Estimating Heterogeneous Elastic Properties of Biological Tissues Using Physics-Informed Neural Networks

Основные понятия

Physics-informed neural networks can accurately estimate the full-field heterogeneous elastic properties of complex biological tissues undergoing large deformations.

Аннотация

This study proposes a physics-informed machine learning approach to identify the elastic modulus distribution in nonlinear, large deformation hyperelastic materials. The authors evaluate the prediction accuracies and computational efficiency of physics-informed neural networks (PINNs) on inferring the heterogeneous material parameter maps across three nonlinear materials with structural complexity that closely resemble real tissue patterns, such as brain tissue and tricuspid valve tissue.
The key highlights and insights are:

The authors introduced a physics-informed machine learning approach to discovering the elastic modulus distribution in complex heterogeneous hyperelastic materials that have traditionally been challenging and mathematically ill-posed.

An improved PINN architecture accurately estimates the full-field elastic properties of three hyperelastic constitutive models, with relative errors of less than 5% across all examples.

PINNs have remarkable potential for providing highly accurate parameter estimations using just one data sample, even when there is a high level of noise in training data.

The proposed approach provides a promising method for studying the effect of material heterogeneity in their macroscopic behaviors and the evolution of material micromechanical properties in response to mechanical load, which is highly applicable to studying tissue growth, remodeling, and detecting early mechanical markers of diseases.

Among the 20 network architectures tested, the network architecture IIB, which partitions output variables into separate independent networks based on their shared features, provided the most accurate estimates of the elastic moduli, with average L2 relative errors below 5% across the three examples, while also being the fastest in terms of computational time.

The selected PINN architecture IIB was found to be robust to noise in the reference strain data, maintaining high accuracy even with up to 10% white Gaussian noise.

The PINN architecture IIB was also able to accurately estimate the full-field material parameters for different material constitutive models, including plane stress Neo-Hookean, incompressible Mooney Rivlin, and incompressible Gent, as well as varying levels of biaxial stretch.

Статистика

The relative errors of the estimated full-field elastic modulus were less than 5% across all three examples.
The maximum pointwise error of the estimated full-field elastic modulus maps was up to 0.32.

Цитаты

"Physics-informed neural networks have remarkable potential for providing highly accurate parameter estimations using just one data sample, even when there is a high level of noise in training data."
"The proposed approach provides a promising method for studying the effect of material heterogeneity in their macroscopic behaviors and the evolution of material micromechanical properties in response to mechanical load, which is highly applicable to studying tissue growth, remodeling, and detecting early mechanical markers of diseases."

Ключевые выводы из

Identifying heterogeneous micromechanical properties of biological tissues via physics-informed neural networks

by Wensi Wu,Mit... в arxiv.org 05-01-2024

https://arxiv.org/pdf/2402.10741.pdf

Дополнительные вопросы

How can the proposed PINN architecture be extended to handle anisotropic and time-dependent material behaviors of biological tissues?

The proposed Physics-Informed Neural Network (PINN) architecture can be extended to handle anisotropic material behaviors by incorporating additional invariant terms in the material constitutive models. Anisotropic materials exhibit different mechanical properties in different directions, and by including these directional dependencies in the material models, the PINN can accurately capture the anisotropic behavior of biological tissues. This extension would involve modifying the network architecture to account for the anisotropy in the material properties and training the network with data that reflects the directional variations in stiffness and elasticity.
To address time-dependent material behaviors, the PINN architecture can be adapted to include temporal information in the form of time-dependent boundary conditions or material properties. By incorporating time as a variable in the network, the PINN can learn the evolution of material properties over time, allowing for the prediction of mechanical responses at different time points. This extension would enable the modeling of dynamic changes in tissue properties, such as viscoelastic behavior or time-dependent remodeling processes, providing a more comprehensive understanding of the mechanical behavior of biological tissues over time.

What are the potential limitations of the PINN approach in accurately estimating the material parameters of biological tissues with complex microstructures and loading conditions?

While the PINN approach offers a promising framework for estimating material parameters of biological tissues, there are potential limitations that may impact the accuracy of the predictions, especially in cases with complex microstructures and loading conditions:

Data Quality: The accuracy of the predictions heavily relies on the quality and quantity of the training data. In cases where the data is noisy or limited, the PINN may struggle to accurately capture the complex relationships between the material parameters and the mechanical responses.

Model Complexity: Complex microstructures and loading conditions can introduce challenges in modeling the material behavior accurately. The PINN architecture may struggle to capture the intricate details of the tissue microstructure, leading to errors in the estimation of material parameters.

Computational Resources: Training a PINN for complex biological tissues with detailed microstructures and loading conditions may require significant computational resources, including high-performance computing and memory capabilities. Limited computational resources could hinder the accuracy and efficiency of the predictions.

Generalization: The ability of the PINN to generalize to unseen data and extrapolate to different scenarios is crucial for accurate predictions. Complex microstructures and loading conditions may introduce variability that the network has not been trained on, leading to potential inaccuracies in the estimations.

How can the insights gained from this study on the relationship between tissue microstructure and its mechanical properties be leveraged to develop novel tissue engineering and regenerative medicine strategies?

The insights gained from studying the relationship between tissue microstructure and mechanical properties can have significant implications for tissue engineering and regenerative medicine:

Customized Scaffold Design: Understanding how tissue microstructure influences mechanical properties can inform the design of customized scaffolds for tissue engineering. By mimicking the natural microstructure of tissues, engineered scaffolds can better replicate the mechanical behavior of native tissues, enhancing their functionality and integration.

Mechanobiology Studies: Insights into how mechanical forces affect tissue microstructure can guide mechanobiology studies aimed at understanding how cells respond to mechanical cues. This knowledge can be leveraged to design strategies for promoting tissue regeneration and repair through mechanical stimulation.

Disease Modeling: Studying the micromechanical behaviors of tissues can provide valuable insights into disease mechanisms and progression. By correlating tissue microstructure with mechanical properties, novel disease models can be developed to study conditions such as cancer invasion, fibrosis, and tissue degeneration.

Therapeutic Interventions: The relationship between tissue microstructure and mechanical properties can be leveraged to develop targeted therapeutic interventions. By modulating the mechanical environment of tissues, novel treatment strategies can be designed to promote tissue regeneration, prevent disease progression, and enhance healing processes.

Overall, the insights from this study can pave the way for innovative approaches in tissue engineering and regenerative medicine, leading to the development of advanced therapies and interventions that leverage the intricate relationship between tissue microstructure and mechanical properties.