Bridging Diverse Physics and Scales of Knee Cartilage With Efficient and Augmented Graph Learning

Abstract

Articular cartilage (AC) is essential for minimizing friction in the human knee, but its healthy function is highly influenced by biomechanical factors such as weight bearing. Non-invasive biomechanical and numerical simulations are widely used to study AC but often require complex and costly numerical approximations. Machine learning (ML) provides a more efficient alternative and uses data from these numerical methods for training. Hybrid ML models (HML) complemented by reduced-order numerical models can achieve similar outcomes with minimal data input but may have problems with generalizability across different scales. In this study, we present an extended HML framework (EHML) for developing a multiscale surrogate model specifically tailored for knee cartilage simulations. Our approach is based on integrating hybrid graph neural networks (GNNs) with tissue-scale data and aims to achieve remarkable few-shot learning and potential zero-shot generalizability for large-scale analysis. The main proposed idea is a physics-constrained data augmentation (DA) technique coupled with a set of pre-processing and customization algorithms to bridge the scales. Specifically, we integrate feature transformations, resampling, and cost-sensitive functions to manage the observed data imbalances, all within a customized, memory-efficient training framework. Our rigorous testing using an advanced multi-physics cartilage model demonstrates the viability of our approach. Comparative analyses underscore the significant role of pre-processing and DA methods in enhancing generalizability and efficiency. They helped reduce the normalized mean squared errors to 0.1 or less (compared to the ablated model with its error of 2 or higher). Therefore, this work represents an important step towards addressing the challenges of limited generalizability and efficiency of existing ML-based surrogate models and opens new possibilities for their application in more complex simulations.

Keywords

• Biomechanics
• cartilage
• knee
• finite element analysis
• graph neural networks
• machine learning