[Paper Review] Multiscale approach for bone remodeling simulation based on finite element and neural network computation

Ridha Hambli, Abdelwahed Barkaoui|arXiv (Cornell University)|Jul 19, 2011

Elasticity and Material Modeling6 references3 citations

TL;DR

This paper presents a novel multiscale computational framework that accelerates bone remodeling simulation by coupling finite element analysis at the macroscopic bone level with a trained artificial neural network to predict mesoscale trabecular structure changes. The neural network substitutes time-intensive finite element computations at the trabecular level, enabling rapid prediction of bone property updates based on mechanical loading, with validation using m-CT-derived 2 mm³ representative volume elements.

ABSTRACT

The aim of this paper is to develop a multiscale hierarchical hybrid model based on finite element analysis and neural network computation to link mesoscopic scale (trabecular network level) and macroscopic (whole bone level) to simulate bone remodelling process. Because whole bone simulation considering the 3D trabecular level is time consuming, the finite element calculation is performed at macroscopic level and a trained neural network are employed as numerical devices for substituting the finite element code needed for the mesoscale prediction. The bone mechanical properties are updated at macroscopic scale depending on the morphological organization at the mesoscopic computed by the trained neural network. The digital image-based modeling technique using m-CT and voxel finite element mesh is used to capture 2 mm3 Representative Volume Elements at mesoscale level in a femur head. The input data for the artificial neural network are a set of bone material parameters, boundary conditions and the applied stress. The output data is the updated bone properties and some trabecular bone factors. The presented approach, to our knowledge, is the first model incorporating both FE analysis and neural network computation to simulate the multilevel bone adaptation in rapid way.

Motivation & Objective

• To develop a computationally efficient method for simulating multiscale bone remodeling across macroscopic and mesoscopic levels.
• To reduce the computational burden of full 3D trabecular finite element modeling by replacing it with a trained neural network surrogate.
• To link macroscopic bone mechanical behavior with mesoscopic trabecular architecture changes through a hierarchical hybrid model.
• To enable rapid simulation of bone adaptation under physiological loading conditions using image-based modeling.
• To validate the approach using m-CT-derived representative volume elements of the femoral head.

Proposed method

• A finite element model is constructed at the macroscopic level to simulate whole bone mechanical response.
• A separate finite element model is used at the mesoscopic level to simulate trabecular network behavior within 2 mm³ representative volume elements from m-CT scans.
• An artificial neural network is trained using input data including bone material properties, boundary conditions, and applied stress, with output being updated bone properties and trabecular factors.
• The trained neural network replaces the mesoscale finite element computation in the macroscopic simulation loop, enabling real-time prediction of structural adaptation.
• The model uses digital image-based finite element meshing to capture the complex geometry of trabecular bone in the femoral head.
• The hierarchical framework updates bone mechanical properties at the macroscopic scale based on mesoscale predictions from the neural network.

Experimental results

Research questions

• RQ1 Can a neural network surrogate accurately replace time-consuming finite element computations at the mesoscale in bone remodeling simulations?
• RQ2 How effectively can a hybrid finite element and neural network model predict changes in trabecular bone structure under mechanical loading?
• RQ3 To what extent does the proposed multiscale model preserve accuracy while significantly reducing computational cost compared to full 3D trabecular modeling?
• RQ4 How well does the model reproduce morphological changes in trabecular architecture based on mechanical stimuli?
• RQ5 Can the trained neural network generalize across different loading conditions and bone material properties in the femoral head?

Key findings

• The proposed hybrid model enables rapid simulation of bone remodeling by replacing mesoscale finite element analysis with a trained neural network.
• The neural network successfully predicts updated bone properties and trabecular factors based on input mechanical loading and material parameters.
• The model achieves significant computational speedup compared to full 3D finite element modeling at the trabecular level.
• The approach is validated using m-CT-based 2 mm³ representative volume elements from the femoral head, ensuring anatomical relevance.
• The framework represents, to the authors' knowledge, the first integration of finite element and neural network computation for multiscale bone adaptation simulation.
• The model maintains accuracy in predicting structural adaptation while drastically reducing simulation time.