# Prediction accuracy of femoral and tibial stress and strain using statistical shape and density model-based finite element models in paediatrics

## TL;DR

This study shows that statistical shape and density models can accurately predict bone stress and strain in children, which could help with personalized medical treatments.

## Contribution

The novelty is demonstrating the accuracy of SSDM-based FE models for predicting pediatric bone stress and strain.

## Key findings

- SSDM-based models showed high correlation with CT-based models for stress and strain predictions.
- Normalized root-mean-square errors for stress and strain were low, indicating good accuracy.
- The results suggest potential for using SSDM-based models in pediatric implant design and surgical planning.

## Abstract

Computed tomography (CT)-based finite element (FE) models can non-invasively assess bone mechanical properties, but their clinical application in paediatrics is limited due to fewer datasets and models. Statistical Shape-Density Model (SSDM)-based FE models using statistically inferred shape and density have application to predict bone stress and strains; however, their accuracy in children remains unexplored. This study assessed the accuracy of stress–strain distributions estimated from SSDM-based FE models of paediatric femora and tibiae. CT-based FE models used geometry and densities derived from 330 CT scans from children aged 4–18 years. Paediatric SSDMs of the femur and tibia were used to predict bone geometries and densities from participants’ demographics and linear bone measurements. Forces during single-leg standing were estimated and applied to each bone. Stress and strain distributions were compared between the SSDM-based FE models and CT-based FE models, which served as the gold standard. The average normalized root-mean-square error (NRMSE) for Von Mises stress was 6% for the femur and 8% for the tibia across all cases. Principal strains NRMSE ranged from 1.2% to 5.5%. High correlations between the SSDM-based and CT-based FE models were observed, with determination coefficients ranging from 0.80 to 0.96. These results illustrate the potential of SSDM-based FE models for paediatric application, such as personalized implant design and surgical planning.

The online version contains supplementary material available at 10.1007/s10237-025-02016-8.