Integrating personalized shape prediction, biomechanical modeling, and wearables for bone stress prediction in runners

Abstract

Running biomechanics studies the mechanical forces experienced during running to improve performance and prevent injuries. This study presents the development of a digital twin for predicting bone stress in runners. The digital twin leverages a domain adaptation-based Long Short-Term Memory (LSTM) algorithm, informed by wearable sensor data, to dynamically simulate the structural behavior of foot bones under running conditions. Data from fifty participants, categorized as rearfoot and non-rearfoot strikers, were used to create personalized 3D foot models and finite element simulations. Two nine-axis inertial sensors captured three-axis acceleration data during running. The LSTM neural network with domain adaptation proved optimal for predicting bone stress in key foot bones-specifically the metatarsals, calcaneus, and talus-during the mid-stance and push-off phases (RMSE < 8.35 MPa). This non-invasive, cost-effective approach represents a significant advancement for precision health, contributing to the understanding and prevention of running-related fracture injuries.

Fig. 1. Von Mises Stress Distribution in Rearfoot and Non-Rearfoot Strikers.

Comparison of Von Mises stress between rearfoot (blue) and non-rearfoot (red) strikers for each foot bone during the midstance (a) and push-off (b) phases. Note: M1–M5 represent the first to fifth metatarsals.

Fig. 2. Violin Plots of MAPE for Predicted Stresses During Gait Phases.

Comparison of MAPE for predicted mean and peak stresses in each region during the mid-stance (a) and push-off (b) phases. Note: MAPE mean absolute percentage error, M1–M5 represent the first to fifth metatarsals.

Fig. 3. Pearson correlation coefficient (r) plot (left) and Bland-Altman plot (right) compare predicted stresses with reference stresses obtained from finite element modeling during the mid-stance (in blue) and push-off (in purple) phases.

Labels (a–e, h–l) represent the first to fifth metatarsals, while (f, g) denote the calcaneus and talus.

Fig. 4. Comparison of RMSE between rearfoot and non-rearfoot strike runners.

a–c Mid-stance phase, while d–f push-off phase. a, b, d, e Pearson correlation coefficients and Bland–Altman plots. c, f Box plots comparing the groups. Note: RMSE root mean square error, and M1–M5 indicate the first to fifth metatarsals. *p < 0.05, and **p < 0.01.

Fig. 5. A hybrid biomechanical modeling approach coupled with data-driven methods predicts von Mises stress in the foot bones from inertial sensors during running.

a Acquisition of sensor data from the foot and ankle joint; b Generation of foot-ankle models from foot scans, informed by statistical shape modeling (SSM) coupled with free-form deformation (FFD); c Application of a data-driven approach, using inertial sensor data as inputs and bone stress as outputs; d Finite element simulation projects bone stress during the mid-stance and push-off phases of running. Note: IMU inertial measurement unit, SSM statistical shape modeling, PC principal component, FFD free-form deformation.

Fig. 6. Finite element modeling and validation.

a Geometry acquisition from foot scanning and reconstruction, informed by statistical shape modeling (SSM) coupled with free-form deformation (FFD); b Finite element simulation for the initial contact, mid-stance, and push-off phases during running, employing plantar pressure as the loading condition; c Model validation was performed by comparing vertical compression to displacement and by comparing plantar pressure during standing across five reconstructed models with experimental measurements.

Fig. 7. Architecture of the proposed domain adaptation-based LSTM.

a Illustration of bidirectional-LSTM; b Use of a gradient reversal layer to distinguish domain-invariant features; c Demonstration of a single LSTM unit. Note: LSTM long short-term memory.