A Gyroid TPMS-based machine learning framework for rapid prediction of cancellous bone mechanical properties

High-fidelity finite-element analysis of cancellous bone is computationally expensive, particularly when large parameter spaces must be explored. This study developed a rapid surrogate-modeling framework integrating parametric Gyroid modeling, finite-element analysis, and machine learning to predict the apparent mechanical properties of cancellous-bone models.

Trabecular tissue Young's modulus (E _t), tissue failure strain (ε _t), bone volume fraction (BV/TV), and degree of anisotropy (DA) were used as inputs. A database of 200 parameter combinations was generated using Latin hypercube sampling, with apparent Young's modulus (E _c) and failure stress (σ _c) obtained from finite-element simulations as separate outputs. Multiple linear regression, quadratic polynomial regression, support vector regression, Kriging, and a backpropagation neural network were evaluated using nested five-fold cross-validation.

The finite-element model reproduced published uniaxial compression responses. BPNN achieved the best prediction of E _c (R₂ = 0.9993 ± 0.0003, NRMSE = 0.0256 ± 0.0027, MAPE = 1.68 ± 0.38%), whereas SVR performed best for σ _c (R₂ = 0.9987 ± 0.0004, NRMSE = 0.0352 ± 0.0030, MAPE = 2.23 ± 0.45%). Response-surface analysis showed that E _t and BV/TV primarily governed apparent stiffness, while failure stress was additionally sensitive to ε _t.

The proposed framework provides an accurate and computationally efficient approach for rapid prediction, parameter screening, response-surface analysis, and structural design exploration within the investigated Gyroid model space.