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- Title
A new method to design energy-conserving surrogate models for the coupled, nonlinear responses of intervertebral discs.
- Authors
Hammer, Maria; Wenzel, Tizian; Santin, Gabriele; Meszaros-Beller, Laura; Little, Judith Paige; Haasdonk, Bernard; Schmitt, Syn
- Abstract
The aim of this study was to design physics-preserving and precise surrogate models of the nonlinear elastic behaviour of an intervertebral disc (IVD). Based on artificial force-displacement data sets from detailed finite element (FE) disc models, we used greedy kernel and polynomial approximations of second, third and fourth order to train surrogate models for the scalar force-torque -potential. Doing so, the resulting models of the elastic IVD responses ensured the conservation of mechanical energy through their structure. At the same time, they were capable of predicting disc forces in a physiological range of motion and for the coupling of all six degrees of freedom of an intervertebral joint. The performance of all surrogate models for a subject-specific L4 | 5 disc geometry was evaluated both on training and test data obtained from uncoupled (one-dimensional), weakly coupled (two-dimensional), and random movement trajectories in the entire six-dimensional (6d) physiological displacement range, as well as on synthetic kinematic data. We observed highest precisions for the kernel surrogate followed by the fourth-order polynomial model. Both clearly outperformed the second-order polynomial model which is equivalent to the commonly used stiffness matrix in neuro-musculoskeletal simulations. Hence, the proposed model architectures have the potential to improve the accuracy and, therewith, validity of load predictions in neuro-musculoskeletal spine models.
- Subjects
SINGLE-degree-of-freedom systems; POLYNOMIAL approximation; MECHANICAL energy; RANGE of motion of joints; ENERGY conservation
- Publication
Biomechanics & Modeling in Mechanobiology, 2024, Vol 23, Issue 3, p757
- ISSN
1617-7959
- Publication type
Article
- DOI
10.1007/s10237-023-01804-4