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 \(\vert\) 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.

中文翻译：

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一种设计椎间盘耦合非线性响应节能替代模型的新方法

摘要

本研究的目的是设计椎间盘 (IVD) 非线性弹性行为的物理保持和精确替代模型。基于来自详细有限元 (FE) 圆盘模型的人工力-位移数据集，我们使用贪心核和二阶、三阶和四阶多项式近似来训练标量力-扭矩势的替代模型。这样做，所得的弹性 IVD 响应模型确保了其结构中机械能的守恒。同时，他们能够预测生理运动范围内的椎间盘力以及椎间关节所有六个自由度的耦合。根据从非耦合（一维）、弱耦合（二维）和随机运动轨迹获得的训练和测试数据来评估特定主题的 L4 \(\vert\) 5 椎间盘几何形状的所有替代模型的性能在整个六维 (6d) 生理位移范围以及合成运动学数据上。我们观察到核代理的精度最高，其次是四阶多项式模型。两者都明显优于二阶多项式模型，二阶多项式模型相当于神经肌肉骨骼模拟中常用的刚度矩阵。因此，所提出的模型架构有可能提高神经肌肉骨骼脊柱模型中负载预测的准确性和有效性。