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Accurate calibration of finite element (FE) models is essential across various biomechanical applications, including human intervertebral discs (IVDs), to ensure their reliability and use in diagnosing and planning treatments. However, traditional calibration methods are computationally intensive, requiring iterative, derivative-free optimization algorithms that often take days to converge. This study addresses these challenges by introducing a novel, efficient, and effective calibration method demonstrated on a human L4-L5 IVD FE model as a case study using a neural network (NN) surrogate. The NN surrogate predicts simulation outcomes with high accuracy, outperforming other machine learning models, and significantly reduces the computational cost associated with traditional FE simulations. Next, a Projected Gradient Descent (PGD) approach guided by gradients of the NN surrogate is proposed to efficiently calibrate FE models. Our method explicitly enforces feasibility with a projection step, thus maintaining material bounds throughout the optimization process. The proposed method is evaluated against state-of-the-art Genetic Algorithm (GA) and inverse model baselines on synthetic and in vitro experimental datasets. Our approach demonstrates superior performance on synthetic data, achieving a Mean Absolute Error (MAE) of 0.06 compared to the baselines' MAE of 0.18 and 0.54, respectively. On experimental specimens, our method outperforms the baseline in 5 out of 6 cases. While our approach requires initial dataset generation and surrogate training, these steps are performed only once, and the actual calibration takes under three seconds. In contrast, traditional calibration time scales linearly with the number of specimens, taking up to 8 days in the worst-case. Such efficiency paves the way for applying more complex FE models, potentially extending beyond IVDs, and enabling accurate patient-specific simulations., Competing Interests: Declaration of competing interest The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: Jan S. Kirschke reports financial support was provided by European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program. Jan S. Kirschke reports a relationship with Bonescreen GmbH that includes: board membership, employment, and equity or stocks. If there are other authors, they declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2025 The Authors. Published by Elsevier Ltd.. All rights reserved.)

Anterior Vertebral Body Tethering (VBT) is a novel fusionless treatment option for selected adolescent idiopathic scoliosis patients which is gaining widespread interest. The primary objective of this study is to investigate the effects of tether pre-tension within VBT on the biomechanics of the spine including sagittal and transverse parameters as well as primary motion, coupled motion, and stresses acting on the L2 superior endplate. For that purpose, we used a calibrated and validated Finite Element model of the L1-L2 spine. The VBT instrumentation was inserted on the left side of the L1-L2 segment with different cord pre-tensions and submitted to an external pure moment of 6 Nm in different directions. The range of motion (ROM) for the instrumented spine was measured from the initial post-VBT position. The magnitudes of the ROM of the native spine and VBT-instrumented with pre-tensions of 100 N, 200 N, and 300 N were, respectively, 3.29°, 2.35°, 1.90° and 1.61° in extension, 3.30°, 3.46°, 2.79°, and 2.17° in flexion, 2.11°, 1.67°, 1.33° and 1.06° in right axial rotation, and 2.10°, 1.88°, 1.48° and 1.16° in left axial rotation. During flexion-extension, an insignificant coupled lateral bending motion was observed in the native spine. However, VBT instrumentation with pre-tensions of 100 N, 200 N, and 300 N generated coupled right lateral bending of 0.85°, 0.81°, and 0.71° during extension and coupled left lateral bending of 0.32°, 0.24°, and 0.19° during flexion, respectively. During lateral bending, a coupled extension motion of 0.33-0.40° is observed in the native spine, but VBT instrumentation with pre-tensions of 100 N, 200 N, and 300 N generates coupled flexion of 0.67°, 0.58°, and 0.42° during left (side of the implant) lateral bending and coupled extension of 1.28°, 1.07°, and 0.87° during right lateral bending, respectively. Therefore, vertebral body tethering generates coupled motion. Tether pre-tension within vertebral body tethering reduces the motion of the spine., Competing Interests: Declaration of competing interest The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: Per Trobisch:, (Copyright © 2023 Elsevier Ltd. All rights reserved.)