Atad Matan, Gruber Gabriel, Ribeiro Marx, Nicolini Luis Fernando, Graf Robert, Möller Hendrik, Nispel Kati, Ezhov Ivan, Rueckert Daniel, Kirschke Jan S
Institute for Neuroradiology, TUM University Hospital, School of Medicine and Health, Technical University of Munich (TUM), Munich, Germany; Chair for AI in Healthcare and Medicine, Technical University of Munich (TUM) and TUM University Hospital, Munich, Germany.
Institute for Neuroradiology, TUM University Hospital, School of Medicine and Health, Technical University of Munich (TUM), Munich, Germany.
Comput Biol Med. 2025 Mar;186:109646. doi: 10.1016/j.compbiomed.2024.109646. Epub 2025 Jan 8.
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.
在包括人体椎间盘（IVD）在内的各种生物力学应用中，准确校准有限元（FE）模型对于确保其可靠性以及在诊断和治疗规划中的应用至关重要。然而，传统的校准方法计算量很大，需要使用无导数的迭代优化算法，这种算法通常需要数天才能收敛。本研究通过引入一种新颖、高效且有效的校准方法来应对这些挑战，该方法以人体L4 - L5椎间盘有限元模型为例进行了演示，使用神经网络（NN）代理模型。该神经网络代理模型能够高精度地预测模拟结果，优于其他机器学习模型，并显著降低了与传统有限元模拟相关的计算成本。接下来，提出了一种由神经网络代理模型的梯度引导的投影梯度下降（PGD）方法，以有效地校准有限元模型。我们的方法通过投影步骤明确地确保了可行性，从而在整个优化过程中保持材料边界。在合成和体外实验数据集上，将所提出的方法与最先进的遗传算法（GA）和逆模型基线进行了评估。我们的方法在合成数据上表现出卓越的性能，平均绝对误差（MAE）为0.06，而基线的MAE分别为0.18和0.54。在实验样本上，我们的方法在6个案例中的5个中优于基线。虽然我们的方法需要生成初始数据集并进行代理模型训练，但这些步骤只执行一次，实际校准时间不到三秒。相比之下，传统校准时间与样本数量呈线性关系，在最坏情况下需要长达8天。这种效率为应用更复杂的有限元模型铺平了道路，可能不仅限于椎间盘，并能够实现准确的患者特异性模拟。
