Institute of Applied Mechanics, RWTH Aachen University, Germany.
Institute of Applied Mechanics, RWTH Aachen University, Germany.
Comput Methods Programs Biomed. 2024 Dec;257:108466. doi: 10.1016/j.cmpb.2024.108466. Epub 2024 Oct 25.
The intricate process of coronary in-stent restenosis (ISR) involves the interplay between different mediators, including platelet-derived growth factor, transforming growth factor-β, extracellular matrix, smooth muscle cells, endothelial cells, and drug elution from the stent. Modeling such complex multiphysics phenomena demands extensive computational resources and time.
This paper proposes a novel non-intrusive data-driven reduced order modeling approach for the underlying multiphysics time-dependent parametrized problem. In the offline phase, a 3D convolutional autoencoder, comprising an encoder and decoder, is trained to achieve dimensionality reduction. The encoder condenses the full-order solution into a lower-dimensional latent space, while the decoder facilitates the reconstruction of the full solution from the latent space. To deal with the 5D input datasets (3D geometry + time series + multiple output channels), two ingredients are explored. The first approach incorporates time as an additional parameter and applies 3D convolution on individual time steps, encoding a distinct latent variable for each parameter instance within each time step. The second approach reshapes the 3D geometry into a 2D plane along a less interactive axis and stacks all time steps in the third direction for each parameter instance. This rearrangement generates a larger and complete dataset for one parameter instance, resulting in a singular latent variable across the entire discrete time-series. In both approaches, the multiple outputs are considered automatically in the convolutions. Moreover, Gaussian process regression is applied to establish correlations between the latent variable and the input parameter.
The constitutive model reveals a significant acceleration in neointimal growth between 30-60 days post percutaneous coronary intervention (PCI). The surrogate models applying both approaches exhibit high accuracy in pointwise error, with the first approach showcasing smaller errors across the entire evaluation period for all outputs. The parameter study on drug dosage against ISR rates provides noteworthy insights of neointimal growth, where the nonlinear dependence of ISR rates on the peak drug flux exhibits intriguing periodic patterns. Applying the trained model, the rate of ISR is effectively evaluated, and the optimal parameter range for drug dosage is identified.
The demonstrated non-intrusive reduced order surrogate model proves to be a powerful tool for predicting ISR outcomes. Moreover, the proposed method lays the foundation for real-time simulations and optimization of PCI parameters.
冠状动脉支架内再狭窄（ISR）的复杂过程涉及到不同介质的相互作用，包括血小板衍生生长因子、转化生长因子-β、细胞外基质、平滑肌细胞、内皮细胞和支架洗脱的药物。模拟这种复杂的多物理现象需要大量的计算资源和时间。
本文提出了一种新颖的非侵入式数据驱动的降阶建模方法，用于处理基础的多物理时变参数化问题。在离线阶段，使用 3D 卷积自动编码器（包含编码器和解码器）对全阶解进行训练，以实现降维。编码器将全阶解压缩到低维潜在空间，解码器则从潜在空间重构全阶解。为了处理 5D 输入数据集（3D 几何形状+时间序列+多个输出通道），本文探索了两种方法。第一种方法将时间作为附加参数，对各个时间步进行 3D 卷积，为每个时间步内的每个参数实例编码一个独特的潜在变量。第二种方法将 3D 几何形状沿着交互性较小的轴展平到 2D 平面，并在第三个方向上堆叠每个参数实例的所有时间步。这种重排为每个参数实例生成了一个更大、更完整的数据集，从而在整个离散时间序列中产生了一个单一的潜在变量。在这两种方法中，卷积自动编码器自动考虑多个输出。此外，还应用了高斯过程回归来建立潜在变量和输入参数之间的相关性。
本构模型揭示了经皮冠状动脉介入治疗（PCI）后 30-60 天内新生内膜的显著生长。应用这两种方法的替代模型在逐点误差方面都表现出了很高的准确性，第一种方法在整个评估期间所有输出的误差都更小。针对药物剂量与 ISR 发生率的参数研究提供了关于新生内膜生长的有价值的见解，其中 ISR 发生率对峰值药物通量的非线性依赖性呈现出有趣的周期性模式。应用训练好的模型，可以有效地评估 ISR 的发生率，并确定药物剂量的最佳参数范围。
所展示的非侵入式降阶替代模型被证明是预测 ISR 结果的有力工具。此外，该方法为 PCI 参数的实时模拟和优化奠定了基础。
