Data-driven reduced order surrogate modeling for coronary in-stent restenosis

Background:

The intricate process of coronary in-stent restenosis (ISR) involves the interplay between different mediators, including platelet-derived growth factor, transforming growth factor-$\beta$, extracellular matrix, smooth muscle cells, endothelial cells, and drug elution from the stent. Modeling such complex multiphysics phenomena demands extensive computational resources and time.

Methods:

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.

Results:

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.

Conclusion:

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.