Deep learning-based surrogate model for 3-D patient-specific computational fluid dynamics (2204.08939v1)

Abstract: Optimization and uncertainty quantification have been playing an increasingly important role in computational hemodynamics. However, existing methods based on principled modeling and classic numerical techniques have faced significant challenges, particularly when it comes to complex 3D patient-specific shapes in the real world. First, it is notoriously challenging to parameterize the input space of arbitrarily complex 3-D geometries. Second, the process often involves massive forward simulations, which are extremely computationally demanding or even infeasible. We propose a novel deep learning surrogate modeling solution to address these challenges and enable rapid hemodynamic predictions. Specifically, a statistical generative model for 3-D patient-specific shapes is developed based on a small set of baseline patient-specific geometries. An unsupervised shape correspondence solution is used to enable geometric morphing and scalable shape synthesis statistically. Moreover, a simulation routine is developed for automatic data generation by automatic meshing, boundary setting, simulation, and post-processing. An efficient supervised learning solution is proposed to map the geometric inputs to the hemodynamics predictions in latent spaces. Numerical studies on aortic flows are conducted to demonstrate the effectiveness and merit of the proposed techniques.

• The paper introduces a deep-learning surrogate framework that maps patient-specific aorta shapes to high-resolution hemodynamic fields with remarkable computational speed.
• It employs PCA-based geometry parameterization and an automated CFD simulation pipeline to generate robust training data for optimized MLP networks.
• Results demonstrate <1–2% RMSE error and a 100,000x speedup, making the method valuable for real-time clinical support and many-query analyses.

This paper, "Deep learning-based surrogate model for 3-D patient-specific computational fluid dynamics" (Deep learning-based surrogate model for 3-D patient-specific computational fluid dynamics, 2022), addresses the significant challenges of computational expense and geometric complexity in applying computational fluid dynamics (CFD) to 3D patient-specific cardiovascular modeling. Traditional CFD requires substantial computational resources and expertise, making it slow for real-time clinical applications or many-query tasks like optimization and uncertainty quantification (UQ). Existing ML approaches often struggle with parameterizing complex 3D geometries and require large datasets, which are difficult to obtain from medical imaging.

The authors propose a novel deep learning surrogate modeling framework for rapid and comprehensive hemodynamic predictions in 3D patient-specific geometries. The core idea is to build a fast data-driven mapping from parameterized vascular geometry to high-resolution hemodynamic fields. The framework consists of three main components:

1. Patient-Specific Geometry Parameterization and Synthesis:
   • The method begins with a small set of patient-specific 3D geometries obtained from medical images (e.g., CTA/MRI), simplified by trimming branches to create homeomorphic structures.
   • An unsupervised shape correspondence is established among these geometries using a controlled-point-based large deformation diffeomorphic metric mapping (LDDMM) algorithm, implemented using the Deformetrica software. This aligns the geometries and allows for geometric morphing between shapes.
   • Principal Component Analysis (PCA) is applied to the registered geometries (represented as point clouds) to project them into a low-dimensional latent space, enabling concise parameterization of the complex 3D shapes.
   • A generative model synthesizes a large number of virtual aorta shapes by sampling from this latent geometric space. Two methods are explored: random linear interpolation and uniform PCA sampling. Uniform PCA sampling is shown to better cover the input space and is adopted for data generation.
2. Automatic CFD Simulation Routine:
   • To generate the large labeled dataset needed for ML training, a Python-based routine automates the entire CFD simulation workflow.
   • This includes geometry pre-processing (extension, smoothing, capping) using tools like the Vascular Modeling Toolkit (VMTK), automated 3D unstructured mesh generation, boundary condition setup (parabolic inlet velocity, zero-gradient outlet pressure, rigid walls), and solving the steady-state incompressible Navier-Stokes equations using the open-source platform OpenFOAM (specifically, the SIMPLE algorithm).
   • Post-processing involves projecting the simulated velocity, pressure, and wall shear stress (WSS) fields onto corresponding surface or volumetric mesh grids via nearest-neighbor interpolation.
   • This routine allows for parallel execution of many simulations to build a large dataset of geometric inputs and corresponding hemodynamic outputs.
3. ML-based Surrogate Model Training and Inference:
   • An encoding-decoding strategy is employed using PCA (or POD) to reduce the dimensionality of both the input geometries (already in PCA latent space) and the output hemodynamic fields (velocity, pressure, WSS). This decouples the encoding from the ML training and reduces learning complexity.
   • Separate multilayer perceptron (MLP) networks are trained to learn the non-linear mapping from the geometry latent space to the latent spaces of the desired hemodynamic fields (pressure, velocity, WSS). Rectified Linear Unit (ReLU) is used as the activation function.
   • Bayesian optimization using RAY-tune and the Asynchronous Successive Halving Algorithm (ASHA) is used to optimize the MLP architecture and hyperparameters (number of layers, neurons, batch size, learning rate) for each field of interest.
   • The performance is evaluated using the relative mean square error (RMSE) between the surrogate prediction and the CFD ground truth on a test set. Vector fields (velocity, WSS) are evaluated based on both vector components and magnitude.

The results demonstrate that the SSM approach effectively parameterizes complex aorta shapes and the uniform PCA sampling generates synthetic geometries that resemble real aortas and cover the shape variations observed in the original dataset. The trained DNN surrogate models achieve low relative errors (e.g., <1% for velocity magnitude, around 1-2% for pressure and WSS) when trained on 1,000 samples, and accuracy improves with larger training set sizes. Visual comparisons show good agreement between DNN predictions and CFD ground truth, although the surrogate is slightly less accurate in capturing sharp gradients or small fluctuations near stenosis regions, particularly for high-severity cases.

A key advantage highlighted is the prediction speed. While training the surrogate model (including data generation) requires significant offline computation (hundreds of CFD simulations), the online inference for a new geometry is extremely fast, taking less than 0.0012 seconds per prediction. This represents a speedup of approximately 100,000x compared to a full CFD simulation, making it suitable for applications requiring numerous model evaluations like UQ, optimization, or real-time clinical support.

The proposed DNN-based surrogate is compared to a state-of-the-art bi-fidelity (BF) surrogate model. The DNN model outperforms the BF model in both accuracy and efficiency (prediction cost) across different training sizes and hemodynamic fields. The DNN model also shows more robust performance in the small data regime.

In summary, the paper presents a practical framework for building fast and accurate surrogate models for 3D patient-specific hemodynamics. By combining statistical shape modeling for geometry handling, automated data generation, and deep learning within a latent space, it overcomes key challenges in applying traditional CFD for many-query and time-sensitive applications in cardiovascular medicine. The method is demonstrated for aortic flows but is presented as applicable to other anatomies.