[Paper Review] Dual Objective Approach Using A Convolutional Neural Network for Magnetic Resonance Elastography

Ligin Solamen, Yipeng Shi+1 more|arXiv (Cornell University)|Dec 2, 2018

Ultrasound Imaging and Elastography21 references4 citations

TL;DR

This paper proposes a novel convolutional neural network (CNN) architecture that directly maps magnetic resonance elastography (MRE) displacement data to elastograms, using a dual-loss training strategy combining mean squared error (MSE) and a physics-inspired loss derived from the Helmholtz equation. The method achieves high-fidelity elastogram reconstruction comparable to nonlinear inversion, demonstrating the feasibility of deep learning for efficient, accurate MRE tissue stiffness mapping.

ABSTRACT

Traditionally, nonlinear inversion, direct inversion, or wave estimation methods have been used for reconstructing images from MRE displacement data. In this work, we propose a convolutional neural network architecture that can map MRE displacement data directly into elastograms, circumventing the costly and computationally intensive classical approaches. In addition to the mean squared error reconstruction objective, we also introduce a secondary loss inspired by the MRE mechanical models for training the neural network. Our network is demonstrated to be effective for generating MRE images that compare well with equivalents from the nonlinear inversion method.

Motivation & Objective

• To overcome the computational burden and complexity of traditional nonlinear inversion methods in MRE by replacing them with a deep learning approach.
• To improve the generalization and physical plausibility of MRE elastogram reconstruction by incorporating mechanical model constraints into the neural network training.
• To demonstrate that a CNN can directly learn the inverse mapping from MRE displacement data to shear modulus elastograms without relying on iterative inversion algorithms.
• To evaluate the performance of the proposed method against standard nonlinear inversion using simulated MRE data across varying actuation frequencies.
• To explore the impact of a physics-based secondary loss function in enhancing the accuracy and robustness of deep learning-based elastography.

Proposed method

• The network employs an encoder-decoder CNN architecture with four 3D convolutional layers in the encoder and four transposed convolutional layers in the decoder, processing 64×64×3 displacement data to reconstruct a 64×64 elastogram.
• The encoder uses strided convolutions for downsampling without pooling layers, reducing parameters and preserving spatial information.
• A primary loss function based on mean squared error (MSE) ensures pixel-wise reconstruction accuracy between predicted and ground-truth elastograms.
• A secondary, physics-inspired loss is derived from the simplified Helmholtz equation (μ∇²u = −ω²ρu), enforcing consistency with the underlying mechanical model of shear wave propagation.
• The network is trained using the Adam optimizer with a batch size of 64 over 2,500 epochs on a Tesla K80 GPU, using a 70/30 training-testing split with a 30% validation subset.
• The training data is generated via a poroelastic mechanical model simulating shear wave propagation in soft tissue at various actuation frequencies (25–100 Hz).

Experimental results

Research questions

• RQ1 Can a deep convolutional neural network effectively learn the inverse mapping from MRE displacement data to elastograms without relying on classical inversion algorithms?
• RQ2 How does incorporating a physics-based loss function derived from the Helmholtz equation improve the accuracy and physical consistency of the reconstructed elastograms?
• RQ3 Does the dual-loss training strategy (MSE + physics loss) lead to better performance than MSE-only training in reconstructing complex stiffness patterns?
• RQ4 How does the proposed CNN perform on challenging cases such as low-contrast regions or high stiffness variations typical in brain MRE?
• RQ5 Can the network generalize across different actuation frequencies and maintain high reconstruction fidelity?

Key findings

• The proposed CNN successfully reconstructs elastograms that visually and quantitatively match those generated by the standard nonlinear inversion method across all tested actuation frequencies.
• The inclusion of the physics-inspired loss function significantly improves the network’s ability to preserve mechanical consistency, particularly in regions with high stiffness variation such as the brain.
• The network demonstrates robust performance on complex elastographic patterns, including areas with high stiffness gradients and low contrast, though minor deviations were observed in low-contrast regions.
• Training the network took approximately 2 hours on a Tesla K80 GPU, indicating a substantial speedup compared to iterative nonlinear inversion methods.
• The dual-loss approach outperforms MSE-only training by reducing artifacts and improving structural fidelity, as evidenced by visual comparisons in Figure 3.
• The method effectively circumvents the need for pre-processing steps such as patch partitioning, which were required in prior deep learning approaches to MRE.