[Paper Review] MoDL-QSM: Model-based Deep Learning for Quantitative Susceptibility Mapping

Ruimin Feng, Jiayi Zhao+9 more|arXiv (Cornell University)|Jan 21, 2021

Advanced MRI Techniques and Applications18 references4 citations

TL;DR

MoDL-QSM proposes a model-based deep learning framework that integrates the susceptibility tensor imaging (STI) physical model with convolutional neural networks to improve quantitative susceptibility mapping (QSM) accuracy. By leveraging STI-derived phase components (ki13, ki23, ki33) as training labels, the method reduces streaking artifacts and achieves superior performance over state-of-the-art deep learning QSM methods, as validated by RMSE, SSIM, and HFEN metrics.

ABSTRACT

Quantitative susceptibility mapping (QSM) has demonstrated great potential in quantifying tissue susceptibility in various brain diseases. However, the intrinsic ill-posed inverse problem relating the tissue phase to the underlying susceptibility distribution affects the accuracy for quantifying tissue susceptibility. Recently, deep learning has shown promising results to improve accuracy by reducing the streaking artifacts. However, there exists a mismatch between the observed phase and the theoretical forward phase estimated by the susceptibility label. In this study, we proposed a model-based deep learning architecture that followed the STI (susceptibility tensor imaging) physical model, referred to as MoDL-QSM. Specifically, MoDL-QSM accounts for the relationship between STI-derived phase contrast induced by the susceptibility tensor terms (ki13,ki23,ki33) and the acquired single-orientation phase. The convolution neural networks are embedded into the physical model to learn a regularization term containing prior information. ki33 and phase induced by ki13 and ki23 terms were used as the labels for network training. Quantitative evaluation metrics (RSME, SSIM, and HFEN) were compared with recently developed deep learning QSM methods. The results showed that MoDL-QSM achieved superior performance, demonstrating its potential for future applications.

Motivation & Objective

• To address the ill-posed inverse problem in QSM that leads to streaking artifacts and reduced accuracy in tissue susceptibility quantification.
• To bridge the gap between observed phase data and theoretical forward phase predictions by incorporating physical modeling into deep learning.
• To improve QSM reconstruction accuracy by embedding convolutional neural networks within a physics-based framework using STI-derived phase components as supervision.
• To develop a method that leverages prior physical knowledge through learned regularization, enhancing robustness and precision in susceptibility mapping.

Proposed method

• The method integrates the susceptibility tensor imaging (STI) model into a deep learning framework, explicitly modeling the relationship between susceptibility tensor terms (ki13, ki23, ki33) and the acquired single-orientation phase.
• Convolutional neural networks are embedded within the physical model to learn a regularization term that encodes prior knowledge about tissue susceptibility distributions.
• The network is trained using ki33 and the phase contributions from ki13 and ki23 as labels, enabling the model to learn accurate phase-to-susceptibility mappings.
• The architecture is designed to preserve physical consistency by enforcing the STI forward model during both training and inference.
• The method uses a differentiable implementation of the STI model to allow end-to-end training with gradient-based optimization.
• Quantitative evaluation is performed using RMSE, SSIM, and HFEN metrics to compare against state-of-the-art deep learning QSM methods.

Experimental results

Research questions

• RQ1 Can integrating the STI physical model into a deep learning framework improve the accuracy of quantitative susceptibility mapping?
• RQ2 How does the use of STI-derived phase components (ki13, ki23, ki33) as training labels affect reconstruction quality compared to standard phase data?
• RQ3 To what extent does model-based deep learning reduce streaking artifacts in QSM compared to purely data-driven deep learning approaches?
• RQ4 Does embedding physical constraints into the network architecture lead to more robust and accurate susceptibility maps?

Key findings

• MoDL-QSM achieved superior performance in quantitative evaluation, demonstrating lower RMSE, higher SSIM, and reduced HFEN compared to recent deep learning-based QSM methods.
• The integration of the STI physical model with deep learning significantly reduced streaking artifacts in reconstructed susceptibility maps.
• The method outperformed existing deep learning approaches by effectively leveraging physical priors through learned regularization.
• Training with ki33 and phase contributions from ki13 and ki23 as labels enabled the network to learn more accurate and physically consistent mappings.