# MoDL-QSM: Model-based Deep Learning for Quantitative Susceptibility Mapping

arXiv: https://arxiv.org/abs/2101.08413 · HTML: https://mlsanity.com/paper/2101.08413/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 64 references that are in the map.
- First posted on arXiv 21 Jan 2021.

## Builds on (most cited first, 11 of 11)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [Learning a Variational Network for Reconstruction of Accelerated MRI Data](https://mlsanity.com/paper/1704.00447/) (2017)
- [Quantitative Susceptibility Mapping using Deep Neural Network: QSMnet](https://mlsanity.com/paper/1803.05627/) (2018)
- [Exploring linearity of deep neural network trained QSM: QSMnet+](https://mlsanity.com/paper/1909.07716/) (2019)
- [QSMGAN: Improved Quantitative Susceptibility Mapping using 3D Generative Adversarial Networks with Increased Receptive Field](https://mlsanity.com/paper/1905.03356/) (2019)
- [Learned Proximal Networks for Quantitative Susceptibility Mapping](https://mlsanity.com/paper/2008.05024/) (2020)
- [Learning-based Single-step Quantitative Susceptibility Mapping Reconstruction Without Brain Extraction](https://mlsanity.com/paper/1905.05953/) (2019)
- [Nonlinear Dipole Inversion (NDI) enables Quantitative Susceptibility Mapping (QSM) without parameter tuning](https://mlsanity.com/paper/1909.13692/) (2019)

## Built on by (most cited first, 8 of 8)

- [Physics-Driven Deep Learning for Computational Magnetic Resonance Imaging](https://mlsanity.com/paper/2203.12215/) (2022)
- [Diffusion Modeling with Domain-conditioned Prior Guidance for Accelerated MRI and qMRI Reconstruction](https://mlsanity.com/paper/2309.00783/) (2023)
- [Quantitative Susceptibility Mapping through Model-based Deep Image Prior (MoDIP)](https://mlsanity.com/paper/2308.09467/) (2023)
- [Affine Transformation Edited and Refined Deep Neural Network for Quantitative Susceptibility Mapping](https://mlsanity.com/paper/2211.13942/) (2022)
- [Accelerating multiparametric quantitative MRI using self-supervised scan-specific implicit neural representation with model reinforcement](https://mlsanity.com/paper/2508.00891/) (2025)
- [NeXtQSM -- A complete deep learning pipeline for data-consistent quantitative susceptibility mapping trained with hybrid data](https://mlsanity.com/paper/2107.07752/) (2021)
- [High-pass filtered fidelity-imposed network edit (HP-FINE) for robust quantitative susceptibility mapping from high-pass filtered phase](https://mlsanity.com/paper/2305.03844/) (2023)
- [IR2QSM: Quantitative Susceptibility Mapping via Deep Neural Networks with Iterative Reverse Concatenations and Recurrent Modules](https://mlsanity.com/paper/2406.12300/) (2024)

## Abstract (arXiv)

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.