PHYSICS-BASED DECODING IMPROVES MAGNETIC RESONANCE FINGERPRINTING

Abstract

Magnetic Resonance Fingerprinting (MRF) is a promising paradigm to perform fast quantitative Magnetic Resonance Imaging (QMRI). However, existing MRF methods suffer from slow imaging speeds and poor generalization performance on radio frequency pulse sequences generated in various scenarios. To address these issues, we propose a novel MRI physics-informed learning approach for MRF. The proposed approach adopts a supervised encoder-decoder framework, where the encoder predicts the target tissue properties and the decoder reconstructs the inputs using the MRF physics. Specifically, the encoder embeds high-dimensional MRF time sequences into a low-dimensional tissue property space, while the decoder exploits an MRI physics model to reconstruct the input signals using the predicted tissue properties and associated MRI settings. It allows to learn better representations by integrating a fast and differentiable MRI physics model as the physics-informed regularization. The physics-based decoder improves the generalization performance and uniform stability by a considerable margin in practical out-of-distribution settings. Extensive experiments verified the effectiveness of the proposed physics-based decoding and achieved state-of-the-art performance on tissue property estimation.

1. INTRODUCTION

Quantitative Magnetic Resonance Imaging (QMRI) is used to identify tissue's intrinsic properties, such as the spin-lattice magnetic relaxation time (T1), the spin-spin magnetic relaxation time (T2), and other physical properties. Compared to conventional weighted (qualitative) MRI that focuses on tissue's contrast of brightness and darkness, QMRI reveals tissue's intrinsic properties with quantitative values and associated physical interpretations. Since different tissues are characterized by their distinct properties values, QMRI shows great potential to reduce subjectivity, with advantages in many areas including diagnosis, tissue characterization, investigation of disease pathologies, etc. [3, 30, 61] . Magnetic Resonance Fingerprinting (MRF) provides an alternative QMRI framework to achieve multi-property quantification simultaneously [43] . Given a pseudo-random radio frequency (RF) pulse sequence, a distinct magnetic response -a.k.a. fingerprint, signature, or signal evolutionfrom each specific tissue is observed and then used to predict the target tissue properties. Therefore, multi-property quantification boils down to an inverse problem that aims to infer underlying tissue properties from the magnetic responses. Various approaches have been developed to solve the MRF problem, using model-based techniques, e.g. dictionary matching (DM), compressive sensing, as well as learning-based / data-driven techniques [6, 8, 9, 11, 15, 16, 18, 25, 38, 43, 46, 47, 50, 55, 57, 58] . In spite of good performance in particular situations, they rarely take the MRI dynamics into consideration. This can cause reduced robustness and generalizability to potential data shifts occurred in practical scenarios with serious negative consequences. For example, the T1 and T2 value range and distribution are patient-specific and subject to pathological tissue types, development phase and other factors, which may cause label shift. In addition, as specific RF settings can often be applied to different situations, hospitals, and MRI instruments, MRF models are naturally expected to be able to handle such varied cases and be generalized to different RF settings. Motivated by these issues, we aim to develop a new MRF approach that combines the benefits of both model-based and learning-based techniques to achieve superior robustness and generalizability. In this work, we propose a physics-based model, called BlochNet, to learn generalizable representations for MRF, as shown in Fig. 1 . BlochNet adopts a supervised encoder-decoder framework where the encoder solves the inverse problem that predicts tissue properties from input magnetic responses, while the decoder leverages a Bloch equation based MRI physics model to reconstructs the input responses from the estimated tissue properties. The Bloch equations, a.k.a. equations of motion of nuclear magnetization, are a set of ordinary differential equations that model the magnetization dynamics and calculate the nuclear magnetization as a function of relaxation times T1 and T2 [4] . They enable the formulation of the magnetic response of a tissue with specific intrinsic properties T1, T2 under varied magnetic field (we provide more details in Section 3.3 and Appendix). The physics-based decoder acts as a causal regularization to perform supervised reconstruction to the input magnetic responses from estimated tissue properties as well as the associated pseudo-random excitation pulse sequence, such as repetition time (TR), time of echo (TE), and radio frequency flip angle (FA) over time. The rationale underlying the design is that domain knowledge such as physics principles can help to reduce the solution space of an inverse problem by applying additional constraints. This contributes to finding a better solution for an (ill-posed) inverse problem [31, 35, 41, 45] . Our results verify that the proposed model exhibits improved generalization performance from synthetic to real MRF data in two different out-of-distribution (OOD) settings, where the test data is generated from seen and unseen RF pulses in the first and second setting, respectively. Our major contributions include: • Our proposed method BlochNet is the first approach to incorporate physics-informed learning to solve MRF problems, where the Bloch equation-based MRI physics model serves as the decoder and guides the encoder to learn underlying robust representations by providing useful feedback for searching possible tissue properties. • Compared to earlier methods, BlochNet shows consistently better generalization performance across synthetic, phantom and real MRF data, and across different types of RF pulse sequences. This demonstrates well the benefits of physics-based decoding in MRF in practical scenarios. • We provide a fast and end-to-end solvable MRI physics model that can be used directly as a differentiable module in neural networks (e.g., it acts as a decoder in BlochNet).

2.1. MODEL-BASED AND LEARNING-BASED MRF APPROACHES

As tissue properties result in magnetic responses through the MRI dynamics, quantifying tissue's properties via QMRI/MRF is an typical anti-causal task. The core idea of MRF is based on fact that



Figure 1: Diagram of the proposed BlochNet, a physics-based encoder-decoder for MRF. BlochNet adopts a supervised encoder-decoder framework where the encoder solves an inverse problem that predicts tissue properties from input magnetic responses while the decoder leverages an Bloch equation based MRI physics model to reconstructs the input responses from the estimated tissue properties. Such design helps the encoder capture generalizable mapping effectively with the aid of physics-based feedback from the Bloch decoder.

