# Multi-Parameter Molecular MRI Quantification using Physics-Informed Self-Supervised Learning

arXiv: https://arxiv.org/abs/2411.06447 · HTML: https://mlsanity.com/paper/2411.06447/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 95 references that are in the map.
- First posted on arXiv 10 Nov 2024.

## Builds on (most cited first, 17 of 17)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)
- [Physics-informed neural networks (PINNs) for fluid mechanics: A review](https://mlsanity.com/paper/2105.09506/) (2021)
- ["Zero-Shot" Super-Resolution using Deep Internal Learning](https://mlsanity.com/paper/1712.06087/) (2017)
- [Machine learning in cardiovascular flows modeling: Predicting arterial blood pressure from non-invasive 4D flow MRI data using physics-informed neural networks](https://mlsanity.com/paper/1905.04817/) (2019)
- [Zero-Shot Self-Supervised Learning for MRI Reconstruction](https://mlsanity.com/paper/2102.07737/) (2021)
- [MR fingerprinting Deep RecOnstruction NEtwork (DRONE)](https://mlsanity.com/paper/1710.05267/) (2017)
- [Generative ODE Modeling with Known Unknowns](https://mlsanity.com/paper/2003.10775/) (2020)
- [Investigating molecular transport in the human brain from MRI with physics-informed neural networks](https://mlsanity.com/paper/2205.02592/) (2022)
- [MRzero -- Fully automated discovery of MRI sequences using supervised learning](https://mlsanity.com/paper/2002.04265/) (2020)
- [Regularization of Inverse Problems by Neural Networks](https://mlsanity.com/paper/2006.03972/) (2020)
- [Joint Design of RF and gradient waveforms via auto-differentiation for 3D tailored excitation in MRI](https://mlsanity.com/paper/2008.10594/) (2020)
- [CEST MR fingerprinting (CEST-MRF) for Brain Tumor Quantification Using EPI Readout and Deep Learning Reconstruction](https://mlsanity.com/paper/2108.08333/) (2021)
- [Accelerated and Quantitative 3D Semisolid MT/CEST Imaging using a Generative Adversarial Network (GAN-CEST)](https://mlsanity.com/paper/2207.11297/) (2022)
- [Dynamic and Rapid Deep Synthesis of Molecular MRI Signals](https://mlsanity.com/paper/2305.19413/) (2023)
- [A Test-Time Learning Approach to Reparameterize the Geophysical Inverse Problem with a Convolutional Neural Network](https://mlsanity.com/paper/2312.04752/) (2023)

## Built on by (most cited first, 3 of 3)

- [Quantitative multi-metabolite imaging of Parkinson's disease using AI boosted molecular MRI](https://mlsanity.com/paper/2507.11329/) (2025)
- [Multiparameter Uncertainty Mapping in Quantitative Molecular MRI using a Physics-Structured Variational Autoencoder (PS-VAE)](https://mlsanity.com/paper/2602.03317/) (2026)
- [DA-UCT: Self-Supervised Domain-Adaptive Ultrasound Computed Tomography for Rapid Musculoskeletal Sound Speed Reconstruction](https://mlsanity.com/paper/2605.25024/) (2026)

## Abstract (arXiv)

Biophysical model fitting plays a key role in obtaining quantitative parameters from physiological signals and images. However, the model complexity for molecular magnetic resonance imaging (MRI) often translates into excessive computation time, which makes clinical use impractical. Here, we present a generic computational approach for solving the parameter extraction inverse problem posed by ordinary differential equation (ODE) modeling coupled with experimental measurement of the system dynamics. This is achieved by formulating a numerical ODE solver to function as a step-wise analytical one, thereby making it compatible with automatic differentiation-based optimization. This enables efficient gradient-based model fitting, and provides a new approach to parameter quantification based on self-supervised learning from a single data observation. The neural-network-based train-by-fit pipeline was used to quantify semisolid magnetization transfer (MT) and chemical exchange saturation transfer (CEST) amide proton exchange parameters in the human brain, in an in-vivo molecular MRI study (n = 4). The entire pipeline of the first whole brain quantification was completed in 18.3 ± 8.3 minutes. Reusing the single-subject-trained network for inference in new subjects took 1.0 ± 0.2 s, to provide results in agreement with literature values and scan-specific fit results.