# Physics-informed neural networks for myocardial perfusion MRI quantification

arXiv: https://arxiv.org/abs/2011.12844 · HTML: https://mlsanity.com/paper/2011.12844/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Nov 2020.

## Built on by (most cited first, 18 of 18)

- [Mitigating Propagation Failures in Physics-informed Neural Networks using Retain-Resample-Release (R3) Sampling](https://mlsanity.com/paper/2207.02338/) (2022)
- [Physics-Informed Computer Vision: A Review and Perspectives](https://mlsanity.com/paper/2305.18035/) (2023)
- [Physics-driven Synthetic Data Learning for Biomedical Magnetic Resonance](https://mlsanity.com/paper/2203.11178/) (2022)
- [Med-Real2Sim: Non-Invasive Medical Digital Twins using Physics-Informed Self-Supervised Learning](https://mlsanity.com/paper/2403.00177/) (2024)
- [Physics-Informed Machine Learning in Biomedical Science and Engineering](https://mlsanity.com/paper/2510.05433/) (2025)
- [Point Neuron Learning: A New Physics-Informed Neural Network Architecture](https://mlsanity.com/paper/2408.16969/) (2024)
- [Towards Optimally Weighted Physics-Informed Neural Networks in Ocean Modelling](https://mlsanity.com/paper/2106.08747/) (2021)
- [Utilising physics-guided deep learning to overcome data scarcity](https://mlsanity.com/paper/2211.15664/) (2022)
- [A Novel Training Framework for Physics-informed Neural Networks: Towards Real-time Applications in Ultrafast Ultrasound Blood Flow Imaging](https://mlsanity.com/paper/2309.04755/) (2023)
- [Gradient Flow Based Phase-Field Modeling Using Separable Neural Networks](https://mlsanity.com/paper/2405.06119/) (2024)
- [An Analysis of Physics-Informed Neural Networks](https://mlsanity.com/paper/2303.02890/) (2023)
- [Quantitative Analysis of Molecular Transport in the Extracellular Space Using Physics-Informed Neural Network](https://mlsanity.com/paper/2401.12435/) (2024)
- [Learning Traveling Solitary Waves Using Separable Gaussian Neural Networks](https://mlsanity.com/paper/2403.04883/) (2024)
- [PINNing Cerebral Blood Flow: Analysis of Perfusion MRI in Infants using Physics-Informed Neural Networks](https://mlsanity.com/paper/2410.19759/) (2024)
- [Are Statistical Methods Obsolete in the Era of Deep Learning? A Study of ODE Inverse Problems](https://mlsanity.com/paper/2505.21723/) (2025)
- [Deep learning motion correction of quantitative stress perfusion cardiovascular magnetic resonance](https://mlsanity.com/paper/2510.00723/) (2025)
- [MARVEL: Universal Murray's Law-informed Vessel Tree Segmentation and Topology Estimation](https://mlsanity.com/paper/2605.25363/) (2026)
- [Physics-Informed Implicit Neural Representations for Improved Myocardial Perfusion MRI Quantification](https://mlsanity.com/paper/2608.11282/) (2026)

## Abstract (arXiv)

Tracer-kinetic models allow for the quantification of kinetic parameters such as blood flow from dynamic contrast-enhanced magnetic resonance (MR) images. Fitting the observed data with multi-compartment exchange models is desirable, as they are physiologically plausible and resolve directly for blood flow and microvascular function. However, the reliability of model fitting is limited by the low signal-to-noise ratio, temporal resolution, and acquisition length. This may result in inaccurate parameter estimates. This study introduces physics-informed neural networks (PINNs) as a means to perform myocardial perfusion MR quantification, which provides a versatile scheme for the inference of kinetic parameters. These neural networks can be trained to fit the observed perfusion MR data while respecting the underlying physical conservation laws described by a multi-compartment exchange model. Here, we provide a framework for the implementation of PINNs in myocardial perfusion MR. The approach is validated both in silico and in vivo. In the in silico study, an overall reduction in mean-squared error with the ground-truth parameters was observed compared to a standard non-linear least squares fitting approach. The in vivo study demonstrates that the method produces parameter values comparable to those previously found in literature, as well as providing parameter maps which match the clinical diagnosis of patients.