Physics Informed Neural Networks for Estimation of Tissue Properties from Multi-echo Configuration State MRI

Abstract

This work investigates the use of configuration state imaging together with deep neural networks to develop quantitative MRI techniques for deployment in an interventional setting. A physics modeling technique for inhomogeneous fields and heterogeneous tissues is presented and used to evaluate the theoretical capability of neural networks to estimate parameter maps from configuration state signal data. All tested normalization strategies achieved similar performance in estimating $T_2$ and $T_2^{*}$ . Varying network architecture and data normalization had substantial impacts on estimated flip angle and $T_1$ , highlighting their importance in developing neural networks to solve these inverse problems. The developed signal modeling technique provides an environment that will enable the development and evaluation of physics-informed machine learning techniques for MR parameter mapping and facilitate the development of quantitative MRI techniques to inform clinical decisions during MR-guided treatments.

Keywords: Physics informed neural networks; Quantitative MRI.

Fig.1.

Configuration state imaging encodes different information in each configuration state. a) Plot of the 0th moment under the frequency encoding gradient over time for a single repetition of the sequence sampling 4 configuration states at 3 echo times with monopolar readout gradients. As area accumulates under the frequency encoding gradient, different configuration states become coherent and measurable. b) Simulated signal magnitude for configuration states −2, −1, 0, +1 for varying combinations of flip angle and $T_1$ in water protons (scale adjusted for visualization).

Fig.2.

Regression plots of neural network parameter estimates (vertical axis) vs simulated parameter (horizontal axis) for networks trained with sample- (a–d) and pathway-based (e–h) normalization for $T_1$ (range 200–1800), $T_2$ (range 20–250), $T_2^{\mathrm{*}}$ (range 0–250), and achieved FA (range 2.5–22.5).

Fig.3.

Sample of real data acquired in salt pork and network evaluation results for $T_1$ (a–c) and $T_2$ (d–f). (a, d) Regression plots of performance estimating $T_1$ and $T_2$; (b, e) ground truth parameter maps; (c, f) parameter maps estimated using trained neural network.