Development of Physics-Informed Neural for Computational Magnetic Resonance Imaging of Noradrenergic Neurons

Abstract

Recently, magnetic resonance imaging (MRI) method has been applied to a transgenic model of Alzheimer’s disease demonstrating its potential use in neuroradiology. Since a decline in locus coeruleus (LC) neuron numbers is associated with aging, dementia, Aβ plaque load, and the progression of Alzheimer’s disease, MRI of Noradrenergic (NA) neurons has been proposed to play an increasing role in translational biomedical research of neurodegenerative diseases. MRI methods are currently being explored for testing whether NA imaging is related to disease progression in neurodegenerative diseases. Characterization of the relationship between MRI measures and neuropathology would be crucial in this direction. This study proposes a characterization method using MR relaxometry and physics-informed neural network. T1 and T2 relaxation times have been known to be fundamental diagnostic feature in MRI assessment. Since noradrenergic neurons have abundant water protons interacting with paramagnetic ions in active cells and molecules, the spin dynamics must be consistent with the Bloch NMR flow equation. Under transient condition, the Bloch NMR flow equation is given as eqn (1). Subject to eqn (2), an analytical solution to eqn (1) is given in eqn (3). This equation has been used to generate training and testing data for a NetChain model using Wolfram Mathematica programming. In the traditional neural network, a simple net class with net function that takes 4 arguments (1 input, 1 outputs, 100 hidden neurons per layer, and 4 layers). The final model was then implemented and tested with relaxometric data presented in table 1. Other parameters used are: C1 = C2 = −0.01, M0 = 50A/m, ω = 28Hz.