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

TL;DR

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 by formulating a numerical ODE solver to function as a step-wise analytical one, thereby making it compatible with automatic differentiation-based optimization.

Abstract

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 $\pm$ 8.3 minutes. Reusing the single-subject-trained network for inference in new subjects took 1.0 $\pm$ 0.2 s, to provide results in agreement with literature values and scan-specific fit results.

Figures (14)

• Figure 1: Schematic representation of the core neural Bloch McConnell fitting (NBMF) pipeline. A quantitative parameter reconstructor parameterized as a multi-layer perceptron (MLP) and a differentiable Bloch-McConnell simulator are serially connected into a single computational graph. Single-subject MRF data serves both as the input and as the regression target for the reconstructor-simulator circuit. The network convergence (a) provides the fitted exchange parameter maps for the examined subject as well as a trained NN reconstructor; the latter can be used to extract parameter maps for new subjects within seconds (b). The simulator can be realized using the exact numerical Bloch McConnell ODE solver or using analytical approximations when available (e.g., for 2-pool semisolid-MT quantification Roeloffs2015). While not shown in the diagram, auxiliary per-voxel data such as T$_1$, T$_2$, B$_0$, and B$_1$ maps can be added as input to the neural reconstructor and the simulator. Furthermore, the pipeline main block can be serially repeated so that estimated semisolid MT volume fraction (f$_{ss}$) and proton exchange rate (k$_{ssw}$) maps inferred at the first stage are joined to the raw data used in a second reconstructor aimed to quantify the amide proton exchange parameters (f$_s$, k$_{sw}$).
• Figure 1: Single-voxel uncertainty and bias analysis in-vitro. Each panel describes a single voxel taken from the center of the respective L-arginine vial shown in Fig. 2. Dot-product matching was performed with all dictionary entries in the {[L-arg], k$_{sw}$} parameter space to create modeling error maps, dictionary-based minima estimates, and NRMSE at c$\times$NRMSE$_{min}$, c=1.1, 1.25, 1.5, 1.75.
• Figure 2: In-vitro study. L-arginine samples were imaged using a pulsed CEST-MRF protocol in a 3T clinical scanner. The NBMF-based L-arginine concentrations (a) and proton exchange-rates (b) were in good agreement with those obtained by dictionary-based pattern matching (c, and d, respectively). The ground truth L-arginine concentrations and pH values are mentioned in white text next to each vial. The pixelwise distributions are further compared in (e,f). Each point in the swarm plot reflects a single 1.8 mm x 1.8 mm x 5.4 mm voxel.
• Figure 2: In-vitro CEST experiment analysis. Comparing VBMF (top) and NBMF (bottom) quantitative estimates of concentration (left) and exchange rate (right) to those obtained using traditional dictionary matchingvladimirov2024quantitative.
• Figure 3: NBMF-based quantification of the semisolid MT proton exchange parameters in the healthy in-vivo human brain. (a-c) Representative reconstructed parameter maps of the semisolid-MT proton volume fraction (a) and exchange rate (b), alongside a fidelity estimation (c) of the data-model agreement, computed as $R^2$=1-NMSE (normalized mean square error). (d-e) Statistical analysis of the resulting proton exchange parameter values across the brain white matter and gray matter (WM/GM) regions of interest (box-plots, n=47K/65K), compared to literature (colored markers)Stanisz2005Liu2013Heo2019Perlman2022_NatureBME_ApoptosisWeigand-Whittier2023.