Investigating the uncertainty of cellular microenvironment parameter estimations via diffusion MRI cytometry

Cell microenvironment characteristics serve as critical biomarkers for early tumor response assessment in radiation therapy. Diffusion MRI (dMRI) provides a noninvasive approach to probe these microenvironment features; however, conventional model-fitting approaches for microenvironment parameter estimation often suffer from high uncertainty and poor robustness.

This study aims to establish a theoretical foundation for identifying cell microenvironment parameters that can be robustly estimated from signals of IMPULSED dMRI and to develop a reliable mapping-based estimation framework for these parameters.

We simulated dMRI signals using the well-established IMPULSED model, incorporating a pulsed gradient spin echo (PGSE) sequence and two oscillating gradient spin echo (OGSE) sequences with two different frequencies. The simulations were based on five cellular parameters: cell diameter ( $d$ ), intracellular diffusion coefficient ( $D_{in}$ ), intracellular volume fraction ( $V_{in}$ ), extracellular diffusion coefficient ( $D_{ex}$ ), and the slope of $D_{ex}$ with respect to oscillation frequency ( ${\beta }_{ex}$ ). Parameter uncertainty was quantified using Jacobian-based sensitivity analysis at a signal-to-noise ratio (SNR) of 30, corresponding to achievable clinical conditions on a 1.5T MRI scanner. To develop direct parameter mapping models, dMRI signals were logarithmically transformed to enhance linearity and reduced in dimension using principal component analysis (PCA). The logarithm-transformed dimension-reduced data were used to estimate microenvironment parameters using three mapping models: linear regression, fourth-order polynomial regression, and a fully connected 4-layer neural network. Model validation was further performed in an in vitro experiment using MC38 cell lines.

Uncertainty analysis identified $d$ , $V_{in}$ , and $D_{ex}$ as robustly derivable parameters, each with relative uncertainty below 1.0. Among the models considered, the 4-layer neural network achieved the best performance, yielding mean absolute errors (MAE) of 1.7  $\mu m$ for $d$ , 5.06% for $V_{in}$ , and 0.28  $\mu m^2$ /ms for $D_{ex}$ . In the in vitro experiment, the model achieved a 6.7% error in cell diameter estimation.

This study identified the cell microenvironment parameters that can be robustly estimated from IMPULSED dMRI signals and established a mapping-based framework for accurate and robust parameter estimation. The proposed approach provided a foundation for noninvasive, quantitative assessment of tumor microenvironment changes for monitoring radiation therapy response.