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

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Abstract

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 ( <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>d</mi> <annotation>$d$</annotation></semantics> </math> ), intracellular diffusion coefficient ( <math xmlns="http://www.w3.org/1998/Math/MathML"> <semantics><msub><mi>D</mi> <mrow><mi>i</mi> <mi>n</mi></mrow> </msub> <annotation>$D_{in}$</annotation></semantics> </math> ), intracellular volume fraction ( <math xmlns="http://www.w3.org/1998/Math/MathML"> <semantics><msub><mi>V</mi> <mrow><mi>i</mi> <mi>n</mi></mrow> </msub> <annotation>$V_{in}$</annotation></semantics> </math> ), extracellular diffusion coefficient ( <math xmlns="http://www.w3.org/1998/Math/MathML"> <semantics><msub><mi>D</mi> <mrow><mi>e</mi> <mi>x</mi></mrow> </msub> <annotation>$D_{ex}$</annotation></semantics> </math> ), and the slope of <math xmlns="http://www.w3.org/1998/Math/MathML"> <semantics><msub><mi>D</mi> <mrow><mi>e</mi> <mi>x</mi></mrow> </msub> <annotation>$D_{ex}$</annotation></semantics> </math> with respect to oscillation frequency ( <math xmlns="http://www.w3.org/1998/Math/MathML"> <semantics><msub><mi>β</mi> <mrow><mi>e</mi> <mi>x</mi></mrow> </msub> <annotation>$\beta _{ex}$</annotation></semantics> </math> ). 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 <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>d</mi> <annotation>$d$</annotation></semantics> </math> , <math xmlns="http://www.w3.org/1998/Math/MathML"> <semantics><msub><mi>V</mi> <mrow><mi>i</mi> <mi>n</mi></mrow> </msub> <annotation>$V_{in}$</annotation></semantics> </math> , and <math xmlns="http://www.w3.org/1998/Math/MathML"> <semantics><msub><mi>D</mi> <mrow><mi>e</mi> <mi>x</mi></mrow> </msub> <annotation>$D_{ex}$</annotation></semantics> </math> 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  <math xmlns="http://www.w3.org/1998/Math/MathML"> <semantics><mrow><mi>μ</mi> <mi>m</mi></mrow> <annotation>$\mu{\rm m}$</annotation></semantics> </math> for <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>d</mi> <annotation>$d$</annotation></semantics> </math> , 5.06% for <math xmlns="http://www.w3.org/1998/Math/MathML"> <semantics><msub><mi>V</mi> <mrow><mi>i</mi> <mi>n</mi></mrow> </msub> <annotation>$V_{in}$</annotation></semantics> </math> , and 0.28  <math xmlns="http://www.w3.org/1998/Math/MathML"> <semantics><mrow><mi>μ</mi> <msup><mi>m</mi> <mn>2</mn></msup> </mrow> <annotation>$\mu{\rm m}^2$</annotation></semantics> </math> /ms for <math xmlns="http://www.w3.org/1998/Math/MathML"> <semantics><msub><mi>D</mi> <mrow><mi>e</mi> <mi>x</mi></mrow> </msub> <annotation>$D_{ex}$</annotation></semantics> </math> . 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.

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