# Modeling, Evaluation, and In Vivo Estimation of Muscle Cell Diameter With the Random Permeable Barrier Model: Correlation With Subject Characteristics and Isometric Torque

## TL;DR

This study evaluates a model for estimating muscle cell diameter and finds that it can provide useful insights into muscle microstructure, especially when considering sex differences.

## Contribution

The study provides a comprehensive evaluation of the RPBM model and identifies optimal parameter constraints for stable estimates.

## Key findings

- Stable RPBM estimates require constraining τ and fixing D0 at ~0.9 of axial diffusivity at long diffusion times.
- Muscle cell diameter varies across muscle groups and is strongly influenced by sex.
- No significant correlation was found between muscle cell diameter and isometric torque.

## Abstract

The random permeable barrier model (RPBM) links the time‐dependent behavior of water diffusion in muscle tissue to its microstructure enabling estimation of average muscle cell diameter and membrane permeability. While RPBM has gained traction, few studies have examined the stability and limitations of the fitting process. Moreover, the added value of RPBM‐derived parameters compared with conventional diffusion tensor imaging metrics, and their relationship to subject characteristics and muscle function in healthy populations, remains underexplored. In this study, we comprehensively evaluated the RPBM by analyzing its forward behavior through simulations and its inverse behavior through model fitting. We further quantified muscle cell diameters across six muscle groups in 100 healthy adults and investigated how the derived parameters relate to DTI metrics, subject characteristics, and isometric muscle torque. The simulations showed that similar RPBM signals can arise from multiple parameter combinations and that the most stable estimates of cell diameter and membrane permeability were achieved by constraining τ and carefully selecting of D0, with the best performance obtained when D0 was fixed at 0.9 the axial diffusivity at long diffusion times. In vivo, muscle cell diameter differed across all muscle groups, and sex emerged as a strong determinant, with men exhibiting consistently larger cell diameters than women, independent of height and weight. However, no significant correlation was observed between peak torque and either cell diameter or membrane permeability. In conclusion, this study provides a comprehensive assessment of RPBM in healthy muscle and highlights its potential as a complementary tool to traditional diffusion metrics, particularly for studies of muscle health, development, and pathology, provided that its modeling limitations are carefully addressed.

We evaluated the random permeable barrier model (RPBM) through simulations, model fitting, and in vivo analysis of 100 healthy adults. Simulations showed that stable estimates of muscle cell diameter and membrane permeability require constraining τ and fixing D
0 at ~0.9 of axial diffusivity at long diffusion times. In vivo, muscle cell diameter varied across muscle groups and was strongly influenced by sex, while no correlation with muscle torque was found, highlighting RPBM's potential as a complementary diffusion metric.