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

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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mi>τ</mml:mi></mml:mrow> <mml:annotation>$$ \tau $$</mml:annotation></mml:semantics> </mml:math> and carefully selecting of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msub><mml:mi>D</mml:mi> <mml:mn>0</mml:mn></mml:msub> </mml:mrow> <mml:annotation>$$ {D}_0 $$</mml:annotation></mml:semantics> </mml:math> , with the best performance obtained when <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msub><mml:mi>D</mml:mi> <mml:mn>0</mml:mn></mml:msub> </mml:mrow> <mml:annotation>$$ {D}_0 $$</mml:annotation></mml:semantics> </mml:math> 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.