A Transient Microsphere Model for Nonlinear Viscoelasticity in Dynamic Polymer Networks

Viscoelastic material behavior in polymer systems largely arises from dynamic topological rearrangement at the network level. In this paper, we present a physically motivated microsphere formulation for modeling the mechanics of transient polymer networks. By following the directional statistics of chain alignment and local chain stretch, the transient microsphere model (TMM) is fully anisotropic and micro-mechanically based. Network evolution is tracked throughout deformation using a Fokker–Planck equation that incorporates the effects of bond creation and deletion at rates that are sensitive to the chain-level environment. Using published data, we demonstrate the model to capture various material responses observed in physical polymers.

Diffusion Tensor Imaging Group Analysis Using Tract Profiling and Directional Statistics

Group analysis in diffusion tensor imaging is challenging. Comparisons of tensor morphology across groups have typically been performed on scalar measures of diffusivity, such as fractional anisotropy (FA), disregarding the complex three-dimensional morphologies of diffusion tensors. Scalar measures consider only the magnitude of the diffusion but not directions. In the present study, we have introduced a new approach based on directional statistics to use directional information of diffusion tensors in statistical group analysis based on Bingham distribution. We have investigated different directional statistical models to find the best fit. During the experiments, we confirmed that carrying out directional statistical analysis along the tract is much more effective than voxel- or skeleton-guided directional statistics. Hence, we propose a new method called tract profiling and directional statistics (TPDS) applicable to fiber bundles. As a case study, the method has been applied to identify connectivity differences of patients with major depressive disorder. The results obtained with the directional statistic-based analysis are consistent with those of NBS, but additionally, we found significant changes in the right hemisphere striatum, ACC, and prefrontal, parietal, temporal, and occipital connections as well as left hemispheric differences in the limbic areas such as the thalamus, amygdala, and hippocampus. The results are also evaluated with respect to fiber lengths. Comparison with the output of the network-based statistical toolbox indicated that the benefit of the proposed method becomes much more distinctive as the tract length increases. The likelihood of finding clusters of voxels that differ in long tracts is higher in TPDS, while that relationship is not clearly established in NBS.