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1. Enhanced Li-Ion Diffusivity of LiFePO ₄ by Ru Doping: Ab Initio and Machine Learning Force Field Results

   https://doi.org/10.1021/acsaem.3c01429  

   Lama, Bhubnesh; Smirnova, Alevtina L; Paudel, Tula R (October 2023, ACS Applied Energy Materials)

   Lama, B; Smirnova, A; Paudel, T (Ed.)

   Ionic diffusivity plays a central role in battery performance. A cathode material for lithium-ion (Li-ion) batteries, LiFePO4 (LFP), performs poorly at high current rates due to low Li-ion diffusivity. An increase in ionic diffusivity is essential to enhance battery performance for high-power-density applications such as hybrid and electric vehicles. Here, we use molecular dynamics simulations with machine learning force field and climbing-image nudged elastic band calculations to show that Li-ion diffusivity in LFP increases when doped with the transition-metal dopant ruthenium. This increase is associated with a reduction in Li diffusion energy barrier, diffusion length, and Li-vacancy formation energy, and it is accompanied by changes in the electronic band structure, specifically the appearance of electronic states in the middle of the band gap and the vicinity of the conduction band. 

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2. Hydrogen Diffusion in the Lower Mantle Revealed by Machine Learning Potentials

   https://doi.org/10.1029/2023JB028333  

   Peng, Yihang; Deng, Jie (April 2024, Journal of Geophysical Research: Solid Earth)

   Abstract Hydrogen may be incorporated into nominally anhydrous minerals including bridgmanite and post‐perovskite as defects, making the Earth's deep mantle a potentially significant water reservoir. The diffusion of hydrogen and its contribution to the electrical conductivity in the lower mantle are rarely explored and remain largely unconstrained. Here we calculate hydrogen diffusivity in hydrous bridgmanite and post‐perovskite, using molecular dynamics simulations driven by machine learning potentials of ab initio quality. Our findings reveal that hydrogen diffusivity significantly increases with increasing temperature and decreasing pressure, and is considerably sensitive to hydrogen incorporation mechanism. Among the four defect mechanisms examined, (Mg + 2H)_Siand (Al + H)_Sishow similar patterns and yield the highest hydrogen diffusivity. Hydrogen diffusion is generally faster in post‐perovskite than in bridgmanite, and these two phases exhibit distinct diffusion anisotropies. Overall, hydrogen diffusion is slow on geological time scales and may result in heterogeneous water distribution in the lower mantle. Additionally, the proton conductivity of bridgmanite for (Mg + 2H)_Siand (Al + H)_Sidefects aligns with the same order of magnitude of lower mantle conductivity, suggesting that the water distribution in the lower mantle may be inferred by examining the heterogeneity of electrical conductivity. 

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3. Machine-learning-powered extraction of molecular diffusivity from single-molecule images for super-resolution mapping

   https://doi.org/10.1038/s42003-023-04729-x  

   Park, Ha H.; Wang, Bowen; Moon, Suhong; Jepson, Tyler; Xu, Ke (December 2023, Communications Biology)

   Abstract While critical to biological processes, molecular diffusion is difficult to quantify, and spatial mapping of local diffusivity is even more challenging. Here we report a machine-learning-enabled approach, pixels-to-diffusivity (Pix2D), to directly extract the diffusion coefficient D from single-molecule images, and consequently enable super-resolved D spatial mapping. Working with single-molecule images recorded at a fixed framerate under typical single-molecule localization microscopy (SMLM) conditions, Pix2D exploits the often undesired yet evident motion blur, i.e ., the convolution of single-molecule motion trajectory during the frame recording time with the diffraction-limited point spread function (PSF) of the microscope. Whereas the stochastic nature of diffusion imprints diverse diffusion trajectories to different molecules diffusing at the same given D , we construct a convolutional neural network (CNN) model that takes a stack of single-molecule images as the input and evaluates a D -value as the output. We thus validate robust D evaluation and spatial mapping with simulated data, and with experimental data successfully characterize D differences for supported lipid bilayers of different compositions and resolve gel and fluidic phases at the nanoscale. 

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4. The combined hydrodynamic and thermodynamic effects of immobilized proteins on the diffusion of mobile transmembrane proteins

   https://doi.org/10.1017/jfm.2019.592  

   Singh, Rohit R.; Sangani, Ashok S.; Daniel, Susan; Koch, Donald L. (October 2019, Journal of Fluid Mechanics)

   The plasma membranes of cells are thin viscous sheets in which some transmembrane proteins have two-dimensional mobility and some are immobilized. Previous studies have shown that immobile proteins retard the short-time diffusivity of mobile particles through hydrodynamic interactions and that steric effects of immobile proteins reduce the long-time diffusivity in a model that neglects hydrodynamic interactions. We present a rigorous derivation of the long-time diffusivity of a single mobile protein interacting hydrodynamically and thermodynamically with an array of immobile proteins subject to periodic boundary conditions. This method is based on a finite element method (FEM) solution of the probability density of the mobile protein diffusing with a position-dependent mobility determined through a multipole solution of Stokes equations. The simulated long-time diffusivity in square arrays decreases as the spacing in the array approaches the particle size in a manner consistent with a lubrication analysis. In random arrays, steric effects lead to a percolation threshold volume fraction above which long-time diffusion is arrested. The FEM/multipole approach is used to compute the long-time diffusivity far away from this threshold. An approximate analysis of mobile protein diffusion through a network of pores connected by bonds with resistances determined by the FEM/multipole calculations is then used to explore higher immobile area fractions and to evaluate the finite simulation cell size scaling behaviour of diffusion near the percolation threshold. Surprisingly, the ratio of the long-time diffusivity to the spatially averaged short-time diffusivity in these two-dimensional fixed arrays is higher in the presence of hydrodynamic interactions than in their absence. Finally, the implications of this work are discussed, including the possibility of using the methods developed here to investigate more complex diffusive phenomena observed in cell membranes. 

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5. Ex-Vivo Hippocampus Segmentation Using Diffusion-Weighted MRI

   https://doi.org/10.3390/math12070940  

   Tang , Haoteng; Dai, Siyuan; Zou, Eric M; Liu, Guodong; Ahearn, Ryan; Krafty, Ryan; Modo, Michel; Zhan, Liang (April 2024, Mathematics)

   The hippocampus is a crucial brain structure involved in memory formation, spatial navigation, emotional regulation, and learning. An accurate MRI image segmentation of the human hippocampus plays an important role in multiple neuro-imaging research and clinical practice, such as diagnosing neurological diseases and guiding surgical interventions. While most hippocampus segmentation studies focus on using T1-weighted or T2-weighted MRI scans, we explore the use of diffusion-weighted MRI (dMRI), which offers unique insights into the microstructural properties of the hippocampus. Particularly, we utilize various anisotropy measures derived from diffusion MRI (dMRI), including fractional anisotropy, mean diffusivity, axial diffusivity, and radial diffusivity, for a multi-contrast deep learning approach to hippocampus segmentation. To exploit the unique benefits offered by various contrasts in dMRI images for accurate hippocampus segmentation, we introduce an innovative multimodal deep learning architecture integrating cross-attention mechanisms. Our proposed framework comprises a multi-head encoder designed to transform each contrast of dMRI images into distinct latent spaces, generating separate image feature maps. Subsequently, we employ a gated cross-attention unit following the encoder, which facilitates the creation of attention maps between every pair of image contrasts. These attention maps serve to enrich the feature maps, thereby enhancing their effectiveness for the segmentation task. In the final stage, a decoder is employed to produce segmentation predictions utilizing the attention-enhanced feature maps. The experimental outcomes demonstrate the efficacy of our framework in hippocampus segmentation and highlight the benefits of using multi-contrast images over single-contrast images in diffusion MRI image segmentation. 

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