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Traumatic brain injury remains a significant global health concern, requiring advanced understanding and mitigation strategies. In current brain concussion research, there is a significant knowledge gap: the critical role of transient cerebrospinal fluid (CSF) flow in the porous subarachnoid space (SAS) has long been overlooked. To address this limitation, we are developing a simplified mathematical model to investigate the CSF pressurization in the porous arachnoid trabeculae and the resulting motion of brain matter when the head is exposed to a translational impact. The model simplifies the head into an inner solid object (brain) and an outer rigid shell (skull) with a thin, porous fluid gap (SAS). The CSF flow in the impact side (coup region) and the opposite side (contrecoup region) is modeled as porous squeezing and expanding flows, respectively. The flow through the side regions, which connect these regions, is governed by Darcy's law. We found that the porous arachnoid trabeculae network significantly dampens brain motion and reduces pressure variations within the SAS compared to a SAS without the porous arachnoid trabeculae (AT). This effect is particularly pronounced under high-frequency, periodic acceleration impacts, thereby lowering the risk of injury. The dampening effect can be attributed to the low permeability of the AT, which increases resistance to fluid movement and stabilizes the fluid and pressure responses within the SAS, thereby reducing extreme pressure fluctuations and brain displacement under impact. This work provides a foundational understanding of CSF flow dynamics, paving the way for innovative approaches to brain injury prevention and management. 

Abstract Measuring the diffusion coefficient of clay-based liner materials is important in estimating and predicting long-term barrier performance in waste containment facilities. Various theoretical models, including the finite cylindrical model, have been commonly used to determine the diffusion properties of clay-based liner materials in leaching tests. However, the assumption of zero-concentration boundary conditions of the traditional finite cylindrical model contradicts the measured variation of concentration in real leaching tests, likely resulting in (1) underestimated and unconservative diffusion coefficient, or (2) requirement of a relatively large liquid-to-soil ratio and frequent leachate replacement in the experiment to maintain the zero-concentration boundary condition. In this study, a theoretical model was developed to evaluate the solute diffusion process within a soil specimen under arbitrary, time-dependent concentration boundary conditions. The proposed model, incorporating the time-dependent boundary conditions, provides efficient calculations of the concentration distribution and the cumulative fraction leached of solute across the soil specimen. The example application of the proposed model to experimental data demonstrates the capability of the proposed model to determine apparent diffusion coefficients of clay-based liner materials without introducing errors associated with the assumption of a zero concentration boundary condition. The proposed model provides a comprehensive method to investigate the dynamic transport behaviors of solutes through clay-based liner materials in future studies. 

This paper presents a theoretical model examining the interaction between a fibrous network and viscous fluid flow driven by an oscillating boundary. The aim is to understand how oscillating impacts are transmitted from the skull, through the arachnoid trabeculae network filled with cerebrospinal fluid, as observed in shaken baby syndrome. The model uses an effective medium approach to determine the fluid velocity field while each fiber is treated as a soft string undergoing deformation. Results indicate that the frequency of oscillation, fiber stiffness, and porous structure resistance significantly influence the oscillating shearing flow, as indicated by the Womersley (Wo), Brinkman (α), and Bingham (Bm) numbers. Application of the model to shaken baby syndrome suggests that oscillations in the cerebrospinal fluid and arachnoid trabeculae can significantly surpass those on the skull, leading to intense shear stress penetration to the brain. This model is the first study to integrate the dynamic response of string-like fibrous networks in fluid flows with oscillating boundaries and offers a quantitative framework for predicting the transmission of shearing forces from the skull to the brain matter.