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Traumatic brain injury (TBI) is a serious health issue. Studies have highlighted the severity of rotation-induced TBI. However, the role of cerebrospinal fluid (CSF) in transmitting the impact from the skull to the soft brain matter remains unclear. Herein, we use experiments and computations to define and probe this role in a simplified setup. A spherical hydrogel ball, serving as a soft brain model, was subjected to controlled rotation within a water bath, emulating the CSF, and filling a transparent cylinder. The cylinder and ball velocities, as well as the ball’s deformation over time, were measured. We found that the soft hydrogel ball is very sensitive to decelerating rotational impacts, experiencing significant deformation during the process. A finite-element code is written to simulate the process. The hydrogel ball is modeled as a poroelastic material infused with fluid and its coupling with the suspending fluid is handled by an arbitrary Lagrangian-Eulerian method. The results indicate that the density contrast, as well as the rotational velocity difference, between the hydrogel ball and the suspending fluid, play a central role in the ball’s deformation due to centrifugal forces. This approach contributes to a deeper understanding of brain injuries and may portend the development of preventive measures and improved treatment strategies. 

Thanks to their softness, biocompatibility, porosity, and ready availability, hydrogels are commonly used in microfluidic assays and organ-on-chip devices as a matrix for cells. They not only provide a supporting scaffold for the differentiating cells and the developing organoids, but also serve as the medium for transmitting oxygen, nutrients, various chemical factors, and mechanical stimuli to the cells. From a bioengineering viewpoint, the transmission of forces from fluid perfusion to the cells through the hydrogel is critical to the proper function and development of the cell colony. In this paper, we develop a poroelastic model to represent the fluid flow through a hydrogel containing a biological cell modeled as a hyperelastic inclusion. In geometries representing shear and normal flows that occur frequently in microfluidic experiments, we use finite-element simulations to examine how the perfusion engenders interstitial flow in the gel and displaces and deforms the embedded cell. The results show that pressure is the most important stress component in moving and deforming the cell, and the model predicts the velocity in the gel and stress transmitted to the cell that is comparable to in vitro and in vivo data. This work provides a computational tool to design the geometry and flow conditions to achieve optimal flow and stress fields inside the hydrogels and around the cell. 

When a hydrogel layer is compressed by a fluid flow normal to it, the flow rate may exhibit hysteresis when the imposed pressure drop varies, and we may observe bistability between a relaxed and a compressed state for the hydrogel. 

Two aspects of hydrogel mechanics have been studied separately in the past. The first is the swelling and deswelling of gels in a quiescent solvent bath triggered by an environmental stimulus such as a change in temperature or pH, and the second is the solvent flow around and into a gel domain, driven by an external pressure gradient or moving boundary. The former neglects convection due to external flow, whereas the latter neglects solvent diffusion driven by a gradient in chemical potential. Motivated by engineering and biomedical applications where both aspects coexist and potentially interact with each other, this work presents a poroelasticity model that integrates these two aspects into a single framework, and demonstrates how the coupling between the two gives rise to novel physics in relatively simple one-dimensional and two-dimensional flows. 

Boundary conditions between a porous solid and a fluid has been a long-standing problem in modeling porous media. For deformable poroelastic materials such as hydrogels, the question is further complicated by the elastic stress from the solid network. Recently, an interfacial permeability condition has been developed from the principle of positive energy dissipation on the hydrogel–fluid interface. Although this boundary condition has been used in flow computations and yielded reasonable predictions, it contains an interfacial permeability g as a phenomenological parameter. In this work, we use porescale models of flow into a periodic array of solid cylinders or parallel holes to determine g as a function of the pore size and porosity. This provides a means to evaluate the interfacial permeability for a wide range of poroelastic materials, including hydrogels, foams and biological tissues, to enable realistic flow simulations. 

Albuminuria occurs when albumin leaks abnormally into the urine. Its mechanism remains unclear. A gel-compression hypothesis attributes the glomerular barrier to compression of the glomerular basement membrane (GBM) as a gel layer. Loss of podocyte foot processes would allow the gel layer to expand circumferentially, enlarge its pores and leak albumin into the urine. To test this hypothesis, we develop a poroelastic model of the GBM. It predicts GBM compression in healthy glomerulus and GBM expansion in the diseased state, essentially confirming the hypothesis. However, by itself, the gel compression and expansion mechanism fails to account for two features of albuminuria: the reduction in filtration flux and the thickening of the GBM. A second mechanism, the constriction of flow area at the slit diaphragm downstream of the GBM, must be included. The cooperation between the two mechanisms produces the amount of increase in GBM porosity expected in vivo in a mutant mouse model, and also captures the two in vivo features of reduced filtration flux and increased GBM thickness. Finally, the model supports the idea that in the healthy glomerulus, gel compression may help maintain a roughly constant filtration flux under varying filtration pressure.