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The squeezing of blood cells and vesicles through narrow constrictions, such as splenic slits, pulmonary capillaries, vascular endothelial gaps, and microfluidic channels, is crucial in physiology and biotechnology, with fluid mechanics playing a central role. The diverse geometries of these constrictions, the associated flow conditions, and the unique mechanical properties of cells and vesicles create a rich subject in fluid mechanics emerging from nonlinear dynamics of fluid–structure interactions involving both lubrication and Marangoni flows. Advances in microfluidics, video microscopy, and computational modeling have enabled investigations into these complex processes. This review surveys the key features and approaches, recent prominent studies, and unresolved challenges related to these processes, offering insights for researchers across biomechanics, biomedical engineering, biological physics, hematology, physiology, and applied mathematics. 

Sickle cell disease (SCD) is a hereditary condition in which red blood cells become rigid and develop a sickle shape due to abnormal hemoglobin S. This leads to obstructed microvasculature and causes vaso-occlusive crises (VOCs). These blockages result in severe complications like pain crises, acute chest syndrome, and strokes. The physical mechanisms behind VOCs are not fully understood, hindering the development of predictive diagnostic tools. Previous studies using microfluidic devices and mathematical modeling to analyze the transit of sickle red blood cells through microvasculature-mimicking slits found that increased viscosity is positively related to longer transit times, which can predict disease severity. Since blood viscosity is positively correlated with the frequency of sickle red cells, we hypothesized that a higher percentage of sickle cells in peripheral blood would correspond to a greater likelihood of VOCs in SCD patients. To test this hypothesis, we used the software ImageJ to analyze blood smear images from 24 SCD patients to quantify the percentage of sickle cells. We found a positive correlation between sickle cell frequency and the incidence of VOC events. These findings suggest that blood smear imaging combined with microfluidic analysis and mathematical modeling could serve as a rapid, non-invasive diagnostic tool to predict pain crises in SCD patients. This approach has significant clinical implications, offering a potential method to predict VOC events for personalized treatment strategies, ultimately aiming to reduce hospital admissions and improve outcomes in SCD patients. 

Abstract A primary cilium, made of nine microtubule doublets enclosed in a cilium membrane, is a mechanosensing organelle that bends under an external mechanical load and sends an intracellular signal through transmembrane proteins activated by cilium bending. The nine microtubule doublets are the main load‐bearing structural component, while the transmembrane proteins on the cilium membrane are the main sensing component. No distinction was made between these two components in all existing models, where the stress calculated from the structural component (nine microtubule doublets) was used to explain the sensing location, which may be totally misleading. For the first time, we developed a microstructure‐based primary cilium model by considering these two components separately. First, we refined the analytical solution of bending an orthotropic cylindrical shell for individual microtubule, and obtained excellent agreement between finite element simulations and the theoretical predictions of a microtubule bending as a validation of the structural component in the model. Second, by integrating the cilium membrane with nine microtubule doublets and simulating the tip‐anchored optical tweezer experiment on our computational model, we found that the microtubule doublets may twist significantly as the whole cilium bends. Third, besides being cilium‐length‐dependent, we found the mechanical properties of the cilium are also highly deformation‐dependent. More important, we found that the cilium membrane near the base is not under pure in‐plane tension or compression as previously thought, but has significant local bending stress. This challenges the traditional model of cilium mechanosensing, indicating that transmembrane proteins may be activated more by membrane curvature than membrane stretching. Finally, we incorporated imaging data of primary cilia into our microstructure‐based cilium model, and found that comparing to the ideal model with uniform microtubule length, the imaging‐informed model shows the nine microtubule doublets interact more evenly with the cilium membrane, and their contact locations can cause even higher bending curvature in the cilium membrane than near the base. 

Abstract The nuclear lamina is widely recognized as the most crucial component in providing mechanical stability to the nucleus. However, it is still a significant challenge to model the mechanics of this multilayered protein network. We developed a constitutive model of the nuclear lamina network based on its microstructure, which accounts for the deformation phases at the dimer level, as well as the orientational arrangement and density of lamin filaments. Instead of relying on homology modeling in the previous studies, we conducted molecular simulations to predict the force‐extension response of a highly accurate lamin dimer structure obtained through X‐ray diffraction crystallography experimentation. Furthermore, we devised a semiflexible worm‐like chain extension‐force model of lamin dimer as a substitute, incorporating phases of initial stretching, uncoiling of the dimer coiled‐coil, and transition of secondary structures. Subsequently, we developed a 2D network continuum model for the nuclear lamina by using our extension‐force lamin dimer model and derived stress resultants. By comparing with experimentally measured lamina modulus, we found that the lamina network has sharp initial strain‐hardening behavior. This also enabled us to carry out finite element simulations of the entire nucleus with an accurate microstructure‐based nuclear lamina model. Finally, we conducted simulations of transendothelial transmigration of a nucleus and investigated the impact of varying network density and uncoiling constants on the critical force required for successful transmigration. The model allows us to incorporate the microstructure characteristics of the nuclear lamina into the nucleus model, thereby gaining insights into how laminopathies and mutations affect nuclear mechanics. 

We conducted a systematic numerical investigation of spherical, prolate and oblate particles in an inertial shear flow between two parallel walls, using smoothed particle hydrodynamics (SPH). It was previously shown that above a critical Reynolds number, spherical particles experience a supercritical pitchfork bifurcation of the equilibrium position in shear flow between two parallel walls, namely that the central equilibrium position becomes unstable, leading to the emergence of two new off-centre stable positions (Foxet al.,J. Fluid Mech., vol. 915, 2021). This phenomenon was unexpected given the symmetry of the system. In addition to confirming this finding, we found, surprisingly, that ellipsoidal particles can also return to the centre position from the off-centre positions when the particle Reynolds number is further increased, while spherical particles become unstable under this increased Reynolds number. By utilizing both SPH and the finite element method for flow visualization, we explained the underlining mechanism of this reverse of bifurcation by altered streamwise vorticity and symmetry breaking of pressure. Furthermore, we expanded our investigation to include asymmetric particles, a novel aspect that had not been previously modelled, and we observed similar trends in particle dynamics for both symmetric and asymmetric ellipsoidal particles. While further validation through laboratory experiments is necessary, our research paves the road for development of new focusing and separation methods for shaped particles. 

Abstract Particle migration dynamics in viscoelastic fluids in spiral channels have attracted interest in recent years due to potential applications in the 3D focusing and label-free sorting of particles and cells. Despite a number of recent studies, the underlying mechanism of Dean-coupled elasto-inertial migration in spiral microchannels is not fully understood. In this work, for the first time, we experimentally demonstrate the evolution of particle focusing behavior along a channel downstream length at a high blockage ratio. We found that flow rate, device curvature, and medium viscosity play important roles in particle lateral migration. Our results illustrate the full focusing pattern along the downstream channel length, with side-view imaging yielding observations on the vertical migration of focused streams. Ultimately, we anticipate that these results will offer a useful guide for elasto-inertial microfluidics device design to improve the efficiency of 3D focusing in cell sorting and cytometry applications. 

Soft objects squeezing through small apertures are crucial for many in vivo and in vitro processes. Red blood cell transit time through splenic inter-endothelial slits (IESs) plays a crucial role in blood filtration and disease progression, while droplet velocity through constrictions in microfluidic devices is important for effective manipulation and separation processes. As these transit phenomena are not well understood, we sought to establish analytical and numerical solutions of viscous droplet transit through a rectangular slit. This study extends from our former theory of a circular pore because a rectangular slit is more realistic in many physiological and engineering applications. Here, we derived the ordinary differential equations (ODEs) of a droplet passing through a slit by combining planar Poiseuille flow, the Young–Laplace equations, and modifying them to consider the lubrication layer between the droplet and the slit wall. Compared to the pore case, we used the Roscoe solution instead of the Sampson one to account for the flow entering and exiting a rectangular slit. When the surface tension and lubrication layer were negligible, we derived the closed-form solutions of transit time. When the surface tension and lubrication layer were finite, the ODEs were solved numerically to study the impact of various parameters on the transit time. With our solutions, we identified the impact of prescribed pressure drop, slit dimensions, and droplet parameters such as surface tension, viscosity, and volume on transit time. In addition, we also considered the effect of pressure drop and surface tension near critical values. For this study, critical surface tension for a given pressure drop describes the threshold droplet surface tension that prevents transit, and critical pressure for a given surface tension describes the threshold pressure drop that prevents transit. Our solutions demonstrate that there is a linear relationship between pressure and the reciprocal of the transit time (referred to as inverse transit time), as well as a linear relationship between viscosity and transit time. Additionally, when the droplet size increases with respect to the slit dimensions, there is a corresponding increase in transit time. Most notably, we emphasize the initial antagonistic effect of surface tension which resists droplet passage but at the same time decreases the lubrication layer, thus facilitating passage. Our results provide quantitative calculations for understanding cells passing through slit-like constrictions and designing droplet microfluidic experiments. 

Our 3D DNS-PT modeling approach can predict the inertial focusing of sperm cells with long tails, bridging the gap in understanding the inertial migration of flagellated cells and facilitating the better design of microfluidic sorting devices.