Understanding mechanobiology in cultured endothelium: A review of the orbital shaker method

A striking feature of atherosclerosis is its highly non-uniform distribution within the arterial tree. This has been attributed to variation in the haemodynamic wall shear stress (WSS) experienced by endothelial cells, but the WSS characteristics that are important and the mechanisms by which they lead to disease remain subjects of intensive investigation despite decades of research. In vivo evidence suggests that multidirectional WSS is highly atherogenic. This possibility is increasingly being studied by culturing endothelial cells in wells that are swirled on an orbital shaker. The method is simple and cost effective, has high throughput and permits chronic exposure, but interpretation of the results can be difficult because the fluid mechanics are complex; hitherto, their description has largely been restricted to the engineering literature. Here we review the findings of such studies, which indicate that putatively atherogenic flow characteristics occur at the centre of the well whilst atheroprotective ones occur towards the edge, and we describe simple mathematical methods for choosing experimental variables that avoid resonance, wave breaking and uncovering of the cells. We additionally summarise a large number of studies showing that endothelium cultured at the centre of the well expresses more pro-inflammatory and fewer homeostatic genes, has higher permeability, proliferation, apoptosis and senescence, and shows more endothelial-to-mesenchymal transition than endothelium at the edge. This simple method, when correctly interpreted, has the potential to greatly increase our understanding of the homeostatic and pathogenic mechanobiology of endothelial cells and may help identify new therapeutic targets in vascular disease

Fluid dynamics of orbitally shaken shallow fluid layers

Motivated by the pathological effect of blood flow on endothelial cells and its relevance in the progress of atherosclerosis, this thesis investigates the fluid dynamics of orbitally shaken shal- low fluid layers in cylindrical containers. The study uses computational and analytical models to characterise flow in 33 case studies, which map the parameter space of the dimensionless numbers that govern the physics. A travelling wave characterises the flow and wave breaking and wall boundaries determine the multidirectional character of the shear stress field. A novel shear stress metric (transWSSmin) has been investigated by combining numerical simulations with laboratory experiments, and evidence is presented that transWSSmin correlates with en- dothelial permeability changes, implying that cells align close to the direction that minimises the transverse shear stresses instead of the mean flow direction, as widely accepted. A potential flow theory has been shown to be a powerful tool to predict the surface amplitude up to the onset of the wave breaking, which allows for classification in non-breaking/breaking regimes based on an amplitude breaking threshold identified in the simulations. An improved analytical model for the prediction of the shear stress, the PT-Stokes WSS model, has been developed, which is a generalisation of the classic Stokes solution. The model consists of a Stokes boundary layer coupled with the potential flow, and thus takes into account the free surface and side walls. Even in highly nonlinear cases, the PT-Stokes model predicts shear stress within 50% accuracy except at resonant conditions. A strong correlation has been found between the bottom wall shear stress and the surface velocity, showing that the largest source of error is the surface velocity predictions by the potential flow model due to the omission of viscous effects. Finally, results are translated into recommendations and tools for the investigation of endothelial cells in orbital shakers.Open Acces

Dimensionamiento de la estación depuradora de aguas residuales

El objeto del presente proyecto consiste en seleccionar el/los proceso/s más adecuados para la depuración de las aguas residuales del municipio de Grazalema (Cádiz)

La responsabilidad patrimonial de las Administraciones Públicas en Semana Santa

Premio extraordinario de Trabajo Fin de Máster curso 2020/2021. Máster en Abogací

Orbitally shaken shallow fluid layers. II. An improved wall shear stress model

A new model for the analytical prediction of wall shear stress distributions at the base of orbitally shaken shallow fluid layers is developed. This model is a generalisation of the classical extended Stokes solution and will be referred to as the potential theory-Stokes model. The model is validated using a large set of numerical simulations covering a wide range of flow regimes representative of those used in laboratory experiments. It is demonstrated that the model is in much better agreement with the simulation data than the classical Stokes solution, improving the prediction in 63% of the studied cases. The central assumption of the model—which is to link the wall shear stress with the surface velocity—is shown to hold remarkably well over all regimes covered

Orbitally shaken shallow fluid layers. I. Regime classification

Orbital shakers are simple devices that provide mixing, aeration, and shear stress at multiple scales and high throughput. For this reason, they are extensively used in a wide range of applications from protein production to bacterial biofilms and endothelial cell experiments. This study focuses on the behaviour of orbitally shaken shallow fluid layers in cylindrical containers. In order to investigate the behaviour over a wide range of different conditions, a significant number of numerical simulations are carried out under different configuration parameters. We demonstrate that potential theory—despite the relatively low Reynolds number of the system—describes the free-surface amplitude well and the velocity field reasonably well, except when the forcing frequency is close to a natural frequency and resonance occurs. By classifying the simulations into non-breaking, breaking, and breaking with part of the bottom uncovered, it is shown that the onset of wave breaking is well described by Δh/(2R) = 0.7Γ, where Δh is the free-surface amplitude, R is the container radius, and Γ is the container aspect ratio; Δh can be well approximated using the potential theory. This result is in agreement with standard wave breaking theories although the significant inertial forcing causes wave breaking at lower amplitudes

Visualization of three pathways for macromolecule transport across cultured endothelium and their modification by flow.

Transport of macromolecules across vascular endothelium and its modification by fluid mechanical forces are important for normal tissue function and in the development of atherosclerosis. However, the routes by which macromolecules cross endothelium, the hemodynamic stresses that maintain endothelial physiology or trigger arterial disease, and the dependence of transendothelial transport on hemodynamic stresses are controversial. Here we visualised pathways for macromolecule transport and determined the effect on these pathways of different types of flow. Endothelial monolayers were cultured under static conditions or on an orbital shaker producing different flow profiles in different parts of the wells. Fluorescent tracers that bound to the substrate after crossing the endothelium were used to identify transport pathways. Maps of tracer distribution were compared with numerical simulations of flow to determine effects of different shear stress metrics on permeability. Albumin-sized tracers dominantly crossed the cultured endothelium via junctions between neighbouring cells, high-density-lipoprotein-sized tracers crossed at tricelluar junctions whilst low-density-lipoprotein-sized tracers crossed through cells. Cells aligned close to the angle that minimised shear stresses across their long axis. The rate of paracellular transport under flow correlated with the magnitude of these minimised transverse stresses, whereas transport across cells was uniformly reduced by all types of flow. These results contradict the long-standing two-pore theory of solute transport across microvessel walls and the consensus view that endothelial cells align with the mean shear vector. They suggest that endothelial cells minimise transverse shear, supporting its postulated pro-atherogenic role. Preliminary data show that similar tracer techniques are practicable in vivo