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Objective Branched stent grafts represent a viable option for left subclavian artery (LSA) revascularisation in patients treated by thoracic endovascular aortic repair (TEVAR) for Zone 2 lesions. This study investigated the haemodynamic performance of different LSA branched stent graft configurations as potential determinants of thrombotic and stroke risks. Methods A three dimensional aortic arch geometry extracted from post-operative computed tomography images of a TEVAR patient using a single LSA branched aortic endograft was modified in silico to obtain ten potential LSA branched stent graft configurations: five down facing (0–5 – 10 mm aortic protrusion with 10–12 mm internal diameter), four curved (30–60° with antegrade/retrograde orientation), and one LSA orifice misalignment. The 0 mm down facing stent graft was considered base configuration. Computational fluid dynamic analyses were performed to identify differences in pressure, energy, and wall shear stress (WSS) based parameters. Results Total pressure drop and energy loss variations among configurations were not greater than 5 mmHg (6% of mean arterial pressure) and 5.7 mW (0.7% of cardiac power), respectively. Protrusions up to 5 mm created clinically insignificant flow disturbances. However, stent graft protrusions further into the aortic lumen created more complex haemodynamics, characterised by larger energy loss and more prominent flow recirculation. Protrusion greater than 5 mm into the lumen was associated with larger areas of elevated maximum WSS (>20 Pa) along the outer surface of the branched stent graft. Conclusion Arterial haemodynamic characteristics are affected by LSA branched stent graft configurations, with pressure drops and energy losses likely to be clinically insignificant. The length of the stent graft protrusion into the aortic lumen generated the largest haemodynamic variations in the aortic system. Protrusions up to 5 mm have smaller risk of potential thrombus generation. Conversely, larger protrusions into the aortic lumen showed more disturbed haemodynamics, suggesting a greater risk of potential thrombus formation, which may be clinically important over time.

Adhesion of leukocytes to substrate involves the coupling of disparate length and timescales between molecular mechanics and macroscopic transport, and existing models of cell adhesion do not use full cellular information. To address these challenges, a multiscale computational approach for studying the adhesion of a cell on a substrate is developed and assessed. The cellular level model consists of a continuum representation of the field equations and a moving boundary tracking capability to allow the cell to change its shape continuously. At the receptor-ligand level, a bond molecule is mechanically represented by a spring. Communication between the macro/micro- and nanoscale models is facilitated interactively during the computation. The computational model is assessed using an adherent cell, rolling and deforming along the vessel wall under imposed shear flows. Using this approach, we first confirm existing numerical and experimental results. In this study, the intracellular viscosity and interfacial tension are found to directly affect the rolling of a cell. Our results also show that the presence of a nucleus increases the bond lifetime, and decreases the cell rolling velocity. Furthermore, it is found that a cell with a larger diameter rolls faster, and decreases the bond lifetime. This study shows that cell rheological properties have significant effects on the adhesion process contrary to what has been hypothesized in most literature.

The paper presents a theory of the flow of a viscous fluid in a falling cylinder viscometer. The velocity profile for the flow in infinite tube and finite tube are obtained in finite form. That allows us to determine quite easily the influence of various parameters involved on the fluid flow and on the motion of the cylinder. Also a formula written in finite form is obtained for the determination of the viscosity coefficient. All these formulae contain a term that can describe the influence of a magnetic field on the motion of the falling cylinder. A comparison of the viscosities determined according to the present theory and with a cone-plate viscometers show a good agreement.

In this work, a mixed Eulerian?Lagrangian algorithm, calledELAFINT(Eulerian Lagrangian algorithm for interface tracking) is developed further and applied to compute flows with solid?fluid and fluid?fluid interfaces. The method is capable of handling fluid flows in the presence of both irregularly shaped solid boundaries and moving boundaries on a fixed Cartesian grid. The field equations are solved on the underlying fixed grid using a collocated variable, pressure-based formulation. The moving boundary is tracked explicitly by the Lagrangian translation of marker particles. The moving boundary passes through the grid and the immersed boundary technique is used to handle its interaction with the underlying grid. The internal solid boundaries are dealt with by using a cut-cell technique. Particular attention is directed toward conservation and consistency in the vicinity of both phase boundaries. The complex geometry feature has been tested for a variety of flow problems. The performance of the immersed boundary representation is demonstrated in the simulation of Newtonian liquid drops. The combination of the two features is then employed in the simulation of motion of drops through constricted tubes. The capabilities developed here can be useful for solving flow problems involving moving and stationary complex boundaries.

The motion at low Reynolds numbers of a sphere oscillating with a small amplitude inside a cylindrical tube containing a viscous fluid (Newtonian or viscoelastic) is investigated. The linear Jeffreys model is used to describe the constitutive relation for the viscoelastic fluid. The governing equations are transformed to, and solved in, the frequency domain where the Fourier components for the flow and drag are obtained using a finite difference method. The numerical results for the Newtonian fluid velocity agree well with those given by a high frequency asymptotic solution. The effects of the Stokes number, ϵ, on the unsteady drag, D R + iD I , are discussed. At small ϵ, the real component of the unsteady drag, D R , is dominated by the quasi-steady term for both Newtonian and viscoelastic fluids. For a Newtonian fluid, the acceleration-dependent terms of D R and D I are proportional to ϵ 4 and ϵ 2 respectively. Whereas D R increases monotonically with ϵ for a Newtonian fluid, it reaches a minimum for a Jeffreys fluid when ϵ ≈ O (1). The difference observed is caused by the shear-thinning property of the viscoelastic fluid. At large ϵ, D R becomes proportional to ϵ, and the imaginary component of the unsteady drag, D I , for both Newtonian and viscoelastic fluids, is dominated by the added-mass force. However, as opposed to a Newtonian fluid, D I changes sign near ϵ ≈ O (1) for a viscoelastic fluid due to shear thinning. Finally, a method for determining the rheological properties of a general viscoelastic fluid from measurements of the unsteady drag in a ball rheometer is presented.

Experiments are performed in which a passive human neutrophil is deformed into an elongated "sausage" shape by aspirating it into a small glass pipette. When expelled from the pipette the neutrophil recovers its natural spherical shape in approximately 1 minute. This recovery process is analyzed according to a Newtonian, liquid-drop model in which a variational method is used to simultaneously solve the hydrodynamic equations for low Reynolds-number flow and the equations for membrane equilibrium with a constant membrane tension. The theoretical model gives a good fit to the experimental data for a ratio of membrane cortical tension to cytoplasmic viscosity of approximately 1.7 x 10(-5) cm/s (0.17 micron/s). However, when the cell is held in the pipette for only a short time period of 5 s or less, and then expelled, the cell undergoes an initial, rapid elastic rebound suggesting that the cell behaves in this instance as a Maxwell viscoelastic liquid rather than a Newtonian liquid with constant cortical tension.