S.I.S. Pinto

Numerical study of wall shear stress-based descriptors in the human left coronary artery

Abstract The present work is about the application of wall shear stress descriptors – time averaged wall shear stress (TAWSS), oscillating shear index (OSI) and relative residence time (RRT) – to the study of blood flow in the left coronary artery (LCA). These descriptors aid the prediction of disturbed flow conditions in the vessels and play a significant role in the detection of potential zones of atherosclerosis development. Hemodynamic descriptors data were obtained, numerically, through ANSYS® software, for the LCA of a patient-specific geometry and for a 3D idealized model. Comparing both cases, the results are coherent, in terms of location and magnitude. Low TAWSS, high OSI and high RRT values are observed in the bifurcation – potential zone of atherosclerosis appearance. The dissimilarities observed in the TAWSS values, considering blood as a Newtonian or non-Newtonian fluid, releases the importance of the correct blood rheologic caracterization. Moreover, for a higher Reynolds number, the TAWSS values decrease in the bifurcation and along the LAD branch, increasing the probability of plaques deposition. Furthermore, for a stenotic LCA model, very low TAWSS and high RRT values in front and behind the stenosis are observed, indicating the probable extension, in the flow direction, of the lesion.

A Numerical Study of the Apparent Selectivity in the Fractionation of Two Macromolecules by Ultrafiltration

The fractionation of two macromolecules by ultrafiltration in a parallel plate cell was studied by computational fluid dynamics (CFD). The in-house code developed takes on account of the pressure drop, the variation of the permeate velocity along the cell, the concentration polarization over the membrane, and the variation of the transport properties and of the osmotic pressure with the concentration of the solutes. A convective-diffusive model, to simulate the solute transmission, was also adopted. The real and apparent selectivity, local and mean, were determined, in order to study the effect of transmembrane pressure, Reynolds number, inlet solute concentrations, specific area of the membrane pores, and membrane resistance. The code was applied to study the separation of Bovine Serum Albumin (BSA) and Dextran-T10 macromolecules. The mean apparent selectivity increases with increasing transmembrane pressures until it reaches a maximum after which it decreases. The mean apparent selectivity increases with increasing Reynolds number consequence of a polarization decrease. Moreover, the selectivity increases with a decrease of the pore size and, also, with an increase of the membrane resistance. For low inlet concentrations of the solutes, the variation of the physical properties with the concentration does not produce any appreciable effect on the apparent selectivity.

The Effect of Variable Transport Properties in the Separation of Two Macromolecules by Differential Diffusivity in a Hybrid Membrane Cell – A CFD Study

A hybrid membrane cell comprising of semi and fully-permeable membrane sections, mounted in series, was employed to study the influence of variable transport properties (diffusivity and viscosity) in the separation of two macromolecules by a differential diffusivity mechanism. Separation pairs of bovine serum albumin (BSA)/dextran-T10 (DT10) and bovine serum albumin (BSA)/lysosyme (LYS) were considered. A numerical code was developed to quantify the effect of variable transport properties in the concentration, permeate velocity, and purity of the outgoing streams. The variation of the transport properties with concentration reinforces the accumulation of solutes over the semi-permeable membrane. The separation is more effective, with a higher concentration of BSA in the stream crossing the fully permeable membrane, when the accumulation of BSA is reinforced, comparatively to that of the other solute, and vice-versa. For high concentration polarization at semi-permeable membranes surface, the ratio between concentrations of BSA/DT10 and BSA/LYS is equal to 2.0 and 1.4, respectively. BSA purity in the outgoing stream reaches 60% and 56.5% for BSA/DT10 and BSA/LYS, respectively, compared to the 50% at the cell inlet. For the same operating conditions, supposing constant transport properties, the differential of purity is 20% lower for BSA/DT10 system and 6% higher for BSA/LYS.

Link between deviations from Murray's Law and occurrence of low wall shear stress regions in the left coronary artery.

Murray developed two laws for the geometry of bifurcations in the circulatory system. Based on the principle of energy minimization, Murray found restrictions for the relation between the diameters and also between the angles of the branches. It is known that bifurcations are prone to the development of atherosclerosis, in regions associated to low wall shear stresses (WSS) and high oscillatory shear index (OSI). These indicators (size of low WSS regions, size of high OSI regions and size of high helicity regions) were evaluated in this work. All of them were normalized by the size of the outflow branches. The relation between Murrays laws and the size of low WSS regions was analysed in detail. It was found that the main factor leading to large regions of low WSS is the so called expansion ratio, a relation between the cross section areas of the outflow branches and the cross section area of the main branch. Large regions of low WSS appear for high expansion ratios. Furthermore, the size of low WSS regions is independent of the ratio between the diameters of the outflow branches. Since the expansion ratio in bifurcations following Murrays law is kept in a small range (1 and 1.25), all of them have regions of low WSS with similar size. However, the expansion ratio is not small enough to completely prevent regions with low WSS values and, therefore, Murrays law does not lead to atherosclerosis minimization. A study on the effect of the angulation of the bifurcation suggests that the Murrays law for the angles does not minimize the size of low WSS regions.

Membrane Characterization Based on PEG Rejection and CFD Analysis

Characterization of membrane pore size by experimental methods is usually done by the determination of the rejection of polymeric molecules having a range of sizes such as PEG. These experiments are affected by concentration polarization, which can lead to erroneous interpretation of the results, mainly because the concentration and the permeate flux change along the membrane surface. Additionally, experimental methods alone are insufficient to obtain the membrane pore size. To improve the current approach, numerical methods are used to understand mass transport limitations in rejection experiments and to predict the membrane pore size. In the current study, the results show that the ultrafiltration membrane has a MWCO of 20 kDa, different from the value set by the manufacturer (30 kDa). For the experimental conditions, concentration dependent viscosity and osmotic pressure do not influence the permeate flow rate or rejection. Moreover, the membrane pore size was found to be 2.59 nm. This value was determined comparing rejection values obtained by numerical and experimental results. Numerical analysis is also important to characterize the flow and mass transport in each point at membrane surface.

The accuracy of the stagnant film equation in the study of electrophoretic migration of solutes near an ultrafiltration membrane—a numerical study

In membrane separation processes, the film equation is frequently used since it is a fast and easy way to predict the permeate velocity. In this work, the applicability of the film equation, based ...