In this study, we show the importance of extensional rheology, in addition to the shear rheology, in the choice of blood analog solutions intended to be used in vitro for mimicking the microcirculatory system. For this purpose, we compare the flow of a Newtonian fluid and two well-established viscoelastic blood analog polymer solutions through microfluidic channels containing both hyperbolic and abrupt contractions/expansions. The hyperbolic shape was selected in order to impose a nearly constant strain rate at the centerline of the microchannels and achieve a quasihomogeneous and strong extensional flow often found in features of the human microcirculatory system such as stenoses. The two blood analog fluids used are aqueous solutions of a polyacrylamide (125 ppm w/w) and of a xanthan gum (500 ppm w/w), which were characterized rheologically in steady-shear flow using a rotational rheometer and in extension using a capillary breakup extensional rheometer (CaBER). Both blood analogs exhibit a shear-thinning behavior similar to that of whole human blood, but their relaxation times, obtained from CaBER experiments, are substantially different (by one order of magnitude). Visualizations of the flow patterns using streak photography, measurements of the velocity field using microparticle image velocimetry, and pressure-drop measurements were carried out experimentally for a wide range of flow rates. The experimental results were also compared with the numerical simulations of the flow of a Newtonian fluid and a generalized Newtonian fluid with shear-thinning behavior. Our results show that the flow patterns of the two blood analog solutions are considerably different, despite their similar shear rheology. Furthermore, we demonstrate that the elastic properties of the fluid have a major impact on the flow characteristics, with the polyacrylamide solution exhibiting a much stronger elastic character. As such, these properties must be taken into account in the choice or development of analog fluids that are adequate to replicate blood behavior at the microscale.

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Extensional flow of blood analog solutions in microfluidic devices.

Important progress has been achieved in recent years in simulating the fluid-structure interaction around cardiac valves. An important step in making these computational tools useful to clinical practice is the development of postprocessing techniques to extract clinically relevant information from these simulations. This work focuses on flow through the aortic valve and illustrates how the computation of Lagrangian coherent structures can be used to improve insight into the transport mechanics of the flow downstream of the valve, toward the goal of aiding clinical decision making and the understanding of pathophysiology.

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Computational analysis of an aortic valve jet with Lagrangian coherent structures.

We undertake here a systematic study of the rheology of blood in steady-state shear flows. As blood is a complex fluid, the first question that we try to answer is whether, even in steady-state shear flows, we can model it as a rheologically simple fluid, i.e., we can describe its behavior through a constitutive model that involves only local kinematic quantities. Having answered that question positively, we then probe as to which non-Newtonian model best fits available shear stress vs shear-rate literature data. We show that under physiological conditions blood is typically viscoplastic, i.e., it exhibits a yield stress that acts as a minimum threshold for flow. We further show that the Casson model emerges naturally as the best approximation, at least for low and moderate shear-rates. We then develop systematically a parametric dependence of the rheological parameters entering the Casson model on key physiological quantities, such as the red blood cell volume fraction (hematocrit). For the yield stress, we base our description on its critical, percolation-originated nature. Thus, we first determine onset conditions, i.e., the critical threshold value that the hematocrit has to have in order for yield stress to appear. It is shown that this is a function of the concentration of a key red blood cell binding protein, fibrinogen. Then, we establish a parametric dependence as a function of the fibrinogen and the square of the difference of the hematocrit from its critical onset value. Similarly, we provide an expression for the Casson viscosity, in terms of the hematocrit and the temperature. A successful validation of the proposed formula is performed against additional experimental literature data. The proposed expression is anticipated to be useful not only for steady-state blood flow modeling but also as providing the starting point for transient shear, or more general flow modeling.

Modeling of the blood rheology in steady-state shear flows

The pulsatile blood flow through human aortic arch and three major branches are computationally studied to investigate the effect of blood rheology on the hemodynamic parameters. The human aorta model is reconstructed from the computed tomography (CT) images of specific patient. The results of nine non-Newtonian (Casson, K-L, Modified Casson, Carreau, Carreau-Yasuda, Cross, Power-law, Modified Power-law, and Generalized Power-law) models are analyzed and compared with those of Newtonian model and reveal very interesting hemodynamic features for each model. Among the applied non-Newtonian models, the Cross model displays significantly different distribution of wall shear stress (WSS) and velocity field through the aorta at diastole. Comparing the local shear stress magnitude in three branches at different critical cardiac instants shows that the shear thinning nature of blood can slightly influence WSS at diastole, in all branches. The effect of blood rheology appears clearly in the brachiocephalic and carotid branches, at peak systole. In the high-shear rate zones, the lowest WSS is estimated by the Carreau model. The Newtonian model has close prediction to the Cross model at peak systole. The power law model predictions remain the nearest to those of the Carreau model along the cardiac cycle.

Effect of rheological models on the hemodynamics within human aorta: CFD study on CT image-based geometry

Patient-specific computational fluid dynamics (CFD) is a promising tool that provides highly resolved haemodynamics information. The choice of blood rheology is an assumption in CFD models that has been subject to extensive debate. Blood is known to exhibit shear-thinning behaviour, and non-Newtonian modelling has been recommended for aneurysmal flows. Current non-Newtonian models ignore rouleaux formation, which is the key player in blood's shear-thinning behaviour. Experimental data suggest that red blood cell aggregation and rouleaux formation require notable red blood cell residence-time (RT) in a low shear rate regime. This study proposes a novel hybrid Newtonian and non-Newtonian rheology model where the shear-thinning behaviour is activated in high RT regions based on experimental data. Image-based abdominal aortic and cerebral aneurysm models are considered and highly resolved CFD simulations are performed using a minimally dissipative solver. Lagrangian particle tracking is used to define a backward particle RT measure and detect stagnant regions with increased rouleaux formation likelihood. Our novel RT-based non-Newtonian model shows a significant reduction in shear-thinning effects and provides haemodynamic results qualitatively identical and quantitatively close to the Newtonian model. Our results have important implications in patient-specific CFD modelling and suggest that non-Newtonian models should be revisited in large artery flows.

https://royalsocietypublishing.org/doi/pdf/10.1098/rsif.2018.0486

Accounting for residence-time in blood rheology models: do we really need non-Newtonian blood flow modelling in large arteries?

The purpose of this study is mainly directed towards present of viewpoints on critical and commentary analysis on blood rheology, blood viscosity models, and physiological flow conditions. Understanding these basics is fundamental to meet the need for a sufficient and reliable CFD model of blood. Most of the used viscosity models on this manner have determined from parameter fitting on experimental viscosity data. Availability of experimental data from literature to define viscosity models of CFD analysis should be accurately chosen and treated in order to avoid any errors. Several basic gaps that limit the CFD model results are identified and given opportunities for future research.

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A critical review on blood flow in large arteries; relevance to blood rheology, viscosity models, and physiologic conditions

This study analyzes especially drag and lift models recently developed for fluid-solid, fluid-fluid or liquid-liquid two-phase flows to understand their applicability on the computational fluid dynamics, CFD modeling of pulsatile blood flow Virtual mass effect and the effect of red blood cells, RBCs aggregation on CFD modeling of blood flow are also shortly reviewed to recognize future tendencies in this field Recent studies on two-phase flows are found as very useful to develop more powerful drag-lift models that reflect the effects of blood cell's shape, deformation, concentration, and aggregation

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Analysis of conventional drag and lift models for multiphase CFD modeling of blood flow

Twisted tapes are used in thermal performance intensification of heat exchangers. The present paper focuses on the last eleven years experimental and numerical studies of the twisted tapes that are inserted into a plain circular horizontal tube with different kind of working fluids such as air, water, nanofluids, high viscosity oil, servotherm medium oil, microencapsulated phase change material slurry, non-Newtonian tomato puree, carboxymethyl cellulose and CuO mixture, lubricating oil. It aims to be a summarising and guiding source with detailed tables, figures, graphs and a criticization for the researchers. Correlation equations of friction and Nusselt number for “plain tube” and “classical twisted tape inserted plain tube” were summarised for laminar/turbulent regimes. Equipment (or used software) list was made, and items were explained for experimental and numerical works. Ranges of some critical parameters were presented from the selected works. Twisted tapes were categorised according to their geometrical designs. Then, performance considerations were made on them (in the category itself) while the flow regimes were also taken into account. Finally, by considering all the geometrical variation groups, the relation between design and performance was tried to be figured out. Some geometrical design suggestions were given for twisted tapes.

The current state on the thermal performance of twisted tapes: A geometrical categorisation approach

This study reports the cross-sectional curvature effect resulted from a twisted tape fabrication or installation into an annular pipe on the enhancement of heat transfer to pay attention to the use of twisted tapes more efficiently Six different twisted tapes having two twist ratios (3 and 4) and three curve ratios (1761, 2252 and 3271) in the Reynolds number range from 5840 to 30,900 were numerically analyzed The analysis method was validated with three different experimental results from loose-fit to tight-fit of a twisted tape According to polyhedral mesh element analysis of curved cross-sectional twisted tapes, capable of having better compatibility with experimental results, Nusselt numbers increased with increasing curve ratio and decreasing Reynolds number and twist ratio While the curved twisted tape is more efficient than the smooth tube, losses on heat transfer efficiency are observed compared to the classical twisted tape Although the losses caused by the curvature on the twisted tape appear to be insignificant at high curve ratios, the effect of low curve ratios increases significantly For the lowest CR and the highest TR under analysis conditions, it was observed that TT lost 28 % of its normal productivity increase due to this effect

Fuat Yilmaz

Papers

A critical review on blood flow in large arteries; relevance to blood rheology, viscosity models, and physiologic conditions

Analysis of conventional drag and lift models for multiphase CFD modeling of blood flow

The current state on the thermal performance of twisted tapes: A geometrical categorisation approach

The cross-sectional curvature effect of twisted tapes on heat transfer performance

Heat transfer augmentation using periodically spherical dimple-protrusion patterned walls of twisted tape