Flow characteristics of blood in microchannel.

Khan, Mohd Nadeem ; Islam, Mohd ; Hasan, M.M. 等

Introduction

Medical micro-assay systems will vastly improve medical diagnosis and patient monitoring by eliminating the often slow and cumbersome processes of conventional clinical laboratories. The basic operations of these minature assay devices will involve the transport and manipulation of blood and blood components at dimensions of tens to hundreds of microns and in volumetric rates of around 1- 10[micro]l/sec [1]. Development of various microfluidic components to process blood in these devices must be based on a firm understanding of its non-Newtonian properties at these dimensions. This understanding will permit determination of fluid flow resistances within fluidic components as well as quantification of the high fluid shear forces incurred on blood constituents in flows through irregular geometries. It has long been established that blood is "shear thining": viscosity decreases as shear rate increases. Many constitutive equations have been demonstrated for blood [2-4]. Based on the expected flow rates and dimensions of microfluidic components [3], the shear stresses generated in these devices will be very high, far exceeding the hypothesized yield stresses for blood. When yield stress is negligible, most Casson-like models simplify to some form of the power law.

Human blood can be regarded as a homogenous fluid from a macroscopic viewpoint, established numerical techniques based on continuum mechanics, such as finite difference method (FDM), finite volume method (FVM) and finite element method (FEM), have been used to analyze blood flow as homogeneous fluid. At the microscopic level, however, blood is regarded as a suspension in which solid blood cells, such as red blood cells (RBCs), white blood cells (WBCs) and platelets are suspended in fluid plasma. The particle method is a natural choice for simulating blood flow on a blood cellular scale, in which each component of blood is modeled by an assembly of discrete particles [5,6].

Composition of Blood

From a rheological point of view, the most important constituents of blood are plasma and the red blood cells (RBCs). RBCs take up about half the volume of whole blood, and have a significant influence on the flow. Plasma consists of 90 % (w/w) water, 7 % (w/w) is proteins, and it behaves like a Newtonian fluid with a constant viscosity [7]. The cells are as mentioned mainly RBCs, the parameter used for modelling purposes is the hematocrit level, which is the volume fraction that RBCs occupy. When blood is left undisturbed, the cells start to coagulate. The process is called blood clotting. There are all together 13 factors in the blood clotting cascade.

Rheological Properties of Blood

To get the behavior of blood in a shear flow, the key features is shear rate which is defined as a measure of the deformation of the liquid. The viscosity of blood can be divided into three regions. At low shear rates, the viscosity is constant, and then it drops until it again reaches a constant plateau. When the viscosity of a liquid is a decreasing function of the shear rate, it is said to be shear thinning. In the figure 1, it is also indicated that, on a microscopic level, the shear thinning is caused by the break down of aggregates and a cell layering of the RBCs. This internal organization of the cells reduces the friction [8].

[FIGURE 1 OMITTED]

Figure 2 shows how the apparent viscosity, the relation between shear stress and shear rate, increases with the hematocrit. It is seen that human whole blood (HWB) has a higher viscosity than HWB without fibrinogen, a protein important for cell aggregation. At zero hematocrit all the fluids behaves Newtonian. At small shear rates cell aggregation has a large influence on the viscosity. For a hematocrit at 45%, the difference between * , x, and [degrees] is more pronounced at small shear rates, compared to hematocrits at zero and 90%. Meaning, the effect of cell aggregation is largest at moderate hematocrits.

Figure 3 shows the importance of aggregation and deformation of RBCs for a hematocrit at 45%. The hematocrit where the aggregation effect was seen to be large. When HWB is compared to a suspension of hardened cells, a large difference in viscosity is seen at high shear rates. In other words, at high shear rates the deformability is important for the shear thinning effect. At low shear rates is another comparison with defibrinated blood. Also cell aggregation has a large influence on the viscosity at low shear rates. It may be noticed that a suspension of hardened cells has a Newtonian behavior.

[FIGURE 2 OMITTED]

[FIGURE 3 OMITTED]

Deformability of red blood cells

As plasma is showing the Newtonian characteristics, it is evident that the red blood cells are responsible for the non-Newtonian behavior. Red blood cells are relatively big in the sense that their Brownian motion has little effect on the flow. Blood is shear thinning, meaning the viscosity decreases with increasing shear rate. This phenomenon can be explained by the blood cells ability to align and deform in the flow.

In Fig. 4 can be seen a comparison of different kinds of particles; even though liquid droplets of oil dispersed in water show higher viscosity than normal blood, they are comparable. The flow of oil droplets in water is, as for blood, maintained at very high volume fractions. Therefore, we may conclude that droplets and RBCs have a similar elastic behavior. The deformability of the RBCs makes blood a remarkable fluid. It is seen, when the volume fraction is more than 50%, most other fluids will stop to flow. Blood, however, can maintain the flow until hematocrits of 98%. Still, a suspension of oil droplets is more viscous than a suspension of red cells. It is therefore believed that a RBC is more deformable than a droplet.

Blood cells are responsible for the shear thinning effect, and the physical explanation for this phenomenon is the cells flexibility and tendency to align with the flow. The red cells align in such a way that the largest dimension is paralleled with the direction of the flow; the fraction of aligned cells increases with the shear rate.

[FIGURE 4 OMITTED]

Flow Analysis of Blood in Microchannels

In complex geometries normal forces may affect the flow and flow resistance [8]. Blood can not be considered as a continuum at very small length scales. Due to the high shear rates, cells migrate away from the wall towards the center. In this way plasma lubricates the flow of the cellular content. As plasma is a Newtonian liquid, this observation speaks for Fung's solution that the liquid near the wall should be expressed with a shear-independent viscosity.

Chang et al [9] study investigated blood flow through three simple "mesoscopic" geometries at flow rates expected for microanalysis system. The results indicate that at the high shear rates expected for microfluidic devices, the flow resistance of blood in simple fluidic geometries does decrease somewhat as flow rates are increased. This result is consistent with predictions of fluid resistances by numerical modeling using a simple power law equation, validating the use of this model for simple geometries at scales of around 100-200 [micro]m. Additionally, simulations with the well- established Walbum-Schneck power law model, which is strongly non- Newtonian, also seemed to indicate that despite the weak non-linearity of pressure vs. flow rate, a linear fit can provide a reasonable first-order estimation of the relationship between flow rates and driving pressure. Another shortcoming the study was that the Fahraeus effect was not account for. When a large reservoir of blood feeds into tubes smaller than about 200 [micro]m, there is a tendency for hematocrit within the tubes to decrease, this effect becoming progressively more pronounced with smaller tubes. With lower hematocrit within the tubes, blood appears less viscous.

Tsubota et al [10] proposed a new simulation technique using a particle method to analyze the microscopic behavior of blood flow. A simulation region, including plasma, red blood cells (RBCs) and platelets, was modeled by an assembly of discrete particles. The proposed method was applied to the motions and deformations of a single RBC and multiple RBCs, and the thrombogenesis caused by platelet aggregation. The simulation results demonstrate that the proposed method enables the analyses of a single RBC motion and deformation, initial thrombogenesis, growth and destruction of a thrombus, and the collective behavior of multiple RBCs. The proposed method is potentially an important and useful approach for investigating the mechanical behavior of blood cells in blood flow at the microscopic level.

Javier et al [11] presented an original approach for the estimation of cross- sectional blood flow velocities in intravital microscopy videos. The approach was developed by exploiting the assumed laminar character of blood flow across most sections of the microvascular network. The proposed approach has been tested on synthetic sequences and real videos (where the assumptions at the basis of the proposed scheme may not strictly hold). The results have shown accurate or predictable (for the case of the in vitro and in vivo videos) velocity estimates.

E.Chavira-Martinez et al [11] propose modifications to the coefficients of basic power law model of viscosity for Non- Newtonian fluids, based on the general behavior of polymeric suspensions allowing reproducing the variation of blood viscosity for several RBC concentrations. The results show good agreement with those for numerical analysis of rheological properties of blood in normal concentrations.

Recommendations for future work

For future and better results of rheological experiments on blood, it will require to measure the hematocrit. This is done in a microhematocrit centrifuge. The hematocrit is a very important rheological parameter. At hematocrits below 8% blood behaves Newtonian, and, in general, the viscosity is an increasing function of the hematocrit. More advanced work will require for expected changes in local hematocrit in various flow geometries. Additionally, it will be important to observe the orientation, deformation and hemolysis of blood cells subject to different flow conditions involving high shear rates.

Reference

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[6] K. Boryczko, W. Dzwinel and D. A. Yuen, Dynamical Clustering of Red Blood Cells in Capillary Vessels, Journal of Molecular Modeling, , 2003,vol.9, pp.16-33.

[7] Fung, Y.C.: Biomechanics, Mechanical Properties of Living Tissues. Springer Verlag, Second Printing, 1984.

[8] Lennart Bitsch M, "Blood Flow in Microchannels" Thesis, Microelectronic Centre MIC, Techanical University of Denmark, 2002.

[9] Wesley Chang, David Trebotich, Luke P. Lee, Dorian Liepmann, "Blood flow in simple microchannels" 1st Annual International Conference IEEE-EMBS special topic conference on Microtechnologies in Medical & Biology, 2000, P.P 311-315.

[10] Ken-ichi Tsubota, Shigeo Wada, Hiroki Kamada, Yoshitaka Kitagawa, Rui Lima and Takami Yamaguchi, "A Particle Method for Blood Simulation, Application to Flowing Red Blood Cells and Platelets" Journal of Earth Simulator, 2006, vol.5, P.P 2-7.

[11] Javier Toro, Boris Chayer, Guy Cloutier, "Estimation of Microcirculatory Blood Flow Velocity Profile" Journal of Molecular Modeling, , 2007,vol.19, pp.26-31.

[12] E. Chavira-Martinez, A. Rangel-Huerta, R. Fournier-Lomas "Simulation of Microfluidic Blood Viscosity for MEMS Devices" 7nd ed. 2003, New York Springer-Verlag.

Mohd Nadeem Khan (1), Mohd Islam (2) and M.M. Hasan (2)

(1) Department of Mechanical Engineering, Krishna Institute of Engineering and Technology, Ghaziabad (India) E-Mail: [email protected]

(2) Department of Mechanical Engineering, Jamia Millia Islamia, New Delhi (India) E-Mail: [email protected]