An energy-rate based blood viscosity model incorporating aggregate network dynamics

Existing time-dependent blood viscosity models that involve aggregation dynamics are mainly based on structural variables and/or viscoelastic models in order to describe the bulk mechanical properties of the fluid, but the implications of important characteristics of blood microstructure, such as the time- and flow-dependent characteristics of the red blood cell network developed due to aggregation at low shear rates, have not been thoroughly investigated. In this paper a time-dependent blood viscosity model is developed based on an energy-rate model previously proposed (Skalak et al., Biophys. J. 35 (1977), 771-781), which describes the total work needed to overcome the various forces developed between aggregated cells, including the adhesive, elastic and dissipative forces. Novel formulations of the forces acting on the fluid are developed and implemented in a volume-averaged version of the energy-rate model. The calculation of the viscosity is based on the relationship between the rate of energy changes and shear stress per unit volume of the fluid. The results show that network characteristics may significantly influence the viscosity blood at low shear rates and exhibit good agreement with experimental observations.

Erythrocyte aggregation at non-steady flow conditions: a comparison of characteristics measured with electrorheology and image analysis

In the present study electro-rheology (Contraves LS30 viscometer-based system) and optical shearing microscopy (Lincam CSS450 system and image analysis) techniques have been utilized in order to provide quantitative data on the behaviour of the microstructural properties of whole normal human blood at non-steady flow conditions. The objective of this work is to contribute towards a better understanding of red blood cell aggregation at flow conditions similar to that occurring in a circulatory system and to aid the interpretation and validation of electro-rheological data through a quantitative comparison with data acquired with optical shearing microscopy. Electro-rheology is a promising technique that has been used to provide bulk fluid properties, showing potential for basic research and diagnostic purposes, whereas optical shearing techniques offer a direct assessment of blood microstructure at a cellular level. However, little information exists in the literature regarding the relationships between electro-rheological measurements and blood microstructural characteristics. The results showed that the different non-steady flow conditions affect differently the dynamics of aggregation varying from a parabolic-decrease to an inverted S-shape curve with time. For a wide range of the non-steady flows results obtained with the two different techniques agree to a difference between 1.2 and 12%.

Coupled human erythrocyte velocity field and aggregation measurements at physiological haematocrit levels

Simultaneous measurement of erythrocyte (RBC) velocity fields and aggregation properties has been successfully performed using an optical shearing microscope and Particle Image Velocimetry (PIV). Blood at 45% haematocrit was sheared at rates of 5.4< or =gamma < or = 252 s(-1) and imaged using a high speed camera. The images were then processed to yield aggregation indices and flow velocities. Negligible levels of aggregation were observed for gamma > or = 54.0 s(-1), while high levels of aggregation and network formation occurred for gamma < or = 11.7 s(-1). The results illustrate that the velocity measurements are dependent on the extent of RBC aggregation. High levels of network formation cause the velocities at gamma > or = 5.4 s(-1) to deviate markedly from the expected solid body rotation profile. The effect of aggregation level on the PIV accuracy was assessed by monitoring the two-dimensional (2D) correlation coefficients. Lower levels of aggregation result in poorer image correlation, from which it can be inferred that PIV accuracy is reduced. Moreover, aggregation is time-dependent, and consequently PIV accuracy may decrease during recording as the cells break up. It is therefore recommended that aggregation and its effects are taken into account in future when undertaking blood flow studies using PIV. The simplicity of the technique, which requires no lasers, filters, or special pretreatments, demonstrates the potential wide-spread applicability of the data acquisition system for accurate blood flow PIV and aggregation measurement.

On the effect of microstructural changes of blood on energy dissipation in Couette flow

Red blood cell aggregation affects the flow of blood at low shear rates; not only the behaviour of the fluid deviates from its Newtonian characteristics, but, depending on the shearing history of the flow, the non-Newtonian characteristics may be influenced. It is not clear how the time and flow-dependent characteristics of the microstructural network developed in blood affect its mechanical properties. The present study aims to improve understanding of the effect of dynamic flow conditions on microstructural characteristics and consequently on the mechanical properties of the fluid. Viscosity measurements on blood samples from healthy volunteers (H=0.45) were taken with a double-walled Couette rheometric cell, under unsteady and quasi-unsteady flow conditions. The aggregation extent index A(alpha), and the microstructural integrity index A(I) were assessed with an optical shearing system and image analysis. Results showed that energy losses in Couette geometries may depend on the structural integrity of the developed RBC network.

Fast response characteristics of red blood cell aggregation

The present work reports on an important feature of the fast response dynamics of blood flow observed after abrupt changes of the shearing conditions: distinctive peak values in conductance and light reflection/transmission have been observed at short times after the abrupt changes in the shearing conditions and have been attributed to red blood cell (RBC) disorientation and shape changes. Optical shearing microscopy results from the present study show that this peak is directly related to the inter-cellular or inter-aggregate spacing, quantified as the plasma gaps present in the captured images. In order to provide a more in-depth understanding of the structural characteristics of blood subjected to abrupt changes in the flow conditions, normal human blood samples at hematocrits of 45, 35, 25 and 10% were sheared at 100 s(-1) and the shear then suddenly reduced to values decreasing from 60 to 0 s(-1). Results from the present study agree qualitatively and quantitatively with results previously reported in the literature: the hematocrit and the magnitude of the final shear rate affect the magnitude of the peak values. The characteristic peak time was mostly influenced by the cell concentration. It is suggested that aggregation forces may play a part in the process of the fast response structural and spatial rearrangements of RBC.

On the effect of dynamic flow conditions on blood microstructure investigated with optical shearing microscopy and rheometry

Red blood cell (RBC) aggregation affects significantly the flow of blood at low shear rates. Increased RBC aggregation is associated with various pathological conditions; hence an accurate quantification and better understanding of the phenomenon is important. The present study aims to improve understanding of the effect of dynamic flow conditions on aggregate formation; whole blood samples from healthy volunteers, adjusted at 0.45 haematocrit were tested in different flow conditions with a plate-plate optical shearing system, image analysis, and a double-walled Couette rheometric cell. Results are presented in terms of aggregation index Aa, aggregate size index As and number of aggregates, which are shown to vary with shear rate γ and with different shear rate variations with time γ. The aggregation index Aa was observed to increase as the shear rate decreased between 10 and 3 s−1. Above 10 s−1, Aa was found to have a minimum value indicating minimal aggregation while, at approximately 3 s−1, Aa reaches a maximum. The aggregation size index As, the number of aggregates, and the blood viscosity were found to vary considerably when the same sample was examined over the same shear rate range, but for different variations of shear rate with time, γ.