Behaviour of Erythrocyte Suspensions in Flow Through a Branched Tube. A Study on the Deposition Hypothesis of Atherogenesis

Introduction

Predilection sites of atherosclerosis and thrombotic events are the inner walls of curved and the outer walls of branched arteries. At these sites similiar hydrodynamic situations exist: elevated hydrostatic pressure, stagnating flow tending to separate, secundary flow or turbulence. Such flow conditions may be involved in atherogenesis by increasing the transport of atherogenetic substances into the wall or depositing blood elements onto the endothelium. Both concepts are still hypothetically.

The aim of our experiments was only to answer one of the unanswered questions: can flow conditions occurring in branched tubes cause deposits of suspended blood cells on (impermeable) tube walls, and what are the hydrodynamic mechanisms involved? The presented experiments deal with the motion and distribution of red blood cells (RBC) studied in stationary branched flow. Corresponding “micro-hydrodynamic” local flow conditions have been studied in parallel experiments.

Materials and Methods

Glass models: 1. straight glass tubes (ID 3.0 mm, wall thickness 0.2 mm) with a side branch (ID 1.5 mm; branch angle 90°); 2. tubes with rectangular section area (2.0 × 1.5 mm) side branch (ID 1.5 mm; branch angle 90°) used for sedimentation experiments; 3. T-tube to produce a stagnation point flow: the inflow tube (ID 3.45 mm) leads the fluid vertically on to the window of a flow chamber (170 × 10 × 5 mm); distance between inflow tube and window was 2.7 mm.

Suspensions: A. Once saline-washed human RBC in isosmotic saline solutions of Dextran (Rheomacrodex®, 6 g%; MW 40,000). B. Washed human RBC in saline solutions of Polyvinylpyrrholidon (1 g%, MW 360,000) added to make the RBC “sticky”. C. RBC in solutions of 1.5 g% Polyvinylpyrrholidon (360,000). Suspensions A and B contained 5 vol% of homologous plasma. Viscosity of suspensions A, B and C: η = 2.6 cp, 2.6 cp and 5.4 cp resp.; volume fraction RBC c ≈ 0.01.

Flow apparatus: A Marione bottle (reservoir for the suspension) kept the hydostatic pressure constant. From here the suspension flowed through a stabilisation tube into the branched tube. The branches were connected to separated cylinders to measure the volume flow per time through the main (Q₁) and the side (Q₁) branch. The main tube was mounted vertically in all except in sedimentation experiments. Particle behaviour within the glass models 1 and 2 and in the stagnation point flow was studied by dark field microscopy. By means of a laser ultra-microscope (Kratzer and Kinder, 1975), velocities of RBC in the stagnation point flow were measured.

Results and discussion

Due to “radial migration” in undisturbed straight tube flow (Q₁ = 0) a RBC free layer adjacent to the wall prevents RBC from contact with the wall (Fig. 2, 3 a). By any flow Q₁ > 0 the thickness of this layer is altered in a definite region opposite the orifice of the side branch. Mere widening is observed with small Q₂ (Fig. 3 b). For Q₂ exceeding a critical value the layer vanishes in the region of reattachment. At the same site “sticky” RBC are deposited, Fig. 4, being torn off with larger Q₂. The flow at the sites of RBC concentrated near wall or deposited can be described as stagnation point flow (Fig. 1), which is characterized by ventrical (V₁) and wall-parallel (V_//) velocity components. The V_I and V_// necessary to allow deposis can be measured in a rotary symmetric stagnation point flow. Under such flow conditions the V_IE and V_//E of RBC necessary to deposit are: V_IE ⩾ 0.45 mm/s 0.3 mm distant from the wall; V_//E < 0.05–0.13 mm/s (wall shear stress τ_W < 0.27–0.7 dyn/cm²). Similiar values have been measured in the branched tube (Fig. 5). Figure 7 shows pathways and velocities of RBC in the stagnation point flow, forming stripes of deposits on the flat cover glass of the perfused T-tube. Deposits formed by sedimented RBC in a branched tube flow are shown and explained in figure 6.

The results indicate that the formation of RBC deposits depend on the existence of velocity components V^I normal to and against the wall of the perfused tube. Minimum V^I are necessary to bring the RBC to the wall (s. a. Forstrom et al., 1974). If moreover the parallel velocity component V_// does not exceed a certain value, deposits can be formed (s. a. Petschek and Weiss, 1970). Deposition sites in branched glass tubes correspond to predilection sites of atherosclerosis in branched arteries (e.g. Wolkoff, 1929).