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Research Papers

Hydrodynamic Interaction Between a Platelet and an Erythrocyte: Effect of Erythrocyte Deformability, Dynamics, and Wall Proximity

[+] Author and Article Information
Koohyar Vahidkhah

Department of Mechanical and Aerospace Engineering,
Rutgers,
The State University of New Jersey,
Piscataway, NJ 08854

Scott L. Diamond

Department of Chemical and Biomolecular Engineering,
University of Pennsylvania,
Philadelphia, PA 19104

Prosenjit Bagchi

Department of Mechanical and Aerospace Engineering,
Rutgers,
The State University of New Jersey,
Piscataway, NJ 08854
e-mail: pbagchi@jove.rutgers.edu

1Corresponding author.

Contributed by the Bioengineering Division of ASME for publication in the Journal of Biomechanical Engineering. Manuscript received July 9, 2012; final manuscript received January 17, 2013; accepted manuscript posted January 29, 2013; published online April 24, 2013. Assoc. Editor: Jeffrey W. Holmes.

J Biomech Eng 135(5), 051002 (Apr 24, 2013) (11 pages) Paper No: BIO-12-1280; doi: 10.1115/1.4023522 History: Received July 09, 2012; Revised January 17, 2013; Accepted January 29, 2013

We present three-dimensional numerical simulations of hydrodynamic interaction between a red blood cell (RBC) and a platelet in a wall-bounded shear flow. The dynamics and large deformation of the RBC are fully resolved in the simulations using a front-tracking method. The objective is to quantify the influence of tank treading and tumbling dynamics of the RBC, and the presence of a bounding wall on the deflection of platelet trajectories. We observe two types of interaction: A crossing event in which the platelet comes in close proximity to the RBC, rolls over it, and continues to move in the same direction; and a turning event in which the platelet turns away before coming close to the RBC. The crossing events occur when the initial lateral separation between the cells is above a critical separation, and the turning events occur when it is below the critical separation. The critical lateral separation is found to be higher during the tumbling motion than that during the tank treading. When the RBC is flowing closer to the wall than the platelet, the critical separation increases by several fold, implying the turning events have higher probability to occur than the crossing events. On the contrary, if the platelet is flowing closer to the wall than the RBC, the critical separation decreases by several folds, implying the crossing events are likely to occur. Based on the numerical results, we propose a mechanism of continual platelet drift from the RBC-rich region of the vessel towards the wall by a succession of turning and crossing events. The trajectory deflection in the crossing events is found to depend nonmonotonically on the initial lateral separation, unlike the monotonic trend observed in tracer particle deflection and in deformable sphere-sphere collision. This nonmonotonic trend is shown to be a consequence of the deformation of the RBC caused by the platelet upon collision. An estimation of the platelet diffusion coefficient yields values that are similar to those reported in experiments and computer simulations with multicellular suspension.

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Figures

Grahic Jump Location
Fig. 1

(a) Schematic of the computation geometry. (b) Discretization of the cell surface. The actual number of triangles (20,480) is much higher than what is shown. The results will be plotted relative to the RBC center-of-mass.

Grahic Jump Location
Fig. 2

Simulation results showing the sequence of two different types of interactions in presence of a tank-treading RBC. Here Ca = 0.7 corresponding to γ·≈1000 1/s. (a)–(e) Crossing-type interaction. (f)–(j) Turning interaction. Marker points are shown in the cell surface which rotates along the surface indicating a tank-treading motion of the RBC. t* = 30 corresponds to a 30 ms interaction.

Grahic Jump Location
Fig. 3

The trajectory of the platelet center-of-mass relative to a tank-treading RBC. The initial location of the platelet is marked by ○ here and hereafter. Results from seven simulations are presented with different initial lateral separation ΔYo. The turning trajectory is observed for ΔYo ≤ 0.56 μm, and the crossing trajectory is observed for ΔYo ≥ 0.7 μm.

Grahic Jump Location
Fig. 4

Effect of initial relative orientation Δθo on turning and crossing events in presence of a tank-treading RBC. (a) Phase plot in Δθo – ΔYo plane. (b) and (c) sample trajectories obtained with different Δθo for turning and crossing events, respectively. The wide variability of the platelet trajectory is illustrated in (c) that is absent in deformable sphere-sphere interaction.

Grahic Jump Location
Fig. 5

(a) Deflection δ of platelet trajectory for the tank-treading RBC as a function of ΔYo and for different values of Δθo = π/4 (Δ), 0 (◊), −π/4 (□), −π/2 (○). The dashed line represents the deflection of passive tracers. (b) The change in RBC deformation index ΔD upon collision with the platelet is plotted. Inset shows the time-dependent deformation index D increases during the collision.

Grahic Jump Location
Fig. 6

Effect of initial relative orientation Δθo on turning, crossing, and riding events in presence of a tumbling RBC. (a) Phase plot in Δθo − ΔYo plane. (b) sample trajectories obtained with different Δθo and ΔYo. Turning, crossing, and riding trajectories are observed for the same ΔYo at different Δθo. (c) Platelet and tracer particle deflections δ in presence of a tumbling RBC.

Grahic Jump Location
Fig. 7

Effect of wall proximity on turning and crossing events in presence of (a) tank treading and (b) tumbling RBC. The RBC/platelet interaction is simulated by releasing the RBC/platelet pair at various distances YC from the wall and for varying initial vertical separation ΔYo. Open symbols indicate turning and filled symbols indicate crossing events.

Grahic Jump Location
Fig. 8

Differential effect of wall proximity: For the same |ΔYo|, a turning trajectory is observed when the platelet is located further away from the wall than the RBC (YPLT > YC), and a crossing trajectory is observed when the platelet is located closer to the wall (YC > YPLT)

Grahic Jump Location
Fig. 9

(a)–(c) Streamlines around a tank-treading RBC (a), and a tumbling RBC [(b)and (c)] showing closed (indicated by the arrow) and open streamlines. The thick dash lines in (b) and (c) indicate the instantaneous alignment of the RBC major axis. (d) Spatially averaged force on the platelet as a function of time for a representative crossing (—) and rolling (- - - - -). (e) and (f) Contours of pressure for rolling at two time instances.

Grahic Jump Location
Fig. 10

A proposed mechanism of continuous platelet dispersal from the RBC-rich region of the vessel towards the wall based on the trajectory deflection by a succession of turning and crossing events occurring due to the interaction with a RBC flowing near the edge of the plasma layer. When the platelet is initially located farther away from the wall than the RBC, a turning event has the higher probability to occur (since ΔYo,crit is large) that would bring the platelet from the RBC-rich region to the plasma layer [scenario (A) in the figure]. If a subsequent interaction occurs, a crossing event is likely to occur (since the platelet is now located closer to the wall than the RBC and ΔYo,crit is small), bringing the platelet even closer to the wall [scenario (B)].

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