Physical mechanisms of red blood cell splenic filtration

Abstract

The splenic interendothelial slits fulfill the essential function of continuously filtering red blood cells (RBCs) from the bloodstream to eliminate abnormal and aged cells. To date, the process by which 8 [Formula: see text]m RBCs pass through 0.3 [Formula: see text]m-wide slits remains enigmatic. Does the slit caliber increase during RBC passage as sometimes suggested? Here, we elucidated the mechanisms that govern the RBC retention or passage dynamics in slits by combining multiscale modeling, live imaging, and microfluidic experiments on an original device with submicron-wide physiologically calibrated slits. We observed that healthy RBCs pass through 0.28 [Formula: see text]m-wide rigid slits at 37 °C. To achieve this feat, they must meet two requirements. Geometrically, their surface area-to-volume ratio must be compatible with a shape in two tether-connected equal spheres. Mechanically, the cells with a low surface area-to-volume ratio (28% of RBCs in a 0.4 [Formula: see text]m-wide slit) must locally unfold their spectrin cytoskeleton inside the slit. In contrast, activation of the mechanosensitive PIEZO1 channel is not required. The RBC transit time through the slits follows a [Formula: see text]1 and [Formula: see text]3 power law with in-slit pressure drop and slip width, respectively. This law is similar to that of a Newtonian fluid in a two-dimensional Poiseuille flow, showing that the dynamics of RBCs is controlled by their cytoplasmic viscosity. Altogether, our results show that filtration through submicron-wide slits is possible without further slit opening. Furthermore, our approach addresses the critical need for in vitro evaluation of splenic clearance of diseased or engineered RBCs for transfusion and drug delivery.

Keywords: boundary integral method; erythrocyte; fluid–structure interaction; spleen red pulp; splenic retention.

Fig. 1.

Principle of the experiment and typical behaviors of RBCs in submicron-wide slits. (A) Schematics of an RBC approaching a slit. The x, y, and z axes indicate the flow direction, width, and depth of the channel, respectively. (B) RBCs can pass through 0.28-$\mathrm{\mu }$m wide slits. Left: Electron microscopy image of a 0.28-$\mathrm{\mu }$m wide silicon bridge (in light gray) used for molding 0.28-$\mathrm{\mu }$m wide slits; (Scale bar, 1 $\mathrm{\mu }$m). Right: Superimposed images of an RBC (in red) passing through a 0.28 $\times$ 1.87 $\times$ 5.0 $\mathrm{\mu }$m${}^3$ slit (Bottom view in the XY plane); the images are extracted from Movie S1; (Scale bar, 10 $\mathrm{\mu }$m). (C) Experimental observations (Top rows) and numerical simulations (Bottom rows) of transiting RBCs displaying dumbbell and tip shapes at slit exit, in 0.74 $\times$ 2.12 $\times$ 4.80 $\mathrm{\mu }$m${}^3$ (Top panel) and 0.86 $\times$ 2.75 $\times$ 4.70 $\mathrm{\mu }$m${}^3$ (Bottom panel) slits, respectively. Time in ms. (Scale bar, 10 $\mathrm{\mu }$m).

Fig. 2.

RBC shape in a slit. (A) Schematics of two equal spheres connected by an infinitely thin tether. (B) Image of an RBC symmetrically positioned in a 0.37 $\times$ 1.33 $\times$ 4.7 $\mathrm{\mu }$m${}^3$ slit at 37 °C, with two arcs of circle superimposed at its front and rear. (Scale bar, 5 $\mathrm{\mu }$m). (C) Radius of front and rear arcs of circle averaged on 10 RBCs symmetrically positioned in slits versus half slit depth $D/2$; temperature from 17 °C to 37 °C; in-slit pressure drop $\mathrm{\Delta }P$ = 500 Pa. The solid line is the bisector. (D) Simulation of an RBC passing through a 0.28 $\times$ 1.9 $\times$ 5.0 $\mathrm{\mu }$m${}^3$ slit at 37 °C under an in-slit pressure drop 500 Pa. Inside the slit is formed a thin neck that does not fill the slit’s depth. (E) Top and tilted views of the 3D reconstruction of an RBC in a 0.67 $\times$ 2.34 $\times$ 4.98 $\mathrm{\mu }$m${}^3$ slit. The slit walls are drawn in blue as a guide to the eyes. (Scale bar, 3 $\mathrm{\mu }$m). (F) Surface area $S$ versus volume $V$ of circulating RBCs corrected from refs. and , two equal-sphere curve (solid green line), and approximate two cone-sphere curve mimicking the experimental slit geometry (dashed purple line).

Fig. 3.

In-slit mechanisms of RBC deformation. (A and B) RBC corrected surface area from ref. (open circles) and computed minimal surface area required to transit through a 0.38 $\times$ 1.3 $\times$ 4.7 $\mathrm{\mu }$m${}^3$ slit at $\mathrm{\Delta }P$ = 500 Pa (solid and dashed lines) versus RBC volume at 25 °C (A, blue lines) and 37 °C (B, red lines), with the two equal-sphere model (green solid line). (C) RBC deformation (principal stretch in color scale) and spectrin unfolding (region with spectrin unfolding is marked in gray), calculated in ABAQUS computation. The volume and surface area of the RBC are 97.9 $\mathrm{\mu }$m${}^3$ and 135.1 $\mathrm{\mu }$m${}^2$ which is close to the red solid curve in (B). The slit dimensions are 0.38 $\times$ 1.3 $\times$ 4.7 $\mathrm{\mu }$m${}^3$, and temperature is 37 °C. (D) Critical pressure drop $\mathrm{\Delta }{P}_c$ required to pass through the reference slit versus sphericity index at 25 °C and 37 °C. The black dashed line represents the average physiological pressure of 500 Pa, and the blue and red arrows represent the maximal sphericity index needed to pass through under this physiological pressure. (E) Critical pressure drop $\mathrm{\Delta }{P}_c$ versus slit width $W$ ($L$ = 1.3 $\mathrm{\mu }$m, $D$ = 4.7 $\mathrm{\mu }$m) for the RBC standard shape. Experimental data were obtained from measurements performed at 37 °C of the RBC transit time ($t_t$) through slits of varying width under different applied pressure drops, by linearly extrapolating the curves 1/$t_t$ versus $\mathrm{\Delta }P$ at 1/$t_t$ = 0 (Fig. 5A). (F) RBC shapes and surface tension (color scale) in a 0.80 $\times$ 2.0 $\times$ 5.0 $\mathrm{\mu }$m${}^3$ slit under an in-slit pressure drop of 350 Pa for various surface area-to-volume ratios (unit: 1/$\mathrm{\mu }$m).

Fig. 4.

No calcium influx is detected during RBC passage through the slits. (A) Epifluorescence images of intracellular calcium in RBCs upstream of, within, and downstream of 0.80 $\times$ 2.77 $\times$ 4.70 $\mathrm{\mu }$m${}^3$ slits, in the absence (Top row) and presence (Bottom row) of 1 mM calcium in the external medium. The RBC contours are drawn in red. The white arrow indicates the flow direction. In-slit pressure drop $\mathrm{\Delta }P$ = 490 Pa. (Scale bar, 10 $\mathrm{\mu }$m). (B) Intracellular calcium fluorescence intensity upstream (in white) and downstream of the slits (in gray) in the absence (Left) and presence (Right) of calcium under $\mathrm{\Delta }P$ = 100Pa. Median values are displayed with 25% and 75% percentiles, and min/max values as whiskers. N: number of analyzed RBCs.

Fig. 5.

Dynamics of RBC passage through the slits. (A) Inverse of transit time $1/t_t$ versus in-slit pressure drop $\mathrm{\Delta }P$ at 37 °C for slits of different dimensions, from 1.09 to 0.28 $\mathrm{\mu }$m in width: experimental data (closed circles), simulations (open squares with cross). The lines are linear fits of the experimental data. (B) Log-log representation of the $1/t_t(\mathrm{\Delta }P-\mathrm{\Delta }{P}_c)$ slope $S_l$ versus slit width at 37 °C. Black closed circles: no calcium, no plasma; black closed squares: no calcium, plasma; red closed squares: 1 mM calcium, plasma; purple closed squares: 1 mM calcium, plasma, 5 $\mathrm{\mu }$M GsMTX4: green closed squares: 1 mM calcium, plasma, 10 $\mathrm{\mu }$M TRAM34. The solid line is a fit of $S_l$ vs. $W^3$.