STIFFNESS INCREASE OF RED BLOOD CELLS DURING STORAGE

Zhensong Xu1, Yi Zheng4, Xian Wang1, Nadine Shehata5, Chen Wang6,7* & Yu Sun1,2,3*

1. AFM validation

To mimic the situation of an RBC experiencing shear force in the microfluidic channel, in the validation

experiments, we fixed the center of the RBC and used an AFM (Bioscope Catalyst, Bruker) tip to deform

an RBC edge.

In microfluidic measurement, RBC is located in the center of the microchannel, and shear-induced force

is symmetrically applied to the cell. As shown in Figure S2, the distributed shear stress (τ y) is equivalent

to a force (F s) acting on a position, y= y ' such that the two force systems are equivalent with the same

resultant force and the same resultant moment.

∫y '

r

τ y ( y− y ')dy=∫0

y '

τ y ( y '− y )dy (1)

τ y at each position y was quantified from finite-element simulation and satisfies

∫0

r

τ y dy=F s (2)

Combining Eq. (1) (2) gives

y '=0.7385r

where r is the radius of the RBC, which is within the range of 3-4 µm but varies from one cell to another.

In experiments, each RBC’s radius was measured via imaging. These results mean that the microfluidic

shear situation is equivalent to the application of F s, along a line, on the position y ' of the RBC body.

Correspondingly, in experiments, each RBC was accurately positioned with a micromanipulator to have

half of the cell adhered on a glass slide while the other half suspended (Figure S3) and a rectangular AFM

cantilever tip (MSNL-10 B: spring constant 0.023 N/m, length 210 µm, width 20 µm, thickness 0.5 µm)

was used to deform the free end. The cantilever tip applied F s on the position y ' of each RBC. An

example force-displacement curve from AFM measurement of an RBC is shown in Figure S3. The same

RBC sample was tested in our microfluidic device. For direct comparison, effective stiffness for the AFM

measured RBCs was calculated as Fs/L.

The results from both groups are summarized in Table S1. It can be seen that the effective stiffness

measured by AFM is slightly higher than the microfluidic device-measured results. Several error sources

could have contributed to the difference. (1) The AFM cantilever’s spring constant was carefully

calibrated with the thermal tune method integrated in the AFM by Bruker. The error of the calibrated

spring constant is within 5%, directly reflected in the AFM applied force. (2) The exact position of AFM

cantilever tip for applying the force F s also contains errors, although the best experimental care was used.

The position error is approximately one pixel (0.1613 µm/pixel), and for a 4 µm RBC, this position error

y '= 2.9 ± 0.1613 µm causes an error of 3.8% in the quantified effective stiffness of the RBC. (3) Finally,

in the derivation of equivalent loading position (Eq. (1) (2)), the force is supposed to be applied along a

line (dy → 0). However, in experiments, when the cantilever tip contacts the RBC, the width of the

contacting area is small but not zero. Finite element simulation of the experimental situation reveals that

the contact width is approximately 0.13 µm, as shown in Figure S4. Putting this width back to the

theoretical calculation (dy= 0.13 µm), it caused an error of 3.5% in the quantified effective stiffness of

the RBC. In summary, the validation experiments contained identifiable error sources as any

measurement; however, the results support the validity of our microfluidic measurement.

Table S1: Microfluidic device and AFM measured effective stiffness of RBCs (6 weeks)

Technique Microfluidic (n=220 RBCs) AFM (n=11 RBCs)

Effective stiffness 95 ± 7 µN/m 108 ± 18 µN/m

Figure S1: Schematic illustrations of area expansion, shear, and bend modes.

Figure S2: Schematic force diagram

Figure S3: AFM experiment and force displacement curve.

Figure S4: Contact width estimation by applying a force of 150 pN.

2. Effect of flow velocity and microchannel width on RBC effective stiffness

Figure S5: Drag force increases linearly with flow velocity. Deflection increases linearly for flow velocities below 0.06m/s. The flow velocity < 0.03 m/s used in experiments was not considered to be

sufficiently high to induce nonlinearity in RBC effective stiffness.

Figure S6: Channel width effect on RBC effective stiffness. The dependence of RBC effective stiffness on channel size becomes negligible for channel widths larger than 11 µm.