Quantitative phase imaging of erythrocytes under microfluidic constriction in a high refractive index medium reveals water content changes

Changes in the deformability of red blood cells can reveal a range of pathologies. For example, cells which have been stored for transfusion are known to exhibit progressively impaired deformability. Thus, this aspect of red blood cells has been characterized previously using a range of techniques. In this paper, we show a novel approach for examining the biophysical response of the cells with quantitative phase imaging. Specifically, optical volume changes are observed as the cells transit restrictive channels of a microfluidic chip in a high refractive index medium. The optical volume changes indicate an increase of cell’s internal density, ostensibly due to water displacement. Here, we characterize these changes over time for red blood cells from two subjects. By storage day 29, a significant decrease in the magnitude of optical volume change in response to mechanical stress was witnessed. The exchange of water with the environment due to mechanical stress is seen to modulate with storage time, suggesting a potential means for studying cell storage.


Figure 7 simulation
In order to demonstrate the changes in OV due to displacement of water through the membrane, typical RBC values from previous literature are used to create a simple model of the cell. The simulation does not utilize QPM data from the experiment to avoid using assumptions along with the data to derive these parameters. The simulation shows a possible increase in OV of an average RBC due to efflux of water from the cells in a high refractive index medium.
Firstly, the number of hemoglobin molecules within the RBC model is calculated using known parameters from previous articles. Using mean corpuscular hemoglobin concentration (MCHC) of a RBC, 330g/L 1 , and molecular weight (MW) of hemoglobin (Hb), 64458 g/mol 2 , initial molar concentration of Hb can be derived as follows, [Hb] = Then, mean corpuscular volume (MCV) of a RBC, 90e-15L 3 , is used along with the concentration of Hb, [Hb] ,to calculate the number of Hb molecules as shown below,

Hb = MCV • [Hb]
Using the Hb and the molar volume (MV) of Hb, 48.227 L/mol 4 , the initial volume of Hb can be calculated as

= •
The volume fraction of Hb using the calculated and MCV is 0.247 which matches values found in literature, 0.25 1 . The volume fraction of water is reported to be 0.72 5 and can be used to calculate the initial volume of water in the RBC as Then, using the refractive index of water, 1.336, along with the refraction increment of Hb, α = 0.144 ml/g 6 , Barer's expression can be used to estimate the initial refractive index of the RBC following, Finally, using these values, changes in as well as OV changes due to the efflux of water from the cell can be calculated. The new RBC volume after water displacement is calculated as, Then, the new concentration of Hb of the cell can be derived by, Ultimately, the OV change in Figure 7b is calculated using,

Osmolarity experiment
In order to correlate the change in optical volume to the displacement of water, stationary RBCs were imaged in 3 separate media with varying osmolarity of 200mOsm, 300mOsm, and 400mOsm. The osmolarity of the medium was controlled by diluting DPBS+/+ 1x and 10x with distilled water. Then, bovine serum albumin was mixed to the solutions and the refractive indexes were measured to be consistent at 1.373 + 9.5e-4. Figure S1 below shows the boxplots of the OV of the RBCs in the 3 different medium.
As can be seen in Fig S1, when the RBCs are in the hypotonic solution in which water enters the cells, the OV of the cells is smaller compared to that of the cells in the isotonic (300 mOsm) solution. This corresponds to a lower internal density of the cell since the increased size of the cell displaces the high index medium which previously occupied this volume, producing a smaller net phase change and in turn a lower OV. In contrast, when the water is displaced from the cell in the hypertonic solution, the optical volume increases relative to the cells at equilibrium. In this case, as water is displaced from the cell, it shrinks, and that volume is now occupied by high index medium, producing an increase in net phase and a higher OV.
The average OV of the cells in the hypotonic, isotonic, and hypertonic solutions are 2.22 + 0.5fL, 3.17 + 0.6fL, and 3.51 + 0.7fL respectively. A 30% decrease in the OV of the cells in the hypotonic solution relative to the cells in the equilibrium, and a 10.7% increase in the OV of the cells in the hypertonic solution was found. Using the measured MCV and MCHC of the subject at 80.8fL and 36.5g/dL respectively with a hematology analyzer, the percent change in the water content relative to the optical volume, shown in Fig S2 below, can be simulated following the method described in the previous section. As can be seen in Fig S2, for the average 30% OV decrease as seen in our hypertonic experiments, there was an expected increase of 4.3% in the water content of the cell. For our hypotonic experiments where an average 10.7% increase in the OV was seen, there is an expectation of a 1.85% decrease in the water content of a cell. The changes in water content predicted by the simulation for the observed OV changes are comparable to water content changes with varying osmolarity in previous literature 7 . These earlier experiments measured a 10% increase in the water content in the solution with osmolarity of 200mOsm. In addition, when fit to an exponential function, the water content decrease at 400mOsm was estimated to be 2.9%.
The discrepancy between our simulation and the water content of cells from the previous literature are likely due to the earlier work providing only a bulk estimate of a cell population. In contrast, our work is evaluating individual cells. As can be seen in Figure S1, there is a large range of OV for each set of cells at a given osmolarity. Further experiments can better help link single cell measurements with those for bulk cell populations However, these experiments help confirm that a change in the water content of the cell can be observed with optical volume measurements using quantitative phase imaging and a high refractive index medium.

OVPre vs ∆OVSP / OVPre vs ∆OVPP
In order to show that the OV change induced by mechanical stress through the constricted channel is not correlated to the increase in optical volume over storage time due to increase in hemoglobin, initial OV before squeeze is plotted against both ∆OVSP and ∆OVPP in the Fig S3  below.   Fig S3 A) OVPre vs. ΔOVSP Correlation between the initial optical volume of the cells and change in optical volume during squeeze relative to the initial volume B) OVPre vs. ΔOVPP Correlation between the initial optical volume of the cells and change in optical volume postsqueeze relative to the initial volume As can be seen, there is no correlation between OVPre and ΔOVSP as well as between OVPre and ΔOVPP where the R-squared values of the linear fits were 0.16 and 0.13 respectively. Therefore, the OV changes induced by the transit through the constricting channel are independent of the optical volume changes over the storage time.

Chemical degradation through glutaraldehyde treatment
Glutaraldehyde treatment has been used as chemical means to degrade RBCs. Given our observations, the RBC storage and the artificial degradation lead to an increase in optical volume. In order to show the changes in the OV of the cells during chemical degradation, RBCs were treated with glutaraldehyde (0.01% and 0.05% v/v) following the protocols by Boas et al 8 .
Then, stationary RBCs in high refractive index medium were imaged using the QPI system. As can be seen in Fig S4, there was a significant difference in OV between the untreated RBCs and those treated with 0.01% of glutaraldehyde (p-value: 0.036) as well as those treated with 0.05% of glutaraldehyde (p-value: 0.0013). The increased difference of OV shows a dosedependence to the glutaraldehyde concentration. The significant difference in OV between the untreated cells and cells treated with glutaraldehyde may be due to an increase in the viscosity of cytoplasm of the cells as an effect of the glutaraldehyde treatment shown in previous study by Forsyth et al 9 . The changes in the OV of the cells through the artificial aging should be explored further in future studies to understand the rheological changes of the cells over storage time. Tables   Table S1 -Average OV and standard deviation for sample 1