necessarily preclude local perturbations of the spectrin network, associated for example with redistribution of anchor protein complexes).

Such perturbations, manifested as changes to mem-brane components, can result in reduced mechanical stability of RBC. That, in turn, leads to accelerated cell fragmentation and hemolysis, which, besides anemia, was implicated in a cascade of detrimental events as-sociated with the release of hemoglobin (e.g. [2]). Mem -brane modifications can also arise through various pathologies and diseases, blood storage, or the action of drugs or blood-contacting devices. While RBC may exhibit high apparent tolerance to fluidic shear stress-es, cells can be altered even when such stress does not reach the hemolytic threshold. Such “sub-hemolytic” damage may lead to later hemolysis in circulation, in addition to any other potential impairment of cell func-tion. etc.

The membrane property of mechanical fragility (MF) defines cells’ ability to withstand applied mechanical stress without rupturing (lysing), and is dependent on a variety of cellular attributes, including, among others, intracellular viscosity, membrane viscoelasticity and in-teraction of lipid bi-layer with cytoskeleton [3] - prop-erties that are not necessarily uniformly affected by external stress. It is considered to be a sensitive indi-cator of sub-hemolytic RBC damage - blood trauma not resulting in direct or overt hemolysis, but nevertheless leading to a shortened RBC life span in circulation [4]. One approach to measure MF is a rocker-bead test that involves slow rocking of a blood vial containing a stain-less steel ball (bead) for a predetermined time [5]. An-other approach involves 20-50 Hz oscillations of a stain-less-steel ball, with the development of a MF profile, reflecting observed levels of induced hemolysis (e.g., from zero to a hundred percent) over the total duration of oscillations [6].

It had been demonstrated previously that for a sphere/ball, hemolysis is caused predominantly by wake tur-bulence, with presumably ball speed (related to os-cillation frequency) and viscosity affecting the nature of turbulence in the medium [7]. Then, an additional ability to vary the type(s) of hemolysis-inducing stress was introduced, regarding when the spherical bead is replaced with a cylindrical bead design [8]. Such cylin-drical beads, oriented longitudinally in a tubular con-tainer, can introduce annular flows, with the length of the annulus depending on the bead’s length, and the gap thickness depending on the relative diameters of the bead and tube. That presents not only a potential-ly different flow type within the annulus itself, but also potentially much more cell interaction at the solid sur-face interface (bead annulus surface). Preliminary re-sults suggested that with cylindrical beads, in addition to effects of wake turbulence, induced hemolysis is also affected by two kinds of annular effects - tentatively associated with in-bulk and surface-related causes. It

the bead in AS3 media, supplemented and not supple-mented with albumin (Figure 1), shows a maximum at about 22 mm, corresponding to about a 0.6 bead-length to tube-length ratio (RBL/TL). With a small cylindrical bead (7 mm in diameter, and 6 or 7 mm in length), unlike when a 7 mm sphere was used, albumin supplementation did not result in a decrease in induced hemolysis. A reverse effect, elevated hemolysis, was instead reproducibly observed (Figure 1, Insert A). For longer cylinders, medi-um supplementation with albumin did result in a sharp decline in observed hemolysis. The magnitude of this protective effect was maximal for beads of 20 mm in length (~ 0.55 RBL/TL; Figure 1, Insert B). When normal-ized to induced hemolysis observed in AS3 un-supple-mented media, the maximum effect remains at 18-20 mm bead length, although the dependency relationship becomes less sharp (not shown).

In the vertical bead mill employed for this work, it is the head of the mill, with the sample tubes inside, that is actually (directly) oscillated. Thus, the bead’s actual movement is determined by a combination including drag forces as the fluid medium around the bead shifts

all beads, regardless of their length, reached both ends on the tube. While longer beads (over 18 mm in length) reached both ends at each oscillation, that was not the case for shorter beads, with very short beads (e.g. 6-7 mm cylindrical beads, or 7 mm ball, Figure 2) reaching the end of the tube only occasionally. For shorter beads, the overall movement appeared to occur with a low frequency oscillation (e.g. 7-8 Hz for a 6-7 mm cylindrical bead), overlaid with a higher frequency 30 Hz oscillations - same as the oscillation frequency of the bead mill, and thus of the sample tube. Similar effect was observed at other oscillation frequencies in the 20-50 Hz range. With increased bead length, the frequency of the low frequency component appeared to increase (12 mm bead, Figure 2); however, its overall contribution to the bead’s movement declined. Longer beads, relative to the tube length (20 mm in length and longer; RBL/TL ≥ 0.55), exhibited only the high frequency oscillation, that of the bead mill and the sample tube (20 mm bead, Figure 2). While variability in bead speed during bead milling was anticipated, as it is an inherent attribute of that method, the significant non-regularity in shorter bead movement was unexpected.

Dependence of average bead speed on bead length

tation of media with albumin resulted in lessening of induced hemolysis, with the magnitude of such protec-tion also varying with bead diameter (Figure 5). This dependence was in general similar to that observed in non-supplemented media, particularly at lower oscilla-tion frequencies. At 50 Hz, the minimum (for induced hemolysis dependence, in the presence of albumin,on bead diameter) observed for 7 mm beads (RBD/TD ≈ 0.8) is sharper, and the increase in hemolysis when larger diameter beads are used is markedly more pronounced (Figure 4). As a result, at this frequency, for beads over 7 mm in diameter, supplementation with albumin pro-vided progressively smaller protection against induced hemolysis. Notably, the magnitude of these effects var-ied between different RBC samples, with some exhib-iting a larger impact of supplementation than others (Figure 4).

Progressively increased diameter of the bead result-ed in a linear decline in bead average speed, likely due to increasing resistance of the medium, which would be negatively correlated with the bead cross-section (Fig-ure 5). Such decline was observed in both albumin-sup-plemented and non-supplemented AS3 media.

Role of bead weight

Bead weight was found to be a factor significantly af-fecting induced hemolysis (Figure 6), with the increased weight corresponding to higher hemolysis in both un-supplemented and supplemented-with-albumin media. In all cases, higher weights were also associated

frequencies, albumin supplementation not only failsto protect RBC against this type of mechanical stress, but even appears to be detrimental to RBC stability (here, resistance to lysis) under stress (Figure 7A and Figure 7C). While this effect was commonly observed when 7 mm-long beads were used, it was also observed with “expired” (over 42-days-old) stored pRBC. Figure 7A, Figure 7B and Figure 7C illustrate the changes observed in a given packed RBC sample when tested repeatedly at 9, 46, and 65 days post-collection. It should be not-ed that the magnitudes of those effects were not only affected by storage time, but also varied for blood sam-ples from different donors. In particular, some “fresh” (under 14 days in storage) packed RBC samples did not exhibit any statistically significant changes in induced hemolysis at low (15-20 Hz) oscillation using either 7 or 18 mm long beads upon supplementation with albumin. The reasons underlying this variability remain to be in-vestigated.

Discussion

As indicated, the specific means of stressing the RBC in MF testing can qualitatively affect the results. For example, it had been demonstrated that albumin sup-plementation of the medium can “protect” RBC against certain types of mechanical stress such as certain bead oscillation approaches [7,10], yet not with some alter-native methods (e.g., a jet/orifice system [11]). It was also found that, even within bead milling with spherical

speed and thus flow speed around the bead would be continuously changing, with the speed distribution as for example shown on inserts in Figure 3, Figure 5 and Figure 6. Thus, over each oscillation period, RBC would be subject to changing levels of mechanical stress. In the present work,we directly determined the bead speed throughout oscillations (via video) and attempted to represent the impact of speed through average speed values. Such approach has clear limitations, and future attempts of linking induced hemolysis directly with dis-tribution profiles could potentially provide additional insight into mechanisms of cell damage.

There is a striking similarity between the induced hemolysis and average bead speed dependencies on bead length (Figure 1 and Figure 3). For RBL/TL < 0.6, the increase in bead speed with increased bead length is likely due to the progressively increasing bead weight (per Figure 6), even though offset by the increased flow resistance, which likely increases linearly with the length of a bead. It should be noted, that the dependence of bead speed on its length, and the dependence of resultant hemolysis on bead’s length, are not a simple (linear) function of the weight and the length of a bead. Normalization for these parameters (assuming linear dependence) does not produce a uniform (per unit of weight and/or length) hemolysis (data not shown). That implies either a higher order function of weight/length dependence or a more complex dependence, which could involve other (e.g., medium related) parameters changing along with (for example) the bead’s length change.

For RBL/TL < 0.6,the bead’s speed and the associated hemolysis decline is likely due to bead movement being constrained by the length of the tube, which imposed a limit on how far a bead may travel during each oscil-lation. That is supported by the pattern of bead move-ment recorded by high-speed camera, which shows that for beads 20 mm and longer, the bead oscillates between the ends of the tube with the frequency of the tube oscillation (Figure 2). (Note that this was not the case for shorter beads, which exhibited a random-move-ment behavior, rarely reaching the ends of the tube, as demonstrated by the ranges of bead movement). Thus, constrained by the tube, longer beads would not be able to reach velocities that would be otherwise expected, with bead velocity approaching zero when RBL/TL is ap-proaching 1. Note that for some bead and tube geome-tries as well as stress application parameters (e.g. oscil-lation frequency and intensity), increasing the length of the cylindrical bead could result in decreased speed of the bead’s movement in the tube (possibly due toa low-er final speed for each oscillation, which in turn may be a function of decreased opportunity for acceleration). This could lead to a more complex manifestation of al-bumin’s protective effect (e.g. a decrease in the effect followed by an increase) with increasing bead length, reflecting changes in the overall composition of me-

constant, making the speed of annulus flow linearly dependent on the bead’s speed, with faster annular flow for faster moving beads. That is no longer true when the diameter of the bead is no longer constant between beads. For beads used in this work, an increase in diameter, and thus in RBD/TD, resulted in progressive linear decrease in measured bead speed (Figure 5). However, the speed of annulus flow would increase nearly exponentially with an associated decrease in annular opening cross-section. Note that while bead weight by itself would be positively correlated with bead speed, in this case, this effect is apparently secondary to a concurrently increasing flow resistance due to increase in bead diameter and smaller annular opening.

Thus, initial decline in the magnitude of induced he-molysis with increase in bead diameter (up to RBD/TB = 0.8) would most likely be associated with a decline in wake turbulence due to decreasing speed of the bead. Follow up increase in induced hemolysis could be due to exponential increase in annular flow rate and associat-ed annulus-related stresses. That implies a marked shift in relative contributions of the stresses with the chang-es in bead diameter, and in the resultant contribution of annulus-associated stresses to overall cell hemolysis.

RBC response to mechanical stress had been previ-ously evaluated using a variety of methods, including capillary or tube flow, jets, rotational disks and concen-tric cylinders, cone and plate arrangements, and bead(s) oscillation or agitation [11,14-19]. Hemolysis was ob-served both in-bulk (including cell-cell and direct shear) and at solid surface and air interfaces (e.g. [20-22]), with the material of the blood-contacting surface potentially able to influence RBC damage (e.g. [13,23]). Both lam-inar and turbulent flows had been implicated in cell fragmentation with different hemolytic thresholds and mechanisms of flow-induced hemolysis [15,22,24]. In laminar flows, the stress across the membrane would be determined by the flow around the cell and relate to velocity gradient and fluid viscosity. In turbulent flow, additional stress would relate to chaotic eddy motion, when Kolmogorov scale approaches the scale of RBC. There the stress would depend on the actual properties of the turbulence, with large eddies transporting cells and resulting in low stress gradient across the cell, and thus low actual stress on the cell membrane. Small (com-pared to the cell size) eddies could, on the other hand, create large velocity gradients across the membrane, resulting in significant stress. Thus, it was suggested that cell damage in turbulent flow arises only through eddies comparable to cell size (described through the Kolmogorov length scale) [25,26]. Such effects cannot be predicted from Reynolds stress alone, as Reynolds stress does not account for potential variability in scale sizes.

Experimentally, in-bulk hemolysis would have two main determinants: Shear stress intensity/level and

in diameter at a given length gave rise to divergent Re changes (Table 1). Oscillations of larger diameter beads were associated with wake flows having smaller Re values, and with larger Re values for annulus flows.

For flow in the bead wake, Reynold numbers’ values would suggest a predominantly turbulent vortex street similar to that suggested previously for spherical beads [7]. The annular flow, however, would also depend on bead and tube dimensions, oscillation frequency and force, and sample media/environment. Notably, for the annulus, the geometry with flow-confining walls, which stiffens the flow, could be expected to increase the threshold Re value for laminar-to-turbulent flow transition. Thus, while for certain bead dimensions (at least for the overall stressing configuration/parameters used here) turbulent flows would be expected, for other bead dimensions turbulent conditions become less favorable, with a substantial part of the flow over time likely occurring in or close to a laminar fashion. Such effect could be further accentuated in albumin-supplemented media.

Limitations

Although the current work is experimentally based, with inferences being drawn largely from such results, some of the interpretations naturally draw upon fluid dynamics principles. Models based on Reynolds stress evaluation had been extensively used to characterize tur-bulence and associated blood damage (e.g. [25,31,32]). However, such models do not account for actual turbu-lence structure and cell microenvironment, and thus cannot fully characterize the stresses that would impact any particular red cell. It had been shown that at least in some cases, predictions based purely upon Reynolds based stresses are inadequate in accounting for actual blood damage in turbulent flows (e.g. [28,33]). Similarly, models based upon evaluation of turbulent eddy length scales also had been shown to be a poor predictor of flow-induced RBC damage [34]. Such reports showcase the difficulties in predicting flow-induced hemolysis,

cussion and manuscript review, and gratefully acknowl-edge Stephen Hampel for providing technical assistance including precision machining of certain components employed in the work.

Interest disclosure

The authors have been employed with Blaze Medi-cal Devices, and authors Tarasev and Chakraborty own equity in Blaze Medical Devices. Blaze Medical Devices is a company that has developed technology relating to bead mills and bead milling based profiling of mechan-ical fragility (MF) of red blood cells (RBC). The Blaze technology has since been licensed out to Functional Fluidics.

References

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8. Alfano KM, Chakraborty S, Tarasev M (2016) Differences in bead-milling-induced hemolysis of red blood cells due to shape and size of oscillating bead. Biomed Mater Eng 27: 405-412.
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10. Kameneva MV, Antaki JF, Yeleswarapu KK, Watach MJ, Griffith BP, et al. (1997) Plasma protective effect on red blood cells exposed to mechanical stress. ASAIO J 43: M571-M575.
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15. Kameneva MV, Burgreen GW, Kono K, Repko B, Antaki JF, et al. Int J Blood Res Disord 2019, 6:041• Page 12 of 14 •et al. (2004) Effects of turbulent stresses upon mechanical hemolysis: Experimental and computational analysis.

Supplement with Additional Materials and Methods for:

c“Impact of the Oscillating Bead Size and Shape on Induced Mechanical Stress on Red Blood Cells and Associated Hemolysis in Bead Milling” (by Michael Tarasev, Marina Muchnik, and Sumita Chakraborty).

Materials and Methods

RBC fragility test

Samples of RBC were diluted to total hemoglobin (Hb) concentration of 1.2 g/dl, corresponding to about 3.5% hematocrit, verified by a Hemoglobin 201 system from HemoCue (Angelholm, Sweden), with AS3 storage buffer, pH 5.8, containing at times additives - as speci-fied in the text. The diluted sample was gently agitated and aliquoted into 2 ml low-retention centrifuge tubes. For each experiment, the volume of this aliquot (rang-ing from 350 μL to 1 mL) was selected to ensure mea-surable hemolysis at the widest range of experimental variables (e.g. different bead lengths or diameters), as lower volumes result in faster and stronger hemoly-sis while larger volumes result in slower and less pro-nounced hemolysis. Mechanical stress was applied to RBC samples with the use of a Tissue Lyser LT (Qiagen, Dusseldorf, Germany) vertical bead mill, in the presence of one spherical bead or one longitudinally oriented cy-lindrical bead (as specified). Cylindrical beads were cus-tom machined to required dimensions. Samples from each RBC unit were subjected to such stress at 10 dif-ferent durations (ranging from 30 seconds to 30 min) to ensure a wide range of induced hemolysis levels - for a fragility “profile”. The sample tube holder of the Tissue Lyser was modified to allow aircooling while in opera-tion, which resulted in sample temperature stabilization to within 2 degrees of the start temperature. Un-lysed cells were precipitated by centrifuging the samples for 5 minutes at 1,300 rpm on an Eppendorf 5417C centri-fuge (Hauppauge, NY). Aliquots of supernatant were collected, and their spectra recorded. All tests were performed at 6 °C, in AS3 storage buffer, pH 5.8, unless indicated otherwise. Such conditions were selected to mimic that of packed RBC storage with AS3, commonly used storage solution, with its low pH value aimed to suppress cell metabolism. Figures present representa-tive results obtained for a given RBC sample, with error bars (± SD) indicating experimental error on three inde-pendent measurements for that value.

RBC hemolysis assessment

Hemolysis (Hem), both as present in untreated sam-ple (“autolysis”) and as induced by the bead mill in fra-gility testing, was determined based on the difference in absorbance at 576 nm, a wavelength of oxygenated Hb maximum, and absorbance at 685 nm, the local min-imum for the oxygenated Hb form. It was expressed as a fraction of free hemoglobin (HBF) relative to total he-