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The Effects of Micro-vessel Curvature Induced Elongational Flows on Platelet Adhesion

The Effects of Micro-vessel Curvature Induced Elongational Flows on Platelet Adhesion BIOMEDICAL Annals of Biomedical Engineering, Vol. 49, No. 12, December 2021 ( 2021) pp. 3609–3620 ENGINEERING https://doi.org/10.1007/s10439-021-02870-4 SOCIETY Virtual Physiological Human The Effects of Micro-vessel Curvature Induced Elongational Flows on Platelet Adhesion 1 1 2 ´ ´ CHRISTIAN J. SPIEKER , GABOR ZAVODSZKY, CLARISSE MOURIAUX, 1 2 2 MAX VAN DER KOLK, CHRISTIAN GACHET, PIERRE H. MANGIN, and ALFONS G. HOEKSTRA Computational Science Lab, Faculty of Science, Institute for Informatics, University of Amsterdam, Amsterdam, The Netherlands; and Universite´ de Strasbourg, INSERM, EFS Grand-Est, BPPS UMR-S 1255, FMTS, Strasbourg, France (Received 31 January 2021; accepted 28 September 2021; published online 19 October 2021) Associate Editor Stefan M. Duma oversaw the review of this article. Abstract—The emerging profile of blood flow and the cross- INTRODUCTION sectional distribution of blood cells have far reaching biological consequences in various diseases and vital internal The effects of curved vessel geometry on blood flow processes, such as platelet adhesion. The effects of several were investigated thoroughly from a macroscopic essential blood flow parameters, such as red blood cell free 2,31 viewpoint, where blood is approximated as a con- layer width, wall shear rate, and hematocrit on platelet tinuum fluid and the biological implications (often in adhesion were previously explored to great lengths in straight connection to cardiovascular diseases) are commonly geometries. In the current work, the effects of channel curvature on cellular blood flow are investigated by simulat- linked to the magnitude or inhomogeneity of wall ing the accurate cellular movement and interaction of red shear stress. On the level of smaller, micron-scale ves- blood cells and platelets in a half-arc channel for multiple sels, or when investigating near-wall processes, the wall shear rate and hematocrit values. The results show continuum description is no longer sufficient. The significant differences in the emerging shear rate values and continuum approximation can lead to several-fold distributions between the inner and outer arc of the channel curve, while the cell distributions remain predominantly differences in shear rate and shear stress close to the uninfluenced. The simulation predictions are also compared wall. The complex nature of blood as a fluid is dic- to experimental platelet adhesion in a similar curved geom- tated primarily by its physiological composition of etry. The inner side of the arc shows elevated platelet blood plasma and immersed deformable cells. These adhesion intensity at high wall shear rate, which correlates cellular components account for approximately half of with increased shear rate and shear rate gradient sites in the simulation. Furthermore, since the platelet availability for the volume fraction. The hematocrit value, corre- binding seems uninfluenced by the curvature, these effects sponding to the red blood cell (RBC) concentration, is might influence the binding mechanics rather than the around 44% in healthy humans. Moreover, blood probability. The presence of elongational flows is detected contains less numerous cells (e.g. platelets (PLTs) and in the simulations and the link to increased platelet adhesion white blood cells (WBCs)) that account for about 1% is discussed in the experimental results. in total blood volume. Due to these cellular components blood behaves as Keywords—Non-trivial vessel geometry, Blood rheology, a non-Newtonian fluid with unique rheological prop- Cell free layer, Cell-resolved simulation, Elongational flow. erties in the confined geometry of blood vessels, giving rise to a multitude of phenomena, such as the Fa˚ hræus and Fa˚ hræus-Lindqvist effects. These two effects occur as a consequence of the formation of the red blood cell free layer (CFL), which in turn is Address correspondence to Christian J. Spieker, Computational caused by the lift force and shear flow induced axial Science Lab, Faculty of Science, Institute for Informatics, University migration of RBCs. The CFL acts as a lubrication of Amsterdam, Amsterdam, The Netherlands. Electronic mail: c.j. layer for the bulk of cellular flow due to the locally spieker@uva.nl 0090-6964/21/1200-3609/0  2021 The Author(s) 3610 SPIEKER et al. reduced blood viscosity. As frequently discussed in MATERIALS AND METHODS literature, an increased hematocrit value results in a Experimental Setup: In Vitro Flow-Based Studies smaller CFL width and an increase in flow velocity has 9,29 the opposite effect, due to a larger lift force. PLTs Experiments using flow-based assays are performed undergo radial migration towards the vessel wall and in the same manner as previously described by Re- into the CFL. This process, called margination, cre- ceveur et al. The polydimethylsiloxane (PDMS)- ates an increased availability of PLTs close to the based microfluidic device (MFD) has a square duct vessel wall. Zydney and Colton attributed this channel with a cross section of 1 1mm and the marginating behaviour to diffusion gradients, while diameter of the inner curve is 100 lm (see Fig. 1a), recently Za´ vodszky et al. showcased a strong depen- creating a 180 angle U-turn. The channel is coated dency on the hematocrit gradient. Kotsalos et al. overnight at 4 C with type I fibrillary collagen (200 lg/ proposed that a Le´ vy flight solution fits the mean-field mL) before being blocked with description of the resulting motion of PLTs. The human serum albumin (HSA) in 1% cellular flow dynamics have far reaching biological phosphate buffered saline (PBS) for 30 min at room implications in various diseases, for instance in the temperature. Hirudinated (>100 U/mL) human whole oxygenation of tumor tissues, or in the margination blood is perfused at 37 C through the U-shape chan- process in the presence of stiffened diabetic cells. One nels at volumetric flow rates of 3 and 16 mL/min using particular process of importance that is influenced is a programmable syringe pump (PHD 2000, Harvard the adhesion of PLTs. This process, which occurs both Apparatus, Holliston, MA, USA). Assuming a con- in physiological hemostasis, as well as pathological tinuous Newtonian fluid these flow rates result in thrombosis, is found to be highly shear dependent and 1 wall shear rates (WSRs) of 300 and 1600 s , respec- 11,19 sensitive to hydrodynamic alterations. The shift of tively, at the midpoint of the wall edges in the straight initially even shear gradients, e.g. caused by a sudden 29 inlet. Previous work, e.g. by van Rooij et al., has reduction in vessel diameter (vasoconstriction), leads shown that this assumption is not accurate for cellular to the presence of so called elongational flows. These blood flow and leads to wrong WSRs. However, as it is flow fields, defined by exerting tensile forces, are found still common practice in experimental work, it is to promote PLT adhesion under certain conditions, enabled by the mediation of prominent plasma mole- 13,23 cule von Willebrand factor (vWF). Furthermore, PLT adhesion is known to depend on the presence of a 29 24 CFL as well as the level of hematocrit. The effects of these essential blood flow parameters on PLT adhesion were investigated under static flow condi- tions, in straight geometries. Here, the effects of curvature are investigated by simulating the cellular movement of RBCs and PLTs in a half-arc channel for multiple wall shear rate and hematocrit values. The simulations show significant differences in the emerging shear rate values and dis- tributions between the inner and outer arc of the channel curve, while the cell positions remain pre- dominantly unaffected. The simulation predictions are also compared to experimental PLT adhesion in a similar curved geometry. The changes in the shear-rate patterns, inducing the presence of elongational flow, correlate to the location of changes in the PLT adhe- sion intensity. The main focus is on the accurate sim- ulation and evaluation of the flow conditions, CFL, FIGURE 1. Experimental and simulation setup. (a) Setup of and cell distributions. However, a comparison to curved MFD blood experiments with highlighted regions of interest in red. (b) Setup of curved channel domain with cross- in vitro assays in a similar curved microfluidic geome- sectional dimensions of 25  25lm . Driving force is set in try is presented as well and the possible implications of negative x-direction inside the periodic pre-inlet (see top elongational flow in vessel curvature on PLT adhesion right). The regions of interest with equal volume (V , V inlet curve and V ) are highlighted in the top view of the channel (see outlet are discussed. left), where the corresponding inner and outer wall division used in the cell distribution evaluation is marked with the letters o and i, respectively. BIOMEDICAL ENGINEERING SOCIETY Micro-vessel Curvature Induced Elongational Flows on Platelet Adhesion 3611 900; 000 PLT=lL, which is larger than physiological adopted here as well. A vascular WSR of 300 s oc- levels (150,000–400; 000 PLT=lL). This allows for curs in the scale of conduit arteries, such as the carotid, increased statistical significance in evaluating the re- as well as venules. Larger WSRs in the range of 1600 sults, while still being dilute enough to avoid influ- s can be observed in the smallest arteries of the encing the overall cellular flow dynamics. vasculature, the arterioles. The values are chosen to The continuous inflow boundary condition for cells cover a wide range of physiological shear rates. (denoted as periodic pre-inlet in Fig. 1b) is imple- In some sets of experiments, hirudinated whole mented according to Azizi et al. Note that this peri- blood is preincubated with a Fab fragment of a odic pre-inlet boundary domain mimicks an infinitely blocking anti-GPIba antibody (10 lg/mL), named long straight channel, ensuring that the incoming cell ALMA12, for 15 min at 37 C before perfusion. distributions are fully developed at the point of entry PLT adhesion is visualized at the regions of interest to the main U-shape domain. All simulations are (see Fig. 1a) using differential interference executed on the Cartesius supercomputer (SURF, contrast (DIC) microscopy images obtained with an Amsterdam, Netherlands; https://userinfo.surfsara.nl/ inverted Leica DMI 4000 B microscope (Leica systems/cartesius). Microsystems, Mannheim, Germany) coupled to a complementary metal-oxide semiconductor (CMOS) camera (ORCA-Flash4.0 LT, Hamamatsu, Massy, Evaluation Method France). The area of the thrombi is determined by To determine the CFL width in the simulated re- utilising the Image J software (National Institutes of sults, it is defined as the distance from the wall where Health) to automatically delineate the surface of the the CFL volume fraction reaches a threshold value of thrombi which is expressed in lm . The results are then 5%. To simplify the calculation it is solely based on the quantified as thrombi coverage fraction of the center of mass of each RBC, neglecting the rotated and observed area. deformed membrane volume. The curved channel domain is evaluated at three Simulation Setup different positions along the flow direction both on the inner and on the outer side of the channel. These The in silico experiments are based on the open- locations are situated in the middle of the curved re- source cell-resolved blood flow model HemoCell, gion, right before, and right after the curvature in the which consists of a lattice Boltzmann method based straight ’inlet’ and ’outlet’ sections, as shown in fluid solver for the incompressible blood plasma and a Fig. 1b. The ’curved’ section is defined as an annulus discrete element method membrane solver for the cell sector with a 60 angle. The volume of the evaluated deformation mechanics. These two components are ’inlet’ and ’outlet’ sections equals the volume of the coupled by the immersed boundary method. Both the ’curved’ section. To calculate the CFL and the overall membrane mechanical models of RBCs and PLTs as cell distribution in each section, the cell position well as the bulk flow rheology of the entire model have coordinates along the flow are projected onto the been thoroughly validated for both single cell and bulk 32–34 center line of the channel. For the cell distribution flow dynamics. evaluation, each section volume is divided into an in- To simulate cellular blood flow in a U-shaped ner and outer wall layer counterpart (see Fig. 1b). This channel geometry the same model parameters are used 32–34 results in a visualisation of an accumulated cell con- as in the validation studies. The cross-section of centration per layer volume. The inner wall refers to the channel is a square duct, following the current 12,30 the half of each section situated at the inner arc of the methods in experimental platelet adhesion assays curve and the outer wall respectively at the outer arc. to allow comparison with the microfluidic experimen- This separation allows to evaluate average behavior in tal results. The width of the channel is 25  25 lm and the layers which reduces statistical noise. the inner diameter of the curved annulus section is also To localise and quantify elongational flows within set to 25 lm (see Fig. 1b). To allow for comparison the domain, the rate of elongation e _ is calculated for with the experimental results, the simulated flow rate is the planar profile. From the rate of strain tensor, given setup to result in WSRs of c _ = 300 s and c _ = 1600 1 by: s , respectively, at the midpoint of the wall edges in 2 3 the straight inlet of the simulated channel using the e e e 11 12 13 same continuous flow assumption as in the experi- 6 7 e ¼ 4 e e e 5 ð1Þ ij 21 22 23 mental setup. The cells are randomly distributed in the e e e 31 32 33 inflow domain to result in a discharge hematocrit of 30%. The PLT concentration is fixed to BIOMEDICAL ENGINEERING SOCIETY 3612 SPIEKER et al. the magnitude of the diagonal elements in flow CFL width. As visualised in Fig. 3c, the results do not dimensions (e and e for x and y) across the center z- expose a significant influence of the curvature on CFL 11 22 plane of the domain is calculated. This results in the width when taking the SD range into account. This magnitude of elongation, i.e. the rate of elongation: proves true for each performed simulation (see Figs. 3a qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi and 3b). 2 2 ð2Þ e ¼ e þ e Tateishi et al. performed blood experiments with 11 22 similar 30% hematocrit in a straight blood vessel at a displayed in s . comparable diameter of 23.5 lm. The measured CFL width of 2.2 lm is in the same order of magnitude as the simulated average width of 3.9 ± 0.4 lm. The RESULTS difference could be attributed to the simplified center of mass based RBC localisation in the simulation In Vitro Results evaluation as well as geometrical disparities (e.g. To study the impact of altered hemodynamic con- square duct channel vs. straight tubular vessel). The 21 21 _ _ ditions generated in a curved vessel geometry on PLT WSR increase from c = 300 s to c = 1600 s does function, the thrombi coverage on the described col- not lead to a significant difference in CFL width. lagen coated MFD surface is evaluated after blood While the CFL width does not differ between the inner and outer wall in a statistically significant way in perfusion. Real-time video-microscopy based on DIC any of the sections, a substantial effect of the geometry imaging indicates that PLTs adhere efficiently in all curvature on the cross-sectional flow distribution is regions observed and form large aggregates (Fig. 2b). observed, here characterised by the respective 1D The color-coded regions on the sketch in Fig. 2a mark velocity and 2D shear rate profiles. Figure 4 highlights the position of the framed microscopic images in this effect by revealing a shift of the initially evenly Fig 2b. At the WSR of 1600 s in the region of the inner wall of the curved section (II.) the PLT aggre- blunted flow profiles towards the inner wall at the gates display a different orientation as compared to the curved section, which is carried on into the outlet five other regions of interest which show a clear ori- section. As an implication, the WSR which is set to entation in flow direction (Fig. 2b). Furthermore, the 1600 s in the straight inlet, shifts in the curved sec- aggregates appear much larger in this region (inner tion to a peak of larger than 2600 s at the inner wall wall II.) compared to the other ones. This is confirmed and around 1200 s at the outer wall. While not as by the fractional surface coverage of the thrombi being pronounced, this effect is carried on into the outlet significantly increased in the inner section of the curved section as well. region (II.) by 10% to a total of 30% compared to the The lower shear rate simulation with the same dis- outer region and to the evenly covered inlet section (I.) charge hematocrit of 30% and an initial WSR of 300 (Fig. 2c). The effect subsides into the outlet section s (see Fig. 5) deviates with roughly the same 2:1 ratio (III.) with no significant difference outside of the between the inner and outer wall at the center of the increased standard error of the mean (SEM) error curved section, with a shear rate of over 480 s at the margin compared to the inlet section. In contrast, the inner wall and around 240 s at the outer wall. lower shear (c _ = 300 s ) experiment exhibits no sig- The inlet velocity profiles of both shear flow cases nificant difference in thrombi coverage between inner (Figs. 4aand 5a) display a dampened parabolic flow and outer surface layer at any of the three sections as profile resembling the typical plug-shape caused by the high cell density at the center of the channel. The shown in Fig. 2c. horizontal lines on Figs. 4a–4cand 5a–5c indicate the respective averaged CFL width ± SD, clearly aligning In Silico Results with a step in the velocity profile. This step is caused by the transition from low local viscosity at the wall to To determine the root cause of the exhibited dif- ference in PLT adhesion in a curved vessel at physio- higher viscosity in the RBC rich bulk flow. logical shear flow, the in silico experiments are Furthermore, by compressing the shear rate profile evaluated with special emphasis placed on assessing towards the inner wall, a shift in shear rate gradient deviations between inner and outer wall of the curva- distribution is induced as well, which is especially vis- ture. For the CFL width this is achieved by comparing ible at the top and bottom of the channel of plot E in the average value ± standard deviation (SD) at the both Figs. 4 and 5. This shift in shear gradient natu- inner and outer wall in the inlet, curved and outlet rally causes the occurrence of elongational flow fields. section. The results, summarised in Figs. 3a and 3b, Figure 6 presents the rate of elongation across the display evidently the influence of (initial) WSR on the plane of the domain. The plane is situated 1 lm below the top boundary of the geometry in z-direction, which BIOMEDICAL ENGINEERING SOCIETY Micro-vessel Curvature Induced Elongational Flows on Platelet Adhesion 3613 FIGURE 2. Impact of flow generated in a curved section on human PLT aggregation to collagen. Hirudinated human whole blood is perfused through channels of a MFD coated with a solution of type I fibrillar collagen (200 lg/mL). (a) Schematic and dimensions of the microfluidic ‘‘U-shaped’’ channel. The color-coded squares indicate the 0.3 mm regions of interest observed by video- microscopy. (b) Representative DIC images of PLT aggregate formation at inner and outer arc on immobilized collagen at 1600 s after 4 min. Scale bar: 50 lm. The frame color refers to the color-coded positions in (a) and the numbered columns to the labeled inlet, curved and outlet section in (a). (c) The quantified surface coverage of platelet aggregates obtained after 4 min of perfusion at 21 21 c _ = 300 s and c _ = 1600 s . The bars indicate the mean 6 SEM thrombi coverage in the 6 highlighted regions of 5 separate experiments performed with different blood donors. is within the same layer observed by the microscope in In order to evaluate to what extent these shifted flow the experimental flow chamber. While both WSR profiles influence the transportation of RBCs and simulations show the highest rate of elongation e right PLTs, the cell distribution in the regions of interest is at the inner arc of the curve, the c _ = 1600 s case investigated as an accumulated cell concentration per reaches significantly higher values of around e _ = 379 inner or outer wall layer volume averaged over time. 21 21 s , compared to a peak value of e _ =71 s in the c _ = As Figs. 7aand 7b shows, the RBC distribution in the 300 s case. curved section exhibits a shift of around 10% towards the inner wall for both the high and low flow velocity BIOMEDICAL ENGINEERING SOCIETY 3614 SPIEKER et al. FIGURE 3. CFL width in silico results. (a) & (b) CFL width results at inner and outer wall of the inlet, curve and outlet section for 21 21 the H = 30% simulations at WSRs c _ = 300 s and c _ = 1600 s , respectively. (c) Visual representation of uniform CFL width in 30WSR of 1600 s simulation at inner and outer wall in the respective sections after 1 s of flow with marginated PLTs. The results are averaged between 0.9 and 1 s in 0.001 s time windows. 21 21 FIGURE 4. Flow profiles at c _ = 1600 s . (a)–(c) 1D velocity profiles of 30% hematocrit and WSR of 1600 s simulation at the center line of the inlet, curved and outlet section, respectively (indicated by the red line in the layout sketch) at half the channel height. (d)–(f) Cross-sectional shear rate profiles at inlet, curved and outlet section, respectively. The positions are indicated by the red line in the layout sketches from (a)–(c). Results are averaged between 0.2 and 1 s. BIOMEDICAL ENGINEERING SOCIETY Micro-vessel Curvature Induced Elongational Flows on Platelet Adhesion 3615 21 21 FIGURE 5. Flow profiles at c _ = 300 s . (a)–(c) 1D velocity profiles of 30% hematocrit and WSR of 300 s simulation at the center line of the inlet, curved and outlet section, respectively (indicated by the red line in the layout sketch) at half the channel height. (d)–(f) Cross-sectional shear rate profiles at inlet, curved and outlet section, respectively. The positions are indicated by the red line in the layout sketches from (a)–(c). Results are averaged between 0.2 and 1 s. FIGURE 6. Top view of elongational flow magnitude accross channel. Z-plane of the domain with magnitude of the diagonal elements of the rate of strain tensor in flow (x- and y-) dimensions, resulting in a 2D elongation profile of the (a) 300 s and (b) 1600 s WSR simulation. The plane is situated 1 lm below the top boundary of the geometry in z-direction, as depicted in the top right inset panel. All results are averaged between 0.2 and 1 s. case. Since the CFL width did not change between the Taking the SDs into account, all remaining inner to inner and outer wall in any section, it can be concluded outer wall comparisons in Fig. 7 show no significant that this observed shift is taking place in the center of difference in hematocrit and PLT volume fraction the channel where the bulk of RBCs is concentrated. distribution. BIOMEDICAL ENGINEERING SOCIETY 3616 SPIEKER et al. FIGURE 7. Cell distributions. Hematocrit (in red) and PLT volume fraction (in yellow) distribution between inner (striped) and 21 21 outer wall (blank) at initial WSRs of (a) 300 s and (b) 1600 s for inlet, curve and outlet, respectively. All cell distribution results are averaged between 0.2 and 1 s. DISCUSSION shown in Fig. 2, the results for the c _ = 1600 s flow experiment present a highly amplified PLT adhesion The effects of channel curvature on CFL width and intensity at the collagen coated surface of the inner arc, cross-sectional flow profile and cellular distributions with a 10% increase in thrombi coverage compared to are investigated, as well as their strongly intercon- the inlet region. This behaviour cannot be attributed to nected relationships. Although, based on the large 180 an increased availability of PLTs in the observed re- curvature of the channel, changes in overall cell dis- gion, considering the static size of the CFL and the tribution might be expected, no such significant devi- already fully accomplished margination. The shift in ations in CFL width and PLT concentration hematocrit concentration towards the inner wall of the distributions are observed between the inner and outer curvature (see Fig. 7) cannot explain the increased arc of the curvature (see Figs. 3 and 7). In contrast to adhesion either since it occurs in both high and low this, a strong compression of the shear rate profile flow velocity cases and can be assumed to be situated towards the curve can be seen, resulting in a discrep- at the center of the channel, due to having no signifi- ancy in the WSR ratio between the inner and outer cant influence on the CFL width. wall of approximately 2:1 (see e.g. Fig. 4e). These One could argue that due to a larger volumetric flow observations are true for the comparatively small rate at the inner arc of the curve compared to the outer simulated channel. To strengthen transferability to the arc, simply more PLTs pass by the observed surface experimental results in a much larger channel, simpli- region, therefore allowing for adhesion to occur more fied Newtonian fluid continuum simulations are per- frequently. While a shift of the profile towards the formed at dimensions of the MFD. The results (see curvature in plot B of Fig. 4 does show, approximately Fig. 8) reveal qualitative similarity in the macroscopic the same relative shift is visible in the low shear sim- continuum quantities to the cellular simulations (see ulation (Fig. 5b). However, comparing the c _ = 1600 21 21 Fig. 6). s and c _ = 300 s in vivo results (Fig. 2c), only the Although cellular distributions in blood flow and high shear experiment exhibits an increase in thrombi width of the CFL are known to be highly shear rate coverage at the inner wall of the curved section. Con- dependent, the observed strong shift in shear rate sequently the discrepancy cannot be explained solely appears to be associated with changes only in the bulk by an increased volumetric flow in the region. flow, away from the walls. This might imply changes in The multimeric plasma protein vWF is a key the local PLT margination process through the shift in mediator in the adhesion and aggregation of PLTs. local hematocrit gradients, however in the presented Multiple domains of the protein enable binding to case, the PLTs are already fully marginated by the time different molecules. Of special interest in our investi- they enter the domain of observation in the simula- gation are the A1 domain with binding sites for tions. The situation is assumed to be the same for the PLT receptor glycoprotein (GP) Iba of the GPIb-V- PLT in the in vivo blood experiments, due to the inlet IX complex and A3 which allows for binding to col- length of the blood perfusion tube and perfusion time lagen. Under physiological flow conditions, circu- of 4 minutes until the microscopic images are taken. As lating plasma vWF is folded and unable to expose its BIOMEDICAL ENGINEERING SOCIETY Micro-vessel Curvature Induced Elongational Flows on Platelet Adhesion 3617 A1 domain which allows interaction with the GPIb-IX coverage between inner and outer wall at the channel complex. After vessel injury, vWF becomes adsorbed curvature (see Fig. 9). Furthermore, while simplified 3D through its A3 domain, to subendothelial proteins, Newtonian fluid continuum simulations of the larger notably collagen, exposed to the flowing blood. geometry already reveal qualitatively similar results (see Immobilized vWF experiencing shear flow (especially Fig. 8), approximating the microfluidic chamber >1000 s ), unfolds and exposes the A1 domain, geometry by up-scaling the simulated domain in He- thereby supporting PLT attachment through GPIb- moCell will allow for a more quantitative transfer of the 7,28 IX. As these necessary conditions are available in-silico observations on the experimental results. throughout the microfluidic channel (in the c _ = 1600 Additionally, investigating the precise mechanical force s case) they do not explain the increased adhesion at which the shear flow applies on PLTs, vWF molecules the inner arc of the curve. Explosive PLT adhesion, as and the wall could be suited better to compare between it occurs in acute arterial stenosis and resulting in the collagen-bound and the plasma vWF mediated thrombosis, is associated with pathological shear rates adhesion. above 5000 s and therefore known as shear-induced The current work presents the foundation for a PLT adhesion. Here, free flowing vWF molecules un- deeper understanding of cellular flow behaviour in coil while not yet bound to a substrate. This has also non-trivial curved geometries, as most blood vessels been reported to be caused by the same interaction at are, and their implications on PLT adhesion. the surface of activated PLTs within a thrombus, ACKNOWLEDGMENTS highlighting a key role of the GPIb-IX/vWF bond formation in thrombus growth. In our simulated re- C.J.S., G.Z., M.V.D.K. and A.G.H. acknowledge sults peak WSRs stay below 2700 s and therefore such pathological shear rates do not occur. Shear financial support by the European Union Horizon gradients, as observed in Figs. 4 and 5e, are known to 2020 research and innovation programme under Grant drive PLT adhesion. Sing and Alexander-Katz ex- Agreement No. 675451, the CompBioMed2 Project. posed that the underlying factor are elongational C.J.S., G.Z., M.V.D.K. and A.G.H. are funded by flows, which naturally occur in the presence of shear CompBioMed2. The use of supercomputer facilities in gradients. These flow fields play a key role in the this work was sponsored by NWO Exacte Weten- adhesion mediation of vWF, by enabling vWF to un- fold already in physiological shear flow conditions. schappen (Physical Sciences). Based on the simulation strong elongational flows are CONFLICT OF INTEREST The authors declare to observed at the inner arc of the channel’s curvature at a WSR of 1600 s (see Fig. 6a), which correlates well have no conflict of interest. with the increased thrombi coverage in the same region OPEN ACCESS and in the same shear flow. Furthermore, vWF mole- cules that unfold in presence of the enabling flow con- ditions and do not immediately come in contact with a This article is licensed under a Creative Commons binding site are in a position to stay unfolded further Attribution 4.0 International License, which permits into the flow, even when the rate of elongation falls be- 25 use, sharing, adaptation, distribution and reproduction low the initially enabling value. The increased error in any medium or format, as long as you give margin in thrombi coverage at the high shear case outlet section might hint at this effect, though a more detailed appropriate credit to the original author(s) and the investigation is necessary. The elongation rate measured source, provide a link to the Creative Commons at the inner arc of larger than 370 s is well within the licence, and indicate if changes were made. The critical rate e _ (300–600 s ) allowing for vWF molecules images or other third party material in this article are to uncoil in elongational flow. In accordance with our included in the article’s Creative Commons licence, assumption, the low shear flow case exhibits a substan- unless indicated otherwise in a credit line to the tially lower rate of elongation at the inner arc peaking at 71 s , which is below e _ . This hypothesis will have to be material. If material is not included in the article’s confirmed in upcoming experiments in which the effect Creative Commons licence and your intended use is of pharmacological anti-PLT agents blocking the GPIb- not permitted by statutory regulation or exceeds the IX complex, the A1 domain of vWF or other PLT permitted use, you will need to obtain permission receptors will be evaluated to proof dependence on the 20 directly from the copyright holder. To view a copy of shear sensitive vWF molecule. Preliminary experi- this licence, visit http://creativecommons.org/licenses/b ments with the Fab ALMA12 blocking agent seem to y/4.0/. confirm this by cancelling out the difference in thrombi BIOMEDICAL ENGINEERING SOCIETY 3618 SPIEKER et al. APPENDIX FIGURE 8. Elongational flow magnitude across 1 mm diameter U-channel in continuum simulation. 3D continuum simulation using the finite element method software FreeFEM (version 4.8, Sorbonne University, Paris, France) resembling a parallel plate flow chamber with Newtonian fluid and a dynamic viscosity m ¼ 3:5 Pas across a U-channel with 1 mm channel diameter and 100 lm inner arc diameter. Boundary conditions are the same as in the cellular (HemoCell) simulations. The magnitude of the diagonal 21 21 elements of the rate of strain tensor in flow dimensions produces the 2D elongation profile of the (a) 300 s and (b) 1600 s initial 21 21 21 21 WSR case. The rate of elongation reaches peak values of e _ = 134 s in the c _ = 300 s case and e _ = 715 s in the c _ = 1600 s case. To allow for better comparison to the results in Fig. 6, the same scale is used. The plane is situated 1 lm below the top boundary of the geometry in z-direction, as depicted in the top right inset panel. FIGURE 9. Impact of Fab ALMA12 preincubation on PLT aggregation to collagen in curved flow chamber. Hirudinated human whole blood is preincubated with fragment ALMA12 and subsequently perfused through channels of a MFD coated with a solution of type I fibrillar collagen (200 l g/mL). (a) Schematic and dimensions of the microfluidic ‘‘U-shaped’’ channel. The squares indicate the regions of interest observed by video-microscopy. (b) The bar graph represents the quantified surface coverage of platelet aggregates obtained after 4 minutes of perfusion at c _ = 1600 s with ALMA12 and control fragment. The bars indicate the mean 6 SEM thrombi coverage in the 2 highlighted regions of 5 separate experiments performed with different blood donors. BIOMEDICAL ENGINEERING SOCIETY Micro-vessel Curvature Induced Elongational Flows on Platelet Adhesion 3619 REFERENCES Papaioannou, T. G., and C. Stefanadis. Vascular wall shear stress: basic principles and methods. Hellenic J. Cardiol. 46(1):9–15, 2005. 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The Effects of Micro-vessel Curvature Induced Elongational Flows on Platelet Adhesion

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BIOMEDICAL Annals of Biomedical Engineering, Vol. 49, No. 12, December 2021 ( 2021) pp. 3609–3620 ENGINEERING https://doi.org/10.1007/s10439-021-02870-4 SOCIETY Virtual Physiological Human The Effects of Micro-vessel Curvature Induced Elongational Flows on Platelet Adhesion 1 1 2 ´ ´ CHRISTIAN J. SPIEKER , GABOR ZAVODSZKY, CLARISSE MOURIAUX, 1 2 2 MAX VAN DER KOLK, CHRISTIAN GACHET, PIERRE H. MANGIN, and ALFONS G. HOEKSTRA Computational Science Lab, Faculty of Science, Institute for Informatics, University of Amsterdam, Amsterdam, The Netherlands; and Universite´ de Strasbourg, INSERM, EFS Grand-Est, BPPS UMR-S 1255, FMTS, Strasbourg, France (Received 31 January 2021; accepted 28 September 2021; published online 19 October 2021) Associate Editor Stefan M. Duma oversaw the review of this article. Abstract—The emerging profile of blood flow and the cross- INTRODUCTION sectional distribution of blood cells have far reaching biological consequences in various diseases and vital internal The effects of curved vessel geometry on blood flow processes, such as platelet adhesion. The effects of several were investigated thoroughly from a macroscopic essential blood flow parameters, such as red blood cell free 2,31 viewpoint, where blood is approximated as a con- layer width, wall shear rate, and hematocrit on platelet tinuum fluid and the biological implications (often in adhesion were previously explored to great lengths in straight connection to cardiovascular diseases) are commonly geometries. In the current work, the effects of channel curvature on cellular blood flow are investigated by simulat- linked to the magnitude or inhomogeneity of wall ing the accurate cellular movement and interaction of red shear stress. On the level of smaller, micron-scale ves- blood cells and platelets in a half-arc channel for multiple sels, or when investigating near-wall processes, the wall shear rate and hematocrit values. The results show continuum description is no longer sufficient. The significant differences in the emerging shear rate values and continuum approximation can lead to several-fold distributions between the inner and outer arc of the channel curve, while the cell distributions remain predominantly differences in shear rate and shear stress close to the uninfluenced. The simulation predictions are also compared wall. The complex nature of blood as a fluid is dic- to experimental platelet adhesion in a similar curved geom- tated primarily by its physiological composition of etry. The inner side of the arc shows elevated platelet blood plasma and immersed deformable cells. These adhesion intensity at high wall shear rate, which correlates cellular components account for approximately half of with increased shear rate and shear rate gradient sites in the simulation. Furthermore, since the platelet availability for the volume fraction. The hematocrit value, corre- binding seems uninfluenced by the curvature, these effects sponding to the red blood cell (RBC) concentration, is might influence the binding mechanics rather than the around 44% in healthy humans. Moreover, blood probability. The presence of elongational flows is detected contains less numerous cells (e.g. platelets (PLTs) and in the simulations and the link to increased platelet adhesion white blood cells (WBCs)) that account for about 1% is discussed in the experimental results. in total blood volume. Due to these cellular components blood behaves as Keywords—Non-trivial vessel geometry, Blood rheology, a non-Newtonian fluid with unique rheological prop- Cell free layer, Cell-resolved simulation, Elongational flow. erties in the confined geometry of blood vessels, giving rise to a multitude of phenomena, such as the Fa˚ hræus and Fa˚ hræus-Lindqvist effects. These two effects occur as a consequence of the formation of the red blood cell free layer (CFL), which in turn is Address correspondence to Christian J. Spieker, Computational caused by the lift force and shear flow induced axial Science Lab, Faculty of Science, Institute for Informatics, University migration of RBCs. The CFL acts as a lubrication of Amsterdam, Amsterdam, The Netherlands. Electronic mail: c.j. layer for the bulk of cellular flow due to the locally spieker@uva.nl 0090-6964/21/1200-3609/0  2021 The Author(s) 3610 SPIEKER et al. reduced blood viscosity. As frequently discussed in MATERIALS AND METHODS literature, an increased hematocrit value results in a Experimental Setup: In Vitro Flow-Based Studies smaller CFL width and an increase in flow velocity has 9,29 the opposite effect, due to a larger lift force. PLTs Experiments using flow-based assays are performed undergo radial migration towards the vessel wall and in the same manner as previously described by Re- into the CFL. This process, called margination, cre- ceveur et al. The polydimethylsiloxane (PDMS)- ates an increased availability of PLTs close to the based microfluidic device (MFD) has a square duct vessel wall. Zydney and Colton attributed this channel with a cross section of 1 1mm and the marginating behaviour to diffusion gradients, while diameter of the inner curve is 100 lm (see Fig. 1a), recently Za´ vodszky et al. showcased a strong depen- creating a 180 angle U-turn. The channel is coated dency on the hematocrit gradient. Kotsalos et al. overnight at 4 C with type I fibrillary collagen (200 lg/ proposed that a Le´ vy flight solution fits the mean-field mL) before being blocked with description of the resulting motion of PLTs. The human serum albumin (HSA) in 1% cellular flow dynamics have far reaching biological phosphate buffered saline (PBS) for 30 min at room implications in various diseases, for instance in the temperature. Hirudinated (>100 U/mL) human whole oxygenation of tumor tissues, or in the margination blood is perfused at 37 C through the U-shape chan- process in the presence of stiffened diabetic cells. One nels at volumetric flow rates of 3 and 16 mL/min using particular process of importance that is influenced is a programmable syringe pump (PHD 2000, Harvard the adhesion of PLTs. This process, which occurs both Apparatus, Holliston, MA, USA). Assuming a con- in physiological hemostasis, as well as pathological tinuous Newtonian fluid these flow rates result in thrombosis, is found to be highly shear dependent and 1 wall shear rates (WSRs) of 300 and 1600 s , respec- 11,19 sensitive to hydrodynamic alterations. The shift of tively, at the midpoint of the wall edges in the straight initially even shear gradients, e.g. caused by a sudden 29 inlet. Previous work, e.g. by van Rooij et al., has reduction in vessel diameter (vasoconstriction), leads shown that this assumption is not accurate for cellular to the presence of so called elongational flows. These blood flow and leads to wrong WSRs. However, as it is flow fields, defined by exerting tensile forces, are found still common practice in experimental work, it is to promote PLT adhesion under certain conditions, enabled by the mediation of prominent plasma mole- 13,23 cule von Willebrand factor (vWF). Furthermore, PLT adhesion is known to depend on the presence of a 29 24 CFL as well as the level of hematocrit. The effects of these essential blood flow parameters on PLT adhesion were investigated under static flow condi- tions, in straight geometries. Here, the effects of curvature are investigated by simulating the cellular movement of RBCs and PLTs in a half-arc channel for multiple wall shear rate and hematocrit values. The simulations show significant differences in the emerging shear rate values and dis- tributions between the inner and outer arc of the channel curve, while the cell positions remain pre- dominantly unaffected. The simulation predictions are also compared to experimental PLT adhesion in a similar curved geometry. The changes in the shear-rate patterns, inducing the presence of elongational flow, correlate to the location of changes in the PLT adhe- sion intensity. The main focus is on the accurate sim- ulation and evaluation of the flow conditions, CFL, FIGURE 1. Experimental and simulation setup. (a) Setup of and cell distributions. However, a comparison to curved MFD blood experiments with highlighted regions of interest in red. (b) Setup of curved channel domain with cross- in vitro assays in a similar curved microfluidic geome- sectional dimensions of 25  25lm . Driving force is set in try is presented as well and the possible implications of negative x-direction inside the periodic pre-inlet (see top elongational flow in vessel curvature on PLT adhesion right). The regions of interest with equal volume (V , V inlet curve and V ) are highlighted in the top view of the channel (see outlet are discussed. left), where the corresponding inner and outer wall division used in the cell distribution evaluation is marked with the letters o and i, respectively. BIOMEDICAL ENGINEERING SOCIETY Micro-vessel Curvature Induced Elongational Flows on Platelet Adhesion 3611 900; 000 PLT=lL, which is larger than physiological adopted here as well. A vascular WSR of 300 s oc- levels (150,000–400; 000 PLT=lL). This allows for curs in the scale of conduit arteries, such as the carotid, increased statistical significance in evaluating the re- as well as venules. Larger WSRs in the range of 1600 sults, while still being dilute enough to avoid influ- s can be observed in the smallest arteries of the encing the overall cellular flow dynamics. vasculature, the arterioles. The values are chosen to The continuous inflow boundary condition for cells cover a wide range of physiological shear rates. (denoted as periodic pre-inlet in Fig. 1b) is imple- In some sets of experiments, hirudinated whole mented according to Azizi et al. Note that this peri- blood is preincubated with a Fab fragment of a odic pre-inlet boundary domain mimicks an infinitely blocking anti-GPIba antibody (10 lg/mL), named long straight channel, ensuring that the incoming cell ALMA12, for 15 min at 37 C before perfusion. distributions are fully developed at the point of entry PLT adhesion is visualized at the regions of interest to the main U-shape domain. All simulations are (see Fig. 1a) using differential interference executed on the Cartesius supercomputer (SURF, contrast (DIC) microscopy images obtained with an Amsterdam, Netherlands; https://userinfo.surfsara.nl/ inverted Leica DMI 4000 B microscope (Leica systems/cartesius). Microsystems, Mannheim, Germany) coupled to a complementary metal-oxide semiconductor (CMOS) camera (ORCA-Flash4.0 LT, Hamamatsu, Massy, Evaluation Method France). The area of the thrombi is determined by To determine the CFL width in the simulated re- utilising the Image J software (National Institutes of sults, it is defined as the distance from the wall where Health) to automatically delineate the surface of the the CFL volume fraction reaches a threshold value of thrombi which is expressed in lm . The results are then 5%. To simplify the calculation it is solely based on the quantified as thrombi coverage fraction of the center of mass of each RBC, neglecting the rotated and observed area. deformed membrane volume. The curved channel domain is evaluated at three Simulation Setup different positions along the flow direction both on the inner and on the outer side of the channel. These The in silico experiments are based on the open- locations are situated in the middle of the curved re- source cell-resolved blood flow model HemoCell, gion, right before, and right after the curvature in the which consists of a lattice Boltzmann method based straight ’inlet’ and ’outlet’ sections, as shown in fluid solver for the incompressible blood plasma and a Fig. 1b. The ’curved’ section is defined as an annulus discrete element method membrane solver for the cell sector with a 60 angle. The volume of the evaluated deformation mechanics. These two components are ’inlet’ and ’outlet’ sections equals the volume of the coupled by the immersed boundary method. Both the ’curved’ section. To calculate the CFL and the overall membrane mechanical models of RBCs and PLTs as cell distribution in each section, the cell position well as the bulk flow rheology of the entire model have coordinates along the flow are projected onto the been thoroughly validated for both single cell and bulk 32–34 center line of the channel. For the cell distribution flow dynamics. evaluation, each section volume is divided into an in- To simulate cellular blood flow in a U-shaped ner and outer wall layer counterpart (see Fig. 1b). This channel geometry the same model parameters are used 32–34 results in a visualisation of an accumulated cell con- as in the validation studies. The cross-section of centration per layer volume. The inner wall refers to the channel is a square duct, following the current 12,30 the half of each section situated at the inner arc of the methods in experimental platelet adhesion assays curve and the outer wall respectively at the outer arc. to allow comparison with the microfluidic experimen- This separation allows to evaluate average behavior in tal results. The width of the channel is 25  25 lm and the layers which reduces statistical noise. the inner diameter of the curved annulus section is also To localise and quantify elongational flows within set to 25 lm (see Fig. 1b). To allow for comparison the domain, the rate of elongation e _ is calculated for with the experimental results, the simulated flow rate is the planar profile. From the rate of strain tensor, given setup to result in WSRs of c _ = 300 s and c _ = 1600 1 by: s , respectively, at the midpoint of the wall edges in 2 3 the straight inlet of the simulated channel using the e e e 11 12 13 same continuous flow assumption as in the experi- 6 7 e ¼ 4 e e e 5 ð1Þ ij 21 22 23 mental setup. The cells are randomly distributed in the e e e 31 32 33 inflow domain to result in a discharge hematocrit of 30%. The PLT concentration is fixed to BIOMEDICAL ENGINEERING SOCIETY 3612 SPIEKER et al. the magnitude of the diagonal elements in flow CFL width. As visualised in Fig. 3c, the results do not dimensions (e and e for x and y) across the center z- expose a significant influence of the curvature on CFL 11 22 plane of the domain is calculated. This results in the width when taking the SD range into account. This magnitude of elongation, i.e. the rate of elongation: proves true for each performed simulation (see Figs. 3a qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi and 3b). 2 2 ð2Þ e ¼ e þ e Tateishi et al. performed blood experiments with 11 22 similar 30% hematocrit in a straight blood vessel at a displayed in s . comparable diameter of 23.5 lm. The measured CFL width of 2.2 lm is in the same order of magnitude as the simulated average width of 3.9 ± 0.4 lm. The RESULTS difference could be attributed to the simplified center of mass based RBC localisation in the simulation In Vitro Results evaluation as well as geometrical disparities (e.g. To study the impact of altered hemodynamic con- square duct channel vs. straight tubular vessel). The 21 21 _ _ ditions generated in a curved vessel geometry on PLT WSR increase from c = 300 s to c = 1600 s does function, the thrombi coverage on the described col- not lead to a significant difference in CFL width. lagen coated MFD surface is evaluated after blood While the CFL width does not differ between the inner and outer wall in a statistically significant way in perfusion. Real-time video-microscopy based on DIC any of the sections, a substantial effect of the geometry imaging indicates that PLTs adhere efficiently in all curvature on the cross-sectional flow distribution is regions observed and form large aggregates (Fig. 2b). observed, here characterised by the respective 1D The color-coded regions on the sketch in Fig. 2a mark velocity and 2D shear rate profiles. Figure 4 highlights the position of the framed microscopic images in this effect by revealing a shift of the initially evenly Fig 2b. At the WSR of 1600 s in the region of the inner wall of the curved section (II.) the PLT aggre- blunted flow profiles towards the inner wall at the gates display a different orientation as compared to the curved section, which is carried on into the outlet five other regions of interest which show a clear ori- section. As an implication, the WSR which is set to entation in flow direction (Fig. 2b). Furthermore, the 1600 s in the straight inlet, shifts in the curved sec- aggregates appear much larger in this region (inner tion to a peak of larger than 2600 s at the inner wall wall II.) compared to the other ones. This is confirmed and around 1200 s at the outer wall. While not as by the fractional surface coverage of the thrombi being pronounced, this effect is carried on into the outlet significantly increased in the inner section of the curved section as well. region (II.) by 10% to a total of 30% compared to the The lower shear rate simulation with the same dis- outer region and to the evenly covered inlet section (I.) charge hematocrit of 30% and an initial WSR of 300 (Fig. 2c). The effect subsides into the outlet section s (see Fig. 5) deviates with roughly the same 2:1 ratio (III.) with no significant difference outside of the between the inner and outer wall at the center of the increased standard error of the mean (SEM) error curved section, with a shear rate of over 480 s at the margin compared to the inlet section. In contrast, the inner wall and around 240 s at the outer wall. lower shear (c _ = 300 s ) experiment exhibits no sig- The inlet velocity profiles of both shear flow cases nificant difference in thrombi coverage between inner (Figs. 4aand 5a) display a dampened parabolic flow and outer surface layer at any of the three sections as profile resembling the typical plug-shape caused by the high cell density at the center of the channel. The shown in Fig. 2c. horizontal lines on Figs. 4a–4cand 5a–5c indicate the respective averaged CFL width ± SD, clearly aligning In Silico Results with a step in the velocity profile. This step is caused by the transition from low local viscosity at the wall to To determine the root cause of the exhibited dif- ference in PLT adhesion in a curved vessel at physio- higher viscosity in the RBC rich bulk flow. logical shear flow, the in silico experiments are Furthermore, by compressing the shear rate profile evaluated with special emphasis placed on assessing towards the inner wall, a shift in shear rate gradient deviations between inner and outer wall of the curva- distribution is induced as well, which is especially vis- ture. For the CFL width this is achieved by comparing ible at the top and bottom of the channel of plot E in the average value ± standard deviation (SD) at the both Figs. 4 and 5. This shift in shear gradient natu- inner and outer wall in the inlet, curved and outlet rally causes the occurrence of elongational flow fields. section. The results, summarised in Figs. 3a and 3b, Figure 6 presents the rate of elongation across the display evidently the influence of (initial) WSR on the plane of the domain. The plane is situated 1 lm below the top boundary of the geometry in z-direction, which BIOMEDICAL ENGINEERING SOCIETY Micro-vessel Curvature Induced Elongational Flows on Platelet Adhesion 3613 FIGURE 2. Impact of flow generated in a curved section on human PLT aggregation to collagen. Hirudinated human whole blood is perfused through channels of a MFD coated with a solution of type I fibrillar collagen (200 lg/mL). (a) Schematic and dimensions of the microfluidic ‘‘U-shaped’’ channel. The color-coded squares indicate the 0.3 mm regions of interest observed by video- microscopy. (b) Representative DIC images of PLT aggregate formation at inner and outer arc on immobilized collagen at 1600 s after 4 min. Scale bar: 50 lm. The frame color refers to the color-coded positions in (a) and the numbered columns to the labeled inlet, curved and outlet section in (a). (c) The quantified surface coverage of platelet aggregates obtained after 4 min of perfusion at 21 21 c _ = 300 s and c _ = 1600 s . The bars indicate the mean 6 SEM thrombi coverage in the 6 highlighted regions of 5 separate experiments performed with different blood donors. is within the same layer observed by the microscope in In order to evaluate to what extent these shifted flow the experimental flow chamber. While both WSR profiles influence the transportation of RBCs and simulations show the highest rate of elongation e right PLTs, the cell distribution in the regions of interest is at the inner arc of the curve, the c _ = 1600 s case investigated as an accumulated cell concentration per reaches significantly higher values of around e _ = 379 inner or outer wall layer volume averaged over time. 21 21 s , compared to a peak value of e _ =71 s in the c _ = As Figs. 7aand 7b shows, the RBC distribution in the 300 s case. curved section exhibits a shift of around 10% towards the inner wall for both the high and low flow velocity BIOMEDICAL ENGINEERING SOCIETY 3614 SPIEKER et al. FIGURE 3. CFL width in silico results. (a) & (b) CFL width results at inner and outer wall of the inlet, curve and outlet section for 21 21 the H = 30% simulations at WSRs c _ = 300 s and c _ = 1600 s , respectively. (c) Visual representation of uniform CFL width in 30WSR of 1600 s simulation at inner and outer wall in the respective sections after 1 s of flow with marginated PLTs. The results are averaged between 0.9 and 1 s in 0.001 s time windows. 21 21 FIGURE 4. Flow profiles at c _ = 1600 s . (a)–(c) 1D velocity profiles of 30% hematocrit and WSR of 1600 s simulation at the center line of the inlet, curved and outlet section, respectively (indicated by the red line in the layout sketch) at half the channel height. (d)–(f) Cross-sectional shear rate profiles at inlet, curved and outlet section, respectively. The positions are indicated by the red line in the layout sketches from (a)–(c). Results are averaged between 0.2 and 1 s. BIOMEDICAL ENGINEERING SOCIETY Micro-vessel Curvature Induced Elongational Flows on Platelet Adhesion 3615 21 21 FIGURE 5. Flow profiles at c _ = 300 s . (a)–(c) 1D velocity profiles of 30% hematocrit and WSR of 300 s simulation at the center line of the inlet, curved and outlet section, respectively (indicated by the red line in the layout sketch) at half the channel height. (d)–(f) Cross-sectional shear rate profiles at inlet, curved and outlet section, respectively. The positions are indicated by the red line in the layout sketches from (a)–(c). Results are averaged between 0.2 and 1 s. FIGURE 6. Top view of elongational flow magnitude accross channel. Z-plane of the domain with magnitude of the diagonal elements of the rate of strain tensor in flow (x- and y-) dimensions, resulting in a 2D elongation profile of the (a) 300 s and (b) 1600 s WSR simulation. The plane is situated 1 lm below the top boundary of the geometry in z-direction, as depicted in the top right inset panel. All results are averaged between 0.2 and 1 s. case. Since the CFL width did not change between the Taking the SDs into account, all remaining inner to inner and outer wall in any section, it can be concluded outer wall comparisons in Fig. 7 show no significant that this observed shift is taking place in the center of difference in hematocrit and PLT volume fraction the channel where the bulk of RBCs is concentrated. distribution. BIOMEDICAL ENGINEERING SOCIETY 3616 SPIEKER et al. FIGURE 7. Cell distributions. Hematocrit (in red) and PLT volume fraction (in yellow) distribution between inner (striped) and 21 21 outer wall (blank) at initial WSRs of (a) 300 s and (b) 1600 s for inlet, curve and outlet, respectively. All cell distribution results are averaged between 0.2 and 1 s. DISCUSSION shown in Fig. 2, the results for the c _ = 1600 s flow experiment present a highly amplified PLT adhesion The effects of channel curvature on CFL width and intensity at the collagen coated surface of the inner arc, cross-sectional flow profile and cellular distributions with a 10% increase in thrombi coverage compared to are investigated, as well as their strongly intercon- the inlet region. This behaviour cannot be attributed to nected relationships. Although, based on the large 180 an increased availability of PLTs in the observed re- curvature of the channel, changes in overall cell dis- gion, considering the static size of the CFL and the tribution might be expected, no such significant devi- already fully accomplished margination. The shift in ations in CFL width and PLT concentration hematocrit concentration towards the inner wall of the distributions are observed between the inner and outer curvature (see Fig. 7) cannot explain the increased arc of the curvature (see Figs. 3 and 7). In contrast to adhesion either since it occurs in both high and low this, a strong compression of the shear rate profile flow velocity cases and can be assumed to be situated towards the curve can be seen, resulting in a discrep- at the center of the channel, due to having no signifi- ancy in the WSR ratio between the inner and outer cant influence on the CFL width. wall of approximately 2:1 (see e.g. Fig. 4e). These One could argue that due to a larger volumetric flow observations are true for the comparatively small rate at the inner arc of the curve compared to the outer simulated channel. To strengthen transferability to the arc, simply more PLTs pass by the observed surface experimental results in a much larger channel, simpli- region, therefore allowing for adhesion to occur more fied Newtonian fluid continuum simulations are per- frequently. While a shift of the profile towards the formed at dimensions of the MFD. The results (see curvature in plot B of Fig. 4 does show, approximately Fig. 8) reveal qualitative similarity in the macroscopic the same relative shift is visible in the low shear sim- continuum quantities to the cellular simulations (see ulation (Fig. 5b). However, comparing the c _ = 1600 21 21 Fig. 6). s and c _ = 300 s in vivo results (Fig. 2c), only the Although cellular distributions in blood flow and high shear experiment exhibits an increase in thrombi width of the CFL are known to be highly shear rate coverage at the inner wall of the curved section. Con- dependent, the observed strong shift in shear rate sequently the discrepancy cannot be explained solely appears to be associated with changes only in the bulk by an increased volumetric flow in the region. flow, away from the walls. This might imply changes in The multimeric plasma protein vWF is a key the local PLT margination process through the shift in mediator in the adhesion and aggregation of PLTs. local hematocrit gradients, however in the presented Multiple domains of the protein enable binding to case, the PLTs are already fully marginated by the time different molecules. Of special interest in our investi- they enter the domain of observation in the simula- gation are the A1 domain with binding sites for tions. The situation is assumed to be the same for the PLT receptor glycoprotein (GP) Iba of the GPIb-V- PLT in the in vivo blood experiments, due to the inlet IX complex and A3 which allows for binding to col- length of the blood perfusion tube and perfusion time lagen. Under physiological flow conditions, circu- of 4 minutes until the microscopic images are taken. As lating plasma vWF is folded and unable to expose its BIOMEDICAL ENGINEERING SOCIETY Micro-vessel Curvature Induced Elongational Flows on Platelet Adhesion 3617 A1 domain which allows interaction with the GPIb-IX coverage between inner and outer wall at the channel complex. After vessel injury, vWF becomes adsorbed curvature (see Fig. 9). Furthermore, while simplified 3D through its A3 domain, to subendothelial proteins, Newtonian fluid continuum simulations of the larger notably collagen, exposed to the flowing blood. geometry already reveal qualitatively similar results (see Immobilized vWF experiencing shear flow (especially Fig. 8), approximating the microfluidic chamber >1000 s ), unfolds and exposes the A1 domain, geometry by up-scaling the simulated domain in He- thereby supporting PLT attachment through GPIb- moCell will allow for a more quantitative transfer of the 7,28 IX. As these necessary conditions are available in-silico observations on the experimental results. throughout the microfluidic channel (in the c _ = 1600 Additionally, investigating the precise mechanical force s case) they do not explain the increased adhesion at which the shear flow applies on PLTs, vWF molecules the inner arc of the curve. Explosive PLT adhesion, as and the wall could be suited better to compare between it occurs in acute arterial stenosis and resulting in the collagen-bound and the plasma vWF mediated thrombosis, is associated with pathological shear rates adhesion. above 5000 s and therefore known as shear-induced The current work presents the foundation for a PLT adhesion. Here, free flowing vWF molecules un- deeper understanding of cellular flow behaviour in coil while not yet bound to a substrate. This has also non-trivial curved geometries, as most blood vessels been reported to be caused by the same interaction at are, and their implications on PLT adhesion. the surface of activated PLTs within a thrombus, ACKNOWLEDGMENTS highlighting a key role of the GPIb-IX/vWF bond formation in thrombus growth. In our simulated re- C.J.S., G.Z., M.V.D.K. and A.G.H. acknowledge sults peak WSRs stay below 2700 s and therefore such pathological shear rates do not occur. Shear financial support by the European Union Horizon gradients, as observed in Figs. 4 and 5e, are known to 2020 research and innovation programme under Grant drive PLT adhesion. Sing and Alexander-Katz ex- Agreement No. 675451, the CompBioMed2 Project. posed that the underlying factor are elongational C.J.S., G.Z., M.V.D.K. and A.G.H. are funded by flows, which naturally occur in the presence of shear CompBioMed2. The use of supercomputer facilities in gradients. These flow fields play a key role in the this work was sponsored by NWO Exacte Weten- adhesion mediation of vWF, by enabling vWF to un- fold already in physiological shear flow conditions. schappen (Physical Sciences). Based on the simulation strong elongational flows are CONFLICT OF INTEREST The authors declare to observed at the inner arc of the channel’s curvature at a WSR of 1600 s (see Fig. 6a), which correlates well have no conflict of interest. with the increased thrombi coverage in the same region OPEN ACCESS and in the same shear flow. Furthermore, vWF mole- cules that unfold in presence of the enabling flow con- ditions and do not immediately come in contact with a This article is licensed under a Creative Commons binding site are in a position to stay unfolded further Attribution 4.0 International License, which permits into the flow, even when the rate of elongation falls be- 25 use, sharing, adaptation, distribution and reproduction low the initially enabling value. The increased error in any medium or format, as long as you give margin in thrombi coverage at the high shear case outlet section might hint at this effect, though a more detailed appropriate credit to the original author(s) and the investigation is necessary. The elongation rate measured source, provide a link to the Creative Commons at the inner arc of larger than 370 s is well within the licence, and indicate if changes were made. The critical rate e _ (300–600 s ) allowing for vWF molecules images or other third party material in this article are to uncoil in elongational flow. In accordance with our included in the article’s Creative Commons licence, assumption, the low shear flow case exhibits a substan- unless indicated otherwise in a credit line to the tially lower rate of elongation at the inner arc peaking at 71 s , which is below e _ . This hypothesis will have to be material. If material is not included in the article’s confirmed in upcoming experiments in which the effect Creative Commons licence and your intended use is of pharmacological anti-PLT agents blocking the GPIb- not permitted by statutory regulation or exceeds the IX complex, the A1 domain of vWF or other PLT permitted use, you will need to obtain permission receptors will be evaluated to proof dependence on the 20 directly from the copyright holder. To view a copy of shear sensitive vWF molecule. Preliminary experi- this licence, visit http://creativecommons.org/licenses/b ments with the Fab ALMA12 blocking agent seem to y/4.0/. confirm this by cancelling out the difference in thrombi BIOMEDICAL ENGINEERING SOCIETY 3618 SPIEKER et al. APPENDIX FIGURE 8. Elongational flow magnitude across 1 mm diameter U-channel in continuum simulation. 3D continuum simulation using the finite element method software FreeFEM (version 4.8, Sorbonne University, Paris, France) resembling a parallel plate flow chamber with Newtonian fluid and a dynamic viscosity m ¼ 3:5 Pas across a U-channel with 1 mm channel diameter and 100 lm inner arc diameter. Boundary conditions are the same as in the cellular (HemoCell) simulations. The magnitude of the diagonal 21 21 elements of the rate of strain tensor in flow dimensions produces the 2D elongation profile of the (a) 300 s and (b) 1600 s initial 21 21 21 21 WSR case. The rate of elongation reaches peak values of e _ = 134 s in the c _ = 300 s case and e _ = 715 s in the c _ = 1600 s case. To allow for better comparison to the results in Fig. 6, the same scale is used. The plane is situated 1 lm below the top boundary of the geometry in z-direction, as depicted in the top right inset panel. FIGURE 9. Impact of Fab ALMA12 preincubation on PLT aggregation to collagen in curved flow chamber. Hirudinated human whole blood is preincubated with fragment ALMA12 and subsequently perfused through channels of a MFD coated with a solution of type I fibrillar collagen (200 l g/mL). (a) Schematic and dimensions of the microfluidic ‘‘U-shaped’’ channel. The squares indicate the regions of interest observed by video-microscopy. (b) The bar graph represents the quantified surface coverage of platelet aggregates obtained after 4 minutes of perfusion at c _ = 1600 s with ALMA12 and control fragment. The bars indicate the mean 6 SEM thrombi coverage in the 2 highlighted regions of 5 separate experiments performed with different blood donors. BIOMEDICAL ENGINEERING SOCIETY Micro-vessel Curvature Induced Elongational Flows on Platelet Adhesion 3619 REFERENCES Papaioannou, T. G., and C. Stefanadis. Vascular wall shear stress: basic principles and methods. Hellenic J. Cardiol. 46(1):9–15, 2005. 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Journal

Annals of Biomedical Engineering – Springer Journals

Published: Dec 1, 2021

Keywords: Non-trivial vessel geometry; Blood rheology; Cell free layer; Cell-resolved simulation; Elongational flow

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