The Effect of Hematocrit on Platelet Adhesion: Experiments and Simulations

Abstract

The volume fraction of red blood cells (RBCs) in a capillary affects the degree to which platelets are promoted to marginate to near a vessel wall and form blood clots. In this work we investigate the relationship between RBC hematocrit and platelet adhesion activity. We perform experiments flowing blood samples through a microfluidic channel coated with type 1 collagen and observe the rate at which platelets adhere to the wall. We compare these results with three-dimensional boundary integral simulations of a suspension of RBCs and platelets in a periodic channel where platelets can adhere to the wall. In both cases, we find that the rate of platelet adhesion varies greatly with the RBC hematocrit. We observe that the relative decrease in platelet activity as hematocrit falls shows a similar profile for simulation and experiment.

Introduction

Hemostasis in the seriously injured hemorrhagic shocked patient is sometimes difficult to achieve and uncontrolled bleeding is the main cause of preventable death after trauma. Transfusion protocols exist in all major hospitals, yet specifics vary in ratios infused of red blood cells (RBCs), to platelets, and to plasma, as well as timing of infusion depending on the functional need for the transfusion. In establishment of clinical diagnosis of a bleeding pathology, plasma- and platelet-function testing are conducted whereas isolated RBC function is not performed as RBCs in isolation tell very little about hemostatic function. Although the platelets constitute the formation of the platelet plug, the presence of an adequate volume of RBCs is important as well and is often overlooked as a critical hemostatic factor (1, 2).

In looking to explain the relationship between RBC hematocrit and bleeding, previous researchers have established that the distribution of platelets in arteries and arterioles (and microchannels of similar dimensions) is not uniform—platelets predominantly reside near the channel walls while RBCs occupy most of the volume close to the center in vitro (3, 4, 5, 6, 7), in silico (8, 9, 10, 11, 12, 13, 14, 15, 16, 17), and in vivo (18, 19). The phenomenon was described and accepted 30 years ago (20).

Many recent articles have elaborated on the process of margination during flow. Previously, three-dimensional (3D) boundary integral simulations of suspensions of platelets and RBCs have been performed by Zhao and Shaqfeh (21) and Zhao et al. (22) showing that the probability distribution of platelets across a microchannel varies strongly with hematocrit. In that article, platelets initially introduced at the center of a periodic channel filled with RBCs marginated to the outside of the channel over time. The probability distribution of platelet locations was found to be visibly different at 10 and 20% RBC hematocrit, with a higher hematocrit of RBCs leading to platelets closer to the wall. Vahidkhah et al. (15) and Vahidkhah and Bagchi (23) have also conducted 3D boundary integral simulations and investigated the effects of clustering in RBCs and platelets that arise during margination. Simulations by Kumar and Graham (24, 25) have found that differences in both size and deformability of cells contribute to margination.

While the current literature has established that margination occurs in a suspension of platelets and RBCs and depends greatly on the RBC hematocrit, there is a need to show that the hematocrit-dependent degree of margination leads to a noticeable effect in platelet activity. This desire to determine whether the effects of hematocrit-dependent platelet margination translate into differences in platelet binding activity leads us to integrate platelet adhesion into a computer simulation of a suspension of RBCs and platelets and compare the results to experiments. In studying the thrombosis process, other researchers have focused on the adhesion of platelets to von Willebrand Factor including Mody et al. (26) and Mody and King (27, 28, 29). These articles model platelet adhesion as occurring from Hookean springs with given equilibrium lengths that attach and detach stochastically according to first-order rate constants. Fitzgibbon et al. (30) used a similar model with no equilibrium length of the spring to show that their simulations could replicate the experimentally determined length distribution of translocation distances of individual rolling platelets before they finally adhered to a wall.

In this work we incorporate a model of platelet adhesion similar to that in the aforementioned work of Fitzgibbon et al. (30) into a simulation containing a suspension of RBCs and platelets with a RBC hematocrit of up to 30%. Thus, our simulation captures all the hydrodynamic interactions between RBCs and platelets, unlike simulations of single platelets near a wall. We compare the simulated platelet binding activity with experiments involving recapitulated thrombin generation-inhibited whole blood, with physiological platelet concentration of 2 × 10⁵/μL, flowing at a velocity inducing a physiological shear rate through a channel coated with type 1 collagen, to demonstrate that the hematocrit-dependent differences in the platelet probability distribution profile are reflected in platelet binding activity.

Materials and Methods

Boundary integral method for suspension of platelets and RBCs

Our numerical methods employ the previous boundary integral simulations of suspensions of RBCs and platelets of Zhao and Shaqfeh (21) and Zhao et al. (22) and add a platelet adhesion model. The specifics of the boundary integral method are only summarized here. For more complete details, see Zhao et al. (22).

We solve the boundary integral equations for Stokes flow (31, 32, 33), which express conservation of momentum as a relation between the velocity u on an object to the applied force $〚\mathbf{f}〛$. The force $〚\mathbf{f}〛$ is the first variation of the sum of the in-plane strain energy and out-of-plane bending energy in Eqs. 5 and 8 below. The viscosity ratio λ represents the ratio between the viscosities the fluids internal and external to the cells:

$$\frac{1+\lambda }{2}\mathbf{u}-\frac{1-\lambda }{8\pi }\mathbf{K}\mathbf{u}+\frac{1}{8\pi \mu }\mathbf{N}〚\mathbf{f}〛={\mathbf{u}}^{\infty }.$$ (1)

Incompressibility values of the fluid as well as the surface area A of a red blood cell are represented as

$$0={\nabla }_D\cdot \mathbf{u}=\frac{1}{\delta \text{A}}\frac{\text{d}\delta \text{A}}{\text{d}t}.$$ (2)

In the above equations, the single and double-layer kernels N and K are defined as

$${\left(\mathbf{N}〚f〛\right)}_j\left({\mathbf{x}}_0\right)=\int {〚f〛}_i\left(\mathbf{x}\right)G_{ij}\left(\mathbf{x},{\mathbf{x}}_0\right)dS\left(\mathbf{x}\right),$$ (3)

$${\left(\mathbf{K}\mathbf{u}\right)}_j\left({\mathbf{x}}_0\right)=\int {\mathbf{u}}_i\left(\mathbf{x}\right)T_{ijk}\left(\mathbf{x},{\mathbf{x}}_0\right){\mathbf{n}}_k\left(\mathbf{x}\right)dS\left(\mathbf{x}\right),$$ (4)

and G and T are the fundamental Green’s function solutions for the Stokeslet and stresslet with periodic boundary conditions as defined in Hashimoto (34). Thus we would naively assume that every mesh vertex $x_0$ interacts with every other mesh vertex for O(N²) interactions to process, but the boundary integral computations are accelerated using a smooth particle mesh Ewald sum (35), which is an O(N log N) method.

Red blood cells are deformable membranes with a membrane shear elasticity and a bending modulus. Platelets are treated as rigid discocytes. For modeling the elasticity of the RBC membrane, a Keller-Skalak law (Skalak et al. (36)) is used for the in-plane strain energy

$$W_S=\frac{E_S}{2}\left(\frac{1}{2}{I}_2^2+I_1-I_2\right)+\frac{E_D}{8}{I}_2^2,$$ (5)

where $E_S$ is the RBC membrane’s shear modulus and the strain invariants $I_1$ and $I_2$ are defined in terms of the principal strains ${\lambda }_1$ and ${\lambda }_2$ as

$$I_1={\lambda }_1^2+{\lambda }_2^2-2,$$ (6)

and

$$I_2={\lambda }_1^2{\lambda }_2^2-1,$$ (7)

Because the bending contribution for RBCs is typically a couple orders-of-magnitude smaller than the shear elasticity term, the out-of-plane bending energy is computed by the edge bending formulation (37) of

$$W_B={\Sigma }_{e}2\sqrt{3}{E}_B\left[1-\text{cos}\left({\beta }_e-{\beta }_0\right)\right],$$ (8)

where $E_B$ is the RBC’s bending modulus, e represents an edge in the mesh, and ${\beta }_e$ is the dihedral angle formed between adjacent mesh triangles that share edge e. For simulations of objects such as vesicles where bending contributions play a greater role, more costly but higher accuracy measures of bending such as those involving subdivision surfaces may be advised (38).

The mesh for each RBC has 1280 triangles and the mesh for each platelet has 706 triangles. Assuming a red blood cell volume of V = 94 μm³ (5), the equivalent radius of a red blood cell is therefore $a={\left(3V/\left(4\pi \right)\right)}^{\left(1/3\right)}=2.82\mu \text{m}$, which is the length scale by which all quantities are nondimensionalized in this simulation. In these nondimensional terms, the channel has height 12 (∼34 μm in dimensional units), periodic length 16 (45 μm), and periodic width 9 (25 μm). The platelet shape is a biconcave disk with diameter 1 and height 0.25 in this nondimensionalized length scale. The plasma viscosity μ = 1.2 mPa s is nondimensionalized to 1. The membrane shear modulus $E_S$ for typical RBCs can be estimated as $E_S=6.8\mu \text{N}/\text{m}$ and the bending modulus $E_B=2\times {10}^{-19}\text{J}$ (39). The simulation is run at capillary number $Ca=\mu \dot{\gamma }a/E_S=2$, resulting in a characteristic shear rate of $\dot{\gamma }=4000{\text{s}}^{-1}$. A nondimensional timescale follows from the dimensional analysis of the length, viscosity, and shear modulus parameters just given.

Platelet binding model

Platelet adhesion is simulated by modeling receptor bonds as Hookean springs that form and dissociate with first-order rate kinetics, motivated by the approach taken by Mody and King (28). Our model considers two types of bonds associated with platelet arrest or surface adhesion. Von Willebrand factor is either released from and tethered to an activated endothelium or is recruited to the collagen surface from blood plasma where it forms bonds with the GPIb platelet receptor. The next step involves Glycoprotein IIb/IIIa, also known as integrin $\alpha IIb\beta 3$, a platelet receptor for fibrinogen. This receptor complex also binds von Willebrand factor. When platelets are activated, GPIIb/IIIa undergoes a calcium-dependent conformational change that allows it to bind fibrinogen and participate in outside-in signaling that mediates other aspects of platelet hemostatic function such as degranulation and clot contraction. We model a bond with four parameters: once a part of the surface area of the platelet approaches within cutoff distance L of the wall, it forms a bond that is a Hookean spring with spring constant k_spring that imparts a force and a torque on the platelet. The bond forms with rate constant k_on that is first-order in surface area. Each bond dissociates with first-order rate constant k_off. Similarly, we also model an effectively permanent bond mediated by Glycoprotein IIb/IIIa (integrin ${\alpha }_{IIb}{\beta }_3$). This bond has a rate constant k_on two orders-of-magnitude smaller than the GPIb rate constant, but effectively it does not dissociate on the timescale of the simulation (40). Both bonds are modeled as having the same spring constant k_spring and bond length L because they are both attached to von Willebrand factor. The rate constant k_on for GPIb is chosen to require several rotations before bonding of a platelet near a wall but accelerated slightly from the values of Doggett et al. (41), and k_off is scaled appropriately. The end effect is that the rate constants for both bond formation and dissociation in the simulation are two orders-of-magnitude higher than their best physical estimates from the aforementioned articles, but this is needed to make the simulation computationally feasible. In nondimensional units L = 0.1, which translates to ∼280 nm and is consistent with the high end of Bonazza et al. (42). The spring constant is based on an estimate from the prior work of Fitzgibbon et al. (30), which used a similar platelet bonding model for a simplified system of a single platelet near a wall and was able to get reasonable agreement to experiments when estimating the translocation distance that a platelet would travel rolling along the wall between the time that it began adhering and the time that it became stationary. The values for parameters are shown in Table 1 and a schematic of the receptor model is shown in Fig. 1. A discussion of how sensitive the simulation is to these parameters can be found in Fitzgibbon et al. (30).

Table 1.

Receptor Model Parameters

Parameter	Description	Weak (GPIb)	Strong $\left({\alpha }_{IIb}{\beta }_3\right)$
kon	Bond formation rate constant	230/μm2⋅s	2.3/μm2⋅s
koff	Bond dissociation rate constant	10/s	0/s
kspring	Spring constant	200 pN/μm	200 pN/μm
L	Maximum binding length	280 nm	280 nm

Figure 1.

Parameters in receptor bond model. To see this figure in color, go online.

A platelet is allowed to form, at most, eight bonds with the wall simultaneously. Although this does not represent a thermodynamic or biological property, bond count was also limited in the aforementioned work of Fitzgibbon et al. (30). The role of this limitation is to prevent the force the bonds exert on the platelet, pushing it toward the wall, from becoming unbounded. By the time eight bonds have formed, the platelet will be essentially stationary and have sufficient exposed surface area so that bonds that release will re-form faster than further releases, thus this does not affect the simulation dynamics.

Initial condition

Before enabling platelets to bind to the wall, we must establish a representative probability distribution of platelets versus channel height. To set the simulation initial conditions, we first randomly place an array of RBCs uniformly in the channel as shown in Fig. 2 a. The simulation is then run with only RBCs, allowing the RBC distribution to equilibrate as in Fig. 2 b. Platelets are then introduced and allowed to marginate. For hematocrit 0.10 and hematocrit 0.20, the marginated state is a continuation further past the end of the simulation state originally documented in Zhao et al. (22), where platelets were introduced near the very center of the channel and marginated as the mean flow in the channel traveled a distance corresponding to 2 cm over many weeks of computational time. To accelerate the finding of a steady platelet probability distribution, the following procedure was used to obtain the initial conditions for hematocrits 0.15, 0.25, and 0.30: The platelet probability distribution for 0.20 at long well-marginated time was computed and discretized into 10 bins. Platelets were then introduced into the equilibrated RBCs with heights chosen from the discretized probability distribution for hematocrit 0.20, with the range of heights compressed so that no platelets are introduced in the Fåhraeus-Lindqvist cell-free layer as demonstrated in Fig. 2 c. In other words, the platelets are introduced closer to the outermost layer of RBCs than the channel center, but most still marginate on thereafter. Each simulation was then continued without platelet adhesion to give platelets adequate time to enter the clear fluid region. This time was always at least 260 nondimensional time, corresponding to a week of computational time in the 30% hematocrit case. When the platelet and RBC distributions had mostly marginated such that the number of platelets in the cell-free layer is not greatly changing over time as shown in Fig. 2 d, the simulation state was declared time t = 0 for the platelet adhesion simulations.

Figure 2.

Schematic of simulation initialization, example shown for 25% hematocrit. (a) RBCs are introduced to fill a gridlike pattern with a uniform probability distribution. (b) The simulation is run with just RBCs to equilibration. (c) Platelets are inserted inside the channel region containing RBCs. (d) The simulation is run with bond formation disabled to allow margination. The state is then labeled time 0 for bond formation simulations. To see this figure in color, go online.

Apparatus preparation for experiments

Fig. 3 is a 3D pictorial representation of the BioFlux1000 (http://fluxionbio.com/bioflux/) microfluidic channel in the foreground (in focus) and inlet and outlet wells in the background. The viewing area identified (Fig. 3) has a width of 350 μm that converges to 200 μm and runs 7 mm in length to the outlet well. To prevent platelet binding along the entire length of the channel during the experimentation phase, type I collagen (100μM, 25 μL) was preloaded into the outlet well and controllably pushed backward through the channel until the fluid front completely filled the viewing area. The plate was then placed in a biosafety cabinet for a 1 h incubation time at room temperature. Excess collagen solution was then aspirated from the outlet well and 500 μL of 0.5% BSA/PBS wash was added to the outlet well and pushed through the entire length of the flow chamber at 5 dyn/cm² for 15 min. The wash solution was removed from both inlet and outlet wells and replaced with PBS temporarily. Just before addition of blood for flow experimentation, PBS was also removed from the inlet and outlet wells. Careful attention to retention of PBS within the chamber prevented air bubble introduction. Preliminary testing showed no platelet binding between the inlet well and viewing window whereas platelet binding did occur within the viewing window, thereby assuring collagen deposition. Collagen deposition was further tested with the inclusion of fluorescent microbeads that showed adherence (data not shown).

Figure 3.

The microfluidic channel used in the experimental apparatus is shown here. Most notably, the image capture region lies ∼165.5-mm downstream from the input well. Images were processed showing platelets adhering to a 300 × 300 pixel (190 × 190 μm) region of interest. The channel is 350-μm wide in the region of data capture. To see this figure in color, go online.

The BioFlux1000 is a commercially available high-throughput microchambered fluidic system incorporative of a fluorescent microscope, microplate, pneumatic flow control, and control and analysis software. At the time that these experiments were performed, the dimensions of the microchamber flow system were determined by the manufacturer and not customizable per our request. “High-shear” and “low-shear” plates are available. All plates are constructed of a clear polystyrene upper and enclosed with a 180-μm glass coverslip on the bottom.

Experimental procedure

Blood was drawn from healthy volunteers via a 19g butterfly syringe and a 50-mL Repeater/CombiTip System (Eppendorf, Hamburg, Germany). Blood was dispensed immediately in 40-mL aliquots into prepared tubes containing 8 μL Phe-Pro-Arg chloromethyl ketone (final concentration in blood 96 μM) for direct thrombin inhibition to assure anticoagulation and maintenance of nonactivated platelets. Blood was centrifuged at 200g for 10 min and platelet-rich plasma was separated from RBCs into respective tubes. The RBC fraction was further centrifuged at 2000g for 20 min for maximal concentration of RBC and separation of plasma. Platelets were prepared for fluorescent microscopy by addition of 80 μL calcein to 8 mL platelet-rich plasma (concentration 10 μM) for 20 min. Components were recombined to give a sample containing 200,000 platelets/μL with control of hematocrit value (40, 30, 20, 10%, and zero). The prepared blood samples were then pressurized in the microchannel to promote a shear rate of 920 s⁻¹ at the viewing window interface and point of image capture. Processing time (from blood draw to flowed experiment) was 1 h or less. Successive experiments were run to incorporate all simulated HCT values for which maximum time would have been 1 h and 20 min.

The microplate was designed to capture fluorescent spectroscopy images and measurements ∼165.5 mm downstream from the input well. Also due to microplate design, at 3.5 mm before the position of the camera, the width of the flow chamber expanded from 200 to 350 μm. Beginning 60 s from the injection of a blood sample, one snapshot was taken per 30 s. All data images were acquired as 8-bit captures using a 10× objective. Images were processed showing platelets adhering to a 300 × 300 pixel (190 × 190 μm) region of interest.

Although no 350 × 70 μm channels exist in the human anatomy, we believe these dimensions to reflect a similar scenario to that of a 100-μm first-order arteriole. Arteriolar shear rates have been calculated between 300 and 1000 s⁻¹, which we mimicked using a 920 s⁻¹ shear rate. Recombination of blood components resulted in whole blood used in experimentation that is identical to that contained within the human, with the only exception being that the plasma could not be activated to initiate coagulation through thrombin generation.

Results and Discussion

Whereas previous studies have established that platelets marginate close to the wall in a channel filled with RBCs, we wish to investigate whether the hematocrit of RBCs creates the difference between platelets being moderately close to the wall and very close to the wall, and that this difference is then reflected in platelet adhesion activity. We first begin by establishing the effect of hematocrit on the platelet distribution after sufficient time for margination, averaged over 15 dimensionless time (i.e., a timescale greater than the tumbling/sliding period of platelets in the cell-free layer). Fig. 4 shows the probability distribution for the surface area for platelets at the time that full margination has occurred before platelet adhesion is enabled in our simulations. We have binned the surface-area distribution over channel height very finely in these graphs—the surface area is counted over 168 bins, so that each bin represents 200 nm of channel height in dimensional units. With this fine binning of channel height, we see that the key observation is that although platelets generally marginate vaguely close to the wall at all hematocrit, at hematocrits >20% a substantially increased portion of the platelet surface area becomes extremely close to the wall. In particular, the probability distributions have been given a choice of binning such that the topmost/bottommost colored piece in the probability distribution represents the amount of surface area within 200 nm of the wall, which has a direct effect on how readily bonds will form. We expect the platelet adhesion activity in the simulation to be somewhat sensitive to the choice of the minimum bonding distance. In this work, the bonding distance is set to 0.1-times the diameter of the platelet.

Figure 4.

The platelet surface area probability distribution at each hematocrit after platelets have marginated but before platelet bonding is enabled according to Fig. 2d. The capillary number is Ca = 2 (corresponding to a characteristic shear rate of $\dot{\gamma }=4000{\text{s}}^{-1}$). To see this figure in color, go online.

The thickness of the cell-free layer near the wall in which no RBCs reside is central to understanding the degree of margination. Comparing the images in Figs. 4 and 5, we see that the higher capillary number results in more RBCs being deformed into a more slender and elongated form, but it does not greatly change the equilibrium distribution of the RBCs’ position within the channel. Fig. 5 b shows the thickness of the cell-free layer in which no RBCs reside is insensitive to the capillary number, and hence insensitive to shear rate, holding constant the mechanical properties of the RBCs. However, there is a big difference in the cell-free layer thickness between 15 and 30% hematocrit. In particular, the cell-free layer is less than the diameter of a platelet at 30% hematocrit but it is greater than a platelet diameter at 15% hematocrit. This agrees with the intuition previously documented by Müller et al. (43, 44) that when the cell-free layer becomes comparable to the size of a platelet, the platelets are much more successful at reaching the wall.

Figure 5.

(a) Images of the marginated state comparable to Fig. 4 with capillary number is Ca = 0.5 (corresponding to a characteristic shear rate of $\dot{\gamma }=1000{\text{s}}^{-1}$). (b) The RBC surface area probability distribution, normalized so that the total area under the curve (including the middle channel region not shown) is equal for 15 and 30% hematocrits. In contrast with Fig. 4, this distribution has been symmetrized so that it measures platelet distance from either the top or bottom wall. To see this figure in color, go online.

Shear rates have been shown to have an effect on the rate of margination (i.e., the drift velocity of platelets initially near the center of a channel), but are only weakly related to the ultimate degree of margination as measured by the platelet probability distribution. Studies by different authors have obtained results where the amount of margination given sufficient time was fairly insensitive to capillary number or, equivalently, shear rate (22, 25, 43). Prior simulations and experiments in a microfluidic channel have demonstrated full margination within 2 cm of flow, and most margination had occurred after even 1 cm (22, 45). The camera in the experimental portion of this work sits 16.5 cm downstream, which is a much greater distance than what is required for margination.

Fig. 6 shows the center-of-mass platelet trajectories at 30% hematocrit. The purpose of this figure is to demonstrate that margination has occurred fully at the time that platelet adhesion is enabled. Although there is still platelet movement at the core of the channel, all platelets remaining near the middle of the channel are now well surrounded by blocks of RBCs. The platelets began at an initial distribution below the outermost layer of the RBCs and now have marginated into the cell-free layer as expected from the Fåhraeus-Lindqvist effect. Once platelet adhesion is enabled, the platelets closest to the wall begin to bind to the wall.

Figure 6.

Platelet trajectories showing the center of mass of all 30 platelets in the simulation for a run at 30% hematocrit. Full margination has occurred at the time when the simulation begins allowing bonds to form with the wall. The capillary number is Ca = 2. To see this figure in color, go online.

Fig. 7 shows a closeup of platelets near the wall at 30% hematocrit. As the teal platelet flows near the wall, it forms a bond briefly. The bond releases and the platelet continues flowing. The series of screenshots on the right of the figure is viewed from the side. From this view, it appears that the platelets are flowing over one another. A bottom view is also presented to show that this is not the case and that the platelets in this instance are further apart from each other. As platelets go near the wall over time and form bonds, the platelets are ratcheted downward by the torque on the bond, at which point more of the surface area is exposed, offering more opportunity for bonds to form and the platelet stays in position. This behavior agrees with observations of the previous simulations of Fitzgibbon et al. (30) of a single-platelet near a wall without the full hydrodynamic effects of RBCs.

Figure 7.

A platelet (green) forms a bond, ratchets downward from the torque, and then releases and continues flowing. Two dimensionless time elapses between each of the side-view screenshots. Additionally, a view from the bottom is shown for the beginning, middle, and end of this process. RBCs are colored red, platelets are white, and bonds are represented as thin blue lines. Hematocrit is 30%. The capillary number is Ca = 2. To see this figure in color, go online.

Because the platelets need to get very close to the wall to form a bond, we want to know what the motion of the platelets looks like as they approach. Furthermore, one feature of our flow is the use of a pressure-driven flow as opposed to a shear flow. In a shear flow, one can expect the shape of the RBCs to be fairly consistently slipperlike. However, in a pressure-driven flow with a parabolic flow profile, the RBCs near the center are parachute-shaped while the RBCs closer to the outside of the channel are slipper-shaped. In Fig. 8, we have plotted the inclination angle versus time for four typical platelets in an instance of suspension at 30% hematocrit. We see that platelets in the cell-free layer near the wall tumble at a much higher frequency than platelets near the middle of the channel due to both the higher shear gradient near the wall and the lack of nearby RBCs that would suppress the tumbling. We find that, at least for the biconcave shape of platelets used in these simulations, the rapid tumbling frequency is important in the dynamics of platelet adhesion, because for some of the platelets it is only during this tumble that the edge of the platelet is brought within the thin bonding range near the wall.

Figure 8.

Inclination angle versus time shown for selected platelets at different heights of the channel at 30% hematocrit and capillary number Ca = 2. To see this figure in color, go online.

Once platelet bonding is enabled in the simulation, we wish to establish the effect of hematocrit on this bonding rate. Fig. 9 shows the average platelet area within bond formation distance from a wall from the time at which bonding was enabled up until the current time for each time displayed on the horizontal axis. This number has some dependence on the observation time because, when a platelet forms multiple bonds with the wall, it eventually ratchets down close to the wall, exposing more surface area to the wall. It would not be correct to simply take the value of the average exposed surface area after an extremely long period of time as a metric for platelet activity because our simulation runs in a periodic channel. Once platelets have formed enough bonds to become stuck to the wall, new platelets do not replace them in the simulation. Because there are only 30 platelets in the channel, counting the number of adhered platelets is subject to discretization issues. If we hypothetically were to introduce new platelets mid-simulation as existing platelets adhered to the wall, then the number of platelets adhered to the wall would depend greatly on the locations of the randomly reintroduced platelets. Conversely, at too short of an observation time, platelets have not had enough time to effectively bond with the wall. Therefore, we need to find a length of observation time that is high relative to the tumbling/sliding period of the platelets but not indefinitely long. For timescales of roughly 200 nondimensional time, the dependence on average exposed area, when normalized relative to the 30% hematocrit simulations, is not very sensitive to time.

Figure 9.

(a) Average platelet-exposed surface area per time within the bonding radius in the simulations at capillary number Ca = 2. (b) The graph normalized by the hematocrit 30% simulation, demonstrating the variability with the choice of observation time. To see this figure in color, go online.

We now wish to compare platelet activity in the simulation and experiment against each other. The experimental data consists of a time series of snapshots as in Fig. 10 and Table 2. We convert these snapshots into a metric for determining the rate of platelet adhesion activity by plotting the surface area of the wall covered by platelets over time. For the experiment, the platelet adhesion metric is defined as the slope of the covered surface area of the viewed region versus time, from the start of the experiment until 4 min. Experimental data are captured for as long as 10 min, but near the end of this time the slide fills with platelets and the rate of further platelet adhesion becomes nonlinear in time. The data from which these slopes are taken is shown in Fig. 11. Beyond this time, the time taken to cover the rest of the wall continues at a different rate, as platelets then have the presence of a large number of other platelets changing the flow and the binding dynamics. For the simulation, the platelet adhesion metric is defined to be the exposed surface area over the 200 dimensionless time after bonding is enabled that is within binding range as shown in Fig. 9. In Fig. 12, this area is normalized to the area of a whole platelet. This is deemed a better measure than the raw number of bonds formed because it is less sensitive to platelets that bind very early.

Figure 10.

Images of platelet adhesion to bottom wall of channel at 40% hematocrit from experimental snapshots, full data for which is presented in Table 2 and Figs. 11 and 12. The camera taking these images is positioned below the flow chamber. Images near the wall are taken every 30 s. To see this figure in color, go online.

Table 2.

Rate of Platelet Adhesion Activity in Fig. 11

Hematocrit (%)	0	10	20	30	40
Donor1	0.0	21.7	62.4	234	473
0.0	8.8	72.1	194	345
Donor2	0.7	3.5	93.4	314	565
0.0	3.8	109.4	202	408
Donor3	0.0	6.1	85.8	240	467
0.0	12.1	117.2	109	295
Donor4	0.6	3.2	40.2	103	157
0.0	−0.3	30.3	128	288
Donor5	0.0	47.5	30.2	267	578
0.0	46.4	65.1	196	517
Mean	0.1	15.3	70.6	199	409

The units are platelet standard area/30 s. The mean values are normalized by the hematocrit 30% value and compared with the simulations in Fig. 12.

Figure 11.

Experimental data for adhered platelet area versus time. Each graph represents two runs from n = 5 different volunteers’ blood samples. The slopes of these lines are averaged and used for Fig. 12. These slopes, used as a measurement of adhesion rates, are presented in numerical form in Table 2. To see this figure in color, go online.

Figure 12.

Comparison of simulation and experimental adhesion activity, normalized against the adhesion activity at 30% hematocrit. Experimental platelet adhesion is defined, in a graph, as a slope of standard area per time for the first 4 min, and is taken from two runs of n = 5 volunteers’ blood samples. Simulation platelet activity is defined as the average exposed platelet surface area within bonding distance per time after enabling bonding for 200 dimensionless time normalized to the area of a whole platelet. Each point was averaged over two simulations that started 15 dimensionless time apart from fully marginated equilibrium (i.e., a long enough time that we expect no autocorrelation in platelet velocity from the previous initial condition). To see this figure in color, go online.

In Fig. 12, we normalize the value of platelet activity by the value observed at 30% hematocrit to assess similarities between simulations and in vitro experiments at the remainder of the hematocrit values investigated. The platelet activity falls off with decreasing hematocrit at a similar rate in both simulations and experiments. Granted, these results must be taken with a grain of salt because the graph in Fig. 12 is by nature a monotonically increasing curve from (0% hematocrit, 0 platelet activity) to (30% hematocrit, normalized to one platelet activity). The variance in how this curve would appear if we chose a different time cutoff from 200 nondimensional time can be seen by examining the right-hand side of Fig. 9—it would not matter too greatly. What Fig. 12 shows is that the hematocrit-dependent varying degree of margination demonstrated in Fig. 4 translates into a measurable difference in the activity of platelets binding to the walls.

Rectangular capillary tubes were utilized for in vitro experimentation because they are optically favorable, yet also were supplied as such by the FluxionBiosciences manufacturer. A 34-μm channel height has been used in simulation for a majority of our numerical simulations whereas the height in the flow experiments was 70 μm due to manufacturer’s specifications. It can be argued that the parabolic flow dimensions and therefore associated shear rates may vary per individual surface points due to this height difference. However, regardless of height of channel, the flow characteristics and force value will dictate binding phenomena and associated calculations and are equal in each system. Overall, we are confident in our comparison.

This study has several limitations. Firstly, it must be reiterated that a direct thrombin inhibitor was used in deliberate and calculated fashion to isolate platelet binding function in the presence of a single variable RBC hematocrit. As a result, claims from these results have limited strength in explanation of hemostatic function. It is well accepted within the scientific community that platelets are necessary for white clot formation on the arterial side of the vascular tree, yet no clots were formed in our experiments as no thrombin was generated. Undoubtedly, the presence versus absence of platelet deposition is a significant finding for which one may speculate that a scenario has been constructed where the well-known initiating factor of hemostasis has been removed or is very severely blunted. The limitation on the simulation side is that increasing the dimensions of the periodic box requires filling the volume with more RBCs to get the same hematocrit. We decided against doubling the channel height and halving the periodic length, because we wanted to be very sure that the RBCs were not acting on periodic images of themselves downstream or forming flow aligned structures that depended on a narrow periodic length. Again, the dimensions of the periodic box when nondimensionalized to the effective radius of a red blood cell are 12 radii tall, 16 radii long, and 9 radii wide, with flow proceeding down the long direction. However, further investigation is needed to truly understand how our findings impact bleeding or the arrest thereof. Another limitation is that flow in both the simulation and the experiments is constant, whereas it is variable and pulsatile in vivo. In the future we hope to improve our simulation algorithms and reach longer timescales to allow simulation of timescales that match the experiments directly.

Conclusions

Hemorrhage remains the major cause of potentially survivable injury resulting in death in civilian and military trauma (46, 47). We have conducted in vitro experiments and 3D boundary integral simulations showing the dependence of platelet adhesion on hematocrit. In both cases, hematocrit has a profound effect on the ability of platelets to adhere to a wall. In the simulations, we see that in general many platelets find their way to the outside of the clear fluid layer. The amount of platelet surface area in the bonding region is dependent on how many RBCs crowd the center of the channel, as the platelets have no way of marginating further in the absence of interactions with RBCs. Previous researchers have documented that the RBC hematocrit can affect the degree of margination in platelets. This work demonstrates that the hematocrit-dependent margination difference between exactly how close platelets approach the wall is then reflected in the process of platelet adhesion.

Biologically, we would expect bifurcations to play a large role as well, in determining the hematocrit and platelet distribution in microcapillaries. Because hematocrit varies between 10 and 20% in capillaries versus 40–50% in systemic circulation, it might be expected that differential margination effects combine with changing red cell buffering capacity across the vascular tree with profound implications for mechanisms of hemostasis in response to different injury patterns (48). However, much can still be learned with the simple long channel geometry used in the experiments in the context of medical blood analysis devices. In summary, the difference between the presence of sufficient hematocrit to bring platelets very close to a wall as opposed to only moderately close to wall has ramifications in how effectively those platelets will adhere to form blood clots. Our simulations and experimental data lend support to clinical transfusion protocols for critically bleeding patients that deliver either blood component mixtures that result in a net infused hematocrit of >25%, such as the 1:1:1 approach of red cells/plasma/platelets, or, preferably, whole blood, with a hematocrit of closer to 40% (49).

Our work also deepens our appreciation of why increasing HCT has been recognized (in some studies) to reduce bleeding risk (50, 51, 52, 53). Note that, beyond normal levels, elevated HCT is actually a thrombosis risk factor such as in polycythemia vera (54). However, more work needs to be done to definitively determine progress toward a clinical application. The available clinical evidence demonstrates that such transfusion strategies are associated with decreased risk of exsanguination (55).

Author Contributions

A.P.S. designed and performed modeling and simulations and wrote the article; J.E.C. and A.R. designed and performed experiments, analyzed data, and contributed to writing the article; S.R.F. contributed the development of the platelet adhesion model used within the simulations; A.P.C. and L.H.B. analyzed data and contributed to writing the article; and E.S.G.S. conducted modeling design and was the principle investigator.

Editor: Cecile Sykes.