The dynamics of red blood cells traversing slits of mechanical heart valves under high shear

Abstract

Hemolysis, including subclinical hemolysis, is a potentially severe complications of mechanical heart valves (MHVs), which leads to shortened red blood cell (RBC) lifespan and hemolytic anemia. Serious hemolysis is usually associated with structural deterioration and regurgitation. However, the shear stress in MHVs’ narrow leakage slits is much lower than the shear stress threshold causing hemolysis and the mechanisms in this context remain largely unclear. This study investigated the hemolysis mechanism of RBCs in cell-size slits under high shear rates by establishing in vitro microfluidic devices and a coarse-grained molecular dynamics (CGMD) model, considering both fluid and structural effects simultaneously. Microfluidic experiments and computational simulation revealed six distinct dynamic states of RBC traversal through MHVs' microscale slits under various shear rates and slit sizes. It elucidated that RBC dynamic states were influenced by not only by fluid forces but significantly by the compressive force of slit walls. The variation of the potential energy of the cell membrane indicated its stretching, deformation, and rupture during traversal, corresponding to the six dynamic states. The maximum forces exerted on membrane by water particles and slit walls directly determined membrane rupture, serving as a critical determinant. This analysis helps in understanding the contribution of the slit walls to membrane rupture and identifying the threshold force that leads to membrane rupture. The hemolysis mechanism of traversing microscale slits is revealed to effectively explain the occurrences of hemolysis and subclinical hemolysis.

Significance

This work focuses on the mechanism of hemolysis in RBCs within cell-scale slits. Using microfluidic devices and a coarse-grained molecular dynamics model of RBCs, we elucidated the dynamics of RBC traversing slits, including deformation, pore formation, and lysis. The results indicate that the combined forces from the fluid and the slit walls directly determine the rupture of the cell membrane, with a significant contribution from wall-induced compressive forces. Moreover, we found that changes in the membrane potential energy reflect the stretching, deformation, and rupture processes during traversal. Our findings reveal the unique mechanism of RBC hemolysis in confined space and providing valuable insights for the design of various medical devices.

Introduction

Hemolysis and subclinical hemolysis are potentially severe complications of prosthetic heart valves (1,2). Clinical studies show that subclinical hemolysis occurs in 18–51% of aortic mechanical heart valves (MHVs) (3,4,5). Subclinical hemolysis can lead to shortening RBC lifespan and anemia in patients with artificial heart valves and ventricular assist devices (6,7,8,9). Serious hemolysis and subclinical hemolysis are usually associated with either structural deterioration or paravalvular leak (1,10,11), which cause regurgitation, high flow velocity, and high shear rate in the slits between the valve components (12,13,14), as shown in Fig. 1, A–C. The time required for RBCs to traverse the aortic valve area is approximately 100 μs, with an even shorter duration for traversing the slit (15,16,17). At this time-scale, although traditional hemolysis models and shear flow experiments suggest that shear stress thresholds for hemolysis higher than shear stress levels in MHVs (18,19,20), hemolysis still occurs, potentially due to RBC contact with slit walls and additional compression (21,22). Therefore, understanding the impact of slits on hemolysis of RBCs is crucial for understanding the mechanisms of the destruction of RBCs caused by MHVs and improving the safety of MHVs.

Figure 1.

Gradual hemolysis during RBCs traversing the mechanical heart valve accompanied by the destruction of the membrane of RBCs in the clinical treatment. (A) Schematics of mechanical heart valve replacement of the aortic valve. (B) The mechanical valve closes during the diastolic phase of the cardiac cycle. (C) The main leakage channels: between the leaflets of the mechanical valve, between the leaflets and the sewing ring, and between the sewing ring and native ring. (D) The different dynamic states of red blood cells (RBCs) during the process of traversing the mechanical valve’s microscale slits. ① RBCs traverse the slits intact. ② RBCs traverse the slits with small restorable pores. ③ RBCs traverse the slits with unrestorable pores. ④ The lysis of RBCs in the slits. ⑤ The retention of RBCs by the slits. ⑥ The retention and lysis of RBCs by the slits.

Traditional hemolysis prediction models’ principles directly correlate hemolysis with fluid stress and exposure time (23). In these models, the hemoglobin release is related to magnitude of shear stress τ and exposure time t to this shear stress value by formula $\mathrm{H}\left(\tau ,t\right)=C{\tau }^{\alpha }{t}^{\beta }$, where H denotes the ratio of released hemoglobin to total hemoglobin within the RBC. These models have variable parameters depending on flow conditions and RBC responses to different types of fluid stresses (such as shear stress (24,25,26,27,28), tensile stress (29,30,31), turbulent stress (32,33,34), etc.), typically addressing specific types of flow conditions but often lacking accuracy in predicting hemolysis under complex conditions in medical devices. Recent advancements in computational simulations have led to cell-scale RBC models that incorporate mechanical and physical properties of RBCs, including the mechanism of fluid stresses transmission to the membrane (35). RBCs have been modeled as an isolated spheroid with flexible membranes (36,37), deformable droplets (38,39), encapsulated capsules (40,41), etc. In cell-scale models, the release of hemoglobin occurs not only through catastrophic rupture of the cell membrane (42,43) but also through traversal after sufficiently large pores are generated due to membrane forces (40,44). While combining these mechanisms improves prediction accuracy (45), these models still struggle with uncertainties, particularly in understanding the relationship between deformation and hemoglobin release, requiring calibration experiments for validation (40). In addition, they fail to capture critical microscopic and mechanical changes during hemolysis, which are essential for analyzing RBC damage mechanisms in cell-scale slits. Understanding these changes is crucial for improving hemolysis prediction in medical devices.

Current research on hemolysis in confined geometries (e.g., slits) includes in vitro experiments and computational models. In vitro experiments use microfluidic tools to assess the mechanical response of individual cells and measure membrane lysis in confined geometries (46,47). RBC deformation and rupture are driven by flow and geometric conditions, with increased pressure in slits, caused by cell entry, raising tensile stress on the membrane and leading to hemolysis (44,48). However, direct observation of these processes is challenging due to the micrometer-scale volume and transparency of RBCs. Computational models provide a numerical method to predict hemolysis and elucidate its intrinsic mechanisms (23,49,50). To investigate microscopic changes and forces on the cell membrane, coarse-grained molecular dynamics (CGMD) models of RBCs have been proposed to simulate the lipid membrane and cytoskeleton, focusing on fluid-structure interaction and RBC mechanics (35,51,52). CGMD models of RBCs have been applied to study the variation of shapes (53), cell membrane stiffness (54), vesicles formation (55), reticulocytes maturation (56), critical strain thresholds for pore formation (57) and adhesion dynamics between the RBC and the macrophage (58,59). CGMD models also have revealed hemolysis mechanisms in the interendothelial slits (IESs) of the spleen and microfiltration slits, showing that excessive pressure and extreme local area expansion of the lipid bilayer can cause RBC lysis (56,60,61,62,63). The size and stiffness of IESs also influence their filtration function for RBCs (64). However, the flow environment in spleen and microfiltration slits differs from that in MHV slits, where higher flow velocity, shorter transit time, and greater shear rates are present. Consequently, the hemolysis processes and mechanisms may vary. Importantly, these CGMD models primarily use membrane strain as the criterion for hemolysis, which may not fully capture the process from pore formation to membrane rupture, nor the changes in the lipid membrane and cytoskeleton during hemolysis.

In this study, we investigated the hemolysis mechanism of RBCs in cell-size slits under high shear rates by establishing in vitro microfluidic devices and a CGMD model of RBCs and slits, considering both fluid and structural effects simultaneously. Six dynamic states of RBC traversal through MHVs' microscale slits were identified, as shown in Fig. 1 D. The dynamic states were influenced not only by fluid forces but also significantly by the compressive force exerted by the slit walls. The variation in cell membrane potential energy indicated membrane stretching, deformation, and rupture. The maximum forces exerted on RBC membrane from water particles and the slit walls served as a critical threshold force for membrane rupture. This analysis helps in understanding the contribution of the slit walls to membrane rupture. The hemolysis mechanism in microscale slits is revealed to effectively explain the occurrences of hemolysis and subclinical hemolysis.

Materials and methods

CGMD model of RBCs

In this work, based on the advantages of the CGMD model in simulating the microscopic changes of RBCs, we implement a CGMD model in LAMMPS to simulate the rupture of the erythrocyte membrane and reveal how hemolysis takes place when erythrocytes pass through narrow slits. The two major components of the RBC membrane are, respectively, named the cytoskeleton and the lipid bilayer. The initial configuration of a coarse-grained model of RBC is shown in Fig. 2 A. The lipid bilayer is composed of lipid particles (red particles) and transmembrane protein particles, including glycoprotein and bond-3 (yellow particles). The cytoskeleton is composed of spectrin particles (green particles), actin junction complex particles (rose red particles), and ankyrin particles (light pink particles). The spectrin is a major component of the cytoskeleton, formed by two identical heterodimers and connected by actin junction complexes. Each spectrin filament of heterodimer is simulated by five spectrin particles and connected by ankyrin. The actin junction complex and ankyrin are connected to the lipid bilayer via transmembrane proteins. The particles are connected by breakable springs with different parameters and interact via a pairwise potential, resembling the Lennard-Jones (L-J) potential. In this one-particle-thick CGMD membrane model, we also include coarse-grained water molecules (explicit solvent) to account for hydrodynamic interactions and RBC shape transition due to volume reduction.

Figure 2.

Simulating a CGMD RBC model passing through a slit. (A) The membrane of the RBC is explicitly represented by CG particles. (a) Lipid particles, (b) transmembrane protein particles, (c) spectrin particles, (d) actin junction complex particles, (e) ankyrin particles, (f) internal water particles, (g) external water particles. (B) From left to right of the snapshots are 1) initial state of RBC, 2) equilibrium state of stress-free RBC, 3) resting shape of RBC after performing the volume control algorithm. (C) The width (W) and height (H) of the simulated slit were 5 μm. The length (L) of the simulated slit was 15 μm.

Interactions in the RBC model

In this work, we implement three types of interactions in the RBC model, including the lipid-lipid interaction of lipid bilayer membrane, the spring bond between spectrin particles, transmembrane protein particles, ankyrin particles and actin junction complex particles, the L-J potentials between lipid particles, cytoskeleton particles, water particles, and slit particles.

Yuan and colleagues have developed an interaction potential between coarse-grained lipid particles, including the head-head, tail-tail, and head-tail interactions between lipid molecules (53,65,66). The lipid-lipid interaction potential is constructed by the repulsive potential $u_R\left(r\right)$ and attractive potential $u_A\left(r\right)$, given by the following formulas.

$$u_R\left(r\right)=ϵ\left[{\left(\frac{r_{\mathit{min}}}{r}\right)}^4-2{\left(\frac{r_{\mathit{min}}}{r}\right)}^2\right]$$

$$u_A\left(r\right)=-ϵ{\mathit{cos}}^{2\delta }\left(\frac{\pi }{2}\frac{\left(r-r_{\mathit{min}}\right)}{\left(r_c-r_{\mathit{min}}\right)}\right)$$

Here, $r=\left|r_{ij}\right|=|r_i-r_j|$. $r_{\mathit{min}}=\sqrt[6]{2}\sigma$, which minimizes the potential energy $u_A\left(r\right)$. $\sigma$ is the length unit and ϵ is the energy unit, which we set $k_{B}T=0.23ϵ$ for numerical simulation. $r_{\mathit{c}}$ is the cutoff radius. $\delta$ controls the slope of the attractive branch.

We use harmonic springs to construct the cytoskeleton network and establish the connectivity between the cytoskeleton and the lipid bilayer through binding with spectrin particles, transmembrane protein particles, ankyrin particles, and actin junction complex particles. The harmonic bond potential is given by:

$$E_{harmonic}=K{\left(r_{ij}-r_0\right)}^2$$

Here, K is a constant that controls the bond force and bond potential between particles, while $r_{\mathit{0}}$ represents the equilibrium distance of each bond. For the model of an RBC, it is important to ensure that the RBC cytoskeleton is stress free in the initial configuration. One way to ensure a stress-free RBC cytoskeleton is by modifying the equilibrium distance of each bond so that initially the harmonic bond energy is zero for the cytoskeleton. Thus, we modified the harmonic bond in LAMMPS by calling initial configuration and calculating the bond length between each pair of particles at the beginning of simulation. The modified harmonic bond potential is given by the following formula.

$$E_{harmonic}=K{\left(r_{ij}-l_0\left(r_i,r_j\right)\right)}^2$$

Where $l_0\left(r_i,r_j\right)$ is the initial length of the bond. This slight modification helps us achieve a stress-free configuration for the cytoskeleton, by minimizing the total elastic energy of the system. For running the equilibrium state of RBC simulations, we use the mix of NPT and NVT fixes as our thermostats to control the system. Using NPT ensemble on water molecules and cytoskeleton network and NVT ensemble for coarse-grained membrane is able to obtain the stress-free state for both membrane and cytoskeleton and acquire numerical stable configurations. The additional data and details of this modification were provided in Fu et al. (53). And then, adjusting the value of the equilibrium radius σ_eq in L-J potential for internal water-water interactions can control the volume of RBC and achieve the shape transition. From left to right of the snapshots in Fig. 2 B are 1) the initial state of the RBC, 2) the equilibrium state of the stress-free RBC, and 3) the resting shape of the RBC after performing the volume control algorithm. The different coefficients of harmonic springs corresponding to various bonds in model are shown in Table 1.

Table 1.

Coefficients of harmonic springs

Bond type	K	${\mathrm{r}}_0$	Application
1	50	1.5	spectrin-spectrin, spectrin-ankyrin, spectrin-actin junction complex
2	20	2.0	actin junction complex-transmembrane protein
3	25	2.0	ankyrin-transmembrane protein

The standard 12/6 L-J potential between lipid particles, cytoskeleton particles, water particles, and slit particles is given by the following formula:

$$u_R\left(r\right)=4{ϵ}_w\left[{\left(\frac{{\sigma }_{eq}}{r_{ij}}\right)}^{12}-{\left(\frac{{\sigma }_{eq}}{r_{ij}}\right)}^6\right]$$

Here, $r_{\mathit{i}\mathit{j}}$ represents the distance between water molecules, the distance between each pair of cytoskeleton particles and the distance between membrane or cytoskeleton particles and water molecules particles. ${ϵ}_{\mathit{w}}$ is a constant that controls the energy of the L-J potential. ${\sigma }_{\mathit{e}\mathit{q}}$ is the equilibrium length of the L-J potential interactions. The different coefficients of L-J potential corresponding to different pairs in model are shown in Table 2. The chosen parameters of interaction models for RBCs in this study were primarily based on the literature by Fu et al. and Yuan et al. (53,66). In Fu et al.’s study, the dynamics of vesicle shape transitions and resting shapes of RBCs from LAMMPS simulations were compared with previous simulation results (66,67).

Table 2.

Coefficients of L-J potential

${ϵ}_w$	${\sigma }_{eq}$	${\mathrm{r}}_c$	Application
0.2	1.0	3.6	membrane-cytoskeleton, cytoskeleton-cytoskeleton
0.2	1.0	3.6	membrane-water, cytoskeleton-water
0.2	2.7–2.55	3.6	water-water
0.2	5.0	5.0	slit-water, slit-membrane, slit-cytoskeleton

For LAMMPS simulations, we nondimensionalize length, time, and temperature units according to LAMMPS unit style (units LJ):

$$\text{distance}=\sigma ,\text{where}{x}^{\ast }=\frac{x}{\sigma }$$

$$\text{energy}=ϵ,\text{where}{E}^{\ast }=\frac{E}{ϵ}$$

$$\text{temperature}=\text{reduced}\text{LJ}\text{temperature},\text{where}{T}^{\ast }=\frac{T{k}_B}{ϵ}$$

$$\text{time}=\tau ,\text{where}{\tau }^{\ast }=\tau \sqrt{\frac{ϵ}{m{\sigma }^2}}$$

Additional details and descriptions of the models were provided in Fu et al. (53).

Model of an RBC passing through a slit

To simulate the geometry of slits in medical devices, we construct a model as shown in Fig. 2 C. The slit is constructed from coarse-grained particles that form a particle-based structure, identical to that of RBCs. The distance between adjacent slit particles is fixed at 2.5 (ensuring sufficient density to prevent other particles from entering the slit region) and they are evenly distributed within the specified space to form a slit of the designated size. For clarity and comprehension, the images presented in this study depict the region influenced by the repulsive forces of the slit particles, rather than the particles themselves. The width and height of the slit are 5 μm. The length of the slit is 15 μm. Flow rates of 25, 50, 75, 100, 125, and 150 nL/min are applied to drive RBCs through the slits. We calculate the average flow velocity based on the flow rates and the sizes of the slits. The particles of the slits are set to move toward the RBCs at a constant speed.

In medical devices, the shear rates in heart pumps and prosthetic heart valves are notably high (68). The average shear rate in the slits of prosthetic heart valves ranges from 1500 to 3500 s⁻¹, with peak shear rates reaching 11,000 to 23,000 s⁻¹ (13,69). In left ventricular assist devices, the maximum shear rate can reach 171,429 s⁻¹, with a wall shear stress of around 600 Pa (70,71). Extracorporeal membrane oxygenation pumps can reach a maximum shear rate of 50,000 s⁻¹, with a wall shear stress of about 175 Pa (72). In percutaneous ventricular assist devices, the maximum wall shear stress exceeds 300 Pa (73,74,75). In our model, when the flow rate reaches 150 nL/min, the maximum shear rate within the slit (5 μm) reaches 293,979 s⁻¹ (with a shear stress of approximately 1029 Pa). At the flow rate of 25 nL/min, the maximum shear rate within the slit (5 μm) reaches 48,555 s⁻¹ (with a shear stress of approximately 170 Pa). Hemolysis does not occur when RBCs are subjected to shear stresses significantly lower than 560 Pa for very short durations (76,77). Similarly, Pan et al.'s study found that, at a flow rate of 25 nL/min, RBCs experienced over 15,000 squeezes before hemolysis gradually began due to fatigue (78). The flow rate was applied to simulate the flow conditions close to those in the microscale slits between the hollow fibers of the extracorporeal membrane oxygenation. Therefore, the selected flow rate range in this study is sufficient to cover the flow conditions that occur in the slits of medical devices, reproducing the physiological dynamics of RBCs.

Method of microfluidic experiments

The polydimethylsiloxane (PDMS) channels were fabricated using soft lithography. The microchannel is a single-layer structure with a height (H) of 5 μm, a compression width (W) of 5 μm, and a compression length (L) of 15 μm. A 2% BSA solution was flowed through the channel for 1 h to coat the inner walls of the channel with BSA. Extra BSA solution was then removed by injecting air into the channel.

Healthy donor RBCs were suspended in PBS buffer and then washed three times. All blood samples were obtained in accordance with relevant laws and guidelines approved by the Ethics Committee of Tsinghua University. The RBCs were then diluted in PBS solution (2%, v/v), which was prepared with 2.0 mM CaCl₂, 5 mM glucose, and 1 mg/mL BSA. The pH of the solution was adjusted to 7.4. For each experiment, the RBC suspension (2%, v/v) was injected into the microchannel at an average flow rate of 0.5 μL/min. The movement of RBCs in the flow was recorded using a high-speed camera (M110, Phantom Co., Wayne, New Jersey, USA) under an inverted microscope (IX83, Olympus Co., Tokyo, Japan). The squeezed RBC samples were extracted and added to a solution of glutaraldehyde (2.5%, v/v). After fixation with glutaraldehyde, the RBC samples were placed on poly-l-lysine-coated slides. After 30 min, the slides were washed with PBS buffer and dehydrated before observation under a scanning electron microscope.

The RBC suspension (2%, v/v) is incubated with 5 μM DiI (Abcam Co., Cambridge, UK) at 4°C for 20 min to stain the lipid membrane red. Subsequently, it is resuspended to observe the variation of the membrane under a high-speed camera (M110, Phantom Co., Wayne, New Jersey, USA) and an invert microscope (IX83, Olympus Co., Tokyo, Japan).

Results

Different dynamic states of RBCs during traversing slits

In this work, we found six different dynamic states of RBCs during traversing slits of different sizes under various shear rate conditions, as shown in Fig. 3. Some of the dynamic states correspond with the results of microfluidic experiments (46,48). If RBCs successfully passed through the slits, four dynamic states occurred: RBCs traversing the slits intact (shown in Fig. 3 A), RBCs traversing the slits with small restorable pores (shown in Fig. 3 B), RBCs traversing the slits with unrestorable pores (shown in Fig. 3 C), and lysis of RBCs in the slits (shown in Fig. 3 D). If RBCs failed to enter the slit, two dynamic states occurred: retention of RBCs by the slits (shown in Fig. 3 E), and retention and lysis of RBCs by the slits (shown in Fig. 3 F). When RBCs failed to enter the slit, they experienced continuous compression from the slit walls. Consequently, except in cases where the flow rate was low and the forces were minimal, the RBCs were likely to undergo lysis.

Figure 3.

Different dynamic states of RBCs during traversing slits of different sizes under various shear rate conditions. (A) RBCs traversing the slits intact. (B) RBCs traversing the slits with small restorable pores. (C) RBCs traversing the slits with unrestorable pores. (D) Lysis of RBCs in the slits. (E) Retention of RBCs by the slits. (F) Retention and lysis of RBCs by the slits.

The pores formed in the RBC membrane during its traversal through slits were categorized into two types: restorable pores and unrestorable pores. The restorable pores referred to those that gradually restored and disappeared after the RBC exited the slit due to the membrane’s fluidity. In contrast, the unrestorable pores referred to those that remained on the cell membrane even after the RBC left the slit and could not restore. After the initial pore formation on the membrane of RBCs, the pore might open larger under loading or might reseal and close under relaxed loading or even compression (57). This characteristic of pore formation and recovery in cell membranes had been widely applied in drug delivery systems as a loading method, demonstrating significant potential (79,80). In our microfluidic experiments, we collected postexperiment RBCs for electron microscopy observation and identified these unrestorable pores. The primary distinction between the two types of pores lay in the membrane’s ability to restore the pores through its fluidity after the RBC exited the high shear stress region of the slit. Typically, the formation of restorable pores resulted in the loss of only a small amount of lipids and cellular contents from the RBC. In contrast, the formation of unrestorable pores led to significant loss of lipids, and even cytoskeletal components, causing a continuous leakage of cellular contents. The lysis of RBCs was defined as occurring through three main criteria: 1) rupture of the cell membrane, leading to the shedding of lipid membrane and leakage of cellular contents, 2) inability to maintain the characteristic RBC shape due to severe damage to the lipid membrane and cell cytoskeleton (if the RBC shape is maintained, it is defined as the formation of pores on the membrane) (63), and 3) significant deformation of the cell membrane due to lysis, resulting in a marked increase in the potential energy of lipid membrane and bond, exceeding the potential energy value when the RBC shape is maintained.

In summary, based on the established CGMD model of RBCs traversing slits, we observed six distinct dynamic states of RBCs during traversing slits. To differentiate these states, we introduced and precisely defined the concepts of restorable pores, unrestorable pores, and lysis of RBCs in the cell membrane, laying the groundwork for further analysis and discussion.

Different dynamic states of an RBC through the slit driven by flow rate gradients

In this work, we choose the flow rates of 25, 50, 75, 100, 125, and 150 nL/min to drive the RBCs, although the slits and the values were sufficient for reproducing the physiological dynamics of RBCs through the slits in medical devices. The average diameter of RBCs is 8 μm, with a thickness ranging from 1 to 2 μm. Based on our final simulation results, if the slit size is greater than 8 μm, the cell does not come into contact with the slit walls. If the slit size is less than 2 μm, the cell reaches a state where it cannot pass through the slit. Therefore, we choose to primarily analyze the slit size of 5 μm ($5\mu \mathrm{m}=\left(8\mu \mathrm{m}+2\mu \mathrm{m}\right)/2$). Fist, we calculate the distribution of flow velocity and shear rate in the slit. Fig. 4, A and B illustrate the distribution of flow velocity and shear rate in the slit at 125 nL/min. The high flow velocity is mainly distributed in the center of the slit. The high shear rate is mainly distributed at the edges of the slit and is especially large at the entrance and exit edges. Both the maximum velocity and the maximum shear rate in the flow field increase linearly with the increasing flow rate, as shown in Fig. 4 C.

Figure 4.

Different states of an RBC through the slit under different flow conditions. (A) The distribution of flow velocity in the slit at 125 nL/min. (B) The distribution of shear rate in the slit at 125 nL/min. (C) The maximum flow velocity and maximum shear rate in the slit at different flow rates. (D) Four successive snapshots (x-y plane view) of a normal RBC passing through the slit at a flow rate of 25 nL/min. The RBC traverses the slit intact. (E) Four successive snapshots (x-y plane view) of a normal RBC passing through the slit at a flow rate of 125 nL/min. The RBC traverses the slit with small restorable pores. (F) Four successive snapshots (x-y plane view) of a normal RBC passing through the slit at a flow rate of 150 nL/min. The RBC traverses the slit with unrestorable pores. (G) Images of the deformation and the destruction of a fluorescent-dyed RBC during the passage through the slits by microfluidic experiments. The length of the scale is 5 μm. (G1–G3) At flow rates ranging from 25 to 100 nL/min, the RBCs pass through the microfluidic channel intact. (G4–G6) At the flow rate of 125 nL/min, the membrane of RBC ruptures upon entering the slit, with partial detachment of the membrane. The membrane is still able to maintain its integrity. (G7–G9) At the flow rate of 150 nL/min, the RBC undergoes excessive stretching and compression as it enters the slit, leading to severe rupture in the middle of the cell membrane. The membrane loses its integrity. (H–J) Observation using scanning electron microscopy revealed the presence of unrestorable pores in the RBCs traversing through the slit. The length of the scale is 2 μm.

Our simulation results show that RBCs are able to pass through the slits driven by these flow rates. However, the membrane of RBCs generates pores upon entry into the slit when driven by high flow rates, instead of remaining intact. Fig. 4 D depicts the dynamic process of RBC traversal through the slit under low flow rate (25 nL/min) and low shear rate (48,555 s⁻¹) conditions, showing the maintenance of the integrity of the cell membrane. Upon entry into the slit, the cell experiences significant deformation along the y axis due to compression from the slit walls, resulting in elongation within the slit. Upon exiting the slit, the volume compressed along the y axis does not fully recover to its initial state. The entire process of a normal RBC passing through the slit (5 μm) at a flow rate of 25 nL/min is shown in Video S1 in the supporting material. Fig. 4 E illustrates the dynamic process of RBC traversal through the slit under a flow rate of 125 nL/min and shear rate of 244,540 s⁻¹. The cell membrane forms small restorable pores. Upon entry into the slit, if the deformation rate of the cell cannot meet the requirements for entering the slit due to compression from the slit walls, rupture may occur. The snapshots (x-y plane view and x-z plane view) of the membrane deformation and the generation of pores at a flow rate of 125 nL/min are shown in Fig. S1, A and B. The green boxes highlight the locations where pores generate on the membrane, while the blue ellipses indicate the areas where cellular contents are leaking (represented by blue particles). However, due to the inherent fluidity of the cell membrane, the membrane possesses a certain self-healing ability. The gradual healing of small pores is depicted in Fig. S2 A. Upon exiting the slit, the cell membrane still maintains its integrity but loses some lipid membrane and contents. The entire process of a normal RBC passing through the slit (5 μm) at a flow rate of 125 nL/min is shown in Video S2 in the supporting material. Fig. 4 F depicts the dynamic process of RBC traversal through the slit under high flow rate (150 nL/min) and high shear rate (293,979 s⁻¹) conditions, forming unrestorable pores on cell membrane. As shear rate increases, the numbers and sizes of pores increase. The snapshots (x-y plane view) of the membrane deformation and the generation of pores at a flow rate of 150 nL/min are shown in Fig. S1 C. These pores cannot be healed by the self-healing ability of the cell membrane. As shear rate increases, the number and size of pores increase. Therefore, after leaving the slit, the membrane of RBCs still contains many pores, and the contents continue to flow out, representing the continuous efflux of hemoglobin and the occurrence of hemolysis. The entire process of a normal RBC passing through the slit (5 μm) at a flow rate of 150 nL/min is shown in Video S3 in the supporting material. In addition, we observed that, with increasing shear rate, membrane rupture initially occurs at the convex edges of the biconcave cells, followed by rupture at positions directly in contact with the edges of the slit. This indicates that, with faster compression rates of the slit, membrane rupture is triggered before the stress can be transmitted to the membrane.

Video S1. Video (x-y plane view) of the entire process of a normal RBC passing through the slit (5 μm) at a flow rate of 25 nL/min

The RBC traverses the slit intact.

Video S2. Video (x-y plane view) of the entire process of a normal RBC passing through the slit (5 μm) at a flow rate of 125 nL/min

The RBC traverses the slit intact. The RBC traverses the slit with small restorable pores.

Video S3. Video (x-y plane view) of the entire process of a normal RBC passing through the slit (5 μm) at a flow rate of 150 nL/min

The RBC traverses the slit with unrestorable pores.

In summary, flow rate and shear rate have a significant impact on the dynamic process of RBC traversal through the slits, determining whether the RBCs can pass through the slit intact. The extent of RBC rupture, such as the sizes and numbers of pores, is closely related to shear rate. Furthermore, the location of membrane rupture and detachment occurs at the point where the RBC experiences the most severe compression from the slit walls as it enters the slits. Moreover, as the flow rate increases, the compression exerted by the slit walls on the cells becomes more severe. We speculate that membrane rupture is not only related to fluid shear forces but also closely associated with the compressive forces from the slit walls. As the sizes of the slits decreases, the compressive forces exerted on the front of the RBC as it enters the slit increases, leading to greater deformation of the cell. Consequently, the compressive forces exerted by the slit walls on the cell intensify, resulting in more severe damage to the membranes of the cells. Therefore, in the subsequent sections, we discuss in detail the influence of slit walls on membrane rupture.

Results of microfluidic experiments

We conducted in vitro experiments using a PDMS microfluidic device fabricated using soft lithography methods (materials and methods). In the microfluidic device, the width of the channel is 200 μm and the height is 5 μm. The length of pillar (compression length) is 15 μm with a width of 5 μm, and the compression width W between adjacent pillars is 5 μm. The cross section of the gap is designed as a square with dimensions of 5 × 5 μm². The microfluidic device featured a pillar array forming slits of the same dimensions as those set in the simulations. Due to the transparency of the PDMS device, dynamic morphological changes of RBCs under compression can be observed, along with the assessment of damage to the membranes of RBCs. The experimental setup was based on the work of Pan et al. (78).

First, we observe the deformation and the destruction of the RBC membrane during the process of passing through the slits by staining the transparent lipid membrane of the RBCs with red fluorescent dye. Different dynamic processes of RBCs traversal through the slits are also observed in microfluidic experiments. As shown in Fig. 4, G1–G3, the RBC passes through the microfluidic channel intact at flow rates ranging from 25 to 100 nL/min. This corresponds to the simulation results in Fig. 4 D. With increasing shear rate, the membrane of the RBC ruptures upon entering the slit, with partial detachment of the membrane at the flow rate of 125 nL/min. The membrane is still able to maintain its integrity, as shown in Fig. 4, G4–G6. This corresponds to the simulation results in Figs. 4 E and S2 A. As the shear rate further increases, the RBC undergoes excessive stretching and compression as it enters the slit, leading to severe rupture in the middle of the cell membrane at the flow rate of 150 nL/min. The membrane loses its integrity, as shown in Fig. 4, G7–G9. This corresponds to the simulation results in Figs. 4 F and S2 B.

Second, we use scanning electron microscopy to observe the presence of unrestorable pores on the membrane of the RBC after passing through the slits. As shown in Fig. 4 H, after the RBCs traverse the slit intact, the cell membrane maintains its integrity without any pores. As shown in Fig. 4 I, after the RBCs traverse the slit with small restorable pores, the pores heal by themselves and the cell membrane maintains its integrity. As shown in Fig. 4 J, we found unrestorable pores on the cell membrane of RBCs after traversing the slit. Various diameter-sized pores are observed on the cell membrane, as shown in Fig. S3, A–C. The diameter of the pores ranges from 0.2 to 1.5 μm. We suppose that pores exceeding this range may lead to the rupture of RBCs, while pores smaller than this range may disappear due to the self-healing capability of the cell membrane. Therefore, the pores observed in the cells collected after the experiment fall within this range.

Finally, to validate the process of RBC traversal through the slits simulated by the CGMD model, we provide the images of RBC passage through the slit under flow rates of 25 and 100 nL/min, as shown in Fig. S3, D and E. We also compared the variation of the RBC’s length-width ratio during the process of traversing through the slits under different flow rates in both the simulation results and the microfluidic experimental results, as well as the morphology of cells at corresponding positions, as shown in Fig. S3, F and G. The length-width ratio of RBCs is around 1 before entering the slit. As the cell enters the slit, it elongates and the length-width ratio increases to 2. Upon exiting the slit, the length-width ratio decreases to 1.2–1.4, without returning to its pre-entry state. With the increase of the flow rate, the maximum length-width ratio exhibited a certain degree of growth and the time of passing through the slit was significantly reduced. Without altering the size of the slits, changes in flow rate had no significant impact on the morphology of the cells in the slits. The microfluidic experimental results demonstrate that the CGMD model accurately simulates the morphological changes of RBCs during the process of crossing slits. In addition, we observed a difference in the timescale between the simulation results and the experimental results. For example, the simulated crossing time was 500 $\tau$ (approximately 1200–1600 μs) under the flow rate of 25 nL/min, while the experimental crossing time was 790 μs. The temporal disparity may arise from the process of erythrocyte coarse graining in the simulation.

In conclusion, the results of our microfluidic experiments show the different dynamic states of RBCs in the traversal process under different shear rates and different membrane states after passing through the slits, which well correspond to the simulation results. The pore formation on the membrane and the rupture of the membrane are observed by cell membrane staining. The validation of the CGMD RBC model by microfluidic experiments confirms the reliability of the CGMD RBC model in simulating the process of traversing through the slits. Therefore, the morphological changes of RBCs and the mechanical analysis of cell membranes based on the CGMD model will aid in understanding the hemolysis issues that occur when RBCs traverse through the slits.

Sizes of slits dictate the dynamics of RBCs through slits at the same level of shear rate

In the preceding sections, we observed a close correlation between membrane rupture and the compression of the slit walls. Therefore, in this section, we analyze the impact of the compression of the slit walls on the dynamic process of RBC traversal through the slit by varying the size of the slit at the same level of shear rate. First, we calculate the maximum shear rate in different slits with different flow rates, as shown in Fig. 5 A. The maximum shear rate inside the slits significantly increases with decreasing sizes of slits. In many studies on RBC dynamics and CGMD models, fixed pressure gradients (56,63) and flow rate gradients (58,59) were both often used. In this study, we chose a flow rate gradient to closely replicate the dynamic of RBCs in the flow environment of medical devices. The selection of flow rates and shear rates was also based on actual parameters from medical devices, which provide more comprehensive data. In addition, our microfluidic experiments used a syringe pump to control the flow rate. Another reason for choosing the flow rate gradient was to enable a direct comparison between experimental and simulation results under identical conditions.

Figure 5.

Comparison of the dynamic states of red blood cells traversing through slits of different sizes under the same level of shear rate. (A) The maximum shear rate in different slits with different flow rates. (B) The simulation conditions for three groups with similar levels of shear rate but different sizes of slits. (C) When the size of the slit is 2 μm, the cell cannot enter the slit and remains intact. (D) When the size of the slit is 3 μm, the cell undergoes lysis upon entering the slit. (E) When the size of the slit is 3 μm, the unrestorable pores appear on the cell membrane upon entering the slit. (F) When the slit size is 5 μm, only restorable pores appear on the cell membrane. (G) When the size of the slit is 4 μm, a large number of unrestorable pores appear on the cell membrane upon entering the slit. (H) When the size of the slit is 6 μm, the RBC can pass through the slit intact.

We compared the results of three groups of simulations with the same levels of shear rate but varying sizes of slits. The simulation conditions are shown in Fig. 5 B. The comparison of results in the first group indicates that, when the size of the slit is 2 μm, the cell cannot enter the slit and remains intact, as shown in Fig. 5 C. However, when the size of the slit is 3 μm, despite a similar level of shear rate, the cell undergoes lysis upon entering the slit, as shown in Fig. 5 D. The comparison of results in the second group shows that, when the size of the slit is 3 μm, the unrestorable pores appear on the cell membrane upon entering the slit, as shown in Fig. 5 E. However, when the slit size is 5 μm, despite a similar level of shear rate, only restorable pores appear on the cell membrane. These pores heal after passing through the slit, and the cell membrane returns to its intact state, as shown in Fig. 5 F. The comparison of results in the third group reveals that when the size of the slit is 4 μm, a large number of unrestorable pores appear on the cell membrane upon entering the slit, as shown in Fig. 5 G. However, when the size of the slit is 6 μm, although the level of shear rate is similar, the RBC can pass through the slit intact, as shown in Fig. 5 H.

The dynamic states of RBCs during passage through slits of different sizes under various shear rate conditions are summarized in Fig. 6. The dynamic states of RBCs during passage through slits of different sizes under various flow rates are summarized in Fig. S4. The green circle marks represent RBCs traversing the slits intact. The yellow oval mark represents RBCs traversing the slits with small restorable pores. The orange hexagon marks represent RBCs traversing the slits with unrestorable pores. The red star marks represent the lysis of RBCs in the slits. The violet rhombus marks represent the retention and lysis of RBCs by the slits. The blue square marks represent the retention of RBCs by the slits. The green area represents that RBCs pass through the slits and remain intact. The red area represents that RBCs pass through the slits and lyse. The blue area represents that RBCs are retained by the slits. The gray area represents that the corresponding flow rate exceeds the reasonable range in both physiological and medical device conditions. It is worth noting that we also simulated the dynamic process of RBCs passing through an 8-μm slit. This size of the slit is larger than the maximum diameter of the RBC, so the slit walls do not directly interact with the cell membrane. Only fluid forces act on the cell membrane, serving as a control group for analyzing the squeezing effect of the slit walls.

Figure 6.

State diagram for RBC dynamics during passage through different slits driven by various flow rates. Six states are observed. The green circle marks represent RBCs traversing the slits intact. The yellow oval mark represents RBCs traversing the slits with small restorable pores. The orange hexagon marks represent RBCs traversing the slits with unrestorable pores. The red star marks represent the lysis of RBCs in the slits. The violet rhombus marks represent the retention and lysis of RBCs by the slits. The blue square marks represent the retention of RBCs by the slits. The yellow, green, and blue boxes represent three groups of RBC states at the same shear rates. The green area represents that RBCs pass through the slits and remain intact. The red area represents that RBCs pass through the slits but undergo hemolysis or lyse. The blue area represents that RBCs are retained by the slits. The gray area represents that the corresponding flow rate exceeds the reasonable range under both physiological conditions and medical device conditions.

According to the simulation results, we found that the dynamic state of RBC traversal through the slit is influenced by both fluid forces and the compressive force exerted by the slit walls. As the slit size decreases, the compressive force exerted by the slit walls on the cell membrane increases, becoming more significant in causing the rupture of the RBC membrane. This inference is supported by the simulation results of the control group, where the cell membrane remains intact in the absence of slit wall forces. Existing hemolysis models mainly focus on fluid forces (such as shear rate and turbulent stress) causing cell damage. However, when the cell passes through confined flow spaces, the membrane collides directly with and is squeezed against the wall surface. Therefore, wall forces are not only nonnegligible but also more important than fluid forces. In the following sections, we analyze in detail the microscopic changes and force conditions of the cell membrane during RBC traversal through the slit, emphasizing the importance of wall forces in membrane alterations.

Variation of the cell membrane during RBC passage through slits

In this section, we analyze the variation of the cell membrane during the passage of RBCs through the slits. This includes analyzing the potential energy of the lipid membrane and bonds, as well as the forces exerted by the slit’s walls and water. The potential energy of the lipid membrane and bonds, respectively, reflect the stretching conditions of the lipid membrane and the connections between the membrane and the cytoskeleton. The forces exerted on the membrane reflect the forces exerted by water particles and the slit walls on the cell membrane, respectively. This analysis helps in understanding the contribution of the slit walls to membrane rupture and identifying the threshold force that leads to membrane rupture. These data can be directly exported from the computational results generated by the LAMMPS and processed using MATLAB and Origin.

Fig. 7 shows the variation of cell membrane when the RBCs either pass through the slits or are retained by the slits, including the potential energy of lipid membrane and bonds. As shown in Fig. 7, A and B, when RBCs initially enter the slit, the compression by the walls of the slit leads to an increase in the potential energy of the lipid membrane and bonds. With increasing flow rate, the potential energy increases correspondingly. After the cell has fully entered the slit, its potential energy will return to the low potential energy state before entry. When cells initially enter the slit, the morphology undergoes deformation due to the compression exerted by the slit, leading to stretching of the bonds and a significant increase in potential energy. As the flow rate increases, cell deformation becomes more pronounced and the magnitude of the increase in potential energy escalates with the rising flow rate. After completion of deformation, the position and distribution of the cytoskeleton in the RBC undergo rearrangement to restore the system to a low potential energy state. Moreover, we found that the peak of potential energy is lower than the peak during the first traversal when the cell traverses the slit again. However, the low potential energy state of the bonds is higher than after the first traversal. This indicates that potential energy of bonds accumulates after traversing the slit, which may be related to RBC fatigue. Further analysis of the RBC fatigue model is presented in the discussion. If the lipid membrane ruptures and generates pores, it will continue to maintain a high potential energy state within the slit, as shown in Fig. 7, C and D. Upon exiting the slit, the potential energy of the lipid membrane rapidly decreases due to the shedding of lipid fragments. This characteristic can serve as a criterion for determining whether the cell membrane remains intact. If the RBCs are lysed in the slit, the peak of potential energy of the lipid membrane and bonds also increases as the flow rate increases, as shown in Fig. 7, E and F. Upon exiting the slit, the potential energy of the lipid membrane also decreases due to severe membrane damage, but remains higher than the initial value before entering the slit. With the increase in flow rate, the peak of the potential energy corresponding to the lysis state increases significantly. These indicate that the increased flow rate subjects the cell membrane to more severe forces from both the slit and the fluid, resulting in more pronounced deformation and a significant increase in the potential energy.

Figure 7.

The variation of cell membrane when the RBCs either passing through the slits or retained by the slits, including the potential energy of lipid membrane and bonds. (A) The variation of potential energy of lipid membrane when the RBC passes through the slits intact. (B) The variation of potential energy of bonds when the RBC passes through the slits intact. (C) The variation of potential energy of lipid membrane when the RBC passes through the slits with pores. (D) The variation of potential energy of bonds when the RBC passes through the slits with pores. (E) The variation of potential energy of lipid membrane when the RBC passes through the slits and lyses. (F) The variation of potential energy of bonds when the RBC passes through the slits and lyses. (G) The variation of potential energy of lipid membrane when the RBC is retained intact by the slits. (H) The variation of potential energy of bonds when the RBC is retained intact by the slits. (I) The variation of potential energy of lipid membrane when the RBC is retained by the slits and lyses. (J) The variation of potential energy of bonds when the RBC is retained by the slits and lyses.

On the other hand, RBCs are retained by the small-size slits. When RBCs are retained by the slits, the cell is gradually compressed into a disk-like shape due to the forces from the fluid particles and the slits, as shown in Fig. 5 C. As shown in Fig. 7 G, the potential energy of lipid membrane remains relatively constant, because the membrane remains intact during compression and experiences deformation at a slow rate. During the deformation phase, the potential energy of bonds shows a noticeable increase and, as the shape of cell stabilizes, the potential energy of bonds remains constant, as shown in Fig. 7 H. As the flow rate increases, the RBCs are still unable to pass through the slit, but they undergo lysis due to the more intense compression. As shown in Fig. 7, I and J, when RBCs undergo lysis, the potential energy of lipid membrane and bonds significantly decreases. In addition, we found that, unlike the lysis caused by passing through the slits, the timing of potential energy reduction is very similar across different flow rates, as shown in Fig. S5, A and B. We suspect that, when RBCs cannot pass through slits, the deformation rate of RBCs under compression is primarily limited by the deformation capacity of the cell membrane itself, rather than the magnitude of the applied force. Therefore, the decreases of cell membrane potential energy over time are not significantly affected by variations in flow rate.

In summary, the dynamic processes of RBCs, including entries into slits, significant deformations, membrane ruptures, and lysis, exhibit distinct changes in potential energy. The variations in lipid and bond potential energies during the cell’s passage through the slits serve as crucial indicators for analyzing cellular dynamic states.

To differentiate the effects of the slit and the fluid on the rupture of the cell membrane, we calculated the forces exerted by the slit particles and fluid particles on the cell membrane, as shown in Fig. 8. Fig. 8 shows the variation of the forces exerted by the water particles and slit particles on the cell membrane during RBCs passing through the slits. When the size of the slit (5 μm) remains constant and the flow rate increases from 25 to 150 nL/min, the peak of force exerted by the fluid on the cell membrane gradually increases, and the peak of force exerted by the slit on the cell membrane also gradually increases, as shown in Fig. 8, A and B. The resultant force exerted on the cell membrane reaches its maximum value at a flow rate of 150 nL/min, resulting in membrane rupture, as illustrated in Fig. 8 C. When the flow rate (25 nL/min) remains constant and the slit size decreases from 6 to 4 μm, cells can all pass through the slit. There is no significant change in the force exerted by the fluid on the cell membrane with decreases in slit size, but the peak of force exerted by the slit on the cell membrane increases, as shown in Fig. 8, D and E. The resultant force exerted on the cell membrane reaches its maximum value when the slit size is 4 μm, resulting in membrane rupture, as illustrated in Fig. 8 F. When the flow rate (25 nL/min) remains constant and the slit size decreases from 3 to 1 μm, RBCs fail to pass through the slit. For slit sizes of 1 and 2 μm, the slits are too small for RBCs to enter, resulting in a water layer between the cell membrane and the slit wall. The force exerted by the fluid on the cell membrane increases with decreasing slit size, while the force exerted by the slit on the cell membrane is minimal, as shown in Fig. 8, G and H. However, when the slit size is 3 μm, RBCs partially enter the slit but cannot pass through it. Therefore, the forces exerted by both the fluid and the slit on the cell membrane are relatively large. The resultant force exerted on the cell membrane reaches its maximum value when the slit size is 3 μm, resulting in membrane rupture, as shown in Fig. 8 I. Fig. 8 J summarizes three distinct hemolysis models: 1) in large-size slits, fluid forces contribute more to hemolysis than slit wall forces, 2) in middle-size slits, slit wall forces contribute more to hemolysis than fluid forces, and 3) RBCs are unable to traverse small size slits, where fluid forces play a dominant role in hemolysis. Fig. 8 K illustrates that the maximum value of the force exerted on the RBC membrane serves as a critical determinant of membrane rupture, with the red dashed line in the figure representing the threshold force (0.0032 $ϵ/\sigma$) that leads to membrane rupture.

Figure 8.

The variation of the forces exerted by the water particles and slit particles on cell membrane during RBCs passing through the slits. (A) The variation of the forces exerted by water particles on cell membrane during the passage through the 5 × 5 μm slit at different flow rates. (B) The variation of the forces exerted by slits on the cell membrane during the passage through the 5 × 5 μm slit at different flow rates. (C) The variation of the forces exerted on cell membrane during the passage through the 5 × 5 μm slit at different flow rates. (D) The variation of the forces exerted by water particles on cell membrane during the passage through the different slits (4–6 μm) at a flow rate of 25 nL/min. (E) The variation of the forces exerted by slits on cell membrane during the passage through the different slits (4–6 μm) at a flow rate of 25 nL/min. (F) The variation of the forces exerted on cell membrane during the passage through the different slits (4–6 μm) at a flow rate of 25 nL/min. (G) The variation of the forces exerted by water particles on cell membrane during the retention of RBCs intercepted by the different slits (1–3 μm) at a flow rate of 25 nL/min. (H) The variation of the forces exerted by slits on cell membrane during the retention of RBCs intercepted by the different slits (1–3 μm) at a flow rate of 25 nL/min. (I) The variation of the forces exerted on cell membrane during the retention of RBCs intercepted by the different slits (1–3 μm) at a flow rate of 25 nL/min. (J) In different sizes of slit, RBCs exhibit three distinct hemolysis models: 1) in large-size slits, fluid forces contribute more to hemolysis than slit wall forces; 2) in middle-size slits, slit wall forces contribute more to hemolysis than fluid forces; 3) RBCs are unable to traverse small-size slits, where fluid forces play a dominant role in hemolysis. (K) The maximum value of force exerted on RBC membrane serves as a critical determinant of membrane rupture. The red dashed line in the figure represents the threshold force that leads to membrane rupture.

In summary, we find that the forces exerted on the cell membrane by both fluid and slits directly determine whether the cell membrane will rupture and lead to RBC hemolysis. Previous researches have shown that reducing fluid stresses (81,82,83,84) and decreasing wall stiffness (85,86,87) can prevent hemolysis. This indirectly confirms that reducing the forces exerted by both fluid and solid walls on the cell membrane can prevent membrane rupture and subsequent hemolysis. However, traditional hemolysis models primarily consider the effect of fluid shear rate on hemolysis while overlooking the direct impact of solid forces on the cell membrane. With the CGMD hemolysis model, we can integrate fluid and solid forces into the forces exerted on the cell membrane to analyze membrane rupture and identify susceptible rupture locations of the membrane. Therefore, this model offers greater accuracy and applicability for analyzing hemolysis of RBCs passing through confined spaces at the cell scale or in frequent contact with solid wall surfaces.

Discussion

The specificity of hemolysis caused by passing through slits

Although the fact that both the shear stress thresholds predicted by traditional hemolysis models and those measured in experiments are significantly higher than the shear stress values in the slits of MHVs, hemolysis and subhemolysis still occur. The reason for this is that, in addition to being damaged by high shear stress, RBCs also directly contact with the walls of slits and are subjected to extra compression when entering confined spaces. Based on our analysis of the forces exerting on RBCs, we found that the force exerted by the walls plays a significant role in contributing to hemolysis. However, the direct impact of solid wall forces on the cell membrane has been largely overlooked in traditional hemolysis mechanism analyses and models. With the CGMD hemolysis model, we can integrate fluid and solid forces into the forces exerted on the cell membrane to analyze membrane rupture and identify susceptible rupture locations of the membrane. When RBCs enter the slits smaller than their size, they need to deform themselves to fit the slit width. During the deformation process, the walls exert a tensile force on the RBCs along the flow direction (x direction in Fig. 4, D–F) and a compressive force perpendicular to the wall (y direction in Fig. 4, D–F). If the flow rate is too high, the cells cannot deform quickly enough, and the slit walls exert a tensile force along the flow direction, stretching the cell membrane. When this stretching exceeds the membrane’s threshold, the cell membrane ruptures and membrane fragments may detach from the cell, as shown in Fig. 4, E and F. As the flow rate continues to increase, the forces exerted by the slit walls on the RBCs increase, leading to compressive forces causing the central part of the cell to rupture. We summarize three distinct hemolysis models: 1) in large-size slits, fluid forces contribute more to hemolysis than slit wall forces, 2) in middle-size slits, slit wall forces contribute more to hemolysis than fluid forces, and 3) RBCs are unable to traverse small size slits, where fluid forces play a dominant role in hemolysis. Furthermore, the model identified a range of slit sizes within which wall forces significantly impact on hemolysis of RBCs. Therefore, this model offers greater accuracy and applicability for analyzing hemolysis of RBCs passing through confined spaces at the cell scale or in frequent contact with solid wall surfaces.

Model of a mechanically fatigued RBC passing through slits

The advantage of the CGMD RBC model lies in its ability to simulate the details of the cell membrane’s lipid layer and cytoskeleton, including the dimensions of the cytoskeleton, the strength of connections within the cytoskeleton, and the strength of connections between the membrane and the cytoskeleton. Mechanical periodic squeezes with low stress but high frequency accelerate the aging of RBCs, leading to mechanical fatigue (78). Senescent RBCs exhibit typical features such as decreased intracellular volume, disruption of membrane-cytoskeleton connections, detachment of connections between cytoskeletal components, and reduced distance of interprotein in the spectrin network of cytoskeleton (56,62,88). The structural changes in the cell membrane lead to RBC transition to a more spherical shape, an increase in the effective bending modulus and membrane stiffness, and less deformable phenotype (88). These features can be simulated using the CGMD model to develop a model of mechanically fatigued, senescent RBCs.

Establishment of a mechanically fatigued RBC model by adjusting the distance between the nodes of the spectrin network and the connectivity between bond-3 and ankyrin in the initial configuration. We analyzed the influence of distance of spectrin network nodes, connectivity between bond-3 and ankyrin, and volume of the cell on the stable morphology of fatigued RBCs, as shown in Fig. S6 A. As the distance between the nodes of spectrin network (d0_network) decreased from 8.5 to 7.5, the stiffness of the cell skeleton increased, leading to a decrease in the deformability of fatigued RBCs, transitioning from concave discoidal shape to a nearly spherical shape. As the connectivity (rate_bond3) between bond-3 and ankyrin decreased from 100 to 0%, the constraint capability of the cell skeleton on the lipid membrane decreased, resulting in an increase in the deformability of fatigued RBCs. With the cell volume parameter (v_scale) decreasing from 2.55 to 2.20, the internal volume of the cell decreased, yet the stable morphology of fatigued cells still tended toward a spherical shape. This observation is consistent with the spherical shape of mechanically fatigued RBCs (spherocytes) observed in experiments (78).

We selected the fatigued RBC with d0_network = 7.5, rate_bond3 = 0, and v_scale = 2.55 as the representative case to simulate the process of fatigued RBCs traversing through slits and compared it with normal RBCs. The dynamic states of mechanically fatigued RBCs during passage through slits of different sizes under various shear rate conditions are summarized in Fig. S6 B. The main difference is evident when the slit size is relatively large (5–6 μm). Due to the spherical shape and smaller volume of the fatigued RBCs, they can pass through the slit more easily. We speculate that this is due to the increased stiffness of the membrane of fatigued RBCs, resulting in reduced deformability. In addition, the decreased volume of fatigued RBCs may result in reduced compression by the slit walls. Furthermore, the increased stiffness of the membrane, on the contrary, would make it more difficult for cells to pass through smaller slits (3 μm).

Conclusion

In this work, we investigated the hemolysis mechanism of RBCs in cell-size slits under high shear rates by establishing in vitro microfluidic devices and a CGMD model of RBCs and slits and considering both fluid effects and structural effects simultaneously. We simulated the complete process of an RBC traversing a microscale slit of MHVs by microfluidic experiments and computational simulation, revealing six distinct dynamic states in the traversal process under different shear rates and slit sizes. The forces exerted by the fluid and the slit walls on the RBC membrane were calculated. This elucidated that the dynamic states of RBC traversal through the slit were influenced not only by fluid forces but also significantly by the compressive force exerted by the slit walls. The variation of the potential energy of the cell membrane reflected the stretching, deformation, and rupture of the membrane during traversing the slits, corresponding to six different dynamic states. The maximum value of the forces exerted on the RBC membrane by water particles and the slit walls directly determined whether the cell membrane ruptured and served as a critical determinant of membrane rupture. We also established a mechanically fatigued RBC model by adjusting the distance between the nodes of spectrin network and the bond-3 and ankyrin connectivity in initial configuration. The fatigued RBCs were found to pass through the slit more easily due to their spherical shape and smaller volume. This analysis helps in understanding the contribution of the slit walls to membrane rupture and identifying the threshold force that leads to membrane rupture. The hemolysis mechanism of traversing microscale slits is revealed to effectively explain the occurrences of hemolysis and subclinical hemolysis.

Acknowledgments

This work is supported by the National Natural Science Foundation of China (nos. 52025051, 82170516, and 51875304), the Beijing Municipal Natural Science Foundation (no. 3242004), and the National Key R&D Program of China (no. 2018YFE0114900).

Author contributions

K.M. conceived the model and performed the computational simulation. K.M. and Y.P. performed the experiments. Y.L. and H.C. conceived and designed the study. K.M., Y.L., and H.C. wrote the paper.

Declaration of interests

The authors declare that they have no known competing interests or personal relationships that could have appeared to influence the work reported in this paper.

Editor: Dimitrios Vavylonis.