Numerical simulation of a single cell passing through a narrow slit

Transient flow-induced deformation of cancer cells in microchannels: a general computational model and experiments

Recently, the present authors proposed a three-dimensional computational model for the transit of suspended cancer cells through a microchannel (Wang et al. in Biomech Model Mechanobiol 22: 1129-1143, 2023). The cell model takes into account the three major subcellular components: A viscoelastic membrane that represents the lipid bilayer supported by the underlying cell cortex, a viscous cytoplasm, and a nucleus modelled as a smaller microcapsule. The cell deformation and its interaction with the surrounding fluid were solved by an immersed boundary-lattice Boltzmann method. The computational model accurately recovered the transient flow-induced deformation of the human leukaemia HL-60 cells in a constricted channel. However, as a general modelling framework, its applicability to other cell types in different flow geometries remains unknown, due to the lack of quantitative experimental data. In this study, we conduct experiments of the transit of human prostate cancer (PC-3) and leukaemia (K-562) cells, which represent solid and liquid tumour cell lines, respectively, through two distinct microchannel geometries, each dominated by shear and extension flow. We find that the two cell lines have qualitatively similar flow-induced dynamics. Comparisons between experiments and numerical simulations suggest that our model can accurately predict the transient cell deformation in both geometries, and that it can serve as a general modelling framework for the dynamics of suspended cancer cells in microchannels.

Experimental measurement and numerical modeling of deformation behavior of breast cancer cells passing through constricted microfluidic channels

During the multistep process of metastasis, cancer cells encounter various mechanical forces which make them deform drastically. Developing accurate in-silico models, capable of simulating the interactions between the mechanical forces and highly deformable cancer cells, can pave the way for the development of novel diagnostic and predictive methods for metastatic progression. Spring-network models of cancer cell, empowered by our recently proposed identification approach, promises a versatile numerical tool for developing experimentally validated models that can simulate complex interactions at cellular scale. Using this numerical tool, we presented spring-network models of breast cancer cells that can accurately replicate the experimental data of deformation behavior of the cells flowing in a fluidic domain and passing narrow constrictions comparable to microcapillary. First, using high-speed imaging, we experimentally studied the deformability of breast cancer cell lines with varying metastatic potential (MCF-7 (less invasive), SKBR-3 (medium-high invasive), and MDA-MB-231 (highly invasive)) in terms of their entry time to a constricted microfluidic channel. We observed that MDA-MB-231, that has the highest metastatic potential, is the most deformable cell among the three. Then, by focusing on this cell line, experimental measurements were expanded to two more constricted microchannel dimensions. The experimental deformability data in three constricted microchannel sizes for various cell sizes, enabled accurate identification of the unknown parameters of the spring-network model of the breast cancer cell line (MDA-MB-231). Our results show that the identified parameters depend on the cell size, suggesting the need for a systematic procedure for identifying the size-dependent parameters of spring-network models of cells. As the numerical results show, the presented cell models can simulate the entry process of the cell into constricted channels with very good agreements with the measured experimental data.

A computational model for the transit of a cancer cell through a constricted microchannel

We propose a three-dimensional computational model to simulate the transient deformation of suspended cancer cells flowing through a constricted microchannel. We model the cell as a liquid droplet enclosed by a viscoelastic membrane, and its nucleus as a smaller stiffer capsule. The cell deformation and its interaction with the suspending fluid are solved through a well-tested immersed boundary lattice Boltzmann method. To identify a minimal mechanical model that can quantitatively predict the transient cell deformation in a constricted channel, we conduct extensive parametric studies of the effects of the rheology of the cell membrane, cytoplasm and nucleus and compare the results with a recent experiment conducted on human leukaemia cells. We find that excellent agreement with the experiment can be achieved by employing a viscoelastic cell membrane model with the membrane viscosity depending on its mode of deformation (shear versus elongation). The cell nucleus limits the overall deformation of the whole cell, and its effect increases with the nucleus size. The present computational model may be used to guide the design of microfluidic devices to sort cancer cells, or to inversely infer cell mechanical properties from their flow-induced deformation.

Simulation of a tumor cell flowing through a symmetric bifurcated microvessel

Microvessel bifurcations serve as the major sites of tumor cell adhesion and further extravasation. In this study, the movement, deformation, and adhesion of a circulating tumor cell flowing in a symmetric microvessel with diverging and converging bifurcations were simulated by dissipative particle dynamics combined with a spring-based network model. Effects of the initial position of the CTC, externally-applied acceleration and the presence of RBCs on the motion of the CTC were investigated. The results demonstrated that the CTC released at the centerline of the parent vessel would attach to the vessel wall when arriving at the apex of diverging bifurcation and slide into the daughter branch determined by its centroid deflection and finally form firm adhesion at relatively lower flow rates. As the external acceleration increases, the increasing shear force enlarges the contact area for the adherent CTC on the one hand and reduces the residence time on the other hand. With the presence of RBCs in the bloodstream, the collision between the adherent tumor cell at the diverging bifurcation and flowing RBCs promotes the firm adhesion of CTC at lower flow rates.

A systematic approach for developing mechanistic models for realistic simulation of cancer cell motion and deformation

Understanding and predicting metastatic progression and developing novel diagnostic methods can highly benefit from accurate models of the deformability of cancer cells. Spring-based network models of cells can provide a versatile way of integrating deforming cancer cells with other physical and biochemical phenomena, but these models have parameters that need to be accurately identified. In this study we established a systematic method for identifying parameters of spring-network models of cancer cells. We developed a genetic algorithm and coupled it to the fluid-solid interaction model of the cell, immersed in blood plasma or other fluids, to minimize the difference between numerical and experimental data of cell motion and deformation. We used the method to create a validated model for the human lung cancer cell line (H1975), employing existing experimental data of its deformation in a narrow microchannel constriction considering cell-wall friction. Furthermore, using this validated model with accurately identified parameters, we studied the details of motion and deformation of the cancer cell in the microchannel constriction and the effects of flow rates on them. We found that ignoring the viscosity of the cell membrane and the friction between the cell and wall can introduce remarkable errors.

A data-driven approach to modeling cancer cell mechanics during microcirculatory transport

In order to understand the effect of cellular level features on the transport of circulating cancer cells in the microcirculation, there has been an increasing reliance on high-resolution in silico models. Accurate simulation of cancer cells flowing with blood cells requires resolving cellular-scale interactions in 3D, which is a significant computational undertaking warranting a cancer cell model that is both computationally efficient yet sufficiently complex to capture relevant behavior. Given that the characteristics of metastatic spread are known to depend on cancer type, it is crucial to account for mechanistic behavior representative of a specific cancer's cells. To address this gap, in the present work we develop and validate a means by which an efficient and popular membrane model-based approach can be used to simulate deformable cancer cells and reproduce experimental data from specific cell lines. Here, cells are modeled using the immersed boundary method (IBM) within a lattice Boltzmann method (LBM) fluid solver, and the finite element method (FEM) is used to model cell membrane resistance to deformation. Through detailed comparisons with experiments, we (i) validate this model to represent cancer cells undergoing large deformation, (ii) outline a systematic approach to parameterize different cell lines to optimally fit experimental data over a range of deformations, and (iii) provide new insight into nucleated vs. non-nucleated cell models and their ability to match experiments. While many works have used the membrane-model based method employed here to model generic cancer cells, no quantitative comparisons with experiments exist in the literature for specific cell lines undergoing large deformation. Here, we describe a phenomenological, data-driven approach that can not only yield good agreement for large deformations, but explicitly detail how it can be used to represent different cancer cell lines. This model is readily incorporated into cell-resolved hemodynamic transport simulations, and thus offers significant potential to complement experiments towards providing new insights into various aspects of cancer progression.

Computational models of cancer cell transport through the microcirculation

The transport of cancerous cells through the microcirculation during metastatic spread encompasses several interdependent steps that are not fully understood. Computational models which resolve the cellular-scale dynamics of complex microcirculatory flows offer considerable potential to yield needed insights into the spread of cancer as a result of the level of detail that can be captured. In recent years, in silico methods have been developed that can accurately and efficiently model the circulatory flows of cancer and other biological cells. These computational methods are capable of resolving detailed fluid flow fields which transport cells through tortuous physiological geometries, as well as the deformation and interactions between cells, cell-to-endothelium interactions, and tumor cell aggregates, all of which play important roles in metastatic spread. Such models can provide a powerful complement to experimental works, and a promising approach to recapitulating the endogenous setting while maintaining control over parameters such as shear rate, cell deformability, and the strength of adhesive binding to better understand tumor cell transport. In this review, we present an overview of computational models that have been developed for modeling cancer cells in the microcirculation, including insights they have provided into cell transport phenomena.

Margination and adhesion dynamics of tumor cells in a real microvascular network

In tumor metastasis, the margination and adhesion of tumor cells are two critical and closely related steps, which may determine the destination where the tumor cells extravasate to. We performed a direct three-dimensional simulation on the behaviors of the tumor cells in a real microvascular network, by a hybrid method of the smoothed dissipative particle dynamics and immersed boundary method (SDPD-IBM). The tumor cells are found to adhere at the microvascular bifurcations more frequently, and there is a positive correlation between the adhesion of the tumor cells and the wall-directed force from the surrounding red blood cells (RBCs). The larger the wall-directed force is, the closer the tumor cells are marginated towards the wall, and the higher the probability of adhesion behavior happen is. A relatively low or high hematocrit can help to prevent the adhesion of tumor cells, and similarly, increasing the shear rate of blood flow can serve the same purpose. These results suggest that the tumor cells may be more likely to extravasate at the microvascular bifurcations if the blood flow is slow and the hematocrit is moderate.

Numerical study on the adhesion of a circulating tumor cell in a curved microvessel

The adhesion of a circulating tumor cell (CTC) in a three-dimensional curved microvessel was numerically investigated. Simulations were first performed to characterize the differences in the dynamics and adhesion of a CTC in the straight and curved vessels. After that, a parametric study was performed to investigate the effects of the applied driven force density f (or the flow Reynolds number Re) and the CTC membrane bending modulus K_b on the CTC adhesion. Our simulation results show that the CTC prefers to adhere to the curved vessel as more bonds are formed around the transition region of the curved part due to the increased cell-wall contact by the centrifugal force. The parametric study also indicates that when the flow driven force f (or Re) increases or when the CTC becomes softer (K_b decreases), the bond formation probability increases and the bonds will be formed at more sites of a curved vessel. The increased f (or Re) brings a larger centrifugal force, while the decreased K_b generates more contact areas at the cell-wall interface, both of which are beneficial to the bond formation. In the curved vessel, it is found that the site where bonds are formed the most (hotspot) varies with the applied f and the K_b. For our vessel geometry, when f is small, the hotspot tends to be within the first bend of the vessel, while as f increases or K_b decreases, the hotspot may shift to the second bend of the vessel.

Improving viability of leukemia cells by tailoring shell fluid rheology in constricted microcapillary

Encapsulated cell therapy has shown great potential in the treatment of several forms of cancer. Microencapsulation of these cancer cells can protect the core from the harmful effects of the neighboring cellular environment and can supply nutrients and oxygen. Such an encapsulation technique ensures cell viability and enables targeted drug delivery in cancer therapy. The cells immobilized with a biocompatible shell material can be isolated from the ambient and can move in constricted microcapillary. However, transportation of these cells through the narrow microcapillary may squeeze and mechanically damage the cells which threaten the cell viability. The cell type, conditions and the viscoelastic properties of the shell can dictate cell viability. A front-tracking numerical simulation shows that the engineered shell material with higher viscoelasticity improves the cell viability. It is also shown that low cortical tension of cells can contribute to lower cell viability.

Dissipative particle dynamics for modeling micro-objects in microfluidics: application to dielectrophoresis

The dissipative particle dynamics (DPD) technique is employed to model the trajectories of micro-objects in a practical microfluidic device. The simulation approach is first developed using an in-house Fortran code to model Stokes flow at Reynolds number of 0.01. The extremely low Reynolds number is achieved by adjusting the DPD parameters, such as force coefficients, thermal energies of the particles, and time steps. After matching the numerical flow profile with the analytical results, the technique is developed further to simulate the deflection of micro-objects under the effect of a deflecting external force in a rectangular microchannel. A mapping algorithm is introduced to establish the scaling relationship for the deflecting force between the physical device and the DPD domain. Dielectrophoresis is studied as a case study for the deflecting force, and the trajectory of a single red blood cell under the influence of the dielectrophoretic force is simulated. The device is fabricated using standard microfabrication techniques, and the experiments involving a dilute sample of red blood cells are performed at two different cases of the actuation voltage. Good agreement between the numerical and experimental results is achieved.

Effects of red blood cell aggregation on the blood flow in a symmetrical stenosed microvessel

In order to figure out whether red blood cell (RBC) aggregation is beneficial or deleterious for the blood flow through a stenosis, fluid mechanics of a microvascular stenosis was examined through simulating the dynamics of deformable red blood cells suspended in plasma using dissipative particle dynamics. The spatial variation in time-averaged cell-free layer (CFL) thickness and velocity profiles indicated that the blood flow exhibits asymmetry along the flow direction. The RBC accumulation occurs upstream the stenosis, leading to a thinner CFL and reduced flow velocity. Therefore, the emergence of stenosis produces an increased blood flow resistance. In addition, an enhanced Fahraeus-Lindqvist effect was observed in the presence of the stenosis. Finally, the effect of RBC aggregation combined with decreased stenosis on the blood flow was investigated. The findings showed that when the RBC clusters pass through the stenosis with a throat comparable to the RBC core in diameter, the blood flow resistance decreases with increasing intercellular interaction strength. But if the RBC core is larger and even several times than the throat, the blood flow resistance increases largely under strong RBC aggregation, which may contribute to the mechanism of the microthrombus formation.

Megakaryocyte volume modulates bone marrow niche properties and cell migration dynamics

All hematopoietic cells that develop in the bone marrow must cross the endothelial barrier to enter the blood circulation. Blood platelets, however, are released by bigger protrusions of huge progenitor cells, named megakaryocytes, and enter the blood stream as so-called proplatelets before fragmenting into mature platelets. Recently, a second function of megakaryocytes has been identified, as they modulate the quiescence of hematopoietic stem cells, mostly via different soluble factors. We know from light sheet fluorescence microscopy images that megakaryocytes are distributed throughout the bone marrow facing a dense vascular network. Here, we used such three-dimensional images to provide a realistic simulation template reflecting the in vivo cell-vessel distributions resulting in reliable whole-bone analysis in silico Combining this approach with an automated image analysis pipeline, we found that megakaryocytes influence migration of neutrophils and hematopoietic stem cells, and thus act as biomechanical restrainers modulating cell mobility and extravasation. Indeed, as a consequence of increased megakaryocyte volumes in platelet-depleted mice neutrophil mobility was reduced in these animals.

Quantifying Shear-Induced Deformation and Detachment of Individual Adherent Sickle Red Blood Cells

Vaso-occlusive crisis, a common painful complication of sickle cell disease, is a complex process triggered by intercellular adhesive interactions among blood cells and the endothelium in all human organs (e.g., the oxygen-rich lung as well as hypoxic systems such as liver and kidneys). We present a combined experimental-computational study to quantify the adhesive characteristics of sickle mature erythrocytes (SMEs) and irreversibly sickled cells (ISCs) under flow conditions mimicking those in postcapillary venules. We employed an in vitro microfluidic cell adherence assay, which is coated uniformly with fibronectin. We investigated the adhesion dynamics of SMEs and ISCs in pulsatile flow under well-controlled hypoxic conditions, inferring the cell adhesion strength by increasing the flow rate (or wall shear stress (WSS)) until the onset of cell detachment. In parallel, we performed simulations of individual SMEs and ISCs under shear. We introduced two metrics to quantify the adhesion process, the cell aspect ratio (AR) as a function of WSS and its rate of change (the dynamic deformability index). We found that the AR of SMEs decreases significantly with the increase of WSS, consistent between the experiments and simulations. In contrast, the AR of ISCs remains constant in time and independent of the flow rate. The critical WSS value for detaching a single SME in oxygenated state is in the range of 3.9-5.5 Pa depending on the number of adhesion sites; the critical WSS value for ISCs is lower than that of SMEs. Our simulations show that the critical WSS value for SMEs in deoxygenated state is above 6.2 Pa (multiple adhesion sites), which is greater than their oxygenated counterparts. We investigated the effect of cell shear modulus on the detachment process; we found that for the same cell adhesion spring constant, the higher shear modulus leads to an earlier cell detachment from the functionalized surface. These findings may aid in the understanding of individual roles of sickle cell types in sickle cell disease vaso-occlusion.

Modeling Cell Adhesion and Extravasation in Microvascular System

The blood flow behaviors in the microvessels determine the transport modes and further affect the metastasis of circulating tumor cells (CTCs). Much biochemical and biological efforts have been made on CTC metastasis; however, precise experimental measurement and accurate theoretical prediction on its mechanical mechanism are limited. To complement these, numerical modeling of a CTC extravasation from the blood circulation, including the steps of adhesion and transmigration, is discussed in this chapter. The results demonstrate that CTCs prefer to adhere at the positive curvature of curved microvessels, which is attributed to the positive wall shear stress/gradient. Then, the effects of particulate nature of blood on CTC adhesion are investigated and are found to be significant in the microvessels. Furthermore, the presence of red blood cell (RBC) aggregates is also found to promote the CTC adhesion by providing an additional wall-directed force. Finally, a single cell passing through a narrow slit, mimicking CTC transmigration, was examined under the effects of cell deformability. It showed that the cell shape and surface area increase play a more important role than the cell elasticity in cell transit across the narrow slit.

Modeling of Biomechanics and Biorheology of Red Blood Cells in Type 2 Diabetes Mellitus

Erythrocytes in patients with type-2 diabetes mellitus (T2DM) are associated with reduced cell deformability and elevated blood viscosity, which contribute to impaired blood flow and other pathophysiological aspects of diabetes-related vascular complications. In this study, by using a two-component red blood cell (RBC) model and systematic parameter variation, we perform detailed computational simulations to probe the alteration of the biomechanical, rheological, and dynamic behavior of T2DM RBCs in response to morphological change and membrane stiffening. First, we examine the elastic response of T2DM RBCs subject to static tensile forcing and their viscoelastic relaxation response upon release of the stretching force. Second, we investigate the membrane fluctuations of T2DM RBCs and explore the effect of cell shape on the fluctuation amplitudes. Third, we subject the T2DM RBCs to shear flow and probe the effects of cell shape and effective membrane viscosity on their tank-treading movement. In addition, we model the cell dynamic behavior in a microfluidic channel with constriction and quantify the biorheological properties of individual T2DM RBCs. Finally, we simulate T2DM RBC suspensions under shear and compare the predicted viscosity with experimental measurements. Taken together, these simulation results and their comparison with currently available experimental data are helpful in identifying a specific parametric model-the first of its kind, to our knowledge-that best describes the main hallmarks of T2DM RBCs, which can be used in future simulation studies of hematologic complications of T2DM patients.

Numerical simulation of a compound capsule in a constricted microchannel

Simulations of the passage of eukaryotic cells through a constricted channel aid in studying the properties of cancer cells and their transport in the bloodstream. Compound capsules, which explicitly model the outer cell membrane and nuclear lamina, have the potential to improve computational model fidelity. However, general simulations of compound capsules transiting a constricted microchannel have not been conducted and the influence of the compound capsule model on computational performance is not well known. In this study, we extend a parallel hemodynamics application to simulate the fluid-structure interaction between compound capsules and fluid. With this framework, we compare the deformation of simple and compound capsules in constricted microchannels, and explore how deformation depends on the capillary number and on the volume fraction of the inner membrane. The computational framework's parallel performance in this setting is evaluated and future development lessons are discussed.

Effects of stiffness and volume on the transit time of an erythrocyte through a slit

By using a fully coupled fluid-cell interaction model, we numerically simulate the dynamic process of a red blood cell passing through a slit driven by an incoming flow. The model is achieved by combining a multiscale model of the composite cell membrane with a boundary element fluid dynamics model based on the Stokes flow assumption. Our concentration is on the correlation between the transit time (the time it takes to finish the whole translocation process) and different conditions (flow speed, cell orientation, cell stiffness, cell volume, etc.) that are involved. According to the numerical prediction (with some exceptions), the transit time rises as the cell is stiffened. It is also highly sensitive to volume increase inside the cell. In general, even slightly swollen cells (i.e., the internal volume is increased while the surface area of the cell kept unchanged) travel dramatically slower through the slit. For these cells, there is also an increased chance of blockage.

Effects of flowing RBCs on adhesion of a circulating tumor cell in microvessels

Adhesion of circulating tumor cells (CTCs) to the microvessel wall largely depends on the blood hydrodynamic conditions, one of which is the blood viscosity. Since blood is a non-Newtonian fluid, whose viscosity increases with hematocrit, in the microvessels at low shear rate. In this study, the effects of hematocrit, vessel size, flow rate and red blood cell (RBC) aggregation on adhesion of a CTC in the microvessels were numerically investigated using dissipative particle dynamics. The membrane of cells was represented by a spring-based network connected by elastic springs to characterize its deformation. RBC aggregation was modeled by a Morse potential function based on depletion-mediated assumption, and the adhesion of the CTC to the vessel wall was achieved by the interactions between receptors and ligands at the CTC and those at the endothelial cells forming the vessel wall. The results demonstrated that in the microvessel of [Formula: see text] diameter, the CTC has an increasing probability of adhesion with the hematocrit due to a growing wall-directed force, resulting in a larger number of receptor-ligand bonds formed on the cell surface. However, with the increase in microvessel size, an enhanced lift force at higher hematocrit detaches the initial adherent CTC quickly. If the microvessel is comparable to the CTC in diameter, CTC adhesion is independent of Hct. In addition, the velocity of CTC is larger than the average blood flow velocity in smaller microvessels and the relative velocity of CTC decreases with the increase in microvessel size. An increased blood flow resistance in the presence of CTC was also found. Moreover, it was found that the large deformation induced by high flow rate and the presence of aggregation promote the adhesion of CTC.