Coupled Flow-Structure-Biochemistry Simulations of Dynamic Systems of Blood Cells Using an Adaptive Surface Tracking Method

Computational analysis of adhesion between a cancer cell and a white blood cell in a bifurcated microvessel

BACKGROUND AND OBJECTIVE

Cancer is one of the diseases caused by irregular and uncontrolled growth of cells and their propagation into various parts of the body. The motion and adhesion of cancer cells in a blood vessel is a critical step in tumor progression that depends on some vascular parameters such as vessel branching. In this study, effect of microvessel branching on the bonds between a cancer cell and a white blood has been investigated as compared to an analogous problem in a straight vessel.

METHODS

The analysis is performed using finite elements and fluid-structure interaction methods. Moreover, the equations for adhesion of the cancer cell to white blood cell are coded in MATLAB for calculating forces between them and the code is coupled directly and simultaneously with the COMSOL software. For fluid-structure interaction analysis, it is assumed that the properties of the blood and the cells are homogeneous and the fluid is incompressible and Newtonian. Cancer cell is modeled as a rigid body and white blood cell is assumed as linear elastic.

RESULTS

The results show that although the geometry of the vessel does not affect on the separation distance of cancer cell considerably, but at the area near a bifurcation, high fluctuations in cancer cell velocity is occurred due to increasing in number of bond formation between the cancer cell and the white blood cell. Accordingly, it can be predicted that higher concentration of adhered particles occurs near the bifurcations. Moreover, shear stress at the point of contact of the cancer cell and the white blood cell in the branched vessel is greater than that in the straight path. In addition to, the probability of breaking of the bond between the cancer cell and the white blood cell increases in the branched vessel.

CONCLUSIONS

Through consideration in the adhesion charts of this study along with observations from medical interventions such as drug delivery to cancer patients, considerable developments on the treatment or prevention of cancer metastasis may be achieved.

The influence of adherent cell morphology on hydrodynamic recruitment of leukocytes

Innate immunity is characterized by the coordinated activity of multiple leukocytes mobilizing at or near the site of tissue injury. Slow rolling and/or adherent leukocytes have been shown to hydrodynamically recruit free-stream leukocytes to a model of inflamed tissue. In this paper, we numerically investigate the hydrodynamic recruitment of free-stream leukocytes due to the presence of a nearby adherent, deformed leukocyte by using a computational model developed from first principles to simulate these types of interactions. For free-stream cells at least one diameter above the surface and subsequently involved in a glancing (out-of-plane) collision with one or more adherent cell, the simulation indicated that the free-stream cell was driven closer to the surface as a function of increasing glancing distance. Further, with increasing deformation of the adherent cell a similar effect was observed beginning at smaller glancing offsets. The influence of binary interactions on the trajectories of free-stream cells that were less than one diameter above the surface was also examined. For fixed glancing distance, increased adherent cell deformation led to enhanced recruiting effectiveness which was quantified by determining the time needed for the free-stream cell to enter the reactive zone; that is, a membrane separation distance such that receptor-ligand binding was possible. This effectiveness was only moderately influenced by variations in shear rate and cell buoyancy. Finally, for large glancing offset the domain of influence of the adherent cell diminished and the trajectory of the free-stream cell was unaffected by the adherent cell, with regard to hydrodynamic recruitment.

Localized Modeling of Biochemical and Flow Interactions during Cancer Cell Adhesion

This work focuses on one component of a larger research effort to develop a simulation tool to model populations of flowing cells. Specifically, in this study a local model of the biochemical interactions between circulating melanoma tumor cells (TC) and substrate adherent polymorphonuclear neutrophils (PMN) is developed. This model provides realistic three-dimensional distributions of bond formation and attendant attraction and repulsion forces that are consistent with the time dependent Computational Fluid Dynamics (CFD) framework of the full system model which accounts local pressure, shear and repulsion forces. The resulting full dynamics model enables exploration of TC adhesion to adherent PMNs, which is a known participating mechanism in melanoma cell metastasis. The model defines the adhesion molecules present on the TC and PMN cell surfaces, and calculates their interactions as the melanoma cell flows past the PMN. Biochemical rates of reactions between individual molecules are determined based on their local properties. The melanoma cell in the model expresses ICAM-1 molecules on its surface, and the PMN expresses the β-2 integrins LFA-1 and Mac-1. In this work the PMN is fixed to the substrate and is assumed fully rigid and of a prescribed shear-rate dependent shape obtained from micro-PIV experiments. The melanoma cell is transported with full six-degrees-of-freedom dynamics. Adhesion models, which represent the ability of molecules to bond and adhere the cells to each other, and repulsion models, which represent the various physical mechanisms of cellular repulsion, are incorporated with the CFD solver. All models are general enough to allow for future extensions, including arbitrary adhesion molecule types, and the ability to redefine the values of parameters to represent various cell types. The model presented in this study will be part of a clinical tool for development of personalized medical treatment programs.

Multi-scale biological and physical modelling of the tumour micro-environment

Paced by advances in high performance computing, and algorithms for multi-physics and multi-scale simulation, a number of groups have recently established numerical models of flowing blood systems, where cell-scale interactions are explicitly resolved. To be biologically representative, these models account for some or all of: (1) fluid dynamics of the carrier flow, (2) structural dynamics of the cells and vessel walls, (3) interaction and transport biochemistry, and, (4) methods for scaling to physiologically representative numbers of cells. In this article, our interest is the modelling of the tumour micro-environment. We review the broader area of cell-scale resolving blood flow modelling, while focusing on the particular interactions of tumour cells and white blood cells, known to play an important role in metastasis.

Study of local hydrodynamic environment in cell-substrate adhesion using side-view μPIV technology

Tumor cell adhesion to the endothelium under shear flow conditions is a critical step that results in circulation-mediated tumor metastasis. This study presents experimental and computational techniques for studying the local hydrodynamic environment around adherent cells and how local shear conditions affect cell-cell interactions on the endothelium in tumor cell adhesion. To study the local hydrodynamic profile around heterotypic adherent cells, a side-view flow chamber assay coupled with micro particle imaging velocimetry (μPIV) technique was developed, where interactions between leukocytes and tumor cells in the near-endothelial wall region and the local shear flow environment were characterized. Computational fluid dynamics (CFD) simulations were also used to obtain quantitative flow properties around those adherent cells. Results showed that cell dimension and relative cell-cell positions had strong influence on local shear rates. The velocity profile above leukocytes and tumor cells displayed very different patterns. Larger cell deformations led to less disturbance to the flow. Local shear rates above smaller cells were observed to be more affected by relative positions between two cells.

Application of Population Dynamics to Study Heterotypic Cell Aggregations in the Near-Wall Region of a Shear Flow

Our research focused on the polymorphonuclear neutrophils (PMNs) tethering to the vascular endothelial cells (EC) and the subsequent melanoma cell emboli formation in a shear flow, an important process of tumor cell extravasation from the circulation during metastasis. We applied population balance model based on Smoluchowski coagulation equation to study the heterotypic aggregation between PMNs and melanoma cells in the near-wall region of an in vitro parallel-plate flow chamber, which simulates in vivo cell-substrate adhesion from the vasculatures by combining mathematical modeling and numerical simulations with experimental observations. To the best of our knowledge, a multiscale near-wall aggregation model was developed, for the first time, which incorporated the effects of both cell deformation and general ratios of heterotypic cells on the cell aggregation process. Quantitative agreement was found between numerical predictions and in vitro experiments. The effects of factors, including: intrinsic binding molecule properties, near-wall heterotypic cell concentrations, and cell deformations on the coagulation process, are discussed. Several parameter identification approaches are proposed and validated which, in turn, demonstrate the importance of the reaction coefficient and the critical bond number on the aggregation process.

Effects of the Tumor-Leukocyte Microenvironment on Melanoma-Neutrophil Adhesion to the Endothelium in a Shear Flow

The primary cause of cancer mortality is not attributed to primary tumor formation, but rather to the growth of metastases at distant organ sites. Tumor cell adhesion to blood vessel endothelium (EC) and subsequent transendothelial migration within the circulation are critical components of the metastasis cascade. Previous studies have shown polymorphonuclear neutrophils (PMNs) may facilitate melanoma cell adhesion to the EC and subsequent extravasation under flow conditions. The melanoma cell-PMN interactions are found to be mediated by the binding between intercellular adhesion molecule-1 (ICAM-1) on melanoma cells and β(2) integrin on PMNs and by endogenously secreted interleukin 8 (IL-8) within the tumor-leukocyte microenvironment. In this study, the effects of fluid convection on the IL-8-mediated activation of PMNs and the binding kinetics between PMNs and melanoma cells were investigated. Results indicate that the shear rate dependence of PMN-melanoma cell adhesion and melanoma cell extravasation is due, at least partly, to the convection of tumor-secreted proinflammatory cytokine IL-8.