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

Abstract

A method for the computation of low Reynolds number dynamic blood cell systems is presented. The specific system of interest here is interaction between cancer cells and white blood cells in an experimental flow system. Fluid dynamics, structural mechanics, six-degree-of freedom motion control and surface biochemistry analysis components are coupled in the context of adaptive octree-based grid generation. Analytical and numerical verification of the quasi-steady assumption for the fluid mechanics is presented. The capabilities of the technique are demonstrated by presenting several three-dimensional cell system simulations, including the collision/interaction between a cancer cell and an endothelium adherent polymorphonuclear leukocyte (PMN) cell in a shear flow.

Figure 1

Schematic representation of the three-component deformable PMN model.

Figure 2

Schematic representation of the software infrastructure.

Figure 3

Velocity profiles above a single cell under low (top) and high (bottom) shear rates from the solver validation test.

Figure 4

System of two-dimensional overset grids used for the quasi-steady assumption verification simulations. Solid line represents the path of the cancer cell in the simulations.

Figure 5

Comparison of the a) drag forces and b) lift forces acting on the cancer cell, calculated in transient and steady simulations.

Figure 5

Comparison of the a) drag forces and b) lift forces acting on the cancer cell, calculated in transient and steady simulations.

Figure 6

Example meshes of the cancer cell-white blood cell system. The large spherical particle is the cancer cell and the smaller deformed particle represents the white blood cell. A clip plane through the center of the three-dimensional mesh and the surface grids are shown.

Figure 7

a) Time history of cell separation distance for simulations in which bonds did and did not form. b) Time history of number of bonds in the simulation in which bonds formed.

Figure 7

a) Time history of cell separation distance for simulations in which bonds did and did not form. b) Time history of number of bonds in the simulation in which bonds formed.

Figure 8

CFD results for three time points during the biochemistry simulation a) 4.5 ms, b) 8 ms, c) 9.8 ms. The cell surfaces are contoured by pressure and the far-field symmetry plane is contoured by velocity magnitude. Flow direction is left to right.

Figure 9

Three time steps in the simulation of a collision between a rigid cancer cell and a deformable white blood cell showing the peeling motion of the white blood cell. The cells are contoured by pressure (in kg/μm-s²) and a center clip plane is contoured by velocity magnitude (in μm/s). Flow direction is left to right.

Figure 10

Time history of number of bonds formed between the white blood cell and cancer cell in the deformable PMN simulation.

Figure 11

Cancer cell a) horizontal velocity, b) vertical velocity, and c) rotational velocity when bonds did (adhesion) and did not (free motion) form between the cells.

Figure 11

Cancer cell a) horizontal velocity, b) vertical velocity, and c) rotational velocity when bonds did (adhesion) and did not (free motion) form between the cells.

Figure 11

Cancer cell a) horizontal velocity, b) vertical velocity, and c) rotational velocity when bonds did (adhesion) and did not (free motion) form between the cells.

Figure 12

Four time steps of the collision simulation in which bonds formed between the cancer cell and white blood cell. Time steps shown are: a) before bonds form, b) when the number of bonds is a maximum, c) immediately after the bonds break, and d) one millisecond later. The cells are contoured by pressure (in kg/μm-s²) and a center clip plane is contoured by velocity magnitude (in μm/s). Flow direction is left to right.