Non-uniform plasma leakage affects local hematocrit and blood flow: implications for inflammation and tumor perfusion - PubMed (original) (raw)

Non-uniform plasma leakage affects local hematocrit and blood flow: implications for inflammation and tumor perfusion

Chenghai Sun et al. Ann Biomed Eng. 2007 Dec.

Abstract

Vessel leakiness is a hallmark of inflammation and cancer. In inflammation, plasma extravasation and leukocyte adhesion occur in a coordinated manner to enable the immune response, but also to maintain tissue perfusion. In tumors, similar mechanisms operate, but they are not well regulated. Therefore, blood perfusion in tumors is non-uniform, and delivery of blood-borne therapeutics is difficult. In order to analyze the interplay among plasma leakage, blood viscosity, and vessel geometry, we developed a mathematical model that explicitly includes blood cells, vessel branching, and focal leakage. The results show that local hemoconcentration due to plasma leakage can greatly increase the flow resistance in individual vascular segments, diverting flow to other regions. Similarly, leukocyte rolling can increase flow resistance by partially blocking flow. Vessel dilation can counter these effects, and likely occurs in inflammation to maintain blood flow. These results suggest that potential strategies for improving perfusion through tumor networks include (i) eliminating non-uniform plasma leakage, (ii) inhibiting leukocyte interactions, and (iii) preventing RBC aggregation in sluggish vessels. Normalization of tumor vessels by anti-angiogenic therapy may improve tumor perfusion via the first two mechanisms.

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Figures

FIGURE 1

FIGURE 1

Model geometry and parameters. At top is an illustration of how the blood suspension is modeled. Red blood cells are represented as 2D capsules and the white blood cells are 2D disks (yellow). The leukocyte interacts with the wall through stochastic receptor–ligand interactions (illustrated at bottom right) and a non-specific repulsive force (_F_C). The leukocyte can interact with the surface when it gets closer than _H_C. The forces and torques of individual bonds are summed to get the total ligand force (_F_L) and torque (_T_L); these are then combined with the hydrodynamic force (_F_H) and the torque (_T_H) to calculate the total force on the leukocyte. Fluid particle velocities of a 2D lattice Boltzmann model with nine velocities are illustrated at bottom left.

FIG. 2

FIG. 2

Representative snapshots of flow during the simulations. The columns represent (a) equal width, non-leaky daughter branches; (b) equal width branches, but the right-hand channel (RHC) leaks; (c) the RHC is 50% wider, and has the same leaks as case b. In each case, Subpanel I is the steady flow of plasma only (without any cells). Subpanel II shows the developed flow of RBCs for feeding hematocrit 0.35 at the inlet. Subpanel III shows the flow with both RBCs and WBCs included. Lattice size: 1000 × 150; one grid point is equal to 0.3 _μ_m. Total time of 0.9 s is normalized to 1, corresponding to 3 × 106 time-steps. The pressure coefficient (P = 2(p – _p_ex)/ρ _U_2, where _p_ex is pressure at the exit) field is represented by the color gradient and the velocity field is represented by small arrows.

FIGURE 3

FIGURE 3

Velocity evolution in each segment. For the simulations with cells, the initial condition is the flow-pressure distribution for plasma only (i.e., panel I from Fig. 2). Here we show the changes in velocity that occur as RBCs (top row) or RBCs and WBCs (bottom row) enter the system. Velocities have been averaged across the channel width, and the inlet hematocrit is 0.35. The geometries of Cases a, b, and c are illustrated to the right of corresponding velocity plots; the colored lines in these diagrams correspond to the locations of the velocities in the plots (i.e., blue is at the inlet, orange is at the entrance to the left-hand branch, etc.). In (b) and (c), the leaking velocity is depicted by the gray line. The initial steady-state velocity distribution is disturbed as cells fill the system; in (b) and (c), plasma leakage causes dramatic drifts in the velocity distributions.

FIGURE 4

FIGURE 4

Summary of hematocrit (Panel a), overall resistance (Panel b) relative to that of plasma flow in a non-leaky vessel (simulation a-I in Fig. 2), and resistance ratio of right branch to left branch (Panel c). Groups a, b, and c represent the Cases a, b, and c shown in Fig. 2. I, II, and III indicate the simulations I, II, and III in Fig. 2. L and R denote the left and right branch, respectively. The values for II and III are the temporal averages over dimensionless time interval from 2/3 to 1.

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