Effect of wall compliance and permeability on blood-flow rate in counter-current microvessels formed from anastomosis during tumor-induced angiogenesis

Abstract

Tumor blood-flow is inhomogeneous because of heterogeneity in tumor vasculature, vessel-wall leakiness, and compliance. Experimental studies have shown that normalization of tumor vasculature by antiangiogenic therapy can improve tumor microcirculation and enhance the delivery of therapeutic agents to tumors. To elucidate the quantitative relationship between the vessel-wall compliance and permeability and the blood-flow rate in the microvessels of the tumor tissue, the tumor tissue with the normalized vasculature, and the normal tissue, we developed a transport model to simultaneously predict the interstitial fluid pressure (IFP), interstitial fluid velocity (IFV) and the blood-flow rate in a counter-current microvessel loop, which occurs from anastomosis in tumor-induced angiogenesis during tumor growth. Our model predicts that although the vessel-wall leakiness greatly affects the IFP and IFV, it has a negligible effect on the intravascular driving force (pressure gradient) for both rigid and compliant vessels, and thus a negligible effect on the blood-flow rate if the vessel wall is rigid. In contrast, the wall compliance contributes moderately to the IFP and IFV, but significantly to the vessel radius and to the blood-flow rate. However, the combined effects of vessel leakiness and compliance can increase IFP, which leads to a partial collapse in the blood vessels and an increase in the flow resistance. Furthermore, our model predictions speculate a new approach for enhancing drug delivery to tumor by modulating the vessel-wall compliance in addition to reducing the vessel-wall leakiness and normalizing the vessel density.

Fig. 1

Simplified model geometry. (a) Schematic of counter-current microvessels (shaded regions) in anastomosis during tumor-induced angiogenesis. Three processes are plotted: sprouting from the parental vessels, sprout branching, and anastomosis. (b) Model geometry: enlarged shaded region in (a) comprises counter-current microvessels that are connected at X = L. The Krogh cylinder of radius R_t represents the tumor tissue surrounding the counter-current vessels. Blood flow is driven by the intravascular pressure at X = 0 in the entrance branch P _a0 and that in the exit branch P _v0. X = 0 represents the outer edge of the tumor tissue, which is the interface between the tumor and normal tissues. The drawing is not to scale.

Fig. 2

Effect of the vessel-wall compliance on the blood-flow rate in an impermeable vessel. The line is the analytical solution; symbols are the results from the numerical computation. For a rigid vessel, δ = ∞.

Fig. 3

Effect of the vessel-wall compliance on intravascular pressures. The intravascular pressure in the entrance branch P_a and that in the exit branch P_v in the microvessels of the tumor tissue (T), the tumor tissue with the normalized vessels (N.V.), and the normal tissue (N): (a) rigid vessels, and (b) compliant vessels. Axis x is the normalized position defined by X/L.

Fig. 4

Effect of the vessel-wall compliance on interstitial fluid pressure (IFP). IFP in the tumor tissue (T), in the tumor tissue with the normalized vessels (N.V.), and in the normal tissue (N): (a) rigid vessels, and (b) compliant vessels. Axis x is the normalized position defined by X/L.

Fig. 5

Effect of the vessel-wall compliance on interstitial fluid velocity (IFV). IFV in the tumor tissue (T), in the tumor tissue with the normalized vessels (N.V.), and in the normal tissue (N): (a) rigid vessels, and (b) compliant vessels. Axis x is the normalized position defined by X/L.

Fig. 6

Effect of the vessel-wall compliance on vessel radius. Vessel radius in the entrance branch R_a and that in the exit branch R_v in the microvessels of the tumor tissue (T), the tumor tissue with the normalized vessels (N.V.), and the normal tissue (N): (a) rigid vessels, and (b) compliant vessels. Axis x is the normalized position defined by X/L.

Fig. 7

Blood-flow rate in rigid and compliant vessels. Blood-flow rate in the entrance branch Q_a and that in the exit branch Q_v in the microvessels of the tumor tissue (T), the tumor tissue with the normalized vessels (N.V.), and the normal tissue (N): (a) rigid vessels, and (b) compliant vessels. Axis x is the normalized position defined by X/L.

Fig. 8

Effect of the vessel-wall compliance on the blood-flow rate. Blood-flow rate in the entrance branch Q_a and that in the exit branch Q_v in the microvessels of (a) the tumor tissue, (b) the tumor tissue with the normalized vessels, and (c) the normal tissue. Axis x is the normalized position defined by X/L.