Functional implications of microvascular heterogeneity for oxygen uptake and utilization

Abstract

In the vascular system, an extensive network structure provides convective and diffusive transport of oxygen to tissue. In the microcirculation, parameters describing network structure, blood flow, and oxygen transport are highly heterogeneous. This heterogeneity can strongly affect oxygen supply and organ function, including reduced oxygen uptake in the lung and decreased oxygen delivery to tissue. The causes of heterogeneity can be classified as extrinsic or intrinsic. Extrinsic heterogeneity refers to variations in oxygen demand in the systemic circulation or oxygen supply in the lungs. Intrinsic heterogeneity refers to structural heterogeneity due to stochastic growth of blood vessels and variability in flow pathways due to geometric constraints, and resulting variations in blood flow and hematocrit. Mechanisms have evolved to compensate for heterogeneity and thereby improve oxygen uptake in the lung and delivery to tissue. These mechanisms, which involve long-term structural adaptation and short-term flow regulation, depend on upstream responses conducted along vessel walls, and work to redistribute flow and maintain blood and tissue oxygenation. Mathematically, the variance of a functional quantity such as oxygen delivery that depends on two or more heterogeneous variables can be reduced if one of the underlying variables is controlled by an appropriate compensatory mechanism. Ineffective regulatory mechanisms can result in poor oxygen delivery even in the presence of adequate overall tissue perfusion. Restoration of endothelial function, and specifically conducted responses, should be considered when addressing tissue hypoxemia and organ failure in clinical settings.

Keywords: flow regulation; microvascular networks; oxygen transport; vascular remodeling.

FIGURE 1

Schematic diagrams illustrating how geometric constraints and basic characteristics of mass transport processes lead to intrinsic heterogeneity in the microcirculation. Arrows indicate directions of blood flow. Color variations indicate oxygen levels in the blood. Structures shown do not represent actual microvascular network geometries. (a) The short diffusion distance of oxygen dictates that microvessels must form a fine mesh throughout the tissue. (b) High flow resistance in capillary‐sized vessels dictates that they must be fed and drained by hierarchical trees of larger‐diameter arterioles and venules, to provide efficient convective transport over larger distances. Actual microvascular networks represent a combination of these two types of structures. (c) The ‘dimensional problem’ of vascular supply. Homogeneous capillary supply to a two‐dimensional tissue region (grey sheet) can be achieved if the feeding and draining vessels form symmetric branching structures in the third dimension. If, however, the region being supplied is three‐dimensional, feeding and draining vessels must lie within the region being supplied and so such a symmetric structure is not possible. (d) Feeding and draining vessels are often adjacent, which leads to heterogeneous path lengths

FIGURE 2

Diagram illustrating lognormal probability density functions corresponding to selected CV values as indicated, for variables with a mean of 1

FIGURE 3

Effect of heterogeneity in blood flow, as measured by CV, on extraction and oxygen consumption. For each level of tissue oxygen demand, the CV of the flow rates is varied, while holding the total flow fixed. Simulations were conducted for a simplified representation of a tissue supplied by multiple identical parallel capillaries with heterogeneous flow rates represented by a lognormal distribution with a given CV. Oxygen transport was simulated in each cylinder using a modified Krogh cylinder model (McGuire & Secomb, 2001), taking into account the axial decline of blood oxygen content along the cylinder and assuming Michaelis‐Menten kinetics for oxygen consumption rate as a function of oxygen tension. Parameters are as specified in McGuire and Secomb (McGuire & Secomb, 2001), with the exception of a half‐maximal oxygen consumption value of 10.5 mmHg, and a capillary density of 787.25 mm⁻² calculated as the average of values cited in the aforementioned study (McGuire & Secomb, 2001). Other parameters include a capillary radius of 2.5 µm and a nominal capillary length of 500 µm (McGuire & Secomb, 2001). Femoral muscle mass is assumed to be 2.3 kg (Andersen & Saltin, 1985). Values of muscle blood flow [L/min] corresponding to four levels of demand (80, 40, 20, and 10 cm³O₂/100 cm³/min) were estimated based on a regression from published data (Andersen & Saltin, 1985) as 1.035 + 5.594 × $\dot{V}{O}_2$ [L/min], where $\dot{V}{O}_2$ is the calculated oxygen consumption rate. The vertical dashed line corresponds to a CV = 1.76 (see text)

FIGURE 4

Schematic representation of factors contributing to the heterogeneity of tissue oxygen levels. Arrow with blunt end represents negative effect. Microvascular networks have heterogeneous structures as a result of the “dimensional problem” and the stochastic processes of angiogenesis, with the consequence that oxygen supply is intrinsically heterogeneous. Oxidative metabolism in tissues and ventilation in the lung vary in both space and time, causing extrinsic heterogeneity in tissue oxygen levels. Multiple control mechanisms act on both short and long time scales to mitigate this heterogeneity and ensure adequate tissue oxygenation under normal conditions

FIGURE 5

Schematic representation of control mechanisms in the circulatory system. (a) Interaction of metabolic and hemodynamic control mechanisms. The solid arrows indicate the property that is primarily controlled by responses to each type of stimulus. All control mechanisms act via changes in vessel diameters, and therefore influence all of the controlled properties. This cross‐talk is represented by the dashed lines. Because of this cross‐talk, multiple variables cannot be controlled individually by a single mechanism (variation in vessel diameters), and some heterogeneity in controlled properties is inevitable. (b) Illustration of feedback and feedforward mechanisms for control of tissue oxygenation. In feedback control, changes in oxygen levels drive changes in vessel diameters. In feedforward control, signals derived directly from the metabolic activity drive changes in vessel diameters