Use of tracers to measure flow within single microvessels

Most techniques for making quantitative measurements of flow within single microvessels rely on tracers which are injected upstream of the microvessel and monitored noninvasively (e.g., optical densitometry) at selected sites along the microvessel. This study examines theoretically the measurement of average flow velocity (v) within individual microvessels from tracer flow data at monitoring sites. Starting with a fundamental convection-diffusion equation, the theory considers tracers which can distribute across both plasma and red cell phases. An integral analysis indicates that v = delta zeta/delta tau, where delta zeta is the distance between monitoring sites, and delta tau is the tracer transit or "residence" time needed to traverse that distance. The residence time which arises explicitly requires measurement of the flow-weighted average tracer concentration at each monitoring site. Because noninvasive tracer measurements provide indices of the unweighted average tracer concentration, a velocity measurement error, delta(zeta), arises, delta(zeta) is quantified in relation to the axial location of the measurement site, the velocity profile, the tracer Peclet number, and the radial distribution of tracer at the vessel inlet. delta(zeta) does not vanish when tracer enters a microvessel with a radially uniform concentration profile, but does vanish past a critical distance, Lc, from the microvessel entrance. The critical distance can be estimated using Lc/d = 0.05(vd)/D (d. vessel diameter; v, average flow velocity; D, tracer diffusivity). Accordingly, tracer data can be used to quantify flow velocity within a microvessel provided the microvessel length allows for monitoring tracer flow beyond the estimated Lc value. This study serves as a necessary precursor to analyses of plasma-phase tracers used to measure microvascular plasma flow.