Flow estimation by indicator dilution (bolus injection)

Abstract

Indicator dilution techniques used for the estimation of flow (F), mean transit time (t̄), dispersion (σ), and mean transit time volume (V) in the circulation are subject to error when (1) flow is not steady and (2) concentrations are obtained by sampling at a constant rate (time averaging) rather than at rates proportional to the instantaneous flow past the sampling site (volume averaging).

Using a simple descriptive model for indicator transport, the effects of simulated aortic flow or of sinusoidal flow of widely variable frequency were assessed. Errors in estimates of F, t̄, σ, and V are greater with bolus injections than with constant-rate injections. Errors are roughly proportional to the amplitude of variation in flow. They are maximal when the period of flow fluctuation is similar to the passage time of dye dilution curve, which, for the human central circulation, is about the time for one respiratory cycle. With sinusoidal flow between 50% and 150% of the mean flow, errors were at worst up to 60% in F, 30% in t̄, 50% in σ, and 70% in V, with a bimodal distribution. Errors are minimal at cardiac frequencies. The troublesome lower frequencies can be avoided. Preliminary tests of a method for converting time- to volume-averaged concentrations gave encouraging results

FIGURE 1

Comparison of model output, y₀(t), labeled S with an experimental dye curve from the ascending aorta, C(t), labeled E when the model was driven by the recorded flowmeter signal F(t). The parameters of the model were V = 250 ml, F̄ = 45 ml/sec, ζ₁=l.l, ζ₂ = 0.8, ω₁/ω₂ = 7.0. The input pulse to the model was 1 second in duration and was delayed 1.6 seconds compared to the actual injection.

FIGURE 2

Effect of frequency and phase of sinusoidal flow on ratio of calculated flow to mean flow. Actual flow is F, flow calculated by equation 4a is F_u, and F̄ and F̄_u are mean flows.

FIGURE 3

Effect of amplitude of flow variation on area of dilution curve.

FIGURE 4

Effect of frequency and phase of sinusoidal variation in flow on estimated mean transit time. Ordinate is scaled twice as large on lower panel as on upper panel.

FIGURE 5

Effect of frequency and phase of sinusoidal variation in flow on relative dispersion of dye dilution curve. In this hypothetical situation described by the model, spatial dispersion of indicator is entirely independent of flow, and therefore frequency of variation in flow has no influence on actual spread of bolus with respect to distance along segment of circulation.

FIGURE 6

Effects of phase of sinusoidal variation in flow on estimates of mean transit time volumes.

FIGURE 7

Probability density functions of errors in estimating A, F, t̄, and V from dye dilution curves during unsteady flow. P is probability of occurrence per 0.01 unit, so total area of each curve is 1.0. For these curves, ω/ω_c = 0.15, K = 0.5, and injections were made at all ϕ with equal probability. (Data obtained from 200 solutions with ϕ at steps of 0.01πfrom 0 to 2π.)