Transcoronary intravascular transport functions obtained via a stable deconvolution technique

Abstract

Following left atrial injection of indocyanine green in closed-chest, anesthetized dogs, 60 simultaneous input-output pairs of dilution curves were sampled via identical catheter sampling systems from the aortic root, C in (t), and the coronary sinus, C out (t). Assuming that C out (t) was the convolution of a transport function, h(t), and C in (t), a new deconvolution technique was used to solve for the h(t)'s which was not sensitive to noise, recirculation, or the form of h(t).The 60 transcoronary h(t)'s were observed to be unimodal, right-skewed frequency distribution functions with mean transit times, t, ranging from 3 to 7 sec. The relative dispersions (standard deviation, σ, divided by t) averaged 0.38 ± 0.05, the skewness averaged 1.40 ± 0.37 and the kurtosis averaged 6.1 ± 1.8; this means that the h(t)'s are more sharply peaked than Gaussian distributions. The fact that parameters were statistically independent of the mean transit time implied the constancy of the shape of the various h (t)'s and this was verified by the coincidence of the h(t)'s plotted as a function of t/t. This "similarity" of the h(t)'s strongly suggests that changes in the transit time through any particular vascular pathway of the coronary bed are in proportion to the changes in other parallel pathways.

Physiology and theory of tracer washout techniques for the estimation of myocardial blood flow: Flow estimation from tracer washout

“…Similarity has been demonstrated for transorgan transport functions in the kidney by Gomez et al, 22 in the lung over a very limited range of alveolar and left atrial pressures by Knopp and Bassingthwaighte,23 and in the coronary bed by Knopp et al 17 Data from the latter study are plotted in Fig. 11, showing a fair degree of similarity.…”

“…This can probably be done with reasonable accuracy, since the shapes of the impulse responses of the coronary vascular bed have not been shown to differ greatly from shapes that could be fitted with an exponential downslope. 17 However, even though the extrapolation may be adequate, this technique does not provide accurate estimates of coronary blood flow from intracoronary artery injections. There are very limited circumstances under which one can use this impulse injection technique for the estimation of total coronary blood flow.…”

“…In this idealized circulatory network in which there is constant proportionality of distribution of flow, the transport functions, h(t), at different flows are related by: (17) where t̄1/t̄2 scales the time t (in the brackets) and the magnitude so that the areas under h 1 (t) and h 2 (t) are both unity.…”

“…The use of the f i as a scalar for time is based on the additional assumption that the ratio of intravascular to extravascular volumes is the same in each region, a point on which more information is needed. When the shape of R′(t) is known, then the determination of the distribution of f i s is a relatively straightforward optimization task of the sort described by Knopp et al 17 When R′(t) is undefined, then the task is more difficult, but not impossible, because the bounds on the possible shapes for R(t) are the monoexponential mixing chamber and the piston flow forms shown in Fig. 7.…”

Temporal fluctuations in regional myocardial flows

“…When tracers are injected into the left atrial cavity and flow downstream to enter the coronary arteries, the concentration-time curve for the entering tracer is spread over several seconds, because of dispersion due to the force of injection and the mixing that occurs in the atrium and ventricle. Using 0.5 s left atrial injections, Knopp et al (1976) observed that dye dilution curves obtained in the root of the aorta had a spread of 4 -10 s depending on the flow. Even with left ventricular injections and high speed sampling, Bassingthwaighte and Ackerman (1967) observed similar spreads.…”