Fractal 15 O-Labeled Water Washout From the Heart

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Abstract
To characterize the washout of water from the heart, we used a flow-limited (not diffusion- or permeability-limited) marker for blood-tissue exchange, namely, tracer-labeled water. Experiments were performed by injecting 15O-labeled water into the inflow to isolated blood-perfused rabbit hearts and by recording the tracer content in the heart and in the outflow simultaneously for up to 5 minutes. The data exhibit a particular combination of power law forms: (1) The downslopes of the residue and outflow curves were both power law functions, with the residue diminishing as t−α and the outflow as t−α−1, where α is interpreted to be the dimensionless exponent of a fractal power law relation characterizing the self-similarity inherent in each curve. (2) The fractional escape rate, given by the outflow curve divided by the residue curve, diminished almost exactly as t−1. In 18 sets of curves, α averaged 2.21±0.27. These results lead to an improved method for extrapolating the downslopes of indicator dilution curves to estimate their areas and therefore the blood flows. The evidence also points strongly to the conclusions that myocardial water washout is a fractal process and that stirred tank models are inappropriate for the heart.