© 1995 American Heart Association, Inc.
Articles |
Fractal 15O-Labeled Water Washout From the Heart
From the Center for Bioengineering, University of Washington, Seattle.
Correspondence to James B. Bassingthwaighte, MD, PhD, Center for Bioengineering, WD-12, University of Washington, Seattle, WA 98195. E-mail jbb@nsr.bioeng.washington.edu.
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-
and the outflow as
t--1, where 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, 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.
Key Words: flow-limited blood-tissue exchange • power law kinetics • positron emission • oxygen-15 • capillary permeability • statistical self-similar processes
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