Fractal Branchings: The Basis of Myocardial Flow Heterogeneities?

The distribution of myocardial blood flows was found by Yipintsoi et al1 to be surprisingly broad, broader than could be expected from variation in the microsphere technique itself in their studies of anesthetized dog hearts. This was observed by others2,3 and was expanded by observations in awake baboons by King et al.,4 who found that the shape of the distribution of regional myocardial blood flows in about 0.2-g pieces was maintained over long periods of time, as estimated by repeated injections of tracer labeled microspheres. In these studies, the microsphere technique variation gave about 8 percent noise, but the heterogeneity of flows had a standard deviation that was about 35 percent of the mean flow, that is, the relative dispersion (RD) or coefficient of variation was 35 percent. The regional flow in a given piece remained almost constant at each of six observation times, spread over many hours, that is, the broad heterogeneity of myocardial blood flows was stable. More detailed analyses of these data by King and Bassingthwaighte5 showed that the temporal fluctuation in regional flows was quite modest compared with the spatial variation. Temporal fluctuations were such that, while flow in a given region showed some apparently random variation with time, local flow in regions with flow less than 50 percent of the mean flow never increased enough to reach the mean. Similarly, regions with flow greater than 150 percent of the mean never diminished to the mean flow. Thus, myocardial regional flows maintained their relative position in the distribution of flows throughout the heart. These observations gave rise to methodologic and physiological questions. Methodologic questions are: Since there are only four to six observations over time in each of these individual pieces, what could one say about the frequency of temporal fluctuations? Were they rhythmic or not? Which regions of the heart had higher flows vs. lower flows? Were there consistent endocardial and epicardial gradients? The physiological questions are: What are the implications of having regions that are of consistently high flow or consistently low flow? Is the metabolic rate more in high-flow regions than in low-flow regions? Do high-flow regions have a plethora of flow and relatively low oxygen extraction? Are low-flow regions on the verge of becoming ischemic under stress? If the myocardium is stressed and lactate production occurs, is the lactate mainly from low-flow regions whose metabolic demands have now exceeded the supply of substrate and oxygen? Do low-flow regions recruit more under stress than high-flow regions? The basic question relating to those just posed is one on which many investigators have sought definite information, namely, What is the relationship between metabolism and flow regionally in the heart? Since the organ is essentially monofunctional, and the tissue is reasonably uniform throughout the left ventricular myocardium, this in turn raises the question of why metabolism might be different in one region than another. But before attempting to answer these methodologic and physiological questions, we had to face a relatively simple methodologic question: What is the appropriate estimate of heterogeneity?