Spatial variation in regional flows within the heart, skeletal muscle, and in other organs, and temporal variations in local arteriolar velocities and flows is measurable even with low resolution techniques. A problem in the assessment of the importance of such variations has been that the observed variance increases with increasing spatial or temporal resolution in the measurements. This resolution-dependent variance is now shown to be described by the fractal dimension, D. For example, the relative dispersion (RD=SD/mean) of the spatial distribution of flows for a given spatial resolution, is given by:where m is the mass of the pieces of tissue in grams, and the reference level of dispersion, RD(m ref ), is taken arbitrarily to be the RD found using pieces of mass m ref , which is chosen to be 1 g. Thus, the variation in regional flow within an organ can be described with two parameters, RD(m ref ) and the slope of the logarithmic relationship defined by the spatial fractal dimension D s . In the heart, this relation has been found to hold over a wide range of piece sizes, the fractal D s being about 1.2 and the correlation coefficient 0.99. A D s of 1.2 suggests moderately strong correlation between local flows; a D s =1.0 indicates uniform flow and a D s = 1.5 indicates complete randomness. Keywords2-iododesmethylimipramine; microspheres; regional myocardial blood flow; flow heterogeneity; heart; fractals; relative dispersion coefficient of variation; sheep; baboons; rabbits It is now well established that regional myocardial blood flows show considerable spatial heterogeneity. This has been thoroughly demonstrated by those laboratories in which small tissue pieces were used and the whole of the myocardium was sampled. Probability density functions of regional flows were generated in this fashion by Yipintsoi et al 1 in the dog, by King et al 2 in the baboon, and by Bassingthwaighte et al 3 in the rabbit. Using pieces that were less than 1% of the ventricular mass, these investigators found local flows ranging from a third of the mean flow to over twice the mean flow. The relative dispersions (RDs) of the distributions (RD=SD/mean) were about 35% in these three species when observations were made by dividing the hearts into 100-250 pieces.This large variability appeared suspect and seemed possibly attributable to inherent variation in the microsphere deposition technique, even though the results were very reproducible. 3 The spheres were recognizably large compared with the vessels in which they were Address for correspondence: James B. Bassingthwaighte, MD, PhD, University of Washington, WD-12, Seattle, WA 98195. NIH Public Access Author ManuscriptCirc Res. Author manuscript; available in PMC 2012 May 29.Published in final edited form as:Circ Res. 1989 September ; 65(3): 578-590. NIH-PA Author ManuscriptNIH-PA Author Manuscript NIH-PA Author Manuscript deposited, and causes of maldistribution with rheology and branching 4 are numerous.Microsphere tracer counting error exacerbates the problem. Howeve...

SUMMARYRegional myocardial blood flow has been thought to be relatively uniform, in accord with the singular function of myocardial cells. However, considerable spatial heterogeneity has been observed in the hearts of anesthetized animals and in isolated hearts. Studies were undertaken in a total of 13 baboons. Eleven were awake, healthy animals sitting in chairs at rest or feeding, some performed mild leg exercise (wheel turning), and others were subjected to whole body heating; two were anesthetized, methodological controls. Microspheres (15 ± 3 μm diameter, 0.5 × 10 6 /kg body weight) were injected via a catheter into the apex of the left ventricle while arterial blood was sampled at a constant rate for calculating cardiac output. Microspheres with different labels were injected at six intervals of 20 minutes to several hours. On sacrifice, the hearts were sectioned into 204 locatable pieces (left ventricle, 168; right ventricle, 27; and atria, 9). Average resting myocardial flow was 2.1 ± 0.2 ml/g per min (mean ± SD, n = 11). Left and right ventricles and atria comprised 70 ± 2% (n = 13), 20 ± 2%, and 10 ± 2% respectively of the total heart mass while receiving 80 ± 3%, 16 ± 2%, and 4 ± 2% of the total myocardial flow. Thus, mean left ventricular flow was 114 ± 5% of the average for the whole heart, right ventricular flow was 81 ± 13%, and atrial flow was 41 ± 13%. Myocardial flow heterogeneity was marked; in left ventricle, regional flows ranged from one-third to two times the mean, the relative dispersion (= standard deviation/mean) of regional flows, corrected for methodological scatter and temporal variation, was 0.33 ± 0.06 (n = 67) in the whole heart, 0.26 ± 0.07 in left ventricle, 0.32 ± 0.11 in right ventricle, and 0.22 ± 0.19 in the atria. The pattern of regional flows in each heart tended to remain stable with time. In each piece averaged over time, the relative dispersion due to temporal heterogeneity was 0.11 ± 0.03 (n = 2040) in the whole heart, 0.09 ± 0.03 in the left ventricle, 0.15 ± 0.05 in the right ventricle, and 0.23 ± 0.06 in the atria. The conclusion is that the degree of spatial heterogeneity of local myocardial flows in conscious primates is similar to that of anesthetized animals and isolated hearts, and is much greater than that due to temporal fluctuations. KeywordsFlow distribution; Coronary arteries; Septal perfusion; Tracer-labeled microspheres; Awake primates; Spatial variation in flow; Temporal variation in flowWith the increasing refinement of biochemical and physiological observations, the variations that occur throughout the myocardium in rates of metabolism (Griggs et al., 1972) We appreciate the help of G. Crookcr in the preparation of the manuscript, and of H. Nurk with the illustrations. Presented in part at FASEB, Fed. P.roc. 37: 875, 1978. NIH Public Access (Gamble et al., 1974;Schubert et al., 1978;Weiss and Sinha, 1978), and in flow (Domenech et al., 1969;Yipintsoi et al., 1973) have become quite evident. It is no longer sufficient either in concept or in practi...

Male snakes typically have longer tails relative to body length than females, but the extent o f this dimorphism varies among species. 'l'hrcc hypotheses have been suggested to explain tail dimorphism. The Morphological Constraint Hypothesis proposes that males have relatively longer tails to accommodate hemipenes and rctrartor muscles. 'The Female Reprodurtivc Output Hypothesis proposes that females have relatively shorter tails as a secondary result of natural selection for increased reproductive capacity. The Male ,Mating Ability Hypothesis proposes that sexual selection Cavours rclatively Iongcr tails in males during courtship. These hypotheses makc different predictions about the relationships among tail length, body morphology, female reproductive output, mode of reproduction, and male mating bchaviour among and within taxa. Prcdictinns were tested using publishcd data for 56 genera in thc family Colubridac and original data for thc water snake, Nerodia Jipednn. Tail length dimorphism was more male-biased in t a m having rclatively short tails ( r = -0.52, P

Summary 1.For gape-limited predators such as snakes, it should be possible to predict the relationship between maximum prey size and body size from the relationship between maximum prey size and gape size and between gape size and body size. Such predictions were generated for Water Snakes, Nerodia sipedon L., using a data subset and then tested with a larger data set. 2. Gape size was computed based on jaw length and width and cyclical regression was used to identify prey of maximum size for snakes of a given gape or mass. 3. Predicted and observed maximum prey cross-section-snake mass allometry were in good agreement. Predicted maximum prey mass-snake mass allometry somewhat exceeded observed allometry which did not differ from 1. 4. Observed minimum prey size-snake size allometry was significantly greater than 0, indicating that larger snakes drop small prey from their diets. 5. Gape size-body size allometry in two other natricine snakes ( Thamnophis sirtalis , Storeria dekayi ) suggest that patterns of ontogenetic change in prey size should differ among species in predictable ways. 6. Sex differences in gape size-snake size allometry suggest that sex differences in maximum prey size should increase with increasing snake size, even when linear measures of head dimensions do not.

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