Regional pulmonary blood flow in dogs under zone 3 conditions was measured in supine and prone postures to evaluate the linear gravitational model of perfusion distribution. Flow to regions of lung that were 1.9 cm3 in volume was determined by injection of radiolabeled microspheres in both postures. There was marked perfusion heterogeneity within isogravitational planes (coefficient of variation = 42.5%) as well as within gravitational planes (coefficient of variation = 44.2 and 39.2% in supine and prone postures, respectively; P = 0.02). On average, vertical height explained only 5.8 and 2.4% of the flow variability in the supine and prone postures, respectively. Whereas the gravitational model predicts that regional flows should be negatively correlated when measured in supine and prone postures, flows in the two postures were positively correlated, with an r2 of 0.708 +/- 0.050. Regional perfusion as a function of distance from the center of a lung explained 13.4 and 10.8% of the flow variability in the supine and prone postures, respectively. A linear combination of vertical height and radial distance from the centers of each lung provided a better-fitting model but still explained only 20.0 and 12.0% of the flow variability in the supine and prone postures, respectively. The entire lung was searched for a region of contiguous lung pieces (22.8 cm3) with high flow. Such a region was found in the dorsal area of the lower lobes in six of seven animals, and flow to this region was independent of posture. Under zone 3 conditions, neither gravity nor radial location is the principal determinant of regional perfusion distribution in supine and prone dogs.

To investigate the influence of the midluteal and midfollicular phases of the menstrual cycle on exercise performance and ventilatory drives, we studied six outstanding female athletes, six controls with normal menstrual cycles, and six outstanding athletes who were amenorrheic. In all menstruating subjects resting minute ventilation (Ve) and mouth occlusion pressures (P0.1) were higher in the luteal phase (p less than k0.0001 and p less than 0.02, respectively),. Hypoxic (expressed as the hyperbolic shape parameter A) and hypercapnic (expressed as S, deltaVE/delta PAco2) ventilatory responses were increase in the luteal phase (p less than 0.01). The athletes had lower A values during the luteal phase than the nonathletes (p less than 0.001). Maximal exercise response, expressed either as total exercise time or maximum O2 consumption or CO2 production (VO2 max or Vco2 max) was decreased during the luteal phase but was significantly different at a p less than 0.05 level only among the nonathletes. Ventilatory equivalent (VE/VO2) during progressive exercise on a bicycle ergometer was significantly increased during the luteal phase. The amenorrheic athletes showed no changes between the two test periods. The luteal phase of the menstrual cycle induced increases in ventilatory drives and exercise ventilation in both athletes and controls, but the athletes, in contrast to controls, demonstrated no significant decrease in exercise performance in the luteal phase.

The heterogeneity of pulmonary blood flow was examined using a fractal analytic procedure, and the results were compared with the traditional gravitational model of flow distribution. 99mTc-labeled macroaggregate was injected intravenously at functional residual capacity in six supine anesthetized dogs. The lungs were fixed in situ and sliced in transverse sections. The slices were imaged on a planar gamma camera, and a three-dimensional array of blood flow measurements was reconstructed for each lung. Fractal analysis was used to examine the spatial heterogeneity or RDs (relative dispersion = SD/mean) as a function of the number of pieces into which the flow array was subdivided. RDs was fractal and could be characterized by a fractal dimension (Ds) of 1.09 +/- 0.02, where a Ds of 1.0 reflects homogeneous flow and 1.5 indicates a random flow distribution. The data fit the fractal model exceptionally well with an average r = 0.98. RDs was examined in gravitational and isogravitational planes and as expected was greatest in the gravitational direction. However, the difference was small, suggesting that gravitation plays a secondary role to an underlying process producing heterogeneity. Within the limits of resolution attained by this study (piece volumes greater than 0.25 cm3), the heterogeneity of pulmonary blood flow is well characterized by a fractal model.

This review describes approaches to the analysis of fractal properties of physiological observations. Fractals are useful to describe the natural irregularity of physiological systems because their irregularity is not truly random and can be demonstrated to have spatial or temporal correlation. The concepts of fractal analysis are introduced from intuitive, visual, and mathematical perspectives. The regional heterogeneities of pulmonary and myocardial flows are discussed as applications of spatial fractal analysis, and methods for estimating a fractal dimension from physiological data are presented. Although the methods used for fractal analyses of physiological data are still under development and will require additional validation, they appear to have great potential for the study of physiology at scales of resolution ranging from the microcirculation to the intact organism.Keywords mathematical analysis; heterogeneity; spatial correlation; temporal correlation; microcirculation; morphology; blood flow distribution The Intent of this Review is to provide physiologists with the basic tools for working with fractals, by use of intuitive, visual, and formal mathematical definitions of the concepts of fractal geometry, self-similarity, scale independence, and fractal dimensions. Although the concepts underlying fractals are new, mathematical sophistication is not a prerequisite for a working knowledge of fractal applications. Applications of fractal analysis in physiology will be reviewed with examples from pulmonary morphology, pulmonary and cardiovascular circulation, and time-dependent analysis of physiological measurements. APPENDICES A and B include a glossary of terms and variables, a listing of the equations, and an illustrative analysis of a simple data set.Fractal analysis is still in the formative stages of development, and its ultimate importance as an investigative tool in physiology is not fully established. Nevertheless, it is providing new perspectives into the physiology of cells, organs, and intact organisms, with mathematical models of branching structures and with descriptors of spatial and temporal correlation. The robust descriptive properties of this approach in the analysis of Address for reprint requests: J. B. Bassingthwaighte, University of Washington, WD-12, Seattle, WA 98195. NIH Public AccessAuthor Manuscript J Appl Physiol (1985). Author manuscript; available in PMC 2014 June 19. Published in final edited form as:J Appl Physiol (1985). 1991 June ; 70(6): 2351-2367. NIH-PA Author ManuscriptNIH-PA Author Manuscript NIH-PA Author Manuscript physiological variability suggest that it may signal the development of a new paradigm (16) compelling the attention of investigators from diverse areas of physiological inquiry. Self-Similarity and Fractal DimensionsA fractal structure or fractal process can be loosely defined as having a characteristic form that remains constant over a magnitude of scales. A structure is fractal if its small-scale form appears similar to its large-scale form...

Original studies leading to the gravitational model of pulmonary blood flow and contemporary studies showing gravity-independent perfusion differ in the recent use of laboratory animals instead of humans. We explored the distribution of pulmonary blood flow in baboons because their anatomy, serial distribution of vascular resistances, and hemodynamic responses to hypoxia are similar to those of humans. Four baboons were anesthetized with ketamine, intubated, and mechanically ventilated. Different colors of fluorescent microspheres were given intravenously while the animals were in the supine, prone, upright (repeated), and head-down (repeated) postures. The animals were killed, and their lungs were excised, dried, and diced into approximately 2-cm3 pieces with the spatial coordinates recorded for each piece. Regional blood flow was determined for each posture from the fluorescent signals of each piece. Perfusion heterogeneity was greatest in the upright posture and least when prone. Using multiple-stepwise regression, we estimate that 7, 5, and 25% of perfusion heterogeneity is due to gravity in the supine, prone, and upright postures, respectively. Although important, gravity is not the predominant determinant of pulmonary perfusion heterogeneity in upright primates. Because of anatomic similarities, the same may be true for humans.