Diameters and cross-sectional areas of branches in the human pulmonary arterial tree


  • Dr. Keith Horsfield,

    Corresponding author
    1. The Midhurst Medical Research Institute, The Surrey Research Park, Guildford, Surrey GU2 5YW, United Kingdom
    • The Midhurst Medical Research Institute, 30 Occam Rd., The Surrey Research Park, Guildford, Surrey GU2 5YW, U.K.
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  • Michael J. Woldenberg

    1. Department of Geography, State University of New York, Buffalo, New York 14260
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Measurements were made of the diameters of the three branches meeting at each of 1,937 difurcations in the pulmonary arterial tree, using resin casts from two fully inflated human lungs. Cross-sectional areas of the parent branch and of the daughter branches were calculated and plotted on a log-log plot, which showed that mean cross-sectional area increases in a constant proportion of 1.0879 at bifurcations. The mean value of the ratio of daughte branch diameters at bifurcations was 0.7849. The mean value of the exponent z in the equation flow = k (diameterz) was found to be 2.3 ± 0.1, which is equal to the optimal value for minimizing power and metabolic costs for fully developed turbulent flow. Although Reynolds number may exceed 2,000 in the larger branches of the pulmonary artery, turbulent flow probably does not occur, and in the peripheral branches Reynolds number is always low, excluding turbulent flow in these branches. This finding seems to be incompatible with the observed value of z. A possible explanation may be that other factors may need to be taken into account when calculating the theoretical optimum value of z for minimum power dissipation, such as the relatively short branches and the disturbances of flow occurring at bifurcations. Alternatively, higher arterial diameters reduce acceleration of the blood during systole, reduce turbulent flow, and increase the reservoir function of the larger arteries. These higher diameters result in a lower value of z.