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Department of Biomedical Engineering, Boston University, Boston, Massachusetts 02215
Received 31 May 1996; accepted in final form 21 October 1996.
Kitaoka, Hiroko, and Béla Suki. Branching design
of the bronchial tree based on a diameter-flow relationship.
J. Appl. Physiol. 82(3): 968-976, 1997.
We propose a method for designing the bronchial tree where the
branching process is stochastic and the diameter
(d) of a branch is determined by its
flow rate (Q). We use two principles: the continuum
equation for flow division and a power-law relationship between
d and Q, given by Q ~ dn,
where n is the diameter exponent. The value of
n has been suggested to be ~3. We
assume that flow is divided iteratively with a random variable for the
flow-division ratio, defined as the ratio of flow in the branch to that
in its parent branch. We show that the cumulative probability
distribution function of Q, P(>Q) is proportional to Q
1. We
analyzed prior morphometric airway data (O. G. Raabe, H. C. Yeh, H. M. Schum, and R. F. Phalen, Report No.
LF-53, 1976) and found that the cumulative probability
distribution function of diameters, P(>d), is
proportional to dn, which supports
the validity of Q ~ dn since
P(>Q) ~ Q1. This allowed us to
assign diameters to the segments of the flow-branching pattern. We
modeled the bronchial trees of four mammals and found that their
statistical features were in good accordance with the morphometric
data. We conclude that our design method is appropriate for robust
generation of bronchial tree models.
airway; diameter exponent; flow distribution; fractals; power law distributions
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