Branching design of the bronchial tree based on a diameter-flow
relationship.
Kitaoka, Hiroko, and B[acute]ela Suki.
Department of Biomedical Engineering, Boston University, Boston, MA
02215
APStracts 3:0511A, 1996.
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 flow rates, P(>Q) is proportional to Q-1. We analyzed the
morphometric airway data by Raabe et al. (1976) and found that the
cumulative probability distribution function of diameters,
P(>d), is proportional to d-n, which supports the validity of
Q dn since P(>Q) Q-1. 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.
Received 31 May 1996; accepted in final form 21 October 1996.
APS Manuscript Number A511-6.
Article publication pending Journal of Applied Physiology.
ISSN 1080-4757 Copyright 1996 The American Physiological Society.
Published in APStracts on 31 December 1996