AIRWAY ANATOMY Classical scaling models of lungs 1. Weibel ? let N = # of branches 2. N(z) = 2z(N(0) where z is the order of branch, with 0 being the trachea 3. Daimeter: 4. See B. West An. Biomed Eng, 18, 1990 5. Assume an ?average? fractal law with periodic change in scale or D. then, A(z) is a periodic series in z 6. Fractal periodic then gives perfect fit to data over classical scaling of power law 7. Propagation of Errors in Anatomy if Let error be equal to a variation in so let vary by a Gaussian random, then a) Results grow as b) For the fractal, 8. Conclude a) A power law branching system would be prone to very large anatomical defects due to any large genetic variation b) Fractal branching does not propagate genetic defects through the anatomy
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