modeling trochea and lunks

[N. J. A. Sloane]

The 3-D model of the human airway down to alveoli is properly afractal over several orders of magnitude.  Tjis has been analyticallymodeled, 3-D graphics represented, and used as the basis for extensivelaboratory testing in humans.  Among other things, this important workstrongly suggests that the standard instruction for using asthmainhalators is simply wrong.
See, for instance:
Branching asymmetry in the lung airway treeArnab MajumdarAdriano M. Alencar, Center for Polymer Studies, Boston UniversitySergey V. Buldyrev, Center for Polymer Studies, Boston UniversityZoltán Hantos, Department of Medical Informatics and Engineering, andInstitute of Surgical Research, University of Szeged, HungaryH. Eugene Stanley, Center for Polymer Studies and Dept. of Physics,Boston UniversityBéla Suki, Dept of Biomedical Engineering, Boston UniversityProc. 6th International Conference on Complex Systems, Boston, 25-30 June 2006
AbstractWe study the distribution P(N,D) of diameters D as a function of ageneration N in asymmetric airway trees of lungs from four mammalianspecies. We find that the airway bifurcations are self-similar in eachspecies such that the ratios of diameters of the major and minordaughters to their parent, kmaj and kmin respectively, are constantsindependent of N until a cut-off diameter Dc is reached. We show thatthis is consistent with a model of the airway tree based on anasymmetric division of flow at each bifurcation. We derive the familyof distributions P(N,D), which are truncated log-normal distributions,in good agreement with experimental data. We also show that thePoiseuille flow resistance of our model airway tree is related to theasymmetry parameter r and only weakly depends on the size parameterQc. Our findings suggest that the primary determinant of the observedheterogeneity is an underlying regular branching asymmetry.
On 1/29/07, N. J. A. Sloane <njas at research.att.com> wrote:> Dear Funsters and SeqFans,  This is neither fun nor to do> with sequences, I'm afraid.  But a friend of a friend> has been talking to me about making a 3-D model> of the trochea and lungs, modeling the flow of air.> This sounds like classical numerical analysis,> and I know there are experts on this list.> Does anyone know of previous work on this problem,> or on similar problems?>> If so please write to me off-line.  Thanks!> Neil (njas at research.att.com)>