Geodesic
Method of constructing an asymmetric human bronchial tree in normal and pathological cases
Matematičeskaâ biologiâ i bioinformatika, Tome 15 (2020) no. 2, pp. 148-157.

Voir la notice de l'article provenant de la source Math-Net.Ru

The goal of the study is the analytical design of the full asymmetric human bronchial tree (irregular dichotomy) for healthy patients and patients with obstructive pulmonary diseases. For this purpose, the author has derived the special analytical formulas. All surfaces of the bronchial tree are matched with the secondorder smoothness (there are no acute angles or ribs). The geometric characteristics of the human bronchial tree in the pathological case are modeled by a “starry” shape of the inner structure of the bronchus; a level of the pathology is defined by two parameters: bronchus constriction level and level of distortion of the cylindrical shape of the bronchus. Closed analytical formulas allow a researcher to construct the human bronchial tree of an arbitrary complexity (up to alveoli); moreover, the parametric dependences make it possible to specify any desirable level of airway obstruction. 
@article{MBB_2020_15_2_a10,
     author = {A. E. Medvedev},
     title = {Method of constructing an asymmetric human bronchial tree in normal and pathological cases},
     journal = {Matemati\v{c}eska\^a biologi\^a i bioinformatika},
     pages = {148--157},
     publisher = {mathdoc},
     volume = {15},
     number = {2},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/MBB_2020_15_2_a10/}
}
TY  - JOUR
AU  - A. E. Medvedev
TI  - Method of constructing an asymmetric human bronchial tree in normal and pathological cases
JO  - Matematičeskaâ biologiâ i bioinformatika
PY  - 2020
SP  - 148
EP  - 157
VL  - 15
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MBB_2020_15_2_a10/
LA  - en
ID  - MBB_2020_15_2_a10
ER  - 
%0 Journal Article
%A A. E. Medvedev
%T Method of constructing an asymmetric human bronchial tree in normal and pathological cases
%J Matematičeskaâ biologiâ i bioinformatika
%D 2020
%P 148-157
%V 15
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MBB_2020_15_2_a10/
%G en
%F MBB_2020_15_2_a10
A. E. Medvedev. Method of constructing an asymmetric human bronchial tree in normal and pathological cases. Matematičeskaâ biologiâ i bioinformatika, Tome 15 (2020) no. 2, pp. 148-157. http://geodesic.mathdoc.fr/item/MBB_2020_15_2_a10/

[1] E. R. Weibel, Morphometry of the Human Lung, Springer Verlag, Berlin, 1963

[2] A. E. Medvedev, P. S. Gafurova, “Analytical design of the human bronchial tree for healthy patients and patients with obstructive pulmonary diseases”, Mathematical Biology and Bioinformatics, 14:2 (2019), 635–648 | DOI

[3] Y. Zhao, B. B. Lieber, “Steady inspiratory flow in a model symmetric bifurcation”, ASME Journal of Biomechanical Engineering, 116 (1994), 488–496 | DOI

[4] Y. Zhao, C. T. Brunskill, B. B. Lieber, “Inspiratory and expiratory steady flow analysis in a model symmetrically bifurcating airway”, ASME Journal of Biomechanical Engineering, 119 (1997), 52–58 | DOI

[5] C. J. Hegedüs, I. Balásházy, Á. Farkas, “Detailed mathematical description of the geometry of airway bifurcations”, Respiratory physiology neurobiology, 141:1 (2004), 99–114 | DOI

[6] T. Heistracher, W. Hofmann, “Physiologically realistic models of bronchial airway bifurcations”, J. Aerosol Sci, 26:3 (1995), 497–509 | DOI

[7] C. Ertbruggen, C. Hirsch, M. Paiva, “Anatomically based three-dimensional model of airways to simulate flow and particle transport using computational fluid dynamics”, J. Appl. Physiol, 98 (2005), 970–980 | DOI

[8] A. F. Tena, P. Casan, J. Fernández, C. Ferrera, A. Marcos, “Characterization of particle deposition in a lung model using an individual path”, EPJ Web of Conferences, 45 (2013), 01079 | DOI

[9] A. F. Tena, J. Fernández, E. Álvarez, P. Casan, D. K. Walters, “Design of a numerical model of lung by means of a special boundary condition in the truncated branches”, International Journal for Numerical Methods in Biomedical Engineering, 33:6 (2017), e2830 | DOI | MR

[10] A. F. Tena, J. F. Francos, E. Álvarez, P. A. Casan, “A three dimensional in SILICO model for the simulation of inspiratory and expiratory airflow in humans”, Engineering Applications of Computational Fluid Mechanics, 9:1 (2015), 187–198 | DOI

[11] T. Gemci, V. Ponyavin, Y. Chen, H. Chen, R. Collins, “CFD Simulation of Airflow in a 17-Generation Digital Reference Model of the Human Bronchial Tree”, Series on Biomechanics, 23:1 (2007), 5–18

[12] T. Gemci, V. Ponyavin, Y. Chen, H. Chen, R. Collins, “Computational model of airflow in upper 17 generations of human respiratory tract”, Journal of Biomechanics, 41 (2008), 2047–2054 | DOI

[13] P. V. Trusov, N. V. Zaitseva, M. Yu. Tsinker, “Modeling of human breath: conceptual and mathematical statements”, Mathematical Biology and Bioinformatics, 11:1 (2016), 64–80 | DOI | MR

[14] P. V. Trusov, N. V. Zaitseva, M. Yu. Tsinker, A. V. Babushkina, “Modelling dusty air flow in the human respiratory tract”, Ross. Zh. Biomekhaniki, 22:3 (2018), 301–314 | DOI

[15] J. Choi, Multiscale numerical analysis of airflow in CT-based subject specific breathing human lungs, PhD Dissertation, University of Iowa, Iowa, 2011, 259 pp.

[16] A. W. Ham, D. H. Cormack, Ham's Histology, Lippincott, Philadelphia, 1979

[17] Anthony L. Mescher, Junqueira's Basic Histology: Text and Atlas, 13th Edition, McGraw Hill Medical, New York, 2013, 560 pp.