Geodesic
Method of constructing an asymmetric human bronchial tree in normal and pathological cases
Matematičeskaâ biologiâ i bioinformatika, Tome 15 (2020), pp. t21-t31.

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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. 
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A. E. Medvedev. Method of constructing an asymmetric human bronchial tree in normal and pathological cases. Matematičeskaâ biologiâ i bioinformatika, Tome 15 (2020), pp. t21-t31. http://geodesic.mathdoc.fr/item/MBB_2020_15_a1/

[1] E. R. Veibel, Morfometriya legkikh cheloveka, Meditsina, M., 1970, 176 pp.

[2] A. E. Medvedev, P. S. Gafurova, “Analiticheskoe postroenie polnogo bronkhialnogo dereva cheloveka v norme i pri obstruktivnoi bolezni legkikh”, Matem. biologiya i bioinform., 14, Suppl. (2019), t62–t75 <ext-link ext-link-type='doi' href='https://doi.org/10.17537/2019.14.162'>10.17537/2019.14.162</ext-link>

[3] Y. Zhao, B. B. Lieber, “Steady inspiratory flow in a model symmetric bifurcation”, ASME Journal of Biomechanical Engineering, 116 (1994), 488–496 <ext-link ext-link-type='doi' href='https://doi.org/10.1115/1.2895800'>10.1115/1.2895800</ext-link>

[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 <ext-link ext-link-type='doi' href='https://doi.org/10.1115/1.2796064'>10.1115/1.2796064</ext-link>

[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 <ext-link ext-link-type='doi' href='https://doi.org/10.1016/j.resp.2004.03.004'>10.1016/j.resp.2004.03.004</ext-link>

[6] T. Heistracher, W. Hofmann, “Physiologically realistic models of bronchial airway bifurcations”, J. Aerosol Sci, 26:3 (1995), 497–509 <ext-link ext-link-type='doi' href='https://doi.org/10.1016/0021-8502(94)00113-D'>10.1016/0021-8502(94)00113-D</ext-link>

[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 <ext-link ext-link-type='doi' href='https://doi.org/10.1152/japplphysiol.00795.2004'>10.1152/japplphysiol.00795.2004</ext-link>

[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 <ext-link ext-link-type='doi' href='https://doi.org/10.1051/epjconf/20134501079'>10.1051/epjconf/20134501079</ext-link>

[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 <ext-link ext-link-type='doi' href='https://doi.org/10.1002/cnm.2830'>10.1002/cnm.2830</ext-link><ext-link ext-link-type='mr-item-id' href='http://mathscinet.ams.org/mathscinet-getitem?mr=3670871'>3670871</ext-link>

[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 <ext-link ext-link-type='doi' href='https://doi.org/10.1080/19942060.2015.1004819'>10.1080/19942060.2015.1004819</ext-link>

[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 <ext-link ext-link-type='doi' href='https://doi.org/10.1016/j.jbiomech.2007.12.019'>10.1016/j.jbiomech.2007.12.019</ext-link>

[13] P. V. Trusov, N. V. Zaitseva, M. Yu. Tsinker, “Modelirovanie protsessa dykhaniya cheloveka: kontseptualnaya i matematicheskaya postanovki”, Matem. biologiya i bioinform., 11:1 (2016), 64–80 <ext-link ext-link-type='doi' href='https://doi.org/10.17537/2016.11.64'>10.17537/2016.11.64</ext-link><ext-link ext-link-type='zbl-item-id' href='https://zbmath.org/?q=an:06658153'>06658153</ext-link>

[14] P. V. Trusov, N. V. Zaitseva, M. Yu. Tsinker, A. V. Babushkina, “Modelirovanie techeniya zapylennogo vozdukha v respiratornom trakte”, Rossiiskii zhurnal biomekhaniki, 22:3 (2018), 301–314 <ext-link ext-link-type='doi' href='https://doi.org/10.15593/RZhBiomeh/2018.3.03'>10.15593/RZhBiomeh/2018.3.03</ext-link>

[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. Khem, D. Kormak, Gistologiya, v. 4, Mir, M., 1983, 245 pp.

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