Mathematical model of airflow and solid particles transport in the human nasal cavity

P. V. Trusov ; N. V. Zaitseva ; M. Yu. Cinker ; A. V. Nekrasova

Matematičeskaâ biologiâ i bioinformatika, Tome 18 (2023) no. 3, pp. t1-t16

Résumé

As part of the mathematical model of the human respiratory system, a submodel is considered for the study of the non-steady airflow with solid particles (suspended particulate matter (PM) / dust particles) and the deposition of particles of various sizes in the human nasal cavity. It is assumed that the nasal cavity is divided by the bone-cartilaginous septum into two symmetrical (relative to the nasal septum) parts; the average geometry of the right part of the human nasal cavity is considered. The inhaled air is considered as a multiphase mixture of homogeneous single-component gas and solid dust particles. The Euler–Lagrange approach to modeling the motion of a multiphase mixture is used: a viscous liquid model is used to describe the motion of the carrier gas phase; the carried phase (dust particles) is modeled as separate inclusions of various sizes. The process of heating the inhaled air due to its contact with the walls is also taken into account. The features of the unsteady flow of a multiphase air mixture with dust particles were obtained using Ansys CFX for several scenarios. It has been noted that when studying the airflow in the nasal cavity, it is necessary to take into account the presence of turbulence, for which it is proposed to use the k$k$–$\omega$ model. The velocity fields of inhaled air in the nasal cavity have been obtained; presented temperature distributions in the nasal cavity at different time points; made estimates of air heating at different temperatures of inhaled air; gave estimates of the proportion of deposited particles in the nasal cavity depending on the particle size for real machine-building production; presented trajectories of movement of suspended particles. Thus, it is shown that more than 99.7% of particles with a diameter of more than 10 microns deposit in the human nasal cavity; as the particle diameter and mass decrease, the proportion of deposited particles decreases. Suspended particles with a size of less than 2.5 microns almost do not deposit in the nasal cavity. They can penetrate deeper into the lower airways and lungs of a person with the inhaled air and, having fibrogenic and toxic effect, can cause diseases. The results obtained are in good agreement with the results of individual studies performed by other scientists. Further development of the model involves studying airflow in the human lungs and modeling the formation of diseases caused by the harmful effects of environmental factors (including dust particles) entering the human body by inhalation.

Bibliographie

[1] B. Brunekreef, S. T. Holgate, “Air pollution and health”, Lancet, 360 (2002), 1233–1242 | DOI | DOI

[2] N. V. Zaitseva, O. Iu. Ustinova, A. I. Aminova, Hygienic aspects of children's health disorders under the influence of chemical factors of the environment, ed. Zaitseva N.V., Perm', 2011, 489 pp. (in Russ.)

[3] Y. F. Xing, Y. H. Xu, M. H. Shi, Y. X. Lian, “The impact of PM2.5 on the human respiratory system”, Journal of Thoracic Disease. 2016, 8:1, E69–E74 | DOI | MR | DOI | MR

[4] E. M. Vlasova, A. A. Vorobeva, T. A. Ponomareva, “Peculiarities of cardiovascular pathology formation in workers of titanium-magnesium production”, Russian Journal of Occupational Health and Industrial Ecology, 9 (2017), 38 (in Russ.)

[5] I. V. Tikhonova, M. A. Zemlyanova, Yu. V. Kol'dibekova, E. V. Peskova, A. M. Ignatova, “Hygienic assessment of aerogenic exposure to particulate matter and its impacts on morbidity with respiratory diseases among children living in a zone influenced by emissions from metallurgic production”, Health Risk Analysis, 3 (2020), 61–69 | DOI | DOI

[6] E. M. Vlasova, O. Yu. Ustinova, A. E. Nosov, S. Yu. Zagorodnov, “Peculiarities of respiratory organs diseases in smelters dealing with titanium alloys under combined exposure to fine-disperse dust and chlorine compounds”, Hygiene and Sanitation, 98:2 (2019), 153–158 (in Russ.) | DOI | DOI

[7] A. L. Grebenev, Propedeutics of Internal Medicine, M., 2001, 592 pp. (in Russ.)

[8] B. S. Shkliar, Diagnostics of internal diseases, Kiev, 1972, 516 pp. (in Russ.)

[9] P. V. Trusov, N. V. Zaitseva, D. A. Kiryanov, M. R. Kamaltdinov, M. Ju. Cinker, V. M. Chigvintsev, D. V. Lanin, “A Mathematical model for evolution of human functional disorders influenced by environment factors”, Mathematical Biology and Bioinformatics, 7:2 (2012), 589–610 (in Russ.) | DOI | MR | DOI | MR

[10] P. V. Trusov, N. V. Zaitseva, M. Yu. Tsinker, “Modeling of human breath: conceptual and mathematical statements”, Mathematical Biology and Bioinformatics, 11:1 (2016), 4–80 (in Russ.) | DOI | MR | DOI | MR

[11] M. R. Kamaltdinov, “3D modeling of antroduodenal zone motility of digestive track for the purpose of health risks evaluation with peroral exposition to chemicals”, Health Risk Analysis, 2 (2014), 68–75 | DOI | DOI

[12] D. A. Kiryanov, D. V. Lanin, V. M. Chigvintsev, “Mathematical model of immune and neuroendocrine systems functioning with regard to evolution of organ synthetic function violations”, Health Risk Analysis, 3 (2015), 68–72 | DOI | DOI

[13] P. V. Trusov, N. V. Zaitseva, M. Yu. Tsinker, A. V. Babuskina, “Modelling dusty air flow in the human resperatory tract”, Russian Journal of Biomechanics, 22:3 (2018), 301–314 (in Russ.)

[14] P. V. Trusov, N. V. Zaitseva, M. Yu. Tsinker, “On modeling of airflow in human lungs: constitutive relations to describe deformation of porous medium”, PNRPU Mechanics Bulletin, 4 (2020), 165–174 (in Russ.) | DOI | DOI

[15] J. Bruning, T. Hildebrandt, W. Heppt, N. Schmidt, H. Lamecker, A. Szengel, N. Amiridze, H. Ramm, M. Bindernagel, S. Zachow, L. Goubergrits, “Characterization of the Airflow within an Average Geometry of the Healthy Human Nasal Cavity”, Scientific Reports, 10:1 (2020), 3755 | DOI | DOI

[16] V. L. Ganimedov, M. I. Muchnaya, A. S. Sadovskii, “Air flow in the human nasal cavity. Results of mathematical modelling”, Russian Journal of Biomechanics, 19:1 (2015), 31–44

[17] V. M. Fomin, V. N. Vetlutsky, V. L. Ganimedov, M. I. Muchnaya, V. N. Shepelenko, M. N. Melnikov, A. A. Savina, “Air flow in the human nasal cavity”, Journal of Applied Mechanics and Technical Physics, 51:2 (2010), 233–240 | DOI | Zbl | DOI | Zbl

[18] A. S. Sadovskii, L. Iu. Bosykh, V. L. Ganimedov, M. I. Muchnaia, The XI All-Russian Congress on Basic Problems of Theoretical and Applied Mechanics, abstracts, 2015, 3298–3300 (in Russ.)

[19] V. L. Ganimedov, M. I. Muchnaya, “Numerical simulation of particle deposition in the human nasal cavity”, Thermophysics and Aeromechanics, 27:2 (2020), 303–312 | DOI | DOI

[20] A. Voronin, G. Luk'yanov, R. Neronov, “Computational modeling of airflow in nonregular shaped channels”, Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 3:85 (2013), 113–118 (in Russ.)

[21] R. V. Neronov, G. N. Luk'yanov, A. A. Rassadina, A. A. Voronin, A. G. Malyshev, “The effect of the nasal cavity form on air flow distribution during inhalation”, Russian Otorhinolaryngology, 1:86 (2017), 83–94 (in Russ.) | DOI | DOI

[22] G. N. Lukyanov, A. A. Voronin, A. A. Rassadina, “Simulation of convective flows in irregular channels on the example of the human nasal cavity and paranasal sinuses”, Technical Physics, 62:3 (2017), 484–489 | DOI | DOI

[23] H. Tang, J. Y. Tu, H. F. Li, B. Au-Hijleh, C. C. Xue, C. G. Li, “Dynamic Analysis of Airflow Features in a 3D Real-Anatomical Geometry of the Human Nasal Cavity”, 15th Australasian Fluid Mechanics Conference (Sydney, Australia), 2004 (accessed 15.06.2021) https://www.aeromech.usyd.edu.au/15afmc/proceedings/papers/AFMC00174.pdf

[24] P. Zamankhan, G. Ahmadi, Z. Wang, P. K. Hopke, Cheng Y-S, W. S. Su, D. Leonard, “Airflow and Deposition of Nano-Particles in a Human Nasal Cavity”, Aerosol Science and Technology, 40 (2006), 463–476 | DOI | DOI

[25] S. E. Saghaian, A. R. Azimian, R. Dadkhah S. Jalilvand, S. M. Saghaian, “Computational analysis of airflow and particle deposition fraction in the upper part of the human respiratory system”, Biology, Engineering and Medicine, 3:6 (2018), 6–9 | DOI | DOI

[26] D. J. Doorly, D. J. Taylor, A. M. Gambaruto, R. C. Schroter, N. Tolley, “Nasal architecture: form and flow”, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2008 | DOI | Zbl | DOI | Zbl

[27] D. J. Doorly, D. J. Taylor, R. C. Schroter, “Mechanics of airflow in the human nasal airways”, Respiratory Physiology and Neurobiology, 163 (2008), 100–110 | DOI | DOI

[28] K. Inthavong, P. Das, N. Singh, J. Sznitman, “In silico approaches to respiratory nasal flows: A review”, Journal of Biomechanics, 97 (2019), 109434 | DOI | DOI

[29] R. Subramaniam, R. Richardson, K. Morgan, J. Kimbell, R. Guilmette, “Computational fluid dynamics simulations of inspiratory airflow in the human nose and nasopharynx”, Inhalation Toxicology, 1998, 91–120 | DOI | DOI

[30] K. Zhao, P. W. Scherer, S. A. Hajiloo, P. Dalton, “Effect of anatomy on human nasal air flow and odorant transport patterns: Implications for olfaction”, Chemical Senses, 29:5 (2004), 365–379 | DOI | DOI

[31] Y. D. Shang, K. Inthavong, J. Y. Tu, “Detailed micro-particle deposition patterns in the human nasal cavity influenced by the breathing zone”, Computers and Fluids, 114 (2015), 141–150 | DOI | MR | Zbl | DOI | MR | Zbl

[32] G. J. Garcia, N. Bailie, D. A. Martins, J. S. Kimbell, “Atrophic rhinitis: A CFD study of air conditioning in the nasal cavity”, Journal of Applied Physiology, 103 (2007), 1082–1092 | DOI | DOI

[33] Q. J. Ge, K. Inthavong, J. Y. Tu, “Local deposition fractions of ultrafine particles in a human nasal-sinus cavity CFD model”, Inhalation Toxicology, 24:8 (2012), 492–505 | DOI | DOI

[34] V. Goodarzi-Ardakani, M. Taeibi-Rahni, M. R. Salimi, G. Ahmadi, “Computational simulation of temperature and velocity distribution in human upper respiratory airway during inhalation of hot air”, Respiratory Physiology and Neurobiology, 223 (2016), 49–58 | DOI | DOI

[35] I. Horschler, C. Brucker, W. Schr?oder, M. Meinke, “Investigation of the impact of the geometry on the nose flow”, European Journal of Mechanics, B/Fluids, 25 (2006), 471–490 | DOI | Zbl | DOI | Zbl

[36] J. Wen, K. Inthavong, J. Tu, S. Wang, “Numerical simulations for detailed airflow dynamics in a human nasal cavity”, Respiratory Physiology and Neurobiology, 161 (2008), 125–135 | DOI | DOI

[37] J. Lindemann, H. J. Brambs, T. Keck, K. M. Wiesmiller, G. Rettinger, D. Pless, “Numerical simulation of intranasal airflow after radical sinus surgery”, American Journal of Otolaryngology Head and Neck Medicine and Surgery, 26:3 (2005), 175–180 | DOI | DOI

[38] I. V. Mai, N. V. Zaitseva, T. S. Ulanova, S. A. Vekovshinina, S. Iu. Zagorodnov, A. A. Kokoulina, E. V. Sedusova, E. V. Popova, Industrial dust atlas. Dust from engineering, metallurgical, mining, mining and processing industries and non-ferrous metallurgy enterprises, Perm', 2014, 285 pp. (in Russ.)

[39] Y. Liu, M. R. Johnson, E. A. Matida, S. Kherani, J. Marsan, “Creation of a standardized geometry of the human nasal cavity”, J. Appl. Physiol., 106 (2009), 784–795 | DOI | DOI

[40] E. I. Borziak, L. I. Volkova, E. A. Dobrovol'skaia, V. S. Revazov, M. R. Sapin, Human anatomy, v. 1, ed. M.R. Sapin, M., 1993, 544 pp. (in Russ.)

[41] Y. Liu, E. A. Matida, M. R. Johnson, “Experimental measurements and computational modeling of aerosol deposition in the Carleton-Civic standardized human nasal cavity”, Journal of Aerosol Science, 41 (2010), 569–586 | DOI | DOI

[42] K. Inthavong, J. Wen, J. Tu, Z. Tian, “From CT scans to CFD modelling-fluid and heat transfer in a realistic human nasal cavity”, Eng. Appl. Comput. Fluid Mech., 3:3 (2009), 321–335 | DOI | DOI

[43] J. M. Garcia, J. D. Schroeter, J. S. Kimbell, “Sniffing out airflow and transport processes in the nasal cavity”, Fluent News Appl. Comput. Fluid Dynamics, 15:3 (2006), 3–5

[44] B. A. Katsnel'son, O. G. Alekseeva, L. I. Privalova, E. V. Polzik, Pneumoconiosis: pathogenesis and biological prevention, Ekaterinburg, 1995, 325 pp. (in Russ.)

[45] J. D. Brain, P. A. Valberg, “Models of lung retention based on the ICRP task group report”, Arch. Environ. Health, 28:1 (1974), 1–11 | DOI | DOI