MATHEMATICAL MODELING OF THE TARGETED ATOMIZATION OF MEDICINAL DRUGS INTO ANATOMICAL AIRWAYS

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Abstract

The known approaches to the mathematical modeling of the processes of targeted atomization of medical drugs into the airways are presented. The testified and promising solutions are distinguished. The governing physical laws, the important effects, and the factors that have the significant influence are analyzed. The problems, which have not been solved to the full extent are formulated. The promising directions of the development of the systems of drug atomization in anatomical airways are determined.

About the authors

D. V Antonov

National Research Tomsk Polytechnic University

Email: dva14@tpu.ru
Tomsk, Russia

S. S Sazhin

National Research Tomsk Polytechnic University; Advanced Engineering Centre, School of Architecture, Technology and Engineering, University of Brighton; Kutateladze Institute of Thermophysics

Tomsk, Russia; Brighton, UK; Novosibirsk, Russia

P. A Strizhak

National Research Tomsk Polytechnic University

Tomsk, Russia

O. V Nagatkina

Sechenov First Moscow State Medical University

Moscow, Russia

References

  1. GBD 2017: a fragile world // Lancet. 2018. V. 392. № 1683.
  2. Collaborators GBD Chronic Respiratory Disease. Prevalence and attributable health burden of chronic respiratory diseases, 1990–2017: a systematic analysis for the Global Burden of Disease Study 2017 // Lancet Respir. Med. 2020. V. 8. P. 585–596. https://doi.org/10.1016/S2213-2600(20)30105-3
  3. Labouta H.I., Langer R., Cullis P.R., Merkel O.M., Prausnitz M.R., Gomaa Y., Nogueira S.S., Kumeria T. Role of drug delivery technologies in the success of COVID-19 vaccines: a perspective // Drug Deliv. Transl. Res. 2022. V. 12. P. 2581–2588. https://doi.org/10.1007/s13346-022-01146-1
  4. Laube B.L., Janssens H.M., Jongh F.H.C., Devadason S.G., Dhand R., Diot P., Everard M.L., Horvath I., Navalesi P., Voshaar T., Chrystyn H., European Respiratory Society, International Society for Aerosols in Medicine. What the pulmonary specialist should know about the new inhalation therapies // Eur. Respir. J. 2011. V. 37. No. 6. P. 1308. https://doi.org/10.1183/09031936.00166410
  5. Newman S.P., Pavia D., Garland N., Clarke S.W. Effects of various inhalation modes on the deposition of adioactive pressurized aerosols // Eur. J. Respir. Dis. Suppl. 1982. V. 63. P. 57-65.
  6. Любимов Г.А., Скобелева И.М. Математическая модель форсированного выдоха // Изв. АН СССР. МЖГ. 1991. № 4. С. 3–10.
  7. Авдеев С.Н. Хроническая обструктивная болезнь легких: обострения // Пульмонология. 2013. № 3. С. 5–19. https://doi.org/10.18093/0869-0189-2013-0-3-5-19
  8. Дьяченко А.И., Любимов Г.А., Скобелева И.М., Стронгин М.М. Обобщение математической модели легких для описания интенсивности трахеальных звуков форсированного выдоха // Изв. РАН. МЖГ. 2011. № 1. С. 21–29.
  9. Любимов Г.А. Обоснование модели неоднородного легкого для описания форсированного выдоха // Изв. РАН. МЖГ. 1999. №5. С. 29-38.
  10. Lippmann M., Yeates D.B., Albert R.E. Deposition, retention, and clearance of inhaled particles // Br. J. Ind. Med. 1980. V. 37. No. 4. P. 337–362. https://doi.org/10.1136/oem.37.4.337
  11. Nahar K., Gupta N., Gauvin R., Absar S., Patel B., Gupta V., Khademhosseini A., Ahsan F. In vitro, in vivo and ex vivo models for studying particle deposition and drug absorption of inhaled pharmaceuticals // Eur. J. Pharm. Sci. 2013. V. 49. P. 805–818. https://doi.org/10.1016/j.ejps.2013.06.004
  12. Li R., Jia Y., Kong X., Nie Y., Deng Y., Liu Y. Novel drug delivery systems and disease models for pulmonary fibrosis // J. Control. Release. 2022. V. 348. P. 95–114. https://doi.org/10.1016/J.JCONREL.2022.05.039
  13. Sakagami M. In vitro, ex vivo and in vivo methods of lung absorption for inhaled drugs // Adv. Drug. Deliv. Rev. 2020. V. 63. P. 161–162. https://doi.org/10.1016/j.addr.2020.07.025
  14. Agnew J.E. Bronchiolar aerosol deposition and clearance // Eur. Respir. J. 1996. V. 9. No. 6. P. 1118–1122. https://doi.org/10.1183/09031936.96.09061118
  15. Svartengren K., Philipson K., Svartengren M., Anderson M., Camner P. Tracheobronchial deposition and clearance in small airways in asthmatic subjects // Eur. Respir. J. 1996. V. 9. No. 6. P. 1123–1129. https://doi.org/10.1183/09031936.96.09061123
  16. Camner P., Anderson M., Philipson K., Bailey A., Hashish A., Jarvis N., Bailey M., Svartengren M. Human bronchiolar deposition and retention of 6-, 8- and 10-micrograms particles // Exp. Lung. Res. 1997. V. 23. No. 6. P. 517–535. https://doi.org/10.3109/01902149709039241
  17. Martin A.R., Moore C.P., Finlay W.H. Models of deposition, pharmacokinetics, and intersubject variability in respiratory drug delivery // Expert. Opin. Drug. Deliv. 2018. V. 15. No. 12. P. 1175–1188. https://doi.org/10.1080/17425247.2018.1544616
  18. Newman S.P. Drug delivery to the lungs: challenges and opportunities // Ther. Deliv. 2017. V. 8. No. 8. P. 647–661. https://doi.org/10.4155/tde-2017-0037
  19. Lalas A., Nousias S., Kikidis D., Lalos A., Arvanitis G., Sougles C., Moustakas K., Votis K., Verbanck S., Usmani O., Tzovaras D. Substance deposition assessment in obstructed pulmonary system through numerical characterization of airflow and inhaled particles attributes // BMC Med. Inf. Decis. Mak. 2017. V. 17. No. 173. https://doi.org/10.1186/s12911-017-0561-y
  20. Fink J.B. Inhalers in Asthma Management: Is Demonstration the Key to Compliance? // Respir. Care. 2005. V. 50. No. 5. P. 598–600.
  21. Darquenne C. Deposition Mechanisms // J. Aerosol. Med. Pulm. Drug. Deliv. 2020. V. 33. No. 4. P. 181–185. https://doi.org/10.1089/jamp.2020.29029
  22. Darquenne C. Aerosol deposition in health and disease // J. Aerosol. Med. Pulm. Drug. Deliv. 2012. V. 25. P. 140–147. https://doi.org/ 10.1089/jamp.2011.0916
  23. Leach C., Colice G.L., Luskin A. Particle size of inhaled corticosteroids: Does it matter? // J. Allergy Clin. Immunol. 2009. V. 124. P. 88–93. https://doi.org/10.1016/j.jaci.2009.09.050
  24. Tsuda A., Henry F.S., Butler J.P. Particle transport and deposition: basic physics of particle kinetics // Compr. Physiol. 2013. V. 3. No. 4. P. 1437–1471. https://doi.org/10.1002/cphy.c100085
  25. Aleksic I., Parojcic J., Duric Z. Computational fluid dynamics: Applications in pharmaceutical technology // Comput. Appl. Pharm. Technol. Deliv. Syst. Dos. Forms, Pharm. Unit Oper. 2023. P. 285–315. https://doi.org/10.1016/B978-0-443-18655-4.00007-8
  26. Modaresi M.A., Shirani E. Developing a novel mucociliary clearance boundary condition (MCBC) to simulate microscale particle transfers inside the respiratory tract system without generating extra computational cells // Chaos, Solitons & Fractals. 2024. V. 179. No. 114463. https://doi.org/10.1016/J.CHAOS.2024.114463
  27. Verbanck S., Ghorbaniasl G., Biddiscombe M.F., Dragojlovic D., Ricks N., Lacor C., Ilsen B., Mey J., Schuermans D., Richard Underwood S., Barnes P.J., Vincken W. Inhaled Aerosol Distribution in Human Airways: A ScintigraphyGuided Study in a 3D Printed Model // J. Aerosol Med. Pulm. Drug Deliv. 2016. V. 29. P. 525–533. https://doi.org/10.1089/jamp.2016.1291
  28. Wedel J., Steinmann P., Strakl M., Hribersek M., Cui Y., Ravnik J. Anatomy matters: The role of the subject-specific respiratory tract on aerosol deposition — A CFD study // Comput. Methods Appl. Mech. Eng. 2022. V. 401. No. 115372. https://doi.org/10.1016/J.CMA.2022.115372
  29. Prinz F., Pokorny J., Elcner J., Lzal F., Misk O., Maly M., Belka M., Hafen N., Kummerlander A., Krause M.J., Jedelsky J., Jcha M. Comprehensive experimental and numerical validation of Lattice Boltzmann fluid flow and particle simulations in a child respiratory tract // Comput. Biol. Med. 2024. V. 170. No. 107994. https://doi.org/10.1016/J.COMPBIOMED.2024.107994
  30. Weibel E.R. Morphometry of the human lung. Berlin, 1963. 151 с.
  31. Kitaoka H., Takaki R., Suki B. A three-dimensional model of the human airway tree // J. Appl. Physiol. 1999. V. 87. P. 2207–2217. https://doi.org/10.1152/jappl.1999.87.6.2207
  32. Heistracher T., Hofmann W. Physiologically realistic models of bronchial airway bifurcations // J. Aerosol Sci. 1995. V. 26. P. 497-509. https://doi.org/10.1016/0021-8502(94)00113-D
  33. Трусов П.В., Зайцева Н.В., Цинкер М.Ю. Моделирование процесса дыхания человека: концептуальная и математическая постановки // Math. Biol. Bioinforma. 2016. V. 11. P. 64–80. https://doi.org/10.17537/2016.11.64
  34. Medvedev A.E., Fomin V.M., Gafurova P.S. Three-Dimensional Model of the Human Bronchial Tree-Modeling of the Air Flow in Normal and Pathological Cases // J. Appl. Mech. Tech. Phys. 2020. V. 61. P. 1–13. https://doi.org/10.1134/S0021894420010010
  35. Cheng K.-H., Cheng Y.-S., Yeh H.-C., Guilmette R.A., Simpson S.Q., Yang Y.-H., Swift D.L. In vivo measurements of nasal airway dimensions and ultrafine aerosol deposition in the human nasal and oral airways // J. Aerosol Sci. 1996. V. 27. P. 785–801. https://doi.org/10.1016/0021-8502(96)00029-8
  36. Zhang Z., Kleinstreuer C., Kim C. Micro-particle transport and deposition in a human oral airway model // J. Aerosol Sci. 2002. V. 33. P. 1635–1652. https://doi.org/10.1016/S0021-8502(02)00122-2
  37. Subramaniam R.P., Richardson R.B., Morgan K.T., Kimbell J.S., Guilmete R.A. Computational fluid dynamics simulations of inspiratory airflow in the human nose and nasopharynx // Inhal. Toxicol. 1998. V. 10. P. 91–120. https://doi.org/10.1080/089583798197772
  38. Wang J., Cai Y., Chen X., Sun B., Tao F. The effects of aerosol concentration on the evolution, transport, and deposition of hygroscopic droplets in the highly idealized MT model: A numerical study // Int. J. Heat Mass Transf. 2024. V. 219. No. 124916. https://doi.org/10.1016/j.ijheatmasstransfer.2023.124916
  39. Xi J., Longest P.W. Numerical predictions of submicrometer aerosol deposition in the nasal cavity using a novel drift flux approach // Int. J. Heat Mass Transf. 2008. V. 51. P. 5562–5577. https://doi.org/10.1016/j.ijheatmasstransfer.2008.04.037
  40. Jin H.H., Fan J.R., Zeng M.J., Cen K.F. Large eddy simulation of inhaled particle deposition within the human upper respiratory tract // J. Aerosol Sci. Sci. 2007. V. 38. P. 257–268. https://doi.org/10.1016/j.jaerosci.2006.09.008
  41. Martonen T.B., Zhang Z., Yue G., Musante C.J. 3-D particle transport within the human upper respiratory tract // J. Aerosol Sci. 2002. V. 33. P. 1095–1110. https://doi.org/10.1016/S0021-8502(02)00060-5
  42. Xu P., Sasmito A.P., Li C., Qiu S. Global and local transport properties of steady and unsteady flow in a symmetrical bronchial tree // Int. J. Heat Mass Transf. 2016. V. 97. P. 696–704. https://doi.org/10.1016/j.ijheatmasstransfer.2016.02.068
  43. Medvedev A.E., Golysheva P.S. Simulation of air motion in human lungs during breathing. Dynamics of liquid droplet precipitation in the case of medicine drug aerosols // Math. Biol. Bioinforma. 2022. V. 17. P. 422–438. https://doi.org/10.17537/2022.17.t14
  44. Medvedev A.E., Gafurova P.S. Analytical design of the human bronchial tree for healthy patients and patients with obstructive pulmonary diseases // Math. Biol. Bioinforma. 2019. V. 14. P. 635–648. https://doi.org/10.17537/2019.14.635
  45. Malve M., Barreras I., Lopez-Villalobos J.L., Ginel A., Doblare M. ` Computational fluid-dynamics optimization of a human tracheal endoprosthesis // Int. Commun. Heat Mass Transf. 2012. V. 39. P. 575–581. https://doi.org/10.1016/j.icheatmasstransfer.2012.03.014
  46. Malve M., del Palomar A.P., Trabelsi O., Lopez-Villalobos J.L., Ginel A., Doblare M. ` Modeling of the fluid structure interaction of a human trachea under different ventilation conditions // Int. Commun. Heat Mass Transf. 2011. V. 38. P. 10–15. https://doi.org/10.1016/j.icheatmasstransfer.2010.09.010
  47. Malve M., del Palomar A.P., Mena A., Trabelsi O., Lopez-Villalobos J.L., Ginel A., Panadero F., Doblare M. ` Numerical modeling of a human stented trachea under different stent designs // Int. Commun. Heat Mass Transf. 2011. V. 38. P. 855–862. https://doi.org/10.1016/j.icheatmasstransfer.2011.04.012
  48. Singh D. Numerical assessment of natural respiration and particles deposition in the computed tomography scan airway with a glomus tumour // Proc. Inst. Mech. Eng. Part E J. Process Mech. Eng. 2021. V. 235. P. 1945–1956. https://doi.org/10.1177/09544089211024063
  49. Kumar D., Singh D. Study on airflow and particle transport in In silico human respiratory tract // J. Braz. Soc. Mech. Sci. Eng. 2023. V. 45. No. 574. https://doi.org/10.1007/s40430-023-04358-9
  50. Luo H.Y., Liu Y. Modeling the bifurcating flow in a CT-scanned human lung airway // J. Biomech. 2008. V. 41. P. 2681–2688. https://doi.org/10.1016/J.JBIOMECH.2008.06.018
  51. De Backer J.W., Vos W.G., Gorle C.D., Germonpre P., Partoens B., Wuyts F.L., Parizel P.M., De Backer W. Flow analyses in the lower airways: Patient-specific model and boundary conditions // Med. Eng. Phys. 2008. V. 30. P. 872–879. https://doi.org/10.1016/J.MEDENGPHY.2007.11.002
  52. Ertbruggen C., Hirsch C., Paiva M. Anatomically based three-dimensional model of airways to simulate flow and particle transport using computational fluid dynamics // J. Appl. Physiol. 2005. V. 98. P. 970–980. https://doi.org/10.1152/japplphysiol.00795.2004
  53. Jin W., Xiao J., Ren H., Li C., Zheng Q., Tong Z. Three-dimensional simulation of impinging jet atomization of soft mist inhalers using the hybrid VOF-DPM model // Powder. Technol. 2022. V. 407. No. 117622. https://doi.org/10.1016/J.POWTEC.2022.117622
  54. Ari A., Fink J.B. Recent advances in aerosol devices for the delivery of inhaled medications // Expert. Opin. Drug. Deliv. 2020. V. 17. P. 133–144. https://doi.org/10.1080/17425247.2020.1712356
  55. Осипцов А.Н. Развитие полного лагранжева подхода для моделирования течений разреженных дисперсных сред (обзор) // Изв. РАН. МЖГ. 2024. № 1. С. 3–51.
  56. Голубкина И.В., Осипцов А.Н. Влияние примеси неиспаряющихся капель на структуру течения и температуру адиабатической стенки в сжимаемом двухфазном пограничном слое // Изв. РАН. МЖГ. 2019. № 3. С. 58–69.
  57. Meng S., Cui W., Lin S., Wang G., Hei Y., Deng B., Ma S., Zhang Z., Liu Y., Xie Y. Modeling the molecular interactions of budesonide with bovine serum albumin guides the rational preparation of nanoparticles for pulmonary delivery // J. Chinese Pharm. Sci. 2018. V. 27. No. 6. P. 415–428. https://doi.org/10.5246/jcps.2018.06.042
  58. Xie J.-F., Sazhin S.S., Cao B.-Y. Molecular dynamics study of the pro- cesses in the vicinity of the n-dodecane vapour/liquid interface // Phys. Fluids. 2011. V. 23. No. 112104. https://doi.org/10.1063/1.3662004

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