Journal of Pharmacokinetics and Pharmacodynamics

, Volume 39, Issue 5, pp 415–428 | Cite as

A geometrical approach to the PKPD modelling of inhaled bronchodilators

  • Claudio Gaz
  • George Cremona
  • Simona Panunzi
  • Beverley Patterson
  • Andrea De Gaetano
Original Paper


The present work introduces a new method to model the pharmacokinetics (PK) and pharmacodynamics (PD) of an inhaled dose of bronchodilator, alternative to classic compartmental representations or computational fluid dynamics. A five compartment PK model comprising alimentary tract absorption (gut), bronchial tree mucosa, bronchial muscles, plasma, and elimination/excretion pathways has been developed. Many anatomical and physiological features of the bronchial tree depend on bronchial generation or on mean distance from the larynx. Among these are diameters, resistances, and receptor density, which determine together the local response to the inhaled drug; integrating these local responses over the whole bronchial tree allows an approximation of total bronchodilator response and airflow resistance. While the PK part of the model reflects classical compartmental assumptions, the PD part adds a simplified geometrical and functional description of the bronchial tree to a typical empirical model of local effect on bronchial muscle, leading to the direct computation of the approximate forced expiratory volume in 1 s (FEV1). In the present work the construction of the model is detailed, with reference to literature data. Simulation of a hypothetical asthmatic subject is employed to illustrate the behaviour of the model in representing the evolution over time of the distribution and pharmacological effect of an inhaled dose of a bronchodilator. The relevance of particle size and drug formulation diffusivity on therapeutic efficacy is discussed.


Inhalation therapy Bronchodilators Mathematical models Ventilation FEV1 



The authors thank an anonymous Reviewer whose insightful and detailed comments were instrumental in improving the model and substantially changing the manuscript. This research has been supported by Novartis Pharma AG, Basel, Switzerland.


  1. 1.
    Agoram BM, Milligan PA, van der Graaf PH (2008) A non-parametric method to analyse time-course of effect in the absence of pharmacokinetic data: application to inhaled bronchodilators. Eur J Pharm Sci 34:250–256PubMedCrossRefGoogle Scholar
  2. 2.
    Anjilvel S, Asgharian B (1995) A multiple-path model of particle deposition in the rat lung. Fundam Appl Toxicol 28:41–50PubMedCrossRefGoogle Scholar
  3. 3.
    Applied Research Associates, Inc. Multiple-path particle dosimetry model (MPPD v. 2.11). Source:
  4. 4.
    Barnes PJ (2004) Distribution of receptor targets in the lung. Proc Am Thorac Soc 1:345–351PubMedCrossRefGoogle Scholar
  5. 5.
    Chalupa DC, Morrow PE, Oberdorster G, Utell MJ, Frampton MW (2004) Ultrafine particle deposition in subjects with asthma. Environ Health Perspect 112:879–882PubMedCrossRefGoogle Scholar
  6. 6.
    Crapo RO, Morris AH, Gardner RM (1981) Reference spirometric values using techniques and equipment that meet ATS recommendations. Am Rev Respirat Dis 123:659–664Google Scholar
  7. 7.
    Derendorf H (2007) Pharmacokinetic and pharmacodynamic properties of inhaled ciclesonide. J Clin Pharmacol 47:782–789PubMedCrossRefGoogle Scholar
  8. 8.
    Derendorf H, Meibohm B (1999) Modeling of pharmacokinetic/pharmacodynamic (PK/PD) relationships: concepts and perspectives. Pharm Res 16:176–185PubMedCrossRefGoogle Scholar
  9. 9.
    Fleming JS, Hashish AH, Conway JH, Nassim MA, Holgate ST, Halson P, Moore E, Bailey AG, Martonen TB (1996) Assessment of deposition of inhaled aerosol in the respiratory tract of man using three-dimensional multimodality imaging and mathematical modeling. J Aerosol Med 9:317–327PubMedCrossRefGoogle Scholar
  10. 10.
    Grimby G, Soderholm B (1963) Spirometric studies in normal subjects. III. Static lung volumes and maximum voluntary ventilation in adults with a note on physical fitness. Acta Med Scand 173:199–206Google Scholar
  11. 11.
    Jaafar-Maalej C, Andrieu V, Elaissari A, Fessi H (2009) Assessment methods of inhaled aerosols: technical aspects and applications. Expert Opin Drug Deliv 6:941–959PubMedCrossRefGoogle Scholar
  12. 12.
    Kawashiro T, Carles AC, Perry SF, Piiper J (1975) Diffusivity of various inert gases in rat skeletal muscle. Pflugers Arch 359:219–230PubMedCrossRefGoogle Scholar
  13. 13.
    Knight V, Yu CP, Gilbert BE, Divine GW (1988) Estimating the dosage of ribavirin aerosol according to age and other variables. J Infect Dis 158:443–448PubMedCrossRefGoogle Scholar
  14. 14.
    Knudson RJ, Lebowitz MD, Holberg CJ, Burrows B (1983) Changes in the normal maximal expiratory flow-volume curve with growth and aging. Am Rev Respirat Dis 127:725–734Google Scholar
  15. 15.
    Levitzky MG (2007) Pulmonary physiology. McGraw-Hill Medical Publishing, New York Google Scholar
  16. 16.
    Martonen TB, Hwang D, Guan X, Fleming JS (1998) Supercomputer description of human lung morphology for imaging analysis. J Nucl Med 39:745–750PubMedGoogle Scholar
  17. 17.
    Martonen TB, Schroeter JD, Fleming JS (2007) 3D in silico modeling of the human respiratory system for inhaled drug delivery and imaging analysis. J Pharm Sci 96:603–617PubMedCrossRefGoogle Scholar
  18. 18.
    Meltzer EO, Kuna P, Nolte H, Nayak S, Laforce C (2011) Mometasone furoate/formoterol reduces asthma deteriorations and improves lung function. Eur Respir JGoogle Scholar
  19. 19.
    Morris JF (1983) Citation classic: spirometric standards for healthy nonsmoking adults. Current contents/life sciences 21Google Scholar
  20. 20.
    Musante CJ, Schroeter JD, Rosati JA, Crowder TM, Hickey AJ, Martonen TB (2002) Factors affecting the deposition of inhaled porous drug particles. J Pharm Sci 91:1590–1600PubMedCrossRefGoogle Scholar
  21. 21.
    Pedley TJ, Schroter RC, Sudlow MF (1970) The prediction of pressure drop and variation of resistance within the human bronchial airways. Respir Physiol 9:387–405PubMedCrossRefGoogle Scholar
  22. 22.
    Persons DD, Hess GD, Muller WJ, Scherer PW (1987) Airway deposition of hygroscopic heterodispersed aerosols: results of a computer calculation. J Appl Physiol 63:1195–1204PubMedGoogle Scholar
  23. 23.
    Roberts CM, Macrae KD, Winning AJ, Adams L, Seed WA (1991) Reference values and prediction equations for normal lung-function in a nonsmoking white urban-population. Thorax 46:643–650PubMedCrossRefGoogle Scholar
  24. 24.
    Rohatagi S, Arya V, Zech K, Nave R, Hochhaus G, Jensen BK, Barrett JS (2003) Population pharmacokinetics and pharmacodynamics of ciclesonide. J Clin Pharmacol 43:365–378PubMedCrossRefGoogle Scholar
  25. 25.
    Stinson JM, Mcpherson GL, Hicks K, Scott V, Sykes R, Cobbs W (1979) Spirometric standards for healthy black adults. Am Rev Respirat Dis 119:237Google Scholar
  26. 26.
    Stober W, Morrow PE, Hoover MD (1989) Compartmental modeling of the long-term retention of insoluble particles deposited in the alveolar region of the lung. Fundam Appl Toxicol 13:823–842PubMedCrossRefGoogle Scholar
  27. 27.
    Stuart BO (1973) Deposition of inhaled aerosols. Arch Intern Med 131:60–73PubMedCrossRefGoogle Scholar
  28. 28.
    Tran CL, Jones AD, Cullen RT, Donaldson K (1999) Mathematical modeling of the retention and clearance of low-toxicity particles in the lung. Inhal Toxicol 11:1059–1076PubMedCrossRefGoogle Scholar
  29. 29.
    van den Berg BT, Derks MG, Koolen MG, Braat MC, Butter JJ, van Boxtel CJ (1999) Pharmacokinetic/pharmacodynamic modelling of the eosinopenic and hypokalemic effects of formoterol and theophylline combination in healthy men. Pulm Pharmacol Ther 12:185–192PubMedCrossRefGoogle Scholar
  30. 30.
    Weibel ER (1963) Morphometry of the human lung. Springer, HeidelbergGoogle Scholar
  31. 31.
    Weibel ER, Gomez DM (1962) Architecture of the human lung. Use of quantitative methods establishes fundamental relations between size and number of lung structures. Science 137:577–581PubMedCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Claudio Gaz
    • 1
  • George Cremona
    • 2
  • Simona Panunzi
    • 1
  • Beverley Patterson
    • 3
  • Andrea De Gaetano
    • 1
  1. 1.Consiglio Nazionale Delle RicercheIstituto di Analisi Dei Sistemi ed Informatica “A. Ruberti”RomeItaly
  2. 2.Unità Funzionale di Pneumologia e Fisiopatologia RespiratoriaIstituto Scientifico Universitario San RaffaeleMilanItaly
  3. 3.Novartis Pharmaceutical UK LimitedWest SussexUK

Personalised recommendations