Chapter VIII: Modeling Deposition of Inhaled Particles
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1 Chapter VIII: Modeling Deposition of Inhaled Particles Kristin K. Isaacs1, Jacky A. Rosati2, and Ted B. Martonen3 1U.S. EPA, National Exposure Research Laboratory, Research Triangle Park, NC 2 U.S. EPA, National Homeland Security Research Center, Research Triangle Park, NC 3Cyberlung, Inc., Laguna Beach, CA Corresponding Author: Kristin Isaacs MD E205-02 U.S. EPA 109 T.W. Alexander Drive Research Triangle Park, NC 27711 [email protected] 2 AUTHOR ADDRESSES Kristin King Isaacs, Ph.D. MD E205-02 U.S. EPA 109 T.W. Alexander Drive Research Triangle Park, NC 27711 Jacky Ann Rosati, Ph.D. MD E343-06 U.S. EPA 109 T.W. Alexander Drive Research Triangle Park, NC 27709 Ted Martonen, Ph.D. CyberMedicine, Inc. 156 Chiquita Street, Laguna Beach, CA 92651 3 TABLE OF CONTENTS I. INTRODUCTION .................................................................................................................... 6 II. FLUID DYNAMICS IN AIRWAYS ................................................................................... 6 A. FUNDAMENTAL EQUATIONS ....................................................................................... 6 B. BOUNDARY CONDITIONS ............................................................................................. 8 C. IDEALIZED VELOCITY PROFILES ................................................................................ 9 D. COMPUTATIONAL FLUID DYNAMICS ...................................................................... 10 III. AEROSOL DEPOSITION MODELS ............................................................................... 11 A. CLASSES OF MODELS ................................................................................................... 11 1. Empirical Models ........................................................................................................... 11 2. Deterministic Models ..................................................................................................... 12 3. Stochastic Models .......................................................................................................... 13 4. Computational Fluid-Particle Dynamics (CFPD) .......................................................... 14 B. MERITS AND LIMITATIONS OF DEPOSITION MODELS ........................................ 15 1. Scientific Foundations .................................................................................................... 16 2. Biological Realism ......................................................................................................... 17 3. Hardware and Software Issues ....................................................................................... 18 4. Advantages of Modeling and Simulation ....................................................................... 18 IV. FACTORS INFLUENCING AEROSOL DEPOSITION PATTERNS ............................ 20 4 A. AEROSOL PROPERTIES................................................................................................. 20 B. INHALABILTY ................................................................................................................ 20 C. RESPIRATORY SYSTEM MORPHOLOGY .................................................................. 21 1. Idealized Models ............................................................................................................ 21 2. Data-Driven Models ....................................................................................................... 21 3. Three Dimensional Morphological Models for Interpretation of Lung Images ............. 22 4. Three-Dimensional Morphological Models for CFPD .................................................. 23 5. Surface Features ............................................................................................................. 24 D. VENTILATORY CONDITIONS ...................................................................................... 24 2. Breathing Pattern ............................................................................................................ 26 E. RESPIRATORY SYSTEM ENVIRONMENT ................................................................. 27 F. CLEARANCE.................................................................................................................... 28 1. Mucociliary Clearance ................................................................................................... 29 2. Macrophage Clearance or Phagocytosis ........................................................................ 31 3. Free Particle Uptake and Translocation to the Interstitium ............................................ 32 4. Importance of Clearance in Particle Deposition Modeling ............................................ 33 G. DISEASE ........................................................................................................................... 34 1. Chronic Obstructive Pulmonary Disease (COPD) ......................................................... 34 2. Asthma ........................................................................................................................... 35 3. Cystic Fibrosis ................................................................................................................ 35 5 4. Effect of Obstructive Disease on Particle Deposition and Distribution ......................... 35 5. Modeling Disease ........................................................................................................... 36 H. AGE ................................................................................................................................... 37 V. THEORY AND EXPERIMENT ....................................................................................... 38 A. PREDICTIONS OF PARTICLE DEPOSITION ............................................................... 38 B. PARTICLE DEPOSITION MEASURMENTS ................................................................. 38 1. Casts and Models ........................................................................................................... 39 2. Deposition Patterns Deduced from Clearance Studies ................................................... 40 3. Light-Scattering Methods ............................................................................................... 40 4. Imaging Studies .............................................................................................................. 41 5. Microdosimetry .............................................................................................................. 42 C. COMPARISON OF MODELING AND DATA ............................................................... 43 1. Simulations of Total Particle Deposition ....................................................................... 44 2. Simulations of Compartmental Particle Deposition ....................................................... 45 3. Simulations of Particle Distribution Generation-By-Generation ................................... 47 4. Simulations of Local Particle Deposition ....................................................................... 47 VI. APPLICATIONS OF DEPOSITION MODELS ............................................................... 48 A. EXPOSURE AND RISK ASSESSMENT ........................................................................ 48 B. DESIGN OF INHALED PHARMACEUTICALS AND DELIVERY SYSTEMS .......... 49 VII. SUMMARY ....................................................................................................................... 50 6 I. II. INTRODUCTION The mathematical modeling of the deposition and distribution of inhaled aerosols within human lungs is an invaluable tool in predicting both the health risks associated with inhaled environmental aerosols and the therapeutic dose delivered by inhaled pharmacological drugs. However, mathematical modeling of aerosol deposition requires knowledge of the intricate geometry of the respiratory network and the resulting complex motion of air and particles within the airways. In this chapter, an overview of the basic engineering theory and respiratory morphology required for deposition modeling are covered. Furthermore, current deposition modeling approaches are reviewed, and many factors affecting deposition are discussed. Experimental methods for measuring lung deposition are presented, albeit briefly, and the comparison between experimental results and modeling predictions are examined for a selection of modeling efforts. III. FLUID DYNAMICS IN AIRWAYS The deposition patterns associated with inhaled particulate matter are intrinsically linked to the airflow patterns within the respiratory system. Therefore, any effort to realistically model particle deposition requires an understanding of the fundamental fluid dynamics theory behind the motion of air in the extrathoracic and lung airways. A. FUNDAMENTAL EQUATIONS Fluid motion is governed by the conservation of mass (continuity) equation and conservation of momentum (Navier-Stokes) equation. The flow of air in the respiratory airways is usually assumed to be incompressible.1 For incompressible flow, the continuity equation is given by 7 V 0 (1) And the Navier-Stokes equation is V V V ρf p μ 2 V (2) t where and 2 are the gradient and Laplacian operators, respectively (defined below), is the fluid density, is the absolute fluid viscosity, and p is the hydrodynamic pressure. The parameter f is any externally applied volumetric force, such as gravity. In studying fluid flow