Modeling Airflow and Particle Deposition in the Lung Bahman Asgharian Health Effects and Medical Response Applied Research Associates Raleigh, NC U.S.A.
Lung Deposition Modeling Develop models based on physical & physiological parameters that govern aerosol transport to Predict regional, lobar and local deposition in the lung Comments: Lung geometry is too complex and has millions of airways Need to make simplifying assumptions The level of accuracy of model predictions depends model assumptions 2
Why Lung Deposition Modeling? Enhances understanding of mechanisms & processes Hypothesis generator. Make a Hypothesis. Test the hypothesis by including in the model and running the model to obtain results. Structured way to deal with complex issue. Go step by step from simple model by considering basic physics and complexity Interpret in vivo data 3
Why Lung Deposition Modeling? Predict results Cheaply & quickly: Experiment can not cover all cases. Can make calculations for situations for which there are not experimentally feasible or there are no data. 4
Why Lung Deposition Modeling? Provides input to calculating body burden Can connect deposition models to PBPK models. Expand deposition models to build physiological models with various compartments for different organs/tissues 5
Applications of Deposition Modeling Risk assessment Facilitates comprehensive exposure dose response characterization Design of inhalation exposure studies Improve interspecies extrapolation Tissue dosimetry: interface with PBPK models Pharmaceutical drug delivery Targeted delivery of drugs to the lung Help with evaluation of pharmaceutical drug devices 6
Deposition Modeling Given: Exposure, lung and breathing parameters Calculate: Deposition fraction of particles in the lung Modeling approaches: 1. Site specific modeling (CFD) 2. Whole lung modeling (typical path, etc.) 7
Site Specific Deposition Modeling Objectives: 1. To identify and study the significance of parameters & mechanisms affecting deposition. 2. To predict localized deposition of particles. 3. To predict airway deposition efficiency. Strength: o Few or no assumptions are made. o Solve the complete set of transport equations. Weakness: o Can model a small part of the lung (up to gen. 6 or 50 ml). o Unrealistic lung ventilation/boundary conditions. 8
Site Specific Deposition Modeling Calculation steps: 1. Reconstruct the selected geometry on the computer (+) 2. Prescribe flow initial and boundary conditions ( ) 3. Compute airflow field using computational fluid dynamics (CFD) (+) 4. Calculate particle transport equations numerically (+) 9
Site Specific Deposition Modeling Airflow: U t i + U j U x i j = 1 ρ P x i + ν x 2 j Ui x j (Navier-Stokes) U x j j = 0 (continuity) Particle transport: du dt dx 18µ C Re D p 2 i i d C ρ c 24 1 4 4 4 44 2 4 4 4 4 43 p i = i + dt i = u p i Drag force ( U u p ) + g () { n gravity { i t random fluctuating 10
Site Specific Deposition Modeling Example 1: Influence of outlet boundary conditions on particle deposition in the first few upper airway. Airway Geometries: 1. Non lobar: Nine common airways of the lung including the trachea, main, lobar, & segmental bronchi (Yeh and Schum, 1980). 2. Lobar: The same central airway network with lobes attached to each segmental bronchus. 11
Site Specific Deposition Modeling 12
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Site Specific Deposition Modeling 14
Site Specific Deposition Modeling 15
Site Specific Deposition Modeling Deposition Fraction (%) 14 12 10 8 6 4 2 0 Regional Deposition Fraction Non lobar Lobar 0.001 0.01 0.1 1 10 Particle size, µm 16
Site Specific Deposition Modeling Example 2. Influence of airway structure on particle deposition in TB airways Lung geometry: Reconstructed Human TB airways 17
Airflow Velocity Laminar Flow Turbulent Flow 18
Site Specific Deposition Modeling Particle Size 0.001 µm or 1 nm 19
Site Specific Deposition Modeling Particle Size 10 µm 20
Site Specific Deposition Modeling 10 µm particles 1nm particles 21
Site Specific Deposition Modeling Deposition Fraction (%) 100 80 60 40 20 Regional Deposition Fraction Reconstructed geometry Lobar 0 0.001 0.01 0.1 1 10 Particle size, µm 22
Whole Lung Deposition Modeling Head Conductive Zone Respiratory Z. BR BL TBL RBL AD AS Trachea 23
Whole Lung Deposition Modeling Objective: To calculate regional and local deposition during one breathing cycle. Regional deposition: Head, TB or PUL deposition Lung Deposition: TB + PUL Total deposition: Head + TB + PUL Deposition = Number Fraction Number Deposited Inhaled Strength: Models the entire respiratory tract. Weakness: Requires various simplifying assumptions. 24
Whole Lung Deposition Modeling Model components: I. Extrathoracic airway deposition From measurements: semi empirical models (+) II. Lung geometry Symmetric and asymmetric ( ) III. Airway flow architecture within the lung Determine flow rates from lung expansion/contraction (uniform, dictated by compliance resistance) (+) Uniform velocity ( ) IV. Mathematical formulation for transport Deposition by sedimentation, impaction, diffusion ( ) 25
Whole Lung Deposition Modeling I. Head Deposition Losses are by diffusion and impaction Diffusion: η = f (Sc, ) or η = f (Q, D) Impaction: η = f (Stk) or η = 2 f (d ae Q) 26
Whole Lung Deposition Modeling II. Lung Geometry Single path symmetric 5 lobe symmetric but each lobe structurally different Stochastic (asymmetric) lungs Typical-path 5 symmetric lobes Stochastic lung RU LU RL RM LL RU: right upper RM: right middle RL: right lower LU: left upper LL: left lower 27
Whole Lung Deposition Modeling Different Human Lung Geometry: 5-lobe symmetric Single path symmetric Stochastic 28
Whole Lung Deposition Modeling III. Lung Ventilation Airflow transport is due to a pressure difference: P Inspiration Intrapleural Pressure Expiration Alveolar Pressure Expiration Inspiration 29
Whole Lung Deposition Modeling III. Lung Ventilation P = ρ V ρ { t Unsteadiness (int er tan ce) ( LV) & + 2 ( V ) 43 V µ 1 2 3 ρ 14 2 (kinetic ρ Convective derivative energy) ρ V Viscous resis tan ce Boundary conditions: lung compliance + tissue resistance 4 7 4 48 P = P + P + P + P + inertia K.E. µ E Compliance P Change in Kinetic Energy = EV Airway resistance + RV& + ( ρ V & 2 ) (EV) (elastic) B ρ V& 2 6 negligible tr Tissue resistance (RV) & (Navier Stokes equations) 30
Whole Lung Deposition Modeling IV. Mathematical Model for Particle deposition m λc : t+ δt mt = m& inδt m& out ( AC) ( QC) t + x = x δt m C DA λc x dep Mass lost / time / volume (i.e. flux) m& in Tidal air x f m dep m& out Reserved air x f x 31
Calculation Steps: 1. Calculate deposition efficiencies per airway. 2. Particle concentrations at the inlet and exit of all airways. 3. Airflow rates at the inlet and exit of airways. 4. The time it takes for the aerosol front to pass the inlet and exit of each airway. 5. Calculate Losses per airway: Losses time dis tan ce = λ CAdxdt 6. Repeat for inhalation, pause, and exhalation Computer code: traverse up and down the airway tree and perform the above steps Deposition Model 32
Multiple-Path Particle Dosimetry model (MPPD) 33
Whole Lung Deposition Modeling Breathing via trachea: Inhalation of 0.5 µm particles 34
Whole Lung Deposition Modeling Pause 35
Whole Lung Deposition Modeling Exhalation 36
Whole Lung Deposition Modeling Regional Deposition: 1 0.8 0.6 TB PUL 0.4 0.2 0 0.01 0.1 1 10 Particle Diameter, µm 37
Whole Lung Deposition Modeling 2 nm 5 nm 10 nm 38
Drug Delivery Vs Passive Inhalation Drug generation and delivery method Control lung ventilation to get drugs to target sites Drug formulation (properties, drug plus carrier, size distribution) Mixture (particle vapor interaction) Hygroscopicity Deposition by various loss mechanisms Patient specific geometry and lung ventilation 39