Transactions on Biomedicine and Health vol 2, 1995 WIT Press, ISSN

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1 Biomedical application of the supercomputer: targeted delivery of inhaled Pharmaceuticals in diseased lungs T.B. Martonen,* I. Katz,* D. Hwang,' Y.Yang* "Health Effects Research Laboratory, U.S.Environmental Protection Agency, Research Triangle Park, NC 27711, and Division of Pulmonary Diseases, Dept. of Medicine, University of North Carolina, Chapil Hill, NC27599, USA. ^Dept. of Engineering Science, Trinity University, San Antonio, 'MCNC-North Carolina Supercomputing Center, P.O.Box 12889, jrasearc/z Ty/^g/efa^ 7VC2770P, U5W. ^DESIGNefic - a Division of Crawford Communications Inc., I. Abstract The primary pathological manifestation of cystic fibrosis (CF) is the obstruction of biological passages throughout the body by mucus. However, all patients will develop chronic obstructive lung disease which accounts for more than 90% of CF mortality. We have used the Cray Y-MP to develop a mathematical model for targeting the delivery of inhaled pharmacologic drugs in the treatment of respiratory tract diseases. The model consists of a three dimensional description of the human lung, physiologically realistic airstream patterns, and a description of particle deposition processes. The supercomputer simulations demonstrate that (i) the polydispersity of an aerosol and (ii) disease-induced changes in airway structures can markedly alter the deposition patterns and, thereby, the efficacies of Pharmaceuticals.

2 242 Computer Simulations in Biomedicine II. Introduction Cystic fibrosis (CF) will be the representative airway disease considered in this study. It is the most common, lethal genetic disease for the Caucasian population. It is a congenital recessive disorder and the disease occurs in about 1 in 2000 births. The cloning of the gene has provided a foundation for genetic diagnosis and new treatment strategies including gene therapy and aerosolized drugs. In this work we shall use the Cray Y-MP supercomputer to address the effects of two factors on the targeted delivery of aerosolized drugs: (i) size distributions of inhaled particles, and (ii) disease-induced changes in airway dimensions. III. Methods A. Airway Disease (Cystic Fibrosis) Progressive lung disease associated with CF is a continuous interaction of the processes of airway obstruction, infection and inflammation [1]. Due to the hypersecretion of mucus, airways become congested, perhaps eventually plugged. Subsequently, various airborne pathogenic particles that are inhaled become deposited and retained within the lung, and mycobacterial colonizations can occur. Infections can, in turn, further stimulate mucus production and exacerbate airway obstruction. The role of inflammatory response is to further reduce airway caliber. B. Lung Morphology Symmetric morphologies have been demonstrated to be suitable for particle deposition modeling within lungs of children and adults [2-6]. Therefore, let us outline the Model A morpholgy of Weibel [7]. It is a dichotomously branching system. The TB airways are numbered in order from the trachea (generation / = 0) to the terminal bronchioles (/ = 16). The pulmonary (P) region, generations I = 17-23, inclusive, is subdivided into three generations of partially alveolated respiratory bronchioles, three generations of alveolar ducts, and alveolar sacs. The bifurcation and gravity angles among the airway network are 70 and 45, respectively. There are 2^ identical airways in each generation.

3 C. Aerosol Motion 1. nomenclature Computer Simulations in Biomedicine 243 Dg = Particle geometric diameter, cm p Particle density, g/cm? X = Mean free path of air = 7.0 x 10~, cm G = Gravitational constant = 980 cm/sec? T = Absolute temperature = 293 K k Boltzmann constant = 1.38 x W~,g cm?/sec~* molecule K L(I) Length of generation / airway, cm D(I) = Diameter of generation / airway, cm rj = Air kinematic viscosity = 1.5 x W~*,cm?/sec IJL Air absolute viscosity = 1.84 x I0~*,g/cmsec U(I) = Mean air velocity in generation / airway, cm/sec (f)(i) = Inclination of generation / airway with respect to horizontal, 9(1) Angle of bend of generation /, Re(I) = Airflow Reynolds number in generation / airway = D(I)U(I)/rj, dimensionless m = Particle mass, g C(Dg) = Particle slip correction factor = 1 -f A(2\/Dg), dimensionless where A z= exp{-l.lD^/(2A)} r = Particle relaxation time = mc(dg)/(37rp.dg), sec V = Particle Stokes terminal settling speed Gr, cm /sec d Particle diffusion coefficient = fctr/ra, cm?/sec t(i) = u(n-i/sl(4>(i)} P^ticle residence time in generation /, sec 2. primary deposition mechanisms The major processes influencing inhaled drugs are inertial impaction (particles of sufficient momentum may be deposited by centrifugal forces), sedimentation (particles of sufficient mass may be deposited by gravity), and diffusion (particle deposition may result from random Brownian motion). As particles are entrained and transported by air, their trajectories are affected by the magnitude and character of an airstream which, in turn, are a function of respiratory tract geometries, particle parameters and breathing conditions. To study aerosol deposition in the lung, the airflow pattern assumed must be physiologically realistic. The followingfluiddynamics pattern will be used in this work: turbulent airflow in bronchial generations I = 0-3 (inclusive of the trachea and main, lobar, and segmental bronchi); and, laminar flow with developing velocity profiles depending on the length-todiameter ratios of the respective airways.

4 244 Computer Simulations in Biomedicine A system of particle deposition equations derived for such physiologically realistic flow patterns as described above has been derived by Martonen [8]. The respective formulas, used herein, are presented in Table 1. The trachea is a special case, particles entrained in the laryngeal jet will be deposited immediately downstream of the larynx producing a "hot spot" described by W^n where 5% = pd^[/(0)/9/id(0), D(0) is the tracheal diameter and (7(0) is the mean velocity in the trachea. To describe particle deposition in the lung we shall follow an inhaled bolus of aerosol throughout the TB and P airways. Particles are continuously removed from the bolus (i.e., deposited on airway surfaces) as it travels throughout the lung during a cycle of breathing. The superposition principle may be used to determine cumulative deposition: P(C) = IV. Results and Discussion In Figure 1 a human lung is described by a supercomputer-generated display. The Cray Y-MP was used to systematically map the airways. In Figure 2 deposition patterns of drugs are studied using the supercomputer model. The effects of disease-induced changes in airway structure are examined by reducing diameters by an airway coefficient (AC) of 0.7 relative to Weibel's (AC =1.0) dimensions. The manifestation of CF as obstruction, inflection and inflammation are demonstrated in each Panel where control and diseased lungs are compared. Aerosols typical of medical nebulizers are addressed in Figure 2 [9]. The respective particle size distributions are polydisperse and may be described by lognormal functions [10] which characterize a distribution in terms of its mass median aerodynamic diameter (MMAD) and geometric standard deviation (GSD). The critical point regarding drug delivery is that aerosols of identical MMAD but different GSD are, in fact, very different physically. By comparing Panel A (GSD = 1.5) with Panel B (GSD = 2.0) it is apparent that drug delivery is markedly affected by the size distribution of an inhaled aerosol. In conclusion, a supercomputer model is presented which permits aerosolized drugs to be targeted to sites within the lung while accounting for effects of CF-induced changes in airway dimensions and operating characteristics of medical nebulizers. DISCLAIMER: This manuscript has been reviewed in accordance with the policy of the Health Effects Research Laboratory, U.S. Environmental Protection Agency, and approved for publication. Approval does not signify that the contents necessarily reflect the views and policies of the Agency,

5 Computer Simulations in Biomedicine 245 nor does mention of trade names or commercial products constitute endorsement or recommendation for use. V. References 1. Davis, P.B. (Editor) Cystic Fibrosis, Marcel-Dekker, Inc., New York, Martonen, T.B. Mathematical model for the selective deposition of inhaled pharmaceuticals, J. P/tarm. &%., 1993, 82, Martonen, T.B. & Katz, I. Deposition patterns of polydisperse aerosols within human lungs, J. Aerosol Med., 1993, 6, Martonen, T.B. & Katz, I. Deposition patterns of aerosolized drugs within human lungs: effects of ventilatory parameters, Pharm. Res., 1993, 10, Martonen, T.B. & Katz, I. Inter-related effects of morphology and ventilation on drug deposition patterns, STP Pharm. Sci., 1994, 4, Martonen, T.B., Graham, R.C. & Hofmann, W. Human subject age and activity level: Factors addresses in a biomathematical deposition program for extrapolation modeling Health Phys., 1989, 57, Weibel, E.R. Morphometry of the Human Lung, Academic Press, New York, Martonen, T.B. Analytical model of hygroscopic particle behavior in human airways, BWf. AM&. BW., 1982, 44, Martonen, T.B. Aerosol therapy implications of particle deposition patterns in simulated human airways, J. Aerosol Med., 1991, 4, Raabe, O.G. Particle size analysis utilizing grouped data and the lognormal distribution, J. Aerosol Sci., 1971, 2,

6 to ^O) O o Flow Condition Inertial Impaction F(7) Laminar - f e (1 e*) + arcsin(e)j T\ TTrti il r*ni" 1 r*vr\ 1 ~^ 1 Table 1. Deposition formulas for drug particles in human airways. Deposition Mechanisms Sedimentation P(S) Diffusion P(D) ^ /-8rGi(/)cos(</>(/))\ ^ /-0.088d^^e(/)^L(/)\ ^l ^(/) J ^\ U(I}D(IY ) I I en I > 5± w h-»«2 w( ' o i P- i ' a. g e = e(i)ru(i)/d(i) = 4dL(I)/U(I)D(I)'*

7 Computer Simulations in Biomedicine 247 TRACHEA Figure 1. Supercomputer simulation of the branching network of airways in the human lung. For clarity only generations 0 (trachea) to 12 are illustrated.

8 248 Computer Simulations in Biomedicine o PL,.2 'S oex a 0.08 A. GSD=1.5 D Control (AC=1.0) <y Disease (AC=0.7) Airway Generation, I i B. GSD= O Control (AC=1.0)..»^.,,.,.. Disease (AC=7.0) i ! I CX, & Aii*way Generation, I Figure 2: Airway-by-airway distributions of aerosolized drugs in control (AC=1.0) and diseased (AC=0.7) lungs. The inspiratory flow rate is 30 1/min. The aerosol MM AD is 3 u,m with a GSD of 1.5 (Panel A) or 2.0 (Panel B).