A mechanistic framework for a priori pharmacokinetic predictions of orally inhaled drugs
AA mechanistic framework for a priori pharmacokinetic predictionsof orally inhaled drugs
Niklas Hartung , Jens Borghardt Institute of Mathematics, University of Potsdam, Potsdam, Germany Drug Discovery Sciences, Research Pharmacokinetics, Boehringer Ingelheim Pharma GmbH & Co. KG,Biberach, Germany* [email protected]
Abstract
The fate of orally inhaled drugs is determined by pulmonary pharmacokinetic processes such as parti-cle deposition, pulmonary drug dissolution, and mucociliary clearance. Even though each single processhas been systematically investigated, a quantitative understanding on the interaction of processes remainslimited and therefore identifying optimal drug and formulation characteristics for orally inhaled drugsis still challenging. To investigate this complex interplay, the pulmonary processes can be integratedinto mathematical models. However, existing modeling attempts considerably simplify these processesor are not systematically evaluated against (clinical) data. In this work, we developed a mathematicalframework based on physiologically-structured population equations to integrate all relevant pulmonaryprocesses mechanistically. A tailored numerical resolution strategy was chosen and the mechanistic modelwas evaluated systematically against data from different clinical studies. Without adapting the mech-anistic model or estimating kinetic parameters based on individual study data, the developed modelwas able to predict simultaneously (i) lung retention profiles of inhaled insoluble particles, (ii) particlesize-dependent pharmacokinetics of inhaled monodisperse particles, (iii) pharmacokinetic differences be-tween inhaled fluticasone propionate and budesonide, as well as (iv) pharmacokinetic differences betweenhealthy volunteers and asthmatic patients. Finally, to identify the most impactful optimization criteriafor orally inhaled drugs, the developed mechanistic model was applied to investigate the impact of inputparameters on both the pulmonary and systemic exposure. Interestingly, the solubility of the inhaleddrug did not have any relevant impact on the local and systemic pharmacokinetics. Instead, the pul-monary dissolution rate, the particle size, the tissue affinity, and the systemic clearance were the mostimpactful potential optimization parameters. In the future, the developed prediction framework shouldbe considered a powerful tool for identifying optimal drug and formulation characteristics.
Introduction
Oral drug inhalation can result in high pulmonary drug exposure while maintaining low systemic exposure.Compared to other routes of administration, this can provide higher local pulmonary efficacy, while simul-taneously reducing systemic adverse effects (“lung selectivity”) [1, 2, 3]. Therefore, orally inhaled drugs areconsidered first-line therapy (amongst other treatment options) to treat respiratory diseases such as asthmabronchial or chronic obstructive pulmonary disease [4, 5].While qualitatively, the pharmacodynamic (PD) selectivity for the lung was previously investigated, asound quantitative understanding about the pulmonary pharmacokinetics (PK) is still lacking. Specificpulmonary PK processes after oral drug inhalation were studied in detail, such as the pulmonary particle1 a r X i v : . [ q - b i o . T O ] J un eposition [6, 7, 8] or mucociliary clearance [9, 10]. For example, it is well understood that the central airwaydeposition increases with an increasing aerodynamic particle size [7] and that the mucociliary clearancedepends on the localization in the airways [10]. Hence, the impact of mucociliary clearance strongly dependson particle deposition patterns. However, in contrast to investigations related to the individual processes, theinterplay of the many pulmonary PK processes has received less attention. A comprehensive quantitativeunderstanding of how these processes contribute to pulmonary and systemic PK, and therefore to lungselectivity after drug inhalation, is often still lacking [11, 12, 13, 14]. Thus, identifying drug and formulationcharacteristics for orally inhaled drugs that maximize lung selectivity as well as long-lasting pulmonaryefficacy is still challenging.To gain a better understanding on the interplay of pulmonary PK processes, mechanistic modelingapproaches can be applied. However, previous modeling approaches either reduced the given complexityor lack adequate model evaluation. For example, the mucociliary clearance was described as a first-orderprocess [15, 16]. Other published population PK models did not differentiate between undissolved anddissolved drug and consider pulmonary drug absorption as a “one-way process”, i.e. back flow of drug tothe lungs from the systemic disposition is not considered [17, 18, 19]. One mechanistic partial differentialequation (PDE)-based model is available, which included all relevant pulmonary PK processes [20]. Thismodel, however, was not evaluated against clinical data. Hence, to our knowledge no fully mechanisticmodel, with an adequate model evaluation based on clinical and in vitro data, is available. Consequently,there is currently no adequate framework to quantitatively identify the most impactful drug and formulationcharacteristics to achieve good lung selectivity.In this work, we aimed at developing such a mechanistic pulmonary PK model to capture the complexityof all relevant pulmonary PK processes (compare Fig 1) and to determine which parameters are the mostsuitable optimization criteria to achieve optimal lung selectivity. The biggest mathematical challenge relatedto such a model is to adequately describe the joint effect of location-dependent nonlinear mucociliary clear-ance and particle size-dependent dissolution. To achieve this, a size- and location-structured PDE modelwas developed. The resulting PDE model was extensively evaluated, in particular based on clinical PKdata for both budesonide and fluticasone propionate, as these inhaled drugs represent the clinically moststudied compounds. Finally, a sensitivity analysis was performed to determine the most impactful drug andformulation characteristics and therefore potential optimization parameters to achieve a high lung selectivity. Models
The mathematical model is introduced in a stepwise manner. First, the (sub)models describing the consideredpulmonary PK processes are given. Next, the full PDE model it presented. The model parametrization isdescribed in the Results section. Full details concerning derivations, numerical resolution, and additionalmodel evaluations are given in S1 Appendix, as referenced below.
Modeling of pharmacokinetic processes in the lung
Pulmonary particle deposition
Since orally inhaled drugs are deposited in the lungs within a single breath, pulmonary drug deposition wasconsidered as an instantaneous rather than a time-dependent process. Pulmonary particle deposition wassimulated with the MPPD software [21] according to the study design of each investigated study (i.e., formonodisperse particle size formulations as well as the specific particle size distributions of the Diskus R (cid:13) andTurbohaler R (cid:13) devices, respectively [22]). To simulate deposition patterns for asthmatic patients, who arecharacterized by a more central deposition compared to healthy volunteers [23, 24], we corrected the depo-sition patterns in healthy volunteers based on scintigraphy data reported in [25]. A full account of input2igure 1: Overview of relevant pulmonary pharmacokinetic processes for orally inhaled drugs.
Adapted and modified from [2].parameters to predict the deposition patterns and the adaption for asthmatic patients is provided in S1Appendix(Section 4).These predictions generated aerodynamic particle size- and lung generation-resolved deposition patterns.The aerodynamic particle size (the size of a water particle experiencing the same aerodynamic forces as theconsidered particle) determines the deposition characteristics of the inhaled particles [26]. In contrast, thereal (geometric) size of an inhaled particle is relevant for dissolution processes [27]. To convert aerodynamicto geometric particle sizes, which is more relevant for dissolution characteristics, we assumed a sphericalshape of particles and considered the relationship d geom = d aero r ρ water ρ substance , where d aero and d geom are aerodynamic and geometric particle diameters, respectively; ρ water and ρ substance denote density of water and the considered inhaled substance, respectively [28].In a post-processing step, the (geometric) particle size- and lung generation-resolved deposition patternswere projected onto the computational grid, ensuring conservation of the number of molecules (full detailsare given in S1 Appendix, Section 2.5.1). Mucociliary clearance
The mucociliary clearance process was parameterized based on a model for mucociliary clearance publishedby Hofmann and Sturm (see S1 Appendix, Section 1.2 for details) [10]. In agreement with clinical data,mucociliary clearance of undissolved particles only depends on the particle location, not on (geometric)particle size [26]: 3 mc ( x ) = 0 . · (cid:18) r br ( x )1 cm (cid:19) . , where r br ( x ) represents the radius of the conducting airways at location x . Pulmonary drug dissolution
The dissolution of particles in the pulmonary lining fluids was based on an adapted version of the Noyes-Whitney equation [27]: d ( s, C flu ) = 4 π k diss ( π ) / ρ · (cid:18) − C flu C s (cid:19) · s / , where s denotes the particle volume, ρ the particle density, C s the saturation solubility, k diss = D · C s themaximum dissolution rate ( D = diffusivity), and C flu the local concentration of dissolved drug in the liningfluid. A derivation of this equation from the Noyes-Whitney equation, assuming spherical particle geometry,is provided in S1 Appendix, Section 1.1. To represent the difference in fluid composition between conductingairways and the alveolar space, in particular in terms of fluid viscosity, different dissolution rate constants( k brdiss / k alvdiss ) were assumed in these two regions, leading to dissolution models d br and d alv , respectively. Absorption into the lung tissues
After drug dissolution in the pulmonary lining fluids, the drug is absorbed through the airway epithelia intothe lung tissue of the respective airway generation or the alveolar space. Based on reported negligible totenfold lower albumin concentrations in epithelial ling fluids in the lung compared to plasma [29, 30, 31],the absorption rate is calculated assuming no drug binding in the lung lining fluids: k a = P app · SA · (cid:18) C flu − C tis K pu,tis (cid:19) , where k a denotes the absorption rate, P app the effective permeability, SA the airway surface area, and K pu,tis describes the lung-to-unbound plasma partition coefficient. Systemic disposition
The systemic disposition models for both budesonide and fluticasone propionate were based on availableliterature information after intravenous administration and oral administration (to include the oral bioavail-ability of swallowed drug). In contrast to many less mechanistic PK models, the backflow of drug from thesystemic circulation into the lung was mechanistically included in the PDE-based PK model.
Partial differential equation model for orally inhaled drugs
Model equations
To mechanistically combine the considered pulmonary processes in the lung (lung deposition, mucociliaryclearance, pulmonary dissolution, pulmonary absorption to the lung tissue and distribution between lungtissue and plasma), we adopted the framework of physiologically structured population models (PSPMs)[32]. In this class of PDE models, the time evolution of a density is described over a state space through aset of processes that modify the state.To describe the fate of undissolved particles deposited in the lung, we considered (i) a PSPM with sizeand location structure in the conducting airways and (ii) a PSPM with size structure in the alveolar space.4n these models, size s represents the geometric volume of particles, and location x (length unit) the positionalong all conducting airways, between trachea and terminal bronchioles. The state ( x, s ) of a particle ischanged by mucociliary clearance (impacts on x ) and pulmonary dissolution (impacts on s ).The PSPMs were coupled to differential equations describing the PK of dissolved drug molecules in lunglining fluids and lung tissues (similar to [33]) and published systemic disposition kinetics [15]. The full set ofequations is stated below, a simplified outline of the underlying geometry is provided in Fig 2 and a a detailedderivation of the full model from the separate PK processes is given in S1 Appendix (Sections 1.3-1.5).For ease of legibility, the following abbreviations are used as sub-/superscripts in the equations: br(bronchial, i.e., conducting airways), alv (alveolar space), sys (systemic), sol (solid, i.e., undissolved), flu(fluid, i.e., dissolved), tis (lung tissue), ctr (central), per (peripheral), mc (mucociliary clearance).The size- and location-structured PSPM for the density of inhaled particles in suspension in the conduct-ing airways reads ∂ t ρ br ( t, x, s ) + ∂ x (cid:2) λ mc ( x ) ρ br ( t, x, s ) (cid:3) − ∂ s (cid:2) d br ( s, C brflu ( t, x )) ρ br ( t, x, s ) (cid:3) = 0 ρ br (0 , x, s ) = ρ br0 ( x, s ) (see S1 Appendix, Sections 2.5.1 and 4)assuming zero inflow boundary conditions (i.e., no additional source of drug in the conducting airways afterdosing). This PDE was complemented by differential equations for the concentration of dissolved drug inlining fluids and lung tissue at a particular airway location x : a brflu ( x ) ∂ t C brflu ( t, x ) = s max Z d br ( s, C brflu ( t, x )) ρ br ( t, x, s )ds | {z } dissolution − πr br ( x ) P app (cid:18) C brflu ( t, x ) − C brtis ( t, x ) K pu,tis (cid:19)| {z } tissue uptake a brtis ( x ) ∂ t C brtis ( t, x ) = 2 πr br ( x ) P app (cid:18) C brflu ( t, x ) − C brtis ( t, x ) K pu,tis (cid:19) − q br ( x ) (cid:18) BP C brtis ( t, x ) K p,tis − C sysctr ( t ) (cid:19)| {z } systemic uptake both with zero initial conditions.In the alveolar space, the size-structured PSPM for the density of inhaled particles in suspension reads ∂ t ρ alv ( t, s ) − ∂ s (cid:2) d alv ( s, C alvflu ( t )) ρ alv ( t, s ) (cid:3) = 0 ρ alv (0 , s ) = ρ alv0 ( s ) (see S1 Appendix, Sections 2.5.1 and 4)Again, zero inflow boundary conditions were assumed (no additional source of drug in the alveolar spaceafter dosing) the and the PDE is complemented by differential equations for the concentration of dissolveddrug in alveolar lining fluids and alveolar lung tissue: V alvflu d C alvflu dt ( t ) = s max Z d alv ( s, C alvflu ( t )) ρ alv ( t, s )d s − P app SA alv (cid:18) C alvflu ( t ) − C alvtis ( t ) K pu,tis (cid:19) V alvtis d C alvtis dt ( t ) = P app SA alv (cid:18) C alvflu ( t ) − C alvtis ( t ) K pu,tis (cid:19) − Q alv (cid:18) BP C alvtis ( t ) K p,tis − C sysctr ( t ) (cid:19) with zero initial conditions.The equations describing the PK in the conducting airways and the alveolar space are coupled through5
Geometry of and key processes in conducting airways represented in the mathematicalmodel.
A representative airway (dark grey) is considered in the mathematical model. At each location x (distance from throat) within this airway, we consider a cylindrical lung model, consisting of concentriclayers of airway (with radius r br ( x )), lung lining fluid (with cross-sectional area a brflu ( x )), and lung tissue(with cross-sectional area a brtis ( x )), respectively. Each drug particle (green) is characterized by its locationand size. Over time, particles are moved upwards by mucociliary clearance (yellow) and dissolve into theairway lining fluid (black arrows). 6he systemic circulation: V ctr d C sysctr dt ( t ) = x TB Z q br ( x ) (cid:18) BP C brtis ( t, x ) K p,tis − C sysctr ( t ) (cid:19) d x | {z } exchange with conducting airways + Q alv (cid:18) BP C alvtis ( t ) K p,tis − C sysctr ( t ) (cid:19)| {z } exchange with alveolar space − Q sys (cid:0) C sysctr ( t ) − C sysper ( t ) (cid:1) − CL · C sysctr ( t ) V per d C sysper dt ( t ) = Q sys (cid:0) C sysctr ( t ) − C sysper ( t ) (cid:1) The following expressions appear in these equations: • x is the location within a prototypical airway, varying from 0 (trachea, corresponding to airway gener-ation 1) to x TB (terminal bronchioles, corresponding to airway generation 16). • s is the geometric particle volume, varying between 0 and s max (device- and formulation-specific max-imum particle size deposited) • ρ br / ρ alv are the PSPM densities, with units number of particlesmL · cm and number of particlesmL , respectively • C yz is the concentrations of dissolved drug in lining fluid (z = flu) or lung tissue (z = tis) in a particularlocation of the conducting airways (y = br) or in the alveolar space (y = alv) • d br / d alv are the dissolution rates in conducting airways / alveolar space, depending on particle size s and concentration of already dissolved drug • λ mc is the mucociliary clearance in the conducting airways, assumed to depend only on location x , noton (geometric) particle size s . • P app is the apparent permeability of the drug • SA alv is the surface area of the alveolar space • r br ( x ) is the airway radius (including lining fluid) at location x (see Fig 2) • K p,tis / K pu,tis are the lung-to-plasma and lung-to-unbound plasma partition coefficients, respectively • BP is the blood-to-plasma ratio of the drug • a brflu ( x ) / a brtis ( x ) is the cross-sectional area of lung lining fluid / lung tissue at location x within theconducting airways • q br ( x ) is the location-resolved blood flow (see section Model parametrization below) Numerical resolution
To solve the mathematical model numerically, we employed an upwind discretization of the PSPMs [34]together with an implicit discretization of all linear processes (MCC, absorption, systemic processes) [35, 36].The fluxes across PDEs (mucociliary elevator and dissolved / absorbed drug) were discretized ensuringthat all conservation laws were fulfilled at the discrete level. The discretized model and all analyses wereimplemented in MATLAB R2018b [37]. A full description of the discretization scheme is given in S1 Appendix(Section 2) and the MATLAB implementation is provided as S1 File.7 esults
Key findings from literature review
As a first step, PK studies for both budesonide and fluticasone propionate were identified. These drugs wereselected as they represent the most studied inhaled drugs for which the interplay between pulmonary deposi-tion, pulmonary dissolution, mucociliary clearance, as well as pulmonary absorption has been systematicallydiscussed [2, 24]. In total, ten different clinical PK studies on these drugs were identified (see S1 Table).After reviewing all PK studies, we identified two important aspects. First, the area under the curvereported by Usmani et al. [38] could not be reproduced considering the systemic clearance for fluticasonepropionate reported by Mackie et al. [39]. Even in the most extreme and certainly unrealistic assumptions,namely with 100% of inhaled drug particles deposited in the lungs and no mucociliary clearance, the systemicAUC would still be at least 25% lower than reported (see calculation in S1 Appendix, Section 3.3).Second, there is a considerable between-study variability in reported (dose-normalized) systemic drug ex-posure (same drug, comparable dose, comparable patient population, same inhalation device). For example,both M¨ollmann et al. [40] and Harrison and Tattersfield [41] investigated the systemic PK after budesonideinhalation with the Turbohaler R (cid:13) for slightly different doses of 1000 µ g, and 1200 µ g. The reported dose-normalized C max and AUC values varied by more than twofold. In contrast, the relative shape of the PKprofiles, which are not dependent on the absolute plasma concentrations, were in good agreement betweenboth studies. A full summary of exposure metrics is given in S1 Table.Based on these findings, we decided that predicting the absolute plasma concentrations of one singleselected PK study is not meaningful or could even result in a selection bias. Instead, PK studies with multiplestudy arms, which allow for a direct within-study comparison of different PK profiles, were considered (i.e.,studies with only a single investigated drug, a single inhaled particle size and a single investigated populationwere not included). A short overview of the reviewed PK studies, including a comment on why specific studieswere considered, can be found in S1 Table. In summary, the selected PK studies comprised the followingaspects relevant for model building and model evaluation: (i) the lung retention profiles for insoluble particles[26], (ii) the impact of different particle sizes on the systemic PK [38], (iii) different systemic PK profilesafter inhalation of either budesonide or fluticasone propionate [40, 41], and (iv) different systemic PK profilesbetween healthy volunteers and asthmatic patients [41]. Model parametrization
The PDE-based model was not adapted to individual studies, i.e., no (pharmacokinetic) parameters wereestimated based on the studies which were used for model evaluation. Instead, the pulmonary part of the PDEmodel was fully parametrized based on physiological and drug-specific in vitro data ( a priori predictions).Both pulmonary drug deposition and mucociliary clearance were considered as drug-independent genericprocesses based on particle size and airway characteristics alone, not requiring any drug-specific parameters.Drug-specific parameters, such as the maximum dissolution rate ( k diss ), as well as drug solubility in pul-monary lining fluids were either based on literature information or in-house data on in vitro dissolution andsolubility. No direct comparison between alveolar and mucus dissolution kinetics could be retrieved fromliterature or in-house data. Therefore, a 5-fold decrease of k diss in the conducting airways compared to thealveolar space was assumed for all model-based simulations. A comprehensive list of parameter values isgiven in Table 1 (physiological parameters) and Table 2 (drug-specific parameters).To achieve a location-resolved parametrization of the conducting airways, we used generation-specificanatomical data of the conducting airways from [53], namely the length l ( g ) and radius r ( g ) of each airwaygeneration g . From these values, location-resolved blood flows and cross-sectional lining fluid and lung tissueareas were calculated by assuming the following: 8able 1: Physiological parameters.Parameter Symbol(s) Value
Perfusion of conducting airways Q br Perfusion of alveolar space Q alv
312 L/h
Bronchial tissue volume V brtis
144 mL
Alveolar tissue volume V alvtis
388 mL
Alveolar fluid volume V alvflu
36 mL [42]Alveolar surface area SA alvflu
130 m [43]Location-resolved parameters r br , a brflu , a brtis , q br see main text calculated based on 2.5 % of cardiac output [44] equal to cardiac output, taken from [45, Table 22] computed from lung tissue weight of 532 g [45], assuming a tissuedensity of 1 g/mL and 27 % central/73 % peripheral lung tissueweight fraction as in [33, Supplement].Summary of physiological parameters obtained from literature.Table 2: Drug-specific parameters.Parameter Symbol Fluticasone propionate Budesonide
Central volume of distribution V ctr
31 L [15] 100 L [15]Peripheral volume of distribution V per
613 L [15] 153 L [15]Clearance CL 73 L/h [15] 85 L/h [15]Intercompartmental clearance Q sys F oral k a – 0.45 1/h [15]Fraction unbound in plasma f u,plasma Lung:plasma partition coefficient K p,tis P app . · − cm/s . · − cm/s[47]Blood:plasma ratio BP 1.83 ρ C s . µ M . µ M Maximum dissolution rate k alvdiss . · − · min . · − · min Inhalation device-specific parameters see S1 Appendix, Section 4 in-house data: fraction unbound was determined with an in vitro binding assay as described in [50],permeability was determined based on an in vitro permeability assay with Calu cells, with assay con-ditions as described for MDCK II cells in [50]. The in vitro assay setup for determining Blood:Plasmaratio and drug solubility in surfactant-containing media is described in S1 Appendix, Section 5. calculated based on f u,plasma (in-house data) and rat lung slice binding [51] determined from in vitro dissolution data from [52] (see S1 Appendix, Section 3.1 for full details).For both drugs, two-compartment systemic PK models proposed in the literature were used. • Using length of airway generations, we determined a continuous representation r br ( x ) of the airwayradius by linear interpolation between airway centerpoints.9 We assessed literature data on lining fluid height h brflu ( x ) for different airway generations and foundan appropriate linear location-to-height of lining fluid-relationship (see S1 Appendix, Section 3.2, fordetails). Using the cylindrical geometry assumption depicted in Fig 2B, a brflu ( x ) could be determinedfrom h brflu ( x ) and the airway radius r br ( x ) via a brflu ( x ) = π (cid:16) r br ( x ) − (cid:0) r br ( x ) − h brflu ( x ) (cid:1) (cid:17) . • We assumed the cross-sectional area of conducting airway tissue a brtis ( x ) to be proportional to cross-sectional lining fluid area a brflu ( x ), with proportionality constant determined by the known total tissuevolume of the central lung V brtis , i.e., via the relation R x TB a brtis ( x )d x = V brtis . • We assumed a homogeneous perfusion of drug tissue within the conducting airway tissue, i.e., a location-resolved blood flow q br ( x ) proportional to a brtis ( x ) and matching the total blood flow in the central lung Q br , i.e. such that R x TB q br ( x )d x = Q br .We emphasize that the pulmonary PDE model was fully parametrized based on in vitro and physiologicaldata, not fitted to the clinical data described in section Model evaluation below. A single adaptation wasdone based on physiological reasoning since no quantitative literature information could be retrieved, namelya 5-fold decrease of dissolution rate in the conducting airways compared to the alveolar space. The reasonfor this adapted dissolution rate constants is that the epithelial lining fluid in the conducting airways –themucus– contains a lower concentration of surfactants (which facilitate dissolution), compared to the alveolarlining fluid. In addition, the upper layer of the mucus is characterized by a high viscosity, which can alsolead to a slower dissolution in comparison to the alveolar space. Model evaluation
The mathematical model was evaluated in a stepwise approach. The first evaluation of the PDE-basedinhalation PK model was based on a simulation of inhaled gold / polystyrene particles. As these particlesdo not dissolve in the pulmonary lining fluids, the interplay of deposition and mucociliary clearance can beevaluated independent of other pulmonary PK processes such as pulmonary dissolution or drug absorption.The initial particle retention was well described with 47% of the deposited particles retained over 8 h and26% retained over 24 h (Fig 3, left). However, the retention after 48 h was underpredicted, i.e. the dataindicated a fraction of 7–36% not being cleared from the lung, whereas the simulation indicated less than5% retention (Fig 3, right).After evaluating the interplay of pulmonary deposition and mucociliary clearance, the pulmonary disso-lution process was evaluated based on data from inhaled monodisperse drug formulations. In this evaluationstep, the systemic PK of 1.5, 3, and 6 µ m-sized particles (aerodynamic diameter) were simulated for theslowly dissolving inhaled drug fluticasone propionate. Simulation results were compared to the determinedAUC , C max , and T max published by Usmani et al. As explained above, the absolute exposure metricsstated in the publication could not be reproduced. Rather than through goodness of prediction of absolute exposure measures, we therefore evaluated the model by comparing the relative change of exposure metricsacross the three considered particle sizes. Of the model-predicted exposure metrics AUC and C max ,67% were within 2-fold and 83% within 3-fold of the reported ratios (compare Table 3). The predicted1.5 µ m : 3 µ m T max ratio matched the experimental data well, however the other predicted T max ratiosshowed larger discrepancies due to a predicted very flat concentration-time profile for 6 µ m particles.As a last step of the PDE model evaluation, systemic PK profiles of fluticasone propionate and budesonidewere simulated for both healthy volunteers and asthmatic patients, the only assumed difference between bothpopulations being a more central particle deposition in asthma patients (see deposition profiles in S2 Fig).For fluticasone propionate inhaled by healthy volunteers with the Diskus R (cid:13) device, a C max of 0.38 nM per10 Time (hours)
Lung r e t en t i on ( % l ung do s e ) Time (days)
Lung r e t en t i on ( % l ung do s e ) PDE model predictionData Subject A (PSL)Data Subject A (Gold)Data Subject B (PSL)Data Subject B (Gold)Data Subject C (PSL)etc.
Figure 3:
Pulmonary retention profiles of inhaled insoluble particles.
Pulmonary retention ofinhaled monodisperse 5 µ m-sized (aerodynamic diameter) gold and polystyrene (PSL) particles. The amountretained is described as a fraction of the initially deposited lung dose. Left: retention-time profile over 24 h,right: retention-time profile over 10 days. Data points: digitized data from six subjects from [26]; solid line:model-based predictions of lung retention.Table 3: Evaluation of model predictions for different particlesizes.Exposure AUC C max T max metric ratio Data Model Data Model Data Model µ m : 3 µ m 1.04 1.65 1.52 4.23 0.40 0.521.5 µ m : 6 µ m 4.16 4.92 5.00 20.7 0.26 0.09 µ m : 6 µ m 4.01 2.98 3.27 4.90 0.63 0.17 For 6 µ m particles, the predicted concentration-time profile was veryflat, resulting in a late T max and therefore low 1.5 µ m : 6 µ m and3 µ m : 6 µ m T max ratios.Comparison of model-predicted and reported PK between three different inhaled monodisperse particleformulations of fluticasone propionate, with aerodynamic diameters of 1.5, 3, and 6 µ m, respectively [25].Due to uncertainty in reported absolute PK parameter readouts, the ratios between both listed particlesizes are reported instead. For example, the 1.5 µ m-sized particles yielded a 4.16 fold higher measuredAUC in comparison to the 6 µ m-sized particles, whereas the model-based prediction resulted in 4.92fold higher AUC . 11g dose, an AUC of 1 . · h per mg dose, and a T max after 41 min were predicted. For budesonide(Turbohaler R (cid:13) ), dissolution as well as absorption to the systemic circulation were predicted to be fastercompared to fluticasone propionate, with a C max of 2.2 nM per mg dose; T max was similar and AUC larger (10 nM · h per mg dose). The comparison of model-predicted PK profiles for fluticasone propionateand budesonide in comparison to observed clinical data from healthy volunteers [40, 41] are displayed inFig 4. For fluticasone propionate, the dose-normalized data from literature were in agreement, and thesimulation results closely matched these data. For budesonide, there was a between-study, but not within-study discrepancy between reported dose-normalized concentration-time profiles; model predictions werewell within the reported range. The discrepancy in the data was not explainable by dose-nonlinear PK,since a 2.5-fold dose change in [40] did not impact on the normalized profiles. Of note, the model-predicteddose-normalized concentration-time profiles based on these scenarios all overlapped, which agrees with theclinically observed absence of dose-dependent pharmacokinetics in plasma for both fluticasone propionateand budesonide. Systemic PK after single dose inhalation (healthy volunteers)
Time (hours) -4 -3 D o s e - no r m a li z ed p l a s m a c on c en t r a t i on [ n M / ug do s e ] Fluticasone propionate
Moellmann et al. 200 ugMoellmann et al. 500 ugHarrison/Tattersfield 1000 ugPDE model
Time (hours) -4 -3 D o s e - no r m a li z ed p l a s m a c on c en t r a t i on [ n M / ug do s e ] Budesonide
Moellmann et al. 400 ugMoellmann et al. 1000 ugHarrison/Tattersfield 1200 ugPDE model
Figure 4:
Pharmacokinetics after drug inhalation of clinical formulations.
Plasma concentration-time profiles after drug inhalation of fluticasone propionate inhaled with the Diskus R (cid:13) inhalation device (leftpanel) and budesonide inhaled with the Turbohaler R (cid:13) inhalation device (right panel). Data points: digitalizedraw data from [40, 41], solid lines: PDE-model based predictions for 200, 500, and 1000 µ g doses of fluticasonepropionate and 400, 1000, and 1200 µ g doses for budesonide (due to an almost dose-linear PK, modelpredictions overlap).The same simulations for asthmatic patients resulted in lower systemic exposure. For fluticasone propi-onate, 28% of the initially deposited lung dose was predicted to be eliminated via mucociliary clearance inhealthy volunteers, compared to 53% in asthmatic patients due to the more central particle deposition. Forbudesonide, 6% and 29% of the initially deposited lung dose were predicted to be eliminated via mucociliaryclearance in healthy volunteers and asthmatic patients, respectively. A comparison of model-predicted and12linically observed differences between healthy volunteers and asthmatic patients is given in Table 4. Forfluticasone propionate, simulations were in good agreement with clinical data, whereas for budesonide, theeffect of the disease was overpredicted. However, the model-predicted stronger disease effect for fluticasonepropionate compared to budesonide –in terms of an AUC increase– was in agreement with the clinical data.Table 4: Evaluation of model-predicted PK differences between healthyvolunteers and asthmatic patients.Healthy:asthmatic AUC C max T max ratio for substance Data Model Data Model Data Model Fluticasone propionate 1.76 1.64 1.67 1.48 1 1.05Budesonide 0.88 1.43 1.07 1.51 NA since the reported T max values both corresponded to the first observed timepoint, no meaningful statement about T max ratios can be made.Comparison of model-based and literature-reported PK difference between healthy volunteers andasthmatic patients. Data are taken from [41] (1000 µ g fluticasone propionate with Diskus R (cid:13) / 1200 µ gbudesonide with Turbohaler R (cid:13) ). Ratios larger than 1 indicate higher values in healthy volunteers, whereasratios smaller than 1 indicate higher values in asthmatic patients. NA, not available. Sensitivity analysis
As a last step of the analysis, a sensitivity analysis was applied to the evaluated PDE model to determinethe most impactful parameters (among formulation-dependent, physiological, and drug-specific parameters)on the following PK readouts:(i) AUC in conducting airway tissue,(ii) the average concentration in the conducting airway tissues after 24 h (which is supposed to correlatewith long-lasting efficacy of an inhaled drug), and(iii) lung selectivity, which is expressed as a ratio between the pulmonary AUC (in conducting airways)and the systemic AUC.This last quantity is supposed to provide a metric of local efficacy weighed against systemic safety, which isan important optimization criterion for inhaled drugs. As the relevance of an input parameter can dependon the complete set of the initial input parameters, the sensitivity analysis was performed starting with theparameters for (i) a 250 µ g fluticasone propionate dose (see Fig. 5) and (ii) a 800 µ g budesonide dose (seeS1 Fig), both representing approved doses [54, 55].Overall, the order of impactful parameters only differed marginally for the different exposure metricsand different drugs. A more than 50% change was observed for tissue volume, tissue partition coefficient,perfusion, dissolution rate and systemic clearance. Particle size had a considerable impact for fluticasonepropionate, and less for budesonide. For fluticasone propionate, the impact of drug solubility in the airwaylining fluids was negligible, whereas for budesonide, although being the more soluble drug, a relevant impactwas predicted since lining fluid concentrations approached the solubility (see S3 Fig). Other parameters, suchas lining fluid volume and all physiological parameters related to the alveolar space were characterized bynegligible impact on the exposure metrics. The impact of deviating the model parameters by a 2-fold increaseand 2-fold decrease was typically antithetical. As a notable exception, the dissolution rate in the conductingairways resulted in lower lung tissue concentration after 24 h, regardless of whether the dissolution rate wasincreased or decreased 2-fold. 13 UC (0-24h) in lung tissue
30 50 100 150 200 300 % of reference value
Solubility (alv)Permeability (alv)Partition coefficient (alv)Solubility (br)Dissolution rate (alv)Permeability (br)Dissolution rate (br)Systemic clearancePartition coefficient (br)Surface area (br)Fluid volume (alv)Surface area (alv)Tissue volume (alv)Perfusion (alv)Fluid volume (br)Mucociliary clearancePerfusion (br)Tissue volume (br)Particle size
Average lung tissue concentration after 24h
30 50 100 150 200 300 % of reference value
AUC (0-24h) ratio (lung selectivity)
30 50 100 150 200 300 % of reference value
Fluticasone propionate (Diskus 250ug asthmatic patient)
Figure 5:
Results of the performed sensitivity analysis for fluticasone propionate.
For each ofthree different exposure measures readouts (AUC, C , and lung selectivity), the impact of a 2-fold increase(blue) and decrease (red) are depicted for a the formulation parameter particle size (top bar) and a set ofphysiological (middle bars) and drug-dependent parameters (bottom bars). The larger a bar, the strongerthe impact of the varied parameter on the respective PK readout. Discussion
The pulmonary pharmacokinetics of orally inhaled drugs are highly complex as pulmonary deposition, pul-monary dissolution, mucociliary clearance, and pulmonary absorption create a complex interplay. Conse-quently, defining adequate optimization parameters for orally inhaled drugs remains challenging. To ade-quately capture and mechanistically predict the complex interplay of all pulmonary PK processes and toidentify optimization parameters, a PDE-based mechanistic PK framework was developed.To build sufficient trust into a pulmonary PK model to use it for identification of optimal compoundcharacteristics, an adequate and systematic model evaluation is a prerequisite. However, previous mechanisticmodeling attempts, most noticeably the ones by Caniga et al. [56] and Boger et al. [20], lack such a thoroughevaluation. Indeed, the approach by Caniga et al., differentiating between airways and alveolar space albeitless mechanistically than in the here-presented model, was evaluated for inhaled mometasone [56] and morerecently for additional fast dissolving drugs (formoterol, salbutamol, and budesonide) [57]. However, thesedrugs would not provide the same insights into the pulmonary interplay of deposition, mucociliary clearance,and dissolution as the slowly dissolving drug fluticasone propionate. An adequate prediction quality forhealthy and diseased populations, different particle sizes, slowly dissolving drugs or even insoluble particlesremains to be demonstrated.A PDE model published by Boger et al. mechanistically included all pulmonary PK processes [20]. How-ever, this model was based on a hypothetical drug, and while most of the characteristics of this hypotheticaldrug can be considered reasonable, such as a K p,lung of 4.9 or the oral bioavailability of 20%, other char-acteristics such as a molecular weight of 250 Da were not considered typical for inhaled drugs (a typical14olecular weight for an inhaled drug was reported to be ≈
370 Da [58]). More importantly, since a modelevaluation based on a hypothetical drug is not feasible, no assessment of the model’s predictive capacitieswas made.Therefore, the here-presented model represents –to the best of our knowledge– the first systematicallyevaluated and publicly available mechanistic pulmonary PK model. First, to evaluate the mechanisticimplementation of the mucociliary clearance, model-based lung retention profiles were compared to thepulmonary retention of insoluble gold and polystyrene particles. 24 h particle retention was adequatelypredicted, whereas long-term retention was underpredicted. One potential explanation could be that theassumed inhaled volume was larger than described, resulting in more particle deposition in the alveolarspace. As the inhaled volume was defined based on the described experimental setup and not measured inthe study, a deviation from the assumption is possible. Since drug deposited in the alveolar space is notcleared by the mucociliary clearance, this would result in higher long-term lung retention than predicted.This explanation is reasonable due to high overall high (inter-subject) variability in pulmonary deposition[59]. As pulmonary drug retention over 10 days should not be relevant for orally inhaled drugs, however,this discrepancy was considered acceptable.Second, to evaluate the mechanistic implementation of the interplay of particle deposition, mucociliaryclearance, and pulmonary drug dissolution, the PK of fluticasone propionate for different monodisperseparticles (1.5, 3, and 6 µ m aerodynamic diameter) were predicted and compared to published data [38]. Ithas to be stated that the reported absolute exposure metrics could not be reproduced. However, they appearextraordinarily high and could not be reached even if the provided dose had been administered intravenously.Nevertheless, the publication by Usmani et al. contains a unique data set, and therefore we still consideredthe dataset, but by comparing the relative, not absolute, differences between the predictions for differentparticle sizes. Based on this evaluation, we considered the model-based predictions for the varying particlesize effect as good.Third, the modeling framework was used (without estimating additional input parameters) to simultane-ously predict the PK of both fluticasone propionate and budesonide. For both drugs, plasma concentration-time profiles in healthy volunteers were very well predicted. In addition, the difference in pharmacokineticsbetween healthy volunteers and asthmatic patients was well predicted for fluticasone propionate. In contrast,the impact of disease on the PK of budesonide was overpredicted, i.e. in asthmatic patients more drug waspredicted to be cleared by mucociliary clearance before it could be absorbed. This can be attributed to thestrongly increased deposition of drug particles in the first airway generations (see S2 Fig), a prediction basedon the assumption that the deposition probability across all airway generations is increased to a similarextent by local airway obstructions. In contrast, it was discussed that airway obstructions in asthma arelocated more peripherally in the conducting airways (in higher airway generations) [60] and therefore thedeposition would increase in more peripheral conducting airways rather than in the trachea and first airwaygenerations (as can be seen in the imaging data in [25]). Unfortunately, we are not aware of quantitativedata or deposition models based on such data, which would allow to better account for these differencesbetween healthy volunteers and asthmatic patients. Therefore, we were unable to integrate a more adequaterepresentation into our mechanistic model.Based on the overall good agreement between the predictions and observed clinical data, we consider thehere-published PDE-based PK model as the currently best-evaluated mechanistic model for orally inhaleddrugs. However, even this mechanistic PK model still represents a simplification of reality and only includesthe above-mentioned pulmonary PK processes; macrophage clearance as well as pulmonary metabolism wereassumed not relevant. For some specific inhaled drugs, this assumption might not hold true. For example,pulmonary metabolism was discussed to be of importance for inhaled macromolecules (e.g., insulin [61, 62]).Macrophage clearance from the alveolar space to the conducting airways was characterized by a very longhalf-life of 35 – 115 days [63, 64]. Consequently, compared to pulmonary absorption and dissolution kineticsof most inhaled drugs, macrophage clearance is expected to be negligible. Furthermore, the considerable15etween-study variability in reported data has to be kept in mind when judging the model evaluationaccuracy. To recognize all of these assumptions, to understand their potential impact on the pulmonary PK,and finally to adequately apply the here presented model framework, a sound understanding of respiratorydrug delivery remains essential.As a last step of the presented analysis, we investigated the most relevant optimization parameters fororally inhaled drugs. To this end, we performed a model-based sensitivity analysis to identify the mostimpactful model parameters on pulmonary exposure metrics. The pulmonary AUC was considered as asurrogate for pulmonary efficacy and the average concentration in the conducting airways after 24 h wasconsidered a surrogate for the effect duration of an inhaled drug. Finally yet importantly, the ratio betweenpulmonary and systemic exposure was considered as a surrogate for lung selectivity of an inhaled drug (i.e.the larger the ratio, the better the lung selectivity).An impactful formulation-dependent model parameter was the particle size distribution of the inhaledfluticasone propionate formulation. This might not be surprising as the particle size simultaneously affectsvarious pulmonary PK processes, i.e., larger particles deposit more centrally, dissolve slower and therefore ahigher fraction of drug would be cleared by the mucociliary clearance. As a result, model-based predictionsfor larger particles indicated less lung exposure, shorter drug residence times in the lung, as well as a lowerlung selectivity. In contrast, smaller fluticasone propionate particles would improve all exposure metrics.In conclusion, the model-based prediction framework indicates that reducing the particle size for inhaledfluticasone propionate would be a reasonable optimization parameter. However, this optimization parameterwas predicted relevant only for fluticasone propionate. In contrast, the sensitivity analysis predicted norelevant impact of the particle size to be expected for a drug like budesonide.Impactful drug-specific optimization parameters for both drugs were (i) the lung partition coefficient, (ii)the systemic clearance, and (iii) the dissolution rate. An increase in the pulmonary partition coefficient, whichindicates an increase in the pulmonary tissue affinity, was already previously suggested as an optimizationparameter for lung selectivity [65, 17, 66]. This parameter however has to be considered carefully as a hightissue affinity / binding also would decrease the free pulmonary concentration. The systemic clearance hadlow impact on the pulmonary drug concentrations, but a higher systemic clearance provided a better lungselectivity. Therefore, especially for drugs with a critical systemic safety profile increasing the systemicclearance can be considered meaningful. In agreement, the relevance of a high systemic clearance to reducesystemic adverse effects for orally inhaled drugs was previously discussed [17, 67]. The pulmonary dissolutionrate for fluticasone propionate already seems to be nearly optimal to achieve a long-lasting efficacy, whichwould be a good property for a once-daily administered drug. An additional decrease in the dissolutionkinetics was predicted to rather decrease the long-lasting efficacy. This finding is in agreement with recentobservations that increasing the tissue affinity might be a better strategy to prolong the efficacy than slowdissolution [68]. Interestingly, while the dissolution rate constant can still be considered an optimizationcriterion, the solubility in the airway lining fluid was not impactful for fluticasone propionate. This underlinesthat actually the dissolution rate and not the solubility is important for pulmonary drug administration.For budesonide, which is characterized by faster dissolution kinetics compared to fluticasone propionate,the solubility was as important as the dissolution rate constant. The reason is that for budesonide, fourparameters simultaneously increased local drug concentrations in the epithelial lining fluids: (i) a higherinhaled dose compared to fluticasone propionate, (ii) a higher fraction of the drug deposited in the lungs,(iii) a lower permeability of budesonide resulting in a higher residence time of dissolved drug, as well as (iv)a faster dissolution, which leads to more dissolved drug in the lining fluids.Even though this sensitivity analysis provides good insights into potential optimization parameters, it hasto be recognized that varying a single input parameter at a time might not always be realistic. For example, ahigher lipophilicity would result in slower dissolution kinetics, higher permeability, and higher tissue affinity.Therefore, as an extension of the here presented sensitivity analysis, a multi-parameter investigation mightbe meaningful during compound optimization. Alternatively, the model-based evaluation allows comparing16ompletely different drugs in a drug optimization program to select the best drug candidate. However, herewe evaluated the impact of the input parameters on the exposure in the conducting airways. These exposuremetrics only represent surrogate parameter and have to be carefully selected based on the mode of actionand the target location, i.e., for a target that would be located in the alveolar space other exposure metricsshould be considered relevant for a sensitivity analysis.In addition to identifying optimization parameters, this sensitivity analysis allows addressing a secondaspect, namely to identify the most impactful (physiological) model parameters which have to be under-stood to adequately predict the PK after oral inhalation. Vice versa , not knowing the exact values of lessimpactful (physiological) parameters is less critical to predict the drug exposure in human. The most im-pactful physiological parameters were tissue volume, perfusion, and mucociliary clearance. Less importantphysiological parameters were, for example, fluid volume or surface area. An additional highly uncertainparameter was the more central deposition pattern for asthmatic patients (these were corrected with anempirical correction factor). Therefore, to improve the PK predictions for patients, it would be valuableto generate and implement quantitative lung imaging data in patients [69]. Another important uncertaintywas the dissolution rate constant in the mucus. To our knowledge, no head-to-head comparison is availablefor in vivo relevant dissolution assays for both dissolution in the mucus and the alveolar lining fluids. Thiswas why we had to make an assumption, namely a fivefold slower dissolution in the conducting airwayscompared to the alveolar lining fluid. The reason for these adapted dissolution rate constants is that theepithelial lining fluid in the conducting airways –the mucus– contains a lower concentration of surfactants,which facilitate dissolution [70], compared to the alveolar lining fluid. In addition, the upper layer of themucus is characterized by a higher viscosity [71], which can also lead to a slower dissolution in comparisonto the alveolar space. However, even though this assumption described the data well, it should be verifiedwith in vitro dissolution experiments. In contrast, other uncertain (physiological) input parameters, such asthe volume of the lung lining fluids, were not impactful and therefore could be considered less critical.The previously mentioned data-based limitations also represent the main opportunities to improve themechanistic PK model. First, it would significantly improve the applicability of the PK model frameworkif an adequate pulmonary deposition model for asthmatics was also implemented (and later also for e.g.,idiopathic pulmonary fibrosis). Furthermore, a more mechanistic representation of tissue distribution (e.g.,separating extra- vs. intracellular concentrations) might increase the predictive power for drugs with ahigh pulmonary tissue binding. Adapting the model to clinical PK data (e.g., by estimating parameters)might improve the description of clinical data, but this would normally not be feasible during compoundoptimization. Therefore, no pulmonary PK parameters were estimated in this work.In conclusion, a PDE-based fully mechanistic pulmonary PK model was developed to perform model-based predictions of the pulmonary and systemic pharmacokinetics of orally inhaled drugs based on in vitro ,formulation-specific, drug-specific, as well as physiological data. To our knowledge, this model is the firstfully mechanistic and systematically evaluated pulmonary PK model. We also have shown that due to a largeinter-study variability, model evaluation based on single (clinical) studies should be considered cautiously.This evaluated PK framework was applied to provide unique insights into optimization criteria for orallyinhaled drugs by applying a model-based sensitivity analysis. It also provided insights which uncertaintiesof the modeling framework still can be improved. Overall, our analysis demonstrated that the model-basedframework offers the potential to increase the quantitative understanding about inhaled drugs and ultimately,the model-based approach is applicable to optimizing drugs and formulations for inhalation therapy.
Supporting information
S1 Appendix. Model development and evaluation details.
Derivations of model components fromfirst principles, a description of the numerical resolution method, model evaluation against nonclinical dataand the strategy for deposition adaptation for asthmatic patients.17
Additional sensitivity analyses for budesonide.
S2 Fig. Deposition patterns.
Deposition patterns in healthy volunteers and asthmatic patients forfluticasone propionate (Diskus R (cid:13) ) and budesonide (Turbohaler R (cid:13) ). S3 Fig. Concentration in lung lining fluids.
Predicted time- and location-resolved lung lining fluidconcentrations of fluticasone propionate (Diskus R (cid:13) , 250 µ g dose) and budesonide (Turbohaler R (cid:13) , 800 µ g dose). S1 File. MATLAB implementation.
MATLAB scripts used for solving the PDE model and for eval-uating it against clinical and experimental data.
S1 Table. Summary of pharmacokinetic studies.
All identified clinical studies on fluticasone propi-onate and budesonide, including their study design and reported pharmacokinetic parameters.
Acknowledgments
We thank Carmen Hummel and the In Vitro ADME and CMC groups from Boehringer Ingelheim Pharma GmbH & Co. KGfor generating the in vitro measurements reported as “in-house data” in the manuscript. Furthermore, wewould like to thank the working group Mathematical Modelling and Systems Biology at the Institute of Math-ematics of University of Potsdam, as well as colleagues from Boehringer Ingelheim Pharma GmbH & Co. KGfor proof-reading the manuscript.
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Report No. 125– Deposition, Retention and Dosimetry of Inhaled Radioactive Substances. NCRP; 1997.[65] B¨ackstr¨om E, Boger E, Lundqvist A, Hammarlund-Udenaes M, Frid´en M. Lung Retention by LysosomalTrapping of Inhaled Drugs Can Be Predicted In Vitro With Lung Slices. J Pharm Sci. 2016;105(11):3432–3439. doi:10.1016/j.xphs.2016.08.014.[66] Stocks MJ, Alcaraz L, Bailey A, Bonnert R, Cadogan E, Christie J, et al. Discovery of AZD3199, AnInhaled Ultralong Acting β Receptor Agonist with Rapid Onset of Action. ACS Med Chem Lett.2014;5(4):416–421.[67] Hochhaus G, M¨ollmann H, Derendorf H, Gonzalez-Rothi RJ. Pharmacokinetic/pharmacodynamic as-pects of aerosol therapy using glucocorticoids as a model. J Clin Pharmacol. 1997;37(10):881–892.[68] Begg M, Edwards CD, Hamblin JN, Pefani E, Wilson R, Gilbert J, et al. Translation of Inhaled DrugOptimization Strategies into Clinical Pharmacokinetics and Pharmacodynamics Using GSK2292767A,a Novel Inhaled Phosphoinositide 3-Kinase δ Inhibitor. J Pharmacol Exp Ther. 2019;369(3):443–453.[69] Boger E, Ewing P, Eriksson UG, Fihn BM, Chappell M, Evans N, et al. A novel in vivo receptoroccupancy methodology for the glucocorticoid receptor: toward an improved understanding of lungpharmacokinetic/pharmacodynamic relationships. J Pharmacol Exp Ther. 2015;353(2):279–287.[70] Wiedmann TS, Bhatia R, Wattenberg LW. Drug solubilization in lung surfactant. J Control Release.2000;65(1-2):43–47.[71] Lai SK, Wang YY, Wirtz D, Hanes J. Micro- and macrorheology of mucus. Adv Drug Deliv Rev.2009;61(2):86–100. 22 mechanistic framework for a priori pharmacokinetic predictionsof orally inhaled drugsS1 Appendix
Niklas Hartung, Jens Borghardt
Contents a r X i v : . [ q - b i o . T O ] J un Derivation of the PDE model
The Noyes-Whitney equation [1] describes the dissolution flux d W dt in terms of properties of the dissolvingparticles and the dissolution medium, d W dt = − D · SA h ( C s − C flu ) , (1)where D is particle diffusivity, SA particle surface area, h height of the diffusion layer, C s particle solubilityand C flu concentration of dissolved substance in the medium.Through geometric assumptions on particles, this equation can be turned into a differential equationdescribing the change of volume of a dissolving particle. We assume particles to be spherical in shape, withradius r , surface area SA = 4 πr , volume s = · πr and mass W = ρs . Furthermore, as suggested previously[2], we assume the height of the diffusion layer to equate particle radius, h ≈ r .Since parametrizing the model in terms of radius r leads to a singularity of the dissolution model when r &
0, in contrast to [2] we choose particle volume s = · πr as a size descriptor instead of particle radius.Differentiating the particle mass equation,d W dt ( t ) = ρ d s dt ( t ) , (2)and equating Eqs. (1) and (2) yieldsd s dt ( t ) = − D · πr ( t ) ρ r ( t ) ( C s − C flu ) = − D · πr ( t ) ρ ( C s − C flu ) = − D · π (cid:16) s ( t ) π (cid:17) / ρ ( C s − C flu ) . We opt to parametrize the dissolution model in terms of maximum dissolution rate k diss = D · C s rather thandiffusivity D , since dissolution rate can be identified more directly from in vitro experiments (see SectionEvaluation of dissolution model against in vitro data). The resulting dissolution model reads d ( s, C flu ) = 4 π k diss ( π ) / ρ · (cid:18) − C flu C s (cid:19) · s / , d s dt ( t ) = − d (cid:0) s ( t ) , C flu (cid:1) . The concentration of dissolved substance, C flu , also changes during dissolution. These processes are coupledin the PDE model described below. As explained in the main text, a continuous representation of airway radius r ( x ) depending on location x within the conducting airways is derived by interpolation. Using the Hofmann/Sturm model v = 0 . · (cid:18) d (cid:19) . , we obtain a location-dependent mucociliary clearance model for a particle at location x ( t ) at time t :d x dt ( t ) = − λ mc (cid:0) x ( t ) (cid:1) = 0 . · (cid:20) r br (cid:18) x ( t )1 cm (cid:19)(cid:21) . = − . · r br (cid:18) x ( t )1 cm (cid:19) . . .3 Individual and population states Physiologically-structured models describe the time evolution of a set of individuals/particles, each exhaus-tively described by a vector of characteristics called state , denoted z , and which changes over time. The timeevolution of the state of any individual is assumed to be governed by a law G , i.e.d z dt ( t ) = G ( t, z ( t )) , z (0) = z . Assuming that a population consists of a large number of individuals, it is natural not to describe eachsingle individual but rather the time evolution of a density ρ ( t, z ) of individuals over the state space. In thisrepresentation, the total number of particles is given by N ( t ) = Z ρ ( t, z )d z, and the number of particles within a particular subregion ω of the state space is given by N ω ( t ) = Z ω ρ ( t, z )d z. For such a domain ω , we set ω ( t ) = { z ( t ) : z ∈ ω } . Assuming that the number of individuals is conservedin the state space, we obtain ddt N ω ( t ) ( t ) ≡ ω ( t ) does not touch the state space boundary. From this expression, a so-called continuity equationcan be derived (see [3]): ∂ t ρ ( t, z ) + div z (cid:2) G ( t, z ) ρ ( t, z ) (cid:3) = 0 . (3) In our application context, the population consists of inhaled undissolved drug particles of different sizes,deposited at different locations within the conducting airways or within the alveolar space. The number ofparticles can only change if particles are (i) cleared to the GI tract by the mucociliary elevator (mucociliaryclearance beyond the trachea, x ( t ) = 0) or (ii) completely dissolved ( s ( t ) = 0). The particle state z = ( x, s ) ∈ [0 , x TB ] × [0 , s max ] can change by mucociliary clearance or dissolution (illus-trated in Fig 1): (cid:18) d x dt ( t ) d s dt ( t ) (cid:19) = (cid:18) − λ mcc ( x ( t )) − d ( s ( t ) , C brflu ( x ( t ) , t )) (cid:19)| {z } =: G br ( t,x ( t ) ,s ( t )) , and Eq. (3) yields the location- and size-structured bronchial PSPM ∂ t ρ br ( t, x, s ) − ∂ x h λ mcc ( x ) ρ br ( t, x, s ) i − ∂ s h d (cid:0) s, C brflu ( t, x ) (cid:1) ρ br ( t, x, s ) i = 0 . (4)3 ocation within airways clearance to GI tract complete dissolutionTrachea Terminal bronchioles P a r t i c l e s i z e at time ! " at time ! > ! " Figure 1: Phase plane representation of a drug particle in the conducting airways. Each particle is charac-terized by its location and size. Over time, particles move within this two-coordinate system until they areeither cleared to the GI tract or completely dissolved.
Since mucociliary clearance is not present in the alveolar space, the particle state z = s ∈ [0 , s max ] canchange by dissolution only: d s dt ( t ) = − d ( s ( t ) , C alvflu ( t )) | {z } =: G alv ( t,s ( t )) , and Eq. (3) yields the size-structured alveolar PSPM ∂ t ρ alv ( t, s ) − ∂ s h d (cid:0) s, C alvflu ( t ) (cid:1) ρ alv ( t, s ) i = 0 . When coupling the PSPM models to equations for dissolved drug in lining fluids, the number of molecules(not particles) have to be conserved during dissolution and mucociliary clearance. This model feature isensured by deriving dissolution and mucociliary clearance rates directly from the PSPMs, which is shown inthe following. The number of undissolved molecules in the conducting airways / the alveolar space are givenby A brsol ( t ) = x TB Z s max Z sρ br ( t, x, s )d x d s, A alvsol ( t ) = s max Z sρ alv ( t, s )d s. We illustrate the derivation for the conducting airways, using integration by parts at step ( ∗ ):4 A brsol dt ( t ) = x TB Z s max Z s∂ t ρ br ( t, x, s )d x d s (4) = − x TB Z s max Z s (cid:16) − ∂ x [ λ mcc ( x ) ρ br ( t, x, s )] − ∂ s [ d ( s, C brflu ( t, x )) ρ br ( t, x, s )] (cid:17) d x d s ( ∗ ) = s max Z s (cid:0) λ mcc ( x TB ) ρ br ( t, x TB , s ) | {z } =0 (no inflow) − λ mcc (0) ρ br ( t, , s ) (cid:1) d s − x TB Z s max Z d (cid:0) s, C brflu ( t, x ) (cid:1) ρ br ( t, x, s )d x d s + x TB Z s max d (cid:0) s max , C brflu ( t, x ) (cid:1) ρ br ( t, x, s max ) | {z } =0 (no inflow) d x = − s max Z s λ mcc (0) ρ br ( t, , s )d s | {z } cleared by mucociliary elevator − x TB Z s max Z d (cid:0) s, C brflu ( t, x ) (cid:1) ρ br ( t, x, s )d x d s | {z } dissolved into lining fluids A similar but simplified reasoning applies to the alveolar space, where only dissolution, not mucociliaryclearance, needs to be considered. 5
Numerical resolution of the PDE model
We consider a uniform time discretization step ∆ t >
0, a location discretization0 = x / < ... < x K +1 / = x TB and a size discretisation 0 = s / < ... < s L +1 / = s max These discretization points are understood as vertices of mesh elements ( k, l ) = [ x k − / , x k +1 / ] × [ s l − / , s l +1 / ] within which unknowns (approximations of ρ br , C brflu , etc.) are defined; they appear in thediscretization of the location- and size-structured model in the conducting airways. The same size grid is alsoused when discretizing the size-structured model in the alveolar space. Furthermore, we define the center( x k , s l ) of mesh element ( k, l ) from the above discretization points, x k := x k − / + x k +1 / , k ∈ { , .., K } ,s l := s l − / + s l +1 / , l ∈ { , .., L } . We use the following notation: • ∆ x k := x k +1 / − x k − / (location length of mesh element ( k, · )) • ∆ s l := s l +1 / − s l − / (size length of mesh element ( · , l )); we also define ∆ s l +1 / := s l +1 − s l (thisexpression will appear later during computations) • Abbreviations for location-structured physiology in conducting airways: λ k := λ mc ( x k ), r br k := r br ( x k ), q br k := q br ( x k ), a brflu ,k := a brflu ( x k ), a brtis ,k := a brtis ( x k ) • ρ br ,nk,l as the numerical approximation of ρ br ( t n , x k , s l ) • ρ alv ,nl as the numerical approximation of ρ alv ( t n , s l ) • C br ,n flu ,k as the numerical approximation of C brflu ( t n , x k ) • C br ,n tis ,k as the numerical approximation of C brtis ( t n , x k ) • C alv ,n flu as the numerical approximation of C alvflu ( t n ) • C alv ,n tis as the numerical approximation of C alvtis ( t n ) • A y ,nx as the numerical approximation of A y x ( t n ) (total amount of drug in a certain state; one of A brsol , A brflu , A brtis , A alvsol , A alvflu , A alvtis , A clearmcc , A clearsys , A systot ), with ’sol’ meaning ’solid’, i.e. undissolved.6 .2 Upwind discretization of physiologically-structured population equations Upwind discretizations, i.e. non-centered finite difference approximations depending on the flow direction,are well tailored to PSPMs, resulting in stable discretizations as long as the timestep ∆ t is small enough(called a CFL condition).The upwind discretization of the conducting airway PSPM ∂ t ρ br ( t, x, s ) − ∂ x (cid:2) λ mc ( x ) ρ br ( t, x, s ) (cid:3) − ∂ s (cid:2) d ( s, C brflu ( t, x )) ρ br ( t, x, s ) (cid:3) = 0is given by ρ br ,n +1 k,l − ρ br ,nk,l ∆ t − λ k +1 / ρ br ,nk +1 ,l − λ k − / ρ br ,nk,l ∆ x k − d ( s l +1 / , C br ,n flu ,k ) ρ br ,nk,l +1 − d ( s l − / , C br ,n flu ,k ) ρ br ,nk,l ∆ s l = 0 , for n ∈ { , ..., N } , k ∈ { , ..., K } , l ∈ { , ..., L } (with ρ br ,nK +1 ,l = ρ br ,nk,L +1 = 0, i.e. no inflow condition). Similarlythe upwind discretization of the alveolar PSPM ∂ρ alv ( t, s ) − ∂ s (cid:2) d ( s, C alvflu ( t )) ρ alv ( t, s ) (cid:3) = 0is given by ρ alv,n+1 l − ρ alv ,nl ∆ t − d ( s l +1 / , C alv ,n flu ) ρ alv ,nl +1 − d ( s l − / , C alv ,n flu ) ρ alv ,nl ∆ s l = 0 . Within this framework, the number of undissolved drug molecules is approximated by A br ,n sol,k := L X l =1 ∆ s l s l ρ br ,nk,l (location k in conducting airways) ,A alv ,n sol := L X l =1 ∆ s l s l ρ alv ,nl (alveolar space) . Recognizing that all processes except for dissolution and mucociliary clearance are linear, we propose animplicit discretization to ensure unconditional stability of these other processes, too. The numerical schemeis formulated in terms of local amounts (in bronchial/alveolar fluid/tissue) rather than concentrations. Tothis end, we define V brflu ,k := ∆ x k a brflu ,k (lining fluid volume at k -th location grid cell) V brtis ,k := ∆ x k a brtis ,k (tissue volume at k -th location grid cell)and obtain the amounts A br ,n flu ,k := C br ,n flu ,k V brflu ,k , A br ,n tis ,k := C br ,n tis ,k V brtis ,k (conducting airways) ,A alv ,n flu := C alv ,n flu V alvflu , A alv ,n tis := C alv ,n tis V alvtis (alveolar space) . Furthermore, it will be useful to definePS brk := ∆ x k πr br k P app (permeability-surface area product at k -th location grid cell) Q br k := ∆ x k q br k (perfusion of k -th location grid cell) .
7o arrive at a numerical scheme formulated on the computational grid, integrals are discretized as follows: Z s max f ( s )d s ⇒ L X l =1 ∆ s l f ( s l ) , Z x TB f ( x )d x ⇒ K X k =1 ∆ x k f ( x k ) Bronchial kinetics A br ,n +1flu ,k − A br ,n flu ,k ∆ t = ∆ x k L X l =2 ∆ s l − / d ( s l − / , C br ,n flu ,k ) ρ br ,nk,l | {z } dissolved (see section below) − PS brk A br ,n +1flu ,k V brflu ,k − A br ,n +1tis ,k V brtis ,k K pl,u ! A br ,n +1tis ,k − A br ,n tis ,k ∆ t = PS brk A br ,n +1flu ,k V brflu ,k − A br ,n +1tis ,k V brtis ,k K pl,u ! − Q br k A br ,n +1tis ,k V brtis ,k RK pl − A sys ,n +1ctr V sysctr ! Alveolar kinetics A alv ,n +1flu − A alv ,n flu ∆ t = L X l =2 ∆ s l − / d ( s l − / , C alv ,n flu ) ρ alv ,nl − PS alv A alv ,n +1flu V alvflu − A alv ,n +1tis V alvtis K pl,u ! A alv ,n +1tis − A alv ,n tis ∆ t = PS alv A alv ,n +1flu V alvflu − A alv ,n +1tis V alvtis K pl,u ! − Q alv A alv ,n +1tis V alvtis RK pl − A sys ,n +1ctr V sysctr ! Systemic kinetics A sys ,n +1gut − A sys ,n gut ∆ t = L X l =1 ∆ s l s l λ / ρ br ,n ,l | {z } mucociliary clearance (see section below) − k A sys ,n +1gut A sys ,n +1ctr − A sys ,n ctr ∆ t = F k A sys ,n +1gut − k A sys ,n +1ctr + k A sys ,n +1per + Q alv A alv ,n +1tis V alvtis RK pl − A sys ,n +1ctr V sysctr ! + K X k =1 Q br k A br ,n +1tis ,k V brtis ,k RK pl − A sys ,n +1ctr V sysctr ! A sys ,n +1per − A sys ,n per ∆ t = k A sys ,n +1ctr − k A sys ,n +1per A n +1clear − A n clear ∆ t = (1 − F ) k A sys ,n +1gut + k A sys ,n +1ctr .4 Mass conservation of PDE discretisation The above terms are chosen such that the number of molecules is conserved, i.e., the total amount of drugin the body plus the amount excreted, given by A n tot = A br ,n sol + K X k =1 (cid:16) A br ,n flu,k + A br ,n tis,k (cid:17)| {z } in conducting airways + A alv ,n sol + A alv ,n flu + A alv ,n tis | {z } in alveolar space + A sys ,n ctr + A sys ,n per + A sys ,n gut + A n clear | {z } in GI tract, systemic circulation or excreted , remains constant for all n . Mass conservation during uptake from lining fluid to lung tissue can be seendirectly from the rates in the equations: the same terms, e.g.PS brk A br ,n +1flu ,k V brflu ,k − A br ,n +1tis ,k V brtis ,k K pl,u ! , appear in both equations with opposing signs (for systemic uptake from conducting airway tissue, contri-butions at different locations are summed). Furthermore, using the upwind formulation, we can decomposethe rate of change of the amount of undissolved drug: A br ,n +1sol − A br ,n sol ∆ t = K X k =1 L X l =1 ∆ x k ∆ s l s l ρ br ,n +1 k,l − ρ br ,nk,l ∆ t = − K X k =1 L X l =1 ∆ x k ∆ s l s l − λ k +1 / ρ br ,nk +1 ,l − λ k − / ρ br ,nk,l ∆ x k − d ( s l +1 / , C br ,n flu ,k ) ρ br ,nk,l +1 − d ( s l − / , C br ,n flu ,k ) ρ br ,nk,l ∆ s l ! = + K X k =1 L X l =1 ∆ s l s l (cid:16) λ k +1 / ρ br ,nk +1 ,l − λ k − / ρ br ,nk,l (cid:17) + K X k =1 L X l =1 ∆ x k s l (cid:16) d ( s l +1 / , C br ,n flu ,k ) ρ br ,nk,l +1 − d ( s l − / , C br ,n flu ,k ) ρ br ,nk,l (cid:17) = − L X l =1 ∆ s l s l λ / ρ br ,n ,l | {z } mucociliary clearance − K X k =1 ∆ x k L X l =2 ∆ s l − / d ( s l − / , C br ,n flu ,k ) ρ br ,nk,l | {z } dissolution at location k and noting that these two terms are matched in the equations for dissolved drug in the lining fluid andof cleared drug, we can conclude that mass is conserved during dissolution and mucociliary clearance. Ananalogous computation shows mass conservation during dissolution in the alveolar space. Mass balance waschecked systematically during all simulations shown. Deposition patterns, as well as several parameters used in the PSPMs, are not resolved at the same scaleas the computational grid. Therefore, a projection step is necessary prior to being able to integrate thesequantities into the model.
Deposition data are given for each airway generation g , ..., g K and for a fixed set of reference particle sizes S , ..., S L , resulting in a discrete deposition pattern ( D k,l ). The dose should be conserved, equivalent toconservation of number of molecules, but not number of particles.9e proceeded as follows (see Fig. 2 for an illustration): • We define a region S εk around S k , given by S εk = [ S k − ε, S k + ε ], with small ε such that all such regionsare disjoint. • From the discrete values D k,l , we define a continuous function D ( x, s ) = X k,l ε | g k | { x ∈ g k ,s ∈ [ S k − ε,S k + ε ] } , such that R g k × S εk D ( x, s )d x d s = D k,l . • We define the initial condition on the computational grid by ρ k,l = 1∆ x k ∆ s l Z C ( k,l ) D ( x, s )d x d s for grid cell C ( k, l ) = (cid:2) x k − , x k + (cid:3) × (cid:2) s l − , s l + (cid:3) For a per-generation parameter (e.g., airway radius, blood flow, ...), generically denoted P , we construct alocation-resolved representation using the previous construction only in the location coordinate, i.e.: • From the discrete values P k , we define a continuous function P ( x ) = X k | g k | { x ∈ g k } , such that R g k P ( x )d x = P k . • We define the location-resolved representation on the computational grid by p k = 1∆ x k x k + 12 Z x k − P ( x )d x. We evaluated the dissolution model against in vitro data from a dissolution study [4], where the authorsevaluated the dissolution kinetics of fluticasone propionate and budesonide particles with defined particlesizes (see Table 1).Based on the in vitro data, we compared different dissolution models: • a first-order dissolution model (estimated empirically; size-independent) • an unsaturable dissolution model (formally corresponding to C s = + ∞ in the dissolution model) • saturable dissolution models with different solubilitiesThe results are shown in Fig. 3. A particle size-dependency is clearly visible, as well as a saturation effect.Among the different saturable dissolution models, the parametrization using in house data resulted in aqualitatively better description than the values reported in [4].10 ocation within airways P a r t i c l e s i z e Data ! ",$ Computational grid cells [& "' ⁄ ) * , & "+ ⁄ ) * ]×[. $' ⁄ ) * , . $+ ⁄ ) * ] generation 1 generation 2 generation 3 Projection of ! ",$ onto state space r e f e r e n c e s i z e s ( d a t a ) Contributions to / ",$0 Figure 2: Resolution of data against computational grid. Deposited amounts of particles with a particularsize and at a particular airway location (black dots) are first distributed evenly within the respective airwaygeneration and a small size range (blue rectangles), yielding a continuous representation of deposition withinstate space. The numerical approximation to the location- and size-structured density is defined on anindependent computational grid. Its initial value within a grid cell is the average of the values of thecontinuous representation. Contributing location-size regions to a particular grid cell are highlighted in gray.
Different values for the thickness of the lining fluid layer in the conducting airways have been reported. Afterreviewing the literature, we concluded that the linear relationship shown in Fig. 4 adequately described thecurrent state of knowledge.We decided not use literature values on total lung lining fluid volume since the reported values arenot experimentally measured values but rather estimates based on height measurements and geometricalconsiderations. However, we note that the total lining fluid volume computed under the our geometrical11ubstance ACI stage Cutoff size range Aerodyn. diam. Geometric diam.Fluticasone propionate 4 2.1 – 3.3 µ m 2.7 µ m 3.2 µ mFluticasone propionate 2 4.7 – 5.8 µ m 5.25 µ m 6.2 µ mBudesonide 4 2.1 – 3.3 µ m 2.7 µ m 2.4 µ mTable 1: Aerodynamic and geometric particle sizes corresponding to the experimental protocols of [4].Particles within defined ranges of aerodynamic particle sizes were obtained from different stages of Andersoncascade impactors (ACI). For simulation of dissolution kinetics, we took the geometric diameter correspond-ing to the mean aerodynamic particle diameter within each impactor stage. Time (in [h]) F r a c t i on d i ss o l v ed Dissolution of fluticasone propionate (ACI stage 4)
Rohrschneider et al. (Fig. 4)Rohrschneider et al. (Fig. 5)First-order kinetics (Weber et al.)Unaturable dissolutionSaturable dissolution,Cs=12 uM (inhouse)Saturable dissolution, Cs=40 uM (Rohrschneider et al.)
Time (in [h])
Dissolution of fluticasone propionate (ACI stage 2)
Rohrschneider et al. (Fig. 5)First-order kinetics (Weber et al.)Unsaturable dissolutionSaturable dissolution,Cs=12 uM (inhouse)Saturable dissolution,Cs=40 uM (Rohrschneider et al.)
Time (in [h])
Dissolution of budesonide (ACI stage 4)
Rohrschneider et al. (Fig. 4)First-order kinetics (Weber et al.)Unsaturable dissolutionSaturable dissolution,Cs=69.8 uM (inhouse)Saturable dissolution,Cs=1090 uM (Rohrschneider et al.)
Figure 3: Comparison of dissolution models based on in vitro dissolution data.assumptions ( ≈ . As stated in the main text, we could not reproduce the fluticasone propionate exposure indices reported byUsmani et al. [9] based on the provided study information. Here we provide full details for this statement.For the smallest particles of 1.5 µ m diameter, Usmani et al. reported an AUC of 923 .
28 pg · h / mL, i.e.in molar units 1 .
84 nM · h. Assuming 100 % lung uptake, no mucociliary clearance and a full systemic uptakewithin 12 h, and taking the literature value for fluticasone propionate clearance of 73 L / h [10], we obtain avery conservative upper bound of AUC max = DoseCL · MW = 1 .
37 nM · h.A more realistic, albeit still conservative calculation and a simulation with the PDE model are shownin Table 2. In conclusion, the reported AUC value is approximately 2-4 times larger than what could bereasonably expected. Accordingly, C max values are also much higher than predicted by the PDE model.12igure 4: Model for height of location-resolved lining fluid (solid black line) compared to reported literaturedata [5, 6, 7, 8]. In order to predict the pulmonary deposition patterns, the MPPD software v2.1 was used [11]. This softwareallows to predict the generation-dependent pulmonary deposition of inhaled particles, where generations 1-17represent the conducting airways (generation 1 = trachea) and generations 18-25 the alveolar space. Threetypes of input data are required in the MPPD software: (1) airway morphometry, (2) particle properties, and(3) exposure condition, as outlined below. The MPPD software was only applied to simulate the depositionpatterns but not used to investigate the clearance of particles from the lung.
Airway morphometry.
For all predictions performed with the MPPD software, the airway morphometrywas represented by the human “Yeh/Schum 5-Lobe” model [12]. The inhalation flow characteristicswere assumed to be represented by uniform expansion of the lung so that consequently also the inhala-tion and exhalation flow were constant over time. The standard airway morphometry defined in theMPPD software was selected for all deposition pattern predictions, i.e. the default values for functional13ssumptions for AUC calculation Calculated AUCLung dose MCC Timespan (compared to reported AUC)100% no AUC ∞
26% lower than reported56% no AUC ∞
58% lower than reported56% yes AUC
74% lower than reportedTable 2: Comparison of calculated AUC vs. reported AUC for different assumptions. Even under themost conservative assumptions, AUC is considerably underestimated, which becomes more pronounced asthe model gets more realistic.residual capacity (3300 mL) and upper respiratory tract volume (50 mL) were used [13].
Particle properties.
The inhaled particle properties were defined based on the information in the re-spective publications, or alternatively for the respective inhalation device (references are provided inTable 3). For all predictions, the density of the particles was set to 1 g / cm ; and the particle diameterwas defined as the mass median aerodynamic diameter, which is typically provided in literature. Asdescribed in the main manuscript, the difference between aerodynamic and geometric diameters wasaccounted for, such that the real surface area could be used as an input parameter to the dissolutionmodel. The MPPD software was only used to predict pulmonary deposition patterns of monodis-perse particles. To predict the deposition patterns for the monodisperse gold/polystyrene particles(Study I) and the inhaled monodisperse fluticasone propionate particles (Study II), this informationwas sufficient. Whenever pulmonary deposition patterns of a particle size distribution were required(Studies III/IV), these were generated in a two-step approach. First, all relevant monodisperse parti-cles size bins of the particle size distribution were simulated as monodisperse particles with the MPPDsoftware. In a second step, the complete deposition pattern was calculated by normalizing the de-posited amount per particle size bin by the dose in this respective bin. The two additional optionsof the MPPD software, namely the “Nanoparticle Model” and “Inhalability Adjustment” were notapplied to predict the deposition patterns. Exposure conditions.
The exposure scenario was set to constant exposure and the body orientation duringthe inhalation process was assumed “upright”. Furthermore, for all predictions, it was assumed thatthe breathing scenario was represented by oral breathing, which is the typical inhalation route fordrugs delivered to the lungs. Breathing frequency, tidal volume, inspiratory fraction as well as pausefraction were all defined based on the inhalation flow properties provided in the respective publications(see Table 3).
Since the MPPD software predicts deposition patterns in healthy volunteers, it cannot directly be used topredict deposition patterns in asthmatic or COPD patients. In these patients, due to narrowed airways,deposition is more central in comparison to healthy volunteers. Whenever patients were considered in astudy rather than healthy volunteers, deposition patterns had to be adapted adequately. To this end, thefraction of the inhaled dose deposited in any specific airway generation was increased by an adjustmentfactor such that the deposited fraction of the lung dose in the alveolar space was 2-fold lower than in healthyvolunteers. This number was derived from published data on conducting airway to alveolar deposition ratios[17]. 14 tudy I Study II Study III Study IVParticle properties
Substance gold /polystyrene fluticasonepropionate fluticasonepropionate budesonideFormulation type monodisperse monodisperse polydisperse polydisperseParticle size(s) 5 µ m diameter 1.5 / 3 / 6 µ mdiameter distributionbased on [14] distributionbased on [14] Exposure scenario
Device custom setup(see [15]) Inhalationchamber Diskus R (cid:13) Turbohaler R (cid:13) Breathing frequency 6/min 5/min 6/min 6/minTidal volume 200 mL 2000 mL 2000 mL 2000 mLInhalation time 1 sec 4 sec 1.33 sec 1.33 secExhalation time 1 sec 3 sec 2.67 sec 2.67 secPause time 8 sec 5 sec 6 sec 6 secInhalation flow 12 L/min 30 L/min 90 L/min 60 L/min
Deposition patterncorrections
Lung dose no correction 56.3% / 51% /46.0% 14.5% based on[16] 35% based on[16]Central/peripheraldeposition ratio no correction centraldepositedfraction: 56.1%/ 65.7% / 75.4% 2-fold loweralveolardeposition forasthma patients[17] 2-fold loweralveolardeposition forasthma patients[17]Table 3: Study-specific input data to the MPPD software.15
Generation of in-house data
For in vivo relevant characterization of the drug solubility, the surfactant-containing medium Alveofact R (cid:13) ,a commercially available product, was taken. Alveofact R (cid:13) contains phospholipids obtained from bovine lung(i.e., surfactants) and is available as dry powder ampoules ready for reconstitution. As reconstitutionmedium, a 0.1 mol/l sodium dihydrogenecarboante buffer with pH 7.4 was used. A suspension with 50mg/ml Alveofact R (cid:13) was produced according to the information and instruction for use of the commercialproduct. At these concentrations, Alveofact R (cid:13) forms a micellar system. 1 mg of drug (either budesonide orfluticasone propionate) is suspended in 1 ml of this medium and shaken for 24 h at 37 ◦ C. Afterwards, thesuspension is filtered with a commercially available Whatman Mini-UniPrep syringeless filter containing a0.45 µ m filter membrane out of glass microfibers. As the micelles pass this membrane and as the concentra-tion of phospholipids is too high to be directly injected in the HPLC system for analysis of the solubilizedamount of drug, the micelles are destroyed by adding DMSO in a 1:1 ratio to the filtered micellar solution.The phospholipids can be separated by an additional 5 – 10 minutes centrifugation step. A small aliquot ofthe remaining solution is taken and injected into a HPLC system for quantitative analysis of the solubilizedamount of drug. To determine the Blood:Plasma (BP) ratio, the respective amount of the drug (i.e., fluticasone propionate)was added to 490 µ L human blood and to 490 µ L plasma samples to obtain a drug concentration of 10 µ M.Both the plasma (plasma sample ◦ C (n=3). Afterwards the blood sample was centrifuged at 3000 rpm to separate the blood cellsfrom the plasma sample (plasma sample
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