Deposition and fine particle production during dynamic flow in a dry powder inhaler: A CFD approach

International Journal of Pharmaceutics 461 (2014) 129–136

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Personalised Medicine

Deposition and fine particle production during dynamic flow in a dry powder inhaler: A CFD approach J. Milenkovic a,b , A.H. Alexopoulos a , C. Kiparissides a,b,c,∗ a b c

CPERI, CERTH, 6th km Harilaou-Thermi rd., Thermi, Greece Department of Chemical Engineering, Aristotle University of Thessaloniki, Thessaloniki, Greece Department of Chemical Engineering, The Petroleum Institute, Abu Dhabi, United Arab Emirates

a r t i c l e

i n f o

Article history: Received 23 September 2013 Received in revised form 21 November 2013 Accepted 24 November 2013 Available online 1 December 2013 Keywords: Dynamic Dry powder inhaler Turbuhaler CFD Fine particle fraction Deposition

a b s t r a c t In this work the dynamic flow as well as the particle motion and deposition in a commercial dry powder inhaler, DPI (i.e., Turbuhaler) is described using computational fluid dynamics, CFD. The dynamic flow model presented here is an extension of a steady flow model previously described in Milenkovic et al. (2013). The model integrates CFD simulations for dynamic flow, an Eulerian-fluid/Lagrangian-particle description of particle motion as well as a particle/wall interaction model providing the sticking efficiency of particles colliding with the DPI walls. The dynamic flow is imposed by a time varying outlet pressure and the particle injections into the DPI are assumed to occur instantaneously and follow a prescribed particle size distribution, PSD. The total particle deposition and the production of fine particles in the DPI are determined for different peak inspiratory flow rates, PIFR, flow increase rates, FIR, and particle injection times. The simulation results for particle deposition are found to agree well with available experimental data for different values of PIFR and FIR. The predicted values of fine particle fraction are in agreement with available experimental results when the mean size of the injected PSD is taken to depend on the PIFR. © 2013 Elsevier B.V. All rights reserved.

1. Introduction The dry powder inhaler (DPI) is one of the principle means of delivering pharmaceuticals due to its ease of use and costeffectiveness. DPIs have been used commercially since 1971 and are continuously being improved and updated with new models (Hickey and Hickey, 1996; Islam and Cleary, 2012). The main function of a DPI is to deliver a specific amount of a drug to a target region of the respiratory system by emission of fine particles from the device (Daniher and Zhu, 2008). Airflow and powder dispersion in a DPI are generated by strong inhalation through the device and are complex and highly dynamic processes. The powder is released into the device as particles and aggregates which move

Abbreviations: CFD, computational fluid dynamics; DEM, discrete element method; DPI, dry powder inhaler; FIR, flow increase rate; FPF, fine particle fraction; HPLC, high performance liquid chromatography; PIFR, peak inspiratory flow rate; PSD, particle size distribution; SST, shear-stress transport; UVS, UV spectrophotometer. ∗ Corresponding author at: Chemical Process and Energy Resources Institute/Centre for Research and Technology Hellas, 6th km Harilaou-Thermi rd., 57001 Thessaloniki, Greece OR Department of Chemical Engineering, Aristotle University of Thessaloniki, P.O. Box 472, 54124 Thessaloniki, Greece. E-mail addresses: [email protected] (J. Milenkovic), [email protected] (A.H. Alexopoulos), [email protected] (C. Kiparissides). 0378-5173/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.ijpharm.2013.11.047

through the DPI, colliding with the DPI walls, undergo breakage and/or deposition, and exit into the oral cavity (Ashurst et al., 2000; Newman and Busse, 2002; Tobyn et al., 2004; Islam and Gladki, 2008; Alagusundaram et al., 2010; Islam and Cleary, 2012). In order to deliver an effective drug dose to a target region of the respiratory system a sufficient dose must be first released by the DPI. The motion of the emitted particles and their deposition in the respiratory tract depends on their velocity, position, and size at the mouthpiece outflow (Matida et al., 2003). The effectiveness of a DPI is often described in terms of two key outflow characteristics, i.e., the total emitted dose as well as the production of fine particles (Alagusundaram et al., 2010). The fine particle fraction (FPF) represents the mass ratio of emitted particles with a diameter less than a critical value, e.g., 4–6 ␮m, and is a frequently used measure of the effectiveness of powder dispersion in a DPI (Mitchell and Nagel, 2004). Drug losses and low production of fines can result from incomplete breakage of particle aggregates or by internal losses due to deposition. In order to understand and improve the function of DPI devices, systematic computational studies have been performed and are reviewed in Islam and Cleary (2012) and Milenkovic et al. (2013). Different computational approaches have been employed including computational fluid dynamics (CFD) (Schuler et al., 1999; Ligotke, 2002; Coates et al., 2004, 2005, 2006) and the discrete element method (DEM) (Tong et al., 2010; Calvert et al., 2011). Methods

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that track the individual particle constituents of aggregates (e.g., DEM) provide valuable information but are not easily applicable to this problem due to the very large number of constituent particles (e.g., ∼108 for 2 ␮m particles). From the current state-of-the-art it is clear that the strength of aggregates as well as their interactions with the DPI walls determine the effectiveness of powder dispersion, the emitted dose as well as the particle size distribution (PSD) and the FPF of the DPI outflow (Kroeger et al., 2010; Adi et al., 2011). In Milenkovic et al. (2013) the steady state airflow and the dynamic particle motion were determined in the Turbuhaler DPI employing a particle adhesion model to determine the sticking efficiency with the DPI walls. Recently DEM has been employed to describe the motion and breakup of representative aggregates released during powder dispersion in an inhaler (Tong et al., 2010; Calvert et al., 2011). These approaches underline the importance of both particle adhesion and cohesion forces in the description of powder release and dispersion, aggregate breakage, and deposition. In general, during a dynamic inhalation through a DPI device the flow rate increases rapidly with time and approaches the peak inspiratory flow rate (PIFR). The flow increase rate (FIR) can be defined as the slope of the flow rate with time at 50% of the PIFR value. Computational efforts to date have focused predominantly on steady state flows in DPIs. However, transient airflow effects can be important and the effects of FIR and PIFR need to be established for dynamic flows. It should be noted that most DPIs function optimally at large values of PIFR (e.g., 60–70 L/min) and FIR (e.g. >5 L/s2 ). However, inhalations at reduced values PIFR or FIR can be exhibited by individuals with impaired or limited respiratory function, e.g., children and elderly. Consequently, it is important to understand the characteristics of particle deposition and FPF of emitted particles for a range of PIFR and FIR values encompassing normal and impaired inhalations. The Turbuhaler (AstraZeneca) is a multidose dry powder inhaler that is widely used to deliver a number of drugs (typically for asthma), e.g., budesonide (as Pulmicort), to the upper respiratory tract (Wetterlin, 1988; Tsima et al., 1994). Experimental investigations have provided detailed information on particle capture as well as the FPF and size distribution of particles in the outlet flow (de Koning et al., 2001; Hoe et al., 2009; Abdelrahim, 2010). Recently CFD simulations have detailed the particle deposition behaviour in the Turbuhaler assuming steady flow (Milenkovic et al., 2013). In this work a multi-scale computational model of the Turbuhaler DPI is employed in which the dynamic airflow is determined by CFD simulations, dynamic particle motion is determined by Eulerian/Lagrangian simulations, and particle/wall interactions are described by a collision/adhesion model. In what follows the DPI geometry, the discretization procedure, the CFD simulations, and the particle model are summarized and the aspects of the dynamic flow simulations are described in detail. Next the results for dynamic airflow are presented followed by the results for particle deposition and fine particle production. Finally, the computational results are compared to available experimental data.

2. Computational model

Fig. 1. Turbuhaler DPI: (a) component geometry, (b) assembled device, and (c) airflow domain of DPI.

facilitate numerical convergence. A computational grid consisting of 1.7 × 106 tetrahedral cells was found to provide sufficiently grid independent solutions in steady flow simulations (in Milenkovic et al., 2013) and was employed in all the dynamic flow simulations of this work. A previous CFD model for steady flow in the DPI (Milenkovic et al., 2013) was extended for dynamic flow. The Navier–Stokes equations are solved using the commercial CFD software FLUENT (v6.3). The PISO scheme was employed to describe pressure–velocity coupling. Second order discretization was used for pressure and third order MUSCL for momentum and turbulent variables. Zero gauge pressure boundary conditions were employed at all the inflows, i.e., two powder loaded cylinders (see bottom of Fig. 1b) and four extra air inlets in the DPI circulation chamber (see Fig. 1a). Different dynamic airflows in the DPI were simulated by imposing dynamic outlet pressures which produced an initial rapid increase in flow which then gradually converged to a steady flow rate, i.e., the PIFR. In this work the instantaneous volumetric outflow rate, Q, is assumed to obey the following equation: Q = PIFR (1 − e−˛t )

(1)

where t is inhalation time and a is a constant that depends on the values of PIFR and FIR according to: ˛ = 2.31FIR/PIFR

(2)

The instantaneous outflow gauge pressure, P, is given by: P = −1.7856Q 2

(3)

established in Milenkovic et al. (2013) for steady flow simulations. The dynamic simulations were performed from an initial quiescent state which was perturbed by the application of a dynamic outflow pressure (Eq. (2)). A very small initial time step of 10−6 s was necessary to obtain stable results and to maintain the solution residuals (i.e., of continuity, momentum, k, and ω) less than 10−4 during the iterations with time. As the flow rate increased with time the numerical solution became more stable and the solution step size was gradually increased up to a maximum value of 5 × 10−3 s.

2.1. CFD model 2.2. Particle model The Turbuhaler DPI geometry was constructed in a CAD/CAM environment (i.e., CATIA v5 R19) (Fig. 1a) and the individual components of the DPI were then assembled to obtain the DPI device (Fig. 1b). Subsequently, the geometry of the airflow domain was extracted and then imported into GAMBIT (v2.1) where several computational grids were constructed (Fig. 1c). It should be noted that a mouthpiece extension was added onto the DPI geometry to

The motion of particles in the DPI was determined by Eulerianfluid/Lagrangian-particle simulations of particles encompassing the size ranges of typical pharmaceutical powders employed in the Turbuhaler. Particle simulations were conducted in the dilute limit, i.e., without considering any effects of particles on flow, as the solids volume ratio in the DPI device was less than 10−2 . For the particles

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considered in this work, i.e., D = 0.5–20 ␮m, inertial forces were the dominating influence on particle motion. In general during a dynamic inhalation the powder is released from its storage site (i.e., the powder loaded cylinders) over a finite period of time as particles and particle aggregates of different size. Due to the rapidly changing flow field at the beginning of an inhalation the instantaneous injected PSD is expected to vary with time in terms of total mass and number concentrations as well as mean size and shape. In this work particles were assumed to be released instantaneously and uniformly from a surface situated 0.5 mm upstream from the powder loaded cylinders. Simulations were performed using a total number of 4 × 104 particles which were assumed to follow a PSD obtained from freely flowing powder of budesonide (Pulmicort) which was found to follow the following distribution: f (D) =

1 D0

e−D/D0

(4)

where D0 = 2.2 ␮m as measured from micrographs (Milenkovic et al., 2013). In order to describe the increased aggregate breakage with flow, the mean particle size was assumed to decrease linearly from D0 = 2.2 ␮m at Q = 30 L/min to 1.6 ␮m at 60 L/min: D0 = 2.8 − 0.02Q

(5)

where D0 in ␮m and Q in L/min. Finally, in this work the effect of finite injection time is examined by considering delayed instantaneous particle injections (i.e., tinj = 0.2 and 0.5 s). As in Milenkovic et al. (2013) it is assumed in this work that breakage of aggregates occurs rapidly during their release from the powder loaded cylinders up to the injection surfaces. Subsequently, no more breakage occurs in the DPI and collisions with walls result in deposition or rebound but not breakage. Although ignoring aggregate breakage due to collisions with the DPI walls is a significant simplification of the problem, the model was able to describe the experimental data for total particle depositions for steady flow (Milenkovic et al., 2013) and is used in this work. The total particle deposition in the DPI device was determined according to a sticking efficiency which is related to a critical normal velocity above which particles reflect with some dissipation of momentum characterized by attenuation coefficients. The sticking efficiency was described according to a model developed by Brach and Dunn (1992, 1995) for spherical particles and is provided in Appendix A. Compared to the steady-flow model developed in Milenkovic et al. (2013) this work deals with dynamic flows imposed by dynamic outlet pressure boundary conditions (e.g., Eqs. (1)–(3)). The particle model is solved simultaneously with the dynamic flow model instead of sequentially and the injected particles are assumed to follow a PSD (i.e., Eq. (4)) with a variable mean diameter (i.e., Eq. (5)) instead of a constant diameter as in Milenkovic et al. (2013). 3. Results and discussion 3.1. Simulations of airflow in the Turbuhaler DPI The range of Reynolds numbers (i.e., Re = Q/A1/2 , where  and  are the density and the viscosity of air and A is the cross-sectional area) encountered during a dynamic inhalation is approximately 0–20,000 for a PIFR of 70 L/min. The transitional SST k–ω model was found to provide the most accurate and grid independent solutions for steady flow (Milenkovic et al., 2013) and is used in this work for dynamic flows. To check for consistency with steady flow simulations, dynamic flow simulations were performed by imposing jump outlet

Fig. 2. Turbuhaler DPI airflow velocity magnitude: (a) PIFR = 30, (b) 50, (c) 70 L/min. Jump outlet pressure. Simulation time t = 2 s. Velocities scaled with average outlet velocities.

pressure boundary conditions at t = 0 which continued until a steady flow was obtained, e.g., at t = 0.1–0.6 s, depending on the FIR and PIFR values. In Fig. 2 the dynamically obtained steady-state velocity magnitudes in the DPI at t = 2 s for Q = 30, 50, and 70 L/min are displayed along an axial plane that intersects the inhalation channel. The flow velocities are scaled in terms of the mean outlet velocity, i.e., 6.8, 11.4, and 16 m/s for Q = 30, 50, and 70 L/min, respectively, to facilitate comparison between different flow rates. It is clear that these flow fields are very similar to each other and are in fact nearly identical with the solutions obtained by steady flow simulations (see Milenkovic et al., 2013). Specifically, the flow in the inhalation channel is dominated by the two injection streams emanating from the powder-loaded cylinders. The circulation chamber with the four additional flow inlets displays a more complicated circulation pattern. Strong tangential flow is developed in the helical section, leading to nonhomogeneous velocity profiles that persist even up to the mouthpiece extension. 3.2. Simulation of particle motion and deposition in the Turbuhaler DPI The number of particles depositing (i.e., on the walls) and emitting (i.e., in the mouthpiece outflow) during dynamic flow in the DPI was determined using the CFD model approach together with the particle model described in Section 2.2. In Fig. 3 the spatial distribution of the deposited particles (visualized using Tecplot) is shown for steady-state flow for two values of Q, i.e., 30 and 60 L/min. It is clear that the deposition sites are strongly dependent on particle size and that the deposition pattern is influenced by the flow rate. Several dynamic flow simulations were conducted with PIFR values ranging from 20 to 70 L/min. Two different values of FIR were examined: a fast (i.e., 8.1 L/s2 ) and a slow (i.e., 2.3 L/s2 ) case corresponding to the experimental studies of de Koning et al. (2001). Large values of PIFR (e.g., 60 L/min) and a rapid FIR (e.g., 8.1 L/s2 ) are considered ideal for proper dispersion and optimal DPI function. Smaller values of PIFR (e.g., 30 L/min) and FIR (e.g., 2.3 L/s2 ) are considered inadequate and reflect impaired respiratory function. The cumulative number of deposited and emitted particles in the DPI during an inhalation (assumed to last 2 s for a PIFR of 30 L/min and 1 s for 60 L/min, both corresponding to a tidal volume of Vt = 1 L) is shown in Figs. 4 and 5, respectively. It is clear that both the total deposited and emitted particles depend on the PIFR and FIR values. Note that most of the particle deposition occurs by 0.2 s. In contrast, there is a lag time of 0.045 to 0.117 s before particles begin to exit the DPI and finish escaping between 0.1 and 0.25 s depending on the inhalation dynamics (i.e., PIFR and FIR values).

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Fig. 6. Instantaneous deposited particles during dynamic flow, tinj = 0 s.

Fig. 3. Deposited particles for steady flow: (a) Q = 30, (b) 60 L/min, tinj = 0 s (particles not drawn to scale).

Fig. 7. Instantaneous emitted particles during dynamic flow, tinj = 0 s.

Fig. 4. Cumulative deposited particles during dynamic flow, tinj = 0 s.

The instantaneous numbers of deposited and emitted particles were obtained by summing over discrete time steps of t = 0.001 s during the course of the particle simulations and are shown in Figs. 6 and 7, respectively. It is clear that the dynamics of particle outflow and deposition vary significantly with PIFR and FIR. In Fig. 6 the curves corresponding to a PIFR value of 30 L/min are broader than the 60 L/min curves (for identical values of FIR) due to a larger particle residence time resulting from the slower airflow. Additionally, the curves due to an FIR value of 2.3 L/s2 are broader than the 8.1 L/s2 curves (for identical values of PIFR) due to the slower development of the flow field. Fig. 7 provides the residence time distributions for the emitted particles for different values of

Fig. 5. Cumulative emitted particles during dynamic flow, tinj = 0 s.

PIFR and FIR. The observed lag time for particle emission is directly related to the dynamics of outlet pressure variation which controls the instantaneous DPI outlet flow rate. Consequently the narrowest particle emission curves display the smallest time-lag. In Fig. 8 the instantaneous number of fine and total particles emitted from the DPI are compared for PIFR = 30 L/min and FIR = 2.3 and 8.1 L/s2 . It is clear that the instantaneous FPF based on the emitted dose (and assuming a cut-off value of 4.7 ␮m) varies with time and FIR. For example, for FIR = 2.3 L/s2 nearly all the outflowing particles after 0.2 s are fines compared to the FIR = 8.1 L/s2 case where the fines constitute between 30% and 70% of the emitted particles after 0.1 s. In Fig. 9 the fractional deposited PSDs are shown together with the injected PSD (i.e., Eq. (4)) for different values of PIFR and FIR. The PSDs are depicted in discrete form and follow a logarithmic diameter discretization rule (i.e., 20 elements with diameter values ranging from 1 to 20 ␮m). It is clear that there is a difference in the injected and deposited PSDs for different values of PIFR and FIR depending on the particle size. Because the sticking efficiency

Fig. 8. Instantaneous emitted particles and fines during dynamic flow. PIFR = 30 L/min, tinj = 0 s.

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Fig. 9. Overall deposited PSD during dynamic flow. tinj = 0 s. Dashed line is the injected PSD.

decreases with particle size due to the size-dependence of vc (see Eq. (A2)) and the collision rate increases with particle size due to the inertial forces, the deposition efficiency, which is the collision rate multiplied by the sticking efficiency, will display a maximum value at some particle size. From the results in Fig. 9 it is observed that the maximum deposition efficiency occurs in the region of fine particles (i.e., 1–4.7 ␮m) illustrating the difficulty in obtained a large fraction of fine particles in the outlet flow. The spatial distribution of the deposited particles is shown in Fig. 10 for PIFR = 30 and 60 L/min and FIR = 2.3 L/s2 . It is clear that the deposition pattern is significantly different to the corresponding steady state patterns depicted in Fig. 3 and that there are sizedependent differences in the deposition patterns in the circulation chamber as well as in the mouthpiece extension. It should be noted that for dynamic flow significant particle deposition is observed in the inhalation channel as well. This deposition is a result of the slow flow experienced by injected particles as they exit the powder-loaded cylinders at the beginning of a dynamic inhalation. Simulations assuming steady flow and tinj = 0 s or dynamic flow with delayed particle injections (e.g., tinj = 0.5 s) both display very limited particle deposition in the inhalation channel (see Fig. 10c). In Fig. 11 the emitted particles from the mouthpiece outflow (before the mouthpiece extension) are shown for steady state, fast inhalation (i.e., FIR = 8.1 L/s2 ), and slow inhalation (i.e., FIR = 2.8 L/s2 ) for both PIFR = 30 and 60 L/min. It is clear that the position of emitted particles is strongly non-uniform and

Fig. 11. Emitted particles from the Turbuhaler mouthpiece during steady and dynamic flow, tinj = 0 s.

segregated in terms of size. These particle emission patterns strongly influence the deposition properties in the respiratory system and especially the losses in the oropharyngeal region (DeHaan and Finlay, 2004). Different DPI component designs could be tested that would generate more homogeneous spatial distributions of emitted particles which would be more likely to penetrate past the oropharyngeal region. It should be noted that even a uniform distribution of emitted particles when injected to the oral cavity display increased deposition due to the nonuniform flow field (Ilie et al., 2008). The dynamics of emitted and deposited particles can also be represented by a discrete bivariate PSD, f(i,j), equal to the fractional number of particles emitted or deposited between ti and ti + t and between Dj , Dj+1 . In Fig. 12 the emitted and deposited particle profiles are shown for PIFR = 60 L/min and FIR = 8.1 L/s2 . It is clear that the deposition and emission patterns depend strongly on particle size and inhalation time and are significantly different. There appears to be two waves of particle emission (at ∼0.08 s and 0.15 s) and there are two distinct regions of deposition one corresponding to particle deposition in the inhalation channel noted before (see Fig. 10) which ends by 0.03 s and a broader peak from 0.05 to 0.18 s. 3.3. Comparison to experimental data

Fig. 10. Deposited particles for slow (FIR = 2.3 L/s2 ) dynamic flow: (a) PIFR = 30, (b) 60 L/min and tinj = 0 s, (c) PIFR = 30 L/min and tinj = 0.5 s (particles not drawn to scale).

The computational results of this work were compared to available experimental results of the literature in terms of flow, particle deposition, and FPF. The effect of a slow (i.e., 2.3 L/s2 ) and fast (i.e., 8.1 L/s2 ) FIR was also examined by comparison to the results of de Koning et al. (2001). For dynamic flow simulations the dependence of the pressure drop to the PIFR in the DPI was found to be nearly identical to the available experimental data of de Koning et al. (2001) just as with the steady flow simulations (Milenkovic et al., 2013) and are depicted in Table 1. The steady CFD results were closer to the experimental values for flow (i.e., 0.6–2.5%) than the dynamic CFD results (i.e., 0.9–4.4%). The differences in these results were due to the different numerical convergence criteria employed in the simulations (i.e., 10−5 compared to 10−4 for steady and dynamic CFD, respectively) and due to the limited flow time that was provided for the dynamic CFD simulations to reach steady state (i.e., t = 2 s).

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Fig. 13. Particle deposition in the Turbuhaler DPI. Comparison between experimental data and CFD results, tinj = 0 s.

Fig. 12. Emitted and deposited particle profiles. PIFR = 60 L/min, FIR = 8.1 L/s2 , tinj = 0 s.

In Fig. 13 the total particle depositions are compared to the experimental data of de Koning et al. (2001) for PIFR = 30, 40, 50, and 60 L/min and for two different values of FIR, i.e., fast (8.1 L/s2 ) and slow (2.3 L/s2 ). It is clear that the dynamic flow results agree well with the experimental data and display a ∼5% difference in deposition for the two FIR cases which the steady flow simulations cannot produce. The steady flow results, assuming injection PSDs based on Eqs. (4) and (5) are also close to the experimental data despite the simplicity of the particle injection model (e.g., instantaneous release). Note that assuming a constant value of D0 = 2.2 ␮m for all values of PIFR does not affect the simulation results significantly (i.e., 3% difference for PIFR = 60 L/min). Although steady flow predictions of deposition are less accurate than dynamic predictions they might be preferable for cases were the flow dynamics

Table 1 Comparison of calculated to experimental steady flow rates for the Turbuhaler DPI. P (Pa)

800 1400 2800 3200 4300 5600 6000 8800

Volumetric flow rate (L/min) de Koning et al. (2001)

Steady CFD

Dynamic CFD

20.76 27.66 – 41.52 – 55.2 – –

20.45 27.48 38.04 42.62 48.00 56.57 57.57 70.74

21.31 28.78 39.09 41.91 49.14 57.63 59.01 71.85

Fig. 14. Fine particle fraction in the Turbuhaler DPI. Comparison between experimental data and CFD results, tinj = 0 and 0.2 s.

are unknown considering also the increased computational cost of dynamic flow simulations. In Fig. 14 the calculated FPF (based on nominal dose) is compared to a wide number of experimental data (de Koning et al., 2001; Dolovich and Dhand, 2011; Hoe et al., 2009; Nadarassan et al., 2010; Sahib et al., 2010). It is clear that the experimental data vary quite a bit between research groups due to the different experimental conditions or powders studied (Table 2). Although the number of available experimental data points is insufficient to perform a detailed statistical analysis, a least squares fit of the available experimental data in Table 2 can be obtained and is given by: F = 1.059Q − 4.175 · 10−3 · Q 2 − 6.385

(6)

where F is the FPF and Q is in L/min. In Table 3 the computational results are compared to the least-squares average of the experimental data of Table 2. It is clear that the dynamic-flow CFD results are significantly better than the steady-flow results. The most accurate results are obtained with a delayed particle injection (i.e., tinj = 0.2 s) in dynamic flow and the least accurate results are

Table 2 Experimental studies of FPF in the Turbuhaler DPI. Author

Year

System

Q (L/min)

Flow

Method

de Boer, A.H. de Koning, J.P. Mendes, P.J. Hoe, S. Sahib, M.N. Nadarassan, D.K. Dolovich, M.B.

1996 2001 2007 2009 2010 2010 2011

BD BD BD, TS, FF BD, TS BD FF BD

20–60 30–70 60 30, 45, 60, 75, 90 60 10, 20, 28.3, 40, 60 30–90

Dynamic Dynamic Steady Steady Steady Steady Steady

UV S UV S UV S HPLC HPLC HPLC –

TS, terbutaline sulphate; BD, budesonide; FF, formoterol fumarate.

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Table 3 Comparison of calculated to experimental FPF for the Turbuhaler DPI. Flow rate (L/min)

FE

Dynamic CFD

Steady CFD

tinj = 0 s F 20 30 40 50 60 70

13.1 21.6 29.3 36.1 42.1 47.3

– 19.5 21.8 27.2 31.6 –

D0 = 2 ␮m

tinj = 0.2 s F (%) – −9.7 −25.6 −24.7 −24.9 –

F – 26.5 28.4 33 38 –

obtained with steady-flow assuming a constant value of D0 = 2 ␮m for all values of Q. The simulation results are found to be sensitive to the type of flow and injected PSD. Assuming an identical injected PSD (i.e., D0 independent of Q) led to FPF values that increased weakly with Q (i.e., 20–23% for PIFR = 30–60 L/min) for dynamic flow or even decreased with Q for steady flow simulations. These results indicate that an accurate description of the initial powder release and breakup into aggregates and particles is necessary to determine accurately the PSD and the FPF. In this work by assuming that the mean diameter decreases linearly with Q, i.e., Eq. (5), the dynamic flow simulations were found to be in good agreement with the experimental data (e.g., slow FIR data of de Koning et al., 2001). Note that even the steady flow results were improved with this assumption (i.e., Eq. (5)). To test the assumption of instantaneous particle injections, simulations were also performed at tinj = 0.2 and 0.5 s. In Fig. 14 it is seen that delayed instantaneous particle injections (i.e., tinj = 0.2 s) resulted in larger values of FPF as the injected particles experience larger flow velocities. 4. Conclusions This work has demonstrated the use of a multi-scale model to describe the dynamic flow, deposition and FPF in the Turbuhaler DPI. The model includes CFD to determine the airflow, an Eulerian/Lagrangian model for particle motion as well as an adhesion model to determine the critical velocity for particle capture as a function of particle size. The main advantages of the model presented in this work over a previous model presented in Milenkovic et al. (2013) for steady flows is the capability to simulate dynamic inhalation flow patterns as well as the more accurate predictions of the FPF. The dynamic flow simulations revealed that the spatial deposition patterns were highly nonuniform and were found to depend on the particle size. The total emitted and deposited PSDs were different to the injected PSD due to the size-dependent particle capture by the DPI walls. Finally, the emitted particle patterns from the DPI mouthpiece were found to be strongly nonuniform potentially leading to increased deposition in the oral cavity. The particle deposition results obtained with dynamic CFD were in agreement to experimental data and could predict differences in deposition with fast (i.e., 8.1 L/s2 ) and slow (i.e., 2.3 L/s2 ) flow developments. The FPF determined by dynamic flow simulations was found to agree fairly well with a broad range of experimental data from the literature as long as the mean size of the injected PSD was taken to depend on the flow rate. On the other hand, steady flow simulations did not predict correct values of the FPF even assuming a flow rate dependent mean particle size (i.e., Eq. (5)). Future work should include more accurate descriptions of powder dispersion and aggregate breakage. Discrete particle simulations are limited by the large number of particles involved but can provide some useful insights into the aggregate breakage rate (e.g., due to collisions with the DPI walls). On the other hand, the

F (%) – 22.7 −3.1 −8.6 −9.7 –

D0 = D0 (Q)

F

F (%)

F

F (%)

– 19.6 22.4 18 14.5 15.4

– −9.3 −22.1 −50.1 −65.6 −67.4

– 19.5 25.1 23.3 22.9 28.4

– −9.7 −14.3 −35.5 −45.6 −40

determination of aggregate population dynamics in a CFD model is limited by the severe computational costs involved. However, hybrid CFD-based compartment and population dynamics models were recently employed to describe particle deposition and FPF in the Turbuhaler DPI (Alexopoulos et al., 2013) and could be applied to efficiently describe the effects of aggregate breakage in a DPI. Acknowledgements The research leading to these results has received funding from the European Union Seventh Framework Programme [FP7/20072013] under grant agreement no. 238013. Appendix A. The sticking efficiency, , depends on the normal velocity of the particle undergoing collision, vn . The sticking efficiency is determined based on a model developed by Brach and Dunn (1992, 1995) in which the critical velocity, vc , is determined based on particle diameter as well as the material properties of the particle and the wall. Consequently, the sticking efficiency is given as:  =1−H

1 − v  n

(A1)

vc

where H is the Heaviside step function. The critical normal velocity is given by:

vc =

 2E 10/7

(A2)

D

where D is the particle diameter and the effective stiffness parameter E is given by E=

1.4(ks + kp )

(A3)

3/5

and ks and kp are determined by: ks =

1 − s2 Es

and kp =

1 − v2p Ep

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