Population balance modeling applied to the milling of pharmaceutical extrudate for use in scale-up

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Contents lists available at ScienceDirect

Advanced Powder Technology journal homepage: www.elsevier.com/locate/apt

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Original Research Paper

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Population balance modeling applied to the milling of pharmaceutical extrudate for use in scale-up

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Maxx Capece

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Drug Product Development, AbbVie Inc., 1 N. Waukegan Road, North Chicago, IL 60064, USA

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a r t i c l e

i n f o

Article history: Received 9 April 2018 Received in revised form 5 October 2018 Accepted 9 October 2018 Available online xxxx Keywords: Hot-melt extrusion Extrudate Population balance modeling Size reduction Formulation

a b s t r a c t This study modeled the particle size distribution (PSD) of pharmaceutical extrudates after milling by developing a so-called time-discrete population balance model (PBM). The PBM, which models size reduction as a series of breakage events, was formulated so that the model parameters separate the effect of material properties and milling process conditions. Because of this novel aspect, the PBM should have excellent predictive capability with specific applications in technology transfer and scale-up. To investigate this application, copovidone extrudate produced by the hot-melt extrusion process was milled using a lab-scale continuous impact mill (Fitz Mill). The effect of impeller speed and classification screen size on PSD of the extrudate was investigated. The PBM with parameters obtained by fitting lab-scale PSD data was then applied to model the PSD of the extrudate following milling by a pilot-scale continuous impact mill (Hosokawa mill). The study found that the parameters determined at the lab-scale can be used to model PSDs at the pilot-scale and may be generally applied to similar classification-type impact mills. Since technology transfer and scale-up can be material and time consuming, this approach may offer significant benefits to the pharmaceutical industry for the development of milling processes. Ó 2018 Published by Elsevier B.V. on behalf of The Society of Powder Technology Japan. All rights reserved.

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1. Introduction

48

The use of solid dispersions in pharmaceutical products is an effective approach to overcome the poor solubility of the drug substance [1]. One common process used to produce solid dispersions is known as hot-melt extrusion [2]. The process entails the mixing and subsequent melting of the drug substance with a carrier polymer as well as plasticizers and surfactants as needed in a twinscrew extruder. The melt is cooled and often extruded as lentil shaped particles though other shapes may be common. Following extrusion, the extrudate must be milled into a fine powder in order to be blended with excipients for eventual inclusion into a capsule or tablet formulation. Particle size distribution (PSD) is a critical property in formulation and processes development since it is known to affect drug content uniformity [3,4], powder flowability [5–8], compression behavior [9,10], dissolution [11], and bioavailability [12]. Because the drug loading of solid dispersions is often low, the milled extrudate may comprise a large portion of the final capsule or tablet blend. Accordingly, the PSD of the extrudate may have significant effect on downstream processes and product per-

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formance. This necessitates the need to precisely control the PSD of the milled extrudate. Population balance models (PBMs) as a mathematical description of particle size reduction are extensively used to model milling processes [13–16]. PBMs have been applied to a wide variety of materials and mill types including those which use grinding media or spinning impellers of both batch and continuous operation. Interestingly, PBMs have not been applied to the milling of extrudate materials common to the pharmaceutical industry despite their increasing use. PBMs are most widely used to investigate breakage behavior, but can also be used to design, control, optimize, or scale-up milling processes. These latter aspects are especially desired for industrial applications but can be difficult to accomplish in practice due to the complexity of the models and the large number of model parameters which must be determined. In this study, a PBM is developed and applied to model the particle size reduction of pharmaceutical extrudates for the first time. A common lab-scale continuous impact mill which uses an internal classification screen (Fitz Mill) is investigated. As a major novelty, the model is developed so that the material dependent parameters are separated from the milling process conditions. Due to this unique aspect, the model should have excellent predictive capability. The model as developed for the lab-scale Fitz mill is then

E-mail address: [email protected] https://doi.org/10.1016/j.apt.2018.10.009 0921-8831/Ó 2018 Published by Elsevier B.V. on behalf of The Society of Powder Technology Japan. All rights reserved.

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Nomenclature a1  a12 AS bij Bij d10 d50 d90 d99 dS fMat ðnÞ mi mp,i M n N PB ðnÞ PB;i

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fitting parameters fraction of screen area open (dimensionless) breakage distribution parameter (dimensionless) breakage distribution parameter, cumulative form (dimensionless) particle diameter 10% passing (m) particle diameter 50% passing (m) particle diameter 90% passing (m) particle diameter 99% passing (m) diameter of screen opening (m) material strength parameter (kg/Jm) mass fraction in size class i after n breakage events (dimensionless) product mass fraction in size class i (dimensionless) total number of size classes (#) number of breakage events (#) total number of breakage events per pass through the milling zone (#) breakage probability (dimensionless) breakage probability in size class i after n breakage events (dimensionless)

applied without modification to a pilot-scale continuous impact mill (Hosokawa Mill). The findings in this study suggest that the model is general enough to be applied to classification mills which break particles by impact. Since technology transfer and scale-up can be material and time consuming, this approach may offer significant benefits to the pharmaceutical industry for the development of milling processes.

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2. Theoretical preliminary: model description

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PBMs applied to milling can describe particle breakage as a rate process [14] or a series of breakage events [17–21]. Particle breakage is most appropriately modeled as a rate process for retention type mills such as ball-mills. For the mills under consideration in this study, residence time is relatively short and particles undergo a small number of impacts. In this case, the so-called time-discrete PBM is commonly used as shown in Eq. (1) which yields the mass fraction particle size distribution (PSD) after n number of breakage events [22–28]. For impact mills that use spinning impellers to break particles (as in this study), a breakage event is defined as a collision between the impeller and a particle.

98 99 100 101 102 103 104 105 106 107

108

ðn Þ

110 111 112 113 114 115 116 117 118 119 120 121 122 123 124

125 127

mi

i1
 X ðn Þ ðn1Þ ðnÞ ðn1Þ ¼ 1  PB;i mi þ bij PB;j mj

ð1Þ

j¼1

here, particle size is discretized into M number of size classes given by the index i or j. The PBM has two parameters, PB,i and bij, which describe the breakage behavior. The breakage probability, PB, as the name implies, is the probability that a particle breaks when subjected to a breakage event. The breakage distribution, b, describes the size distribution of particles obtained when the parent particle is broken. Accordingly, the first term on the r.h.s. gives the mass fraction of particles of a particular size class i left unbroken after a breakage event while the second term gives the mass fraction of particles entering size class i due to breakage of particles in size classes j < i. To describe the breakage probability of particles subject to one or more impactions, Vogel and Peukert [29,30] developed the expression given in Eq. (2).

   PB ¼ 1  exp f Mat xn W m  W m;min

ð2Þ

PC;i tS

v tip

Wm,min Wm,min 0

W m;min x xi

classification probability of size class i (dimensionless) thickness of screen (m) impeller tip speed (m/s) impact energy, (J/kg) threshold energy, nomenclature of Vogel and Peukert [29,30] (J/kg) threshold energy, Nomenclature of the current study (Jm/kg) particle diameter (m) particle diameter of size class i (m)

Greek letters a critical size factor (dimensionless) b classification parameter (dimensionless) l breakage distribution parameter (dimensionless) Subscripts i, j size class indices

In Eq. (2), fMat is a material strength parameter which describes a particle’s resistance to breakage, x is particle diameter, n is the number of impactions (i.e. breakage events) that a particle is subjected to before breaking, Wm is the mass-specific impact energy, and Wm,min is the threshold energy. The threshold energy is the mass-specific energy that must be surpassed to initiate particle breakage by a single or multiple impacts. Below this energy threshold, breakage will never occur regardless of the number of impacts. Based on fracture mechanical considerations and dimensional analysis used in derivation of Eq. (2), the threshold energy is particle size dependent but the product xW m;min is a material constant [29,30]. For the purposes of this study, this particle size

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0

independent threshold energy, xW m;min , is defined as W m;min and simply referred to as the threshold energy hereafter. Noting the difference in this nomenclature, the redefined threshold energy is substituted into Eq. (2) which is also written for any breakage event, n, and particle size class, i, for use in the PBM of Eq. (1) as shown below.

"

ðnÞ PB;i

0

W m;min ¼ 1  exp f Mat xi n W m;i  xi

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!# ð3Þ

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0

While emphasizing the equivalency of Eqs. (2) and (3), W m;min =xi gives the mass-specific energy that must be surpassed to initiate breakage either through a single or multiple impacts for a particular size class. This breakage probability equation is useful as it separates

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0

material properties (fMat, x, W m;min ) from milling process conditions (n, Wm). For impact mills which use spinning impellers, the impact energy can be estimated from the collision energy (kinetic energy) which is approximated from the impeller tip speed, v tip , and substituted into Eq. (3) as shown in Eq. (4). It is also important to note that Eqs. (2)–(4) take into account that fact that particles which do not fracture from one breakage event have an increased probability of fracturing at the next breakage event due to damage incurred.

"

ðnÞ

PB;i

0

W 1 2 ¼ 1  exp f Mat xi n v  m;min 2 tip xi

!#

ð4Þ

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In the case of the breakage distribution, an empirical normalized function is used as shown in Eq. (5). This power law breakage distribution function is one of the simplest which can describe a distribution of particles resulting from breakage. The fitting parameter l is dependent on both material properties and process conditions.

 l xi1 Bij ¼ ; where bij ¼ Bij  Biþ1j and bMj ¼ BMj xj

Once the particles pass through the milling zone of the spinning impellers to the classification screen, they are either retained to be broken into finer particles or pass through to the product chamber if their size allows. While the PBM can employ a heavy side function along with a pre-defined maximum size for which particles are able to leave the mill [31], this work defines a classification probability Pc and uses a particle size dependent function as shown in Eq. (6).

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ð5Þ



Pc;i

b xi ¼1 ds a

ð6Þ

here, ds is the diameter of the screen opening, a is the critical size factor which accounts for the tangential motion of particles relative to the screen, and b is a fitting parameter which determines the sensitivity of particle size on classification efficiency. dsa is the maximum particle size that can leave the mill. As particle size approaches the maximum particle size that can leave the mill, the classification probability approaches nil. For particle sizes xi > dsa, Pc;i ¼ 0 (i.e. retained by the mill for further breakage). Finally, the product mass fraction distribution obtained per pass through the milling zone is given by Eq. (7). Here, N is the total number of breakage events that a particle is subjected to per pass through the milling zone as it reaches the classification screen. Particles that are retained by the screen are returned to the milling zone and undergo another number of breakage events equal to N. It should be noted that the total number of breakage events per pass through the milling zone, N, is different than n given in Eq. (4). N is a fixed quantity for a particular mill and milling condition and used to determine the product PSD. The quantity n is the number of breakage events that a particle undergoes until breakage and used to determine breakage probability for particles still retained by the mill. The value of n can exceed N for a given size class if a portion is retained by the classification screen as determined by Eq. (6) and returned to the milling zone. In these set of equations, it is also assumed that the feed material leaves the mill quickly and does not accumulate inside the mill which is a reasonable assumption for a continuous operation. Overall, this set of equations con0

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tains six total parameters (fMat, W m;min , l, a, b, N) which must be determined in order to solve the PBM and the resultant product particle size distribution.

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ðN Þ

mp;i ¼ mi P c;i

ð7Þ

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3. Materials and methods

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3.1. Extrusion

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Copovidone lentils were prepared using a lab-scale twin-screw extruder (ZSK-26, Coperion). Copovidone powder (Kollidon VA64, BASF) was fed at 6.3 kg/h with a screw speed set to 200 rpm. The temperature at the die was maintained at 145 °C. The copovidone melt was calendered and cooled to form a solid extrudate. The lentil shaped (i.e. ellipsoid) extrudate has dimensions of 9.0 mm, 9.0 mm, and 6.0 mm respectively for the major, minor, and vertical

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axis. For the purpose of modeling, an equivalent volume of a sphere was calculated which has a diameter of 8.0 mm.

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3.2. Milling

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For model development, copovidone lentils were milled using a lab-scale impact mill (Fitz Mill L1A, Fitzpatrick Company). The Fitz mill is a continuous impact mill which has an internal classification screen. The milling zone contains 4 hammer-type impellers which are alternately off-set at 90°. Lentils were fed at 100 g/min. Four round-hole classification screens were used to investigate the effect of screen properties on product PSD. Screen properties are listed in Table 1. Lentils were also milled in the absence of a screen. Additionally, three impeller speeds were used for each screen used: 4000, 6000, and 8000 rpm which correspond to impeller tip speeds of 28.3, 42.4, and 56.5 m/s. To investigate the use of the PBM for scale-up, copovidone lentils were also milled using a pilot-scale impact mill (Hosokawa Mill UPZ100, Hosokawa Alpine). Similar to the Fitz mill, the Hosokawa is also a continuous classification mill but the milling zone contains a fan-beater shaped impeller with 8 fans. Lentils were fed at 2 kg/min. Only one round-hole classification screen was used with properties specified in Table 1. Five impeller speeds were used: 8000, 10,000, 12,000, 14,000, and 16,000 rpm which correspond to impeller tip speeds of 41.8, 52.3, 62.7, 73.2, and 83.6 m/s.

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3.3. Particle size analysis

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Particle size distributions of the milled lentils were measured by a Helos (Sympatec, USA) laser diffraction sensor in combination with the Rodos air dispersion unit (Sympactec, USA) with an air dispersion pressure of 0.1 bar. The Fraunhofer theory was used to calculate the particle size distributions. For samples milled without a classifications screen, 2.0 mm, 1.4 mm, and 1.00 mm sieves were used to separate coarse particles from the fine fraction which was measured by laser diffraction as detailed above. The sieve data for the coarse fraction (>1.00 mm) and the laser diffraction data for the fine fraction (<1.00 mm) were combined to produce one particle size distribution.

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3.4. Parameter determination

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0

The threshold energy W m;min was obtained directly by experimentation. The impeller speed of the Fitz mill was varied in 25 rpm increments to determine the maximum speed which did not cause breakage of the lentil after 20 passes through the mill ðnÞ (PB;i

¼ 0). In consideration of the breakage probability of Eq. (4),

the threshold energy is determined by Eq. (8).

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269 0

W m;min ¼

1 xi v 2tip 2

ð8Þ

The critical size factor was also obtained directly by experimentation. The maximum particle size that can leave the mill was assumed to be equal to d99 which was determined from the meaTable 1 Fitz mill and Hosokawa mill screen properties. Mill

Screen opening diameter, dS (lm)

Screen thickness, tS (mm)

Fraction of screen area open AS (–)

Fitz mill (L1A)

305 508 838 1295 1100

0.476 0.397 0.635 0.635 0.650

0.048 0.30 0.28 0.33 0.29

Hosokawa (UPZ 100)

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sured particle size distributions. The critical size factor which is unique for each screen and impeller speed is calculated as shown in Eq. (9).

maximum impeller speed that does not result in breakage of a lentil. This impeller speed was determined to be 450 rpm which corresponds to a tip speed of 3.2 m/s. In this case, the threshold energy is 0.0405 Jm/kg and valid for all milling experiments regardless of impeller speed or screen size since it is a material dependent parameter. The critical size factor was determined from the d99 obtained from the experimental PSD (cumulative mass fraction undersize distribution) and use of Eq. (9). The critical size factor was determined for each classification screen size and impeller speed and listed in Table 2. As expected, this parameter is unique for each screen size and impeller speed. The critical size factor decreases with increasing impeller speed and screen size opening which corresponds to lower maximum particle size able to exit the mill. To determine the remaining four model parameters (fMat, l, b, N), the PBM was fit to the PSD data for the milled lentils obtained from the Fitz mill operated at 4000, 6000, and 8000 rpm without a screen and with each of the four screens (305 lm, 508 lm, 838 lm, 1295 lm) as shown in Figs. 1–5. Lentils were milled without a screen to evaluate the suitability of the breakage distribution function without the confounding effects of the classification screen. Furthermore, the cumulative mass fraction undersize distribution is shown for the data obtained without a screen due to the low resolution of the data on the coarse end obtained by sieving. Density distributions are shown for all remaining data which were determined solely by laser diffraction. As Figs. 1–5 show, the PBM can fit the particle size data with accuracy for all three

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a¼

d99 ds

ð9Þ

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The remaining four model parameters (fMat, l, b, N) were determined using a sum-of-least-squares approach by fitting the PSD obtained from the PBM (Eqs. (1)–(7), excluding Eq. (2)) to the experimental PSD. A total of M = 180 size classes were selected for the PBM. Each size class was represented by its upper edge size, xi, that progresses from x1 = 8000 lm downward with a geometric progression ratio of 21/16. The non-linear optimizer ‘‘fmincon”, part of the Matlab v R2014b optimization toolbox was used to minimize the error between the model and experimental cumulative mass fraction undersize distribution. The optimizer stopping criteria includes the termination tolerance on the function value and termination tolerance on the parameters which were both set to 104. Additionally, while the model equations were verified to conserve mass, it was found computationally prudent to stop calculation of the product PSD, mp;i , (Eq. (7)) during the non-linear optimization routine when the cumulative mass fraction surpassed 0.99. The resultant product PSD was normalized by the cumulative mass. The model was fit simultaneously to the experimental PSD obtained without using a screen and the four classifications screen each at speeds of 4000, 6000, and 8000 rpm (15 total PSDs). It should be noted that fMat is a material property and is common to all impeller speeds and screen sizes. The model parameters l, and N are only expected to depend on impeller speed and thus are common to all screen sizes at corresponding impeller speeds. Only the parameter b, associated with the classification efficiency, is unique for each screen size and impeller speed. Since N must be an integer for solution of the PBM, PSDs were determined for noninteger values of N by using a weighted average. For example, to determine the PSD for N = 3.6, the PBM was solved for N = 3 and N = 4 and linear interpolation was applied to the cumulative mass fraction undersize distribution. It was also assumed that N does not depend on particle size.

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4. Results and discussion

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4.1. Development of the PBM at the lab-scale (Fitz Mill)

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Before fitting the PBM to the experimental PSD data, two model

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parameters (W m;min and a) were determined directly. The threshold

0

Fig. 1. Experimental and model particle size distributions obtained for the Fitz mill operated at 4000, 6000, and 8000 rpm without a screen.

0

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energy W m;min can be calculated from Eq. (8) after determining the Table 2 Fitted and calculated parameters for various screens and impeller speeds. Screen opening diameter, dS (lm) 305

508

838

1295

Impeller speed (rpm)

4000 6000 8000 4000 6000 8000 4000 6000 8000 4000 6000 8000

Tip speed, (m/s)

v tip

28.3 42.4 56.5 28.3 42.4 56.5 28.3 42.4 56.5 28.3 42.4 56.5

Breakage events per pass, N

Breakage distribution parameter, l

Classification parameter, b

Critical size factor, a

W m;min (Jm/kg)

Material strength, fMat (kg/Jm)

0.0405

0.70

3.00 3.85 4.88

1.31 1.34 1.42

0.43 0.90 1.51 2.25 3.15 4.11 2.17 2.32 2.60 3.25 3.73 5.10

1.04 0.99 0.87 0.94 0.80 0.73 0.87 0.73 0.71 0.63 0.55 0.50

Threshold energy, 0

Same as 305 lm screen Same as 305 lm screen Same as 305 lm screen

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Fig. 2. Experimental and model particle size distributions obtained for the Fitz mill operated at 4000, 6000, and 8000 rpm using a 305 lm screen.

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impeller speeds with or without a screen. The particle size statistics (d10, d50, d90) determined experimentally and from the model are shown in Fig. 6 also show excellent agreement. The model parameters determined by the fitting are shown in Table 2. The material strength parameter fMat was determined to 0

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be 0.70 kg/Jm. As was the case for the threshold energy, W m;min , this is a material dependent parameter and valid for all milling conditions. The material strength parameter and the threshold energy can be used to determine the breakage probability of copovidone (see Eq. (4)) for various impeller speeds. Furthermore, the param0

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eters fMat and W m;min are similar and are on the same order of magnitude as those determined previously by Meier et al. [32] for

Fig. 3. Experimental and model particle size distributions obtained for the Fitz mill operated at 4000, 6000, and 8000 rpm using a 508 lm screen.

various pharmaceutical powders using a single particle impact device. The number of breakage events per pass through the milling zone, N, was determined to be 3.00, 3.85, and 4.88 for impeller speeds of 4000, 6000, and 8000 rpm respectively. This increase is expected since the lentils should be subjected to more breakage events per pass as the speed of the impeller increases. The number of breakage events per pass is valid for all screen sizes since this parameter should not depend on screen properties. The breakage distribution parameter l is also shown to increase, albeit slightly, from 1.31 to 1.42 for impeller speeds 4000–8000 rpm. Similar

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Fig. 4. Experimental and model particle size distributions obtained for the Fitz mill operated at 4000, 6000, and 8000 rpm using a 838 lm screen.

Fig. 5. Experimental and model particle size distributions obtained for the Fitz mill operated at 4000, 6000, and 8000 rpm using a 1295 lm screen.

0

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behavior was also found by Vogel and Peukert [29] in single particle impact test. As was the case for N, the breakage distribution parameter is valid for all screen sizes. The classification parameter b also increases as impeller speed increases which corresponds to greater classification efficiency. This parameter is unique for each screen size and impeller speed as expected.

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4.2. Development of the PBM for scale-up

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Because the goal of this work is to develop a PBM suitable for tech transfer and scale-up, it is necessary to separate the effect of material properties and processing conditions for all model parameters. This is already accomplished for the breakage probability of Eq. (4) as developed by Vogel and Peukert [29,30]. Furthermore, Eq.

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(4) along with the material dependent parameters fMat and W m;min that were determined for copovidone should also be valid for other mills which break particles by impact using an impeller. This leaves the parameters of the breakage distribution function (l), the classification probability function (a and b) and the product mass fraction function (N). For the number of breakage events per pass through the milling zone, N, a linear function was found to be suitable (r2 > 0.99) to describe the effect of impeller speed as shown by Eq. (10).

N ¼ a1 þ a2 v tip

ð10Þ

The parameter values a1 and a2 are shown in Table 3. The number of breakage events per pass, N, is related to the mill geometry, number of impellers, and impeller speed and should not signifi-

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Fig. 6. Experimental and model particle size statistics obtained for the Fitz mill operated at 4000, 6000, and 8000 rpm using various screens.

Table 3 List of equations and parameters for prediction of copovidone extrudate PSD. Property Mass fraction Breakage probability

Equation
 P ðnÞ ðnÞ ðn1Þ ðnÞ ðn1Þ mi ¼ 1  P B;i mi þ i1 j¼1 bij P B;j mj h
i 0 ðnÞ 1 2 P B;i ¼ 1  exp f Mat xi n 2 v tip  W m;min =xi mp;i ¼

Breakage distribution

Bij ¼

Classification probability

P C;i ¼ 1 




xi1 xj

l


xi dS a

f Mat = 0.70 kg/Jm W m;min = 0.0405 Jm/kg

N ¼ a1 þ a2 v tip

ðN Þ mi P c;i

Product mass fraction

Parameter value

l ¼ a3 þ a4 v tip b

a ¼ a5 þ a6 v tip þ a7 dS þ a8 t S

b ¼ a9 v tip þ a10 dS þ a11 tS þ a12 AS

396 397 398 399

cantly depend on material properties. Accordingly, the parameters a1 and a2 can be considered specific to the Fitz mill. It should not have to be determined again for other extrudates which contain active ingredients.

Fitz Mill: a1 = 1.09 a2 = 6.66  102 (m/s)1 Hosokawa Mill: a1 = 4.33 a2 = 4.70  102 (m/s)1 a3 = 1.19 a4 = 3.92  103 (m/s)1 a5 = 1.14 a6 = 5.87  103 (m/s)1 a7 = 4.86  104 lm1 a8 = 4.63  101 mm1 a9 = 5.13  102 (m/s)1 a10 = 2.40  103 lm1 a11 = 4.88 mm1 a12 = 5.36

The breakage distribution parameter, l, is a process dependent (i.e. impeller speed) parameter, but unlike N, it is also material dependent. The breakage distribution parameter can be written as a function of tip speed as shown in Eq. (11). A linear function was found to be suitable (r2 = 0.96) and serves as a good approxi-

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As was done for N and l, the classification parameter, b, and the critical size factor, a, were also separated into material dependent parameters and processing conditions. For the critical size factor, a simple regression model as shown in Eq. (12) was determined in Minitab (v. 17.1.0) using the tip speed, screen opening size, and screen thickness as dependent variables. The open area was found to be statistically insignificant (p-value > 0.05). The parameter values a5 -a8 are shown in Table 3 for copovidone and can be considered material dependent. Fig. 7 shows Eq. (12) fits the data well for all milling conditions. Thus, if the screen properties and impeller speed is known, the critical size factor can be predicted for copovidone.

a ¼ a5 þ a6 v tip þ a7 dS þ a8 tS

Fig. 7. Fitted and experimental values of the critical diameter factor obtained for the Fitz mill.

ð12Þ

An identical approach was used to determine an appropriate model for the classification parameter which is shown in Eq. (13). For this case, the tip speed, screen opening size, screen thickness, and open area were all determined to be statistically significant (p-value < 0.05). The parameter values a9 -a12 are shown in Table 3 for copovidone and are also material dependent. Fig. 8 shows that Eq. (13) fits the data well.

b ¼ a9 v tip þ a10 dS þ a11 t S þ a12 AS

ð13Þ

It should also be noted that without an exhaustive set of data collected for screen with various opening diameters, open areas, and thicknesses, Eqs. (12) and (13) are best used to predict classification behavior for screens with properties similar to those used to determine the model. Using these equations for extrapolation purposes could result in large deviations from experimental behavior. Thus far, this study successfully formulated a PBM to model the size reduction of lentil shaped copovidone extrudate for the Fitz mill. The model parameters are all separated in terms of material

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0

Fig. 8. Fitted and experimental values of the classification parameter b obtained for the Fitz mill.

406

mation to the breakage distribution parameter over the range of impeller speeds investigated.

407 409

l ¼ a3 þ a4 v tip

405

410 411 412 413 414 415 416

ð11Þ

Only the impeller speed should have any effect on the breakage distribution for a given material, thus the parameters a3 and a4 are material dependent and can be used to determine the breakage distribution function for any milling condition. The parameter values are shown in Table 3 for copovidone. Eq. (11) should also be valid for copovidone lentils milled in other mills which break particle by impact with a hammer-type impeller.

properties and process conditions. fMat and W m;min are material dependent parameters used to describe the breakage probability, a1 and a2 are mill dependent parameters which determine the number of impacts through the milling zone, a3 and a4 are material dependent parameters that describe the breakage distribution, and a5  a12 are material dependent parameters that describe the classification behavior. The processing conditions simply include the tip speed of the impeller and the properties of the classification screen (screen opening size, thickness, and open area). The final model with parameters determined for copovidone is shown in Table 3. Due to the separation of material dependent parameters and process conditions, the PBM should have excellent predictive capability in determining the product PSD using new milling conditions for a given material. Additionally, since the model captures all pertinent breakage and classification behavior, it may be used to predict the product PSD between similar type mills (i.e. classification mills which break particles by impaction). As a result it may be useful for tech-transfer and scale-up purposes which is explored in the next section.

Table 4 Parameters used to determine PSD for the Hosokawa mill.

a

Impeller speed (rpm)

Tip speed, v tip (m/s)

Threshold energy, Wm,min (Jm/kg)

Material strength, fMat (kg/Jm)

Breakage events per pass, Na

Breakage distribution parameter, l

Classification parameter, b

Critical size factor, a

8000 10,000 12,000 14,000 16,000

41.8 52.3 62.7 73.2 83.6

0.0405

0.70

6.05 7.02 7.48 7.64 8.20

1.35 1.39 1.43 1.48 1.52

3.15 3.68 4.22 4.76 5.29

0.66 0.60 0.54 0.48 0.41

N was used as a fitting parameter.

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4.3. Application of the PBM at the pilot-scale (Hosokawa Mill)

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Technology transfer and scale-up may not be straightforward due to the size and geometric differences between lab-scale and manufacturing-scale equipment. In the current case of extrudate milling, a lab-scale Fitz mill and a pilot-scale Hosokawa mill are compared. Since both are classification mills that use round-hole screens and spinning impellers, the PBM as shown in Table 3 may be applicable to the Hosokawa although it was developed for the Fitz mill. For the Hosokawa mill, the tip speed can be easily calculated, properties of the classification screen can be measured, and all material dependent parameters for copovidone have already been determined at the lab-scale. Accordingly, the breakage probability, breakage distribution, and classification behavior can be predicted. However, one unknown parameter still exists

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for the Hosokawa mill. Because of the size difference of the milling chamber and the shape and number of impellers are different, the number of impaction events per pass through the milling zone (N) must still be determined. The PBM with parameters detailed in Table 4 (determined from the equations of Table 3) was fit to the PSD obtained from the Hosokawa mill using an 1100 lm screen. The only free parameter was N, which was determine to be 6.05, 7.02, 7.48, 7.64, and 8.20 for impeller speeds of 8000, 10,000, 12,000, 14,000, and 16,000 rpm respectively. Similar to the Fitz mill, the number of breakage event per pass through the milling zone increases along with impeller speed. The model fitting is shown in Fig. 9 along with the particle size statistics shown in Fig. 10. The PBM is shown to fit the pilotscale data with accuracy using the parameters determined at the lab-scale. While N had to be determined, it can be considered a

Fig. 9. Experimental and model particle size distributions obtained for the Hosokawa mill operated at 8000, 10000, 12000, 14000, and 16000 rpm using a 1100 lm screen.

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produced milled material with similar median particle sizes (d50 ) using either the Fitz or Hosokawa mill. However, a larger span
 d90 d10 of the PSD was obtained using the pilot-scale Hosokawa d50

525

mill as seen in Fig. 11. The Fitz mill produced material with spans in the range 1.49–1.99 while the Hosokawa mill produced spans in the range of 2.01–2.51. Accordingly, the pilot-scale extrudate contains coarser and/or finer particles for a given median particle size which can have significant effect on flowability, tabletability, or content uniformity. This knowledge, if predicted from the PBM, can be taken into account early into formulation development even before pilot or manufacturing studies take place.

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5. Conclusions

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Due to the significant impact of PSD on product manufacturability and product performance, this study sought to formulate a PBM to model the particle size reduction of pharmaceutical extrudates. As a major novelty, the model separates material dependent parameters and process conditions. This is critical for applications such as scale-up where material properties remain constant but processing conditions must be determined in order to obtain the desired product PSD. Material dependent parameters can be determined at the lab-scale using small amounts of material and the PBM can be used to predict the PSD at manufacturing scale. This can result in time and material saving effort during milling development. While the PBM was shown valid for a lab-scale and a pilot-scale continuous classification mills which break particles by impact, similar approaches can possibly be used for other types of mills.

537

6. Disclosure

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The author is an employee of AbbVie. The design, study conduct, and financial support for this research was provided by AbbVie. AbbVie participated in the interpretation of data, review, and approval of the publication.

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Fig. 11. Spans for various screen sizes and impeller speeds for the Fitz Mill and Hosokawa Mill. Spans were determined from model fitting results.

References

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property of the mill and should not have to be determined again for lentils of a different material. Similar to the Fitz mill, Eq. (10) can be applied to the Hosokawa mill in order to determine the effect of impeller tip speed on the number of impacts per pass through the milling zone. The parameters of Eq. (10) for the Hosokawa mill are specified in Table 3. Given the results of this section, the PBM can be used for a true prediction of PSD in scale-up activities for an active extrudate once all material dependent parameters are determined at the lab-scale. As discussed, a total of 15 milling experiments were performed in order to determine the material dependent parameters of copovidone and the effect of processing conditions (i.e. impeller speed and classification screen properties). The methodology given in this paper may serve as a basis for those interested in application though some optimization in the parameter determination procedure may be gained. In addition, the methodology put forth in this study may possibly be considered together with recent advances in the use of the discrete element method (DEM) to model milling processes and to determine model parameters of the PBM [33– 35]. Regardless, the relatively small amount of material used at the lab-scale can result in significant material and time savings when determining the proper processing conditions at the manufacturing-scale. In addition, the PBM can also predict critical differences in material PSD produced at different scales. For example, this study

[1] C. Leuner, J. Dressman, Improving drug solubility for oral delivery using solid dispersions, Eur. J. Pharm. Biopharm. 50 (2000) 47–60. [2] J. Breitenbach, Melt extrusion: from process to drug delivery technology, Eur. J. Pharm. Biopharm. 54 (2002) 107–117. [3] B. Rohs, G. Amidon, R. Meury, P. Secreast, H. King, C. Skoug, Particle size limits to meet usp content uniformity criteria for tablets and capsules, J. Pharm. Sci. 95 (2006) 1049–1059. [4] Y. Qiu, Y. Chen, G. Zhang, Developing Solid Oral Dosage Forms, first ed., Academic Press, New York, 2009. [5] J. Prescott, R. Barnum, On powder flowability, Pharm. Technol. 24 (2000) 60– 85.. [6] J. Osorio, F. Muzzio, Effects of powder flow properties on capsule filling weight uniformity, Drug Dev. Ind. Pharm. 39 (2013) 1464–1475.. [7] W. Yu, K. Muteki, L. Zhang, G. Kim, Prediction of bulk powder flow performance using comprehensive particle size and particle shape distributions, J. Pharm. Sci. 100 (2011) 284–293. [8] M. Mullarney, P. Matthew, N. Leyva, Modeling pharmaceutical powder-flow performance using particle-size distribution data, Pharm. Technol. 33 (2009) 126–134. [9] Z. Huang, J. Scicolone, X. Han, R. Davé, Improved blend and tablet properties of fine pharmaceutical powders via dry particle coating, Int. J. Pharm. 478 (2015) 447–455. [10] L. Liu, I. Marziano, A. Bentham, J. Litster, E. White, T. Howes, Influence of particle size on the direct compression of ibuprofen and its binary mixtures, Powder Technol. 240 (2013) 66–73. [11] W. Higuchi, E. Hiestand, Dissolution rates of finely divided drug powders I: effect of a distribution of particle sizes in a diffusion-controlled process, J. Pharm. Sci. 52 (1963) 167–171. [12] R. Hintz, K. Johnson, The effect of particle size distribution on dissolution rate and oral absorption, Int. J. Pharm. 51 (1988) 9–17. [13] C. Prasher, Crushing and Grinding Process Handbook, Wiley, Chichester, 1987. [14] L. Austin, A review: introduction to the mathematical description of grinding as a rate process, Powder Technol. 5 (1971) 1–17.

558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590

Fig. 10. Experimental and model particle size statistics obtained for the Hosokawa mill operated at 8000, 10000, 12000, 14000, and 16000 rpm using a 1100 lm screen.

500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524

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[15] A. Randolph, M. Larson, Theory of Particulate Processes, Academic Press, San Diego, 1988. [16] E. Bilgili, M. Capece, A. Afolabi, Modeling of milling processes via DEM, PBM, and microhydrodynamics, in: P. Pandey, R. Bharadwaj (Eds.), Predictive modeling of pharmaceutical unit operations, Woodhead Publishing, Cambridge, 2017, pp. 159–204. [17] S. Broadbent, T. Callcott, A matrix analysis of processes involving particle assemblies, Phil, Trans. R. Soc. Lond., A 249 (1956) 99–123. [18] S. Broadbent, T. Callcott, Coal breakage processes: I. A new analysis of coal breakage processes, J. Inst. Fuel 29 (1956) 524–528. [19] S. Broadbent, T. Callcott, Coal breakage processes: II. A matrix representation of breakage, J. Inst. Fuel 29 (1956) 528–539. [20] S. Broadbent, T. Callcott, Coal breakage processes III. The analysis of a coal transport system, J. Inst. Fuel Lond. 30 (1957) 13–17. [21] E. Bilgili, M. Capece, Quantitative analysis of multi-particle interactions during particle breakage: a discrete non-linear population balance framework, Powder Technol. 213 (2011) 162–173. [22] G. Campbell, C. Webb, On predicting roller milling performance part I: the breakage equation, Powder Technol. 115 (2001) 234–242. [23] A. Fistes, G. Tanovic, Predicting the size and compositional distributions of wheat flour stocks following first break roller milling using the breakage matrix approach, J. Food Eng. 75 (2006) 527–534. [24] L. Vogel, W. Peukert, Characterisation of grinding-relevant particle properties by inverting a population balance model, Part. Part. Syst. Char. 19 (2002) 149– 157. [25] H. Wong, B. O’Neill, A mathematical model for Escherichia coli debris size reduction during high pressure homogenization based on grinding theory, Chem. Eng. Sci. 52 (1997) 2883–2890.

11

[26] N. Bas, P. Pathare, M. Catak, J. Fitzpatrick, K. Cronin, E. Byrne, Mathematical modeling of granola breakage during pipe pneumatic conveying, Powder Technol. 206 (2011) 170–176. [27] S. Teng, P. Wang, L. Zhu, M. Young, C. Gogos, Mathematical modeling of fluid energy milling based on a stochastic approach, Chem. Eng. Sci. 65 (2010) 4323–4331. [28] P. Vervoorn, L. Austin, The analysis of repeated breakage events as an equivalent rate process, Powder Technol. 63 (1990) 141–147. [29] L. Vogel, W. Peukert, From single particle impact behaviour to modeling of impact mills, Chem. Eng. Sci. 60 (2005) 5164–5176. [30] L. Vogel, W. Peukert, Breakage behaviour of different materials – construction of a mastercurve for the breakage probability, Powder Technol. 129 (2003) 101–110. [31] G. Reynold, Modelling of pharmaceutical granule size reduction in a conical screen mill, Chem. Eng. J. 164 (2010) 383–392. [32] M. Meier, E. John, D. Wieckhusen, W. Wirth, W. Peukert, Characterization of the grinding behavior in a single particle impact device: studies on pharmaceutical powders, Eur. J. Pharm. Sci. 34 (2008) 45–55. [33] M. Capece, R. Davé, E. Bilgili, A pseudo-coupled DEM-non-linear PBM approach for simulating the evolution of particle size during dry milling, Powder Technol. 323 (2018) 374–3784. [34] E. Ardi, K. Dong, A. Yu, R. Yang, A combined experimental and DEM approach to determine the breakage of particles in an impact mill, Powder Technol. 318 (2017) 543–548. [35] N. Metta, M. Ierapetritou, R. Ramachandran, A multiscale DEM-PBM approach for a continuous comilling process using a mechanically developed breakage kernel, Chem. Eng. Sci. 178 (2018) 211–221.

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