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Preparation of submicron drug particles via spray drying from organic solvents
International Journal of Pharmaceutics 567 (2019) 118501
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International Journal of Pharmaceutics journal homepage: www.elsevier.com/locate/ijpharm
Preparation of submicron drug particles via spray drying from organic solvents
T
Adrian Dobrowolski, Ramona Strob, Jan Felix Dräger-Gillessen, Damian Pieloth, ⁎ Gerhard Schaldach, Helmut Wiggers, Markus Thommes Laboratory of Solids Process Engineering, TU Dortmund University, Germany
A R T I C LE I N FO
A B S T R A C T
Keywords: Electrostatic precipitation Organic solvent spray drying Submicron particles Solubility Bioavailability Nanoparticles API
Manufacturing poorly water-soluble active pharmaceutical ingredients (API) with sufficient bioavailability is a significant challenge in pharmaceutical research. A higher bioavailability can reduce both the applied dosage and the side effects for the patient. One method of increasing the bioavailability is to reduce the particle size of the drug down to the nanoscale. An innovative procedure for the preparation of particles in the submicron size range is spray drying with aerosol conditioning, followed by subsequent separation of the particles in an electrostatic precipitator (ESP). This process has been tested before in an earlier work with aqueous model substances at high production rates (1 g/h) and narrow particle-size distributions (mannitol: d50,0 = 455 nm, span = 0,8) in the submicron range. Spray drying from an aqueous solution with low drug concentrations (< 1 wt-%) leads to particles in the lower nanosize range, but the low concentrations make this process inefficient. A custom-made plant was modified in order to handle the organic spray-drying process. In addition, explosion protection had to be considered. This work focuses on the spray drying of submicron particles from organic solvents for the purpose of increasing the dissolution rate of the API griseofulvin. API particles were successfully produced in the submicron size-range, characterized and the dissolution behavior was investigated. The dissolution time to dissolve 80% of the drug, t80, was reduced from 21.5 min for the micronized grade API to 8.5 min for the submicron product.
1. Introduction A major challenge in the utilization of new active substances (API) for human application is the water solubility. Approximately 90% of newly-discovered drugs are poorly soluble in water (Bhakay et al., 2018), making low bioavailability likely. Through miniaturization of the particles, the dissolution of the active ingredients can be positively influenced. An enlargement of the particle surface results in an increase of the mass transfer rate (Noyes and Whitney, 1897). Saturation concentration can also be increased by using particles in the submicron range (Freundlich, 1922). Spray drying is one possibility to produce submicron particles. The process has been industrially established since 1940 in the production of food and pharmaceutical excipients (Broadhead et al., 1992). It is particularly well-suited for the processing of temperature-sensitive substances, enables targeted delivery and reduces toxic side effects (Davis and Walker, 2018). Spray drying is a continuous, fast, reproducible and scalable technology which allows the production of high quality powders at low moisture contents (Arpagaus ⁎
et al., 2018; Schmid et al. 2011). In the manufacturing of pharmaceutical submicron particles by spray drying, current research projects encounter problems with respect to yield and throughput (Sosnik and Seremeta, 2015). The production of submicron particles (0.1–1 µm) from aqueous solutions has already been investigated successfully and in detail in previous work using the model substance mannitol and polyvinylpyrrolidone (Dobrowolski et al., 2018; Strob et al., 2018). The use of an aqueous material system was mainly used to characterize the former plant. For this purpose, a substance-laden solution was sprayed into a cyclone. Large droplets were separated and reused, while small droplets entered the drying stage. The dried submicron particles were then charged and collected in an electrostatic precipitator. So far, ambient and compressed air has been used as the atomizing and drying gas. Due to the low water-solubility of the used API, the spray-drying time was high when using water as a solvent. Therefore, a modified plant concept has to be developed, which enables the use of organic solvents with higher solubility limits of APIs. However, spray drying of
Corresponding author at: Laboratory of Solids Process Engineering, TU Dortmund University, Emil-Figge-Str. 68, 44227 Dortmund, Germany. E-mail address: [email protected] (M. Thommes).
https://doi.org/10.1016/j.ijpharm.2019.118501 Received 16 May 2019; Received in revised form 4 July 2019; Accepted 5 July 2019 Available online 06 July 2019 0378-5173/ © 2019 Elsevier B.V. All rights reserved.
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an organic solution creates additional challenges compared to aqueous solutions. The use of solvent-resistant parts is necessary for safe operation. In addition, the generation of an explosive atmosphere is a risk, especially since the separation of the particles is carried out in an electrostatic precipitator, which contains a constant ignition source. Explosion protection can be provided by controlling the composition of the gas mixture. A lean gas mixture with a solvent concentration below the lower explosion limit cannot explode even in the presence of an ignition source. The use of an inert gas instead of ambient air also prevents explosion, despite the presence of both an ignition source and ignitable solvent concentration. In spray drying plants, a closed loop is often used with organic solvents in order to circulate the inert gas and condense the solvent from the process stream to save costs. Typically nitrogen or carbon dioxide are used as inert gases in combination with e.g. acetone, dichloromethane, ethanol or methanol. The choice of the organic solvent is mainly based on the solubilisation of the API in the given substance (Arpagaus et al., 2018). The aim of the study was, first, the characterization of an existing plant with an API in an aqueous environment. The second aim was the modification of the plant for spraying organic solvents. Finally, spray drying tests on organic solvents were carried out, in which the produced submicron particles were analysed with respect to their morphology, size and dissolution behavior to determine whether shifting into the submicron range would improve the dissolution rate.
Fig. 1. Flow sheet of the setup for spray drying experiments.
particles thus produced formed a powder layer on the outer electrode of the electrostatic precipitator and could be harvested with a scraper. During the tests, flow rates, drug concentration, oxygen content of the ambient air, temperature of the drying gas, mass flows of the gas supply and pressure of the gas cylinders were continuously monitored. An optimization of the plant in earlier work provided the aqueous operating conditions shown in Table 1. Due to changing the drying and atomizing gas to CO2 and the liquid to acetone, it was necessary to adjust the operating conditions of the spray drying plant to ensure laminar flow in the electrostatic precipitator. This can be seen in the organic operating conditions in Table 1.
2. Materials & methods 2.1. Materials Spray drying experiments were conducted with hydrochlorothiazide (HCT, Unichem Laboratories Ltd, Raigad, India) and griseofulvin (Fulvicin, Hawkins Inc., Roseville, Minneapolis, USA). According to Biopharmaceutical Classification System (BCS), griseofulvin is classified as a Class IIb active substance (Butler and Dressman, 2010) and is thus solubility-limited in terms of its bioavailability. HCT is a Class IV drug and limited in terms of solubility and permeability (Sanphui et al., 2015). Due to its low solubility in water, spray drying must be carried out with a suitable solvent. Acetone (propanone, Merck, Darmstadt, Germany) was chosen based on a compromise between good solubility of the active ingredient (HCT > 150 g/L, griseofulvin 26.5 g/L) (Hu et al., 2010) and lower toxicity compared to other organic solvents.
2.2.2. Characterization of submicron particles 2.2.2.1. Scanning electron microscopy. The particle size and morphology were assessed with a scanning electron microscope (Hitachi H-S4500 FEG, Hitachi High-Technologies Europe, Krefeld, Germany; Particles unsputtered) operating at 1 kV. Aluminum sample holders on the collection electrode were used to create particle monolayers and resolve time dependent effects. An initial particle-size distribution was determined by image analysis with ImageJ (Version 1.51, U. S. National Institutes of Health, Bethesda, Maryland, USA). The particlesize distribution was estimated by classifying 300 particles per image.
2.2. Methods 2.2.1. Preparation of submicron particles The production of submicron particles requires a defined process to ensure safety. A schematic of the setup, especially developed for this purpose (Strob et al., 2018), is shown in Fig. 1. The UV/Vis (QI) was rinsed with pure acetone to adjust the baseline. Subsequently, the spray solution with the desired concentration of active ingredient was added to the feed reservoir and all tubes were filled. The oxygen sensor was zeroed against ambient air. First, the pressure regulator at the drying gas supply was opened and the heating cartridge was switched on. Next, the pressure reducer for the atomizer gas was opened. The prepared feed solution was sprayed using a two-fluid nozzle, which was operated with an HPLC pump at a volume flow of 100 ml/min. Carbon dioxide was used as the atomizing inert gas at a pressure of 3.5 bar. The aerosol entered a cyclone through a two-fluid capillary nozzle. In the cyclone, large droplets (> 3 µm) were separated and small droplets (< 3 µm) remained in the gas stream to form a conditioned aerosol, which entered the drying section through the dip pipe. Carbon dioxide was supplied as drying gas into the drying line. After switching on the acetone dosing, it was possible to safely leave the lab. The electrostatic precipitator was then switched on. Afterwards, the dried particles were first charged in a two-stage electrostatic precipitator and then separated in an electric field. The
2.2.2.2. Laser diffractometry. Laser diffractometry is a method for determining the particle-size distribution in the submicron range. For this purpose, the Mastersizer 3000 (Malvern Instruments, Malvern, Worcestershire, UK) was used. Particles dispersed in water were measured. In order to prevent the dissolution of the active agents, the particles were measured in a saturated solution. The sample was first dispersed using an IKA gear rim disperser (IKA, Staufen, Germany). The surfactant sodium dodecyl sulfate (SDS) was added to stabilize the isolated primary particles so that the particles did not agglomerate Table 1 Operating conditions of the spray drying plant.
Feed mass flow Drying gas mass flow Drying temperature Atomizing gas mass flow Atomizing pressure Electrostatic precipitator voltage
2
Aqueous spraying (Strob et al., 2018)
Organic spraying
100 ml/min 4.5 kg/h 50 °C 2.5 kg/h 5 bar ~20 kV
100 ml/min 7.5 kg/h 50 °C 3.75 kg/h 3 bar ~20 kV
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again. SDS is known to serve as a solubilizer (Pearlman and Wang, 2006). Dissolution tests in the literature showed a significant change in the dissolution of formulations with SDS concentrations above 0.01 wt% (Reitz, 2014). Therefore, only 0.01 wt-% SDS is used in relation to the active ingredient to stabilize and not dissolve the drug.
deconvoluted mathematically from the measured kinetics. A convolution is a mathematical operation which combines or folds two functions, and demonstrates how the shape of one is changed by the other (Sidney Burrus, 2012; Keßler, 1989; Press et al., 1992; Selesnick, 2013). The definition of a convolution is:
2.2.2.3. Inline particle size measurement. A portable, optical, inline, particle counter (1.109, GRIMM AEROSOL Technik, Ainring, Germany) was used to determine the particle concentrations in the exhaust gas of the ESP. This device determines the number and size of particles per unit volume of gas. The sampling point was located in the middle of the outlet pipe of the ESP. The sample flow rate was 1.2 ml/ min and the probe design allowed isokinetic sampling. The tests were initially carried out without applied voltage in order to record the raw gas data as a reference. The particle-size distribution of clean gas was then measured and compared with the raw gas to determine the separation efficiency.
(f *g )(t ) =
∞
∫−∞ f (τ ) g (t − τ ) dτ
where (f *g )(t ) is the convolution and in this case measured kinetics, f (τ ) is the pure dissolution kinetics and g (t − τ ) is the response function of the system. The deconvolution procedure (see Appendix) was used to generate all dissolution kinetics from the measured data in this work (Keßler, 1989; Press et al., 1992; Selesnick, 2013). 2.2.2.7. Safety concept. Acetone used to produce spray-dried submicron particles is volatile and forms an explosive atmosphere with air (Hattwig and Steen, 2004). In the presence of a potential ignition source (e.g. corona discharge in an ESP) an immediate explosion hazard can arise which must be avoided. As a consequence, CO2 was used as an inert gas to prevent the limiting oxygen concentration from ever being exceeded (11.5 %v/v for acetone (Alfa Aesar, 2009)), to ensure safe operation and a sufficient ionization in the submicron range compared to nitrogen. Supplementary to a complete seal, the environment of the setup was controlled by an oxygen warning device (BW Clip Real Time, Honeywell, Morristown, USA) near the floor in order to detect a potential leakage of CO2.
2.2.2.4. Ozone measurement. The presence of high voltages in gaseous media can lead to ozone production. In wastewater treatment, ozone (> 1 ppm) (Antoniou et al., 2013) is used to degrade API. The ozone concentration must be monitored in order to avoid degradation of the active substance just produced. An ozone sensor (POM, twobtech, Colorado, USA) was used for this purpose. The inlet point of the sensor was positioned in the ionization zone. This extracts the test gas where ozone formation takes place. 2.2.2.5. Dissolution measurement. Initial estimates of the dissolution behavior of drugs in the body (in vivo), for example in the intestine, can be made using in-vitro dissolution measurements. A dissolution apparatus (Paddle Apparatus 2, DT 6, ERWEKA, Heusenstamm, Germany) was used for this purpose. A physical mixture was produced with mannitol from the active ingredients with a drug loading of 1 wt-%. The physical mixtures were prepared according to the principle of geometric gradation in the laboratory mixer (Turbula T10B, W.A. Bachofen AG, Muttenz, Switzerland.) in a 1 L stainless steel container. The powders were then examined in the dissolution apparatus at a temperature of 37 °C. The dissolution medium was 900 ml of demineralized water, and the speed of the paddle stirrer was set to 50 rpm (United States Pharmacopeial Convention, 2012). After addition, the stirrer was set for 5 s at maximum speed (300 rpm) to achieve immediate wetting of the powder. The dissolution measurement was then started at a wavelength of 295 nm in a UV/Vis spectrometer (Lambda25, Perkin Elmer, USA).
2.2.2.8. Concentration of spray solution. In this process, unconditioned aerosol was reused. It was known from earlier experiments that additional evaporation already occurs in the cyclone. In order to keep the feed concentration and, consequently, the particle properties constant, acetone was added continuously. The concentration was monitored via a UV/Vis spectrometer. Deviations were buffered by the use of pure acetone which is pumped with a gear pump. 3. Results & discussion 3.1. Preliminary investigations First, spray-drying experiments with HCT from aqueous medium were performed to test the system. Due to the low concentration (0.7 g/ L) of the active substance in the solution, which correlates with the particle mass produced, it was necessary to carry out the experiments for longer than 12 h in this case in order to produce sufficient powder for the analysis. The SEM images in Fig. 2 (left) show no isolated primary particles but rather a fused surface. In contrast the SEM image in Fig. 2 (right), where HCT was collected just for 5 min, shows isolated primary particles on the aluminum sample holder whose size can be estimated at smaller than 100 nm. Due to the strongly-fused structure, an irreversible aggregation of the particles is assumed. The examination
2.2.2.6. Dissolution kinetic deconvolution. During the measurement of the active substance dissolution, it must be noted that the kinetics recorded with the spectrometer are composed of the actual dissolution kinetics and the mixing kinetics of the tubing system. In order to obtain the pure dissolution kinetics, the mixing kinetics must be unfolded or
Fig. 2. Spray dried HCT from aqueous solution t = 12 h, Mag: 15,000× (left) isolated HCT particles on aluminum t = 5 min, Mag: 40,000× (right), HV: 1 kV. 3
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Fig. 3. Spray dried HCT from acetone, Mag: 3000×, HV: 1 kV (left) Cumulative volume distribution of spray dried HCT from acetone, determined by image analysis (right).
It can be assumed that spray drying under constant operating conditions also provides constant results in the form of uniform particles in the first ESP stage. The particles were spherical and solid bridges were not visible. Fig. 4 (right) clearly shows the constant particle-size distribution over a test period of 90 min. The examination of the separated particles was continued in the second stage of the electrostatic precipitator. Within the first 15 to 30 min of operation a similar picture to the first stage can be seen. After 30 min, in addition to submicron particles, areas with coral-like structures are also visible, as shown in Fig. 5 (left). The image shows the transition between the two areas. Below right, the powder layer still consists of recognizable primary particles, however, solid bridges can already be recognized much more frequently here. The morphology of these structures suggests that they were formed not only by deposition but rather by particle growth at the ends. SEM images after 60 and 90 min support this conjecture. After one hour of operation, the entire sample was covered with these structures. The griseofulvin powder harvested from the electrostatic precipitator was measured and compared to commercially available micronized griseofulvin particles with the Mastersizer 3000 to check whether the agglomeration is reversible. Fig. 5 (right) shows the results of the particle size measurements. The spray dried powder is ten times smaller than commercially available micronized griseofulvin. A possible cause for the formation of the coral structure, is the temporary amorphousness of the particles. Very small droplets produced at the two-fluid nozzle dry so quickly that the active substance molecules have no time to form the crystalline lattice structure. An amorphous particle is formed, which has a significantly lower viscosity than a crystal. Since smaller particles can only receive fewer charges during separation, they are separated in the electrostatic precipitator mainly in the second stage. After separation, the particles flow amorphously and the round structure collapses. As the separated material is already crystallized and thus represents a crystallization
of the sample by laser diffractometry could not detect any particles in the submicron range, which is inevitably due to aggregation of the particles. Inadequate drying could be disproved with the method of loss on drying. The powder had a relative residual moisture content of less than 1%. During the generation of nanoparticles, amorphous structures can occur during sudden evaporation. This results in a so-called amorphous flowing were particles aggregate on the surface of the ESP. Based on these results, it is assumed that the low feed-concentration is the main reason for particle aggregation. In order to prevent amorphous flow, the active substance concentration of the solution was increased in subsequent experiments. As a consequence, the particles were larger and the drying time increased.
3.2. Organic spray drying tests Hydrochlorothiazide was also used as a model compound for organic spray drying to determine the production quantity at an active substance solution concentration of 5 wt-%. The morphology of spray-dried HCT particles was investigated by scanning electron microscopy. Spherical, submicron particles deposited on an aluminum sample holder became visible as shown in Fig. 3 (left). Conversely, the spherical particles indicate a large influence of the feed concentration compared to the aqueous spray drying of HCT where a fused surface dominated the layer appearance. A first evaluation of the SEM image is shown in Fig. 3 (right). The powder produced consists exclusively of particles in the submicron range. Spray drying experiments of griseofulvin as the second model compound were realized especially with respect to its dissolution behavior compared to the micronized product. The feed-concentration was set to 2 wt-% due to the lower solubility. As shown in Fig. 4 (right), submicron particles were produced over the entire operating time.
Fig. 4. Spray dried griseofulvin from acetone after 90 min, first ESP stage, Mag: 5000×, HV: 1 kV (left) Time dependent cumulative volume distribution of spray dried griseofulvin from acetone, first ESP stage, determined by image analysis (right). 4
International Journal of Pharmaceutics 567 (2019) 118501
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Fig. 5. Spray dried griseofulvin from acetone after 90 min, second ESP stage, Mag: 1000×, HV: 1 kV (left) Number density distribution of spray dried submicron griseofulvin particles (●) and commercially available micronized griseofulvin particles as reference (▲), determined by laser diffraction (right).
nucleus for the new particle, the coral-shaped structures are formed, which are crystalline despite the short-term amorphousness of the particles. It is described in the literature that griseofulvin also tends to recrystallize far below its glass transition temperature of 88 °C. The recrystallization on the particle surface is 10–100 times faster, which means that no amorphous phase can be detected, especially with micronized active agents (Rowe, 2013). These results show that the agglomeration must be avoided in order to produce a powder with a uniform particle-size distribution. For this purpose, it is also necessary to guarantee the crystallinity of the active ingredient during the deposition process. Submicron HCT particles were produced successfully for 5 h at a production rate of 190 mg per hour. Earlier work with the test substance mannitol was able to produce up to 1 g/h. The main reason for the reduced production volume is the lower concentration of the active ingredient (5 wt-%) compared to the tests with aqueous mannitol (10 wt-%). In addition, the feed volume flow in these tests was limited to 100 ml/min due to a system limitation. At the same time, the yield of the conditioned aerosol was limited to the number of fine droplets produced by the nozzle. In a future optimization, both the mass flow and the concentration of the fluid need to be adjusted. Secondary droplet disintegration was investigated to increase the fine fraction of aerosol (Strob, 2019).
Fig. 6. Deconvolved dissolution kinetics of spray dried and micronized physical griseofulvin in mannitol mixtures (av ± Ci, α = 0.05, n = 6).
is approximately 50 ppb (Umweltbundesamt, 2014). A test with CO2 as drying and atomizing gas and an operating voltage of 20 kV resulted in an ozone concentration of 111 ± 14 ppb. This value is low compared to operating with ambient air where a value of 1424 ± 267 ppb was reached. It is therefore recommended that, if the system is to be used for spray drying of ozone-sensitive active substances, inert gases like CO2 be used. It is possible to reduce the ozone production in the ESP by reversing the polarity of the electrostatic precipitator to positive corona, or by changing the discharge electrode material to silver, for example, which is known for its ozone-reducing properties. This version is already used in electrostatic precipitators for ventilation and air conditioning systems in order not to pollute the indoor air with ozone (Verein Deutscher Ingenieure, 2011).
3.3. Dissolution tests In order to analyze the accelerated dissolution rate of spray-dried submicron formulations, they were compared with their physical mixtures. The particles produced by spray drying, d50,0 = 0.327 µm ± 0.002, and micronized griseofulvin, d50,0 = 3.070 µm ± 0.016, as shown in Fig. 5 (right) were investigated with regard to their dissolution behavior (see Fig. 6). The material produced by spray drying shows a higher dissolution rate than the unprocessed powder. The time to dissolve 80% of the active ingredient is 500 s for spray-dried griseofulvin and 1200 s for unprocessed griseofulvin. The difference is particularly pronounced in the first minute. After that, the curve of the spray-dried powder flattens out. The manufacturing process of the physical mixture is obviously not able to disintegrate the coral structures. The flattening curve can be justified by the fact that particles present individually at this point in time are completely dissolved. Poorly wettable agglomerates decrease the dissolution rate. It can be stated that the production of spray-dried submicron active-substance particles can lead to improved dissolution kinetics even in comparison to micronized particles. If the challenges of particle agglomeration can be overcome, a further significant improvement in dissolution can be expected.
4. Conclusion Pharmaceutical active-ingredient particles in the submicron range (0.1–1 µm) were successfully produced via organic spray-drying and electrostatic precipitation. It was possible to manufacture spherical submicron hydrochlorothiazide and griseofulvin as model particles. As shown in SEM pictures, the robust production process guarantees constant particle-size distributions. Safe operation of the spray-drying plant is ensured by the use of carbon dioxide. The use of inert gases in the separation of APIs in electrostatic precipitators reduces the risk of the drug being degraded by ozone formed in the ESP. A potential improvement of the bioavailability of APIs is demonstrated by dissolution tests of the griseofulvin powder produced. The release time t80 is twice as fast with spray-dried particles compared to commercially micronized particles.
3.4. Ozone production The naturally occurring average ozone concentration in ambient air 5
International Journal of Pharmaceutics 567 (2019) 118501
A. Dobrowolski, et al.
In first experiments it was possible to manufacture up to 190 mg/h. This value can be increased in future work by increasing the fine fraction of the conditioned aerosol, and through process parameter optimization. Research is currently in progress on an additional impact atomization in the cyclone.
interests or personal relationships that could have appeared to influence the work reported in this paper.
Declaration of Competing Interest
The authors are grateful for the assistance of Elizabeth Ely (EIES, Lafayette, IN, USA) in preparing the manuscript.
Acknowledgement
The authors declare that they have no known competing financial Appendix: Dissolution kinetics deconvolution During the measurement of the active substance dissolution, it must be noted that the kinetics recorded with the spectrometer are composed of the actual dissolution kinetics and the mixing kinetics of the tubing system. In order to obtain the pure dissolution kinetics, the mixing kinetics must be unfolded or deconvolved mathematically from the measured kinetics. A convolution is a mathematical operation which combines or folds two functions, and demonstrates how the shape of one is changed by the other (Sidney Burrus, 2012; Keßler, 1989; Press et al., 1992; Selesnick, 2013). The definition of a convolution is:
(f *g )(t ) =
∞
∫−∞ f (τ ) g (t − τ ) dτ
where (f *g )(t ) is the convolution and, in this case, measured kinetics, f (τ ) is the pure dissolution kinetics and g (t − τ ) is the response function of the system. The function g can be determined by injecting an already dissolved substance into the dissolution tester and measuring the resulting signal recorded in the UV/VIS. The aim is now to determine the function f (τ ) from the measured functions g (t − τ ) and (f *g )(t ) , for the purpose of better comparability and to remove the mixing kinetics. If the functions were continuous polynomial functions and several times differentiable, polynomial division would generate the deconvolution solution. However, in many cases, a fitted polynomial leads to large deviations. A further possibility for visualizing the convolution of discrete measured values for a finite duration M is the following: M /2
∑
(f *g )(t ) =
f (τ ) g (t − τ )
τ =− M + 1 2
This means if the function g would have the value 2 at the time of measurement τ = 10 and otherwise continuously 0, the folded output signal would look like the input signal, only multiplied by the value 2 and shifted by 10 measured values. This simple example becomes more complex with dissolution kinetics and an impulse signal response. Deconvolution can be expressed by finding the input of a linear time-invariant system,
y = Hx when the convolved output signal y is known and given by
y (n) = h (0) x (n) + h (1) x (n − 1) + ⋯+h (N ) x (n − N ) where x(n) is the input signal and h(n) is the impulse response. H defines a so-called Toeplitz matrix, which is constant-valued along its diagonals.
⎡ h (0) ⎤ ⎢ h (1) h (0) ⎥ H=⎢ ⎥ h (2) h (1) h (0) ⎢ ⎥ ⋱⎦ ⎣ ⋮ A deconvolution of the resulting linear system often cannot be solved due to H being singular. Using the technique “diagonal loading” overcomes this limitation and regularizes the problem to obtain the input signal x.
x = (H T H + λI )−1H T y For this purpose, the regularization parameter λ is added. Even a small value of λ is sufficient to make the matrix invertible but results in a noisy solution. In reality the available data are always noisy. An improvement of the deconvolution result can be made by minimizing the energy of the second-order derivative of x. A solution can be obtained introducing the second-order difference matrix D
x = (H T H + λDT D)−1H T y This procedure is used to generate all dissolution kinetics from the measured data in this work (Keßler, 1989; Press et al., 1992; Selesnick, 2013).
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International Journal of Pharmaceutics journal homepage: www.elsevier.com/locate/ijpharm
Preparation of submicron drug particles via spray drying from organic solvents
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Adrian Dobrowolski, Ramona Strob, Jan Felix Dräger-Gillessen, Damian Pieloth, ⁎ Gerhard Schaldach, Helmut Wiggers, Markus Thommes Laboratory of Solids Process Engineering, TU Dortmund University, Germany
A R T I C LE I N FO
A B S T R A C T
Keywords: Electrostatic precipitation Organic solvent spray drying Submicron particles Solubility Bioavailability Nanoparticles API
Manufacturing poorly water-soluble active pharmaceutical ingredients (API) with sufficient bioavailability is a significant challenge in pharmaceutical research. A higher bioavailability can reduce both the applied dosage and the side effects for the patient. One method of increasing the bioavailability is to reduce the particle size of the drug down to the nanoscale. An innovative procedure for the preparation of particles in the submicron size range is spray drying with aerosol conditioning, followed by subsequent separation of the particles in an electrostatic precipitator (ESP). This process has been tested before in an earlier work with aqueous model substances at high production rates (1 g/h) and narrow particle-size distributions (mannitol: d50,0 = 455 nm, span = 0,8) in the submicron range. Spray drying from an aqueous solution with low drug concentrations (< 1 wt-%) leads to particles in the lower nanosize range, but the low concentrations make this process inefficient. A custom-made plant was modified in order to handle the organic spray-drying process. In addition, explosion protection had to be considered. This work focuses on the spray drying of submicron particles from organic solvents for the purpose of increasing the dissolution rate of the API griseofulvin. API particles were successfully produced in the submicron size-range, characterized and the dissolution behavior was investigated. The dissolution time to dissolve 80% of the drug, t80, was reduced from 21.5 min for the micronized grade API to 8.5 min for the submicron product.
1. Introduction A major challenge in the utilization of new active substances (API) for human application is the water solubility. Approximately 90% of newly-discovered drugs are poorly soluble in water (Bhakay et al., 2018), making low bioavailability likely. Through miniaturization of the particles, the dissolution of the active ingredients can be positively influenced. An enlargement of the particle surface results in an increase of the mass transfer rate (Noyes and Whitney, 1897). Saturation concentration can also be increased by using particles in the submicron range (Freundlich, 1922). Spray drying is one possibility to produce submicron particles. The process has been industrially established since 1940 in the production of food and pharmaceutical excipients (Broadhead et al., 1992). It is particularly well-suited for the processing of temperature-sensitive substances, enables targeted delivery and reduces toxic side effects (Davis and Walker, 2018). Spray drying is a continuous, fast, reproducible and scalable technology which allows the production of high quality powders at low moisture contents (Arpagaus ⁎
et al., 2018; Schmid et al. 2011). In the manufacturing of pharmaceutical submicron particles by spray drying, current research projects encounter problems with respect to yield and throughput (Sosnik and Seremeta, 2015). The production of submicron particles (0.1–1 µm) from aqueous solutions has already been investigated successfully and in detail in previous work using the model substance mannitol and polyvinylpyrrolidone (Dobrowolski et al., 2018; Strob et al., 2018). The use of an aqueous material system was mainly used to characterize the former plant. For this purpose, a substance-laden solution was sprayed into a cyclone. Large droplets were separated and reused, while small droplets entered the drying stage. The dried submicron particles were then charged and collected in an electrostatic precipitator. So far, ambient and compressed air has been used as the atomizing and drying gas. Due to the low water-solubility of the used API, the spray-drying time was high when using water as a solvent. Therefore, a modified plant concept has to be developed, which enables the use of organic solvents with higher solubility limits of APIs. However, spray drying of
Corresponding author at: Laboratory of Solids Process Engineering, TU Dortmund University, Emil-Figge-Str. 68, 44227 Dortmund, Germany. E-mail address: [email protected] (M. Thommes).
https://doi.org/10.1016/j.ijpharm.2019.118501 Received 16 May 2019; Received in revised form 4 July 2019; Accepted 5 July 2019 Available online 06 July 2019 0378-5173/ © 2019 Elsevier B.V. All rights reserved.
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an organic solution creates additional challenges compared to aqueous solutions. The use of solvent-resistant parts is necessary for safe operation. In addition, the generation of an explosive atmosphere is a risk, especially since the separation of the particles is carried out in an electrostatic precipitator, which contains a constant ignition source. Explosion protection can be provided by controlling the composition of the gas mixture. A lean gas mixture with a solvent concentration below the lower explosion limit cannot explode even in the presence of an ignition source. The use of an inert gas instead of ambient air also prevents explosion, despite the presence of both an ignition source and ignitable solvent concentration. In spray drying plants, a closed loop is often used with organic solvents in order to circulate the inert gas and condense the solvent from the process stream to save costs. Typically nitrogen or carbon dioxide are used as inert gases in combination with e.g. acetone, dichloromethane, ethanol or methanol. The choice of the organic solvent is mainly based on the solubilisation of the API in the given substance (Arpagaus et al., 2018). The aim of the study was, first, the characterization of an existing plant with an API in an aqueous environment. The second aim was the modification of the plant for spraying organic solvents. Finally, spray drying tests on organic solvents were carried out, in which the produced submicron particles were analysed with respect to their morphology, size and dissolution behavior to determine whether shifting into the submicron range would improve the dissolution rate.
Fig. 1. Flow sheet of the setup for spray drying experiments.
particles thus produced formed a powder layer on the outer electrode of the electrostatic precipitator and could be harvested with a scraper. During the tests, flow rates, drug concentration, oxygen content of the ambient air, temperature of the drying gas, mass flows of the gas supply and pressure of the gas cylinders were continuously monitored. An optimization of the plant in earlier work provided the aqueous operating conditions shown in Table 1. Due to changing the drying and atomizing gas to CO2 and the liquid to acetone, it was necessary to adjust the operating conditions of the spray drying plant to ensure laminar flow in the electrostatic precipitator. This can be seen in the organic operating conditions in Table 1.
2. Materials & methods 2.1. Materials Spray drying experiments were conducted with hydrochlorothiazide (HCT, Unichem Laboratories Ltd, Raigad, India) and griseofulvin (Fulvicin, Hawkins Inc., Roseville, Minneapolis, USA). According to Biopharmaceutical Classification System (BCS), griseofulvin is classified as a Class IIb active substance (Butler and Dressman, 2010) and is thus solubility-limited in terms of its bioavailability. HCT is a Class IV drug and limited in terms of solubility and permeability (Sanphui et al., 2015). Due to its low solubility in water, spray drying must be carried out with a suitable solvent. Acetone (propanone, Merck, Darmstadt, Germany) was chosen based on a compromise between good solubility of the active ingredient (HCT > 150 g/L, griseofulvin 26.5 g/L) (Hu et al., 2010) and lower toxicity compared to other organic solvents.
2.2.2. Characterization of submicron particles 2.2.2.1. Scanning electron microscopy. The particle size and morphology were assessed with a scanning electron microscope (Hitachi H-S4500 FEG, Hitachi High-Technologies Europe, Krefeld, Germany; Particles unsputtered) operating at 1 kV. Aluminum sample holders on the collection electrode were used to create particle monolayers and resolve time dependent effects. An initial particle-size distribution was determined by image analysis with ImageJ (Version 1.51, U. S. National Institutes of Health, Bethesda, Maryland, USA). The particlesize distribution was estimated by classifying 300 particles per image.
2.2. Methods 2.2.1. Preparation of submicron particles The production of submicron particles requires a defined process to ensure safety. A schematic of the setup, especially developed for this purpose (Strob et al., 2018), is shown in Fig. 1. The UV/Vis (QI) was rinsed with pure acetone to adjust the baseline. Subsequently, the spray solution with the desired concentration of active ingredient was added to the feed reservoir and all tubes were filled. The oxygen sensor was zeroed against ambient air. First, the pressure regulator at the drying gas supply was opened and the heating cartridge was switched on. Next, the pressure reducer for the atomizer gas was opened. The prepared feed solution was sprayed using a two-fluid nozzle, which was operated with an HPLC pump at a volume flow of 100 ml/min. Carbon dioxide was used as the atomizing inert gas at a pressure of 3.5 bar. The aerosol entered a cyclone through a two-fluid capillary nozzle. In the cyclone, large droplets (> 3 µm) were separated and small droplets (< 3 µm) remained in the gas stream to form a conditioned aerosol, which entered the drying section through the dip pipe. Carbon dioxide was supplied as drying gas into the drying line. After switching on the acetone dosing, it was possible to safely leave the lab. The electrostatic precipitator was then switched on. Afterwards, the dried particles were first charged in a two-stage electrostatic precipitator and then separated in an electric field. The
2.2.2.2. Laser diffractometry. Laser diffractometry is a method for determining the particle-size distribution in the submicron range. For this purpose, the Mastersizer 3000 (Malvern Instruments, Malvern, Worcestershire, UK) was used. Particles dispersed in water were measured. In order to prevent the dissolution of the active agents, the particles were measured in a saturated solution. The sample was first dispersed using an IKA gear rim disperser (IKA, Staufen, Germany). The surfactant sodium dodecyl sulfate (SDS) was added to stabilize the isolated primary particles so that the particles did not agglomerate Table 1 Operating conditions of the spray drying plant.
Feed mass flow Drying gas mass flow Drying temperature Atomizing gas mass flow Atomizing pressure Electrostatic precipitator voltage
2
Aqueous spraying (Strob et al., 2018)
Organic spraying
100 ml/min 4.5 kg/h 50 °C 2.5 kg/h 5 bar ~20 kV
100 ml/min 7.5 kg/h 50 °C 3.75 kg/h 3 bar ~20 kV
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again. SDS is known to serve as a solubilizer (Pearlman and Wang, 2006). Dissolution tests in the literature showed a significant change in the dissolution of formulations with SDS concentrations above 0.01 wt% (Reitz, 2014). Therefore, only 0.01 wt-% SDS is used in relation to the active ingredient to stabilize and not dissolve the drug.
deconvoluted mathematically from the measured kinetics. A convolution is a mathematical operation which combines or folds two functions, and demonstrates how the shape of one is changed by the other (Sidney Burrus, 2012; Keßler, 1989; Press et al., 1992; Selesnick, 2013). The definition of a convolution is:
2.2.2.3. Inline particle size measurement. A portable, optical, inline, particle counter (1.109, GRIMM AEROSOL Technik, Ainring, Germany) was used to determine the particle concentrations in the exhaust gas of the ESP. This device determines the number and size of particles per unit volume of gas. The sampling point was located in the middle of the outlet pipe of the ESP. The sample flow rate was 1.2 ml/ min and the probe design allowed isokinetic sampling. The tests were initially carried out without applied voltage in order to record the raw gas data as a reference. The particle-size distribution of clean gas was then measured and compared with the raw gas to determine the separation efficiency.
(f *g )(t ) =
∞
∫−∞ f (τ ) g (t − τ ) dτ
where (f *g )(t ) is the convolution and in this case measured kinetics, f (τ ) is the pure dissolution kinetics and g (t − τ ) is the response function of the system. The deconvolution procedure (see Appendix) was used to generate all dissolution kinetics from the measured data in this work (Keßler, 1989; Press et al., 1992; Selesnick, 2013). 2.2.2.7. Safety concept. Acetone used to produce spray-dried submicron particles is volatile and forms an explosive atmosphere with air (Hattwig and Steen, 2004). In the presence of a potential ignition source (e.g. corona discharge in an ESP) an immediate explosion hazard can arise which must be avoided. As a consequence, CO2 was used as an inert gas to prevent the limiting oxygen concentration from ever being exceeded (11.5 %v/v for acetone (Alfa Aesar, 2009)), to ensure safe operation and a sufficient ionization in the submicron range compared to nitrogen. Supplementary to a complete seal, the environment of the setup was controlled by an oxygen warning device (BW Clip Real Time, Honeywell, Morristown, USA) near the floor in order to detect a potential leakage of CO2.
2.2.2.4. Ozone measurement. The presence of high voltages in gaseous media can lead to ozone production. In wastewater treatment, ozone (> 1 ppm) (Antoniou et al., 2013) is used to degrade API. The ozone concentration must be monitored in order to avoid degradation of the active substance just produced. An ozone sensor (POM, twobtech, Colorado, USA) was used for this purpose. The inlet point of the sensor was positioned in the ionization zone. This extracts the test gas where ozone formation takes place. 2.2.2.5. Dissolution measurement. Initial estimates of the dissolution behavior of drugs in the body (in vivo), for example in the intestine, can be made using in-vitro dissolution measurements. A dissolution apparatus (Paddle Apparatus 2, DT 6, ERWEKA, Heusenstamm, Germany) was used for this purpose. A physical mixture was produced with mannitol from the active ingredients with a drug loading of 1 wt-%. The physical mixtures were prepared according to the principle of geometric gradation in the laboratory mixer (Turbula T10B, W.A. Bachofen AG, Muttenz, Switzerland.) in a 1 L stainless steel container. The powders were then examined in the dissolution apparatus at a temperature of 37 °C. The dissolution medium was 900 ml of demineralized water, and the speed of the paddle stirrer was set to 50 rpm (United States Pharmacopeial Convention, 2012). After addition, the stirrer was set for 5 s at maximum speed (300 rpm) to achieve immediate wetting of the powder. The dissolution measurement was then started at a wavelength of 295 nm in a UV/Vis spectrometer (Lambda25, Perkin Elmer, USA).
2.2.2.8. Concentration of spray solution. In this process, unconditioned aerosol was reused. It was known from earlier experiments that additional evaporation already occurs in the cyclone. In order to keep the feed concentration and, consequently, the particle properties constant, acetone was added continuously. The concentration was monitored via a UV/Vis spectrometer. Deviations were buffered by the use of pure acetone which is pumped with a gear pump. 3. Results & discussion 3.1. Preliminary investigations First, spray-drying experiments with HCT from aqueous medium were performed to test the system. Due to the low concentration (0.7 g/ L) of the active substance in the solution, which correlates with the particle mass produced, it was necessary to carry out the experiments for longer than 12 h in this case in order to produce sufficient powder for the analysis. The SEM images in Fig. 2 (left) show no isolated primary particles but rather a fused surface. In contrast the SEM image in Fig. 2 (right), where HCT was collected just for 5 min, shows isolated primary particles on the aluminum sample holder whose size can be estimated at smaller than 100 nm. Due to the strongly-fused structure, an irreversible aggregation of the particles is assumed. The examination
2.2.2.6. Dissolution kinetic deconvolution. During the measurement of the active substance dissolution, it must be noted that the kinetics recorded with the spectrometer are composed of the actual dissolution kinetics and the mixing kinetics of the tubing system. In order to obtain the pure dissolution kinetics, the mixing kinetics must be unfolded or
Fig. 2. Spray dried HCT from aqueous solution t = 12 h, Mag: 15,000× (left) isolated HCT particles on aluminum t = 5 min, Mag: 40,000× (right), HV: 1 kV. 3
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Fig. 3. Spray dried HCT from acetone, Mag: 3000×, HV: 1 kV (left) Cumulative volume distribution of spray dried HCT from acetone, determined by image analysis (right).
It can be assumed that spray drying under constant operating conditions also provides constant results in the form of uniform particles in the first ESP stage. The particles were spherical and solid bridges were not visible. Fig. 4 (right) clearly shows the constant particle-size distribution over a test period of 90 min. The examination of the separated particles was continued in the second stage of the electrostatic precipitator. Within the first 15 to 30 min of operation a similar picture to the first stage can be seen. After 30 min, in addition to submicron particles, areas with coral-like structures are also visible, as shown in Fig. 5 (left). The image shows the transition between the two areas. Below right, the powder layer still consists of recognizable primary particles, however, solid bridges can already be recognized much more frequently here. The morphology of these structures suggests that they were formed not only by deposition but rather by particle growth at the ends. SEM images after 60 and 90 min support this conjecture. After one hour of operation, the entire sample was covered with these structures. The griseofulvin powder harvested from the electrostatic precipitator was measured and compared to commercially available micronized griseofulvin particles with the Mastersizer 3000 to check whether the agglomeration is reversible. Fig. 5 (right) shows the results of the particle size measurements. The spray dried powder is ten times smaller than commercially available micronized griseofulvin. A possible cause for the formation of the coral structure, is the temporary amorphousness of the particles. Very small droplets produced at the two-fluid nozzle dry so quickly that the active substance molecules have no time to form the crystalline lattice structure. An amorphous particle is formed, which has a significantly lower viscosity than a crystal. Since smaller particles can only receive fewer charges during separation, they are separated in the electrostatic precipitator mainly in the second stage. After separation, the particles flow amorphously and the round structure collapses. As the separated material is already crystallized and thus represents a crystallization
of the sample by laser diffractometry could not detect any particles in the submicron range, which is inevitably due to aggregation of the particles. Inadequate drying could be disproved with the method of loss on drying. The powder had a relative residual moisture content of less than 1%. During the generation of nanoparticles, amorphous structures can occur during sudden evaporation. This results in a so-called amorphous flowing were particles aggregate on the surface of the ESP. Based on these results, it is assumed that the low feed-concentration is the main reason for particle aggregation. In order to prevent amorphous flow, the active substance concentration of the solution was increased in subsequent experiments. As a consequence, the particles were larger and the drying time increased.
3.2. Organic spray drying tests Hydrochlorothiazide was also used as a model compound for organic spray drying to determine the production quantity at an active substance solution concentration of 5 wt-%. The morphology of spray-dried HCT particles was investigated by scanning electron microscopy. Spherical, submicron particles deposited on an aluminum sample holder became visible as shown in Fig. 3 (left). Conversely, the spherical particles indicate a large influence of the feed concentration compared to the aqueous spray drying of HCT where a fused surface dominated the layer appearance. A first evaluation of the SEM image is shown in Fig. 3 (right). The powder produced consists exclusively of particles in the submicron range. Spray drying experiments of griseofulvin as the second model compound were realized especially with respect to its dissolution behavior compared to the micronized product. The feed-concentration was set to 2 wt-% due to the lower solubility. As shown in Fig. 4 (right), submicron particles were produced over the entire operating time.
Fig. 4. Spray dried griseofulvin from acetone after 90 min, first ESP stage, Mag: 5000×, HV: 1 kV (left) Time dependent cumulative volume distribution of spray dried griseofulvin from acetone, first ESP stage, determined by image analysis (right). 4
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Fig. 5. Spray dried griseofulvin from acetone after 90 min, second ESP stage, Mag: 1000×, HV: 1 kV (left) Number density distribution of spray dried submicron griseofulvin particles (●) and commercially available micronized griseofulvin particles as reference (▲), determined by laser diffraction (right).
nucleus for the new particle, the coral-shaped structures are formed, which are crystalline despite the short-term amorphousness of the particles. It is described in the literature that griseofulvin also tends to recrystallize far below its glass transition temperature of 88 °C. The recrystallization on the particle surface is 10–100 times faster, which means that no amorphous phase can be detected, especially with micronized active agents (Rowe, 2013). These results show that the agglomeration must be avoided in order to produce a powder with a uniform particle-size distribution. For this purpose, it is also necessary to guarantee the crystallinity of the active ingredient during the deposition process. Submicron HCT particles were produced successfully for 5 h at a production rate of 190 mg per hour. Earlier work with the test substance mannitol was able to produce up to 1 g/h. The main reason for the reduced production volume is the lower concentration of the active ingredient (5 wt-%) compared to the tests with aqueous mannitol (10 wt-%). In addition, the feed volume flow in these tests was limited to 100 ml/min due to a system limitation. At the same time, the yield of the conditioned aerosol was limited to the number of fine droplets produced by the nozzle. In a future optimization, both the mass flow and the concentration of the fluid need to be adjusted. Secondary droplet disintegration was investigated to increase the fine fraction of aerosol (Strob, 2019).
Fig. 6. Deconvolved dissolution kinetics of spray dried and micronized physical griseofulvin in mannitol mixtures (av ± Ci, α = 0.05, n = 6).
is approximately 50 ppb (Umweltbundesamt, 2014). A test with CO2 as drying and atomizing gas and an operating voltage of 20 kV resulted in an ozone concentration of 111 ± 14 ppb. This value is low compared to operating with ambient air where a value of 1424 ± 267 ppb was reached. It is therefore recommended that, if the system is to be used for spray drying of ozone-sensitive active substances, inert gases like CO2 be used. It is possible to reduce the ozone production in the ESP by reversing the polarity of the electrostatic precipitator to positive corona, or by changing the discharge electrode material to silver, for example, which is known for its ozone-reducing properties. This version is already used in electrostatic precipitators for ventilation and air conditioning systems in order not to pollute the indoor air with ozone (Verein Deutscher Ingenieure, 2011).
3.3. Dissolution tests In order to analyze the accelerated dissolution rate of spray-dried submicron formulations, they were compared with their physical mixtures. The particles produced by spray drying, d50,0 = 0.327 µm ± 0.002, and micronized griseofulvin, d50,0 = 3.070 µm ± 0.016, as shown in Fig. 5 (right) were investigated with regard to their dissolution behavior (see Fig. 6). The material produced by spray drying shows a higher dissolution rate than the unprocessed powder. The time to dissolve 80% of the active ingredient is 500 s for spray-dried griseofulvin and 1200 s for unprocessed griseofulvin. The difference is particularly pronounced in the first minute. After that, the curve of the spray-dried powder flattens out. The manufacturing process of the physical mixture is obviously not able to disintegrate the coral structures. The flattening curve can be justified by the fact that particles present individually at this point in time are completely dissolved. Poorly wettable agglomerates decrease the dissolution rate. It can be stated that the production of spray-dried submicron active-substance particles can lead to improved dissolution kinetics even in comparison to micronized particles. If the challenges of particle agglomeration can be overcome, a further significant improvement in dissolution can be expected.
4. Conclusion Pharmaceutical active-ingredient particles in the submicron range (0.1–1 µm) were successfully produced via organic spray-drying and electrostatic precipitation. It was possible to manufacture spherical submicron hydrochlorothiazide and griseofulvin as model particles. As shown in SEM pictures, the robust production process guarantees constant particle-size distributions. Safe operation of the spray-drying plant is ensured by the use of carbon dioxide. The use of inert gases in the separation of APIs in electrostatic precipitators reduces the risk of the drug being degraded by ozone formed in the ESP. A potential improvement of the bioavailability of APIs is demonstrated by dissolution tests of the griseofulvin powder produced. The release time t80 is twice as fast with spray-dried particles compared to commercially micronized particles.
3.4. Ozone production The naturally occurring average ozone concentration in ambient air 5
International Journal of Pharmaceutics 567 (2019) 118501
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In first experiments it was possible to manufacture up to 190 mg/h. This value can be increased in future work by increasing the fine fraction of the conditioned aerosol, and through process parameter optimization. Research is currently in progress on an additional impact atomization in the cyclone.
interests or personal relationships that could have appeared to influence the work reported in this paper.
Declaration of Competing Interest
The authors are grateful for the assistance of Elizabeth Ely (EIES, Lafayette, IN, USA) in preparing the manuscript.
Acknowledgement
The authors declare that they have no known competing financial Appendix: Dissolution kinetics deconvolution During the measurement of the active substance dissolution, it must be noted that the kinetics recorded with the spectrometer are composed of the actual dissolution kinetics and the mixing kinetics of the tubing system. In order to obtain the pure dissolution kinetics, the mixing kinetics must be unfolded or deconvolved mathematically from the measured kinetics. A convolution is a mathematical operation which combines or folds two functions, and demonstrates how the shape of one is changed by the other (Sidney Burrus, 2012; Keßler, 1989; Press et al., 1992; Selesnick, 2013). The definition of a convolution is:
(f *g )(t ) =
∞
∫−∞ f (τ ) g (t − τ ) dτ
where (f *g )(t ) is the convolution and, in this case, measured kinetics, f (τ ) is the pure dissolution kinetics and g (t − τ ) is the response function of the system. The function g can be determined by injecting an already dissolved substance into the dissolution tester and measuring the resulting signal recorded in the UV/VIS. The aim is now to determine the function f (τ ) from the measured functions g (t − τ ) and (f *g )(t ) , for the purpose of better comparability and to remove the mixing kinetics. If the functions were continuous polynomial functions and several times differentiable, polynomial division would generate the deconvolution solution. However, in many cases, a fitted polynomial leads to large deviations. A further possibility for visualizing the convolution of discrete measured values for a finite duration M is the following: M /2
∑
(f *g )(t ) =
f (τ ) g (t − τ )
τ =− M + 1 2
This means if the function g would have the value 2 at the time of measurement τ = 10 and otherwise continuously 0, the folded output signal would look like the input signal, only multiplied by the value 2 and shifted by 10 measured values. This simple example becomes more complex with dissolution kinetics and an impulse signal response. Deconvolution can be expressed by finding the input of a linear time-invariant system,
y = Hx when the convolved output signal y is known and given by
y (n) = h (0) x (n) + h (1) x (n − 1) + ⋯+h (N ) x (n − N ) where x(n) is the input signal and h(n) is the impulse response. H defines a so-called Toeplitz matrix, which is constant-valued along its diagonals.
⎡ h (0) ⎤ ⎢ h (1) h (0) ⎥ H=⎢ ⎥ h (2) h (1) h (0) ⎢ ⎥ ⋱⎦ ⎣ ⋮ A deconvolution of the resulting linear system often cannot be solved due to H being singular. Using the technique “diagonal loading” overcomes this limitation and regularizes the problem to obtain the input signal x.
x = (H T H + λI )−1H T y For this purpose, the regularization parameter λ is added. Even a small value of λ is sufficient to make the matrix invertible but results in a noisy solution. In reality the available data are always noisy. An improvement of the deconvolution result can be made by minimizing the energy of the second-order derivative of x. A solution can be obtained introducing the second-order difference matrix D
x = (H T H + λDT D)−1H T y This procedure is used to generate all dissolution kinetics from the measured data in this work (Keßler, 1989; Press et al., 1992; Selesnick, 2013).
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