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Inhalation August 2022 23 is can be explained by assuming that the mecha- nism behind the FPF increase is related to smearing of coating agent onto the API, which will take lon- ger for a higher drug content. As for the subsequent decrease in FPF, the rate constant seems to depend on leucine concentration only. It is pointed out that the FPF level obtained also depends on the inhaler used, as will be discussed below. Investigations indicate this type of behavior is com- mon. For instance, the same type of curve was observed for three different coating agents (magnesium stearate, leucine and PRUV), for two different drugs and for formulations with and without added lactose fines, further analyzed using different inhalers [2]. e interaction between the mixing process and the composition for formulations with a coating agent, therefore, provides general insight, which helps shed light on some of the much-debated questions regard- ing performance of adhesive mixtures. It can be con- cluded that: • Carriers of different size (mass) should not be compared using the same mixer speed, as this will provide different force fields in the mixing process. applied mixing energy in Figure 1A, and correspond- ing profiles for formulations with 3% leucine are shown in Figure 1B. e equation for calculating the mixing energy, ME, was presented in the first article and can be written as: ME = 8π 3 m carrier rpm 3 r 2 t 60 Equation 1. where m carrier is the mass of the carrier, t is the mixing time, r is the radius of the mixing bowl and rpm is the speed in revolutions per minute. Along the same lines, the mixing force exerted, MF, can be expressed by: MF = 4π 2 m carrier rpm 2 r 60 Equation 2. e dotted lines in Figures 1A and 1B are gener- ated using modeling equations that address both the fine particle fraction (FPF) increase and subsequent decrease, using rate constants k1 and k2, respectively. FPF = A + B e -k 2 x 1+e -k 1 x Equation 3. where x is the mixing energy, per Equation 1. As is seen in Figure 1, the dotted lines fit well to the data, which means that the rate constants k1 and k2 describing the increase in FPF and the subsequent decrease in FPF can be calculated. ese rate con- stants are specific to the interaction between the API and the coating agent but also depend on the com- position. Rate constants for the studied Bud/leucine systems are shown in Table 1. As can be seen, the initial increase in FPF occurs more rapidly for 1% Bud formulations than for 5% Bud formulations. Table 1 Rate constants k1 and k2 for Bud/leucine formulations, obtained using Equation 3. System k1 k2 1% Leucine 1% Bud 5% Bud > 20* 1.2 0.33 0.31 3% Leucine 1% Bud 5% Bud 9.4 1.9 0.13 0.14 *could not be precisely detected Figure 1 Fine particle fraction as a percentage of delivered dose for formulations consisting of Bud and lactose carrier Lactohale LH100 (DFE Pharma, Goch, Germany), with leucine as a coating agent, administered using the "Screenhaler" prototype dry powder inhaler. The leucine concentration is 1% in A and 3% in B. Circles refer to 1% Bud and squares to 5% Bud. Adapted from reference 2. 0 1 2 3 4 5 6 0 1 2 3 4 5 6 60 50 40 30 20 10 0 60 50 40 30 20 10 0 FPF [% of DD] FPF [% of DD] Mixing energy (mJ/carrier) Mixing energy (mJ/carrier) (A) (B)