(94g) Blend Uniformity Prediction Based on Discrete Element Method

Prediction
of Blend Uniformity by utilizing Discrete Element Method simulation

Shuichi
Tanabe^{1, 2, 3}, Srikanth R. Gopireddy¹, Shuichi Ando²,
Hidemi Minami², Nora A. Urbanetz¹, Regina Scherlieb³

1
Pharmaceutical Development, Daiichi Sankyo Europe GmbH, Pfaffenhofen 85276,
Germany

2
Formulation Technology Research Laboratories, Daiichi Sankyo Co., Ltd.,
Hiratsuka 2540014, Japan

3
Department of Pharmaceutics and Biopharmaceutics, Kiel University, Grasweg 9a,
24118 Kiel, Germany

This
work presents the prediction of the probability density distribution of blend
uniformity of a binary granular blend using Discrete Element Method (DEM). Sample
Blend Uniformity (BU), i.e., %SD of the active ingredient concentration in samples
taken from various locations of bulk blend, was evaluated to assure the quality
of finished drug product such as content uniformity. There exists three key
factors in BU analysis (BUA) for assuring homogeneity of the bulk blend, and
these include (1) particle size of components in the blend, (2) the sampling
regimen that defines sampling locations and the number of samples taken from
each sampling location, and (3) the acceptance criteria. The acceptable ranges
of the particle size of the components at a given sampling regimen and
acceptance criteria can be confirmed based on experiments. However, as
resources are limited it is practically difficult to conduct comprehensive
experiments to identify the physical propertiesf allowable ranges in commercial
scale, which makes the gedge of failureh setting difficult and conservative in
manufacture. With the increasing computational capabilities over the last
years, computationally intensive in-silico experiments using DEM are becoming
an important tool to understand production processes such as blending. The
advantage of DEM compared to other simulation techniques is that it is able to
capture the trajectory of each and individual particle in the system through
Newton's equation of motion, by calculating the new positions and velocities of
the particles based on the forces acting on it at a defined time step. The
forces acting on each particle which may be due to particle-particle or
particle-wall contacts or the non-contact forces such as gravity, cohesion,
etc. enter as source terms in the equation of motion (Zhu et al., 2007). Herein
this study aims at predicting the sample BU at a given combination of key
factors based on DEM simulation, and thus selecting the appropriate sampling
regimen.

The
blending process of a binary granular blend (active : placebo = 14 : 86 w/w%)
using a 50 L bin blender is considered. After filling of more than 50% of total
placebo granules the active granules are filled into the blender. Following to
the active granule filling the remaining portion of the placebo granules are
filled, result in a sandwich like filling. Blender rotation speed is 6 rpm, the
Froude number is 0.02. Both granules are mono-sized (180 micrometre in
diameter) having a spherical shape and no cohesiveness. In order to keep the
simulation time reasonably low, upscaling of particle size and downscaling the
blender geometry were applied. This decreases the computational time as less
particles are involved. At a given blending time, the blend is divided into M
equivalent mass spaces as sampling locations. Each of these M sampling
locations is sub-divided into N equivalent mass spaces. The mass present
in one of those M x N mass spaces is assumed to be a sample. Sample
BU is calculated using only those samples taken according to a sampling
regimen, i.e., 1 sample each from 10 (M = 10) locations (10x1). The 10x1
sampling regimen at N = 8 will have 10⁸ ways of sampling
resulting in 10⁸ sample BU values giving the probability density
distribution of the sample BU. In total, 14 DEM simulations were performed having
different particle size expansion level (F_PS = 3, 5, 7), blender
geometry reduction level (F_G = 0.05, 0.1, 0.2), and number of samples
in a sampling location (N = 4 and 8) of a same blend. The equation below
has been derived that allows the prediction of the sample BU of an actual blend
in a given blender based on the DEM simulation which was performed with
enlarged particles and reduced blender geometry.

BU_S1/BU_S2
= (PN_S2/PN_S1)^0.5

Here
PN_S1 and PN_S2 are the number of particles
in a sample of the DEM condition 1 and 2, respectively. Root mean square error
normalized by the mean (nRMSE) was calculated based on the equation by
considering the sample BU at (F_PS, F_G) = (5, 0.1), N
= 8, 25% fill level as a reference.

Qualitative
and quantitative prediction of sample BU probability density distribution in a
binary blend was successfully demonstrated, which have not been addressed
previously. The sample BU was decreased gradually until 60 to 80 sec, and reached
a plateau state after 80 to 100 sec (8 to 10 rotations) of blending. The powder
blending dominated by diffusion was also observed visually in the snapshots of
the time-series DEM simulation. The blending pattern shown at 100 s (10
rotations of blending), shows that blending is complete, and any further
blending may not be necessary. At the plateau state the probability density
distribution of the sample BU was normally distributed, which is a reasonable
approximation of a binomial distribution for a complete random mixture of a
binary blend. The mean sample BU became small as the number of particles in a
sample increase as reported in the previous study (Muzzio et al., 2002). The
sample BU probability density distribution with 10x1, N = 4 having ca.
3200 particles in a sample was smaller than those with 1x10, N = 8
having ca. 1600 particles in a sample, while they have overlapping portion. The
relative standard deviation (RSD) of the sample BU was constant regardless of
the mean sample BU in a given blend. The sample BU of the blends was
successfully predicted where the nRMSE was 0.2, suggesting a feasible prediction
accuracy. The number of particles in a sample was considered to be a critical
parameter in predicting the mean sample BU based on DEM results. Therefore, quantitative
sample BU probability density distribution prediction of a given blend having different
physical properties of granules should be possible at a similar prediction
accuracy considering the principle of DEM. Further verification studies will be
performed for blends having a particle size distribution and cohesiveness.

With
the proposed DEM simulation a sophisticated in-silico design of experiments for
setting proven acceptable ranges can be performed, which has been considered
practically difficult to perform in experiment due to limited resources. The DEM
simulation will provide not only the mean sample BU that will be obtained in
experiments but also the
probability density distribution, which will provide a forecast of the
possibility to pass/fail the acceptance criteria for sample BU. A detailed visualization
enabled by simulation also reveals intriguing blending development, and helps
e.g. to identify the critical regions of blending thereby optimizing the
sampling locations. These in-silico
experiments would provide comprehensive understanding of the allowable particle
size range of components at a given sampling regimen and acceptance criteria,
which helps in setting a reliable gedge of failureh specification.

References

Muzzio,
F.J., Sudah, O.S. Coffin-Beach, D, 2002. Effects of blender rotational speed
and discharge on the homogeneity of cohesive and free-flowing mixtures. Int. J.
Phram. 247, 57-68

Zhu,
H.P., Zhou, Z.Y., Yang, R.Y., Yu, A.B., 2007. Discrete particle simulation of
particulate systems: theoretical developments. Chem. Eng. Sci. 62, 3378–3396.