Virtual Prototyping and Parametric Design of 3D-Printed Tablets Based on the Solution of Inverse Problem.

The problem of designing tablet geometry and its internal structure that results into a specified release profile of the drug during dissolution was considered. A solution method based on parametric programming, inspired by CAD (computer-aided design) approaches currently used in other fields of engineering, was proposed and demonstrated. The solution of the forward problem using a parametric series of structural motifs was first carried out in order to generate a library of drug release profiles associated with each structural motif. The inverse problem was then solved in three steps: first, the combination of basic structural motifs whose superposition provides the closest approximation of the required drug release profile was found by a linear combination of pre-calculated release profiles. In the next step, the final tablet design was constructed and its dissolution curve found computationally. Finally, the proposed design was 3D printed and its dissolution profile was confirmed experimentally. The computational method was based on the numerical solution of drug diffusion in a boundary layer surrounding the tablet, coupled with erosion of the tablet structure encoded by the phase volume function. The tablets were 3D printed by fused deposition modelling (FDM) from filaments produced by hot-melt extrusion. It was found that the drug release profile could be effectively controlled by modifying the tablet porosity. Custom release profiles were obtained by combining multiple porosity regions in the same tablet. The computational method yielded accurate predictions of the drug release rate for both single- and multi-porosity tablets.

Effect of hydrophobic inclusions on polymer swelling kinetics studied by magnetic resonance imaging.

The rate of drug release from polymer matrix-based sustained release formulations is often controlled by the thickness of a gel layer that forms upon contact with dissolution medium. The effect of formulation parameters on the kinetics of elementary rate processes that contribute to gel layer formation, such as water ingress, polymer swelling and erosion, is therefore of interest. In the present work, gel layer formation has been investigated by magnetic resonance imaging (MRI), which is a non-destructive method allowing direct visualization of effective water concentration inside the tablet and its surrounding. Using formulations with Levetiracetam as the active ingredient, HPMC as a hydrophilic matrix former and carnauba wax (CW) as a hydrophobic component in the matrix system, the effect of different ratios of these two ingredients on the kinetics of gel formation (MRI) and drug release (USP 4 like dissolution test) has been investigated and interpreted using a mathematical model.

Distribution of breakage events in random packings of rodlike particles.

Uniaxial compaction and breakage of rodlike particle packing has been studied using a discrete element method simulation. A scaling relationship between the applied stress, the number of breakage events, and the number-mean particle length has been derived and compared with computational experiments. Based on results for a wide range of intrinsic particle strengths and initial particle lengths, it seems that a single universal relation can be used to describe the incidence of breakage events during compaction of rodlike particle layers.

Computational and experimental investigation of needle-shaped crystal breakage.

Needle-shaped crystals are a common occurrence in many pharmaceutical and fine chemicals processes. Even if the particle size distribution (PSD) obtained in a crystallization step can be controlled by the crystal growth kinetics and hydrodynamic conditions, further fluid-solid separation steps such as filtration, filter washing, drying, and subsequent solids handling can often lead to uncontrolled changes in the PSD due to breakage. In this contribution we present a combined computational and experimental methodology for determining the breakage kernel and the daughter distribution functions of needle-shaped crystals, and for population balance modeling of their breakage. A discrete element model (DEM) of needle-shaped particle breakage was first used in order to find out the appropriate types of the breakage kernel and the daughter distribution functions. A population balance model of breakage was then formulated and used in conjunction with experimental data in order to determine the material-specific parameters appearing in the breakage functions. Quantitative agreement between simulation and experiment has been obtained.

Structural characterization and statistical properties of two-dimensional granular systems.

A recently developed method is used for the analysis of structures of planar disordered granular assemblies. Within this method, the assemblies are partitioned into volume elements associated either with grains or with more basic elements called quadrons. Our first aim is to compare the relative usefulness of description by quadrons or by grains for entropic characterization. The second aim is to use the method to gain better understanding of the different roles of friction and grain shape and size distributions in determining the disordered structure. Our third aim is to quantify the statistics of basic volumes used for the entropic analysis. We report the following results. (1) Quadrons are more useful than grains as basic ''quasiparticles'' for the entropic formalism. (2) Both grain and quadron volume distributions show nontrivial peaks and shoulders. These can be understood only in the context of the quadrons in terms of particular conditional distributions. (3) Increasing friction increases the mean cell size, as expected, but does not affect the conditional distributions, which is explained on a fundamental level. We conclude that grain size and shape distributions determine the conditional distributions, while their relative weights are dominated by friction and by the pack formation process. This separates sharply the different roles that friction and grain shape distributions play. (4) The analysis of the quadron volumes shows that Gamma distributions, which are accepted to describe foamlike structures well, are too simplistic for general granular systems. (5) A range of quantitative results is obtained for the ''density of states'' of quadron and grain volumes and calculations of expectation values of structural properties are demonstrated. The structural characteristics of granular systems are compared with numerically generated foamlike Dirichlet-Voronoi constructions.

The strength of liquid bridges in random granular materials.

The strength of capillary bridges in randomly packed granular media was analyzed by means of computer simulations. A novel simulation method, based on the tracking of moving interfaces, has been implemented and used for determining the equilibrium shape of capillary bridges in a granular medium under a range of liquid saturations and solid-phase geometry. The net force acting on each grain due to the capillary bridges was evaluated, as well as the aggregate force acting between two wet granular media during their separation in the normal directions. The simulation results are consistent with previous experimental observations and reveal interesting phenomena such as the existence of a maximum in the tensile strength of a wet granular medium as function of liquid saturation.

Pore-scale modelling and tomographic visualisation of drying in granular media.

Spatio-temporal evolution of liquid phase clusters during drying of a granular medium (realised by random packing of cylindrical particles) has been investigated at the length-scale of individual pores. X-ray microtomography has been used to explicitly resolve the three-dimensional spatial distribution of the solid, liquid, and gas phases within the wet particle assemblies. The propagation of liquid menisci through the granular medium during drying was dynamically followed. The effect of contact angle on the degree of dispersion of the drying front has been studied by observing drying in a layer of untreated (hydrophilic) and silanised particles; the drying front was found to be sharper in the case of the silanised (less hydrophilic) particles. This observation was confirmed by direct numerical simulations of drying in a digitally encoded porous medium identical in structure to the experimental one. The simulations also revealed that the average gas-liquid interfacial area in a given porous microstructure strongly depends on the contact angle.