Dissolution testing is now an established and standardised method for measuring the performance of drug products. It allows results for different batches of the same product, similar products from different suppliers, or tests from different labs to be compared. It is, therefore, a useful tool for quality control and for formulation development, so much so that the Food and Drug Administration (FDA) has made it a regulatory requirement for approval of new drugs.
However, being an empirical method, it does have some drawbacks for formulation development. For example, existing empirical data or formula may be of little help for every new formulation and a new series of tests may have to be performed. For every dissolution test, the sample product must have already been physically made. Both significantly add to the time and cost of taking a new drug to market. A theoretical model, on the other hand, can help to explain experimental observations and to predict the likely outcome of a new formulation at the design stage, thereby reducing the number of physical tests that have to be conducted and the total cost and time of drug development.
There is a new computer modelling approach called DigiPac, which is based on a patented digital approach. It differs from existing models in two important ways. First of all, it is a mesoscale digital approach. In comparison, most existing models take a macroscopic vector-based approach. Secondly, it handles real particle shapes with ease, rather than some idealised geometrical models.
Being a particle-level, numerical model, DigiPac predicts the influence of real particle shape and size distributions on the microstructure of granules and of tablets, and from the microstructure, the dissolution behaviour. The software implementation of the DigiPac approach includes modules for particle packing, flow calculation and dissolution simulation. For tabletting, DigiPac links fundamental properties of excipient and incipient particles, through the initial packing and ultimately compaction to the structure of the tablets.
For dissolution, the starting point is a digitised microstructure of mixed components. The digital structure is either a simulated one using DigiPac packing module or a real one obtained using 3D scanning techniques such as X-ray microtomography (XMT).
Diffusion-convection equation is solved for each component using a finite difference scheme. The flow field, which is another input for dissolution simulations, is calculated using a numerical technique called Lattice Boltzmann Method (LBM).
At present, XMT is probably the only non-destructive technique for obtaining full 3D structural information of samples. However, the technique requires physical samples to be made available in advance, and in this sense, it is mostly a tool for 'post-mortem' analyses. A computational model, on the other hand, can be a more cost effective tool for product formulation and design, as it can help either to understand retrospectively the observed behaviour of a finished product or to predict the likely behaviour or properties of a new product before it is actually produced. DigiPac is one such software model. It has the two aforementioned capabilities because it provides a quantitative link between properties of individual particles in the feedstock and properties of an assembly of these particles that is the product.
DigiPac takes digitised real particle shapes as input to predict packing structures. In DigiPac, both the packing space (and container) and the particles are mapped in a lattice grid and particles move one grid cell at a time following a pre-defined set of rules. The use of a lattice approach simplifies collision and overlap detection between particles of complex shapes, making it easier to pack particles of any sizes and shapes in a container of arbitrary geometry. Once digitised, complex shapes are no more difficult to handle than spheres for generating a packed structure using the DigiPac approach.
There are several ways to digitise particles. They include:
● Converting from CAD data for designed objects
● Directly generating objects using computer software for mathematically describable simple shapes such as ellipsoids, cylinders and crystals
● Reconstructing from 2D SEM or photo images using customised software routines
● 3D optical or X-ray scanning of particles
Achieving uniform blending is a recurring problem in the production of solid form drugs. Uniformity also affects the dissolution rate of the drug. It is well known that particles of different sizes tend to segregate as the powder is poured into a container and/or if the container is vibrated or shaken. However, the part played by particle shape in segregation is less extensively studied.
Modelling flow throughgranules & tablet structures
The LBM is a digital equivalent of the convectional computational fluid dynamics (CFD). While CFD solves numerically the Navier-Stokes equation, the governing equation of fluid flow, directly, LBM, which has its root in the kinetic theory for gas, treats fluid as imaginary 'particles' of varying density, residing in a regular grid and only interacting with their immediate neighbours in the grid. This lattice approach and data localisation makes it adept at dealing with complex geometries such as those of porous media. It is a natural choice for the digital structures obtained either by DigiPac or from 3D scans.
The LBM maps physical space onto a regular lattice grid. Associated with each node is a set of mass probability distributions, also referred to as particle distribution functions or simply density. These distributions propagate to neighbouring nodes as part of mass and momentum transfer, along fixed velocity vectors at each time step, followed by simple collisions designed to conserve mass and momentum.
Simulation of dissolution
Drug dissolution is an important issue for the pharmaceutical industry. The usual approach currently taken by the industry is essentially an empirical one. Theoretical models exist, but most only deal with regular geometries. DigiPac has the advantage of easy and direct incorporation of real particle shapes as they are measured (by XMT). The structure, either simulated using DigiPac or acquired using XMT, is described in a lattice grid that is also used by the LBM simulation to calculate the flow field. With the finite difference method, the same grid can be used to solve the governing equations for dissolution.
Four different scenarios can be simulated - transient or steady state with or without convection. It is assumed that at the solid/liquid interface, dissolution can be described as a first-order reaction.
To most drug testing practitioners, the release profile is of the most interest. This can be obtained by running DigiFlow in the transient state, i.e., retaining the time-dependent term and following through the evolution of concentration distribution over time. A solid pixel is deemed to have completely dissolved, if the remaining density (or mass concentration) of the pixel drops below the value of saturation concentration, and thereafter the pixel is treated as part of the liquid phase. Both concentration distribution and velocity fields are updated at specifiable intervals. The intervals can be specified based either on the time or the number of solid pixels or layers dissolved.
The dissolution model can be applied at several different length scales - the whole tablet, individual granules, or individual fine particles - to assess how shape, internal (porous) structure and the presence of obstacles affect the overall dissolution rate with or without a superimposed flow field.
The input microstructure may contain any number of different components; the governing equations are solved for each individual component. This allows interactions between the dissolving components and their effects on subsequent dissolution of individual components to be taken into account, if such interactions can be predefined.
The results and observations from DigiPac are explicit, graphical, and can be loaded into other applications for further analysis if required.
(The authors are with Structure Vision)