Pharmaceutical Manufacturing Handbook: Production and

1016 TABLET DESIGN
Mechanical Properties The percolation approach was also employed to model the
tensile strength of tablets [47, 48] . A critical tablet density was here understood as
a minimal solid fraction needed to build a network of relevant contact points spanning
the entire tablet. A rising tablet density led to a power law increase of the
tensile strength showing an universal exponent T f = 2.7.
It was shown that a power law based on percolation theory was suitable to fi t
the obtained tensile strength data of the binary matrix tablets studied. The best
fi tting was observed for a model where an initial tensile strength σ 0 was supposed
[49] :
σ = k( ρ− ρ ) + σ . 27
t c
The observed critical relative densities are understood as threshold values for the
tensile strengths of the tablets. One practical consequence of these works is to avoid
the manufacture of matrix tablets close to these critical densities. The formulation
may not be robust in this critical range from the viewpoint of mechanical tablet
stability.
6.3.7.4
Artifi cial Neural Networks
Artifi cial neural networks (ANNs) are computer programs designed to model the
relationships between independent and dependent variables. They are based on the
attempt to model the neural networks of the brain [50] . Functions are performed
collectively and in parallel by the units, rather than there being a clear delineation
of subtasks to which various units are assigned.
This methodology represents an alternative modeling technique that has been
applied to pharmaceutical technology data sets, including tableting parameters [51] .
The main advantage with respect to classical statistical techniques, such as response
surface methodology, is that ANNs do not require the prior assumption of the nature
of the relationships between input and output parameters, nor do they require the
raw data to be transformed prior to model generation [51] . ANNs are capable of
modeling complex, nonlinear relationships directly from the raw data.
The functional unit of ANNs is the perceptron. This is a basic unit able to generate
a response as a funtion of a number of inputs received from others perceptrons.
For example, the response value can be obtained as follows:
{
1 if WI 0 0+ WI 1 1+
Wb>
0
Y =
0 if WI + WI + W ≤0
0 0 1 1
where I x is the input received from perceptron x and W x the weight assigned to this
input by the perceptron. The weights can be changed to adapt the answer to the
desired one using a learning algorithm.
Usually complex structures with more than 15 layers are employed, called the
multilayer perceptron (MLP). Some of the commercial programs which have been
used to fi t tableting parameters are INForm (Intelligensys, Billingham Teesside),
CAD/Chem (AI Ware, Cleveland, OH), which is no longer commercially available,
and the Neural Network Toolbox of MATLAB (MathWorks, Natick, MA).
0
b