![](bg6.png)
Here, the elastic gelatin spherical capsule is sub-
jected to an external pressure (P
ext
) at its outer sur-
face r = a and an internal pressure (P
int
) at its inter-
nal surface r = b. Equation (1) is used in the optimi-
sation routine as the objective function. The thick-
ness of the capsule shell is measured by considering
the radial displacement of the pressurised sphere.
The displacement is determined by making use of
the Love’s stress function subjected to particular
boundary conditions (González and Fitt, 2002)
=−
−
)
3+2
)
−
)
−
−
)
4
−
)
,
(17)
where λ and µ are the Lame modulus and shear
modulus respectively.
A pressure of 153 µN/mm
2
is applied on the out-
er surface of the capsule while the pressure on its
inner surface is 39 µN/mm
2
. As far as the material
properties are concerned, the Young modulus and
Poisson’s ratio of the gelatin are 0.11 N/mm
2
and 0.4
respectively (Markidou et al., 2005). For this partic-
ular example, the volume of the spherical capsule is
fixed to 14.14 mm
3
.
With the above formulation, the automatic opti-
misation was performed about 72 minutes on a
Matlab R2008a with 2.20 GHz Intel Core 2 Duo
T7500 processor. The resulting optimal thickness of
capsule’s shell is shown in Figure 4(b). This shape
has a relative reduction in thickness and size of 46 %
and 40 % respectively. The maximum tensile
strength for the capsule was found to be 10.89
N/mm
2
.
4 CONCLUSIONS
This work outlines a methodology for shape optimi-
sation of pharmaceutical dosage forms based on the
PDE method enabling efficient shape definition and
parameterisation of complex geometries. The shape
of a tablet and capsule is generated from a small set
of design parameters and can be controlled by the
chosen boundary curves. Thus, the optimised shape
is obtained after carrying out an optimisation analy-
sis and relating the pertaining results to the solution
of the corresponding PDE as given in Equation (4).
It is worth mentioning that the concise parameterisa-
tion characteristics of the PDE method can be used
to carry out automatic design optimisation in a prac-
tical setting where the time taken for tablet testing
can be significantly reduced and encourages future
development of pharmaceutical technologies.
Figure 4: Optimal shape of a tablet (a) and optimal
thickness of capsule shell with maximum tensile strength
(b).
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