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coformulated with crystalline excipients or when crystalline nanosuspensions form
within an otherwise amorphous dispersion [170].
4.11 COMPUTATIONAL MODELS
Studies of crystalline pharmaceutical systems have bene
tted greatly from computer
simulations that primarily make use of density functional
eld
calculations. These models can assist with interpretation of data by allowing calculation
of observables such as NMR spectral parameters, vibrational frequencies, optical
properties, X-ray scattering, and bulk physical properties for comparison with exper-
imental characterization data. Interpretation of the data obtained from many of the
characterization techniques described above can similarly bene
theory and force-
t from the availability of
computational models. However, the modeling of amorphous systems presents addi-
tional challenges beyond those encountered in the crystalline state because of the lack of
a crystal structure to use as input for calculations. Instead, more complex models of the
amorphous state must be built. Periodic models using large cubic cells that contain
initially random distributions of drug and polymer are often used to provide a starting
point for structures of amorphous solid dispersions, which can then be progressed
through time using a molecular dynamics (MD) calculation to create a set of models that
can be used to obtain probabilistic information about structural motifs and properties in
dispersions. Several recent studies have shown the potential of force-
eld calculations to
model the properties of amorphous dispersions and closely related systems using
periodic boundary condition models [171
field-based MD calcu-
lations are generally preferred at the present time because of their balance of accuracy
and performance in handling the large systems required for modeling the properties of
amorphous dispersions relative to the more accurate but expensive quantum MD
calculations (such as those based on density functional theory) or the faster but less
accurate coarse-grained MD calculations. Although the present focus in the literature has
largely been upon MD calculations, other techniques such as Monte Carlo calculations
are also of importance [175].
An illustration of the structural model used in a periodic boundary condition MD
calculation for a drug
-
174]. Atomistic force
polymer amorphous solid dispersion is given in Figure 4.18a,
which represents a single initial frame in a larger ensemble of frames showing the
evolution of the amorphous solid dispersion. To prepare the model for a MD simulation
using the Dreiding force
-
field and a constant volume and temperature (
NVT
) ensemble,
two preparatory calculations were performed using the microcanonical constant volume
and energy (
NVE
) ensemble (to stabilize the energy and relax the molecular structures)
and constant pressure and temperature (
NPT
) ensemble (to allow the large cubic cell to
relax and obtain a realistic density) [175]. A 200 ps
NVT
MD simulation was then
executed after the preparation steps for collection of structural data for analysis. A
common data analysis method is to utilize a PDF analysis of the MD trajectories as
shown in Figure 4.18b for selected interatomic distances. In Figure 4.18b, two distances
involving the drug and the polymer are compared. The PDF (also referred to as a radial
distribution function (RDF)) involving the distance between the hydrogen donor in the
