Biomedical Engineering Reference
In-Depth Information
examples for which growth models with clusters as units are thought to fit the
data well. Viewed qualitatively, a number of reasons for this may be offered.
Examples include (1) an extremely low growth rate despite the high supersaturation,
(2) difficulty growing giant crystals that retain high crystallinity under normal
temperature and pressure, and (3) ease of producing an amorphous phase. These
characteristics reflect phenomena observed in the growth of protein crystals. In
proteins, in which growth proceeds as a result of the aggregation of giant molecules,
two types of growth driving forces need to be considered: supersaturation, which is
determined thermodynamically, and intermolecular interactions. The latter factor
is normally not considered in the growth of ionic crystals. If we imagine the
simplest situation, intermolecular interactions are determined by the competition
of repulsive forces due to the average charge of the molecular surface and the van
der Waals attraction force between molecules. When intermolecular interactions are
involved, complex phenomena arise. For example, even under conditions of very
high concentrations of the solute itself, the growth rate becomes extremely low when
very weak attractive interaction operates, and sometimes no crystal growth occurs
and only an amorphous phase precipitates due to the solubility difference between
crystal and amorphous phases. Therefore, if biomineral growth proceeds in a manner
similar to that of protein crystal growth, the growth unit should be considered as an
aggregate (a cluster) and there is intermolecular interaction between units.
Two lines of circumstantial evidence can be offered for the suggestion that the
growth unit for HAP (at least in environments resembling those within the human
body) takes the form of a cluster. The first involves the physical constants related
to growth. The values for the edge free energy and the step kinetic coefficients
diverge widely from typical values for soluble inorganic crystals and, in fact,
are closer to those of protein crystals [
77
]. The second is that dynamic light-
scattering measurements of pseudo-body fluid show the existence of aggregates with
a hydrodynamic radius of about 0.5 nm [
81
,
82
]. Since these aggregates disappear
when calcium or phosphate ions are removed from the solution, it is highly likely
that they are calcium phosphate clusters. Initially, these clusters were thought to
be Posner clusters (Ca
9
(PO
4
)
6
), and a crystal growth model based on the simple
aggregation of clusters was proposed.
When assuming the presence of Posner clusters within the HAP crystal structure,
it is possible to define two types of chiral clusters. The two types correspond to the
L
-and
D
-forms of amino acids and comprise structures with threefold symmetry
in which six phosphate ions are arranged around the calcium ion at the center of
the cluster. An ab initio calculation was performed to estimate whether or not a
structure with the chemical composition Ca
9
(PO
4
)
6
could exist in a stable form. In
this calculation, the relative energies of clusters were compared by obtaining stable
structures of Ca
3
(PO
4
)
2
[
83
], and then combining up to four of these structures
[
84
-
86
]. First, energy calculations were performed for Ca
3
(PO
4
)
2
(corresponding
to the monomer), taking into consideration the spatial arrangements (three types)
that could be assumed given a pair of calcium and phosphate ions. Ten types of
isomers with a local energy minimum were defined. Among these, an isomer with
D
3h
symmetry and basket-like morphology was overwhelmingly stable compared
