Endodontics. Problem -Solving in Clinical Practice

Abstract

The microstructure of dentin suggests a hierar-chical approach to the understanding of its mechanical properties. At the smallest length scales are the constituent materials: a carbonated nanocrystalline apatite mineral phase (approxi-mately 50% by volume) and a felt-work of type I collagen fibrils (see Fig. 1). The collagen fibrils, approximately 30% by volume, are roughly 50-100 nm in diameter; they are randomly oriented in a plane perpendicular to the direction of dentin formation (Jones and Boyde, 1984). The mineral occupies two sites within this collagen scaffold: intrafibrillar (inside the periodically spaced gap zones in the collagen fibril) and extrafibrillar (in the interstices between the fibrils). The partition-ing between these two sites is uncertain, although it is believed that between 70 and 75% of the min-eral may be extrafibrillar (Bonar et al., 1985; Pidaparti et al., 1996). The mineral crystallites are needle-like near the pulp; the shape continuously progresses to plate-like with proximity to the enamel (Kinney et al., 2001b). The crystallite thick-ness, ~ 5 nm, is invariant with location. At a higher level of organization is an inter-mediate, or composite, length scale. At this length scale, dentin can be modeled as a contin-uous fiber-reinforced composite, with the intertubular dentin forming the matrix and the tubule lumens with their associated cuffs of peritubular dentin forming the cylindrical fiber rein-forcement (see Fig. 2). The tubules run continuously from the dentin-enamel junction to the pulp in coronal dentin, and from the cementum-dentin junction to the pulp canal in the root. The regular, almost uni-axial, alignment of the tubules has led some to suggest that they play an important function in the orienta-tion dependence of the mechanical properties (Waters, 1980). At the greatest length scale are the effective, or continuum, properties of dentin. The effective properties of dentin describe the response of the tooth to applied loads, and allow for predictions of tooth strength and fracture properties. Young's modulus, tensile and compressive strength, and fracture toughness are examples of these effective properties, and reflect the complex interactions of the constituent materials and the microstructure. At this largest length scale, we anticipate that the effective properties will depend on tubule density, orientation, and the local average den-sity of the mineral phase. Ultimately, measurement of the effective properties, particularly the properties of altered forms of dentin (such as carious or transparent), will benefit from an understand-ing of the material behavior at all of these length scales. The elastic properties of dentin are of paramount importance in all discussions of tooth strength. The elastic constants, usually defined in terms of a stiffness (C ij) or compliance (S ij) matrix, include the Young's modulus, shear modulus, and Poisson's ratio. Depending on the symmetry of the microstructure, the elastic constants have different degrees of independence. For example, an isotropic structure has only two independent elas-tic constants, while an orthotropic structure has nine indepen-dent elastic constants. Therefore, any study of the elastic prop-erties of dentin must consider its symmetry.