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THE MECHANICAL PROPERTIES OF HUMAN DENTIN: A CRITICAL REVIEW AND RE-EVALUATION OF THE DENTAL LITERATURE

Division of Biomaterials and Bioengineering, Department of Preventive and Restorative Dental Sciences, Mail Stop 0758, University of California, San Francisco, San Francisco, CA 94143-0758;

View larger version (183K): [in a new window]   Figure 1. (a) SEM image of a fixed, demineralized dentin specimen showing the collagen fibrils that are randomly oriented in the plane perpendicular to the tubule lumens (after Marshall et al., 1997). (b) A higher-resolution AFM image of an unfixed specimen obtained in water. The AFM image shows the periodic 67-nm hole and overlap zones characteristic of the Type I collagen fibrils found in dentin and bone (after Marshall et al., 2001; Habelitz et al., 2002b).

View larger version (99K): [in a new window]   Figure 2. (a) SEM and (b) AFM images of fully mineralized dentin specimens showing the tubule lumens with surrounding cuffs of peritubular dentin. The bar in the SEM photomicrograph is 10 µm. Labeling: L = tubule lumen, PT = peritubular dentin, IT = intertubular dentin matrix. SEM image after Kinney et al. (2001a). AFM image after Kinney et al. (1993).

View larger version (14K): [in a new window]   Figure 3. The Young’s modulus as reported in the literature over the past 50 years. The data prior to 1999 appear in tabular form in the reference by Kinney et al. (1999). Data after 1999 are from Huo et al. (2000), Kinney et al. (2001a), Kishen et al. (2000), and Palamara et al. (2000). In the past few years, there has been a four-fold variation in the reported magnitude of the Young’s modulus; the uncertainty in its value appears to be expanding with time. The uncertainty in the magnitude of the Young’s modulus is probably not reflective of the actual variations in the mechanical properties of dentin. Rather, the uncertainty most likely arises from either a viscoelastic response (stress relaxation) or experimental artifact.

View larger version (18K): [in a new window]   Figure 4. The upper (dashed line) and lower (solid line) theoretical bounds for the Young’s modulus of a composite of hydroxyapatite mineral and type I collagen fibrils as calculated from Eqs. 1 and 2. The experimental data are shown as the solid bar at a volume percent mineral phase (45%) corresponding to the known composition of dentin. The graph emphasizes the difficulties of modeling mineralized tissues with bounds; The large difference in moduli between the two phases separates the upper and lower bounds by too great a magnitude to be useful.

View larger version (17K): [in a new window]   Figure 5. A typical load-displacement curve during AFM indentation of hydrated dentin. The slope of the initial unloading segment, dP/dh, is used to calculate the Young’s modulus.

View larger version (15K): [in a new window]   Figure 6. The Young’s modulus of dentin as measured by AFM indentation. The solid circles represent repeated measurements obtained in water over the course of several days. The open circles show measurements obtained in Hanks’ Balanced Salt Solution (HBSS). The water-stored specimens exhibited a rapid decline in modulus over 14 days. This decline was attributed to a loss of mineral from the near surface layer. The specimens stored in HBSS, in contrast, maintained relatively constant modulus values over the same time period. The error bars are the standard deviations of the means of several specimens. Data from Habelitz et al. (2002a).

View larger version (21K): [in a new window]   Figure 7. The Young’s modulus of dentin as a function of orientation of the tubules as calculated from the elastic constants of Lees and Rollins (1972). There was a pronounced hexagonal (transverse isotropic) anisotropy in the Young’s modulus, a result that was forced by a priori assumptions of the symmetry. The Young’s modulus was greatest in the direction of the tubules (36 GPa) and much less in the orthogonal direction (29 GPa). The Young’s modulus is compared with the values from the resonant ultrasound spectroscopy (RUS) measurements of Kinney et al. (2002). The RUS measurements, which were made without assumption as to material symmetry, also show hexagonal symmetry, but the stiffest orientation is now perpendicular to the axis of the tubules. This result is more consistent with what is known about the orientation of the collagen fibrils, which lie in a plane perpendicular to the tubule axis.

View larger version (23K): [in a new window]   Figure 8. The applied force (solid line) and the tip displacement (dashed line) graphed as a function of time for a typical AFM indentation of hydrated intertubular dentin. In this example, the profile of the applied force was trapezoidal: a three-second loading phase, a three-second hold at maximum load, and a three-second unloading phase. At constant load, the indenter tip continues its inward displacement at a rate (dh/dt) that is approximated by the slope of the dashed line at the midpoint of the hold phase. The unloading rate is given by dP/dt. These factors are used to correct the AFM data for creep relaxation. In this example, the correction to the contact stiffness raises the Young’s modulus by about 20%.

View larger version (12K): [in a new window]   Figure 9. Ultimate tensile strength data from Lehman (1967) (open circles) and Staninec et al.2002 (solid circles). The data have been graphed in the form of a Weibull probability distribution function, with the abscissa given by the natural log of the failure stress, and the failure probability, Pf, given by Eq. 23. Both sets of data fit the Weibull distribution function (R2 = 0.97), although the slopes, m, are different. The slope of the curve determines the sensitivity of the tensile strength to specimen size. Weibull behavior is an indication that a distribution of flaws determines the magnitude of the tensile strength of dentin.

View larger version (18K): [in a new window]   Figure 10. The critical flaw size in dentin as a function of far-field applied stress (MPa). The critical flaw size is calculated for an elliptical flaw according to Eq. 25. The dashed line corresponds to the fracture toughness established by El Mowafy and Watts (1986): Kc = 3.08 MPa m. The solid line corresponds to the more conservative estimate of the fracture toughness determined by Imbeni et al. (2002): Kc = 1.8 MPa m. Knowledge of the critical flaw size is of great importance in lifetime modeling.

View larger version (19K): [in a new window]   Figure 11. The number of required cycles for growing a flaw from an initial to critical size for two different far-field stresses (Eq. 27). The solid line is for a far-field stress of 20 MPa; it corresponds to the stresses of mastication. The dashed line corresponds to a slightly elevated stress level (30 MPa). An initial flaw 0.3 mm long will grow to catastrophic size in roughly 106 cycles at 30 MPa (approximately one year); at 20 MPa, a pre-existing flaw would have to be 0.9 mm long to grow to catastrophic size in the same number of cycles. Lifetime models such as Eq. 27 depend critically on the Paris law exponent, m (Eq. 26), the critical flaw size (Eq. 25), and the stress intensities at the head of the crack tip.