J. Lawrence Katz

Adhesive/Dentin Interface: The Weak Link in the Composite Restoration

Results from clinical studies suggest that more than half of the 166 million dental restorations that were placed in the United States in 2005 were replacements for failed restorations. This emphasis on replacement therapy is expected to grow as dentists use composite as opposed to dental amalgam to restore moderate to large posterior lesions. Composite restorations have higher failure rates, more recurrent caries, and increased frequency of replacement as compared to amalgam. Penetration of bacterial enzymes, oral fluids, and bacteria into the crevices between the tooth and composite undermines the restoration and leads to recurrent decay and premature failure. Under in vivo conditions the bond formed at the adhesive/dentin interface can be the first defense against these noxious, damaging substances. The intent of this article is to review structural aspects of the clinical substrate that impact bond formation at the adhesive/dentin interface; to examine physico-chemical factors that affect the integrity and durability of the adhesive/dentin interfacial bond; and to explore how these factors act synergistically with mechanical forces to undermine the composite restoration. The article will examine the various avenues that have been pursued to address these problems and it will explore how alterations in material chemistry could address the detrimental impact of physico-chemical stresses on the bond formed at the adhesive/dentin interface.

Ultrasonic wave propagation in human cortical bone—II. Measurements of elastic properties and microhardness☆☆☆

Abstract The microtextural symmetry of dry human cortical bone was found to be consistent with hexagonal symmetry, based on microstructural observations as well as on the ultrasonic velocity measurements at 5 MHz and at room temperature using a pulse transmission method. Five independent elastic stiffness constants were obtained therefrom and are (in 10 10 N/m 2 ): c 11 = 2.34, c 33 = 3.25, c 44 = 0.871, c 12 = 0.906, c 13 = 0.911. Microhardness measurements on the cross section of the bone show that it is ‘intrinsically’ uniform from the endosteal to the periosteal side and for the four quadrants. The dependence of the elastic stiffnesses on the polar angle is plotted to show how the elastic stiffnesses are interrelated to the orientations in the bone. Characteristics of ultrasonic wave propagation in the bone were shown to be somewhat analogous to those in a fiber-reinforced composite material; the bone filters and polarizes ultrasonic waves.

Hard tissue as a composite material—I. Bounds on the elastic behavior☆

Abstract Recent determination of the elastic moduli of hydroxyapatite by ultrasonic methods permits a re-examination of the Voigt or parallel model of the elastic behavior of bone, as a two phase composite material. It is shown that such a model alone cannot be used to describe the behavior of bone. Correlative data on the elastic moduli of dentin, enamel and various bone samples indicate the existence of a non-linear dependence of elastic moduli on composition of hard tissue. Several composite models are used to calculate the bounds on the elastic behavior of these tissues. The limitations of these models are described, and experiments to obtain additional critical data are discussed.

Shape and size of isolated bone mineralites measured using atomic force microscopy

The inorganic phase of bone is comprised primarily of very small mineralites. The size and shape of these mineralites play fundamental roles in maintaining ionic homeostasis and in the biomechanical function of bone. Using atomic force microscopy, we have obtained direct three‐dimensional visual evidence of the size and shape of native protein‐free mineralites isolated from mature bovine bone. Approximately 98% of the mineralites are less than 2 nm thick displaying a plate‐like habit. Distributions of both thickness and width show single peaks. The distribution of lengths may be multimodal with distinct peaks separated by ∼6 nm. Application of our results is expected to be of use in the design of novel orthopaedic biomaterials. In addition, they provide more accurate inputs to molecular‐scale models aimed at predicting the physiological and mechanical behavior of bone.

The Effects of Remodeling on the Elastic Properties of Bone

SummaryCortical bone can be modeled as a complex hierarchical composite interrelating both structure and material properties on four levels of structural organization: molecular, ultrastructural, microscopic, and macroscopic. In young animals, the microstructural systems are long parallel lamellar units, plexiform bone, which in older or more mature animals converts by internal remodeling into multiple concentric lamellar units, secondary osteons, forming haversian bone. Ultrasonic wave propagation measurements performed on both plexiform and haversian bone clearly show a definitive relationship with microstructure; haversian bone can be described as a transversely symmetric material whereas plexiform bone appears to be orthotropic in nature. The anisotropy of the elastic constants are found to reflect the tissue symmetry; moreover, plexiform bone is stiffer and more rigid in all directions than is haversian bone. Similar experiments were performed on osteoporotic and osteopetrotic bone. While the results for osteoporotic bone are understandable in terms of the increased porosity, the results for the osteopetrotic bone are anomalous with respect to its density. Since Wolff, the remodeling of bone has been interpreted as a way of altering the mechanical properties to suit some need. For haversian remodeling from plexiform bone, the argument that adaptation occurs to optimize properties requires additional clarification since haversian bone appears to have inferior mechanical properties to plexiform bone.

The elastic anisotropy of bone.

In modeling the anisotropic properties of hydroxyapatite (HAp), Katz found that two kinds of phenomenological relationships held among the elastic stiffness coefficients. Firstly, there are three linear combinations--(c11 + c22 + c33), (c44 + c55 + c66), (c12 + c13 + c23)--which arise naturally when computing the isotropic averages of anisotropic crystal systems over all possible spatial orientations. Secondly, the degree of elastic anisotropy in such crystal systems is characterized by two specific factors: (a) the ratio of the linear compressibility along the unique axis to that perpendicular to it, (c11 + c12 - 2c23)(c33 - c13); and (b) the ratio of the two shear moduli, c44/c66. There have been a number of experiments in recent years which have used either mechanical methods or ultrasonic techniques to measure the anisotropic elastic properties of bovine and human cortical bone. Analyses of data from these experiments show that the above relationships also play a significant role in characterizing the elastic anisotropy in bone.

Viscoelastic properties of wet cortical bone—I. Torsional and biaxial studies

Abstract The dynamic moduli for frequencies between 2 × 10−3 and 100 Hz and the relaxation modulus between 1 and 105 sec have been measured in torsion for human and bovine cortical bone kept wet in Ringers solution, as a function of temperature, strain-level and a superposed axial load. At body temperature, the dynamic loss tangent increased from 0.009 at 100 Hz, to 0.013 at 1 Hz, to 0.025 below 0.1 Hz. The total change in shear modulus over 8 decades of time-scale was 15–35%, most of this change occurring at long times in relaxation. Bovine bone, although stiffer, exhibited viscoelastic behavior similar to that of human bone. Nonlinear viscoelastic response, in the form of the isochronous shear modulus increasing with strain level, became apparent for strains above 10−4, and was observed to be less pronounced in dynamic tests than in relaxation. Recovery at long times occurred more slowly than relaxation, but always approached completion asymptotically. This effect, small in human bone and negligible in bovine bone, is accentuated by the superposition of an axial stress on the torsion sample. Biaxial experiments were performed, since bones in the body are subjected to stresses which are more complex than uniaxial tension or shear. An axial tensile stress of 17.2 MN/m2 increased the high frequency loss tangent of human bone by ⋍20% and changed the shear modulus by ⋍1.5%; for bovine bone, the shear modulus was changed by 0.6% by an axial stress of 22.1 MN/m2. The temperature dependence of the viscoelastic response was found to be thermorheologically complex. This implies that bone experiments must be done at body temperature to be relevant to the in vivo situation, and that time-temperature superposition is of questionable validity for bone.

Ultrasonic wave propagation in human cortical bone—I. Theoretical considerations for hexagonal symmetry

Abstract From the theory of wave propagation in an anisotropic elastic medium are derived the basic equations relating the five independent second-order elastic stiffness constants (fourth-rank tensor) to the ultrasonic wave speeds in a hexagonal medium, with special emphasis on determining the microtextural symmetry of human cortical bone. In addition, the three pure mode directions of high symmetry in a hexagonal medium are explicitly shown. Finally, expressions relating the ‘technical moduli’ such as Youngs modulus, shear modulus and bulk modulus to the elastic compliances are presented for the most general case (triclinic symmetry) and then are specialized for the hexagonal system.

Ultrasonic wave propagation and attenuation in wet bone

The propagation of ultrasonic longitudinal waves in bovine plexiform and human Haversian bone has been studied over the range 0.5-16 MHz. In wet bone little velocity dispersion was observed, in contrast to the results of earlier studies on dry bone. Large values of attenuation were observed.

Scanning Acoustic Microscope Studies of the Elastic Properties of Osteons and Osteon Lamellae

Scanning acoustic microscopy (SAM) provides the means for studying the elastic properties of a material at a comparable level of resolution to that obtained by optical microscopy for structural studies. SAM is nondestructive and permits observation of properties in the interior of materials which are optically opaque. Two modes of ultrasonic signals have been used in a Model UH3 Scanning Acoustic Microscope (Olympus Co., Tokyo, Japan) as part of a continuing study of the microstructural properties of bone. The pulse mode, using a single narrow pulse in the range of 30 MHz to 100 MHz, has been used to survey the surface and interior of specimens of human and canine femoral compact cortical bone at resolutions down to approximately 30 microns. To obtain more detailed information at significantly higher resolution, the burst mode, comprised of tens of sinusoids, has been used at frequencies from 200 MHz to 600 MHz. This has provided details of both human and canine single osteons (or haversion systems) and ostenoic lamellae at resolutions down to approximately 1.7 microns, well within the thickness of a lamella as viewed in a specimen cut transverse to the femoral axis.