Hyo Sub Yoon

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.

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.

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.

The Structure and Anisotropic Mechanical Properties of Bone

Compact 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.

Ultrasonic wave propagation in human cortical bone--III. Piezoelectric contribution.

Abstract In a piezoelectric medium such as bone, the wave propagation and elastic constants are modified by the piezoelectric coupling. This piezoelectric “stiffening” or contribution is calculated for dry cortical bone, using the piezoelectric constants and dielectric constants reported for bone in the literature, and is compared with the corresponding values of two typical piezoelectric materials, α-quartz (single crystal) and “poled” barium titanate ceramic (polycrystalline). It is found that the piezoelectric contribution to the elastic stiffnesses of bone is negligibly small.

Temperature Dependence of the Ultrasonic Velocities in Bone

In orthopaedic and dental procedures involving bone cutting such as drilling, sawing, tapping and trepanning, it is desirable to know at what temperature thermal damage or thermal necrosis t akes place in bone. Changes in elastic properties appear likely to accompany such damage. Therefore, an ultrasonic r ight-angle reflector technique has been employed to measure the bulk (longitudinal and transverse) and surface wave velocities in bone in the temperature range from room temperature to 90°C. In these measurements, bovine femoral specimens were immersed in a constant temperature bath of purified water. Typical ultrasonic velocities (km/s) along the bone axis are: VL (longitudinal) = 4.29 and Vs (surface) = 1.96 at 21OC; VL - 3.99 and VS = 1.89 at 80OC. The transverse wave peaks of reflection spectra are broad, and the reflection curves at 90°C are badly distorted. From these results, there appears to be no structural change taking place below 9OOC, contrary to the tensile test results by other investigators.

Is bone a Cosserat solid

In a viscoelastic composite material including bone, acoustic waves undergo both geometric and viscoelastic dispersions as they propagate through the medium. The viscoelastic dispersion is characterized by an increase in phase velocity with increase in frequency, while the geometric dispersion is well-known. By comparing the dispersion data on these and other types of materials, it has been noted that the increases in the ultrasonic velocities for bones are much larger than those for simple viscoelastic solids and composites, suggesting an additional dispersion mechanism. This additional dispersion can be explained by Mindlins theory on the Cosserat continuum with microstructure.

Ultrasonic Characterization of Some Pathological Human Femora

For noninvasive ultrasonic diagnosis of bone abnormalities (e.g., by a modified acoustic emission technique), as well as for understanding bone formation/resorption processes, it is desirable to know the ultrasonic properties of abnormal or pathological bones relative to normal bone. As part of our long-range plan to catalog these data on various types of bone diseases and fractures, the ultrasonic velocities of some human osteoporotic and osteopetrotic femoral bones (formalin fixed and immersed in water) have been measured at room temperature and at 5 MHz based on the hexagonal system, and correlated to their respective densities and microstructures. Typical longitudinal (V ) and transverse (V ) velocities (km/s) along and perpendicular (z, or X2) to the bone axis (X ) for normal, osteoporotic and osteopetrotic bones in this order are: V = 4.01, 3.86, 3.40; V = 3.31, 3 .21, 3.10; JL = 1.86, 1.84, 1.65 anaLV = 1.65, 1.51, 1.68: The ages of the subjects (male and female) range from 12 to 87. In addition, the microhardness of these bones has been measured. L 3.

Further Studies on the Acoustic Emission of Fresh "Malian Bones"

In an extension of our previous work on bovine femora (1977 Ultrasonics Symp. Proc.), acoustic emission testinBhave been performed on bones from several different species of mammals and from different types of bone within the same species: canine skulls, femora, tibiae/fibulae, humeri, and ulnaqradii, porcine skulls and femora; and bovine tibiae and femora. Three types of acoustic emission (AE) parameters were obtained for each specimen: (1) cumulative AE counts vs. loading time, (2) number of AE events vs. pulse width, and (3) number of AE events vs. peak amplitude. The AE spectra from these bones are similar, somewhat independent of the s pecies of mammals and the type of bone, but different from those of other natural and synthetic materials. The surrounding soft tissues in canine long bones appear to attenuate AE signals, thus lowering the number of AE events in both pulse width and amplitude distributions, compared to bones without soft tissues. However, effects of the soft t issues in canine skulls seem to be insignificant. In order to simulate abnormal or defective bones, a drilled hole or EDTA treatment was introduced into the specimen.