Charles R. Steele

Influence of physical activity on the regulation of bone density

Using a mathematical model which relates bone density to daily stress histories, the influence of physical activities on the apparent density of the calcaneal cancellous bone was investigated. Assuming that the mechanical bone maintenance stimulus is constant for all bone tissue, bone apparent density was calculated by a linear superposition of the mechanical stimulus provided by different daily physical activities. An empirical weighting factor, m, accounted for possible differences in the relative importance of load magnitude and number of cycles in each activity. By considering hypothetical variations in body weight and occupational activity levels, the range of probable m values was established. The model was then applied to the results of two previous running studies in which calcaneal density was measured to obtain an estimate of the stress exponent parameter, m. The results indicate that stress magnitudes (or joint forces) have a greater influence on bone mass than the number of loading cycles. We demonstrate that by carefully considering the magnitudes of imposed skeletal forces and the number of loading cycles, it may be possible to design exercise programs to achieve predictable changes in bone mass.

A three-dimensional nonlinear active cochlear model analyzed by the WKB-numeric method

A physiologically based nonlinear active cochlear model is presented. The model includes the three-dimensional viscous fluid effects, an orthotropic cochlear partition with dimensional and material property variation along its length, and a nonlinear active feed-forward mechanism of the organ of Corti. A hybrid asymptotic and numerical method combined with Fourier series expansions is used to provide a fast and efficient iterative procedure for modeling and simulation of the nonlinear responses in the active cochlea. The simulation results for the chinchilla cochlea compare very well with experimental measurements, capturing several nonlinear features observed in basilar membrane responses. These include compression of response with stimulus level, two-tone suppressions, and generation of harmonic distortion and distortion products.

New Evidence for the Role of Mechanical Forces in the Shoot Apical Meristem

A bstractThe mechanism for initiation of lateral organs in the shoot apical meristem is still unknown. In this article we investigate one critical component of a buckling mechanism of organ initiation (that is, the presence and distribution of compressive stresses in the meristem). Direct evidence for compression in the sunflower capitulum was obtained from the gaping pattern of shallow cuts and the propagation of fractures. Cuts gaped widely in the central region of the capitulum but remained closed, or nearly so, in the generative and differentiation regions, suggesting the presence of circumferential compression at these locations. Fractures were initiated in the generative region and propagated circumferentially over most of their length. They did not cross the generative region perpendicularly, suggesting again the presence of compressive stresses in the circumferential direction. This conclusion was confirmed by the stress distribution computed from the geometry of the capitulum at three stages of development. One interpretation of these results is that the generative region corresponds to a zone of compression that could control the initiation of new primordia by means of buckling of the tunica layer.

Mechanical properties of the lateral cortex of mammalian auditory outer hair cells.

Mammalian auditory outer hair cells generate high-frequency mechanical forces that enhance sound-induced displacements of the basilar membrane within the inner ear. It has been proposed that the resulting cell deformation is directed along the longitudinal axis of the cell by the cortical cytoskeleton. We have tested this proposal by making direct mechanical measurements on outer hair cells. The resultant stiffness modulus along the axis of whole dissociated cells was 3 x 10(-3) N/m, consistent with previously published values. The resultant axial and circumferential stiffness moduli for the cortical lattice were 5 x 10(-4) N/m and 3 x 10(-3) N/m, respectively. Thus the cortical lattice is a highly orthotropic structure. Its axial stiffness is small compared with that of the intact cell, but its circumferential stiffness is within the same order of magnitude. These measurements support the theory that the cortical cytoskeleton directs electrically driven length changes along the longitudinal axis of the cell. The Youngs modulus of the circumferential filamentous components of the lattice were calculated to be 1 x 10(7) N/m2. The axial cross-links, believed to be a form of spectrin, were calculated to have a Youngs modulus of 3 x 10(6) N/m2. Based on the measured values for the lattice and intact cell cortex, an estimate for the resultant stiffness modulus of the plasma membrane was estimated to be on the order of 10(-3) N/m. Thus, the plasma membrane appears to be relatively stiff and may be the dominant contributor to the axial stiffness of the intact cell.

The discordant eardrum

At frequencies above 3 kHz, the tympanic membrane vibrates chaotically. By having many resonances, the eardrum can transmit the broadest possible bandwidth of sound with optimal sensitivity. In essence, the eardrum works best through discord. The eardrums success as an instrument of hearing can be directly explained through a combination of its shape, angular placement, and composition. The eardrum has a conical asymmetrical shape, lies at a steep angle with respect to the ear canal, and has organized radial and circumferential collagen fiber layers that provide the scaffolding. Understanding the role of each feature in hearing transduction will help direct future surgical reconstructions, lead to improved microphone and loudspeaker designs, and provide a basis for understanding the different tympanic membrane structures across species. To analyze the significance of each anatomical feature, a computer simulation of the ear canal, eardrum, and ossicles was developed. It is shown that a cone-shaped eardrum can transfer more force to the ossicles than a flat eardrum, especially at high frequencies. The tilted eardrum within the ear canal allows it to have a larger area for the same canal size, which increases sound transmission to the cochlea. The asymmetric eardrum with collagen fibers achieves optimal transmission at high frequencies by creating a multitude of deliberately mistuned resonances. The resonances are summed at the malleus attachment to produce a smooth transfer of pressure across all frequencies. In each case, the peculiar properties of the eardrum are directly responsible for the optimal sensitivity of this discordant drum.

Comparison of WKB and finite difference calculations for a two‐dimensional cochlear model

There are many points of uncertainty in the subject of cochlear models. In this paper only the question of efficient computing methods is addressed. For the cochlear model with a one-dimensional approximation for the fluid motion, Zweig, Lipes, and Pierce [J. Acoust. Soc. Am. 59, 975-982 (1976)] have shown that the WKB method agrees well with a direct numerical integration. For the two-dimensional fluid model, Neely [E.D. thesis, California Institute of Technology, Pasadena, CA (1977)] has shown that a direct finite difference solution is an order of magnitude faster than the integral equation approach used by Allen [J. Acoust. Soc. Am 61, 110-119 (1977)]. In the present work, a formal WKB solution is derived following Whitham [Linear and Nonlinear Waves (Wiley, New York, 1974)]. The advantage of this formulation is simplicity, but the disadvantage is that no error estimate is available. We find that the numerical results from the WKB solution agree well with those of Neely (1977), while the computer time is reduced by another order of magnitude. Thus, the WKB method seems to offer the satisfactory accuracy, efficiency, and flexibility for treating the more realistic cochlear models.

Orthotropic piezoelectric properties of the cochlear outer hair cell wall

The mammalian outer hair cell has been shown to possess significant coupling between mechanical and electrical properties. This electromotile property may play a key role in cochlear tuning. In order to characterize quantitatively the electrical and mechanical behavior, the cell wall is modeled as a thin linear elastic piezoelectric material. Experimental findings from several investigators are used to determine the mechanical and electrical generalized stiffness coefficients described by the model. The model analysis indicates that orthotropic mechanical properties in the plane of the cell wall are required to match experimental behavior. The calculated orthotropic coefficients predict that the outer hair cell deforms due to cilia deflection with a force gain of 0.5 for perfectly constrained end conditions and a displacement gain of 3.6 for free end conditions. These values reflect the potential role of the OHC as a feedback mechanism to the basilar membrane. Results are for small deformation and quasi-static conditions with viscosity and inertial effects neglected. It is further assumed that cell permeability is negligible at the time scale of the fast deformation considered here.

Tibial changes in experimental disuse osteoporosis in the monkey.

SummaryWe studied the mechanical properties and structural changes in the monkey tibia with disuse osteoporosis and during subsequent recovery. Bone bending stiffness was evaluated in relationship to microscopic changes in cortical bone and Norland bone mineral analysis. Restraint in the semireclined position produced regional losses of bone most obviously in the anterior-proximal tibiae. Following 6 months of restraint, the greatest losses of bone mineral in the proximal tibiae ranged from 23% to 31%; the largest changes in bone stiffness ranged from 36% to 40%. Approximately 8 ½ months of recovery were required for restoration of normal bending properties. However, even after 15 months of recovery, bone mineral content did not necessarily return to normal levels. Histologically, resorption cavities in cortical bone were seen within 1 month of restraint; by 2 ½ months of restraint there were large resorption cavities subperiosteally, endosteally, and intracortically. After 15 months of recovery, the cortex consisted mainly of first-generation haversian systems. After 40 months, the cortex appeared normal with numerous secondary and tertiary generations of haversian systems.

Behavior of the basilar membrane with pure‐tone excitation

Three successively more elaborate models for the fluid‐elastic interaction in the cochlea are analyzed by asymptotic methods, with which an a priori assumption of “long” or “short” wavelengths is not necessary. Appropriate stiffnesses are estimated from Bekesys static‐point and pressure‐load measurements. The last model admits an independent motion of the arches of Corti and the remaining portion of the basilar membrane. Results indicate that the maximum arch displacement does occur about 5 mm closer to the stapes than the maximum basilar‐membrane displacement, which seems to provide an explanation for the difference in “place” according to Bekesys observation and damage evidence. Furthermore, the calculated results for the phase agree remarkably with Bekesys observation for low frequency and with the recent observations by Rhode for high frequency.

Tympanic-membrane and malleus–incus-complex co-adaptations for high-frequency hearing in mammals

The development of the unique capacity for high-frequency hearing in many mammals was due in part to changes in the middle ear, such as the evolution of three distinct middle-ear bones and distinct radial and circumferential collagen fiber layers in the eardrum. Ossicular moment(s) of inertia (MOI) and principal rotational axes, as well as eardrum surface areas, were calculated from micro-CT-based 3-D reconstructions of human, cat, chinchilla, and guinea pig temporal bones. For guinea pig and chinchilla, the fused malleus-incus complex rotates about an anterior-posterior axis, due to the relatively lightweight ossicles and bilateral symmetry of the eardrum. For human and cat, however, the MOI calculated for the unfused malleus are 5-6 times smaller for rotations about an inferior-superior axis than for rotations about the other two orthogonal axes. It is argued that these preferred motions, along with the presence of a mobile malleus-incus joint and asymmetric eardrum, enable efficient high-frequency sound transmission in spite of the relatively large ossicular masses of these species. This work argues that the upper-frequency hearing limit of a given mammalian species can in part be understood in terms of morphological co-adaptations of the eardrum and ossicular chain.