Factors that determine a post-menopausal woman's bone mineral density (BMD) include her mass at the time of skeletal maturity (peak BMD), menopause and the rate of loss she experiences as she ages. Understanding the relative influence of each of these factors may help identify important preventive treatments and provide new ways to identify women at risk for osteoporosis. In this analysis we utilize a computer model of the bone remodeling process to predict the relative influences of peak BMD, menopause and age-related bone loss on the development of osteoporosis. The delay in the onset of osteoporosis (defined as BMD <2.5 SD from the young adult mean) caused by modifying peak BMD, age-related bone loss or the age at menopause is quantified. A 10% increase in peak BMD is predicted to delay the development of osteoporosis by 13 years, while a 10% change in the age at menopause or the rate of non-menopausal bone loss is predicted to delay osteoporosis by approximately 2 years, suggesting that peak BMD may be the single most important factor in the development of osteoporosis.

A time-dependent approach for emulating bone modeling and remodeling in response to the daily loading history is presented. We postulate that genotype, systemic metabolic conditions, and local tissue interactions establish the level of local tissue mechanical stimulation (attractor state) appropriate for the maintenance of bone tissue. The net daily rate of apposition or resorption on a bone surface is determined by the difference between the actual stimulus and the tissue attractor state and can be modulated by other biologic factors. In calculating the net change in local bone apparent density, the technique takes into account the bone surface area available for osteoblastic and osteoclastic activity. Endosteal, periosteal, haversian, and cancellous bone modeling and remodeling are thereby treated in a consistent, unified fashion.

A general theory for the role of intermittently imposed stresses in the differentiation of mesenchymal tissue is presented and then applied to the process of fracture healing. Two-dimensional finite element models of a healing osteotomy in a long bone were generated and the stress distributions were calculated throughout the early callus tissue under various loading conditions. These calculations were used in formulating theoretical predictions of tissue differentiation that were consistent with the biochemical and morphological observations of previous investigators. The results suggest that intermittent hydrostatic (dilatational) stresses may play an important role in influencing revascularization and tissue differentiation and determining the morphological patterns of initial fracture healing.

In a companion paper, we presented a time-dependent theory for bone modeling and remodeling in response to a daily loading history. This paper represents a preliminary attempt to use the theory to determine the distribution of bone density within the adult proximal femur under an assumed normal loading history. Subsequent functional adaptation of the internal structure due to changes in the loading history are then determined. Throughout this preliminary study, the external geometry of the proximal femur is considered to be fixed, i.e., changes in the external shape are neither stimulated nor allowed. Linear and trilinear (dead-zone nonlinearity) rate remodeling laws were compared. Computer emulations using two-dimensional finite element models were successful in creating a normal-appearing distribution of bone tissue when remodeling was initiated from a solid structure of homogeneous bone density. Subsequent reduction in the loading history caused regional bone atrophy. Reinstatement of the normal loading history caused a generalized increase in bone mass but resulted in a slightly different bone distribution than was calculated for a constant loading history. These results demonstrate the utility of the remodeling theory and are consistent with the hypothesis that similar stress-related phenomena are responsible for both normal morphogenesis and functional adaptation in response to changes in the bone loading.

This study tested the effects of fluid-induced shear on high density monolayer cultures of adult articular chondrocytes. Fluid-induced shear (1.6 Pa) was applied by cone viscometer to normal human and bovine articular chondrocytes for periods of 24, 48, and 72 hours. At 48 and 72 hours, fluid-induced shear caused individual chondrocytes to elongate and align tangential to the direction of cone rotation. Fluid-induced shear stimulated glycosaminoglycan synthesis by 2-fold (p < 0.05) and increased the length of newly synthesized chains in human and bovine chondrocytes. In human chondrocytes, the hydrodynamic size of newly synthesized proteoglycans also was increased. After 48 hours of fluid-induced shear, the release of prostaglandin E2 from the chondrocytes was increased 10 to 20-fold. In human chondrocytes, mRNA signal levels for tissue inhibitor of metalloproteinase increased 9-fold in response to shear compared with the controls. In contrast, mRNA signal levels for the neutral metalloproteinases, collagenase, stromelysin, and 72 kD gelatinase, did not show such major changes. This study demonstrated that articular chondrocyte metabolism responds directly to physical stimulation in vitro and suggests that mechanical loading may directly influence cartilage homeostasis in vivo.

In vivo studies have suggested that mechanical factors are involved in the regulation of the morphology and biochemical composition of tendons that wrap around bones. In these tendons, fibrocartilage is found in the segment wrapped around the bone, and tendon far from the bone displays normal tendon histomorphology. Recent in vitro studies have shown that intermittently loaded connective tissue cells are sensitive to changes in cellular shape and hydrostatic pressure: stretching and distortion of the cells enhances production of fibrous matrix and hydrostatic pressure enhances production of cartilaginous matrix. We used finite-element analysis to determine whether the regions of increased development of cartilaginous matrix in tendons that wrap around bones correspond to regions in which tendon cells are subjected to higher pressures, and whether the maintenance and rearrangement of fibrous extracellular matrix in these tendons is associated with regions of stretching and distortion of cells. We found that regions of cartilaginous matrix and fibrous matrix formation and turnover correlate well with patterns of hydrostatic compressive stress and distortional strain in the tendon. Although further experiments clearly are needed to establish the predictive value of our approach, hydrostatic stress and distortional strain history--parameters intimately related to changes in cellular pressure and shape, respectively--appear to be important tissue-level mechanical stimuli that regulate cartilaginous and fibrous matrix composition of connective tissues.

The development of normal joints depends on mechanical function in utero. Experimental studies have shown that the normal surface topography of diarthrodial joints fails to form in paralyzed embryos. We implemented a mathematical model for joint morphogenesis that explores the hypothesis that the stress distribution created in a functional joint may modulate the growth of the cartilage anlagen and lead to the development of congruent articular surfaces. We simulated the morphogenesis of a human finger joint (proximal interphalangeal joint) between days 55 and 70 of fetal life. A baseline biological growth rate was defined to account for the intrinsic biological influences on the growth of the articulating ends of the anlagen. We assumed this rate to be proportional to the chondrocyte density in the growing tissue. Cyclic hydrostatic stress caused by joint motion was assumed to modulate the baseline biological growth, with compression slowing it and tension accelerating it. Changes in the overall shape of the joint resulted from spatial differences in growth rates throughout the developing chondroepiphyses. When only baseline biological growth was included, the two epiphyses increased in size but retained convex incongruent joint surfaces. The inclusion of mechanobiological-based growth modulation in the chondroepiphyses led to one convex joint surface, which articulated with a locally concave surface. The articular surfaces became more congruent, and the anlagen exhibited an asymmetric sagittal profile similar to that observed in adult phalangeal bones. These results are consistent with the hypothesis that mechanobiological influences associated with normal function play an important role in the regulation of joint morphogenesis.

Cylindrical specimens of bovine subchondral trabecular bone were tested to uniaxial compressive strain levels of 75% to study energy absorption during pore collapse. Stress-strain curves were characterized by macroscopic yield at about 8% strain followed by a significant horizontal pore collapse regime. Energy absorption occurred largely in this postyield regime. Yield strength and energy absorption capacity were found to increase linearly with specimen apparent density. Microstructural analysis of the deformed specimens verfied that the mechanism for energy absorption was primarily fracture and buckling of trabeculae. The results suggest that during fracture, the collapse of trabecular bone (and the consequent absorption of energy) serves to attenuate stresses transmitted through the skeleton and thus protect vital structures such as the brain.