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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.

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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.

The Achilles tendon is one of the most frequently injured tendons in humans, and yet the mechanisms underlying its injury are not well understood. This study examines the ex vivo mechanical behavior of excised human Achilles tendons to elucidate the relationships between mechanical loading and Achilles tendon injury. Eighteen tendons underwent creep testing at constant stresses from 35 to 75 MPa. Another 25 tendons underwent sinusoidal cyclic loading at 1 Hz between a minimum stress of 10 MPa and maximum stresses of 30-80 MPa. For the creep specimens, there was no significant relationship between applied stress and time to failure, but time to failure decreased exponentially with increasing initial strain (strain when target stress is first reached) and decreasing failure strain. For the cyclically loaded specimens, secant modulus decreased and cyclic energy dissipation increased over time. Time and cycles to failure decreased exponentially with increasing applied stress, increasing initial strain (peak strain from first loading cycle), and decreasing failure strain. For both creep and cyclic loading, initial strain was the best predictor of time or cycles to failure, supporting the hypothesis that strain is the primary mechanical parameter governing tendon damage accumulation and injury. The cyclically loaded specimens failed faster than would be expected if only time-dependent damage occurred, suggesting that repetitive loading also contributes to Achilles tendon injuries.

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