An approach for time‐dependent bone modeling and remodeling—theoretical development

Abstract

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.

Stress fracture in military recruits: gender differences in muscle and bone susceptibility factors

“…However, the differences in height, weight, body mass index [weight in kg/ (height in m) 2 ], and most girth dimensions were somewhat smaller than those reported previously. 3 Pelvic widths as an index of skeletal size were narrower in male cases than in controls, but not in females, whereas bicondylar breadth, a measure of joint size, was essentially identical in cases and controls of both genders.…”

“…The shafts of long bones, however, retain the ability to adapt to changes in loading throughout adult life. 20 Generalized models of physical adaptation of long bones, as proposed by Beaupre et al 2 and later refined by van der Meulen et al, 26 assume that bones adapt to produce stress magnitudes corresponding to a specific normal range of strains, consistent with the "mechanostat" of Frost. 9 These generalized models are based on the view that the maximum strain that can be generated in a given bone is proportional to the strength of the muscles acting on that bone.…”

A cartilage growth mixture model for infinitesimal strains: solutions of boundary-value problems related to in vitro growth experiments

“…4 Linearization of the multiplicative decompositions of the deformation gradient tensors (A1) leads to e = e e + e g ,…”

“…4 The superscript α will be used to designate the proteoglycans (p), collagens (c), and others (oth). …”

A nonlinear finite element model of cartilage growth

“…Since a stimulus is filtered by various tissue properties before signaling the cell nucleus to initiate mRNA production, continuum growth models attempt to model the temporal evolution of tissue composition and, consequently, biomechanical properties. For many years, bone-remodeling theories have been used to describe how a scalar measure of bone density and, consequently, the tissue's mechanical properties change in response to mechanical stimuli (Cowin and Hegedus 1976;Carter and Wong 1988;Beaupre et al 1990;Cowin 1993). More recent theories have instead represented volumetric growth by a tensor quantity (Skalak et al 1996(Skalak et al , 1997 and were first used to study the growth of vascular tissues (Rodriguez et al 1994;Taber and Eggers 1996;Taber 1998).…”