Trabecular bone density and loading history: Regulation of connective tissue biology by mechanical energy

Carter, D. R.; Fyhrie, David P.; Whalen, Robert T.

doi:10.1016/0021-9290(87)90058-3

Cited by 456 publications

(248 citation statements)

References 19 publications

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“…The SED ratio for the strut model was between 30.0 Bone volume fractions of 10, 20, and 30% were and 60.0 at 10% BV/TV and decreased to between The spherical void SED ratios were between 30.0 and 120.0 at 10% BV/TV and decreased to between 10.0 and 30.0 at 30% BV/TV. Since it is obvious that apparent SED will not represent the true tissue SED, some investigators have suggested using the apparent SED modified by the volume fraction to estimate the tissue SED (Carter et al, 1987;Huiskes et al, 1987). Dividing the apparent SED by the bone volume fraction will accurately predict the average hard tissue SED if two conditions are satisfied: (1) the exact apparent stiffness matrix was used to predict the apparent SED and (2) the stress in the marrow is negligible compared with the hard tissue stress.…”

Section: The Best Fits Between Predicted and Experimentalmentioning

confidence: 99%

“…the trabecular microstructure (Goldstein, 1987;Snyder et al, 1989). Investigators have also stated that tissue stress estimates may be necessary to accurately quantify and predict mechanically adaptive trabecular bone remodeling (Carter et al, 1987;Cheal et al, 1987;Huiskes et al, 1987). These two factors suggest that microstructural analysis is needed to further our understanding of the mechanical and remodeling characteristics of trabecular bone.…”

Section: The Best Fits Between Predicted and Experimentalmentioning

confidence: 99%

“…While some investigators have introduced modifications of apparent stress predictions to approximate trabecular tissue stresses (Carter et al, 1987), no direct estimate of trabecular tissue stress for models of large regions of bone have been presented. In this paper, the homogenization theory is used to obtain estimates of individual trabeculae stress and strain states for large regions of cancellous bone.…”

Section: Introductionmentioning

confidence: 99%

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Application of homogenization theory to the study of trabecular bone mechanics

Hollister

Fyhrie

Jepsen

et al. 1991

Journal of Biomechanics

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137

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Ah&act-It is generally accepted that the strength and stiffness of trabecular bone is strongly affected by trabecular microstructure. It has also been hvoothesized that stress induced adaptation of trabecular bone is affected by trabecular tissue level stress and;& strain. At this time, however, there is no generally accepted (or easily accomplished) technique for predicting the effect of microstructure on trabecular bone apparent stiffness and strength or estimating tissue level stress or strain. In this paper, a recently developed mechanics theory specifically designed to analyze microstructured materials, called the homogenization theory, is presented and applied to analyze trabecular bone mechanics. Using the homogenization theory it is possible to perform microstructural and continuum analyses separately and then combine them in a systematic manner. Stiffness predictions from two different microstructural models of trabecular bone show reasonable agreement with experimental results, depending on metaphyseal region, (R">0.5 for proximai humerus specimens, R* ~0.5 for distal femur and proximal tibia specimens). Estimates of both microstructural strain energy density (SED) and apparent SED show that there are large differences (up to 30 times) between apparent SED (as calculated by standard continuum finite element analyses) and the maximum microstructural or tissue SED. Furthermore, a strut and spherical void microstructure gave very different estimates of maximum tissue SED for the same bone volume fraction (BV/TV). The estimates from the spherical void microstructure are between 2 and 20 times greater than the strut microstructure at lo-20% W/TV INTRODUCTION Stress and strain fields in individual trabeculae are determined by both overall metaphyseal geometry and the microstructural organization of a local region of trabeculae. However, directly calculating stress and strain fields for each trabecula of a whole metaphysis is impossible with current computational technology. Current techniques for determining trabecular stress have focused on either analyzing very small regions of bone with a limited number of trabeculae, or analyzing a much larger region of bone assuming it to be a solid with apparent material properties. Neither technique provides direct information about trabecular tissue stresses and strains in an entire metaphyseal region. The homogenization theory is a recently developed method which provides a systematic way to combine stress analyses at the metaphyseal and individual trabecula level. This paper presents the initial application of homogenization theory to the study of trabecular bone mechanics.Microstructural analyses are generally used to predict apparent moduli and stress distributions within representative pieces of a given microstructure. These analyses assume that the whole microstructure within a material is constructed by repeating the representative piece analyzed. This type of analysis is quite Received infinalform 14 February 1991.

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Section: The Best Fits Between Predicted and Experimentalmentioning

confidence: 99%

Section: The Best Fits Between Predicted and Experimentalmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Application of homogenization theory to the study of trabecular bone mechanics

Hollister

Fyhrie

Jepsen

et al. 1991

Journal of Biomechanics

Self Cite

137

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show abstract

“…Since articular surface apposition and resultant contact force both vary appreciably throughout functional activities, however, conventional "snapshot" contact stress distributions at a specific instant of the duty cycle provide only limited information regarding the habitual mechano-stimulus at any given site. Appreciable precedent exists in the bone mechano-stimulus literature for including the effects of multiple loading configurations representative of dominant functional activities (Carter et al 1987;Adams et al 1996), although such work has involved prescribed external tractions rather than contact solutions. Therefore, a contact finite element formulation was specifically configured to address whole-duty-cycle joint surface engagement histories.…”

Section: Introductionmentioning

confidence: 99%

Intra-articular Contact Stress Distributions at the Ankle Throughout Stance Phase–patient-specific Finite Element Analysis as a Metric of Degeneration Propensity

Anderson

Goldsworthy

Shivanna

et al. 2006

Biomech Model Mechanobiol

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A contact finite element (FE) formulation is introduced, amenable to patient-specific analysis of cumulative cartilage mechano-stimulus attributable to habitual functional activity. CT scans of individual human ankles are segmented to delineate bony margins. Each bone surface is projected outward to create a second surface, and the intervening volume is then meshed with continuum hexahedral elements. The tibia is positioned relative to the talus into a weight-bearing apposition. The articular members are first engaged under light preload, then plantar-/dorsi-flexion kinematics and resultant loadings are input for serial FE solutions at 13 instants of the stance phase of level walking gait. Cartilage stress histories are post-processed to recover distributions of cumulative stress-time mechano-stimulus, a metric of degeneration propensity. Consistency in computed contact stress exposures presented for seven intact ankles stood in contrast to the higher magnitude and more focal exposures in an incongruously reduced tibial plafond fracture. This analytical procedure provides patient-specific estimates of degeneration propensity due to various mechanical abnormalities, and it provides a platform from which the mechanical efficacy of alternative surgical interventions can be estimated.

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“…Skalak et al (1982) later formulated a continuum model of growth. Carter et al (1987) proposed bone remodelling was targeted to produce a homeostatic level of an 'effective stimulus ' and Huiskes et al (1987) proposed that the process of bone remodelling was an adaptation that returned the strain energy density in the tissue to a homeostatic value. Bone growth models incorporating both biological and mechanobiological influences have been proposed by van der Meulen et al (1993), for modelling the cross-sectional growth of long bones, and by Stevens et al (1999), for modelling endochondral growth using a finite element model.…”

Section: Introductionmentioning

confidence: 99%

Evolution of mechanoregulation of bone growth will lead to non-optimal bone phenotypes

Nowlan

Prendergast

2005

Journal of Theoretical Biology

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Mechanical forces acting on the bones during growth affect their final shape and strength.Mechanoregulation of bone growth may be recognised in embryogenesis, and also in the adaptation of the adult skeleton to changes in mechanical loading. Mechanoregulatory responses for tissues have arisen during evolution, but does evolution give rise to responses that produce optimal skeletal phenotypes? In this paper, we investigate the emergence of an optimal mechanoregulation response in a population.By combining equations describing long bone growth with a genetic algorithm to describe evolutionary change, we created a computational model to simulate the evolution of mechanoregulation in bone growth. A population of individuals is created where each individual is assigned a diploid gene set which controls the growth and remodelling of the bone. At maturity, each bone is assessed and its 'fitness' calculated; fitness is quantified as bone strength relative to bone mass. The simulation continues for many generations, and includes mutations and a varying environment. The genes present in the population are tracked and the evolution of parameters governing mechanoregulation is calculated.The results indicate that a population may converge to one bone growth algorithm but, more usually, a range of mechanoregulation algorithms for different individuals will persist after many generations. Even if the population converges to one mechanoregulation law, convergence to the 'optimum' bone was never found. Although many researchers propose that natural selection has pushed skeletal structure towards an optimum, our computational model suggests that this is unlikely to be the case.

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Trabecular bone density and loading history: Regulation of connective tissue biology by mechanical energy

Cited by 456 publications

References 19 publications

Application of homogenization theory to the study of trabecular bone mechanics

Application of homogenization theory to the study of trabecular bone mechanics

Intra-articular Contact Stress Distributions at the Ankle Throughout Stance Phase–patient-specific Finite Element Analysis as a Metric of Degeneration Propensity

Evolution of mechanoregulation of bone growth will lead to non-optimal bone phenotypes

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