Mathematical and experimental studies on the mechanics of plated transverse fractures

Rybicki, E.F.; Simonen, F.A.; Mills, E. J.; Hassler, Craig; Scoles, P.; Milne, David T.; Weis, Edmund B.

doi:10.1016/0021-9290(74)90033-5

Cited by 29 publications

(9 citation statements)

References 7 publications

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“…Their continuous interface three-dimensional model agreed very well with composite beam theory for determining the bone stresses in the midplate region far from the screws. This finding corroborated previous work comparing composite beam theory to finite element predictions (20,21). Their studies also have demonstrated the significant influence that longitudinal bone compression, during plating, can have on the stress fields.…”

supporting

confidence: 89%

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Changes in long‐bone structural properties during the first 8 weeks of plate implantation

Carter

Shimaoka

Harris

et al. 1984

Journal Orthopaedic Research

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The midplate structural rigidities of metal- and plastic-plated intact canine femora were experimentally determined after initial plate application and 8 weeks after in vivo implantation. Composite beam theory significantly overestimated the bending rigidities of the metal-plated bones. The rigidities of the plastic-plated bones were nearly identical to that of the isolated bone, as composite beam theory predicted. Plating with either plate increased the intracortical porosity and caused the deposition of periosteal new bone, which was greater with plastic than with metal plates. The increased rigidities provided by the attachment of the metal plates and, hence, the degree of bone strain shielding were variable. Platings for 8 weeks which provided little strain shielding with either metal or plastic plates caused an increase in bone flexural rigidity (measured after plate removal) with respect to the contralateral control. Platings that provided increasing amounts of strain shielding caused a decreasing midplate bone rigidity (measured after plate removal) and increasing bone deposition at the outer screws. These findings suggest that the surgical implantation of any plate (metal or plastic) will provide a net stimulus to bone formation and consequently increased bone structural rigidity, even though intracortical porosity is increased. If the plate significantly reduces the normal loads borne by the bone, however, there is a net stimulus to remove bone, resulting in a loss of midplate structural rigidity within 8 weeks of implantation.

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confidence: 89%

“…the resulting altered vascular supply to the bone fracture site, (c) strain-related bone remodeling due to the strain shielding effect of the plate on the long bone, and (d) a possible reaction to the biomaterials introduced (1,3,5,6,9,(11)(12)(13)(14)(15)17,(20)(21)(22)(23)(24)(25)(26).…”

mentioning

confidence: 99%

Changes in long‐bone structural properties during the first 8 weeks of plate implantation

Carter

Shimaoka

Harris

et al. 1984

Journal Orthopaedic Research

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“…The distribution of longitudinal normal strain acting upon a mid‐diaphyseal cross‐section was quantified using linear beam theory 18. This method models the TMT mid‐diaphysis as a prismatic beam subjected to axial loading and bending moments; it is assumed that points in a plane passing through the unloaded bone remain in this plane during loading.…”

Section: Methodsmentioning

confidence: 99%

Strain Gradients Correlate with Sites of Exercise-Induced Bone-Forming Surfaces in the Adult Skeleton

Judex

Gross

Zernicke

1997

Journal of Bone and Mineral Research

197

156

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Physical activity is capable of increasing adult bone mass. The specific osteogenic component of the mechanical stimulus is, however, unknown. Using an exogenous loading model, it was recently reported that circumferential gradients of longitudinal normal strain are strongly associated with the specific sites of periosteal bone formation. Here, we used high-speed running to test this proposed relation in an exercise model of bone adaptation. The strain environment generated during running in a mid-diaphyseal tarsometatarsal section was determined from triplerosette strain gages in six adult roosters (>1 year). A second group of roosters was run at a high speed (1500 loading cycles/day) on a treadmill for 3 weeks. Periosteal surfaces were activated in five out of eight animals. Mechanical parameters as well as periosteal activation (as measured by incorporated fluorescent labels) were quantified site-specifically in 12 30°sectors subdividing a mid-diaphyseal section. The amount of periosteal mineralizing surface per sector correlated strongly (R 2 ‫؍‬ 0.63) with the induced peak circumferential strain gradients. Conversely, peak strain magnitude and peak strain rate were only weakly associated with the sites of periosteal activation. The unique feature of this study is that a specific mechanical stimulus (peak circumferential strain gradients) was successfully correlated with specific sites of periosteal bone activation induced in a noninvasive bone adaptation model. The knowledge of this mechanical parameter may help to design exercise regimens that are able to deposit bone at sites where increased structural strength is most needed. (J Bone Miner

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“…To characterize midshaft strain environment in the tibia and metatarsal, digitized transverse cross-sections of each midshaft were analyzed with a macro (written by S. Martin, University of Melbourne, Australia) for NIH Image to calculate and graph the neutral axis (NA) and gradients of normal strain across the section, under two assumptions: that the bone shafts are beams loaded axially and in bending, and that the strain distribution is linear (formulae in Rybicki et al, 1974;Biewener, 1992;Gross et al, 1992). These isoclines were used to estimate the magnitude of peak maximum (tensile) and minimum (compressive) normal strains at the cortex of the midshaft of the tibia and metatarsal.…”

Section: Strain Gauge Analysesmentioning

confidence: 99%

Optimization of bone growth and remodeling in response to loading in tapered mammalian limbs

Lieberman

Pearson

Polk

et al. 2003

Journal of Experimental Biology

181

230

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In most mammals, especially those adapted for cursoriality, distal limb bones are thinner than more proximal bones, giving the limb skeleton a tapered shape (Smith and Savage, 1956;Alexander, 1980Alexander, , 1996Hildebrand, 1985;Lieberman and Pearson, 2001;Currey, 2002). In sheep, for example, midshaft cortical areas decrease about 16% between the femur and tibia, and 24% between the tibia and metatarsal. Limb tapering is generally thought to save energy by reducing a limb's moment of inertia (Hildebrand, 1985). How much energy is saved by distal tapering has been the subject of debate, but is probably considerable in most species. While Taylor et al. (1974) found that three species (cheetah, gazelle and goats) with different limb configurations had similar energy costs (VO∑·g -1 ·h -1 ) over a range of speeds, the conclusions of the study may be flawed because the animals were not run at comparable speeds. The results of Taylor et al. (1974) contradict not only theoretical predictions (for example, see Hildebrand, 1985), but also more controlled studies such as by Myers and Steudel (1985), who found that redistributing 3.6·kg from the thigh to the ankles in trained humans increases the metabolic cost of running at 2.68·m·s -1 by 15%.Limb tapering may save energy during swing, but may also affect bone strength during stance. Limbs during stance are usually modeled as cylinders subject to a combination of bending and axial compression from body mass and ground reaction forces. At midstance, when ground reaction forces (GRFs) are typically highest and approximately vertical, bending stress/strain at midshaft (the likely location of maximum bending) is a function of many factors, including the magnitude and orientation of GRF relative to the element and the cross-sectional and the material properties of the bone (Biewener et al., 1983). Distal tapering, therefore, leads not How bones respond dynamically to mechanical loading through changes in shape and structure is poorly understood, particularly with respect to variations between bones. Structurally, cortical bones adapt in vivo to their mechanical environments primarily by modulating two processes, modeling and Haversian remodeling. Modeling, defined here as the addition of new bone, may occur in response to mechanical stimuli by altering bone shape or size through growth. Haversian remodeling is thought to be an adaptation to repair microcracks or prevent microcrack propagation. Here, we examine whether cortical bone in sheep limbs modulates periosteal modeling and Haversian remodeling to optimize strength relative to mass in hind-limb midshafts in response to moderate levels of exercise at different growth stages. Histomorphometry was used to compare rates of periosteal growth and Haversian remodeling in exercised and sedentary treatment groups of juvenile, subadult and young adult sheep. In vivo strain data were also collected for the tibia and metatarsal midshafts of juvenile sheep. The results suggest that limb bones initially optimize responses to loading...

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Mathematical and experimental studies on the mechanics of plated transverse fractures

Cited by 29 publications

References 7 publications

Changes in long‐bone structural properties during the first 8 weeks of plate implantation

Changes in long‐bone structural properties during the first 8 weeks of plate implantation

Strain Gradients Correlate with Sites of Exercise-Induced Bone-Forming Surfaces in the Adult Skeleton

Optimization of bone growth and remodeling in response to loading in tapered mammalian limbs

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