Damaged-bone adaptation under steady homogeneous stress

Buckling of adaptive elastic bone-plate: theoretical and numerical investigation

During day-to-day activities, many bones in the axial and appendicular skeleton are subjected to repetitive, cyclic loading that often results directly in an increased risk of bone fracture. In clinical orthopedics, trabecular fatigue fractures are observed as compressive stress fractures in the proximal femur, vertebrae, calcaneus and tibia, that are often preceded by buckling and bending of microstructural elements (Müller et al. in J Biomechanics 31:150 1998; Gibson in J Biomechanics 18:317-328 1985; Gibson and Ashby in Cellular solids 1997; Lotz et al. in Osteoporos Int 5:252-261 1995; Carter and Hayes in Science 194:1174-1176 1976). However, the relative importance of bone density and architecture in the etiology of these fractures are poorly understood and consequently not investigated from a biomechanical point of view. In the present contribution, an attempt is made to formulate a bone-plate buckling theory using Cowin's concepts of adaptive elasticity (Cowin and Hegedus in J Elast 6:313-325 1976; Hegedus and Cowin J Elast 6:337-352 1976). In particular, the buckling problem of a Kirchhoff-Love bone plate is investigated numerically by using the finite difference method and an iterative solving approach (Chen in Comput Methods Appl Mech Eng 167:91-99 1998; Hildebland in Introduction to numerical analysis 1974; Richtmyer and Morton in Difference methods for initial-value problems 1967).

Smart intramedullary rod for correction of pediatric bone deformity: a preliminary study

We were interested in determining if a smart intramedullary rod made of nitinol shape-memory alloy is capable of correcting deformed immature long bones. Because of limitations in our study design the process was reversed in that we examined the smart rod's ability to create a deformity rather than to correct one. Smart rods of different lengths and diameters were heat-treated to resume a radius of curvature of 30 to 110 mm. The low and high temperature phases of the smart rods were set, respectively, at 0 degrees C to 4 degrees C and 36 degrees C to 38 degrees C. The preshaped smart intramedullary rods were implanted in the cooled martensite phase in the medullary canal of the tibia in eight rabbits, where they restored their austenite form, causing a continuous bending force. On a weekly basis anteroposterior and lateral radiographs of the surgically treated tibia and the contralateral tibia were obtained for comparison. Rabbits were euthanized 6 weeks after surgery and computed tomography scans of both tibias were used for image analysis. Smart rods with a larger radius of curvature showed only minimal signs of remodeling; however, rods with a radius of curvature of 50 and 70 mm generated enough force history to create bone remodeling and deformation. The amount of bone deformation was highly magnified when unicortical corticotomy on the tension side was done. Based on this preliminary study the technology of the smart intramedullary rod may provide a valuable alternative method to correct pediatric skeletal deformities.

Computer simulation of an adaptive damage-bone remodeling law applied to three unit-bone bars structure

It is well admitted that the mechanical loading plays an important role in the growth and maintenance of our skeleton, and that microdamage (i.e.: microcracks) occurs naturally when the bone is overloaded during day-to-day activities. It is also argued, from experimental and theoretical viewpoint, that the cells which built and rebuilt the skeleton are sensitive for both strain and microdamage. The recent damage-bone remodeling theory is employed here to study the mechanical response of the three unit-bone bars that simulate bone trabeculae in the form of truss. It is shown that under constant load, such a structure exhibit inhomogeneous strain and it's response to external applied load depends strongly upon the manner in which the microdamage is distributed.