The rates of fracture at sites with different relative amounts of cortical and trabecular bone (hip, spine, distal radius) have been used to make inferences about the pathomechanics of bone loss and the existence of type I and type II osteoporosis. However, fracture risk is directly related to the ratio of tissue stress to tissue strength, which in turn is dependent not only on tissue composition but also tissue geometry and the direction and magnitude of loading. These three elements determine how the load is distributed within the tissue. As a result, assumptions on the relative structural importance of cortical and trabecular bone, and how these tissues are affected by bone loss, can be inaccurate if based on regional tissue composition and bone density alone. To investigate the structural significance of cortical and trabecular bone in the proximal femur, and how it is affected by bone loss, we determined the stress distributions in a normal and osteoporotic femur resulting from loadings representing: (1) gait; and (2) a fall to the side with impact onto the greater trochanter. A three-dimensional finite element model was generated based on a representative femur selected from a large database of femoral geometries. Stresses were analyzed throughout the femoral neck and intertrochanteric regions. We found that the percentage of total load supported by cortical and trabecular bone was approximately constant for all load cases but differed depending on location. Cortical bone carried 30% of the load at the subcapital region, 50% at the mid-neck, 96% at the base of the neck and 80% at the intertrochanteric region. These values differ from the widely held assumption that cortical bone carries 75% of the load in the femoral neck and 50% of the load at the intertrochanteric region. During gait, the principal stresses were concentrated within the primary compressive system of trabeculae and in the cortical bone of the intertrochanteric region. In contrast, during a fall, the trabecular stresses were concentrated within the primary tensile system of trabeculae with a peak magnitude 4.3 times that present during gait. While the distribution of stress for the osteoporotic femur was similar to the normal, the magnitude of peak stress was increased by between 33% and 45%. These data call into question several assumptions which serve as the basis for theories on the pathomechanics of osteoporosis. In addition, we expect that the insight provided by this analysis will result in the improved development and interpretation of non-invasive techniques for the quantification of in vivo hip fracture risk.

Stress distributions within the proximal femur during gait and falls: Implications for osteoporotic fracture

Are the etiologies of cervical and trochanteric hip fractures different

The effect of endodontic therapy, post-hole preparation, and post placement on tooth models of maxillary central incisors was investigated. Two-dimensional photoelastic analysis of birefringent models, under load in a polariscope, indicated the relative stress magnitudes and concentrations at the cervical and apical regions. Within the limits of the method, the results suggest that enlargement of the canal increases cervical stresses and that post placement will decrease stresses in this region. Nevertheless, conservative enlargement of the root canal may render post placement unnecessary for largely intact teeth. Post length appeared more important than post diameter in determining relative stresses at the cervical region. However, short wide posts led to elevated stress concentrations in this region. Post placement beyond two thirds of the root depth did not further decrease cervical stresses but usually increased stresses in the apical region.

Effects of post placement on endodontically treated teeth

Three dimensional stress analysis of the human femur

(1981). Trochanteric Fractures: An Epidemiologic Clinical and Biomechanical Study. Acta Orthopaedica Scandinavica: Vol. 52, No. sup188, pp. 1-100.

Trochanteric fractures. An epidemiological, clinical and biomechanical study.

The paper is concerned with the experimental analysis of the distribution of stress across the neck of the femur (thigh bone). The case considered was that of a man supported on one leg, a position which imposes maximum static load on the femur. The frozen stress method of three dimensional photoelasticity was adopted as the means of solution. A procedure was devised for correcting the results obtained from a homogeneous photoelastic model to apply to the case of bone which was considered to be composed of two main regions, a hard shell and a softer core. The bending and axial stress components so determined show a distribution which can be predicted by an engineering analysis but the shear stress distribution is not so satisfactory.

An experimental stress analysis of the neck of the femur.

A mathematical model of the seated driver subjected to a rear-end impact is developed using a lumped parameter model which,inter alia, allows for the investigation of the effect of an elastic—perfectly plastic head restraint device on the overall motion of the head and torso. The most satisfactory seatback-head restraint combination is found to be a seatback having a high rotational stiffness with a viscous damping coefficient of near ‘critical’ value combined with an energy absorbing head restraint having e plastic collapse load of approximately 890 N. The model confirms recent results which indicate that tensing of neck musculature prior to impact reduces injury potential.

J. F. Williams

Papers

An experimental stress analysis of the neck of the femur.

Mathematical model for investigating combined seatback-head restraint performance during rear-end impact