The prediction of stress fractures using a ‘stressed volume’ concept

Abstract

This paper addresses an anomaly which exists in the current literature regarding stress fractures. Analysis of the data on fatigue strength of bone samples in vitro would conclude that these fractures should never occur at the strain levels known to occur in vivo. This anomaly can be resolved by including in the analysis the effect of stressed volume, whereby larger volumes of material are expected to have worse fatigue properties. A Weibull analysis was used to predict the probability of failure, pt; this was an upperbound prediction because it did not include the effects of remodelling and adaptation. Combining this analysis with a finite element model of the human tibia, we predicted a Pf value of 21% after five weeks of strenuous exercise, which is comparable with reported incidences in military personnel. The high incidence of stress fractures in the cannon bone of racehorses could also be predicted (Pr = 62'%, compared to 70% experimentally). The approach can be used to investigate the effect of variables in the exercise regime such as the distance run per day and the use of improved footwear. It can also predict the increased risk of stress fractures in elderly people. The results suggest certain simple rules which may be of clinical value in designing exercise regimes and in understanding the risk factors for this type of injury.

The effect of bone microstructure on the initiation and growth of microcracks

“…The process of microcrack accumulation in bone may eventually lead to stress fractures. These fractures occur commonly in athletes and soldiers engaged in high intensity, repetitive activities such as marching or run-ning and happen when microcracks accumulate at a rate that exceeds the capacity for bone repair [23]. Alternatively, the process of microcrack accumulation in bone may be one of the causes of fragility fractures, which can occur in aging bone when damage accumulates at 'normal' rates but the bone's repair mechanism is deficient [21].…”

Predicting stress fractures using a probabilistic model of damage, repair and adaptation

“…The introduction of repair and adaptation processes into the model has certainly made it more realistic than our earlier model [20]. We now predict a lower incidence of stress fractures, giving values which are more typical of clinical findings worldwide.…”

“…In our previous paper [20] we adapted the Weibull equation for use in fatigue by replacing o with Ao,, the fatigue strength, defined as the range of stress (i.e. the difference between maximum and minimum stress in the cycle) that causes a fatigue failure after a given number of cycles, Nf.…”

“…We did this by using the concept of an 'equivalent stress range' Acreq. This was defined in our previous paper [20], where it was used to incorporate the varying levels of cyclic stress which occur during daily activities (walking, running, etc.). The equivalent stress is a weighted average of all the stresses which occur over a given time period.…”

“…In a previous publication [20] we developed a theoretical model which was based on concepts currently used to predict failures of engineering materials under cyclic loading: 'fatigue' failures. The method is a statis-*Corresponding author.…”