Stiffness, strength and healing assessment in different bone fractures--a simple mathematical model

External fixators can only be removed safely when fractures have healed sufficiently to restore mechanical integrity to the bone. A bending stiffness of 15 N m/ degrees has been suggested as a means of estimating mechanical integrity. To examine whether this end point stiffness value can be applied to all fractures, the present study examined the degree of variability in predicted stiffness and strength that arises from variations in bone dimensions. Results imply that there is no common value for the end-point of bending stiffness in different bones. At an end point value of 15 N m/degrees, the maturity of the fracture repair tissue (represented by its elastic modulus) can vary 500-fold between an adult femur with a 0.5-mm gap to a child's mid diaphyseal tibia with a 1.0-mm gap. Fortunately, the strength does not vary by as large an extent as the modulus. However, even though two fractures each have reached a stiffness of 15 N m/degrees, a fracture in a bone of 50 mm diameter may exhibit only 60% of the strength of repair in a bone of 30 mm diameter. Therefore, caution should be exercised when using the bending stiffness as an end point indicator for different bones.