Bone curvature: sacrificing strength for load predictability?


Bertram JE, Biewener AA. Bone curvature: sacrificing strength for load predictability?. J Theor BiolJ Theor BiolJ Theor Biol. 1988;131 :75-92.

Date Published:

Mar 7


Nearly all long bones of terrestrial mammals that have been studied are loaded in bending. Yet bending requires greater bone mass than axial compression for effective support of equivalent static loads. Most long bones, in fact, are curved along their length; their curvature augmenting rather than diminishing stresses developed due to bending. The most "efficient" design of a bone (maximal strength per unit mass) should be a form which is straight and resists axial compression. Bone curvature and the bending developed in the long bones of most species studied, therefore, poses a paradox in design. However, under natural conditions an animal's skeleton must support a range of dynamic loads that vary in both direction and magnitude. Thus, improved predictability of dynamic loading should represent an important feature in the design of the bone, in addition to its absolute strength. We present an explanation of long bone curvature, based on the conditions of stability for bending vs. axial compression in a column, that describes this apparent design paradox as a mechanism for improving the predictability of loading direction (and, consequently, the pattern of stresses within the bone). Our hypothesis argues that in order to understand the design "effectiveness" of long bone shape the role of the bone as a structural unit must be redefined to one in which bone strength is optimized concurrently with loading predictability. In agreement with our hypothesis, bone curvature appears to meet this requirement.


Bertram, J EBiewener, A AengResearch Support, Non-U.S. Gov'tENGLAND1988/03/07J Theor Biol. 1988 Mar 7;131(1):75-92.