The importance of accounting for the area of the medullary cavity in cross-sectional geometry: A test based on the femoral midshaft

In cross-sectional geometric (CSG) studies, both the subperiosteal and endosteal contours are considered important factors in determining bone bending rigidity. Recently, regression equations predicting CSG properties from a section's external dimensions were developed in a world-wide sample of human long bones. The results showed high correlations between some subperiosteally derived and actual CSG parameters. We present a theoretical model that further explores the influence of endosteal dimensions on CSG properties. We compare two hypothetical femoral midshaft samples with the same total subperiosteal area but with percentages of cortical bone at the opposite ends of published human variation for population sample means. Even in this relatively uncommon scenario, the difference between the samples in the resultant means for predicted femoral polar second moment of area (J) appears to be modest: power analysis indicates that a minimum sample size of 61 is needed to detect the difference 90% of the time via a t-test. Moreover, endosteal area can be predicted-although with substantial error-from periosteal area. Despite this error, including this relationship in subperiosteally derived estimates of J produces sample mean estimates close to true mean values. Power analyses reveal that when similar samples are used to develop prediction equations, a minimum sample of hundreds or more may be needed to distinguish a predicted mean J from the true mean J. These results further justify the use of regression equations estimating J from periosteal contours when analyzing behaviorally induced changes in bone rigidity in ancient populations, when it is not possible to measure endosteal dimensions. However, in other situations involving comparisons of individual values, growth trends, and senescence, where relative cortical thickness may vary greatly, inclusion of endosteal dimensions is still important.