The relationship of angulation to translation in fracture deformities

We measured both angulation and translation on anteroposterior and lateral roentgenograms of 100 fixed post-traumatic deformities (either malunions or stiff [hypertrophic] non-unions) of long bones. We used trigonometric formulae to calculate the true planes and actual magnitude of both the angulation and the transverse translation of each deformity. We found that the planes of angulation and translation for each osseous deformity were rotated 43 +/- 25 degrees (mean and standard deviation) with respect to each other; in fact, we found almost as many instances in which the planes of angulation and translation of the fragments were within 10 degrees of perpendicular to each other as we did instances in which the angulation and translation were within 10 degrees of being in the same plane. Only seven angular deformities and six translational deformities occurred along either the sagittal or the coronal plane; the remaining deformities were in planes that were oblique to the standard reference planes.