The intermetatarsal and metatarsal declination angles: geometry as a source of error

The measurements on radiographs of the foot are believed to give an objective impression of foot deformities. In patient management, the outcome of these measurements is one of the factors that the physician takes into consideration. In fact, the radiograph is a projection of three-dimensional structures and is as such liable to a certain amount of distortion. To our knowledge this distortion has not been quantified, although it seems important for the interpretation of the measurements.

First, mathematical models based on the geometry of standard anteroposterior and lateral radiographs were constructed and analyzed. Then, we simulated radiography with these models on three-dimensional data of metatarsals originating from CT scans of 10 normal volunteers.

The distortion of the declination angles of the metatarsals was practically negligible. The intermetatarsal angles were distorted up to 5.4 degrees. The measured angles underestimated the three-dimensional angles.

In interpreting the measurements of the metatarsal declination angles, distortion was not a factor. For intermetatarsal angles variability of distortion was only about one third of the reported interobserver variability, but it may have cumulative effects on the error of measured intermetatarsal angles. Moreover, the theoretical models predicted larger distortions in patients with deformities. In interpretation of angular measurements the physician should be aware of these pitfalls.