Femoral Torsion in CT: Why We Should Add Some Trigonometry

Abstract

Purpose: In our department, we routinely perform Computed Tomography (CT) or Magnetic Resonance Imaging (MRI) of the lower extremity to assess femoral torsion for preoperative planning prior correcting osteotomies. It might be difficult to assess the FA, because on axial images the depicted part of the femoral neck is too short to allow correct alignment of the axis of the femoral neck. Measurements can also be performed on oblique axial images with improvement of depiction of the femoral neck but are smaller than those of measurements on axial images, due to the fact that images depend on rules of trigonometry. The aim is to provide a trigonometrical formula to calculate the value for FA, allowing precise assessment of femoral anteversion on oblique axial images similar to those on axial images. Materials and Methods: Trigonometrical transformation is performed in three steps. Initial measurement of femoral anteversion on oblique images is transformed via a corresponding rectangular triangle from coronal images to calculated femoral anteversion on axial images. Results: The first triangle is labelled with a1, b1, c1 for the sides and alpha1, beta1for the angles. Second and third triangle is labelled correspondingly. Length of both cathetus a1 and b1 are calculated as follows: cathetus a1=sin alpha1*c1 and cathetus b1=cos alpha 1*c1. Cathetus b2 is calculated as follows: b2=cos alpha2*c2. alpha3=tan-1 (a3/b3). Initial calculation of angle alpha3=tan-1 (a3/b3)=tan-1 (a1/b2), with a3=a1=sin alpha1*c1 and b3=b2=cos alpha2*b1*c, with b1=cos alpha1*c1 and b3=cos alpha2*cos alpha1*c1². The final formula is then: alpha3=tan-1 ((sin alpha1*c1)/(cos alpha²*cos alpha1*c12)) = tan-1 ((sin alpha1/(alpha2*cos alpha1*c1)) Conclusion: In this study we can provide a formula: alpha3=tan-1 ((sin alpha1/(cos alpha2*cos alpha1*c1)), which allows to calculate the femoral anteversion for true axial reconstructed images with the increased accuracy of measurements on oblique images and the ability to use the already known reference values from the literature.