Pose determination of a blade implant in three dimensions from a single two-dimensional radiograph

The aim of the study was to introduce a mathematical method to estimate the correct pose of a blade by evaluating the radiographic features obtained from a single two-dimensional image. Blade-form implant bed preparation was performed using the piezosurgery device, and placement was attained with the use of magnetic mallet. The pose determination of the blade was described by means of three consecutive rotations defined by three angles of orientation (triplet φ, θ and ψ). Retrospective analysis on periapical radiographs was performed. This method was used to compare implant (axial length along the marker, i.e. the implant structure) vs angular correction factor (a trigonometric function of the triplet). The accuracy of the method was tested by generating two-dimensional radiographic simulations of the blades, which were then compared with the images of the implants as appearing on the real radiographs. Two patients had to be excluded from further evaluation because the values of the estimated pose angles showed a too-wide range to be effective for a good standardization of serial radiographs: intrapatient range from baseline to 1-year survey was > of a threshold determined by the clinicians (30°). The linear dependence between implant (CF°) and angular correction factor (CF^) was estimated by a robust linear regression, yielding the following coefficients: slope, 0.908; intercept, -0.092; and coefficient of determination, 0.924. The absolute error in accuracy was -0.29 ± 4.35, 0.23 ± 3.81 and 0.64 ± 1.18°, respectively, for the angles φ, θ and ψ. The present theoretical and experimental study established the possibility of determining, a posteriori, a unique triplet of angles (φ, θ and ψ) which described the pose of a blade upon a single two-dimensional radiograph, and of suggesting a method to detect cases in which the standardized geometric projection failed. The angular correction of the bone level yielded results very close to those obtained with an internal marker related to the implant length.