1 Department of Surgical, Medical, Molecular and Critical Area Pathology, University of Pisa , Pisa , Italy.
2 Tuscan Dental Institute, Fortis Dental Center , Forte dei Marmi , Italy.
Dentomaxillofac Radiol. 2018 May;47(4):20170258. doi: 10.1259/dmfr.20170258. Epub 2018 Jan 11.
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.
本研究旨在介绍一种数学方法，通过评估从单个二维图像获得的放射特征来估计叶片的正确位置。使用压电骨刀制备叶片形种植床，并使用磁性橡皮锤进行放置。叶片的位置通过三个连续的旋转来描述，这些旋转由三个方向角（方向角三元组 φ、θ 和 ψ）定义。对根尖片进行回顾性分析。该方法用于比较种植体（沿标记的轴向长度，即种植体结构）与角度校正因子（三元组的三角函数）。通过对叶片的二维放射模拟生成来测试该方法的准确性，然后将其与真实放射片中出现的植入物图像进行比较。由于估计的位置角度值的范围太宽，无法有效地对连续放射片进行良好的标准化，因此有两名患者必须排除在进一步评估之外：患者内从基线到 1 年调查的范围>临床医生确定的阈值（30°）。通过稳健线性回归估计了种植体（CF°）和角度校正因子（CF^）之间的线性关系，得到以下系数：斜率，0.908；截距，-0.092；和确定系数，0.924。对于角度 φ、θ 和 ψ，准确性的绝对误差分别为-0.29±4.35、0.23±3.81 和 0.64±1.18°。本理论和实验研究确立了在后验确定描述单个二维放射片上叶片位置的唯一三元组（φ、θ 和 ψ）的可能性，并提出了一种检测标准化几何投影失败的病例的方法。骨水平的角度校正得到的结果与与植入物长度相关的内部标记非常接近。
