内固定物尖端与股骨头边缘安全距离的几何学探讨

A geometric study of the safe distance from the tip of screw to the edge of femoral head on radiographs

目的通过几何学模型探讨内固定物尖端与股骨头边缘的安全距离，以避免内固定物穿出股骨头。方法把股骨头作为一个球体处理，正、侧位投影所得为两个平面圆形影像。平面圆形影像所代表的空间结构为两个互相垂直的圆柱体，两者的公共部分即为正、侧位影像所代表的空间区域。分析股骨头的正、侧位投影所得的二维影像与其三维空间结构的几何关系，通过两者立体结构及体积的比较，计算为确保内固定物位于股骨头内所要求的内固定物尖端与股骨头边缘的安全距离。结果股骨头的二维正、侧位影像所构成的空间结构为一个外切于股骨头球体的牟合方盖，其与股骨头球体的体积比为4：1π。正、侧位x线影像中内固定物尖端均位于股骨头内的情况下，其实际上穿出股骨头的危险性约为21．5％。为了降低内固定物穿出股骨头的危险性，必须使牟合方盖的体积变小，即内固定物的尖端距股骨头边缘有一定的距离。当牟合方盖小到恰好内切于球体时，内固定物穿出股骨头的危险性降为零。此时通过几何学计算可知X线影像上内固定物尖端与股骨头中心的距离约为股骨头半径的0．71倍。即当x线影像上股骨头直径为5cm时，内固定物尖端与股骨头边缘的距离约为0．7cm。结论为确保内固定物位于股骨头内，X线影像上内固定物尖端与股骨头中心的距离应小于股骨头半径的0．71倍。即当正、侧位X线影像上股骨头直径为5em时，内固定物尖端与股骨头边缘的安全距离应〉0．7cm。

Objective To determine the geometric safe distance from the tip of screw to the edge of femoral head （tip-to-edge distance, or TED） on radiographic images. Methods Using geometric methods to analyze the position of internal fixation implants on anteroposterior （AP） and lateral X-ray images and to correlate them with the three-dimensional structure of the femoral head. To calculate the safe distance from the tip of screw implants to the edge of femoral head （TED） on images to ensure it within the femoral head by comparing both of their structure and volumes. Results The imaginary spatial structure created from the AP and lateral X-ray images, designated as a ＂Steinmetz Solid＂ in geometry, had a volume proportional to the femoral head with a ratio of 4π. The risk of the screw implant penetrating the femoral head when the tip located inside the shadow on both AP and lateral X-ray images was about 21.5%. To ensure that the screw implant was entirely within the femoral head, this imaginary spatial structure should be internally tangential to the femoral head. The distance from the implant＇s tip to the center of femoral head was about 0.71 times to the diameter of femoral head on images, which meant the TED was about 0.7 cm when the diameter of femoral head was 5 cm. Conclusion The distance from the screw implant＇s tip to the center of femoral head should be at most 0.71 times the diameter of femoral head, and the TED should be more than 0.7 cm when the radius of the femoral head is 2.5 cm on images, in order to ensure that the implant is entirely within bone and not in the joint space.