title: A mathematical simulation of the tip-apex distance and the calcar-referenced tip-apex distance for intertrochanteric fractures reduced with lag screws.
abstract: BACKGROUND
  As a predictor of the risk of lag screw cutout, it was recommended that keeping tip-apex distance (TAD)<25mm and placing the screw centrally or inferiorly, but positioning the lag screw too inferiorly in the head would produce TAD>25mm. We aim to simulate various positions of the lag screw in the femoral head and identify whether 25mm is a suitable cut-off value that favours all sizes of femoral heads with intertrochanteric fractures of the hip.
  
  
  METHODS
  Using a general mathematical software, the positions of the screw tip points were simulated. The virtual anterior-posterior and lateral views were then visualised, and the locus of the screw tips was projected into a Cartesian coordinate system according to the TAD and calcar-referenced tip-apex distance (CalTAD) formulas. Each original virtual anterior-posterior and lateral image was zoomed and compiled to match a calculated average image. The screw tip points were recorded, traced and compiled into volumes which could be used to visualise the screw's movements and positioning within the femoral head. The extracted volumes were calculated when 10mm<TAD<25mm and 10mm<CalTAD<25mm, and the region where these two volumes overlapped was also calculated. Suitable positions for the screw tip were then assessed.
  
  
  RESULTS
  For the TAD calculation, the shape of the traced screw tip points had a pancake-like appearance, while the CalTAD plot produced a teardrop-shaped region. The volume ratios of TAD, CalTAD and overlapping region relative to the femoral head volume were respectively 3.51±1.30%, 5.19±1.62% and 2.64±1.32%. The volumes of the traced TAD, CalTAD and overlapping regions increased slower than the volume of an idealised sphere.
  
  
  CONCLUSIONS
  Positioning the lag screw should address geometrical effects of both tip-apex distance and femoral head size, with an emphasis on measuring the position of the screw tip for the suitable zone by volume ratio. The previous 25mm TAD cut-off value should be adjusted according to the individual femoral head size.
authors.affiliation: Department of Orthopaedic Surgery, Yangpu Hospital, Tongji University School of Medicine, Shanghai, China.
authors.forename: Shuang
authors.initials: S
authors.lastname: Li
authors.affiliation: Department of Orthopaedic Surgery, Yangpu Hospital, Tongji University School of Medicine, Shanghai, China. Electronic address: shiminchang11@aliyun.com.
authors.forename: Shi-Min
authors.initials: SM
authors.lastname: Chang
authors.affiliation: College of Surveying and Geo-Informatics, Tongji University, China.
authors.forename: Yan-Min
authors.initials: YM
authors.lastname: Jin
authors.affiliation: Department of Orthopaedic Surgery, Yangpu Hospital, Tongji University School of Medicine, Shanghai, China.
authors.forename: Ying-Qi
authors.initials: YQ
authors.lastname: Zhang
authors.affiliation: Yang Zhi Rehabilitation Hospital, Tongji University School of Medicine, Shanghai, China.
authors.forename: Wen-Xin
authors.initials: WX
authors.lastname: Niu
authors.affiliation: Department of Orthopaedic Surgery, Yangpu Hospital, Tongji University School of Medicine, Shanghai, China.
authors.forename: Shou-Chao
authors.initials: SC
authors.lastname: Du
authors.affiliation: Department of Orthopaedic Surgery, Yangpu Hospital, Tongji University School of Medicine, Shanghai, China.
authors.forename: Li-Zhi
authors.initials: LZ
authors.lastname: Zhang
authors.affiliation: Department of Orthopaedic Surgery, the First Rehabilitation Hospital of Shanghai, China.
authors.forename: Hui
authors.initials: H
authors.lastname: Ma
mesh_terms: D001696:Biomechanical Phenomena; D001863:Bone Screws; D003198:Computer Simulation; D005270:Femur Head / Q000033:anatomy & histology / Q000601:surgery*; D005593:Fracture Fixation, Internal / Q000295:instrumentation / Q000379:methods*; D005594:Fracture Fixation, Intramedullary / Q000295:instrumentation / Q000379:methods*; D006620:Hip Fractures / Q000473:pathology / Q000601:surgery*; D006801:Humans; D008432:Mathematical Computing; D012016:Reference Values; D012984:Software
keywords: CalTAD; Calcar-referenced tip-apex distance; Intertrochanteric fracture; TAD; Tip-apex distance