title: Cluster analysis as a method for determining size ranges for spinal implants: disc lumbar replacement prosthesis dimensions from magnetic resonance images.
abstract: METHODS
  Statistical analysis of clinical radiologic data.
  
  
  OBJECTIVE
  To develop an objective method for finding the number of sizes for a lumbar disc replacement.
  
  
  BACKGROUND
  Cluster analysis is a well-established technique for sorting observations into clusters so that the "similarity level" is maximal if they belong to the same cluster and minimal otherwise.
  
  
  METHODS
  Magnetic resonance scans from 69 patients, with no abnormal discs, yielded 206 sagittal and transverse images of 206 discs (levels L3-L4-L5-S1). Anteroposterior and lateral dimensions were measured from vertebral margins on transverse images; disc heights were measured from sagittal images. Hierarchical cluster analysis was performed to determine the number of clusters followed by nonhierarchical (K-means) cluster analysis. Discriminant analysis was used to determine how well the clusters could be used to classify an observation.
  
  
  RESULTS
  The most successful method of clustering the data involved the following parameters: anteroposterior dimension; lateral dimension (both were the mean of results from the superior and inferior margins of a vertebral body, measured on transverse images); and maximum disc height (from a midsagittal image). These were grouped into 7 clusters so that a discriminant analysis was capable of correctly classifying 97.1% of the observations. The mean and standard deviations for the parameter values in each cluster were determined.
  
  
  CONCLUSIONS
  Cluster analysis has been successfully used to find the dimensions of the minimum number of prosthesis sizes required to replace L3-L4 to L5-S1 discs; the range of sizes would enable them to be used at higher lumbar levels in some patients.
authors.affiliation: School of Engineering, Mechanical Engineering, University of Birmingham, Edgbaston, Birmingham, B15 2TT United Kingdom.
authors.forename: Dang
authors.initials: D
authors.lastname: Lei
authors.forename: Roger L
authors.initials: RL
authors.lastname: Holder
authors.forename: Francis W
authors.initials: FW
authors.lastname: Smith
authors.forename: Douglas
authors.initials: D
authors.lastname: Wardlaw
authors.forename: David W L
authors.initials: DW
authors.lastname: Hukins
mesh_terms: D000328:Adult; D000368:Aged; D016000:Cluster Analysis; D006801:Humans; D007403:Intervertebral Disc / Q000033:anatomy & histology* / Q000601:surgery; D008159:Lumbar Vertebrae / Q000033:anatomy & histology* / Q000601:surgery; D008279:Magnetic Resonance Imaging; D008875:Middle Aged; D019736:Prostheses and Implants; D019919:Prosthesis Implantation