title: Optimized lower leg injury probability curves from postmortem human subject tests under axial impacts.
abstract: OBJECTIVE
  Derive optimum injury probability curves to describe human tolerance of the lower leg using parametric survival analysis.
  
  
  METHODS
  The study reexamined lower leg postmortem human subjects (PMHS) data from a large group of specimens. Briefly, axial loading experiments were conducted by impacting the plantar surface of the foot. Both injury and noninjury tests were included in the testing process. They were identified by pre- and posttest radiographic images and detailed dissection following the impact test. Fractures included injuries to the calcaneus and distal tibia-fibula complex (including pylon), representing severities at the Abbreviated Injury Score (AIS) level 2+. For the statistical analysis, peak force was chosen as the main explanatory variable and the age was chosen as the covariable. Censoring statuses depended on experimental outcomes. Parameters from the parametric survival analysis were estimated using the maximum likelihood approach and the dfbetas statistic was used to identify overly influential samples. The best fit from the Weibull, log-normal, and log-logistic distributions was based on the Akaike information criterion. Plus and minus 95% confidence intervals were obtained for the optimum injury probability distribution. The relative sizes of the interval were determined at predetermined risk levels. Quality indices were described at each of the selected probability levels.
  
  
  RESULTS
  The mean age, stature, and weight were 58.2±15.1 years, 1.74±0.08 m, and 74.9±13.8 kg, respectively. Excluding all overly influential tests resulted in the tightest confidence intervals. The Weibull distribution was the most optimum function compared to the other 2 distributions. A majority of quality indices were in the good category for this optimum distribution when results were extracted for 25-, 45- and 65-year-olds at 5, 25, and 50% risk levels age groups for lower leg fracture. For 25, 45, and 65 years, peak forces were 8.1, 6.5, and 5.1 kN at 5% risk; 9.6, 7.7, and 6.1 kN at 25% risk; and 10.4, 8.3, and 6.6 kN at 50% risk, respectively.
  
  
  CONCLUSIONS
  This study derived axial loading-induced injury risk curves based on survival analysis using peak force and specimen age; adopting different censoring schemes; considering overly influential samples in the analysis; and assessing the quality of the distribution at discrete probability levels. Because procedures used in the present survival analysis are accepted by international automotive communities, current optimum human injury probability distributions can be used at all risk levels with more confidence in future crashworthiness applications for automotive and other disciplines.
authors.affiliation: a Department of Neurosurgery , Medical College of Wisconsin , Milwaukee , Wisconsin.
authors.forename: Narayan
authors.initials: N
authors.lastname: Yoganandan
authors.forename: Mike W J
authors.initials: MW
authors.lastname: Arun
authors.forename: Frank A
authors.initials: FA
authors.lastname: Pintar
authors.forename: Aniko
authors.initials: A
authors.lastname: Szabo
mesh_terms: D000063:Accidents, Traffic / Q000706:statistics & numerical data*; D000328:Adult; D000368:Aged; D002102:Cadaver; D006801:Humans; D007869:Leg Injuries / Q000209:etiology*; D016013:Likelihood Functions; D008875:Middle Aged; D011336:Probability; D016019:Survival Analysis
keywords: Weibull distribution; biomechanics; fracture; lower extremities; probability distributions; survival analysis