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 re-examined lower leg 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 non-injury 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 co-variable. 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: 58.2 ± 15.1 years, 1.74 ± 0.08 m and 74.9 ± 13.8 kg. Excluding all overly influential tests resulted in the tightest confidence intervals. The Weibull distribution was the most optimum function compared to the other two 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-old at five, 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.

Survival Model for Foot and Leg High Rate Axial Impact Injury Data

“…For a 50th percentile male, the current statistical model predicts a 50% probability of injury given a plantar force of 10.2 kN, compared to 8.3 kN predicted by Funk et al (2002) and Yoganandan et al (2014) at the mid-and proximal tibia ( Figure 4). These results are reasonable when considering that inertia due to location of the load cell could add, on average, 2.6 kN to the mid-tibia force, assuming the mass inferior to the mid-tibia is 1.96 kg for a 75 kg male (one quarter of the mass of the leg plus the foot mass; Plagenhoef et al 1983), and the average acceleration at the mid-tibia is around 136 g (calculated from Funk et al's [2002] accelerations).…”

“…Summary of previous injury risk functions Study Boundary condition Injury definition Injury predictor for 50% injury probability Yoganandan et al (1999) Potted proximal tibia, unbooted, ballasted AIS 2+ 0.348 * Age + 0.415 * Axial tibia force = 4.4 6.8 kN axial mid-tibia force Funk et al (2002) Potted proximal tibia, unbooted Bony foot/ankle fracture 45-year-old 50% male: 8.3 kN mid-tibia force 65-year-old 50% male: 6.1 kN mid-tibia force 45-year-old 5% female: 5.0 kN mid-tibia force 65-year-old 5% female: 3.7 kN mid-tibia force Bass et al (2004) a Potted mid-femur, booted AFIS-S 2+ 8.6 kN mid-tibia force McKay and Bir (2009) a Potted femur, unbooted AFIS-S 4+ 6.4 kN axial tibia force, 10.8 m/s velocity Quenneville et al (2010) Potted tibia, unbooted No foot Bony tibia fracture 7.9 kN = 10% risk of injury Henderson et al (2013) a Potted proximal tibia, unbooted, ballasted AIS 2+ 7.34 kN distal tibia force 6.16 kN proximal tibia force Gallenberger et al (2013) Potted proximal tibia, unbooted, ballasted Bony fracture Neutral position: 6.8 kN proximal tibia force 20 • dorsiflexion: 7.9 kN prox. tibia force Yoganandan et al (2014) Potted proximal tibia, unbooted, ballasted AIS 2+ 25-year-old: 10.4 kN proximal tibia force 45-year-old: 8.3 kN proximal tibia force 65-year-old: 6.6 kN proximal tibia force a Studies aimed at replicating UBB or landmine blast events.…”

“…Furthermore, the proximal boundary conditions for the included data were different, which enhances the potential for inertial differences between the tests and increases the need for a common location of force measurement. Though the data from Yoganandan et al (1996) were reanalyzed to use distal forces (Yoganandan et al 2014), the analysis still fails to account for the effect of ankle flexion.…”

Foot–Ankle Fractures and Injury Probability Curves from Post-mortem Human Surrogate Tests

“…Interval censoring has also been used in an analysis of foot-ankle fracture data from different experimental sources. 38,39 The reduction of the fracture threshold due to interval censoring reflects the conservativeness of the estimate in occupant safety.…”

“…The maximum likelihood approach was used to perform the survival analysis, and the log-likelihood estimates were also obtained. 15,39 The Weibull, log-logistic and log-normal distributions were identified as potential candidates for describing the human injury probability curves. The most optimum distribution was selected based on the corrected Akaike information criterion.…”