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. Author manuscript; available in PMC: 2021 Jul 31.
Published in final edited form as: Traffic Inj Prev. 2019 Nov 25;20(SUP2):S137–S142. doi: 10.1080/15389588.2019.1682565

Pelvis injury risk curves in side impacts from human cadaver experiments using survival analysis and Brier Score metrics

Narayan Yoganandan 1, John R Humm 1, Nicholas DeVogel 2, Anjishnu Banerjee 2, Frank A Pintar 1, Jeffrey T Somers 3
PMCID: PMC8325432  NIHMSID: NIHMS1722598  PMID: 31762331

Abstract

OBJECTIVE:

Post Mortem Human Surrogate (PMHS) experiments are used for tolerance and improve safety. For nearside impacts, the United States Standard Federal Motor Vehicle Safety Standards (FMVSS-214) used PMHS tests and binary regression. Since this promulgation, Parametric Statistical Survival Modeling (PSSM) has become a de facto standard for developing injury risk curves (IRCs). This study is focused on pelvic injuries from side impacts. Objectives: Analyze impactor-based intact PMHS tests and develop IRCs at different AIS levels using the force metric and examine the effectiveness of other force-related variables on IRCs.

METHODS:

Impactor-driven pelvic tests conducted using whole body PMHS were selected from published studies. The dataset had 63 tests. Peak force, 3-ms clip force, and impulse were used to develop IRCs for Abbreviated Injury Score (AIS) AIS2+ and AIS3+, i.e., groups A and B. Brier Score Metric (BSM) was used for ranking metrics. 95% confidence intervals were computed, Normalized Confidence Interval Sizes (NCIS) were determined, and quality of the IRCs were obtained.

RESULTS:

Impulse best described the underlying response of the pelvis. BSMs were the lowest for the impulse for both groups. At 10% and 50% probabilities, impulses were 71 Ns and 125 Ns for group A and 79 Ns and 160 Ns for group B; peak forces were 3.8 kN and 7.1 kN, and 4 kN and 10 kN for groups A and B; and c-forces were 2.7 kN and 6.5 kN and 3.6 kN and 8.6 kN, for groups A and B. NCIS at discrete probability levels, qualities of risk curves, and individual IRCs are given.

CONCLUSION:

This study underscores the importance of using impulse to describe pelvis injury criteria in lateral impacts. These findings are applicable to anthropomorphic test devices, as matched pair tests are done to determine dummy-based injury criteria/injury assessment risk curves (IARCs). Although IRCs have been developed for WorldSID, it may be appropriate to use impulse-based IARCs. Because THOR is a potential device for automated vehicle environments, it may be appropriate to develop THOR-based IARCS. The present IRCs act as fundamental human-based injury criteria. These responses can also be used in human body models and subsystem computational models.

Keywords: Injury risk curves, survival analysis, pelvic tolerance, side impact

INTRODUCTION

Experiments based on field studies using Post Mortem Human Surrogates (PMHS) are used to determine tolerance criteria and improve safety via crashworthiness studies (Kuppa et al., 2003; Maltese et al., 2002; Yoganandan et al., 2000; Yoganandan et al., 2007b). The United States (US) Federal Motor Vehicle Safety Standards, FMVSS-214 used this approach in its original and revised/updated promulgations for occupant protection in the nearside impact. In the earlier version, acceleration-based measures were used for thoracic and pelvic tolerances. In the later version of the updated standards, deflection- and force-based measures are used, and for the pelvic region, pubic symphysis force is used in the ES2-re anthropomorphic test device. This dummy is also currently used in consumer information tests.

A brief review of PMHS studies from literature is given to place the current study in the perspective of determining the probability of injury to the pelvis in side impacts. Tests at the Organisme National de Sécurité Routière (ONSER) involved subjecting ten seated intact PMHS to side impacts, delivered using a 17.3 kg impactor at velocities ranging from 5 to 13 m/s (Cesari and Ramet, 1980). A repeated testing protocol was used to conduct 36 tests. A tolerance value of 5 kN for the force and 100 N-s for the impulse was suggested. In a later publication, 27 tests from 12 PMHS were added (Cesari and Ramet, 1982). From the combined analysis of data, a peak force of 10 kN force was suggested as the pelvic injury tolerance for a mid-size male occupant. Researchers at the Highway Safety Research Institute (HSRI), now the University Michigan Transportation Research Institute (UMTRI), subjected 12 seated intact PMHS to side impacts, delivered using a 25 kg or a 56 kg impactor at velocities ranging from 4 to 14 m/s (Nusholtz et al., 1982). The peak forces in this dataset ranged from 3 to 14 kN, however, analysis from these cited studies did not associate the force magnitudes to a probability level. Experiments conducted at the Wayne State University (WSU) consisted of side impact tests to intact PMHS, and the loading was delivered using a 23.4 kg impactor at velocities ranging from 4 to 9 m/s (Viano, 1989). A peak force of 12.0 kN was associated with 25% risk of pelvic fracture.

Another series of tests were conducted at the Institut National de Recherche sur les Transports et leur Sécurité (INRETS) wherein seven seated intact PMHS were subjected to side impacts using a 23.4 kg impactor at velocities ranging from 3 to 7 m/s. This study was extended to include 14 additional PMHS at velocities ranging from 9 to 14 m/s, and the impactor mass was 12 or 16.2 kg (Bouquet et al., 1998). A combined analysis of data from these two studies indicated that a force of 7.6 kN is associated with a 25% risk of pelvic fracture at the AIS 2 level (Abbreviated Injury Score, AIS), and at the 3 level, the force was 11.4 kN. During the development of the injury criteria in the US standards, information from these tests were used to develop pelvic injury risk curves (IRCs) and the peak impact force was the response variable. As stated, the pubic symphysis force is specified for the ES2-re dummy.

Other studies have been conducted since the updated standards, and they include tests at the Centre Européen d’Etude de Sécurité et d’Analyse des Risques (CEESAR) and LAB PSA Peugeot Citroen RENAULT, in France. Eight seated intact PMHS were subjected to side impacts at velocities ranging from 3 to 6 m/s, No injuries were observed to the pelvis, and maximum forces ranged from 4.4 to 6.3 kN, suggesting that at these levels, fracture is not an outcome (Leport et al., 2007). An additional nine intact PMHS were tested at the same facilities for the next phase of the project. They were conducted at velocities ranging from 5 to 8 m/s, all but one specimen sustained injuries, scored using the AIS 2005 version, and the forces ranged from 5.1 to 14.5 kN (Petit et al., 2015). In addition to these impactor-based studies, sled tests and isolated pelvic bone tests using other methods have been conducted to determine forces and other variables associated with pelvic injuries in the side impact mode. While this is not an all-inclusive presentation of PMHS studies, literature reviews are available (Rupp, 2015; Yoganandan et al., 2007a).

The published IRCs from PMHS studies and IRCs for the test device used in the regulations are based on binary regression models. This type of regression analysis does not account for data censoring, and information from repeated tests on the same specimen are treated as independent data points. Because Parametric Statistical Survival Modeling (PSSM) can accommodate censoring and repeated testing protocols, it has essentially become the de facto standard for developing IRCs. Initial recommendations by the International Standards Organization and later improvements of the PSSM are available (Yoganandan et al., 2016). To date, a reanalysis of pelvic injury tolerances using the PSSM has not been conducted, and this is the objective of this investigation.

Specifically, the aim of this study is to analyze impactor-based intact PMHS tests and develop IRCs at different AIS levels using the force as the primary response variable. Another objective is to examine the effectiveness of other force-related variables (clip-force and impulse) on the IRCs. The metric that best represents the underlying response to injury is obtained from the analysis.

METHODS

Data were gathered from tests that included the following general protocol and findings. The first group of tests included ONSER tests (Cesari and Ramet, 1980). Briefly, the intact PMHS specimens were seated in a driving posture and was unbelted without lateral support. Thirty-six tests were performed on ten unembalmed subjects, equally divided between males and females. The guided-linear impactor was centered on the tuberosity of the greater trochanter. It had a mass of 17.3 kg with a rigid impacting surface, and velocities ranged from 6 to 11 m/s. In addition to pretest x-rays, repeated tests were done using a protocol that permitted obtaining x-rays after each impact to ensure the absence of fracture. A necropsy was done after the final test. Velocity, peak impactor force (termed as force hereafter), 3-ms clip of the force (termed c-force), and impulse variables were reported along with the injury status. The resulting injuries were categorized using the Abbreviated Injury Score, AIS. In a later investigation, this study was extended to include an additional 12 subjects in which five subjects were tested once while the remaining subjects sustained repeated impacts at velocities ranging from 4 to 14 m/s (Cesari and Ramet, 1982). Data collection and injury assessments remained the same as in the previous study. The combined dataset consisting of 63 PMHS tests were used in the analysis to meet the objectives of this investigation.

For the statistical analysis, force, c-force, and impulse outputs were selected as three primary response variables. Injury outcomes were categorized into AIS2+ and AIS 3+ injuries, termed as groups A and B, respectively. In the AIS 3+ injury category, group B, following the final test, specimens that remained intact and those sustaining injuries at AIS less than or equal to 2 level were treated as no injury data points. In the AIS 2+ category, group A, specimens sustaining injuries at AIS greater than or equal to 2 level were treated as injury data points. Injury data associated with a specimen that underwent only one test was left censored. Noninjury data associated with a specimen that underwent only one or more tests without any pathology was considered right censored. Repeated tests on the same specimen that produced noninjury and injury response variables were considered interval censored data points. The PSSM was performed using the R-software. The cumulative density functions for the Weibull, lognormal, and log-logistic distributions are given by the following equations:

Weibull:1−exp⁡−t/λγ
Log-logistic:11+t/λ−γ
Lognormal:Φγlog⁡λt

where, Φt=∫−∞t12πexp⁡−y22dy, t represents a value, and γ and λ are estimated by the maximum likelihood approach. The optimal distribution was selected based on the lowest Akaike Information Criterion (AIC), and the Brier Score Metric (BSM) was calculated for each response variable and covariate for each of the three groups of injury outcomes (Akaike, 1974; Brier, 1950). The response variable that produced the lowest BSM was considered to the best metric that describes the pelvic injury response to side impact. The ±95% confidence intervals were computed based on the delta method (Parr, 1983). The Normalized Confidence Interval Size (NCIS), defined as the ratio of confidence interval width to the magnitude of the metric, at a specific probability of injury, was determined. It is given by the following equation,

NCIS=ULp−LLpMp,

where p represents the probability of injury, Mp is the mean value of the metric, and ULp and LLp represent the upper and lower limits of the confidence intervals at that probability. NCIS values of <0.5, between 0.5 and 1, >1 to 1.5, and >1.5 were attributed to adjectival ratings of good, fair, marginal, and unacceptable (Petitjean et al., 2015). They were calculated at 5%, 10%, 25%, 50%, 75%, 90%, and 95% probability levels.

In other words, data from all the 22 PMHS tests were included in both groups, with the above described treatment for censoring to account for noninjury and injury outcomes.

RESULTS

The mean age, stature, total body mass, and body mass index were 70.1 ± 8.6 years, 1.67 ± 0.1 m, 67.0 ± 14.4 kg, and 23.9 ± 3.97 kg/m2, respectively. Individual specimen data are given in the original publications. For groups A and B, there were 3 right censored, 7 left censored, and 12 interval censored; and 11 right censored, 4 left censored, and 7 interval censored observations, respectively. For group A, the AIC statistics for the Weibull, lognormal, and log-logistic distributions for the forces were 89.89, 89.73, 89.88; for the clip forces were 97.95, 98.25, and 98.54; and for the impulse were 74.67, 77.95, and 78.28, respectively. Forces of 3.8 kN and 7.1 kN were associated with 10% and 50% probability levels (Figure 1). The qualities of the IRCs were in the fair and good categories at these risk levels. C-forces of 2.7 kN and 6.5 kN were associated with 10% and 50% probabilities (Figure 2), and the qualities of the IRCs were in the marginal and fair categories, at these risk levels. Impulse magnitudes of 71 Ns and 125 Ns were associated with 10% and 50% probabilities (Figure 3), and the qualities of the IRCs were in the fair and good categories, at these risk levels. The magnitudes of lambda and gamma coefficients for the forces, c-forces and impulses were: 0.00014 and 2.00; 7656 and 2.17, and 140.3 and 3.3, respectively, for the lognormal, Weibull, and Weibull distributions. A summary of the magnitudes of the variables and NCIS at various probability levels are given for all these variables (Table A1). For group B, the AIC statistics for the Weibull, lognormal, and log-logistic distributions for the forces were 73.34, 72.40, and 72.50; for the clip forces were 76.28, 75.62, and 75.67; and for the impulse were 62.60, 63.42, and 63.05, respectively. The magnitudes of lambda and gamma coefficients for the forces, c-forces and impulses were: 0.0001 and 1.40, 045; 0.00012 and 1.46, and 184.2 and 2.7, respectively, for the lognormal, lognormal, and Weibull distributions. Forces of 4 kN and 10 kN were associated with 10% and 50% probability levels (Figure 4). The qualities of the IRCs were in the marginal and fair categories at these risk levels. C-forces of 3.6 kN and 8.6 kN were associated with 10% and 50% probabilities (Figure 5), and the qualities of the IRCs were in the acceptable and fair categories, at these risk levels. Impulse magnitudes of 79 Ns and 160 Ns (Figure 6) were associated with 10% and 50% probabilities, and the qualities of the IRCs were in the fair and good categories, at these risk levels. A summary of the magnitudes of the variables and NCIS at various probability levels for all these variables are given (Table A2). The magnitudes of the BSM are shown (Figure A1) for all variables and both groups. These metrics were the lowest for the impulse parameter in both groups.

Figure 1:

Figure 1:

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IRCs for force from group A analysis. Solid curve represents the estimate and dashed curves correspond to lower and upper bound confidence intervals.

Figure 2:

Figure 2:

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IRCs for c-force from group A analysis. Solid curve represents the estimate and dashed curves correspond to lower and upper bound confidence intervals.

Figure 3:

Figure 3:

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IRCs for impulse force from group A analysis. Solid curve represents the estimate and dashed curves correspond to lower and upper bound confidence intervals.

Figure 4:

Figure 4:

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IRCs for force from group B analysis. Solid curve represents the estimate and dashed curves correspond to lower and upper bound confidence intervals.

Figure 5:

Figure 5:

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IRCs for c-force from group B analysis. Solid curve represents the estimate and dashed curves correspond to lower and upper bound confidence intervals.

Figure 6:

Figure 6:

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IRCs for impulse from group B analysis. Solid curve represents the estimate and dashed curves correspond to lower and upper bound confidence intervals.

DISCUSSION

As stated in the Introduction, to meet the objectives of this investigation, IRCs were developed at two AIS levels using the force as the primary response variable. This approach is traditionally used in automotive crashworthiness studies (Kuppa et al., 2003). For example, in the upgraded/revised side impact standards and for the pelvis region, to obtain injury criteria for the ES2-re test device, IRCs were developed at the AIS2+ and AIS3+ severities/levels using binary logistic regression models.

The qualities of the IRCs were not evaluated for the ES2-re test device, and confidence intervals were not reported, to the best knowledge of the authors of this investigation, and this was probably because of the timely focus, i.e., develop injury criteria for the dummy. It should however be noted that the assessment of the qualities of the IRCs were not the norm at the time of the development of injury criteria for the standards. The currently used quality indices were developed through a consensus process during the development of PSSM-based IRCs. These indices/adjectival ratings have also been used for other body regions and in other environments (Chirvi et al., 2017; Petitjean et al., 2015; Yoganandan et al., 2014b; Yoganandan et al., 2018). It has been used in dummy evaluations for the WorldSID.

The second objective of this investigation was to develop IRCs from two additional variables, the c-force and impulse, both parameters related to the force-time histories. A time-based metric mechanistically captures the temporal response and accounts for the viscoelastic properties of biological materials. This was also accomplished for the two groups of injury severities. While all the 63 tests from 22 PMHS were examined, the total number of data points varied between the two groups due to interval censoring. As expected, the c-force magnitudes were lower, and IRCs demonstrated a leftward shift, compared to the force-based IRCs because of the use of the peak magnitude in the latter risk curves. At probabilities of 10% and 50%, the ratio of the c-force to the peak force was 0.72 and 0.91, and 0.78 and 0.89 for group A and group B datasets, respectively. Across all probabilities, however, the mean ratio was 0.81 ± 0.11 for group A and 0.83 ± 0.10 for group B datasets. These results suggest that the 3-ms clip force is approximately 20% lower than the peak force, regardless of the severity of the injury to the pelvis. The c-force and impulse IRCs developed in the present investigation may not be directly applicable to dummy injury criteria specifications as similar attempts have not been made in the past via matched pair tests with the dummy. These IRCs can, however, be used in human body computational models paralleling the force-based IRCs from PMHS. This type of PMHS-based IRCs to the pelvis adds to the body of knowledge already available for other body regions and impact directions. From this perspective, the present IRCs serve as a dataset for modeling efforts.

The currently developed IRCs for the force, clip force, and impulse for the two severity groups from PSSM have the advantage that data were gathered from the same laboratory and similar groups of researchers, while other impactor tests have been published over time. While other studies have tested PMHS using am impactor (briefly described in the introductory paragraphs), all these variables were not reported, and hence, not included in the present investigation. In addition, the selected dataset had the largest sample size. While data from injury-producing tests can be treated as uncensored, the original study lacked supporting information. Because uncensored assignments generally result in a right shift of the estimated curves, the present IRCs serve as conservative estimates for advancing human safety and in crashworthiness studies.

The current side impact injury criterion is based on extrapolation from the PMHS tests to dummy pelvic loads as the physical device measures pubic symphysis forces. Using the presently developed IRCs, it is possible to derive improved injury criteria for the dummy as they are more robust and account for data censoring. Because repeated tests were conducted, and the timing of fracture was not identified, interval censoring for paired data points was used in the development of IRCs. Studies using instrumentation devices such as acoustic sensors and or strain gages possess the ability to detect fracture timings, and the output from such tests will add to certainty in the data and even more robust IRCs. The stated instrumentation techniques are being increasingly adopted in the recent design of experiments, including methods to process sensor-based signals, and they are aimed to derive IRCs with enhanced certainty (Chirvi et al., 2017; Goodwin et al., 2017).

A comparison of the forces reported in earlier impactor studies indicate the following. In a standing posture, the force of 12 kN was associated with 25% risk of injury, obtained from logistic regression (Viano, 1989). While this magnitude is considerably greater than the present study, it should be noted that the authors only provided the magnitude without the actual logistic regression-based IRCs. Another study in which the specimen was suspended before impact, stated that the lowest force to induce pelvic injury was 7.1 kN, and loads from 8.5 to 17 kN produced pelvic fractures (Nusholtz et al., 1982). The threshold matches well with the IRC at the LD50 level from group A analysis. Forces ranging from 7.7 to 16.2 kN were reported for pelvic fractures, and these magnitudes exceed the LD50 levels of the present IRCs (Bouquet et al., 1998; Bouquet et al., 1994). Acknowledging differences in the experimental designs, forces from the previous studies are in line with the risk-based forces from this investigation. The same type of analysis, however, was not extended to the c-force and impulse as these data were not available.

The BSM and AIC were both lowest for the impulse variable for both group A and group B, indicating that this biomechanical metric best represents the underlying response to pelvic injuries. It should be underscored that the BSM is based on predictive/discriminative ability, based on the squared error loss, while the AIC is based on the model likelihood. The two statistical measures related to different aspects of the data and model. Thus, the robustness of the identified impulse metric is enhanced from a statistical perspective. This finding suggests that future experimentalists in similar impact biomechanical studies should compute and report the impulse metric in addition to the more commonly reported primary variables such as the peak force.

The present study used PSSM instead of binary regression methods because PSSM can handle the censoring aspect of the data inherently present in biomechanical tests. Ignorance of this aspect, such as the use of binary regression methods, loses information contained within the data and thus, may not accurately reflect the true underlying biomechanical mechanisms. Common binary regression methods, such as logistic regression, often also necessitate a non-zero chance of injury at zero impulse, something that is difficult to interpret. It is possible that the binary regression methods give similar results to PSSM for a specific dataset, however, this is not the justification for its use. The method to analyze data should be decided upon before data is analyzed and there is no strong statistical argument to choose binary methods over the PSSM presented for these types of tests. One could use binary regression methods, but one would also need to acknowledge the limitations given above, none of which are present when using PSSM.

The pulse durations of the pubic force response of the WorldSID in NHTSA full-scale vehicle tests in a modern vehicle with contemporary restraint systems peaked at approximately 40 ms (Yoganandan et al., 2017). While actual signals were not available for all PMHS tests, the duration of loading in the ATD experiments appear to be line with the current data provided in the original paper.

Although risk curves have been developed for the WorldSID device, it may be appropriate to use the impulse metric to derive dummy-based IRCs. Furthermore, because the THOR is being suggested as an additional device for automated vehicle environments, it may be appropriate to develop THOR-specific injury criteria. Matched-pair tests should be evaluated to develop these dummy-based risk curves for injury assessments and prediction, and the present IRCs serve as fundamental human-based injury criteria. The present findings can also be used in computational models.

Normalization of data is frequently done in crashworthiness research to develop tolerance criteria. While the development of normalized IRCs was not the objectives of this investigation, data from the three metrics were normalized to the mid-size male and small-size female weight and develop IRCs using the equal stress equal velocity approach (Yoganandan et al., 2014a). Figure A2 in the Appendix show the IRCs for the two groups A and B, and for the three metrics, force, c-force, and impulse. All curves for the small-sized female anthropometry were left shifted, as expected. Additional references are available in the supplemental materials.

CONCLUSIONS

Using the PSSM, IRCs for pelvic injuries from lateral impactors tests were developed for AIS2+ and AIS3+ severities for the force, c-force, and impulse variables, and the two chosen levels of severity are typically used in automotive crashworthiness studies. In addition to the development of the IRCs, novel statistical methods were used to determine the hierarchy of the biomechanical variables. The impulse was found to be the best ranked metric that described the underlying injury response of the pelvis to lateral impact. This was true for both groups of data. Future experimentalists in similar impact biomechanical studies should compute and report the impulse variable in addition to the more commonly reported primary variables such as the peak force. It may be appropriate to evaluate the WorldSID and THOR devices via matched pair tests to determine the impulse variables and develop dummy-based injury criteria using the impulse metric.

Supplementary Material

Supp 1

Figure A1: BSM for the three variables (F represents force, C-F represents C-force, Imp represents impulse) from group A and B analysis.

Figure A2: IRCs for group A (top row): NW: small-size weight and NM: mid-size male weight, A and B represent the groups, f, c-f, and Imp represent the force, c-force, impulse. IRCs for group B (bottom row): NW: small-size weight and NM: mid-size male weight, A and B represent the groups, f, c-f, and Imp represent the force, c-force, impulse.

ACKNOWLEDGEMENTS

This material is the result of work supported by the U.S. Department of Defense, Medical Research and Materiel Command, Grant W81XWH-16-1-0010; with the resources and use of facilities at the Zablocki VA Medical Center, Milwaukee, Wisconsin; the Center for NeuroTrauma Research (CNTR) from the Department of Neurosurgery; the NASA Human Research Program through the HHPC contract (NNJ15HK11B); and the National Center for Advancing Translational Sciences, National Institutes of Health, Award Number UL1TR001436. Narayan Yoganandan and Frank Pintar are part-time employees of the VA Medical Center, Milwaukee, Wisconsin. The content is solely the responsibility of the author(s) and does not necessarily represent the official views of any of the funding organizations.

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Associated Data

This section collects any data citations, data availability statements, or supplementary materials included in this article.

Supplementary Materials

Supp 1

Figure A1: BSM for the three variables (F represents force, C-F represents C-force, Imp represents impulse) from group A and B analysis.

Figure A2: IRCs for group A (top row): NW: small-size weight and NM: mid-size male weight, A and B represent the groups, f, c-f, and Imp represent the force, c-force, impulse. IRCs for group B (bottom row): NW: small-size weight and NM: mid-size male weight, A and B represent the groups, f, c-f, and Imp represent the force, c-force, impulse.

NIHMS1722598-supplement-Supp_1.docx (236.6KB, docx)

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