The Hybrid III Dummy as a Discriminator of Injurious and Non-Injurious Restraint Loading

Abstract

This study evaluates the ability of the Hybrid III dummy and its associated injury criteria to discriminate sled tests with injurious conditions from those without. Ninety-three matched human cadaver and Hybrid III frontal sled tests over a range of impact speeds and restraint conditions are considered. Chest acceleration, deflection, and CTI are used as predictors of rib fracture outcome in the matched cadaver tests. Univariate and multivariate models are developed to evaluate the importance of the dummy measures relative to three experimental parameters (test speed, restraint condition, seating position) and three cadaver characteristics (age, gender, mass). The primary findings are, first, that chest acceleration has no utility for injury discrimination (Kruskal’s Gamma = 0.0319, area under the receiver-operator characteristic = 0.500). Second, the functional relationship between any Hybrid III injury measure and injury risk is sensitive to all three experimental factors. Injury risk models with consideration of this dependence are presented. It is shown that the Hybrid-III chest deflection corresponding to a given level of injury risk is greatest for air bag loading, lowest for belt loading, and intermediate for combined loading. This is shown to be non-biofidelic, since chest deflection as measured directly on the cadaver does not exhibit this sensitivity.

The Hybrid III dummy is the current standard for evaluating vehicle crashworthiness and restraint performance in frontal impacts. It is an important research and development tool used by industry as well as the specified dummy for frontal impact compliance and new car assessment program (NCAP) testing in the U.S. and in other countries. It is not clear, however, that this dummy is appropriate for estimating injury risk from restraint loading. The specifications for the Hybrid III dummy were generated at a time when seat belt use was very low (<10%) and air bag availability was almost zero (Figure 1). As a result, the dummy was designed to match thoracic force-deflection corridors that were developed using blunt hub impacts (Schneider et al. 1989) rather than the restraint loading that is more common today (Figure 2). It has been shown that the dummy’s thorax is stiffer than a human’s under seat belt loading (e.g., Cesari and Bouquet 1994) and Kent et al. (2002a) hypothesized that the degree to which the dummy is non-biofidelic may depend on the restraint system. This restraint-specific lack of biofidelity is a critical limitation of the dummy for predicting injurious restraint loading environments when the restraint condition varies.

Figure 1.

Development of Hybrid III specifications relative to belt use and air bag availability trends in the U.S. (see Kent et al. 2002b).

Figure 2.

Trends in overall belt use and reported use in fatal crashes in the U.S. (data from FARS and Kent et al. 2002b). Note that the fatality belt use is over-reported (see Malliaris and DeBlois 1998), but the degree of over-reporting has likely not changed over time.

The purpose of this paper is to evaluate the utility of the Hybrid III dummy for discriminating between injurious and non-injurious sled tests with diverse restraint conditions. Three dummy injury measures were considered in the analysis: the 3-ms clip maximum resultant chest acceleration (A_max), the maximum mid-sternal chest deflection (C_max), and the combined thoracic index (CTI). CTI is a linear combination:

$$\text{CTI}={\text{A}}_{max}/{\text{A}}_{int}+{\text{C}}_{max}/{\text{C}}_{int}$$ [1]

where A_int and C_int are constants defined for various dummy sizes. For the 50^th percentile male Hybrid III dummy, the values are A_int = 90 g and C_int = 103 mm (Eppinger et al. 1999).

METHODS

Data Collection

Sixty cadaver sled tests with thirty-three matched Hybrid III tests, taken from the literature and described in detail by Kent et al. (2001a), were used in this analysis (Figure 3). The entire database is presented in Appendix A. Restraint conditions include two-point shoulder belt systems, three-point lap-and-shoulder (L/S) belt systems, air bag-only systems, standard L/S-and-air bag systems, and force-limiting (F/L) belt-and-air bag systems. For the purposes of this analysis, all restraints were grouped as one of three “restraint conditions” 1) Belt-only, 2) air bag-only, or 3) combined belt-and-bag. Occupants seated in both the driver and front passenger positions were considered.

Figure 3.

Typical matched set of tests involving the Hybrid III (left) and a human cadaver (right) in nominally identical impacts.

Data Analysis

The set of thoracic injury predictors considered in this analysis is listed in Table 1. In all cases, the thoracic maximum abbreviated injury scale (MAIS) was used to define the outcome. Injury was modeled as binary, with MAIS values of 3 or greater equaling injury (Y = 1) and values less than 3 equaling no injury (Y = 0).

Table 1.

Evaluated Predictors of Thoracic Injury Sustained by Cadavers in Sled Tests

	Predictor	Variable Type, DOF, and Range
Cadaver Characteristics	Age at Death	Continuous, 1, 24 to 72 years
	Mass	Continuous, 1, 47 to 117 kg
	Gender	Classification, 1, Male = 1, female = 0
Dummy Measures	Amax	Continuous, 1, 24.6 to 57.0 g
	Cmax	Continuous, 1, 13.0 to 75.4 mm
	CTI	Continuous, 1, 0.56 to 1.15
Experimental Parameters	Position	Classification, 1, Driver = 1, pass. = 0
	Sled Speed	Continuous, 1, 24.6 to 58.9 km/h
	Restraint Cond.	Classification, 2, Belt-dominated = 1 (30 cadavers), air bag-dominated = 1 (9 cadavers), combined belt-bag = 1 (21 cadavers).

The analyses were conducted by way of the generalized estimating equation method (GEE), which is designed to model non-normally distributed, correlated data (Liang and Zeger 1989). The GEE model coefficients were estimated using a generalized linear model (GLM) (McCullagh and Nelder 1984). The GLM distribution family was specified as binomial, and a logit link function was utilized to model the logit of the probability of thoracic injury, P(I), as a linear function of the value of the predictor, x_i:

$$\text{P}(\text{I})=\frac{1}{1+{\text{e}}^{-\text{q}}}$$ [2]

where

$$\text{q}=\alpha +\underset{\text{i}}{\Sigma }{\beta }_{\text{i}}{\text{x}}_{\text{i}}$$ [3]

is the logit link function, α is the intercept, x_i are the model predictors, and β_i are the coefficients associated with each predictor.

Model variance-covariance parameters were estimated by the Huber-White estimator (Huber 1967, White 1982) with the dummy test number functioning as a clustering factor, since in several instances multiple cadaver tests were performed under the same test configuration that was utilized during a single dummy test. In cases of multiple dummy tests in an identical configuration, the mean dummy measures were used as if they had occurred in a single test.

Several parameters were utilized to evaluate the utility of the various predictors, including Kruskal’s Gamma and the area under the receiver operator characteristic (ROC) curve. A pair of observations with different outcomes (injury and non-injury) is concordant if the model predicts a higher risk of injury for the case with injury than for the case without. A pair of observations is discordant if the injury case has a lower model-predicted risk than the non-injury case. Kruskal’s Gamma is defined by the number of concordant and discordant pairs in the dataset, so it is a measure of the model’s ability to discriminate injury from non-injury cases:

$$\gamma =\frac{{\text{N}}_{\text{conc}}-{\text{N}}_{\text{disc}}}{{\text{N}}_{\text{conc}}+{\text{N}}_{\text{disc}}}$$ [4]

where N_conc is the number of concordant pairs and N_disc is the number of discordant pairs. A Gamma value of zero indicates that the model has no predictive ability, while a value of one indicates perfect prediction.

The value for the area under the ROC curve (Metz 1978, Metz 1986, Hanley 1989) was also used as a criterion for judging the ability of the predictors to distinguish between injurious and non-injurious tests. A unitless measure, this area summarizes the functional relationship between the sensitivity and the specificity of the discrimination tool to classify observations as injury or non-injury. In this application, the value of the area under the ROC curve can be interpreted as the probability of a randomly selected test that resulted in injury being viewed as more likely of being injurious than a randomly selected test that did not result in injury. The advantage of the area under the ROC over Kruskal’s Gamma is that ties are intrinsically considered (see Equation [4]).

For a predictor or a set of predictors that produce an area under the ROC curve value of 0.50, the utility of the model to correctly classify the outcomes is no better than basing the classification decision on the flip of a fair coin, while perfect discrimination corresponds to a value of 1.0. As a general guideline, models that produce an area within the range of 0.50 to 0.60 are considered to have little or no utility as a discriminating tool, 0.60 to 0.70 poor utility, 0.70 to 0.80 moderate utility, 0.80 to 0.90 good utility, and 0.90 to 1.0 excellent utility (Hanley 1989).

In this analysis the area under the ROC curve was estimated by way of the trapezoid rule and confidence interval construction was based on the variance estimator of Hanley and McNeil (1982), with the length of the interval specified as a 95% level of confidence.

To obtain a bias-corrected estimate for the area under the ROC curve, a model validation was carried out by way of a boot-strap re-sampling procedure (Efron and Tibshirani 1993, Harrell 2001). The bias-adjusted estimate for the area under the ROC curve corrects for the optimism in the observed area under the ROC curve that is induced as a consequence of utilizing the data at hand to estimate the model parameters. The bias-corrected estimate reflects more closely the discrimination performance of the model to classify a new sample of sled tests when the model coefficients are not optimized to fit the data at hand.

As a first step, three univariate models were developed using the dummy measures listed in Table 1 as predictors. Three multivariate models were then developed to evaluate the importance of CTI and C_max relative to the cadaver characteristics and experimental parameters. As described below, A_max was found to be a poor predictor of injury in the univariate analysis and was therefore not considered in the subsequent multivariate analysis. The relative importance of the various predictors in the multivariate models was evaluated using the Type III Wald Chi-Square statistic minus the degrees of freedom (χ²-DOF) associated with each predictor. This is a normalization technique commonly used for comparing predictors having different degrees of freedom.

RESULTS

Univariate Analysis of C_max, A_max, and CTI

The model coefficients for the three predictors are shown in Table 2 and the indicators of predictive performance are shown in Table 2 and Figure 4. Both CTI and C_max were found to be significant predictors (p < 0.005), while A_max was not (p = 0.649). Likewise, A_max was found to be a poor discriminator of injury outcome, with Kruskal’s Gamma (0.0319) and the bias-corrected area under the ROC curve (0.500) indicating essentially no utility. C_max had good utility as a discriminator of injury (Kruskal’s Gamma = 0.7130, bias-corrected area under ROC = 0.842) and CTI had moderate utility (Kruskal’s Gamma = 0.5556, bias-corrected area under ROC = 0.767). The injury models (Figure 5) indicate that, for this set of cadavers, 50% probability of MAIS 3+ thoracic hard tissue injury occurred at C_max = 26 mm and at CTI = 0.63. The univariate model with A_max shows a decreasing injury risk with increasing A_max.

Table 2.

Results of the Univariate GEE Analyses

Predictor	Intercept α	Coeff. β	Standard Error in β	p	Kruskal’s Gamma
Amax	1.8378	−0.0206	0.0451	0.649	0.0319
Cmax	−2.9868	0.1143	0.0406	0.005	0.7130
CTI	−3.7984	6.0182	1.6384	<0.001	0.5556

Figure 4.

Ability of three dummy measures to predict injury outcome in matched cadaver tests (univariate analysis). A value of 0.5 indicates no utility; 1.0 indicates perfect discrimination.

Figure 5.

Injury risk functions for three dummy measures (univariate analysis) with 95% confidence limits and data points.

Multivariate Analysis

Due to the poor performance of the A_max univariate model, this dummy measure was excluded from further analysis. Three multivariate models were therefore developed. Model 1 included CTI, the three experimental parameters, and the three cadaver characteristics as predictors. Model 2 was identical to Model 1, except C_max was used instead of CTI. Model 3 was identical to the other two, except no dummy measure was considered.

The predictors, regression coefficients, and overall performance of the multivariate models are shown in Tables 3 through 5. The analyses of variance (ANOVA) are shown in Tables 6 through 8. All models were significant predictors of injury with good discrimination utility. Of the individual predictors, the restraint condition and the sled speed were significant predictors in both models. C_max was also significant (p = 0.020), while CTI was not (p = 0.176). The restraint condition and sled speed were the most important covariates in all models based on the χ²-DOF metric. When the predictors were grouped according to type (experimental parameters, cadaver characteristics, and dummy measures), the most important group in terms of discriminating injurious tests from non-injurious tests was the experimental parameters (Figure 6), followed by the cadaver characteristics, with the dummy measure being the least important. The dummy measure’s lack of importance is apparent when the injury discrimination ability of the three models is compared. Model 1 and model 2 have area under the ROC values of 0.848 and 0.888. When any consideration of the dummy measure is removed (i.e., model 3), the value drops only to 0.843, indicating that the model retains equivalent injury discrimination.

Table 3.

Regression Parameters and Performance of Multivariate Model 1 (Using CTI)

Predictor	β	Standard Error of β
Intercept	−7.5969	9.7623
Gender (male = 1)	−2.2036	1.5787
Mass (kg)	−0.0196	0.0512
Age (years)	0.0547	0.0974
Sled Speed (km/h)	0.1257	0.0619
Position (driver = 1)	1.2473	1.0329
Restraint = air bag (no belt)	−9.5257	1.9189
Restraint = combined	−3.2320	1.3360
CTI	5.1665	3.8194

Kruskal’s Gamma = 0.83

Apparent Area Under the ROC = 0.917±0.053

Bias-Corrected Area Under the ROC = 0.848

Table 5.

Regression Parameters and Performance of Multivariate Model 3 (No Dummy Measure)

Predictor	β	Standard Error of β
Intercept	−3.478	5.718
Gender (male = 1)	−2.082	1.308
Mass (kg)	−0.001	0.032
Age (years)	0.023	0.066
Position (driver = 1)	0.965	0.944
Sled Speed (km/h)	0.142	0.055
Restraint = air bag (no belt)	−10.518	2.007
Restraint = combined	−3.734	1.340

Kruskal’s Gamma = 0.81

Apparent Area Under the ROC = 0.905±0.056

Bias-Corrected Area Under the ROC = 0.843

Table 6.

ANOVA Summary for Multivariate Model 1 (Using CTI)

Source	Type III Wald χ2	χ2 - DOF	p
Restraint	24.650	22.650	<0.001
Sled Speed	4.122	3.122	0.042
Gender	1.949	0.949	0.163
CTI	1.830	0.830	0.176
Position	1.458	0.458	0.227
Age	0.315	−0.685	0.574
Mass	0.146	−0.854	0.702
TOTAL	152.159	144.159	<0.001

Table 8.

ANOVA Summary for Multivariate Model 3 (No Dummy Measure)

Source	Type III Wald χ2	χ2 - DOF	P
Restraint	30.495	28.495	<0.001
Sled Speed	6.745	5.745	0.009
Gender	2.533	1.533	0.111
Position	1.045	0.045	0.307
Age	0.123	−0.877	0.726
Mass	0.002	−0.998	0.965
TOTAL	270.913	263.913	<0.001

Figure 6.

Importance of various predictors of injury outcome (grouped by type).

The results of the multivariate models are presented graphically in Figure 7 for a 60-year old, 50^th percentile male driver with a sled speed of 48 km/h. This represents the median age and speed in the dataset and the size of the Hybrid III. In the upper plot, the results are compared against four data points taken from the literature (Horsch et al. 1991).

Figure 7.

Results of multivariate models (60-year-old, 50^th percentile male driver, 48 km/h). The points on the upper plot are from Horsch et al. (1991): A: 60.3 years, belt loading; B: 31.4 years, belt loading; C: 67.3 years, belt loading, AIS 4+; D: 61.1 years, distributed loading. Note that the dataset contains only 2 non-injury cases with belt loading, so the lower portion of that curve is not well defined.

DISCUSSION

Chest Acceleration as an Injury Criterion for Restraint Loading

This analysis resulted in two findings of primary importance. The first is that A_max was essentially useless for discriminating between injurious and non-injurious tests when the restraint condition, and hence the load distribution on the chest, varied. Furthermore, the inclusion of A_max as a component of CTI degrades this criterion’s performance relative to C_max. It is well established that a change in the area of force application on the chest results in a change in the magnitude of force required to generate hard tissue injury. It follows that when the restraint condition varies the acceleration level at which hard tissue injury occurs also varies. Therefore, even if acceleration were to be used only as a surrogate predictor of rib fracture risk, then the tolerance level would be highly sensitive to the degree of load sharing between the belt and air bag. For belt-dominated loading, rib fractures would be expected at substantially lower chest acceleration than they would be for air bag-dominated loading. Contemporary restraint systems involve air bags of different size, shape, and pressure characteristics and belt systems having varying amounts of belt force limit and pretensioning. To assume that an acceleration-based injury criterion would remain an objective indicator of rib fracture risk for these disparate loading conditions is not appropriate.

The general applicability of this finding is limited, however, by the use of rib fractures sustained by cadavers to define injury. A cadaver model is not appropriate for evaluating some types of injuries due to post-mortem changes in soft tissue characteristics and the lack of physiological response. Acceleration has been shown to correlate with certain types of injuries in living humans. Tears at soft tissue attachment sites, for example, are an injury type that can be mechanistically related to acceleration. Based on work by Stapp (1970), Mertz and Gadd (1971), Eiband (1959), and others, a level of 60 g was identified as a reasonable upper limit for human tolerance and was specified as the maximum allowable under FMVSS 208. This tolerance level was not, however, based on the attainment of severe thoracic soft tissue injuries in living humans. Rather, this level is approximately 30% greater than the acceleration level at which human volunteers began sustaining hyphema, other soft tissue trauma, and became unwilling to continue to higher levels. Recent results from Indy car crashes, however, have challenged the conclusion that 60 g is the human tolerance. In an analysis of 141 crashes, Melvin et al. (1998) measured peak chassis acceleration levels exceeding 60 g in approximately 1/3 of the cases and some cases of acceleration over 125 g with the 60 g threshold exceeded for nearly 20 ms. They estimated that the chest acceleration experienced by the occupant was greater (by approximately a factor of 1.5) than the chassis acceleration, which would result in chest acceleration levels over three times the 60 g limit. Despite these acceleration levels, no serious thoracic soft tissue injuries were sustained. Furthermore, no mention was made of hyphema or other soft tissue injuries with the exception of concussion.

Vehicle Compliance and Assessment Testing

The findings of the current study combined with the findings of Melvin et al. (1998), call into question the use of a 60 g acceleration limit in FMVSS 208 tests and the use of an acceleration-based thoracic injury criterion for assigning star ratings in frontal NCAP tests. This is particularly important because chest acceleration is the criterion most likely to cause a suboptimal NCAP rating. In a search of the NHTSA test database, we identified 410 vehicles (model year (MY) of 1990 or later) that were tested using the frontal NCAP configuration (Figure 8). Of those vehicles, 283 received a rating of less than 5 stars. Of those 283, chest acceleration was responsible for the suboptimal rating in 56% of cases (ties credited to both criteria).

Figure 8.

Importance of chest acceleration for dictating NCAP star rating. Column shows the rating breakdown of 410 NHTSA tests performed using frontal NCAP configuration. Pie chart shows the measure responsible for the rating in all vehicles with <5 stars.

In particular, NCAP’s use of a continuous, constant, and monotonically increasing chest acceleration injury probability function (Figure 9) is inappropriate since the relative degree of belt and air bag loading likely differs among vehicles. In fact, the tests used in this paper indicated a trend of decreasing injury risk with increasing chest acceleration (Figure 5). This is likely a result of including tests with belts, air bags, and both. Consider two tests having a comparable probability of injury. In one test a combined belt-and-bag restraint is used and in the other a belt-only restraint is used. The combined system will generate a higher level of chest acceleration than the belt-only system since the well-distributed air bag force can be better tolerated. When tests with varying levels of air bag loading are considered, it is logical that chest acceleration would be a good surrogate indicator of the degree of air bag loading. Since air bag loading decreases the amount of belt force required to arrest the occupant’s forward motion, the increased chest acceleration associated with air bag loading will correspond to a decreased risk of the cadaver sustaining rib fractures. While there are important differences between living humans and cadavers, it is not unreasonable to presume that a similar protective benefit from a well-distributed air bag load would result in an inverse correlation between chest acceleration and living human injury risk up to the point at which a whole-body acceleration tolerance is exceeded. Based on the Melvin et al. (1998) study discussed above, this tolerance level may be well above the value used in FMVSS 208 (60 g) or the values used to decrease the star rating in an NCAP test (Figure 9). Limiting the chest acceleration to a value that is clearly below the human injury tolerance limits the benefit that could be attained by a restraint system. Well-distributed forces on the chest, even if they result in chest acceleration levels above 60 g, can provide a benefit to the occupant by limiting forward excursion and by reducing the magnitude of force required from the belt. As advanced concepts such as four-point belts (which can generate large restraining forces with relatively low levels of chest deformation) move closer to the market, this critical limitation of chest acceleration as an injury criterion will become even more important.

Figure 9.

Constant, continuous, monotonically increasing function used to assign NCAP star rating based on chest acceleration. Compare this function with the top plot in Figure 5.

The Hybrid III Dummy as a Tool for Predicting Rib Fracture Risk due to Restraint Loading

The use of the Hybrid III dummy to rank vehicles or to evaluate design options contains the inherent assumption that the dummy’s measures are an objective indicator of injury risk (i.e., the relationship between the injury measure and injury risk does not change as experimental factors change). The results of this study show that this assumption is not valid. In this study, several experimental factors were significant predictors of injury even when the dummy measure was considered. The importance of this finding is that the evaluation of injury risk between diverse restraint conditions, for different seating positions, or over wide speed ranges is not straightforward. The injury probability functions associated with these criteria are not constant when these experimental factors change. In other words, the functions shown in Figure 5 and in Figure 9 are not equally appropriate for all experimental conditions.

The important question that arises from this finding is whether the change in experimental conditions (seating posture, relative belt-to-bag load sharing, etc.) associated with testing different vehicles in NCAP is sufficient to hamper relative injury risk assessment using the Hybrid III. This study is insufficient to answer that question, but the large effect of experimental factors relative to the dummy measure suggests that this possibility should not be ignored.

Figure 7 illustrates the dummy’s pronounced sensitivity to restraint type, and this study has shown that the restraint condition is the most important covariate when using dummy measures to predict injury. In contrast, Kent et al. (2003) showed that the loading condition (belt, hub, air bag, combined) is not a necessary covariate when chest deflection as measured on the cadaver is used (compare Figure 7 with Figure 10). In other words, the relationship between chest deflection and injury risk does not change substantially with loading condition when chest deflection is measured directly on the cadaver. A reasonable interpretation of this finding is that the degree to which the dummy lacks biofidelity depends on the restraint condition. While the dataset used in this paper lacks critical datapoints (e.g., only 2 of 30 cadavers with belt loading were uninjured), the trends in Figure 7 are supported by previous research. The Hybrid III chest deflection level that corresponds to “injury” is lower with belt loading than it is with distributed loading.

Figure 10.

Injury risk functions based on chest deflection measured directly on a cadaver (Kent et al. 2003). Compare the insensitivity illustrated here with the Hybrid III sensitivity shown in Figure 7.

The sensitivity illustrated in Figure 7 may resolve some seemingly inconsistent results in the literature. Petitjean et al. (2002) found that the Hybrid III chest deflection was greater (22.5 mm vs. 18.5 mm) with a combined air bag and 4-kN force-limiting belt system than with a 6-kN belt with no air bag in otherwise identical collisions. In contrast to these dummy measures, field crashes and cadaver tests indicated a lower injury risk associated with the combined restraint. When one considers, however, that the relationship between chest deflection and injury risk is different for belt loading than for combined loading, this apparent inconsistency can be reconciled. According to the multivariate Model 2 developed here, the risk of injury associated with the 22.5 mm deflection under combined loading is approximately 77%, while the risk of injury associated with the 18.5 mm of deflection under belt loading is 99% (60-year-old, male driver in a 64 km/h test). While this sled speed is outside the range used to develop the multivariate model and the “combined” condition as defined here includes both standard and force-limiting belts, the relative risk is consistent with the cadaver results of Petitjean et al., who generated AIS 3+ injury in 1/2 cadavers with the combined restraint and 2/2 with the belt-only, and with similar tests performed in our laboratory (Kent et al. 2001c).

The generality of the injury risk functions shown in Figure 7 is limited. While they are consistent with previous research (see the data points from Horsch et al. 1991), the dataset from which they were derived is imperfect for this use of the data. These tests were compiled retrospectively from a population of tests that were performed to address a variety of research questions. For example, test 172 and its associated cadaver tests (see Appendix A) were performed at a relatively low test speed (24 km/h), yet they resulted in some of the highest chest deflection values in the dataset because they involved tests without a knee bolster. Test 355 and its associated cadaver tests involved substantial steering wheel loading through the air bag, so they do not represent a pure air bag loading environment. These interactions among test speed, restraint condition, and other test conditions confound the multivariate models and should be considered in their interpretation.

Dummy Biofidelity and Cadaver Variability

This study has shown that any dummy measurement is relatively unimportant in an injury risk model that includes several experimental and cadaver characteristics as predictors. While a lack of dummy biofidelity contributes to this finding, the large variability in cadaver injury tolerance is also important. In other words, the dummy’s utility may be “washed out” by the large variability in cadaver injury tolerance. While this study controlled for three cadaver characteristics (age, gender, mass), it is not possible to control for all characteristics that influence a cadaver’s risk of sustaining rib fractures in a collision. As a result, the dummy measure’s relative lack of importance in the multivariate models is likely due to both a lack of biofidelity and to the cadaver variability that cannot be controlled for using the available data. The univariate models showed that the dummy measures C_max and CTI exhibited appropriate trends in relationship to injury risk, so they do have utility for evaluating risk. The multivariate models showed that the functional relationship between these dummy measures and injury risk is not constant for all experimental conditions.

Besides the lack of ability to control for variability in cadaver injury tolerance, another limitation of this study is the use of different size cadavers to evaluate the 50^th percentile male Hybrid III. No attempt was made to scale the injury outcome or the collision exposure to account for variability in cadaver size. For example, test speed was used as a predictor in the model without consideration of the fact that the cadaver’s mass also influences the severity of the collision (in terms of kinetic energy) experienced by that cadaver. In fact, a preliminary analysis using an energy equivalent (sled speed squared times occupant mass) covariate instead of sled speed showed a slight improvement in model performance. Additional efforts to minimize the effects of 1) inherent variability in cadaver tolerance and 2) variability in cadaver size may increase the importance of the dummy measure and should be an area of future research.

Another limitation of the multivariate models is the compiling of both standard and force-limiting belts in the “combined” restraint category. The relative degree of belt and air bag loading will logically shift the “combined” injury risk curve (Figure 7) to any location between the “belt” curve and the “air bag” curve. Unfortunately, the data used in this study are insufficient to further divide the restraint types.

CONCLUSIONS

Chest acceleration is not a valid injury criterion for evaluating rib fracture risk with diverse restraint conditions. In the set of sled tests evaluated here, a univariate injury risk model using maximum chest acceleration as the predictor resulted in a bias-corrected area under the ROC of 0.500, indicating that this predictor has no utility for discriminating between injurious and non-injurious tests.

The second primary conclusion of this study is that the functional relationship between any Hybrid III injury measure and actual injury risk is highly sensitive to experimental factors such as test speed, restraint condition, and seating position. As a result, the use of Hybrid III measures to compare different design options is not straightforward since the competing options may change the experimental environment to the extent that this functional relationship does not remain equal for both options. Restraint-specific functions are presented that quantify the relationship between injury and injury risk for belt loading, air bag loading, and combined loading.

Table 4.

Regression Parameters and Performance of Multivariate Model 2 (Using C_max)

Predictor	β	Standard Error of β
Intercept	−14.4135	10.1809
Gender (male = 1)	−2.1944	1.8097
Mass (kg)	−0.0425	0.0611
Age (years)	0.0692	0.0824
Sled Speed (km/h)	0.2518	0.0990
Position (driver = 1)	1.0193	0.8667
Restraint = air bag (no belt)	−8.4238	1.4633
Restraint = combined	−3.8875	1.5407
Cmax	0.1696	0.0727

Kruskal’s Gamma = 0.89

Apparent Area Under the ROC = 0.945±0.043

Bias-Corrected Area Under the ROC = 0.888

Table 7.

ANOVA Summary for Multivariate Model 2 (Using C_max)

Source	Type III Wald χ2	χ2 - DOF	P
Restraint	37.233	35.233	<0.001
Sled Speed	6.469	5.469	0.011
Cmax	5.439	4.439	0.020
Gender	1.470	0.470	0.225
Position	1.383	0.383	0.240
Age	0.706	−0.294	0.401
Mass	0.485	−0.515	0.486
TOTAL	110.381	102.381	<0.001

Appendix A – Database of Matched Dummy and Cadaver Tests

Test No.	Test Subject ID	Ref.*	Age	Gender	Wt. (kg)	Ht. (cm)	Sled ΔV (km/h)	Rest.	Rib Fx	MAIS	Amax (g)	Cmax (mm)	CTI
52	Hybrid III						34.8	2-pt			33	50	0.85
53	91-W-03	1	61	F	61	153	34.9	2-pt	19	4
54	Hybrid III						38.1	2-pt			35	74	1.11
55	91-EF-10	1	62	F	91	176	36.9	2-pt	11	3
101	Hybrid III						33.8	2-pt			30	57	0.88
102	92-UM-23	1	60	M	95	176	33.1	2-pt	19	4
103	92-EM-21	1	57	M	103	179	32.5	2-pt	13	4
104	92-EF-25	1	66	F	105	179	32.3	2-pt	11	4
112	Hybrid III						46.8	2-pt			36	75	1.13
113	92-EF-22	1	24	F	57	159	47.3	2-pt	12	4
114	92-FF-24		60	F	65	164	47.0	2-pt	27	4
172	Hybrid III						24.6	L/S			25	56	0.82
173	92-EM-33		61	M	72	167	24.6	L/S	9	3
174	93-EF-35	1	57	F	62	168	25.9	L/S	12	3
175	93-EM-27	1	58	M	117	185	25.7	L/S	3	2
222	Hybrid III						53.4	2-pt			45	64	1.12
223	93-EM-32	1	51	M	61	169	55.0	2-pt	13	4
224	93-EM-26	1	58	M	65	175	54.4	2-pt	16	4
225	93-EM-37	1	36	M	68	177	53.9	2-pt	16	4
226	Hybrid III						53.3	2-pt			41	64	1.08
227	93-FM-29	1	53	M	70	165	53.5	2-pt	12	3
228	92-FM-18	1	47	M	85	177	54.7	2-pt	16	4
229	93-EM-36	1	37	M	60	183	54.0	2-pt	17	4
249	Hybrid III						54.1	2-pt			45	57	1.05
250	94-EM-39	1	39	M	50	177	54.9	2-pt	12	4
251	Hybrid III						58.9	2-pt			52	59	1.15
252	94-EM-38		37	M	67	177	58.2	2-pt	17	4
256	Hybrid III						56.5	2-pt			46	52	1.02
257	94-EM-40		33	M	112	179	56.7	2-pt	10	4
258	94-EM-43	1	69	M	64	178	55.3	2-pt	14	4
259	94-EF-41	1	64	F	77	163	56.4	2-pt	15	4
293	Hybrid III	2					56.8	L/S			47	37	0.88
294	94-EF-44	1,2	68	F	55	148	56.8	L/S	10	4
295	94-EM-42	1,2	57	M	104	187	56.8	L/S	15	4
296	94-EM-45	1,2	59	M	74	181	59.8	L/S	26	4
302	Hybrid III	2					57.5	L/S+AB			51	31	0.86
303	93-EM-34	1,2	64	M	50	154	57.5	L/S+AB	4	2
304	94-EM-47	1,2	65	M	57	168	59.4	L/S+AB	15	4
305	94-EF-48	1,2	66	F	58	161	59.4	L/S+AB	12	4
332	Hybrid III	2					58.2	F/L+AB			37	30	0.70
333	95-EM-51	1,2	51	M	64	170	58.2	F/L+AB	6	3
334	94-EM-49	1,2	49	M	79	186	58.2	F/L+AB	5	3
335	95-EM-50	1,2	50	M	66	172	58.6	F/L+AB	2	2
355	Hybrid III						55.7	AB only			46	58	1.08
356	95-EM-52	1	64	M	74	176	57.2	AB only	30	4
357	96-EM-55	1	48	M	80	183	57.2	AB only	19	4
358	96-EM-56	1	40	M	81	177	59.0	AB only	17	4
410	Hybrid III						57.0	F/L+AB			32	25	0.60
411	96-EM-57		60	M	72	172	57.5	F/L+AB	19	4
412	96-EM-60		70	M	91	178	56.8	F/L+AB	14	4
532	Hybrid III	3					48.6	F/L+AB			27	27	0.56
537	Hybrid III	3					48.9	F/L+AB			27	29	0.58
538	Hybrid III	3					48.1	F/L+AB			25	26	0.53
533	99-EF-104	3	67	F	64	163	48.6	F/L+AB	1	1
534	97-EM-76	3	47	M	51	170	48.4	F/L+AB	4	3
535	98-EF-95		57	F	53	163	48.1	F/L+AB	16	4
544	97-EF-83	3	59	F	56	168	49.2	F/L+AB	9	4
545	99-EM-103	3	67	M	74	176	48.1	F/L+AB	3	2
571P	Hybrid III						47.6	F/L+AB			26	29	0.57
572P	Hybrid III						48.1	F/L+AB			28	28	0.58
576P	Hybrid III	4					48.1	F/L+AB			28	30	0.60
577P	99-FM-111	5	57	M	70	174	47.4	F/L+AB	0	0
578P	99-FF-107	5	69	F	53	155	47.6	F/L+AB	4	3
579P	99-FF-106	5	72	F	59	156	47.6	F/L+AB	11	4
580P	99-FF-105	5	57	F	57	177	47.6	F/L+AB	0	0
648P	Hybrid III						48.6	AB only			44	19	0.67
649P	Hybrid III						47.6	AB only			44	20	0.68
650P	00-FRM-124	5	40	M	47	150	48.9	AB only	4	2
651P	00-FRM-121	5	70	M	57	176	48.6	AB only	0	0
652P	00-FRM-118	5	46	M	74	175	49.7	AB only	0	0
663P	Hybrid III						48.0	L/S+AB			45	40	0.89
664P	Hybrid III						48.0	L/S+AB			43	40	0.87
665P	99-FRM-112	5	55	M	85	176	48.0	L/S+AB	3	2
666P	99-FRM-115	5	69	M	84	176	48.0	L/S+AB	3	2
667P	00-FRF-120	5	59	F	79	161	48.0	L/S+AB	13	4
668P	00-FRF-127	5	54	F	55	162	48.0	L/S+AB	23	4
1	Hybrid III	6					50.8	L/S			51	34	0.90
M1	Cadaver	6	58	M	82	180	49.0	L/S	10	4
2	Hybrid III	6					49.7	L/S			44	39	0.87
D2	Cadaver	6	57	M	73	178	49.0	L/S	10	4
3	Hybrid III	6					50.0	L/S			43	40	0.87
V3	Cadaver	6	66	M	77	178	50.0	L/S	7	3
4	Hybrid III	6					51.8	L/S			40	29	0.73
F4	Cadaver	6	58	M	70	178	50.0	L/S	14	4
5	Hybrid III	6					49.0	L/S			39	27	0.70
A5	Cadaver	6	67	M	73	175	50.0	L/S	12	3
9001D	Hybrid III	7					47.0	L/S			43	22	0.69
9002D	Hybrid III	7					48.0	L/S			45	28	0.77
9013C	Cadaver	7	34	M	71	180	48.0	L/S	0	1
9003D	Hybrid III	7					48.0	AB only			57	13	0.76
9014C	Cadaver	7	31	M	70	170	47.0	AB only	0	0
9207C	Cadaver	7	25	M	74	184	49.0	AB only	0	0
9212C	Cadaver	7	38	M	79	174	47.0	AB only	0	0

Restraint Codes: 2-pt – shoulder belt only, L/S – lap and shoulder belt, F/L – force-limiting L/S, AB – airbag. Note: “P” in the test number represents tests performed with subjects in the right-front passenger position.

^*Test details may be found in the listed references: 1. Kuppa and Eppinger 1998, 2. Crandall et al. 1997, 3. Shaw et al. 2000, 4. Kent et al. 2001b, 5. Kent et al. 2001c. 6. Yoganandan et al. 1991, 7. Kallieris et al. 1995. If reference not given more information is available from author.