Construction and evaluation of thoracic injury risk curves for a finite element human body model in frontal car crashes

Accident Analysis and Prevention 85 (2015) 73–82

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Construction and evaluation of thoracic injury risk curves for a finite element human body model in frontal car crashes Manuel Mendoza-Vazquez ∗ , Johan Davidsson, Karin Brolin Vehicle Safety Division, Department of Applied Mechanics, Chalmers University of Technology, Gothenburg, Sweden

a r t i c l e

i n f o

Article history: Received 18 September 2014 Received in revised form 27 July 2015 Accepted 3 August 2015 Keywords: Injury risk curves Thoracic injury Rib fracture Human body model Finite element analysis

a b s t r a c t There is a need to improve the protection to the thorax of occupants in frontal car crashes. Finite element human body models are a more detailed representation of humans than anthropomorphic test devices (ATDs). On the other hand, there is no clear consensus on the injury criteria and the thresholds to use with finite element human body models to predict rib fractures. The objective of this study was to establish a set of injury risk curves to predict rib fractures using a modified Total HUman Model for Safety (THUMS). Injury criteria at the global, structural and material levels were computed with a modified THUMS in matched Post Mortem Human Subjects (PMHSs) tests. Finally, the quality of each injury risk curve was determined. For the included PMHS tests and the modified THUMS, DcTHOR and shear stress were the criteria at the global and material levels that reached an acceptable quality. The injury risk curves at the structural level did not reach an acceptable quality. © 2015 Elsevier Ltd. All rights reserved.

1. Introduction Frontal crashes account for 10% of all fatalities and 21% of all MAIS3+ of belted occupants in the US (Eigen and Martin, 2005). It has also been shown that thoracic injuries are frequent and severe in this type of crashes, Cuerden et al. (2007) found that as many as 84% of all drivers killed in frontal crashes sustained AIS3+ thoracic injuries. The most common thoracic injuries are rib fractures as described by Carroll et al. (2010) and Eigen et al. (2007). Crandall et al. (2000) found that approximately 61% of all AIS2+ thoracic injuries were rib fractures and that the maximum thoracic AIS was defined by rib fractures for approximately 72% of the occupants sustaining a maximum thoracic AIS2+. Furthermore, Wanek and Mayberry (2004) found that the number of rib fractures is a good indicator of other thoracic and abdominal injuries. A review of the literature illustrated that age was the most important occupant characteristic that influences the injury risk (Mendoza-Vazquez, 2014). Tools that assess the risk of rib fractures and are sensitive to restraint design changes are important for the improvement of

∗ Corresponding author at: Vehicle Safety Division, Department of Applied Mechanics, Chalmers University of Technology, SAFER, Lindholmspiren 3, SE-417 56 Gothenburg, Sweden. E-mail addresses: [email protected] (M. Mendoza-Vazquez), [email protected] (J. Davidsson), [email protected] (K. Brolin). http://dx.doi.org/10.1016/j.aap.2015.08.003 0001-4575/© 2015 Elsevier Ltd. All rights reserved.

restraint systems in cars, which help to reduce the occurrence of rib fractures in frontal car crashes. Anthropomorphic test devices (ATDs) and finite element human body models (FE-HBMs) are tools used to develop and evaluate restraint systems. Typically, ATDs for frontal crashes are instrumented to measure chest compression and spine acceleration, often referred to as global criteria, to study the thoracic injury risk. The maximum chest compression (Cmax) (Kroell et al., 1974), defined as the mid-sternal chest deflection divided by the original chest depth, is a thoracic injury criterion used in regulations and consumer tests to assess the risk of thoracic injuries in frontal crashes. The maximum viscous criterion (VCmax) (Lau and Viano, 1986) was developed in order to predict soft tissue injuries in the thorax by taking the product of the chest deflection and the deflection rate. The maximum chest deflection (Dmax) (Kleinberger et al., 1989) was proposed to capture localised deflections in the chest, as produced by a belt, by measuring the maximum deflection of five different points on the chest. The combined deflection criterion (DC) (Song et al., 2011) and differential deflection criterion (DcTHOR) (Davidsson et al., 2014) were proposed to account for asymmetry in the compression of the thorax. FE-HBMs represent humans in greater detail than ATDs, which allow FE-HBMs to measure these global criteria as well as criteria at the structural and material levels. Development of global criteria for ATDs is ongoing (Song et al., 2011; Trosseille et al., 2013; Davidsson et al., 2014) and FE-HBMs can provide valuable fundamental knowledge on the differences between and potential strength of these global criteria (Brolin et al., 2012).

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With criteria at the material level the FE-HBMs can potentially analyse injury mechanisms at a tissue level (Wismans et al., 2005) and predict injuries to specific organs and tissues. Shen et al. (2005) found that stress obtained from subject specific models best correlated with rib fractures induced by high speed impacts in animal tests. Song et al. (2011) and Forman et al. (2012) have assessed the rib fracture risk using strain-based criteria with FE-HBMs. For criteria at the structural level (Charpail et al., 2005) found that rib deflection at fracture was about 21% in tests for isolated ribs under anteroposterior loading. Several FE-HBMs have been developed in recent years (Iwamoto et al., 2002; Vezin and Verriest, 2005; Vavalle et al., 2013). One frequently used model is the Total HUman Model for Safety (THUMS) (Iwamoto et al., 2002; Shigeta et al., 2009). The rib cortical bone material in THUMS, and other state of the art FE-HBMs, is modelled with an isotropic elasto-plastic material that eliminates elements that reach a certain strain level, indicating the occurrence of a rib fracture. This approach is deterministic in the sense that an exact number of fractures can be predicted given a single set of occupant characteristics, as in Kitagawa and Yasuki (2013). Deterministic approaches are limited for prediction of injury occurrence in a population with varying physical characteristics (Forman et al., 2012), who compared the greatest strain for every rib with a distribution of ultimate strain values obtained from tensile tests and calculated the risk of rib fractures. Hence, material criteria that are not coupled to element elimination can be used to create injury risk curves that capture variability in occupant characteristics. Furthermore, the use of an isotropic model to represent the anisotropic material of rib cortical bone (Viano, 1986), may limit the use of injury criteria at the material level. Therefore, it is not evident that material criteria are best suited to predict thoracic injuries with the FE-HBMs available today, hence structural and global level criteria should also be considered for FE-HBMs. The objective of this study was to recommend a set of injury risk curves for an FE-HBM that predict rib fractures in frontal car crashes. To achieve this, injury risk curves were constructed by relating PMHS injury outcome with computed injury criteria at the global, structural and material levels extracted from a modified THUMS v3 in matched simulations. In addition, age was included as a covariate to construct age adjusted injury risk curves. Finally the injury risk curves for each criterion were compared using the Akaike Information Criterion (AIC) and quality index. The recommended injury risk curves have the potential to contribute to a reduction of thoracic injuries by increasing the use of FE-HBM during the development of restraint systems.

2. Method The FE-HBM used in this study was a modified THUMS v3 (Mendoza-Vazquez et al., 2013), hereafter referred to as modified THUMS. This model represents the trabecular rib bone with hexahedral elements and the cortical bone with shell elements with an elastic modulus of 13 GPa, and a yield stress of 93.5 MPa. For the modified THUMS, the element elimination controlled by plastic strain was deactivated and a refined mesh in the intercostal muscles, bones and flesh of the ribcage was introduced as described by Mroz et al. (2010) and Pipkorn and Kent (2011). This finer mesh, illustrated in Fig. 1, resulted in a mean element length of 3.5 mm for the rib cortical bone elements, compared to 8.4 mm in THUMS v3. The solid elements representing the thoracic flesh in the modified THUMS have a bulk modulus of 1.33 MPa compared to the original 2.29 MPa. The strain–stress curve for the solid elements representing the thoracic internal organs in the modified THUMS was scaled down to provide a better correlation to experimental data (Mendoza-Vazquez et al., 2013). The biofidelity of the modified

Fig. 1. Detail of the finer mesh, showing the ribs, intercostal muscles, rib cartilage, sternum and thoracic flesh.

THUMS has been verified against impactor, table top and sled tests by Mendoza-Vazquez et al. (2013). The pre- and post-processor used were LS-PREPOST (v2.4, LSTC, Livermore, CA, USA), Primer (v10.0, Oasys Ltd., UK), respectively. The finite element solver was LS-DYNA (version 971 R4.2.1, LSTC, Livermore, CA, USA). Data was analysed using in-house code developed in MATLAB (R2007b, The Math Works Inc., Natick, MA, USA). A total of twenty-three PMHS tests with an average stature of 1.77 m, average weight of 70.2 kg and average age of 61 years at time of death were reproduced with the modified THUMS, as shown in Table 1. These tests include impactor, table top and sled tests illustrated in Fig. 2. The impactor tests were reported by Nahum et al. (1970), Kroell et al. (1974) and Bouquet et al. (1994); table top tests by Kent et al. (2004) and sled tests by Shaw et al. (2009). In all impactor tests, the PMHSs were impacted at the middle of the thorax at the height of the 4th intercostal space with a cylindrical pendulum of 152 mm in diameter. In the table top tests, PMHSs were laying freely on a rigid bench while loads were applied at a displacement rate of 1 m/s. The load was either of a hub, belt, double diagonal belt or band type. In the sled tests, PMHSs were seated on a rigid plate, restrained with a three point belt and a knee bolster and subjected to an acceleration pulse. Only tests with rib fracture data and performed on fresh PMHSs, weighing between 54 and 88 kg at a stature between 1.57 and 1.92 m were included. If a PMHS was subjected to multiple tests, as in the table top test case and MRS04 impactor test, only one test per PMHS was considered and only if rib fractures were not detected after that test. A scaling law was applied to the mass of the impactor hitting the modified THUMS, without making any changes to the initial velocity or the modified THUMS. The scaling was based on the method proposed by Mertz (1984), who advised basing the scaling on the effective mass and chest depth, a brief description of this method is included in Appendix A. Injury criteria were extracted from simulations at the time when the chest compression in the modified THUMS reached the same level as the matched PMHS in the table top test. Sled tests were not scaled. The results for the scaling of the impactor tests are shown in Table 2. The descriptions of the models used in the simulations are available in Mendoza-Vazquez et al. (2013). For each simulation, injury criteria were calculated according to the definitions in Appendix B. The global level criteria were maximum chest compression (Cmax) (Kroell et al., 1974), maximum viscous criterion (VCmax) (Lau and Viano, 1986), maximum deflection (Dmax) (Kleinberger et al., 1989), combined deflection (DC) (Song et al., 2011), combined deflection for THOR (DcTHOR) (Davidsson et al., 2014), and total internal energy in the rib cortical bones (TIE). The structural level

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Table 1 PMHS tests reproduced with the modified THUMS for the construction of injury risk curves. Test

PMHS

Reference

Gender

Age at time of death

Weight (kg)

Stature (m)

55

09FM

Nahum et al. (1970)

M

73

76

1.85

NFR 0

60 76 79 83

11FF 18FM 20FM 22FM

Kroell et al. (1971)

F M M M

60 78 29 72

59 66 57 75

1.60 1.76 1.80 1.83

6 11 0 10

171 177 189 200

42FM 45FM 53FM 60FM

Kroell et al. (1974)

M M M M

61 64 75 66

54 64 77 79

1.83 1.82 1.74 1.80

0 10 3 9

MRS04

MRT02

Bouquet et al. (1994)

M

57

76

1.74

1

CADVE87 CADVE54 CADVE246 CADVE190 CADVE155

170 145 189 186 176

Kent et al. (2004)

M M M F F

75 54 79 58 85

65 88 57 61 58

1.78 1.92 1.59 1.78 1.57

0 0 0 0 0

1294 1295 1358 1359 1360 1378 1379 1380

411 403 425 426 428 443 433 441

Shaw et al. (2009)

M M M M M M M M

76 47 54 49 57 72 40 37

70 68 79 76 64 81 88 78

1.78 1.77 1.77 1.84 1.75 1.84 1.79 1.80

6 17 10 8 5 7 8 2

Fig. 2. Modified THUMS in the impactor, table top and sled tests.

criteria were rib end-to-end displacement (E2E) (Charpail et al., 2005; Kindig, 2009), angular change, and internal energy for each rib cortical bone. Criteria at the material level included maximum principal strain and stress, plastic strain, maximum shear stress and maximum von Mises stress. The global criteria in the modified THUMS were measured with respect to a local coordinate system fixed at T8. Cmax was calculated as the maximum deflection along X, as in Fig. 2, of a node at

the mid sternum divided by 230 mm, the original chest depth. All other deflections used to calculate Dmax, DC and DcTHOR were calculated from the time histories of deflection along X of each of the points illustrated in Fig. B1. The total internal energy was computed as the sum of all internal energies of the rib cortical bones for the second to the tenth ribs. The modified THUMS was instrumented with null stiffness springs between the anterior and posterior ends of each rib from

Table 2 Scaled impactor test data used in the reproductions with the modified THUMS. Test

PMHS effective mass (kg)

PMHS chest depth (mm)

Impactor velocity (m/s)

Impactor mass (kg)

Scaled impactor mass (kg)

55 60 76 79 83 171 177 189 200 MRS04

13.8 19.1 41.1 22.2 40.8 29.4 33.8 26.8 35.7 13.6

238 208 219 203 226 216 254 241 222 230

5.1 6.3 6.7 6.7 6.7 4.9 5.1 5.2 4.3 5.8

19.3 19.5 23.6 23.6 23.6 22.9 23.0 23.0 23.0 23.4

14.4 24.8 28.7 33.9 25.6 28.0 16.8 19.1 26.2 17.8

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Table 3 AIC values and chosen distributions for no age and age adjusted survival analysis. Level

Injury criterion

Without age adjustment

Age adjustment

Distribution

AIC

Distribution

AIC

Global

Cmax (%) VCmax (m/s) Dmax (%) DC (mm) DcTHOR (mm) TIE (mJ)

Log-logistic Log-logistic Log-logistic Log-normal Log-logistic Log-logistic

26.9 31.9 25.1 23.3 19.0 26.4

Log-logistic Log-logistic Log-normal Log-normal Weibull Log-logistic

28.8 33.8 26.4 23.8 16.3 28.1

Structural

E2E (%) IE (mJ) Angular change (%)

Log-logistic Log-logistic Weibull

32.8 23.6 25.9

Log-logistic Log-normal Weibull

34.7 24.1 27.4

Material

Max principal strain (%) Plastic strain (%) Max principal stress (MPa) Shear stress (MPa) von Mises stress (MPa)

Log-logistic Weibull Log-logistic Log-normal Log-logistic

26.5 22.7 24.1 20.0 24.7

Log-logistic Log-normal Log-normal Weibull Log-normal

28.4 24.1 25.2 15.6 26.0

the second to the tenth rib. The length of the springs was projected on the corresponding rib plane, and end-to-end displacement was computed for each rib as the percentage change of the projected length. The angular change was measured as the percentage change of the angle between the anterior end, most lateral point and posterior end of each rib. The internal energy was calculated with LS-DYNA for each rib cortical bone for ribs two to ten. The criteria at material level were calculated as in Appendix B and based on the principal stresses, principal strains and plastic strains in the rib cortical bone elements of the second to the tenth rib. Any elements having at least one node attached to truss or beam elements were not considered in the analysis. Elements sharing nodes with the shell elements representing the intercostal muscles were also discarded. To construct the injury risk curves, a PMHS test was considered injurious if the number of fractured ribs (NFR) was two or more, corresponding to an AIS2+ injury (Association for the Advancement of Automotive Medicine, 2008). Then, the maximum of each global injury criteria obtained with the modified THUMS was matched to the injury outcome of the respective PMHS test. For the structural and material criteria, the maximum value for each criterion and rib was calculated and the second greatest rib value was matched to the injury outcome of the respective PMHS test. The maximum value for each material criterion and rib was defined based on the element in the rib cortical bone reaching the greatest criterion value. All injurious tests were considered as left censored, since the threshold values were less than or equal to the corresponding computed criteria values, and all non-injurious tests as right censored, since the threshold values were greater than the computed criteria values, during the parametric survival analysis performed in R (R Core Team, 2012). The Weibull, log-normal and log-logistic distributions were calculated for each injury criterion, since they yield zero risk of injury for zero stimulus. Then, the AIC was computed for each distribution and each injury criterion. In the next step, age was included as a covariate in the survival analysis. The AIC was also calculated for these curves followed by the construction of a nonage adjusted and an age adjusted curve for each injury criterion. The age adjusted curve corresponds to 61 years, the median age at time of death in the sample. The distribution presenting the lowest AIC (Burnham et al., 2002) was then selected for each injury criterion and age adjustment condition. Finally, the injury risk curve presenting the lowest AIC among the age adjustment conditions was established as the injury risk curve for that particular criterion. The relative width of the 95% confidence interval to the value of the stimulus was calculated for 5%, 25% and 50% injury risks. The quality index for these values was assessed as in Petitjean et al.

(2012). The criteria with the lowest AIC and a relative width of the 95% confidence interval less than 1.5 at the three stated injury risk levels were selected for each criteria level. The model configurations and injury risk curves described previously are referred to as baseline in the following parametric study. A parametric study in form of a fractional factorial design with four variables and two levels for each variable was implemented to detect the sensitivity of the different criteria and corresponding injury risk curve to small variations in the restraint position and rib cortical bone material properties. The variables included vertical position of the impactor/belt, horizontal position of the impactor/belt, elastic modulus of the rib cortical bone, and yield stress of the rib cortical bone. The levels of each variable related to the position were ±2 mm with respect to the baseline position and the variables related to the material properties varied by ±2% with respect to the baseline values. The injury risk curves are defined by two parameters, shape and location; that were considered the responses for the fractional factorial design. The curve parameters were evaluated for the distribution and age adjustment condition that generated the lowest AIC value for each criterion in the baseline configuration. The ratio range of the injury risk curve parameters was defined as the range of all ratios for each parameter with respect to the parameter in the baseline injury risk curve. 3. Results All injury criteria were extracted from the simulations and processed as described. The AIC for each injury risk curve with and without age adjustment is shown in Table 3. The inclusion of age as a covariate in the survival analysis reduced the AIC for the DcTHOR and shear stress criteria with more than two units, improving the injury risk curve fit. Age was a statistically significant covariate at the 5% level for both DcTHOR and shear stress injury risk curves. In all other cases the AIC difference between the curves with and without age adjustment was less than two. The lowest AIC is indicated in bold in Table 3 for each injury criterion and age adjustment condition. As described in Section 2, the material criteria were extracted from the element with the greatest value on each rib. Extracting the material criteria from the element with the second or third greatest value increased the AIC for all injury risk curves with respect to these criteria. DcTHOR and shear stress injury risk curves with age adjustment are the curves with the lowest AIC among all curves constructed in this study. The quality indexes for each criterion, and the distribution and age adjustment condition with the lowest AIC value are displayed

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Fig. 3. Injury risk curves, age adjusted to 61 years, with 95% confidence interval for the DcTHOR and shear stress injury criteria.

Table 4 Distribution and parameters for the age adjusted curves.

parameter, calculated as in (2) and  is the shape parameter, calculated as in (3)

Criterion

Distribution

Intercept

Age coefficient

Log scale

DcTHOR Shear stress

Weibull Weibull

4.618 4.338

−0.011 −0.003

−2.388 −4.096



∀ x ≥ 0; 0 ∀ x < 0

(2)

where age is the age of interest, in years; AC is the age coefficient from Table 4 and I is the intercept value from Table 4

in Table 5. All risk curves at a relative width less than 1.5 at the three evaluated risk levels appear in bold in Table 5. The relative width of the 95% confidence interval is also less than 1.5 for all three chosen injury risk levels. The internal energy (IE) is the criterion at the structural level with lowest AIC, although the relative width of the 95% confidence interval was greater than 1.5 at two of the three chosen injury risk levels. No other criteria at the structural level reached a 95% confidence interval under 1.5. The injury risk curves for the DcTHOR and shear stress criterion adjusted for age 61 are displayed in Fig. 3. The equations, the cumulative distribution function (CDF), and the parameters for these two injury risk curves are provided in Table 4 and Eq. (1): CDFWeibull = 1 − exp−(x/y)

 = exp(age × AC + I)

(1)

where CDFWeibull is the cumulative distribution function for a Weibull distribution; x is the injury criterion;  is the scale

=

1 exp(LS)

(3)

where LS is the log scale value from Table 4. The results of the parametric study are displayed in Table 6. The global criteria were less sensitive to the small variations in impactor and restraint position and rib cortical bone material properties explored in this study since their curve parameters varied less among all three criteria levels. At the structural and material levels, it was the shape parameter that showed the largest variations. The ratio range for the location parameter of the maximum principal strain risk curve was the greatest among all criteria, while the angular change criterion showed the greatest ratio range for the shape parameter. The baseline curve for the DcTHOR and shear stress, together with the injury risk curves constructed in the fractional factorial design are displayed in Fig. 4. As indicated by the narrow ratio ranges, the DcTHOR injury risk curve has less variation between the baseline curve and those from the fractional factorial design. The ratio range for the shape of the shear stress curves was

Table 5 Relative width of the 95% confidence interval at 5%, 25% and 50% risk levels. Level

Injury criterion

Distribution

Age adjustment

Relative width of the 95% confidence interval 5% risk

25% risk

50% risk

Global

Cmax (%) VCmax (m/s) Dmax (%) DC (mm) DcTHOR (mm) TIE (mJ)

Log-logistic Log-logistic Log-logistic Log-normal Log-logistic Log-logistic

No No No No Yes No

2.1 97.4 1.3 1.5 0.6 4.4

1.0 9.2 0.7 0.9 0.3 1.9

0.6 2.7 0.4 0.5 0.2 1.1

Structural

E2E (%) IE (mJ) Angular change (%)

Log-logistic Log-logistic Weibull

No No No

39.0 3.6 2.6

5.6 1.7 1.1

1.7 1.0 0.6

Material

Max principal strain (%) Plastic strain (%) Max principal stress (MPa) Shear stress (MPa) von Mises stress (MPa)

Log-logistic Weibull Log-logistic Log-normal Log-logistic

No No No Yes No

3.0 3.4 0.5 0.2 0.5

1.4 1.4 0.3 0.1 0.3

0.8 0.8 0.2 0.1 0.2

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Table 6 Ratio ranges for the fractional factorial design. Level

Injury criterion

Location Baseline

Global

Cmax (%) VCmax (m/s) Dmax (%) DC (mm) DcTHOR (mm) TIE (mJ)

Structural

E2E (%) IE (mJ) Angular change (%)

Material

Max principal strain (%) Plastic strain (%) Max principal stress (MPa) Shear stress (MPa) von Mises stress (MPa)

Shape Ratio range

Baseline

Ratio range

3.092 −1.667 3.220 4.064 50.55 9.429

0.98–1.00 0.96–1.00 0.96–1.00 0.98–1.00 0.99–1.00 1.00–1.01

0.252 1.080 0.169 0.304 10.896 0.443

0.97–1.14 0.95–1.03 0.97–1.47 0.97–1.11 1.02–1.08 0.92–0.95

1.920 7.638 1.008

1.05–1.09 0.99–1.01 1.07–1.15

0.702 0.341 0.328

0.65–0.92 0.89–0.96 1.28–1.92

0.592 3.526 4.771 63.20 4.717

0.89–1.36 0.85–0.95 0.99–1.00 0.97–1.01 0.99–1.00

0.310 2.226 0.061 60.13 0.062

0.55–0.99 1.11–1.72 0.80–1.19 0.33–0.96 0.91–1.22

among the greatest, consistent with the varying slopes of the curves in Fig. 4. 4. Discussion In this study, fourteen NFR2+ risk curves for a modified THUMS have been constructed at the global, structural and material levels. Shear stress in the rib cortical bone presented the best AIC value and quality index. DcTHOR presented the best value and index among the global criteria and internal energy among the structural criteria. In a similar study, but with an updated THOR ATD, Davidsson et al. (2014) found that DcTHOR obtained a good injury risk quality index. The findings in the current work and those from Davidsson et al. (2014) support the idea that a global criterion should not only consider chest deflection, but differential deflection as well to capture effects of asymmetric loads on the chest, i.e. from a diagonal belt. None of the injury risk curves for the criteria at the structural level showed acceptable quality; their AIC and relative width of the confidence intervals were not within specified limits. The high AIC and wide confidence intervals for both end-to-end displacement and angular change criteria might be due to the measures mainly being of the anteroposterior compression of the ribs. Additional mechanisms, i.e. rotation of the ribs and bending out of the plane were found by Vezin and Berthet (2009) while dynamically loading eviscerated rib cages. These additional mechanisms were also identified by Mendoza-Vazquez et al. (2013) in simulations of impactor

and sled tests with the modified THUMS. These mechanisms may also contribute to rib fractures in frontal crashes, but are not sensed by the rib end-to-end displacement or the angular change criteria. The internal energy criterion is based on the sum of the distortion energy in all elements representing the rib cortical bone for each rib, under the premise that a rib can accommodate a limited amount of distortion energy before it fails. Since the internal energy criterion is based on the sum, distinction has not been made between a state where the internal energy is distributed evenly among all elements and a state where the internal energy is concentrated in a small number of elements. This is likely the reason why internal energy, as defined in this study, was found to have a low quality index. For the same reason, injury risk curves for internal energy would probably improve their AIC and relative width of the confidence interval if they are constructed at the material level, i.e. assessed at individual shell elements, which would be similar to measuring the von Mises stress. The cortical bone shear stress value at 50% risk of rib fracture (NFR2+) obtained in this study was 59.4 MPa, compared to an average shear strength of 51.6 MPa and 65.3 MPa reported by Turner et al. (2001) from shear tests on human femoral cortical bone along the longitudinal and transversal directions respectively. The first principal stress value at 50% risk obtained in the current study was 119.7 MPa. This value is also comparable to the values reported in the literature. The average ultimate tensile stress in coupon tests of rib cortical bone reported by Kemper et al. (2005, 2007) was

Fig. 4. Injury risk curves for the baseline conditions (solid line) and injury risk curves for the fractional factorial design (dashed lines).

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127.5 MPa. Also from a series of rib cortical bone coupon tests, Subit et al. (2011) found an average ultimate tensile stress of 124.6 MPa. The first principal strain at 50% risk of rib fracture at the NFR2+ level obtained in the current study was 1.92%, which also compares favourably with the average ultimate strain of 1.05% reported by Subit et al. (2011), and with the 2.6 reported by (Kemper et al., 2005, 2007). In conclusion, the stress and strain results at 50% risk of NFR2+ in this study are similar to the average stress and strain values in previous studies on human cortical bone. The injury risk curves at the material level were constructed based on the criteria value of the rib with the second greatest value. This construction method implies that the injury risk curves at the material level describe the fracture threshold of rib cortical bone. To separate injurious from non-injurious cases a value of a 50% risk of injury is usually applied (Forman et al., 2012). Therefore, the comparison of stress and strain values at 50% risk of NFR2+ to the average stress and strain values for human cortical bone is relevant. The inclusion of age as covariate improved the AIC value for the DcTHOR and shear stress criteria but not for any other criteria. The result of this improvement was as expected; an increment in age shifted the injury risk curve to the left. Wall et al. (1979) found when investigating the change of tensile ultimate stress in human femoral cortical bone, a decrease by 20% when comparing age groups 30–39 to 70–79. The shear stress at 50% risk of NFR2+ decreased in this study by 12% when comparing ages 35–75. The age effect found in this study for stress in the rib cortical bone seems to be in line with previous studies. Since the sizes of the PMHSs were different to the 50th percentile male, scaling of the test conditions was performed. The simulations of the table top tests were halted at the same ratio chest deflection initial chest depth as the corresponding PMHS tests. The sled tests were not scaled since it is the inherent inertia of the modified THUMS or the PMHS that loads their ribcages. In the impactor tests, scaling was performed on the impactor mass while the impactor velocity was kept as in the original tests in order to keep the loading rate, and by that the viscous responses, identical in the simulations and the original tests. The applied scaling method assumes geometric similarity between subjects, which is a generally accepted assumption in the development of injury risk curves for ATDs as seen in the WorldSID in (Petitjean et al., 2012). An alternative approach would have been to scale THUMS to match the anthropometry of each subject, but this was not carried out due to the lack of detailed PMHS anthropometry data. This study focused on frontal crashes and most of the evaluated injury criteria, especially those at the global and structural levels, were based on measures related to chest compression or anteroposterior compression of the ribs. Therefore, one advantage of the material level criteria is that they could potentially be used in other crash configurations, since they are not based on measures of the chest compression or anteroposterior compression of the ribs. A criterion at the material level seems to be better suited for use in different crash configurations. In this study, rib cortical bone was considered as an isotropic and homogeneous material with a piecewise linear plastic behaviour. In all injurious PMHS tests simulated with the modified THUMS, the rib cortical bone reached the plastic region. In the plastic region, the secant modulus decreases with respect to the elastic modulus. In the modified THUMS and from plasticity onset to a strain of 1.4%, the secant modulus is around 30% of the elastic modulus. After the rib strain has reached 1.4%, the secant modulus in the modified THUMS is approximately 12% of the elastic modulus. Such reductions in the moduli cause stresses to vary at a lower rate and strains at a higher rate; which could explain the fact that stress based criteria performed better than strain based criteria in the current study. The injury risk curves developed in this study were based on matched PMHS tests. It is known that PMHSs are more fragile than

79

living humans. Foret-Bruno et al. (1978) found that tests with fresh PMHSs matching real world accidents overestimated the number of rib fractures by about three to five fractures. In the present study, the NFR in the PMHS was assigned to the matching simulation and correction was not applied to account for differences between PMHSs and living humans. As such the new injury risk curves may overestimate the risk of rib fractures potentially sustained living humans. Some of the PMHSs used in this study suffered clavicle or sternum fractures. These fractures could affect the response of the rib cage and potentially change the injury outcome. However, clavicle and sternum fractures were only present in PMHS’s with NFR2+. Therefore, compensation for the NFR was not necessary to account for clavicle or sternum fractures. About half of the PMHS tests considered in this study were subjected to a symmetric load applied to the chest, as in the impactor tests. Despite this proportion of symmetric and asymmetric loads, the injury curve corresponding to the DcTHOR performed best among the global criteria. DcTHOR has been developed to consider asymmetrical loads, like those generated by a diagonal belt, in an updated THOR ATD. The DcTHOR calculation includes parameters specifically developed for the updated THOR ATD. A new combined deflection criterion for the modified THUMS (DcTHUMS) could be developed by finding specific parameters for the modified THUMS. A larger proportion of tests with asymmetric loads on the chest would be needed for this task. In this study, the same parameters as those for an updated THOR have been used, with good results. Carter et al. (2014), utilising the 2000–2010 National Automotive Sampling System (NASS-CDS) dataset, found that females were more likely to sustain thoracic injuries than males, and that this difference increased with age. Two of the three female PMHSs included in the construction of injury risk curves in this study were considered not injured. The third PMHS was considered injured, but the corresponding simulation showed injury criteria values greater than other male PMHSs. A check of the most influential observations did not identify the female PMHS as any of the most influential subjects. Thus, there is no indication that the inclusion of these female PMHSs would affect the construction of the injury risk curves. In the future when the results of enough number of PMHS tests have been made available, it should be considered to construct injury risk curves specific for males and females. Apart from the limitations discussed above, an important consideration while interpreting the results from the current study is that the injury risk curves are developed using the modified THUMS and applicable to this version. These curves are therefore influenced by the geometry, material models and material properties defined in the modified THUMS. Even if the biofidelity of the modified THUMS has been verified, the risk curves provided in this study might not be directly applicable to other FE-HBMs. It is suggested that the methodology of this paper is applied to construct injury risk curves for other FE-HBMs. In the parametric study and among the curves with acceptable relative widths of the confidence interval, the injury risk curves for DcTHOR varied the least. In a previous study by Brolin et al. (2012), the THUMS showed at the most a drop of 16% in the thoracic effective stiffness while reducing the rib cortical elastic modulus by 50%. Since the variation in elastic modulus in the fractional factorial design was only ±2%, a small variation due to this factor was expected for the criteria based on measures of chest compression as in DcTHOR. DcTHOR is based on the deflection of four points on the chest, making it less sensitive to the shifts of ±2 mm of the impactor, band or belt. In contrast Cmax and Dmax, that only consider the deflection at one point on the chest, displayed a greater ratio range. The shape parameter for the injury risk curves of shear stress in the parametric study displayed a larger variation than for the injury risk curves of DcTHOR, while shear stress is influenced

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by the position of the impactor and restraint loading device as well as the rib cortical material properties. A change in position may modify the rib that sustains the second greatest stress value among the ribs, and more importantly, a change in the yield stress value directly affects the onset of plastic behaviour. Therefore, anatomical and material changes in humans with age, size and gender should be further investigated and eventually implemented in FE-HBMs. The AIC describe how well the constructed injury risk curves model the injuries in the original PMHS tests. The injury risk curves in this study were constructed using data from simulations of twenty-three PMHS tests. This number of tests provided useful injury risk curves but did not allow for checking the different distribution assumptions introduced while constructing the injury risk curves. Neither did this number allow checking for dual injury mechanisms. Hence, there is a need to evaluate the performance of the injury risk functions using other datasets, for example using real world accident data. 5. Conclusions

where Cxxth is the chest compression in percentage; V0xxth is the impactor speed of the xxth percentile PMHS; Lxxth is the characteristic length of the xxth percentile PMHS (chest depth); mxxth is the effective mass of the xxth percentile PMHS; mimpxxth is the impactor mass of the xxth percentile PMHS and kxxth is the stiffness of the xxth percentile PMHS. For a 50th percentile THUMS: C50th =

Acknowledgements Funding for this study was provided by VINNOVA – Swedish Governmental Agency for Innovation Systems through the FFI – Vehicle and Traffic Safety research programme and the industrial partners in the project. The work was carried out at SAFER – Vehicle and Traffic Safety Centre at Chalmers, Gothenburg, Sweden. Project partners were Chalmers, Autoliv Research, Volvo AB, and Volvo Car Corporation. The simulations were performed on resources at Chalmers Centre for Computational Science and Engineering (C3SE) provided by the Swedish National Infrastructure for Computing (SNIC) and resources at Volvo AB.

L50th



×

m50th × mimp50th

×

m50th + mimp50th

1 k50th

(A2)

where C50th is the chest compression in percentage; V050th is the impactor speed of the 50th percentile PMHS; L50th is the characteristic length of the 50th percentile PMHS (chest depth); m50th is the effective mass of the 50th percentile PMHS; mimp50th is the impactor mass of the 50th percentile PMHS and k50th is the stiffness of the 50th percentile PMHS. The compression is equal in both cases, hence from (A1) and (A2):



V0xxth

The best performing thoracic injury criteria calculated with a modified THUMS based on the AIC and quality index of the corresponding injury risk curve with age as the covariate was the shear stress criterion and DcTHOR. Criteria at the structural level did not perform at an acceptable level. This study has also shown that injury risk curves for criteria at the global level that include calculations of deflection of several points on the chest, like DC and DcTHOR, were less sensitive to variations in the material properties of the rib cortical bone and restraint positions than injury risk curves for criteria that include only one deflection measure, such as Cmax. The injury criteria at the material level showed critical values or an injury risk criterion value at 50% risk for NFR2+, consistent with values reported in literature for human cortical bone failure. Finally, this study has provided the injury risk curves for DcTHOR and shear stress to predict risk of NFR2+ using the modified THUMS.

V050th

×

Lxxth

mxxth + mimpxxth



V050th

=

mxxth × mimpxxth

×

L50th

×

1 kxxth

m50th × mimp50th m50th + mimp50th

×

1 k50th

(A3)

If the same velocities are used and the compression in THUMS and the PMHS is equal, the mass of the impactor to be used in the THUMS 50th percentile can be obtained from: L50th × Lxxth



k50th × kxxth



mxxth × mimpxxth mxxth + mimpxxth



=

m50th × mimp50th m50th + mimp50th

(A4)

Following the hypothesis of geometrical similarity, even density distribution and that the elastic modulus for the tissues remain constant between the PMHSs, k =

kxxth 1/3 = m k50th

(A5)

L =

Lxxth 1/3 = m L50th

(A6)

m =

mxxth m50th

(A7)

and from (A4) the impactor mass can be calculated as: mimp50th =

A × m50th m50th − A

(A8)

where mxxth × mimpxxth 12 11/3 × × mxxth + mimpxxth L m

Appendix A. Scaling method

A=

Since the PMHSs are usually not of the same size as the 50th percentile male, scaling is necessary. The objective of this scaling is to expose THUMS 50th percentile to an impact that can be comparable to the impact received by a PMHS with an arbitrary size, like an xxth percentile. The scaling method is based on the spring mass system introduced by Mertz (1984). The main assumption is that THUMS will sustain the same chest deflection (in percentage) as the represented PMHS test. The impactor velocity was kept the same in THUMS and the PMHS tests to avoid changes due to the viscous response. For an xxth percentile PMHS:

The characteristic length is the chest depth and the characteristic mass the effective mass of the thorax.

Cxxth =

V0xxth Lxxth



×

mxxth × mimpxxth mxxth + mimpxxth

×

1 kxxth

(A1)

(A9)

Appendix B. Injury criteria definitions VCmax (Lau and Viano, 1986) was calculated based on Eq. (B1) VCmax =

D(t) dD(t) × dt b

(B1)

where D(t) is the time history of the deflection along X of a node at the mid sternum and b is 230 mm, the initial chest depth. Dmax (Kleinberger et al., 1989) was calculated according to Eq. (B2) Dmax =

max(D(t), UR(t), UL(t), LR(t), LL(t)) × 100 b

(B2)

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81

The von Mises stress (Boresi and Schmidt, 2003) was computed as in Eq. (B9)



vM =

1 [(1 − 2 )2 + (2 − 3 )2 + (3 − 1 )2 ] 2

(B9)

References

Fig. B1. Location of the points on the chest to calculate the global criteria.

where D, UR, UL, LR and LL(t) are the time histories of the deflection along X of each of the points illustrated in Fig. B1 and b is the initial chest depth, 230 mm. The combined deflection DC (Song et al., 2011) was proposed based on simulations of PMHS tests with HUMOS2LAB and was computed as in Eq. (B3) DC = D(t) + Cf · [(dD − Lc) + |(dD − Lc)|]

(B3)

where D(t) is as previously defined, dD = LR(t) − LL(t), Cf is the contribution factor and Lc the characteristic length. For the HUMOS2LAB, Cf = 0.15 and Lc = 24 mm (Song et al., 2011). These values were used for the modified THUMS in this study. DcTHOR was calculated as in Eq. (B4) DcTHOR = Dm + dDup + Ddlw Dm =

(|UR(t)|max + |UL(t)|max + |LR(t)|max + |LL(t)|max 4



|UL(t) − UR(t)|max − A

(B4)

dDup =



0 if |UL(t) − UR(t)|max ≤ A or min(|UL(t)|max , |UR(t)|max ) ≤ B |LL(t) − LR(t)|max − A

dDlw = 0 if |LL(t) − LR(t)|max ≤ A or min(|LL(t)|max , |LR(t)|max ) ≤ B

where previously defined variables are applied. The constants A = 20 and B = 5, proposed by Davidsson et al. (2014) for a THOR ATD, were used for the modified THUMS in this study. The end-to-end displacement (Charpail et al., 2005; Kindig, 2009) for each rib was computed as in Eq. (B5) E2Es,r =

0 −L | max |Ls,r s,r 0 Ls,r

× 100

(B5)

where Ls,r is the instantaneous length of the spring attached to a 0 is the initial length of the spring rib on side s and rib level r. Ls,r attached to a rib on side s and rib level r. The maximum principal stresses and strains (Boresi and Schmidt, 2003) were calculated as in Eqs. (B6) and (B7)  = max(|1 |, |2 |, |3 |)

(B6)

ε = max(|ε1 |, |ε2 |, |ε3 |)

(B7)

where  1 ,  2 , and  3 are the principal stresses and ε1 , ε2 , and ε3 are the principal strains. The maximum shear stresses (Boresi and Schmidt, 2003) were calculated as in Eq. (B8)  = max

 | −  | | −  | | −  |  2 3 3 1 1 2 2

;

2

;

2

(B8)

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