Head injury criteria assessment using head kinematics from crash tests and accident reconstructions

Abstract Objective The aim of this study was to assess head injury criteria based on their correlation to brain strain in a Finite Element (FE) head model (the KTH Royal Institute of Technology model), by simulation of head kinematics data from frontal and side crash tests with Anthropomorphic Test Devices (ATDs), and from Human Body Model (HBM) accident reconstructions. Methods Six Degrees of Freedom (DoF) head kinematic data was extracted from 221 crash tests, consisting of frontal impacts with the THOR-50M ATD, near-side and far-side impacts with the WorldSID-50M ATD, and from 19 FE HBM accident reconstructions. The head injury criteria HIC15, HIP, BrIC, UBrIC, DAMAGE and CIBIC were calculated, and FE head model simulations were conducted using the six DoF kinematics data. The 100th, 99th, and 95th percentile Maximum Principal Strains (MPS) of the brain were extracted and linear regression models with respect to the injury criteria were created. The injury criteria were then evaluated based on the coefficient of determination, R2, and the Normalized Root Mean Square Error (NRMSE) of each regression model. Results For all the data sets combined and for the WorldSID far-side data, CIBIC had the best goodness of fit, with R2 of 0.76 and 0.85. For frontal impacts with THOR and the combined ATD data set, DAMAGE had highest R2, 0.83 and 0.78, respectively. Injury criteria including translational accelerations were ranked lower, and BrIC were among the three lowest ranked for most data sets evaluated. UBrIC generally ranked after DAMAGE and CIBIC with respect to the goodness of fit but had the lowest NRMSE for all data sets. Conclusions The two mass-spring-damper brain surrogate model criteria, DAMAGE and CIBIC, were best in capturing the head model MPS response for both the THOR and WorldSID data sets. BrIC had lower correlation to the head model MPS and performed marginally better than the linear acceleration only criteria for all the data sets combined. This study supports the suitability of DAMAGE and CIBIC as brain injury criteria to be used with THOR-50M and WorldSID-50M in vehicle crash test conditions, as they outperform BrIC.


Introduction
Traumatic brain injury remains as one of the most frequent injuries for vehicle occupants. A review of NASS-CDS head AIS2þ injuries for 1993-2015 showed that while the risk of skull fracture in frontal impacts was constant over the period, the risk of brain MAIS2þ injury increased (Craig et al. 2020). For this reason, the Brain Injury Criterion (BrIC, Takhounts et al. 2013), was suggested to be introduced for use with the THOR-50M Anthropometric Test Device (ATD, Craig et al. 2020). BrIC is a function of the head peak rotational velocities. Hence, it accounts for head rotational motion which is an important predictor for brain injury. Rotational induced brain injuries can be diffuse brain injuries ranging from mild concussion to cerebral concussion and diffuse axonal injury including disruption of axons (Schmitt et al. 2019).
The advancement of Finite Element (FE) models of the human head and brain has enabled the creation of functions relating six Degrees of Freedom (DoF) head kinematics to the deformation of the brain tissue. In a validated human FE head model (Kleiven 2007;Takhounts et al. 2008;Mao et al. 2013), the strain of the brain tissue should be proportional to the deformation of a human brain subject to the same impact. This has been used by several authors to create brain injury criteria relating head kinematics, which can be measured in a vehicle crash test using an ATD, to brain Maximum Principal Strain (MPS) and thereby ultimately estimating the risk of brain injury (Wu et al. 2022). This was the basis for BrIC that relates peak rotational velocities in the impact to brain deformation in the form of MPS. The parameters for BrIC were established through linear regression of brain MPS and a Cumulative Strain Damage Measure (CSDM) using the GHBMC 50th percentile male (M50) FE head model (Mao et al. 2013) and the SIMon M50 FE head model (Takhounts et al. 2008) in simulations with ATD head kinematics from crash tests and pendulum impacts (Takhounts et al. 2013). Later studies have followed the same method, but different novel criteria formulations have been proposed. Gabler et al. (2018b) simulated 1,595 head impacts from a range of impact conditions (automotive frontal, oblique, side, and pedestrian impact, as well as impactor tests), with the GHBMC M50 head model and SIMon, and formulated the Universal Brain Injury Criterion (UBrIC) based on the head's three peak rotational velocities and accelerations. Furthermore, two other criteria utilized simplified multibody models with mass-spring-damper systems to predict brain deformation. The Diffuse Axonal Multi-Axis General Evaluation (DAMAGE, Gabler et al. 2018a) criterion was proposed as a function of the max resultant displacement of three coupled one-dimensional mass-spring-damper systems, and model parameters were optimized to fit the GHBMC M50 head model MPS response using synthetic signals and verified with respect to a large range of head impact simulations with the same head model. The Convolution of Impulse response for Brain Injury Criterion (CIBIC, Takahashi and Yanaoka 2019) was suggested as the resultant displacement of three individual mass-spring-damper systems, one for each rotational axis, and was fit to correlate with the GHBMC M50 head model MPS and verified with respect to 230 frontal, oblique, side and pedestrian impacts. These studies evaluated the relative performance of the suggested brain injury criteria based on the strength of the correlation with MPS using the coefficient of determination (R 2 ). For most of the studies, high goodness of fit (high R 2 ) values were reported. For instance, BrIC was reported as related to head model MPS by 1.19 Ã MPS with an R 2 of 0.98 (Craig et al. 2020); UBrIC had an R 2 of 0.93 to GHBMC M50 head model MPS (Gabler et al. 2018b); DAMAGE had an R 2 of 0.96 for a linear regression to GHBMC M50 head model MPS in 1,747 assessment impacts (Gabler et al. 2018a); and, lastly, CIBIC which had an R 2 of 0.83 for the combined crash data set that it was assessed with respect to (Takahashi and Yanaoka 2019).
Some of these novel brain injury criteria are currently being suggested to be used for vehicle assessment, such as DAMAGE, which was proposed to be used as a modifier for the THOR-50M ATD in the Euro NCAP movable progressive deformable barrier test (Euro NCAP 2021), and the use of BrIC for THOR-50M by NHTSA (Craig et al. 2020). There has been some previous work to assess the general applicability of these new brain injury criteria by assessing them with respect to other FE head models, than they were originally developed with. van Slagmaat et al. (2019) showed quite poor correlation to two other FE head model responses, while the correlation was relatively high for DAMAGE and UBrIC to the GHBMC M50 head model, which the criteria were developed with.
The aim of the present study was to expand the assessment of some newly proposed brain injury criteria by comparing their ability to predict brain strain from another head FE model than the one they were developed with. As all these new brain injury criteria include head rotational kinematics only, two head injury criteria including linear head accelerations were included as well. The criteria were assessed by simulation of head kinematics data from frontal and side crash tests with ATDs, and from Human Body Model (HBM) accident reconstructions.

Method
The KTH Royal Institute of Technology FE head model (Kleiven 2007;Fahlstedt et al. 2021Fahlstedt et al. , 2022 was used for simulations with six DOF head kinematics data from 240 automotive impacts. Three six DOF head kinematic data sets were extracted from the Volvo Cars crash test database: 64 frontal impact tests with the THOR-50M ATD as driver (42) and passenger (22), in mainly oblique (18) and movable progressive deformable barrier (37) tests were included. Furthermore, six DOF head data from the WorldSID-50M ATD in 95 near-side and 62 far-side impacts were included in the analysis, from barrier impacts (89) and from pole impacts (68). The ATD data was recorded using a combination of three linear accelerometers and three angular rate gyroscope sensors. Additionally, as a fourth data set, head kinematics from 19 detailed frontal impact accident reconstructions with an FE HBM ) were included. The ATD translational accelerations were processed by a SAE J211 Channel Filter Class (CFC) 1000 filter while a CFC180 filter was used for the accident reconstruction translational accelerations. For the rotational velocity data from all data sources, a CFC60 filter was used.
The six DOF head kinematics data was applied to the head center of gravity as the boundary condition for a simulation with the head model over a time interval of 0.0-0.17 s to exclude any secondary head impacts from the analysis. Simulations were run using LS-DYNA SMP R6.1.0 double precision (ANSYS/LST, Livermore, California) on Intel Xeon E5-2690 v4 CPUs (28 cores per simulation). The first principal Green-Lagrange MPS for each element of the brain was evaluated using META version 21.1.3 (BETA CAE Systems, Luzern, Switzerland). The MPS value of any element in each simulation (the 100th percentile strain value), as well as the 99th and 95th percentile peak strain values were analyzed, as the method to extract the peak strain can affect injury prediction from the head model's responses (Fahlstedt et al. 2022).
Six head injury criteria were calculated for each set of data. Two of these included head translational accelerations, the Head Injury Criterion with a maximum 15 ms interval (HIC 15 ) and Head Impact Power (HIP, Newman et al. 2000), utilizing a combination of translational and rotational head accelerations. Two were empirical derived brain injury criteria using head rotational velocity information only: BrIC (Takhounts et al. 2013) with critical values x xC ¼ 66.25 rad/s, x yC ¼ 56.45 rad/s, and x zC ¼ 42.87 rad/s, and UBrIC (Gabler et al. 2018b) with critical values (x xcr ¼ 211 rad/s, x ycr ¼ 171 rad/s, x ycr ¼ 115 rad/s, a xcr ¼ 20 krad/ s, 2 a ycr ¼ 10.3 krad/s, 2 a ycr ¼ 7.76 krad/s 2 ) fit to brain MPS of the GHBMC M50 head model using r ¼ 2. Two brain injury criteria utilizing head rotational acceleration data only and multibody mass-spring-damper models which have been optimized toward FE head model MPS were included. DAMAGE (Gabler et al. 2018a) was calculated as a function of the max resultant displacement of three coupled onedimensional mass-spring-damper systems. CIBIC (Takahashi and Yanaoka 2019) was calculated as the resultant displacement of three individual mass-spring-damper systems, one for each rotational axis. Rotational acceleration signals for DAMAGE and CIBIC were generated from the filtered rotational velocity signals through differentiation with the central difference method.
Linear regression models were created for each head injury criterion relative to peak brain MPS using Matlab's (Mathworks, Natick, MA) fitlm function. The goodness of fit for each generated model was assessed by comparing the coefficient of determination, R 2 , for the models as well as the Coefficient of Variation (CV) or Normalized Root Mean Square Error (NRMSE, Takhounts et al. 2013;Gabler et al. 2018a) which were calculated as the RMSE divided by mean of the dependent variable for each model.

Results
Filtering the data from the 100th percentile to 99th or 95th percentile decreased the ranges and median values of the brain MPS distributions for the 240 head model simulations made, Figure 1. For the THOR frontal, WorldSID near-side and WorldSID far-side impacts, the median values were similar for the filtered MPS, and were 0.21, 0.21, and 0.23 for the 99th percentile strain values, respectively. For the frontal and nearside impacts, a few MPS values above 0.43 were found, which was the high end of the range for the far-side impact data. The accident reconstruction data set had a larger range, up to 0.84, and median value of 0.33 for the 99th percentile MPS value.
The larger range of the accident reconstruction data was visible also in the fitted linear models, Figure 2 and Figure  For all the linear models of brain MPS relative to each of the six head injury criteria, Table 1, all the evaluated criteria were related to brain MPS (p ( 0.05), except HIP for the accident reconstruction data set. For the 100th percentile strain and all data combined, the best goodness of fit relative to the peak brain MPS was found for CIBIC, which had an R 2 value of 0.69, followed by UBrIC and DAMAGE at 0.58 and 0.56, respectively, Table 1. Filtering the MPS data to the 99th and 95th percentile values increased the goodness of fit for all linear models. The step was largest when comparing the 100th value to the 99th value, for instance DAMAGE was improved to 0.68 for the 99th percentile MPS, while additional filtering to the 95th percentile only increased it to 0.70. The filtering did not change the ranking of any of the criteria.
The HBM accident reconstruction data provided a different ranking than the ATD data, with UBrIC being the best predictor for brain MPS, followed by BrIC. For ranking the ATD data only, without the accident reconstruction data, DAMAGE was the best predictor with an R 2 of 0.78, and for frontal impact with THOR DAMAGE was also performing best with an R 2 of 0.83, while for side impact with WorldSID CIBIC had high R 2 values, 0.81 and 0.85, for near-side and far-side impact, respectively.
Ranking the injury criteria for their NRMSE resulted in less variation in rank, Table 2 in the Online Appendix. UBrIC had the lowest NRMSE for all evaluated data sets, with a range of 0.09-0.15, followed by CIBIC (0.17-0.32) which had the second lowest NRMSE for all datasets except for the THOR frontal impacts, for which DAMAGE (0.21-0.42) came in second. BrIC (range 0.20-0.33) came in third for most datasets, followed by DAMAGE, HIP (range 0.3-0.74) and HIC 15 (0.41-0.82).

Discussion
In this study, six head injury criteria were assessed by comparing their ability to predict the brain strain from a FE head model (Kleiven 2007) in simulations of six DOF head kinematics data from 240 automotive impacts, coming from frontal impact tests with the THOR ATD, side impact tests with the WorldSID, and from frontal impact accident reconstructions with a FE HBM. For each set of head kinematics data, brain MPS was extracted, and a number of brain injury criteria were calculated with the aim to verify or refute their ability to predict human brain deformation using another head model and sets of head impact data than they were developed to fit (the GHBMC M50 head model and SIMon). In addition to the brain injury criteria, two injury criteria utilizing translational accelerations, HIC 15 and HIP, were included. The underlying assumption for this approach, just as for the studies which developed the included brain injury criteria (Takhounts et al. 2013;Gabler et al. 2018aGabler et al. , 2018b Takahashi and Yanaoka 2019) is that FE head model brain MPS correspond to the risk of brain injury, as shown for instance by Wu et al. (2022). This study only assesses the ability of the evaluated head injury criteria to predict FE head model MPS, and not the ability of the criteria to predict the risk of injury which requires an injury risk function relating the criteria severity metric to injury risk. The KTH head model was chosen to be used based on its availability. Some of its features relative to other FE head models are that it uses lower number of elements (25,000) compared to the GHBMC M50 (271,000) and SIMon (46,000). Furthermore, it utilizes a hyperelastic Ogden material model with Prony series viscoelasticity, while the other two models have linear viscoelastic material models. Two of the assessed brain injury criteria, DAMAGE and CIBIC, are based on linear viscoelastic models, hence this study provides comparison of these criteria to a time dependent viscoelastic FE head model. A study (Miller et al. 2017) comparing head FE models showed that the KTH head model with the Ogden model had CORA scores of the same magnitude as the GHBMC M50 and SIMon models when predicting local brain deformation in experimental human head impact tests. While the present study with the KTH head model contributes as an independent check of the assessed brain injury criteria, it should also be mentioned that this model, just as all FE head models, have their limitations in capturing human brain deformation, as shown for instance by Miller et al. (2017) and Fahlstedt et al. (2021).
Filtering the strain data, from using the MPS of all elements (100th percentile MPS) to the 99th or 95th percentile value, reduced the range of the data, Figure 1, and increased the goodness of fit to brain MPS for all evaluated head and brain injury criteria, Table 1. However, the highest MPS cases for the THOR frontal impacts and WorldSID near-side impacts remained outside the cluster of data, also after filtering, indicating that these cases were indeed high strain events and not caused by local numerical instabilities, Figure  1. The effect of strain filtering on the goodness of fit was evaluated for all the data combined and showed that there was a considerable increase in R 2 when going from the 100th percentile strain value to the 99th percentile value. For the KTH head model this means removing the 40 highest strain elements from the evaluation, as the model has approximately 4,000 elements in the brain. Filtering out more elements to the 95th percentile strain only gave marginally higher goodness of fit. This was similar to the findings of Fahlstedt et al. (2022) who showed that the precision of injury prediction was increased when more filtering was applied for element MPS from the 100th to 99th, 95th and 50th percentile strain values with the KTH head model, but that the largest improvement was found for the 100th to 99th percentile step. Several previous studies (Gabler et al. 2018a(Gabler et al. , 2018bWu et al. 2022) have used the 95th percentile strain value, but for this study the 99th percentile was concluded sufficient and used for the majority of the analysis.
The accident reconstruction data set had larger range and median MPS value than the three ATD data sets, which were all comparable to each other, Figure 1. Furthermore, the accident reconstruction data showed a different ranking order than the ATD data, Table 1. Hence, this data set contributed to lower goodness of fit models with all the combined data than for models with only the combined ATD data. For the accident reconstructions the delta V varied from 34 to 90 km/h , which explains the larger variability in head kinematics than for the ATD  data. The ATD data represented a narrower set of crash conditions. For the wider range accident reconstruction data, the rotational kinematics only criteria UBrIC and BrIC had the highest rank based on goodness of fit, Table 1, which might be an indication that such criteria have better applicability in this type of more varying condition. When assessing the NRMSE for the accident reconstruction data models, UBrIC (NRMSE ¼ 0.11) and BrIC (NMRSE ¼ 0.20) were also the highest ranked models.
The findings in the present study were partially different from a previous study also utilizing the KTH head model to evaluate the head injury criteria. van  For the WorldSID-50M near-side impacts, CIBIC and DAMAGE, which only account for the rotational motion of the head, had the highest coefficients of determination, Table 1. For Rank 3-4 though, a different trend than for the other data sets was found. HIP and HIC 15 , which include or were based solely on the linear head accelerations, had higher R 2 values than for the frontal and far-side impacts, 0.72 and 0.69, respectively, and outperformed the rotational kinematics-based criteria UBrIC and BrIC. The head kinematics in near-side impact was different, with a short distance before head contact with an inflatable curtain (which was present in all the included tests), compared to frontal and far-side impact which gives rise to a longer curved head trajectory. The results here could indicate that for a padded lateral head impact, linear acceleration could play a larger role for brain strain than in frontal or far-side impact.
This study showed that DAMAGE and CIBIC, two simplified multibody mass-spring-damper brain surrogate models, were best suited for capturing the strain response of the KTH head model for both the THOR-50M and WorldSID-50M compared to the other criteria evaluated. BrIC, another candidate for brain injury prediction with ATD, had lower correlation to the KTH FE head model strain. The present study supports the suitability of DAMAGE and CIBIC as brain injury criteria to be used with THOR-50M and WorldSID-50M, showing that they outperform BrIC and the linear acceleration head injury criteria. The rotational kinematics based UBrIC was ranked in third place for the frontal and far-side ATD data sets, and had the highest coefficient of determination for the accident reconstructions, indicating that it might be a better candidate for responses which are outside what is commonly tested in vehicle research and development tests with ATDs.