Implementation and calibration of active small female and average male human body models using low-speed frontal sled tests

Abstract Objective The objective of this study was to implement active muscles in a computationally efficient small female finite element model (54.1 kg, 149.9 cm) suitable for predicting occupant response during precrash braking and low-speed frontal sled tests. We further calibrate and compare its results against an average male model (78.4 kg, 174.9 cm) using the same developmental approach. Methods The active female model (F05-OS + Active) was developed by adding active skeletal muscle elements (n = 232) to the Global Human Body Models Consortium (GHBMC) 5th percentile female simplified occupant model (F05-OS v2.3). The muscle properties and physiological cross-sectional area (PCSA) for each muscle were taken from the M50-OS + Active v2.3 model but PCSAs were mass scaled to a 5th percentile female. A total of 8 simulations were conducted; 2 acceleration pulses (1.0 g and 2.5 g), 2 models (F05-OS + Active and M50-OS + Active), and 2 muscle states (activation and control; e.g., no activation). Each model’s kinematics and reaction forces were compared with experimental data. Occupant responses of 6 5th percentile female and 6 50th percentile male volunteers (n = 12 total) were used. The data depict occupant response in precrash braking and low-speed frontal sled tests in a rigid test buck. All procedures were reviewed and approved by the Virginia Tech institutional review board. Each volunteer was in a relaxed state before the applied acceleration. Results The occupant peak forward excursion results of both active models reasonably match the volunteer data for both pulse severities. The differences between active and control models were found to be significant by Wilcoxon signed-rank test (p < .05). The reaction loads of the active and control models lie within the experimental corridors. Conclusions To the authors’ knowledge, this study is the first to concurrently calibrate and compare equivalently developed computational models of females and males in precrash and low-speed impacts. The modeling approach is capable of capturing the varied kinematics observed in the relaxed condition, which may be an important factor in studies focused on the effects of low-g vehicle dynamics on the occupant position. Finally, the computationally efficient modeling approach is imperative given the long duration (>500 ms) of the events simulated.


Introduction
The World Health Organization (2018) estimated that 1.35 million deaths occur every year due to road traffic accidents. Engineers and policymakers attempt to reduce this number through improved design and effective regulations. The success of such efforts is evident in the year-over-year decrease in the fatality rate per vehicle mile traveled in the United States (NHTSA 2021). Yet more work can be done and much of this is driven by new technology. Approximately 62% of motor vehicle collision fatalities were in frontal collisions in the United States in 2017 (NHTSA 2019). Therefore, it remains necessary to study frontal collisions and improve safety system performance in this condition. However, most safety systems are designed and tested considering occupants in standard seating posture, yet precrash events like autonomous braking, driver-initiated braking, or steering maneuvers may move occupants out of position (Osth et al. 2013;Reed et al. 2018). This deviation from standard seating posture reduces the effectiveness of existing safety systems (Ejima et al. 2008).
Finite element human body models (HBMs) are an increasingly popular and versatile tool available for engineers to use in the design of safety systems. This popularity is due to their greater kinematic biofidelity (i.e., they represent human anatomy) than anthropomorphic test device counterparts (Sarfare et al. 2018). HBMs are generally validated against experimental data in various scenarios before they are deployed in the design process. Most of the existing models (Iwamoto and Nakahira 2015;Davis et al. 2016) are validated in high-speed impact scenarios using experimental data from postmortem human subjects (PMHS) and are suitable for the crash phase. For low-speed impact or precrash events, PMHS subjects fail to represent human response (Beeman et al. 2012). This is due to their lack of muscle activity. The longer duration of precrash and lowspeed events allows ample time for volunteers to react and brace themselves (Meijer et al. 2012). The effect of muscle bracing on occupant kinematics has been reported in many studies (Osth et al. 2013;Huber et al. 2015). Therefore, human volunteer experimental data are necessary for validating HBMs in low-speed and precrash events.
There are many prior studies (Carlsson and Davidsson 2011;Beeman et al. 2012;Osth et al. 2013;) that have collected experimental data for volunteers in similar events, but there remains a lack of volunteers representing small female vehicle occupants. One study (Osth et al. 2013) had 9 female (59.4 ± 5.2 kg) and 11 male (77.5 ± 5.6 kg) volunteers. Another study (Carlsson and Davidsson 2011) had 8 females and 9 males representing various hybrid III anthropomorphic test device sizes based on seating height (4 small females: 54.3 ± 4.9 kg, 4 mid-size females: 68 ± 5.4, 6 mid-size males: 77.8 ± 10.5, and 3 large males: 72 ± 8.2). Both of these studies experimented with only braking events. However, the data were collected in an actual car driving on the road and thus limited the amount of validation that could be put to use for model validation.
This work is further motivated by emerging evidence that the incidence of injury in the female driving population is greater than that of males. Recently, the Insurance Institute for Highway Safety conducted a study using frontal and side crash data from NASS-CDS. They reported that females are at higher risk of Abbreviated Injury Scale 2 extremity injuries than males, which was attributed to physiological differences, and suggested that female-specific crashworthiness improvements are necessary to reduce these injuries (Brumbelow and Jermakian 2021). Similar findings were reported by other researchers (Bose et al. 2011;Parenteau et al. 2013) in the past, which indicates the need for safety systems that take into account the size as well as the sex of the vehicle occupants. HBMs are well positioned to answer this need. Numerous HBMs with active musculatures were developed and validated using volunteer data (Meijer et al. 2012;Iwamoto and Nakahira 2015;Devane et al. 2019;Mishra et al. 2020). Perhaps adding to the discrepancy in outcomes based on sex noted previously, most of these models use volunteer data that are more representative of the mid-size male population rather than other vehicle occupant sizes like small females.
The objectives of this study are 2-fold. The first is to implement active musculature in a 5th percentile female model and calibrate it using experimental data from volunteers of the same body habitus. The second objective is to calibrate the existing 50th percentile male model using experimental data from male volunteers of the same size and compare these 2 model responses in precrash braking and low-speed impact events. Though there are female models previously developed with active musculature (Iwamoto et al. 2013;Mishra et al. 2020), none of them have been exclusively validated using 5th percentile female volunteer data in precrash braking and low-speed frontal impact tests.

Methods
Global Human Body Model Consortiums (GHBMC) simplified occupant average male (M50-OS) and small female (F05-OS) models were used in this study. The active female model (F05-OS þ Active v2.3) was developed by adding all of the major skeletal muscles of the body (n ¼ 232) as 1D beam elements. Muscle properties for each muscle element were taken from the M50-OS þ Active model (v2.3). The physiological cross-sectional areas (PCSAs) for the female F05-OS þ Active were mass scaled from the M50-OS þ Active model PCSAs. The neural excitation delay and muscle activation/deactivation delays were implemented using a first-order low-pass filter (Meijer et al. 2012;Osth et al. 2015). The reaction delay was modeled using a method described in a previous study (Meijer et al. 2012). An updated muscle activation scheme building on prior research (Devane et al. 2019) was employed to account for the various delays mentioned above. The muscle activation strategy is a proportional-integral-derivative (PID) controller-based method that uses joint angles and muscle length as the control variables. The muscles in the neck use both joint angle and muscle length as control variables to model vestibulocollic and cervicocollic muscle reflexes similar to a previous study (Putra et al. 2019). The rest of the muscles in the body use only joint angles to calculate muscle activation.

Volunteer experimental data
A total of 24 tests were carried out with 6 volunteers representing 5th percentile females and 6 50th percentile males in a rigid buck at 2 pulse severities (1.0 g and 2.5 g) and with relaxed muscle conditions  in the frontal direction. The volunteers were unaware of the start of the acceleration pulse. The acceleration pulses in the frontal direction are shown in Figure A1 (see online supplement). The volunteer motion was captured using a VICON motion capture system. The detailed experimental procedure and the volunteers' kinematics were reported by . The steering column, seat back, seat pan, left, and right foot pedal forces were measured using multi-axis load cells and are shown in Figure A2 (see online supplement). The shoulder and lap belt forces were measured using the Denton-3255 seat belt load cell. All forces were inertially compensated and zeroed using an average of 0.75 s pretrigger data for each channel and then the resultant force of each load cell was calculated. The mean and standard deviation of the load cell data were calculated for the female and male volunteers separately. All load cell data were transformed to the SAE J211 coordinate system. All test procedures were reviewed and approved by the Virginia Tech institutional review board (IRB #17-1008). All volunteers were required to sign an informed consent form before participating in the study and at the beginning of each test day.

Simulation setup
Both F05-OS þ Active (v2.3) and M50-OS þ Active (v2.3) models were gravity settled, positioned, and belted in the rigid buck as per the process mentioned in the previous study (Devane et al. 2019). The models were positioned in the buck in such a way that the initial joint angles and static test buck reaction forces match with the volunteer data (Chan, Devane, et al. 2021). The rigid buck was modeled using geometrical data of the test buck. A total of 8 simulations were carried out with 2 models at 2 pulse severities (1.0 g and 2.5 g) and 2 muscle activation states (with and without muscle activation) in relaxed muscle condition (Table A1, see online supplement). The models without muscle activation (F05-OS and M50-OS) were simulated as controls in this study. The simulation setup differences between the male and female models are shown in Figures  1a and 1b. A 3-point belt system similar to the experimental condition was used in the model. The handgrip at the steering was modeled with a contact that constrained the model's hands to the wheel. The simulations were carried out per the methods of the previous study (Devane et al. 2019). The simulations use initial joint angles as target values for the PID controllers for maintaining posture.
The forces at the steering column, seat back, seat pan, left foot, and right foot were measured using contact forces. The shoulder seat belt force was measured at the upper Dring and the lap belt force was measured near the anchor point similar to the test measurement locations. The displacements of the different body markers of the model are measured using the nodal coordinates and compared against volunteer data ). The objective evaluation was carried out using CORA analysis (CORAplus 4.04) and the CORA settings used are reported in Table A2 (see online supplement). The force time-history data were used in the CORA analysis. The CORA score ranges from 0 to 1, with 0 being no correlation and 1 as a perfect correlation. The peak forward excursions of the different body markers were used to test whether the differences between control and active models are statistically significant by performing a Wilcoxon signed-ranked test and a significance value of alpha ¼ .05.

Tuning of controller parameters
Each model consists of 32 joint angle PID controllers for the whole body (Devane et al. 2019) and 210 muscle length PID controllers for neck muscles. The 32 joint angle controllers were grouped into 4 groups (neck, upper extremity, trunk, and lower extremity) and all muscle length controllers were grouped into one for simplicity. The integral gain for the PID controllers is used for removing steady-state error and hence it was assumed that integral gain is the same for all body regions with one exception. No integral gain was used for both joint angle and muscle length controllers in the neck to make sure that the modeling approach is in line with the previous research (Putra et al. 2019). The neck has been the focus of a disproportionate number of studies on active muscle in the past. These assumptions reduced the number of parameters to be tuned to 11 for both models.
To tune the controller parameters, 2 design of experiments (DOEs) were performed for the male and female models. The relaxed 1.0 g and 2.5 g experiments were simulated and analyzed. A total of 236 simulations each were carried out with male and female models. The DOE was performed using LS-OPT (v5.2.1 LST). The space-filling method was used for sampling simulation points. For each simulation, an overall CORA score was calculated by taking the average of all CORA scores and overall relative error was calculated by averaging relative error between peak forward excursion values of simulation and volunteer data for all body markers. An overall score for each simulation was calculated by summing the overall CORA score and overall relative error subtracted from 1 (overall score ¼ overall CORA score þ (1 À overall relative error)). For the female model, the sampling point with the maximum overall score  was used and for the male model, the sampling point with the second-best overall score was selected. The simulation with a maximum overall score had a comparatively low overall CORA score suggesting poor reaction load correlation with volunteer data. The final controller gains used for both the models are provided in Table A3 (see online supplement).

Results
The comparison of peak forward excursions of the different body markers for the models and the volunteers is shown in Figures 2-5. These peak forward excursion values are also reported in Tables A6 and A7 (see online supplement) along with the p-value of the Wilcoxon signed-ranked test. Peak forward excursions indicate improved occupant kinematic prediction with the use of the active modeling scheme. The p-value for all cases for both the models is lower than .05, suggesting that the difference between the control and active model peak forward excursion is statistically significant (Table 1). This indicates that the active modeling approach provides a more accurate representation of volunteer kinematics than the passive modeling approach. The overall CORA scores for both female and male models are reported in Table 1 The reaction forces at the steering column, seat back, seat pan, left foot, and right foot and seat belt forces for both male and female models are plotted against volunteer data in Figures A43-A56 (see online supplement). The force plots contain data for the volunteer (50th percentile male/5th percentile female) mean, mean ± SD, and mean±2SD corridors and model data with (M50-OS þ Active/F05-OS þ Active) and without muscle activation (M50-OS/F05-OS). The experimental reaction force data are being reported for the first time in this study. For each model, a total of 14 timehistory traces are reported. The peak muscle activation values for some major muscles calculated by both models in both pulse severities are reported in Table A8 in the online supplement.

Discussion
The effect of muscle activation and the benefit of an active human body modeling approach for predicting occupant kinematics in precrash braking (1.0 g) and low-speed impacts (2.5 g) is supported by the results in Figures 2-5. The peak forward excursion was reduced for both models with muscle activation in comparison with the models with no activation and active models correlate well with volunteer data. The differences in peak forward excursion between active and control models are statistically significant (p-value < .05; Table 1,  Tables A6 and A7). All body marker trajectories in the sagittal and transverse planes support that the active models perform better than the control models ( Figures A3-A42). In particular, reduction in head center of gravity displacement is highlighted at both pulse severities. Visual comparison of both male and female models at 2.5 g acceleration is shown in Figure 1. For all cases, unlike volunteers and the active model, the control model failed to return to its initial posture. Both   peak excursion and return to posture are critical aspects of accurate model kinematics for the use of active models in the analysis of onboard vehicle safety systems, underscoring the utility of the active modeling approach.
Based on the overall CORA score reported in Table 1, both female and male models with muscle activation demonstrate a better correlation with volunteer data than control models, which do not include any active response and can be thought of as more PMHS-like. All of the signals used for calculating CORA scores are provided in Figures A43-A56. A total of 7 signals were used to calculate the overall CORA score for each case per model. The left and right pedal forces are compared in Figures A43-A46. The CORA score was higher for the male control model than for the active model in 1.0 g cases due to higher foot force in the initial part of the simulation, whereas for other cases both active models had higher CORA values than the control. Due to the presence of active muscle forces, steering column forces were higher with active models than with control models (Figures A47 and A48) and it is also evident from higher CORA scores for them (Tables A4 and A5). The belt forces for 1.0 g cases were higher in the control model and came down slowly compared to active models ( Figures  A53-A55). All of these kinematics and reaction force data suggest that both active models are better at representing volunteer responses than control models at both pulse severities.
The controller parameters from DOE for both male and female models are different. This is attributed to the variation in muscle properties such as PCSA values for both models as well as morphological differences between the models. The controller parameters are specific to the control system for which they are being tuned. The forces generated by the muscles are dependent on the PCSA values and both of these models have different PCSA values for each muscle. Osth et al. (2013) reported that the females have shorter electromyography onset times than male volunteers. The female model used in this study has shorter reaction times than the male model, which is in line with what Osth et al. (2013) reported. Proportional gain for the female model is higher than that for the male model for all body regions except the trunk. Integral gain is also higher for the female model. No specific trend was observed for derivative gain. Previous studies have used different methods to tune controller gains. Few studies have optimized PID controller parameters using experimental data (Cappon et al. 2007;Putra et al. 2019), and others have used DOE to tune controller parameters (Osth et al. 2015). Considering the number of PID controllers in the full-body model, optimization was not viewed as a feasible option for tuning all controller parameters. Instead, the DOE approach similar to Osth et al. (2015) was used in this study. If body region data become available, an optimization study could be carried out to tune controller gains for the muscles of the various body regions (Cappon et al. 2007;Putra et al. 2019).
Similar to the experimental data for 5th percentile female and 50th percentile male volunteers, F05-OS þ Active and M50-OS þ Active kinematics were different . For most of the body markers, the forward excursion of female volunteers was lower than that of male volunteers, and similar observations were made with male and female models (Figures 2-5). Similar findings were reported with reaction forces, and both models were able to capture these differences ( Figures A43-A56). They both were able to correlate well with the volunteer data of their respective size. The data reported in this study therefore highlight not only the importance of active musculature in computer models to represent volunteer responses in precrash braking and low-speed impact tests but also the importance of concurrently studying data representing both the male and female responses.
A 5th percentile female and 50th percentile male model with active musculature were modeled and calibrated in precrash braking and low-speed sled tests. The active model responses demonstrated significantly greater CORA scores than the control models. Control models greatly overpredicted occupant peak excursion, whereas active models were generally closer to the mean volunteer response. The active models demonstrated the ability to maintain posture even after an acceleration pulse was applied, whereas the control models failed to do so. The study demonstrates that the modeling approach is capable of capturing the varied kinematics observed in volunteer experiments, which may be an important factor in studies focused on the effects of low-g vehicle dynamics on the occupant position.

Limitations
Due to the lack of muscle PCSA data for the female model, this study mass-scaled PCSA values from the male model. Data reporting PCSA values for the 5th percentile female were unavailable. Alternative approaches to mass scaling (Mishra et al. 2020) that scale PCSA data from the male model using sex and size scaling factors for each body region or empirical PCSA data from the 5th female will improve the F05-OSþ Active model response. However, it should be noted that the scaling approach decreased the PCSA values proportionally, which was thought to be a reasonable solution because the female volunteers were uniformly lower weight than the males and tissue densities were similar across the sexes. It is well known that controller parameters will affect model response. Due to the high number of parameters to be tuned, a DOE was used for both models. A body region-wise controller parameter optimization similar to prior studies (Cappon et al. 2007;Putra et al. 2019) would help further improve model responses if data isolated by body region were available. This study used a single set of controller parameters for all cases for each sex. Different sets of controller parameters for different cases could improve model performance; however, such an approach could lead to overfitting and thus was not employed here. The tied contact used for modeling handgrip was observed to affect model kinematics. The selected contacts are recommended where there is no rotational degree of freedom but in reality rotation is possible. More analysis of the hand-to-wheel interaction is necessary but was beyond the scope of this study.

Disclosure statement
Scott Gayzik is a member of Elemance, LLC, which distributes academic and commercial licenses for the use of GHBMC-owned computational human body models.