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Hindawi Applied Bionics and Biomechanics Volume 2019, Article ID 4930803, 13 pages https://doi.org/10.1155/2019/4930803 Research Article A Computationally Efficient Finite Element Pedestrian Model for Head Safety: Development and Validation 1 1 2,3 4 Guibing Li , Zheng Tan, Xiaojiang Lv, and Lihai Ren School of Mechanical Engineering, Hunan University of Science and Technology, Xiangtan 411201, China State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha 410082, China Zhejiang Key Laboratory of Automobile Safety Technology, Geely Automobile Research Institute, Ningbo 315336, China Key Laboratory of Advanced Manufacturing Technology for Automobile Parts, Ministry of Education, Chongqing University of Technology, Chongqing 400054, China Correspondence should be addressed to Lihai Ren; firstname.lastname@example.org Received 4 March 2019; Revised 23 May 2019; Accepted 25 June 2019; Published 24 July 2019 Academic Editor: Le Ping Li Copyright © 2019 Guibing Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Head injuries are often fatal or of suﬃcient severity to pedestrians in vehicle crashes. Finite element (FE) simulation provides an eﬀective approach to understand pedestrian head injury mechanisms in vehicle crashes. However, studies of pedestrian head safety considering full human body response and a broad range of impact scenarios are still scarce due to the long computing time of the current FE human body models in expensive simulations. Therefore, the purpose of this study is to develop and validate a computationally eﬃcient FE pedestrian model for future studies of pedestrian head safety. Firstly, a FE pedestrian model with a relatively small number of elements (432,694 elements) was developed in the current study. This pedestrian model was then validated at both segment and full body levels against cadaver test data. The simulation results suggest that the responses of the knee, pelvis, thorax, and shoulder in the pedestrian model are generally within the boundaries of cadaver test corridors under lateral impact loading. The upper body (head, T1, and T8) trajectories show good agreements with the cadaver data in vehicle-to-pedestrian impact conﬁguration. Overall, the FE pedestrian model developed in the current study could be useful as a valuable tool for a pedestrian head safety study. 1. Introduction For example, literatures [6, 7] investigated pedestrian head kinematics in real-world crashes via accident reconstructions Pedestrian is the important part of vulnerable road users, and using multibody human body models; Elliott et al.  used the multibody modelling method to understand the inﬂu- about 22% of the deaths in road traﬃc accidents in the world are pedestrians . Accident data shows that 64% fatalities ences of vehicle impact speed, pedestrian speed, and pedes- and 43% seriously injured pedestrians suﬀered from head trian gait on pedestrian head kinematics. However, a injuries [2, 3]. Although much eﬀort has been made in the detailed analysis of injury biomechanical is not available in vehicle safety design for pedestrian protection, pedestrians their study due to the highly simpliﬁcation of multibody still have a high injury risk when struck by current vehicles human body models. Therefore, FE modelling was more [4, 5]. Numerical simulations using human body models pro- commonly used for the prediction of pedestrian head injury vide an eﬀective approach to understand pedestrian head biomechanics in vehicle collisions. Accident reconstruction injury mechanisms in vehicle crashes, which is the founda- using an isolated FE dummy head model or an isolated FE tion for pedestrian head protection. human head model is a widely used approach for the study Multibody and ﬁnite element (FE) human body models of pedestrian head injury biomechanics. Yao et al.  recon- are the main tools for predicting pedestrian head kinematics structed pedestrian head injuries using an isolated FE human and injuries in vehicle-to-pedestrian collisions. The former head model to build the relationships between predicted was usually used in analyses of pedestrian head kinematics. physical parameters and real brain injuries in passenger 2 Applied Bionics and Biomechanics car-to-pedestrian impacts. The similar approach was also employed in latter studies [10–12] to build a pedestrian head injury risk in real-world crashes. Although these studies were based on the real-world accident scenarios, constrains from the neck have not been considered, while neck constrains have signiﬁcant inﬂuences on head kinematics and injuries [13, 14]. Furthermore, most studies of pedestrian head injury using full body FE models only considered limited impact conditions [15, 16] (e.g., impacts at 40 km/h). However, the variation of pedestrian accident scenarios and their inﬂu- ences on pedestrian head kinematics and injuries were ignored . Therefore, the study of pedestrian head safety using a full body FE model and considering a broad range of impact scenarios is likely to be more valid. However, this kind of studies is still scarce due to the long computing time of the current full body FE models required in expensive sim- ulations. For example, the THUMS (Total Human Model for Safety) Academic Version 4.02 AM50 pedestrian model con- tains around 2,000,000 elements , and a simpliﬁed pedes- trian model (M50-PS) developed based on the GHBMC (Global Human Body Models Consortium) occupant model still has 827,000 elements . Therefore, the purpose of this study is to develop and validate a computationally eﬃcient FE pedestrian model Figure 1: The pedestrian FE model for head safety (PeMHS). for future studies of pedestrian head safety. For this pur- pose, the FE pedestrian model developed in the current study should have a relatively small number of elements than the original THUMS model being constructed. In total, and a high bioﬁdelity to predicted pedestrian head kine- the current full body pedestrian FE model contains 173,390 matics and injuries. nodes and 432,694 elements. To ensure a good bioﬁdelity, the same material properties as the THUMS model were employed by the PeMHS for the 2. Materials and Methods head, neck, skeletal structures of the torso and pelvis, soft tis- 2.1. Development of the FE Pedestrian Model for Head Safety sues in the spine, shoulder and hip joint, and outer ﬂesh (PeMHS). The FE PeMHS model was developed by using LS- parts. For other simpliﬁed body parts, viscoelastic material DYNA, which includes the head, neck, torso, and upper and properties (MAT 06 in LS-DYNA) were deﬁned for the ﬁlling parts in thoracic and abdominal cavity, elastic-plastic mate- lower limbs (see Figure 1). To ensure the bioﬁdelity for pre- dicting head injury, the head and neck models were directly rial properties (MAT 024 in LS-DYNA) were used for the extracted from the THUMS Academic Version 4.02 AM50 simpliﬁed long bones, and seatbelt material properties (average size male) pedestrian model . The skeletal struc- (MAT B01 in LS-DYNA) with a nonlinear load curve (force tures of the torso and pelvis from the THUMS pedestrian vs. engineering strain) were employed for knee ligament. model were employed in the current study with these parts The material parameters for these simpliﬁed body parts are being remeshed using lager sized elements. The long bones given in Table 1, and Figure 2 shows the load curve of the of the upper and lower limbs were modelled as cylinders with material for knee ligaments. The selection of these material properties was mainly based on previous studies of the devel- the changes in the cross-section area being considered (Figure 1). Particularly, the femur and long bone in the lower opment of FE human body models [21–23]. leg (representing the tibia and ﬁbula) was modelled by shell elements with a thickness of 6 mm and 5 mm, respectively. 2.2. PeMHS Model Validation at the Segment Level. The The hip and shoulder joint were developed similar to the focuses in model validation at the segment level are on repre- sentative body regions which may aﬀect pedestrian head THUMS model to keep the physiological characteristics. The bones and ligaments of the knee joint were modelled kinematics in vehicle collisions. Therefore, validations on using simpliﬁed geometry and line elements with nonlinear the knee, pelvis, abdomen, thorax, and shoulder were con- mechanical characteristics, respectively. This approach is ducted against cadaver test data from the literature, similar similar to that of the FLEX-PLI leg impactor  and conve- to a previous study . The material properties for these body parts of the model were optimized during the validation nient for gait posture conﬁguration. The ankle was simpliﬁed as a spherical joint with constrains by using line elements. process to match the cadaver data. The internal organs were modelled as two cavity ﬁlling struc- Knee lateral sharing and bending are the main kinematics tures for the thoracic and abdominal cavities, respectively, of pedestrians’ lower limb in vehicle collisions , and then similar to a previous study . The outer ﬂesh parts were dynamic response of the lower limb may aﬀect pedestrian upper body kinematics . Thus, the lower limb model modelled using hexahedral elements but with a thin fat layer Applied Bionics and Biomechanics 3 Table 1: Material deﬁnition of the skeleton components. (a) Material model Material parameters Tissues ρ (kg/m ) E (MPa) δ (MPa) Pr Femur Elastic-plastic 2,080 13,500 115 0.3 Tibia 1,900 20,033 125 0.315 (b) Material model Material parameters Tissues ρ (kg/m ) k (MPa) G (kPa) G (kPa) 0 i Viscoelastic Thoracic cavity 1,000 4.5 7.15 4.15 0.25 Abdominal cavity 1,000 0.25 54 40 0.25 ρ: density; E: Young’s modulus; δ: yield stress; Pr: Poisson’s ratio; k: Bulk modulus; G : short-term shear modulus; G : long-term shear modulus; β: decay 0 i constant. 400 N 400 N Fixed Fixed Fixed Fixed 40 km/h P2 P2 P1 P1 40 km/h 0 0.5 1 Impactor Engineering strain Fixed plate Mobile plate Figure 2: Load curve of the material for knee ligaments. Figure 4: Simulation models for lower limb lateral bending (a) and shearing (b) tests. Extension bars Knee FE model from Kajzer et al. , a ﬁxed foot plate was used to rep- resent the normal friction from the ground in bending tests, while the foot was placed on a moveable plate in shearing teats. The proximal of the femur was ﬁxed with Tibia side support Cylindrical cups Femur side support screws, while the distal of the femur was ﬁxed with a ﬁxed Figure 3: Simulation model for the knee four-point bending test. plate to limit its horizontal movement. A force of 400 N was loaded at the hip to simulate the weight of the upper body. The impact load was conducted at 40 km/h with an under lateral impact loading was validated against cadaver impactor of 6.25 kg, where a foam was wrapped at the knee four-point bending tests conducted by Bose et al.  front to obtain a soft contact. The impact location is at and lateral shearing and bending impact experiments from the ankle joint and the knee joint (not contact with the Kajzer et al. , respectively. Figure 3 shows the simulation femur condyle) for bending and shearing tests, respec- model for the knee four-point bending test, where the knee tively. Similar to previous studies of pedestrian lower limb ends were rigidly attached to cylindrical cups of two exten- model validation [22, 28], displacement from two targets sion bars. The extension bars were constrained by revolute (P1 and P2 in Figure 4) on the tibia was extracted from joints to the corresponding support which was either fully simulations to compare with the cadaver test data. ﬁxed (tibia side) or partially ﬁxed (femur side). A rotational The bioﬁdelity of the pelvis, abdomen, thorax, and shoul- velocity of 1 deg/ms to the knee was deﬁned to simulate the der regions was validated against cadaver test data under lat- lateral impact of the vehicle-to-pedestrian knee at 40 km/h. eral impact loading from previous studies [29, 30]. Figure 5 The simulation models for lateral bending and shearing shows the simulation models for these validation tests, and impact validation are shown in Figure 4. In the cadaver tests the corresponding information is summarized in Table 2. Force (N) 4 Applied Bionics and Biomechanics (a) (b) (c) (d) Figure 5: Simulation models for pelvis (a), abdomen (b), thorax (c), and shoulder (d) validation. Table 2: Information of impact conditions for pelvis, abdomen, thorax, and shoulder validation. Segment Impact speed Impact direction Impact location Pelvis 5.2 and 9.8 m/s Medial-lateral direction Greater trochanter Abdomen 6.8 and 9.4 m/s 30 toward the medial-lateral direction 7.5 cm below the xiphoid process Thorax 6.5 and 9.5 m/s 30 toward the medial-lateral direction Aligned to the xiphoid process Shoulder 4.5 and 6.8 m/s Medial-lateral direction Shoulder region For impact tests to the pelvis, abdomen, and thorax, the of a pedestrian human body model . The time history impactor is 23.4 kg in weight and 150 mm in diameter, of impact force was calculated for each impact simulation while the impactor mass is 23 kg with the same dimension and compared to the corresponding test data to validate for the shoulder impact test. The impact direction for the the FE model. pelvis and shoulder tests was deﬁned at the medial-lateral direction, while this was deﬁned as 30 toward the medial- 2.3. PeMHS Model Validation at the Full Body Level. The FE lateral direction for the abdomen and thorax impact tests. PeMHS model was validated against the vehicle-to- pedestrian impact tests using post mortem human subject The impact location was deﬁned at the level of greater tro- chanter, 7.5 cm down from the xiphoid process, aligned to (PMHS) from the literature, where specimens with a stature the xiphoid process and the shoulder region for the pelvis, between 170 and 175 cm and a weight between 50 and abdomen, thorax, and shoulder tests, respectively. In these 85 kg were chosen . A simpliﬁed sedan front FE model tests, the impactors were freely suspended and accelerated was developed based on the geometry of the car used in the to the impact speeds and the cadavers were in an upright PMHS tests. This simpliﬁcation approach of a car front supported posture with hands and arms overhead to avoid model has been used in previous studies [31, 32]. Figure 6 interference between the arm and impactor. In the simula- shows the vehicle-to-pedestrian impact simulation model tions, the arm (abdomen and thorax validation) or fore- which was set according to the initial conditions of the arm (pelvis and shoulder validation) was removed from PMHS test. In the tests, the hands of the HBMP model were the full body model to avoid interference, but the corre- tied in front and the legs were set in a walking posture with sponding mass was attached to the adjacent parts (shoul- the left leg backward and the right leg forward; positioning der or elbow) to keep the inertial force. This approach was achieved with the help of harness straps directed under has also been used in a previous study of the validation the arms, which was released prior to impact; the vehicle Applied Bionics and Biomechanics 5 Head T1 T8 0 5 10 15 20 40 km/h Knee bending angle (deg) Test corridor Simulation Figure 7: Predicted knee bending moment-bending angle curve versus cadaver test data of knee four-point bending. Figure 6: The simulation model for full body validation. impact velocity was at 40 km/h from the right sight of the pelvis, abdomen, thorax, and shoulder, respectively. Gener- specimens. In the study of Kerrigan et al. , boxed corri- ally, the predicted curves from the simulations are within dors based on a percentage of trajectory path length were the cadaver test corridors. developed from the PMHS trajectory data. The 10% path length corridors from Kerrigan et al.  were used for the 3.2. Model Validation at the Full Body Level. Figure 13 validation of the PeMHS upper body trajectories, including compares the overall pedestrian kinematics between the the head, T1, and T8. Thus, trajectories of the upper body PeMHS model and cadaver test data from Kerrigan (head, T1, and T8) were calculated in the simulation accord- et al. . The predicted overall kinematics of FE pedes- ing to the corresponding locations of the record mark ﬁxa- trian models is reasonably close to the test data, though tion points in the PMHS tests (see Figure 6). For a further some diﬀerences are observed in the pelvis and lower limbs for the PeMHS model at the latter stage (>100 ms) evaluation on the bioﬁdelity of the PeMHS model, the pre- diction from the PeMHS model was compared with that and the time of head contact on the windshield. The from the THUMS model under the same impact conﬁgura- global pedestrian kinematics and trajectories of the head, tion as shown in Figure 6. T1, and T8 predicted from the PeMHS model are com- In order to quantitatively assess the correlation between pared with that from the THUMS model and cadaver test the predictions and cadaver test data, the CORA (correlation data in Figure 14, and the quantitative assessment results and analysis) method was applied. The CORA rating results referring to the test average data are being summarized are within the range from 0% (no correlation) to 100% (per- in Table 3 (see Figures 15 and 16 for detailed CORA rat- fect match). The CORA has two methods to assess the corre- ing data). Overall, the predicted trajectories are similar lation between signals, where the corridor method (CORA- between the PeMHS model and THUMS model, and both match those of test average well in the initial phases of CD) calculates the deviation between the predicting curve and the reference corridors; the cross correlation method motion, though there are some diﬀerences towards the (CORA-CL) evaluates speciﬁc curve ﬁtness to the target end of the simulation. Nevertheless, the trajectories of through parameters such as the phase shift or shape of the the FE models do always remain within the PMHS test signals . Here, an equal weighting was employed for corridors, and the CORA rating results (>99%) are all close to 100% (perfect match). CORA-CD and CORA-CL, i.e., CORA = 0 5 CORA‐CD + 0 5 CORA‐CL. Figure 17 compares the predicted head linear and angular acceleration curves between PeMHS model and THUMS model, respectively. The predictions from the PeMHS model 3. Results are generally similar to those from the THUMS model as to the curve trend and peak time, though there are some diﬀer- 3.1. Model Validation at the Segment Level. Figure 7 com- pares the predicted knee bending moment-bending angle ences in the peak value. curve with the corridor adapted from cadaver test data of knee four-point bending. Figure 8 shows the predicted tibia 4. Discussion displacement (P1 and P2) time history curves in lower limb bending and shearing impacts together with the cadaver data 4.1. Computational Eﬃciency. The main purpose of the of Test-7B, Test-6B, Test-8S, and Test-16S from Kajzer et al. current study is to develop a computationally eﬃcient full , for which the height and weight of the sample are rela- body FE model for pedestrian head kinematics and injury tively close to the PeMHS model. prediction. The original THUMS head models have been Figures 9–12 show the predicted impact force time his- previously evaluated to be generally credible for human tory together with the corridor in the corresponding test for head injury prediction [32, 34]. Thus, the original head Knee bending moment (Nm) 6 Applied Bionics and Biomechanics 140 40 P1 P2 0 −10 0 5 10 15 20 25 0 5 10 15 20 25 Time (ms) Time (ms) Test-7B Test-6B Simulation (a) 100 100 80 80 60 60 40 40 20 20 P2 P1 0 0 0 5 10 15 20 25 0 5 10 15 20 25 Time (ms) Time (ms) Test-8S Test-16S Simulation (b) Figure 8: Predicted tibia displacement (P1 and P2) time history versus cadaver test data of lower limb bending (a) and shearing (b). 9 16 010 20 30 0 102030 Time (ms) Time (ms) Test corridor Test corridor Simulation Simulation (a) (b) Figure 9: Predicted impact force time history versus cadaver test data in pelvis impact: impact speed = 4 5 m/s (a) and 6.8 m/s (b). Displacement (mm) Displacement (mm) Force (kN) Force (kN) Displacement (mm) Displacement (mm) Applied Bionics and Biomechanics 7 9 9 6 6 3 3 0 1020304050 0 10 20304050 Time (ms) Time (ms) Test corridor Test corridor Simulation Simulation (a) (b) Figure 10: Predicted impact force time history versus cadaver test data in abdomen impact: impact speed = 6 8 m/s (a) and 9.4 m/s (b). 8 8 6 6 4 4 2 2 0 0 0 1020304050 0 1020304050 Time (ms) Time (ms) Test corridor Test corridor Simulation Simulation (a) (b) Figure 11: Predicted impact force time history versus cadaver test data in thorax impact: impact speed = 6 5 m/s (a) and 9.8 m/s (b). 6 6 4 4 2 2 0 1020304050 0 1020304050 Time (ms) Time (ms) Test corridor Test corridor Simulation Simulation (a) (b) Figure 12: Predicted impact force time history versus cadaver test data in shoulder impact: impact speed = 4 5 m/s (a) and 6.8 m/s (b). Force (kN) Force (kN) Force (kN) Force (kN) Force (kN) Force (kN) 8 Applied Bionics and Biomechanics 20 ms 60 ms 100 ms 140 ms Figure 13: Predicted overall kinematics of the PeMHS model versus cadaver test data in vehicle-to-pedestrian impact. and neck models from the THUMS were employed in the model is generally plausible given the purpose of model use. For the validation at the full body level, the trajecto- PeMHS model to keep the injury prediction capability for head injuries. To reduce the total element number, the ries of the PeMHS model (head, T1, and T8) and cadaver body parts below the neck were redeveloped using simpli- data showed very good agreement, especially at the early ﬁed geometry (e.g., upper and lower limbs and internal stage (<60 ms) of the impact. However, at the latter stage organs) or bigger sized elements (e.g., spine and ribcage). (>100 ms) of the impact, the trajectories of T1 and T8 In particular, the element number (432,694) of the PeMHS showed some diﬀerences from the cadaver average data is only about 25% of the THUMS Academic Version 4.02 and the head contact time is earlier in the simulation AM50 pedestrian model (about 2,000,000 elements ) (Figures 13 and 14). These discrepancies are probably and the original GHBMC model (about 2,100,000 elements due to anthropometric diﬀerences, uncertainty with respect ) and half of the M50-PS model (about 827,000 ele- to the initial position of the PMHS, simpliﬁcation of the ments ). The smaller number of elements can improve lower limb anatomical structure, and model tissue level the computational eﬃciency of the human body model in properties (such as knee ligaments and internal organs). simulations, especially when a big number of simulations It seems that the lower limb of the PeMHS is kind of too stiﬀer since an excessive rebound was observed in were needed. According to the theory of FE modelling, using a bigger computing time step and deﬁning some the leg and pelvis (Figure 13). This is largely due to the body parts as rigid bodies can improve the computational properties of the long bones in the model; further eﬃciency of the human body FE model. However, these improvement to these parts is still needed. Kinematics dif- may aﬀect simulation accuracy and pedestrian kinematics ferences between the FE model and cadaver data could also be found in the original validation  and further . Thus, the simpliﬁcation approach used in the current study is logically feasible. evaluation of THUMS  and validation of the M50-PS model . This highlights challenges in validating pedes- 4.2. Model Bioﬁdelity. For bioﬁdelity of the PeMHS model, trian human body models against PMHS data when full both the validation results at the segment level and full details of the cadaver characteristics are not exactly the same as the models. Nevertheless, the predicted pedestrian body level show good agreement with cadaver test data (Figures 7–14). Particularly, all predictions at the segment upper body trajectories are within the cadaver corridors level are in the cadaver test ranges. However, the predic- and close to the cadaver average value (CORA rating tions are mostly close to the lower boundary (Figures 7 scores > 99%). The comparisons between the PeMHS and 9–12). Similar results were also observed in a previous model and THUMS model also showed good agreements for both upper body trajectories (Figure 14) and head study of simplifying a pedestrian model . Many factors could aﬀect model response such as impact boundary con- accelerations (Figure 17). This also implies that the model ditions, material properties, and thoracic cavity ﬁlling developed in this study is potentially capable of predicting approach. Further analysis is still necessary to improve pedestrian head kinematics and injuries in vehicle colli- model bioﬁdelity. Nevertheless, the bioﬁdelity of the knee, sions, given the recognized bioﬁdelity of the THUMS model [32, 34, 36, 37]. pelvis, abdomen, thorax, and shoulder of the PeMHS Applied Bionics and Biomechanics 9 0 500 1000 1500 2000 0 1000 2000 Horizontal displacement (mm) Horizontal displacement (mm) Test average Test average Test 10% path length Test 10% path length Simulation-PeMHS Simulation-PeMHS Simulation-THUMS Simulation-THUMS (a) (b) 0 1000 2000 Horizontal displacement (mm) Test average Test 10% path length Simulation-PeMHS Simulation-THUMS (c) Figure 14: Predicted trajectories of the head (a), T1 (b), and T8 (c) versus cadaver test data in vehicle-to-pedestrian impact. Table 3: CORA rating results for trajectories of the head, T1, and T8. PeMHS THUMS Signal CORA-CD CORA-CL CORA CORA-CD CORA-CL CORA Head 100% 99.77% 99.88% 100% 99.81% 99.90% T1 100% 99.46% 99.73% 100% 98.96% 99.48% T8 100% 99.29% 99.64% 99.84% 99.96% 99.90% 4.3. Limitations. There are some limitations in this study. validation process due to limited availability of test data; More precision treatment is still needed for the simpliﬁ- a broad range of impact scenarios should be considered cation approach to the anatomical structure of human in further evaluations to prove the PeMHS model as a body parts, and the material properties for these simpli- robust tool for a pedestrian head safety study. However, this is one of the common diﬃculties in FE human body ﬁed body regions, though the predictions of the PeMHS, are generally comparable to cadaver test data and predic- evaluation [19, 32, 36, 37], and the lateral impact conﬁg- tions of the THUMS model. Only a single vehicle model uration is dominant in real-world vehicle-to-pedestrian and the lateral impact scenario were considered in the accidents . Vertical displacement (mm) Vertical displacement (mm) Vertical displacement (mm) 10 Applied Bionics and Biomechanics 3, 000 Begin End 2, 500 2, 000 1, 500 1, 000 Cell score = 99.88% CORA = 99.88% CORA−CD = 100.00% cora_begin cora_end CORA−CL = 99.77% 0 500 1, 000 1, 500 2, 000 [Ref ] test Inner corridors [Sim] simu Outer corridors (a) 2, 500 Begin End 2, 000 1, 500 1, 000 Cell score = 99.73% CORA = 99.73% cora_begin cora_end CORA−CD = 100.00% CORA−CL = 99.46% 0 200 400 600 800 1, 000 1, 200 1, 400 1, 600 [Ref ] test Inner corridors [Sim] simu Outer corridors (b) 2, 500 Begin End 2, 000 1, 500 1, 000 Cell score = 99.64% CORA = 99.64% cora_begin cora_end CORA−CD = 100.00% CORA−CL = 99.29% 0 200 400 600 800 1, 000 1, 200 1, 400 [Ref ] test Inner corridors [Sim] simu Outer corridors (c) Figure 15: CORA rating results for the trajectories of the head (a), T1 (b), and T8 (c) predicted from the PeMHS model versus cadaver test data in vehicle-to-pedestrian impact. Applied Bionics and Biomechanics 11 3, 000 Begin End 2, 500 2, 000 1, 500 1, 000 Cell score = 99.90% cora_begin cora_end CORA = 99.90% CORA−CD = 100.00% CORA−CL = 99.81% 0 500 1, 000 1, 500 2, 000 [Ref ] test Inner corridors [Sim] simu Outer corridors (a) 2, 500 Begin End 2, 000 1, 500 1, 000 Cell score = 99.48% CORA = 99.48% cora_begin cora_end CORA−CD = 100.00% CORA−CL = 98.96% 0 200 400 600 800 1, 000 1, 200 1, 400 1, 600 [Ref ] test Inner corridors [Sim] simu Outer corridors (b) 2, 500 Begin End 2, 000 1, 500 1, 000 Cell score = 99.90% cora_begin cora_end CORA = 99.90% CORA−CD = 99.84% CORA−CL = 99.96% 0 200 400 600 800 1, 000 1, 200 1, 400 [Ref ] test Inner corridors [Sim] simu Outer corridors (c) Figure 16: CORA rating results for the trajectories of the head (a), T1 (b), and T8 (c) predicted from the THUMS model versus cadaver test data in vehicle-to-pedestrian impact. 12 Applied Bionics and Biomechanics 400 25000 0 0 0 50 100 150 0 50 100 150 Time (ms) Time (ms) PeMHS PeMHS THUMS THUMS (a) (b) Figure 17: Comparisons of predicted head linear acceleration (a) and angular acceleration (b) between the PeMHS model and THUMS model in vehicle-to-pedestrian impact. 5. 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