Effects of Loading Conditions on the Pelvic Fracture Biomechanism and Discrimination of Forensic Injury Manners of Impact and Run-Over Using the Finite Element Pelvic Model

Abstract

This study aimed to systematically simulate the responses of pelvic fracture under impact and run-over to clarify the effects of boundary and loading conditions on the pelvic fracture mechanism and provide complementary quantitative evidence for forensic practice. Based on the THUMS finite element model, we have validated the simulation performance of the model by a real postmortem human pelvis side impact experiment. A total of 54 simulations with two injury manners (impact and run-over), seven loading directions (0°, 30°, 60°, 90°, 270°, 300°, 330°), and six loading velocities (10, 20, 30, 40, 50, and 60 km/h) were conducted. Criteria of effective strain, Von-Mises stress, contact force, and self-designed normalized eccentricity were used to evaluate the biomechanism of pelvic fracture. Based on our simulation results, it’s challenging to distinguish impact from run-over only rely on certain characteristic fractures. Loads on the front and back were less likely to cause pelvic fractures. In the 30°, 60°, 300° load directions, the overall deformation caused a “diagonal” pelvic fracture. The higher is the velocity (kinetic energy), the more severe is the pelvic fracture. The contact force will predict the risk of fracture. In addition, our self-designed eccentricity will distinguish the injury manner of impact and run-over under the 90° loads. The “biomechanical fingerprints” based on logistic regression of all biomechanical variables have an AUC of 0.941 in discriminating the injury manners. Our study may provide simulation evidence and new methods for the forensic community to improve the forensic identification ability of injury manners.

1. Introduction

In 2019, road traffic accidents were among the top ten leading causes of death in different countries worldwide [1]. The 2018 “Global Status Report on Road Safety” released by the World Health Organization pointed out that in 2016, the number of deaths due to traffic accidents globally reached 1.35 million, and vulnerable road users (pedestrians, cyclists and motorcycle cyclists) accounted for more than half of the total deaths [2]. Research based on the Pedestrian Crash Data Study (PCDS) found that the main collision direction of pedestrians (approximately 70%) is side impact, and pelvis and lower limb injuries accounted for the highest proportion of traffic injuries [3]. Even after excluding minor injuries (such as bruises), the lower limb and pelvis remain the most vulnerable parts [4]. Pelvic anatomy is complex, and numerous complications exist after pelvic fractures often leading to internal organ injuries and hemorrhage [5], and the mortality is extremely high, reaching 19–31% [6]. The injury mechanism of pelvic fractures in traffic accidents is complicated, primarily caused by impact and run-over, which represents one of the challenges in forensic identification. Classic identification relies on expert judgment and is relatively subjective. Therefore, more objective and quantitative methods are needed to evaluate the mechanism of pelvic fractures [7].

Research on the mechanism of pelvic injury generally focuses on epidemiological investigations [3,8,9,10], postmortem cadaver tests [11,12] and digital dummy simulations [4,13,14,15,16]. The current FE human models with detailed geometries and biofidelic material will accurately reconstruct the injury biomechanical responses [17], which can obtain the displacement, stress and strain data of all nodes in the model and will help identify the injury mechanisms and patterns of different loading conditions.

Distinguishing the injury manners and force directions is important in forensic identification. Presently, the clinical classification of pelvic fractures is dependent on the Tile, Tile/AO, Young and Burgess classification [18,19,20], which cannot cover most of the forensic problems and is difficult to apply directly to practice. Additionally, a lack of systematic studies exists on the effects of boundary and loading conditions on pelvic fracture based on biomechanical approaches [21].

Therefore, based on the common pelvic impact and run-over injuries in traffic accidents, we employed the Total Human Model for Safety (THUMS) model system to simulate impacts and run-over manners in different directions and at different velocities and analyzed the effects of boundary and loading conditions on pelvic fractures. The study findings will improve our understanding of the biomechanism of pelvic injuries and provide more objective evidence to the forensic community.

2. Materials and Methods

2.1. THUMS Pelvis FE Model

We used the THUMS (Total Human Model for Safety, academy version 4.02) finite element (FE) model, developed by Toyota Motor Corporation and Toyota Central R&D [22,23], to investigate the pelvic fracture biomechanism (Figure 1). The model is a 50th percentile adult male model, with a height of 175 cm and a weight of 77.3 kg. The pelvic bones are defined as elasto-plastic material models, and soft tissues, such as skin and muscles are set as hyper-elastic material models. The THUMS 4.0 model comprises approximately 770,000 nodes and 1.97 million elements, of which the pelvic model was verified by component validations of the dynamic lateral impact tests performed by Guillemot et al. [24] and the knee-thigh-hip front impact tests conducted by Rupp et al. [25], and the whole body validation of collision with minivan type vehicle performed by Schroeder et al. [26]. The THUMS model can be reliable for predicting human injury responses in real accidents [27]. The material model and parameters of the main pelvic bones are listed in

Table 1. Material parameters of the constitutive model of THUMS pelvic bones.

Part	LS-DYNA Material Type	Material Properties
Hipbone/Acetabulum cortical	Piecewise_linear_plasticity	ρ = 2000 kg/m3, E = 1730 MPa, υ = 0.3, σY = 34.5 MPa, εfail = 0.0257, C = 360.7, p = 4.605, with plasticity strain-stress curve ((0.000, 34.5), (0.001, 56.4), (0.003, 73.4), (0.004, 89.6), (0.006, 104.0), (0.009, 114.0), (0.012, 121.0), (0.026, 127.5))
Sacrum cortical	Plasticity_with_damage	ρ = 2000 kg/m3, E = 1302 MPa, υ = 0.3, σY = 80 MPa, C = 360.7, p = 4.605, with plasticity strain-stress curve ((0.000, 80.0), (0.003, 110.0), (0.015, 120.0))
Sacrum spongy	Damage_2	ρ = 1000 kg/m3, E = 40 MPa, υ = 0.45, σY = 1.8 MPa, G = 13.3 MPa, εfail = 1, with plasticity strain-stress curve ((0.02, 2.066), (0.04, 2.306), (0.05, 2.320), (0.06, 2.320))
Hipbone spongy	Damage_2	ρ = 862 kg/m3, E = 15 MPa, υ = 0.45, σY = 0.675 MPa, G = 4.99 MPa, εfail = 1, with plasticity strain-stress curve ((0.02, 0.775), (0.04, 0.865), (0.06, 0.870), (0.50, 0.870))

Notation: ρ, density; E, Young’s modulus; σ_Y, yield stress; ε_fail, plastic strain at failure; G, shear modulus; C & P, strain rate parameter; υ, Poisson’s ratio.

. Failure criteria are defined in the model and can simulate the fracture process by the element deletion method.

2.2. Pelvic Fracture Prediction Performance Validation by Published Experiment Data

The pelvic fracture predictive capability of the THUMS pelvis was validated by reconstructing an existing pelvic impact experiment performed by Ma et al. [12]. The original experimental setup included a horizontal sled test table, a 22.1 kg impactor, a 500 N vertical load cell and a vertical baffle. As shown in the referenced experiment, the pelvis was cut from the third lumbar vertebra to the middle femur, was seated upright and 500 N was loaded on the third lumbar vertebra. Next, the 22.1 kg impactor ran at 4–5.2 m/s and collided with the left great trochanter. The vertical baffle was fixed on the right side 30 cm from the pelvis, and the time history of the mutual distance between the left anterior superior iliac spine (LASIS) and right anterior superior iliac spine (RASIS) was recorded by an optoelectrical motion capture system.

An FE simulation model was established in accordance with the referenced experiment in the LS-DYNA (LSTC, Livermore, CA, USA) software (Figure 2). Since the RASIS-LASIS distance involved in the experiment data is 222.4 mm while the distance of THUMS model is 216.45 mm, we scaled the THUMS pelvic model with a factor of 1.027 (222.4/216.45). The rotations about the X, Y, Z axes of the model were restricted; The translations in the X, Z directions of the lower nodes were restricted (Boundary-Spc); a lumped mass of 50 kg was loaded onto the top surface of the sacrum; global gravity was applied; the impactor was modeled as a rigid plane with a mass of 22.1 kg and initial velocity of 4 m/s; the right baffle was modeled as a fixed rigid wall, and the contact between the impactor and pelvis was modeled by the keyword * AUTOMATIC_CONTACT_SURFACE_TO_SURFACE with a friction coefficient of 0.2 [28].

As shown in Figure 3, the predicted time history curves of the mutual RASIS-LASIS distance were roughly consistent with the reported experimental data. The peak true compression ratio of simulation is 29.3% (peak deflection of 65 mm) and that of the experiment is 31.9% (peak deflection of 67 mm), with a deviation of 2.6%. The final compression ratio of simulation is 11.3% and that of the experiment is 13.8%, with a deviation of 2.5%. The deviations in magnitude and topology of the curves are relatively small. Thus, the THUMS model could predict pelvic fractures and could be applied in subsequent studies.

2.3. Pelvic Impact and Run-Over Simulation Matrix

To evaluate the pelvic injury biomechanisms under impact and run-over loading conditions on the pedestrians in traffic accidents, we performed a matrix of series of impact and run-over simulations on the original THUMS model. The loading matrix is given in

Table 2. The matrix of impact and run-over loading conditions.

Loading Conditions	Directions (Degree)	Velocity (km/h)
Impact	0°, 30°, 60°, 90°, 270°, 300°, 330°	10, 20, 30, 40, 50, 60
Run-over	90°, 270°	10, 20, 30, 40, 50, 60

.

2.3.1. Impact Loading Conditions

The current study simulated the direct impact of a large blunt surface (like a car hood) on the pelvis. We constructed a vertical blunt rigid plane (300 mm × 300 mm, larger than the upper and lower diameters of the pelvis to ignore the effect of the plane size) on the left side of the pelvis model, and the plane mass was 1500 kg (general car mass).

Considering the midpoint of the line of the dummy’s bilateral iliac crest as the circle center, the line of the bilateral iliac to the right as the 0° axis, an impact normal was set every 30 degrees counterclockwise, and the impactor plane was perpendicular to the normal. Because the pelvis is symmetrical and the two sides are equivalent, only the left impacts had been simulated. Therefore, seven impact directions of 0°, 30°, 60°, 90°, 270°, 300° and 330° were used (Table 2, Figure 4; the results of 120°, 150°, 180°, 210° and 240° are mirrored from the result of their symmetrical orientation). The impact velocities in each direction were 10 km/h, 20 km/h, 30 km/h, 40 km/h, 50 km/h and 60 km/h, respectively.

For the boundary conditions, a global gravity was set. The rigid impactor could move freely in the X and Y directions, the translation in the Z direction and rotation about the X, Y, Z directions were restricted, and the blunt rigid plane was set in contact with the human body (the dynamic friction coefficient was 0.25 [29]; Figure 4).

2.3.2. Run-Over Loading Conditions

We constructed a wheel model with a diameter of 655 mm and a width of 210 mm to simulate the run-over effects on the pelvis. The wheel comprised a rim and tire, both of which were modeled by shell elements. The rim is a rigid body, the tire is an elastic material (

Table 3. Material parameters of the constitutive model of the wheel.

Part	LS-DYNA Material Type	Material Properties
Wheel tire	Elastic	ρ = 3800 kg/m3, E = 2461 MPa, υ = 0.32
Wheel rim	Rigid	ρ = 7830 kg/m3, E = 20,100 MPa, υ = 0.3

Notation: ρ, density; E, Young’s modulus; υ, Poisson’s ratio.

), and a lumped mass of 375 kg (1/4 of 1500 kg) is added to the rim. The contacts between the tire and body (dynamic friction coefficient of 0.25 [29]), tire and ground coefficient of 0.65 [29]) are defined as surface-surface contacts. The boundary conditions of the wheel were: free translation in the X and Z directions, and restricted translation and rotation in the Y direction. The loading conditions of the wheel were set as follows: the translation velocities were 10 km/h, 20 km/h, 30 km/h, 40 km/h, 50 km/h and 60 km/h, and the rotation speed was calculated based on the radian and diameter, and we used the * BOUNDARY_PRESCRIBED_MOTION to define the rotation and translation velocities, respectively.

We developed the tire model using different sizes of 16 mm, 8 mm and 4 mm elements and conducted the mesh convergence analyses under load conditions of 90° run-over at 20 km/h. The results indicate that all three models produced almost the same response and the mesh was convergent. Considering the computational time saving, we choose the 16 mm model.

We have established the back and front run-over pelvic conditions to be consistent with the impact definition, defined as 90° and 270° run-over, respectively (Table 2). The ground was modeled as a fixed rigid plane, and global gravity was applied. The final run-over models are shown in Figure 5.

2.4. Postprocessing and Statistical Analyses of the Results

All the quality of the simulation results will be checked to meet the quality criteria defined by the Pedestrian Human Model Certification [30]. The criteria include the initial penetration, total energy, hourglass energy, artificial energy, artificial mass increase and so on.

Pelvic fracture can be investigated under various parametric responses, such as the peak impact force, peak strain, and peak stress [31]. We evaluated the pelvic fracture responses under different loading using qualitative and quantitative approaches. To qualitatively evaluate the possible injury regions, the effective strain was plotted using the fringe-range plot menu in LS-PREPOST 4.8 (LSTC, Livermore, CA, USA). The elements with effective strain values higher than 0.03 [32,33] were highlighted in the fringe plots and compared among different loading conditions. Effective strain was selected because several studies were published to evaluate strain thresholds for pelvic fracture [17,32,33]. In the quantitative assessments, we extracted the maximum effective strain, Von-Mises stress, maximum principal stress of pelvic bones from 16 interesting sites, and the contact force between the pelvis and impactor/wheel, and the intercristal (IC) and the conjuata vera (CV) diameters. We investigated the criteria differences among different loading conditions. The statistical analyses of pairwise t-test, survival analysis principal components analysis and logistic regression and corresponding plots were performed using Jamovi 2 (jamovi.org), ggstatsplot [34] and Microsoft Office (Microsoft, Redmond, WA, USA), with p < 0.05 indicating statistical significance. We calculated the area under the receiver operating characteristic (ROC) to evaluate the prediction ability in discriminating the forensic injury manners of impact and run-over using Von-Mises stress, effective strain and maximum principal stress of all simulated loading conditions. The area under the ROC curve (AUC) determines the prediction power. The value of AUC greater than 0.9 shows the high predictive power [35].

The 16 data extraction sites included the following parts: right hip joint (RH), right iliac crest (RIC), right ischial notch (RIN), right sacroiliac articular surface (RSAS), right sacrum (RS), top surface of the sacrum (TSA), right inferior pubic ramus (RIPR), right superior pubic ramus (RSPR), left superior pubic ramus (LSPR), left inferior pubic ramus (LIPR), pubic symphysis (PS), left hip joint (LH), left iliac crest (LIC), left ischial notch (LIN), left sacroiliac articular surface (LSAS), and left sacrum (LS). All the interesting sites are plotted in Figure 6.

3. Results

3.1. The Quality Checks of All Simulation Results

For all the simulation results, we did not find any initial penetrations after the contact check. There is no contact force between the impactor/tire and the THUMS model at the beginning of the simulation. Total energy remains constant with a fluctuation far less than 1%. The mean value of the ratio of hourglass energy to total energy is less than 1%. The mean fluctuation in artificial mass is less than 0.1%. All our simulation results meet the quality requirements outlined in the Pedestrian Human Model Certification [30].

3.2. Pelvic Strain Responses and Reconstructed Fractures

We extracted the effective strain (≥0.03) contour map of the pelvic bones and deformed results after element deletions. Both were comprehensively plotted in Figure 7, which reveals the following: (1) Under all loading conditions, the pubic symphysis has a large deformation, and its effective strain is greater than 0.03; in addition to the front impact, the sacroiliac joint is also a vulnerable site. (2) As the impact velocity increases, the fracture becomes more serious. (3) The impact direction has significant effects on fracture performance. Under 0° impact, the main fractures are located at the left hip joint, left superior pubic ramus and pubic symphysis, while 30° and 60° impacts can easily lead to overall pelvic deformation. Fractures on the impact side can also cause contra-pelvic ring fractures. Under impact loading conditions of 90° (back) and 270° (front), the pelvis has an open-book tendency with no significant fractures. The 300° and 330° impacts lead to severe fractures at the impact site (ilium, pubic bone, etc.), of which the 330° impact is the most significant.

Figure 8 shows the pelvic fracture in the run-over conditions. Both back and front run-over can result in characteristic open-book fractures along the anterior-posterior compression, mainly with fractures of the pubic and sacroiliac joints. This fracture pattern and mechanism could be verified by the clinical cases [36,37]. The compression of the pelvic ring caused by back run-over is more obvious, while the hip fracture and femoral head dislocation caused by front run-over are more severe. As the velocity increases, the degree of pelvic fracture increases significantly.

3.3. Relationship between the Loading Conditions and Severity of Pelvic Fractures

We used the number of element deletions to evaluate the severity of pelvic fractures and plotted the loading conditions and deletion numbers (Figure 9). The higher is the velocity (kinetic energy), the more severe is the pelvic fracture, but the severity of the fracture has a non-linear relationship with the impact velocity. At an impact of 20 km/h or less, the fracture is 0. When the velocity was higher than 20 km/h, the deleted element numbers increased rapidly. In addition, we found the following results:

(1)

Compared with the impact, run-over was more adequate under kinetic energy conduction. At the same velocity, run-over was more severe than the impact on the pelvis, and the front run-over was relatively more serious.

(2)

In general, the lateral impact was most likely to cause pelvic fracture, and the risk of front impact injury was relatively small. The influence of the run-over direction was relatively low, without an evident difference.

3.4. Relationship between the Injury Manners, Loading Direction and Pelvic Normalized Eccentricity

We regard the pelvis as an approximate ellipse and use the ellipse eccentricity to quantify the pelvic deformation. The intercristal diameter (IC) is taken as the long axis, and the conjuata vera (CV) is taken as the short axis (shown in Figure 10) to define the eccentricity of the pelvis as shown in Equation (1).

$${\mathrm{Eccentricity}}_{\mathrm{pelvis}}=\frac{\mathrm{IC}-\mathrm{CV}}{\mathrm{IC}+\mathrm{CV}}$$

(1)

The eccentricity of the original undeformed THUMS pelvis was calculated as 0.67. We extracted the peak values of IC and CV under each loading condition to calculate the eccentricity and then divided the original eccentricity of 0.67 to obtain the normalized eccentricity of each loading condition. A normalized eccentricity equal to 1 refers to the undeformed pelvis. When the normalized eccentricity is greater than 1, the pelvis is compressed in the anterior-posterior direction to an open-book deformation (Figure 10a). When the normalized eccentricity is less than 1, the pelvis is compressed in the left-right direction (Figure 10b).

Using the t-student tests, we found that the loading direction and injury manner affected pelvic deformation. Under the 90° loading conditions, the pelvic deformation caused by impact and run-over was significantly different (p = 0.003; Figure 11a). The mean pelvic eccentricity under impact was 0.90, while the mean value of run-over was 1.3. In the 270° loading direction, no significant difference was found between the two injury manners (p = 0.223; Figure 11b).

Without distinguishing the directions, the mean pelvic eccentricity value during impact was 1.02, and the mean value during run-over was 1.09 (Figure 11c). No significant difference was found between the two injury manners in pelvic deformation (p = 0.585).

3.5. Relationship between the Impact Directions and Pelvic Normalized Eccentricities

As shown in Figure 12, under the impact loading conditions, the impact direction has a significant effect on pelvic deformation. Under most of the loading conditions, the pelvis was mainly left-right compressed (normalized eccentricity less than 1), and the 270° impact caused open-book deformation by anteroposterior compression (normalized eccentricity is 1.14), in which the front impact and anterolateral impacts (240° and 330°; normalized eccentricity is 0.59) were significantly different (p < 0.05).

3.6. Relationship between the Contact Force and Fracture Risk

We extracted the contact force between the impactor/tire and pelvis. With increasing loading velocity, the contact force showed an increasing tendency (red line in Figure 13). The maximum contact force was 43,060 N. As the velocity increased, the range of force fluctuation increased significantly (Figure 13).

Through artificial inspection of the simulation results, the fractured simulation was defined as 1, and the nonfractured simulation was defined as 0. Survival analysis based on the contact force (Figure 14) revealed a 10% probability of pelvic fractures at 7650 N and a 50% probability of pelvic fractures at 16,625 N. Additionally, the number of deleted elements was positively correlated with the contact force, and run-over was more serious than the injury caused by impact (Figure 15).

3.7. The Discrimination of Forensic Injury Manners of Impact and Run-Over by Logistic Regression

The biomechanical criteria of Von-Mises stress, effective strain and maximum principal stress in the different 16 interesting sites may predict the characteristic of injury manners. Due to the large numbers of 48 variables (sites * 3 criteria), we conducted a principal component analysis of all variables, to reduce the interaction between different variables and get a smaller condensed data set. We used the eigenvalue of 1 to determine the number of principal components and got nine principal components for all variables, with 86.3% of the variance explained (

Table 4. The principal component analysis of the total 42 biomechanical variables of the pelvis fracture simulations.

Simulation Biomechanical Variables	Principal Components									Uniqueness
	1	2	3	4	5	6	7	8	9
Cumulative % of variance	20.7	34.7	46.1	56.2	64.4	71.0	77.1	81.9	86.3	/
VMstress *-LIN	0.435	0.410	0.564							0.1711
VMstress-LIC		0.833								0.0929
VMstress-LH		0.846								0.0959
VMstress-LSAS	0.533	0.373	0.556							0.1047
VMstress-LS	0.872						0.307			0.0742
VMstress-LIPR	0.404	0.674					0.412			0.0675
VMstress-LSPR	0.473	0.582					0.429			0.0801
VMstress-RIN	0.421		0.778							0.0811
VMstress-RIC				0.848	0.364					0.0672
VMstress-RH					0.830					0.0733
VMstress-RSAS	0.563		0.603							0.0811
VMstress-RS	0.847			0.307						0.0817
VMstress-RIPR	0.453			0.351	0.599	0.346				0.0713
VMstress-RSPR	0.491			0.386	0.476	0.341				0.0988
VMstress-TSA	0.794		0.383							0.0935
VMstress-PS						0.777	0.523			0.0367
MPstress *-LIN		0.621	0.579							0.0844
MPstress-LIC	0.866									0.1155
MPstress-LH		0.635	0.332	0.363				0.385		0.1164
MPstress-LSAS		0.848								0.1280
MPstress-LS	0.460	0.398	0.616							0.1273
MPstress-LIPR	0.493	0.392	0.513				0.311			0.1918
MPstress-LSPR	0.493	0.489				0.456				0.1151
MPstress-RIN	0.308	0.313	0.586	0.365	0.391					0.0844
MPstress-RIC				0.880						0.0854
MPstress-RH			0.328		0.808					0.0849
MPstress-RSAS	0.534		0.489	0.472					0.304	0.0853
MPstress-RS	0.730			0.532						0.1189
MPstress-RIPR	0.635			0.349					0.308	0.2041
MPstress-RSPR	0.485				0.369		0.516			0.1077
MPstress-TSA	0.800		0.311	0.323						0.1058
MPstress-PS						0.824	0.525			0.0393
Estrain*-LIN				0.387					0.698	0.2565
Estrain-LIC		0.857								0.1280
Estrain-LH		0.607								0.5204
Estrain-LSAS	0.469								0.380	0.3692
Estrain-LS	0.849						0.336			0.0910
Estrain-LIPR	0.306	0.622					0.519			0.1221
Estrain-LSPR							0.836			0.1834
Estrain-RIN	0.307		0.759							0.2091
Estrain-RIC				0.835	0.315					0.1454
Estrain-RH					0.648					0.5273
Estrain-RSAS	0.334		0.563						0.321	0.4046
Estrain-RS	0.863									0.0956
Estrain-RIPR				0.423	0.409	0.327			0.582	0.1357
Estrain-RSPR						0.865				0.1708
Estrain-TSA								0.979		0.0236
Estrain-PS								0.979		0.0237

* VMstress refers to Von-Mises stress; MPstress refers to Maximum Principal stress; Estrain refers to Effective strain.

). After that, we used the binomial logistic regression of the nine principal components to predict the injury manners of impact and run-over.

We observed that the binomial logistic regression of nine principal components can discriminate the impact and run-over well (Figure 16), with the AUC of 0.941. The obtained regression equation can be employed to quantitatively identify the injury manners, just like “biomechanical fingerprints”. In the same way, we analyzed the principal components of three criteria and corresponding regression equations, respectively. The Von-Mises stress-related AUC is 0.713, the effective strain-related AUC is 0.939, and the maximum principal stress-related AUC is 0.935 (Figure 16). It shows that the regression analysis based on the principal components of all variables has the best predictive performance.

4. Discussions

Pedestrian injuries in road traffic accidents are common and serious. Among them, the pelvis and lower limbs are vulnerable parts. Pelvic fractures are a common cause of morbidity and mortality [38]. The complex mechanism of pelvic fractures is a challenging forensic issue. Commonly, the identification opinions about injury mechanisms and injury manners are often the key evidence for liability distribution, insurance compensation, and even criminal convictions. However, identification mostly relies on clinical classification and expert experience, and there is a lack of systematic understanding of the mechanism of pelvic fractures exists [21].

The commonly used clinical classification systems of pelvic fracture include the Tile [18], Young-Burgess [20] and AO [19] classification methods. However, these classifications cannot cover most of the issues encountered in forensic practices. Therefore, the application of injury biomechanical methods is necessary to evaluate the mechanism of pelvic fractures and represents a more accurate, repetitive, safer and cost-effective method for forensic purposes [39]. The correlation between injury manner and biomechanism and consequences will be established using systematic simulations, which will be conducive to forensic injury identification.

The pelvis FE model has been applied to various studies. Phillips et al. [40] found that muscles and ligaments can reduce the stress concentration in the cortical bone based on pelvic FE simulations. Watson et al. [41] and Li et al. [42] found that the pubic symphysis significantly affects the pelvic stress distribution. Weaver et al. [16] established the injury risk curve of key pelvic parts based on pelvic injury simulation data that can be used for injury quantification. Additionally, some studies on the biomechanism of pelvic injury have been close to forensic practices. Bridget et al. [43] found that the force on the hip joint directly affects the distribution of pelvic stress, and gait will significantly affect the pelvic stress concentration.

These studies are focused on modeling and related validation, mainly applied to automotive safety and clinical treatment. The loading conditions are relatively simple and unsystematic and cannot be directly applied to forensic identification. Our study is based on the THUMS model, which has been widely used and fully validated, to carry out systematic injury conditions to investigate the effects of different impact and run-over loading on pelvic fractures. We employed a real postmortem human pelvis side impact experiment result to validate the fracture performance of the THUMS model, indicating that the model can predict the fracture response and is suitable for this study.

A total of 54 simulations consist of two injury manners (impact and run-over), seven loading directions (0°, 30°, 60°, 90°, 270°, 300°, 330°), and six loading velocities (10 km/h, 20 km/h, 30 km/h, 40 km/h, 50 km/h, 60 km/h) were conducted (Table 2). The quality of all simulation results has been checked and all of them comply with the current industry standard requirements, which indicates that the results are credible under the current state of the art [30]. Because the prediction ability of the strain criteria has been verified experimentally [32,33], we used the effective strain contours to compare the fracture responses among all the loading conditions. The results show that the loading directions have a significant effect on the fracture responses; for example, the 90° and 270° impacts resulting in fractures were obviously slight, likely attributed to the cushioning effect of amounts of soft tissue in the buttocks and easy flexion and movement of the pelvis during front impact. Additionally, we found fractures on the opposite side of the impact (e.g., 30°, 60° and 300°), which should be related to the overall pelvic ring deformation. As illustrated in Figure 17, the negative correlation between the CV and IC change rates (deformed distance/original distance) is likely to cause overall deformation. This effect should be considered in forensic practices.

Although under the same loading condition, the injury caused by run-over is significantly more serious than that of by impact (Figure 9), we cannot distinguish the two injury manners only by this feature. When the loading direction is unclear, we cannot distinguish the injury manners through pelvic normalized eccentricity (Figure 11). However, when the loading direction is clear, such as the 90° loading, we will distinguish the impact and run-over using eccentricity, which is a good quantitative criterion for forensic practice.

The contact force between the injured instruments and the body is directly related to the occurrence of the injury. The survival curve illustrated in Figure 14 is consistent with the data reported by Weaver CM [16] et al. and Peres J et al. [44]. This curve may qualitatively analyze the occurrence of pelvic fractures but cannot assess the severity of fractures.

According to the logistic regression analysis, the nine principal components from all 48 biomechanical variables show the discriminative ability of impact and run-over, which we firstly called “biomechanical fingerprints” of injury manners. Although it may be difficult for us to directly measure the strain and stress of the pelvis in actual cases, this method provides us with a quantitative description of the characteristics of pelvic fractures.

The biomechanical mechanism of pelvic injury is a complex system. This study did not fully consider the influence of human factors on pelvic injuries, such as height, weight, and age, which require further study. Because of the lack of data on pelvic injury in traffic accidents, we cannot assess the effects of all injury loading conditions on pelvic fracture that require more simulations of real cases to further verify the validity of the finite element model as forensic evidence.

5. Conclusions

In conclusion, a series of pelvic impact and run-over injury simulation experiments were carried out. These simulation results demonstrate the ability of the finite element method and the THUMS model to reconstruct the biomechanism of pelvic fractures under different loading conditions. Since the pelvic fracture features are affected by various factors, including loading directions and velocity, etc., it’s challenging to distinguish impact from run-over based on certain characteristic fractures. Loading on the front and back sides has a lower risk of pelvic fractures. In some loading directions (30°, 60°, 300°), the overall deformation will cause a “diagonal” pelvic fracture distribution, which should be considered in forensic practices. The higher is the velocity (kinetic energy), the more severe the pelvic fracture. The contact force will predict the risk of pelvic fracture. In addition, our self-designed eccentricity will distinguish the injury manner of impact and run-over under the 90° loads. The “biomechanical fingerprints” based on logistic regression of biomechanical variables can quantitatively discriminate the injury manners well. Our study may provide simulation evidence and new methods to improve the forensic identification of injury manners.