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The objective of the present study is to develop an age-specific lower extremity finite element model for pedestrian accident simulation. Finite element (FE) models have been used as a versatile tool to simulate and understand the pedestrian injury mechanisms and assess injury risk during crashes. However, current computational models only represent certain ages in the population, the age spectrum of the pedestrian victims is very large, and the geometry of anatomical structures and material property of the lower extremities changes with age for adults, which could affect the injury tolerance, especially in at-risk populations such as the elderly. The effects of age on the material mechanical property of bone and soft tissues of the lower extremities as well as the geometry of the long bone were studied. Then an existing 50th percentile male pedestrian lower extremity model was rebuilt to depict lower extremity morphology for 30- to 70-year-old (YO) individuals. A series of PMHS tests were simulated to validate the biofidelity and stability of the created age-specific models and evaluate the lower extremity response. The development of age-specific lower extremity models will lead to an improved understanding of the pedestrian lower extremity injury mechanisms and injury risk prediction for the whole population in vehicle-pedestrian collision accidents.

Pedestrians are road users vulnerable to traffic accidents, who suffer high injury rate and mortality rate. WHO reported that more than one-fifth of the people killed on the world’s roads each year are pedestrians [

Pedestrian injuries are preventable; however, successful interventions to protect pedestrians and promote safe traveling require a better understanding of the injury mechanisms and risk factors for pedestrian crashes. Many researchers established lower extremity models to study its injury mechanisms in pedestrian collision accidents. Zhang et al. [

On the other hand, with the continued rapid growth of the elderly population of adults aged 60+ years, which has increased to 210 million (15.5% of the total population by the end of 2014 [

The finite element model provides a useful tool to assess injury risk and to study the injury biomechanics, while current models are limited to certain ages in the population. Therefore, it cannot reflect the difference of pedestrian injury at different ages in the accident. The objective of the present study is to investigate the geometric changes and material property changes with aging for pedestrian lower extremities and to develop and validate the age-specific FE models of pedestrian lower extremities to accurately model lower extremity morphology and material property for ages between 30 and 70 years.

In total, 320 femoral and 99 tibial midshafts derived from individuals aged 21–99 years were examined and measured [

Figure _{P}) and internal diameter (_{M}).

Idealized long bone section.

According to the values of TA, MA, and CA of different ages obtained by Ruff et al. [_{P} and _{M} of the adult male long bone at 5 cross-sections can be calculated, as shown in Figure _{P} and _{M} of a certain age can be scaled from the basic model via the corresponding scale ratio. As for the fibula, due to the shortage of anthropometry data related with age, its geometric change with age is assumed to be the same with the tibia.

Variation of geometric dimensions of long bone cross-section (male).

Taking a 70-YO adult male for example, the basic lower extremity model used in this manuscript is derived from an adult male aging 26 years, according to Figure _{P}_{M} of the femur and tibia are shown in Table _{P} and _{M} of the 70-YO adult can be scaled from the basic model via the corresponding scale ratio at five cross-sections.

The scaling ratio of long bone cross-section for a 70-YO adult.

Section position | Femur | Tibia | ||
---|---|---|---|---|

_{P} (%) |
_{M} (%) |
_{P} (%) |
_{M} (%) | |

20% | 1.3 | 4.3 | 5.0 | 12.9 |

35% | 1.3 | 9.6 | 3.7 | 16.6 |

50% | 1.8 | 15.2 | 3.3 | 15.7 |

65% | 2.6 | 19.4 | 4.3 | 14.8 |

80% | 4.9 | 19.2 | 5.3 | 11.1 |

Geometric changes of anatomical structures with aging were implemented by changing the long bone cross-section—model morphing can be used to generate models of all ages accurately and efficiently [

Changes of skeletal mesh with age in finite element model.

The cancellous bone of the lower extremity is a kind of porous structure composed of irregularly arranged trabecular bones; its mechanical properties are similar to foamed aluminum. When compressed, there is a significant elastic phase and the stress is nearly unchanged after the yield point; the limit stress is almost equal to the yield stress. The material properties of the cancellous bone showed obvious changes with aging because of the loss of calcification and fibrosis. Its material properties can be simulated by the material model of dynamic elastoplastic (

The quasistatic compression test data of the cancellous bone from the ages of 16 to 83 years [

The material properties of the cortical bone are simulated by the material model of isotropic elastoplastic (

The elastic modulus, ultimate stress, and failure strain of the cortical bone of different age groups are obtained by regression analysis of corresponding test data in literatures [

Based on the research results of the literature [

The long bone material properties of lower extremity model.

Material parameters | The young (30 YO) | The elderly (70 YO) | |
---|---|---|---|

Femoral cortical bone | Density (kg/m^{3}) |
2000 | 2000 |

Elastic modulus (MPa) | 16.2 | 13.9 | |

Poisson’s ratio | 0.3 | 0.3 | |

Yield stress | 100.22 | 94.4 | |

Limit strain | 0.032 | 0.019 | |

Tibial cortical bone | Density (kg/m^{3}) |
2000 | 2000 |

Elastic modulus (MPa) | 18.3 | 15.7 | |

Poisson’s ratio | 0.3 | 0.3 | |

Yield stress | 120.3 | 113.28 | |

Limit strain | 0.034 | 0.020 | |

Femur cancellous bone | Density (kg/m^{3}) |
1000 | 1000 |

Elastic modulus (MPa) | 752 | 816.4 | |

Poisson’s ratio | 0.45 | 0.45 | |

Yield stress | 13.25 | 10.22 | |

Limit strain | 0.134 | 0.134 | |

Tibial cancellous bone | Density (kg/m^{3}) |
1000 | 1000 |

Elastic modulus (MPa) | 752 | 591.6 | |

Poisson’s ratio | 0.45 | 0.45 | |

Yield stress | 11.04 | 8.24 | |

Limit strain | 0.134 | 0.134 |

The ligaments in the knee are connected to the bones, which stabilize and restrict the movement of the knee, including the patellar ligament, meniscofemoral ligament, medial collateral ligament (MCL), lateral collateral ligament (LCL), anterior cruciate ligament (ACL), and posterior cruciate ligament (PCL). The diameter of collagen fibers decreased, while the fiber content increased with aging. For example, the maximum fiber diameter is 180 nm when a man is 15–19 YO and reduced to 110 nm after 60 YO [

In the present study, the ligaments are simulated by the solid elements to accurately model the geometrical shape of each ligament and their contact with the surrounding tissue. The hyperelastic material constitutive model (

The experiments of the knee joint ligament carried out by Woo et al. [

Knee ligament simulation model.

Table

The ligament material properties.

Material parameters | The young (30 YO) | The elderly (70 YO) | |
---|---|---|---|

Knee ligament | Density (kg/m^{3}) |
1000 | 1000 |

Volume modulus (GPa) | 4.31 | 3.5 | |

C1 | 34.29 | 22.13 | |

C3 | 1.54 | 0.6 | |

C4 | 152.85 | 147.8 | |

C5 | 836.42 | 695.66 | |

Failure strain | 0.45 | 0.263 |

C1: first Mooney-Rivlin constant; C3: constant scaling of the collagen exponential stresses; C4: constant controlling rate of the rise of collagen exponential stresses; C5: modulus of straightened collagen fibers.

The baseline pedestrian lower extremity model is derived from the Global Human Body Models Consortium (GHBMC) average male occupant model. The GHBMC is representative of a 50th percentile male adult and was based on medical images of a 26 YO individual. The lower extremity model includes the long bone, muscle, ligament, skin, and other tissues. The cortical bone and cancellous bone of the long bone shaft are modeled using hexahedral elements. The cortical bone covering the long bone ends is modeled using quadrilateral shell elements. Muscle and skin are modeled using the solid element and shell element, respectively. Ligaments are modeled using the solid element and one-dimensional beam element together. The baseline model is adjusted according to the pedestrian’s standing posture. Then the previous research results of the geometric changes and material property changes with aging are applied to build the age-specific lower extremity FE models—including the adjustment of the material properties and the geometry morphing of the femur, tibia, and fibula, as shown in Figure

Finite element model of human lower extremity with age characteristics.

A series of cadaver test data were used to validate the biofidelity and stability of age-specific pedestrian lower extremity FE models, as shown in Table

Biomechanical cadaver tests for lower extremities.

Item | Cadaver test | Age of the PMHS (YO) |
---|---|---|

Thigh and calf | Kerrigan et al. [ |
58.5 ± 4.8/9.3 |

Ligaments | Dommelen et al. [ |
63 ± 3.3; 53.4 ± 9.9 |

Knee | Bose et al. [ |
53.4 ± 9.9 |

The whole lower extremities | Kajzer et al. [ |
51 ± 15 |

In Kerrigan’s test [

Thigh and calf three-point bending test model: (a) thigh and (b) calf.

Ligament failure caused by lateral bending is a common knee injury for pedestrian during vehicle-pedestrian collision accident. Kerrigan et al. [

Four-point bending test device and finite element model.

To evaluate the whole lower extremity response, 2 loading cases, bending and shear, were simulated to assess the importance of geometric and material property changes with aging.

According to the tests of Kajzer et al. [

Lower extremity bending (a) and shear (b) simulation model.

The force displacement curves of the impactor in thigh and calf three-point bending simulations are shown in Figure

Force displacement curves of the impactor in three-point bending simulation of the (a) thigh and (b) calf.

In thigh three-point bending simulation, the femoral fracture occurred in both cases of the young (30 YO) and the elderly (70 YO), as shown in Figure

Femur fracture location in thigh three-point bending simulation.

In calf bending simulation, both the tibia and fibula are fractured, while the fracture locations are different, as shown in Figure

Tibia and fibula fracture location in calf three-point bending simulation: (a) the young and (b) the elderly.

The comparison among the ligament displacement force is shown in Figure

Ligament ACL displacement force curve comparison between experiment and simulation.

Figure

Knee four-point bending simulation process.

The bending-angle-to-bending-moment curves of the knee joint are shown in Figure

Curve of bending angle and bending moment of knees in four-point bending simulation.

The simulation results of the elderly are in the test corridor, while the peak of the young is outside the corridor. This may be due to the ages of the PMHS, as they are between 44 YO and 80 YO—therefore, it is reasonable that the peak of the young (30 YO) is outside the corridor. The simulation curves coincide with the test curves before MCL rupture, which indicates that the material properties of the ligaments are reasonable. At the beginning, the bending moment increases with the bending angle and reaches the maximum value when the MCL is about to rupture and then the bending moment decreases sharply. The maximum bending moment of the elderly is about 110 Nm with a bending angle of 11°, while the maximum bending moment of the young is about 270 Nm with a bending angle of 18°, far greater than the elderly.

The time history curves of impactor force, knee joint bending angle, and knee joint shear displacement in lower extremity bending simulation are shown in Figure

Lower extremity bending simulation results: (a) impact force, (b) knee joint bending angle, and (c) knee joint shear displacement.

For the impact force, there is not much difference between the simulation results of the young and the elderly. They both reach their maximum value of 4.5 kN at 4 ms. This may be due to the same kinetic energy of the impactor and the quality of the lower extremity. While the bending angle of the elderly is obviously bigger than the young beyond 10 ms, and reached 5° at 20 ms, the similar trend occurred in knee joint shear displacement curves. This is because the knee ligament strength of the elderly is much lower than the young and their ligaments usually rupture earlier in the same collision condition. For example, the MCL and PCL ruptured at 11.5 ms and 14.5 m, respectively, in the simulation. It was significantly ahead of the results of the young, which is 18.5 ms and 20 ms, respectively, and then induced larger knee bending angle and shear displacement. The kinematics of lower extremity and ligament rupture in a bending test simulation is shown in Figure

Dynamic simulation of the lower extremity simulation process.

The time history curve of the impact force and knee joint shear displacement in the lower extremity shear simulation are shown in Figure

Lower extremity shear simulation results: (a) impact force and (b) knee joint shear displacement.

The peak impact force of the elderly is 5.2 kN, lower than 6.0 kN of the young, and appeared earlier at about 8 ms, while the knee joint shear displacement of the elderly is obviously larger than that of the young beyond 8 ms. It is possibly related to the elderly’s femur fracture occurring at around 8 ms, resulting in the increase of rotation and lateral movement at the fracture point and the decrease of the impact force. The detailed injuries of the elderly and the young are compared in Figure

Comparison of long bone injury: (a) the young and (b) the elderly.

In the present study, the changes of geometric and material properties of the lower extremity with aging were studied and age-specific FE models of the lower extremity for pedestrian-vehicle accident simulation were developed for 30-YO and 70-YO male pedestrian using morphing techniques. To evaluate the lower extremity response, a series of PMHS tests were simulated to validate the confidence of the models and to assess the importance of geometric and material property changes with aging. The whole age-specific FE models of pedestrian lower extremity showed numerical stability, and, in all validation simulations, the response of the young model and the elderly is different from each other. Development of age-specific FE models of the lower extremity will provide valuable tools for understanding variations in lower extremity injury patterns due to vehicle-pedestrian collision accidents across populations and in the design of new vehicles with devices for pedestrian protection.

Further study will involve the sex factor and the geometry changes of the femoral head/neck and ankle with age. These would be investigated to establish a pedestrian lower limb model with higher biofidelity. The more elaborate model and the understanding of age- and sex-specific biomechanics of the lower extremity will lead to the development of improved pedestrian protection and advancement in vehicle safety design.

The views and opinions expressed in this paper are those of the authors and not GHBMC.

The authors declares that they have no conflicts of interest.

The authors are grateful for the support from the GHBMC, who provide the baseline model. The authors also acknowledge the financial support by the National Natural Science Foundation of China under Grant no. 51775178 and the Natural Science Foundation of Hunan Province under Grant no. 2017JJ2034.