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A finite element (FE) model of the foot and leg was developed to improve understanding of injury mechanisms of the ankle and subtalar joints during vehicle collisions and to aid in the design of injury countermeasures. The FE model was developed based on the reconstructed geometry of a male volunteer close to the anthropometry of a 50th percentile male and a commercial anatomical database. While the forefoot bones were defined as rigid bodies connected by ligament models, the surrounding bones of the ankle and subtalar joints and the leg bones were modeled as deformable structures. The material and structural properties were selected based on a synthesis of current knowledge of the constitutive models for each tissue. The whole foot and leg model was validated in different loading conditions including forefoot impact, axial rotation, dorsiflexion, and combined loadings. Overall results obtained in the model validation indicated improved biofidelity relative to previous FE models. The developed model was used to investigate the injury tolerance of the ankle joint under brake pedal loading for internally and externally rotated feet. Ligament failures were predicted as the main source of injury in this loading condition. A 12% variation of failure moment was observed in the range of axial foot rotations (±15°). The most vulnerable position was the internally rotated (15°) posture among three different foot positions. Furthermore, the present foot and ankle model will be coupled together with other body region FE models into the state-of-art human FE model to be used in the field of automotive safety.

A finite element (FE) model of a vehicle occupant's lower limb was developed in this study to improve understanding of injury mechanisms during traffic crashes. The reconstructed geometry of a male volunteer close to the anthropometry of a 50th percentile male was meshed using mostly hexahedral and quadrilateral elements to enhance the computational efficiency of the model. The material and structural properties were selected based on a synthesis of current knowledge of the constitutive models for each tissue. The models of the femur, tibia, and leg were validated against Post-Mortem Human Surrogate (PMHS) data in various loading conditions which generates the bone fractures observed in traffic accidents. The model was then used to investigate the tolerances of femur and tibia under axial compression and bending. It was shown that the bending moment induced by the axial force reduced the bone tolerance significantly more under posterior-anterior (PA) loading than under anterior-posterior (AP) loading. It is believed that the current lower limb models could be used in defining advanced injury criteria of the lower limb and in various applications as an alternative to physical testing, which may require complex setups and high cost.

This article reviews the attributes of the human surrogates most commonly used in injury biomechanics research. In particular, the merits of human cadavers, human volunteers, animals, dummies, and computational models are assessed relative to their ability to characterize the living human response and injury in an impact environment. Although data obtained from these surrogates have enabled biomechanical engineers and designers to develop effective injury countermeasures for occupants and pedestrians involved in crashes, the magnitude of the traffic safety problem necessitates expanded efforts in research and development. This article makes the case that while there are limitations and challenges associated with any particular surrogate, each provides a critical and necessary component in the continued quest to reduce crashrelated injuries and fatalities. Clin. Anat. 24:362-371, 2011. V V C 2011 Wiley-Liss, Inc.

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To perform vibration analysis, many structures could be modeled entirely or partially as beams with variable or constant cross section. In this study, the differential equations for free bending vibrations of straight beams with variable cross section are solved using Bessel’s functions. Then, the general equations for one-step conical beams are used together with corresponding equations of cylindrical beams to model multi-step beams with various boundary conditions. The natural frequencies of a cantilever conical beam, calculated using its derived field matrix, were shown to be close to those obtained experimentally. In addition, the influence of geometrical factors upon the value of fundamental frequencies is investigated for both cantilever and clamped-clamped conical beams. It was shown numerically that changing a cantilever cylindrical beam into a conical beam by reducing the diameter of the free end increases its fundamental natural frequency even though its rigidity decreases. This property was not observed in a clamped-clamped conical beam. Finally, the effectiveness of a proposed transfer matrix on the calculation of natural frequencies for a multi-step beam was verified. It is believed that the current method could help in the design of various structures, including beams with variable cross section.

Valgus bending and shearing of the knee have been identified as primary mechanisms of injuries in a lateral loading environment applicable to pedestrian-car collisions. Previous studies have reported on the structural response of the knee joint to pure valgus bending and lateral shearing, as well as the estimated injury thresholds for the knee bending angle and shear displacement based on experimental tests. However, epidemiological studies indicate that most knee injuries are due to the combined effects of bending and shear loading. Therefore, characterization of knee stiffness for combined loading and the associated injury tolerances is necessary for developing vehicle countermeasures to mitigate pedestrian injuries. Isolated knee joint specimens (n=40) from postmortem human subjects were tested in valgus bending at a loading rate representative of a pedestrian-car impact. The effect of lateral shear force combined with the bending moment on the stiffness response and the injury tolerances of the knee was concurrently evaluated. In addition to the knee moment-angle response, the bending angle and shear displacement corresponding to the first instance of primary ligament failure were determined in each test. The failure displacements were subsequently used to estimate an injury threshold function based on a simplified analytical model of the knee. The validity of the determined injury threshold function was subsequently verified using a finite element model. Post-test necropsy of the knees indicated medial collateral ligament injury consistent with the clinical injuries observed in pedestrian victims. The moment-angle response in valgus bending was determined at quasistatic and dynamic loading rates and compared to previously published test data. The peak bending moment values scaled to an average adult male showed no significant change with variation in the superimposed shear load. An injury threshold function for the knee in terms of bending angle and shear displacement was determined by performing regression analysis on the experimental data. The threshold values of the bending angle (16.2 deg) and shear displacement (25.2 mm) estimated from the injury threshold function were in agreement with previously published knee injury threshold data. The continuous knee injury function expressed in terms of bending angle and shear displacement enabled injury prediction for combined loading conditions such as those observed in pedestrian-car collisions.