Reverse-engineering and modeling the 3D passive and active responses of skeletal muscle using a data-driven, non-parametric, spline-based procedure.

In this work we present a non-parametric data-driven approach to reverse-engineer and model the 3D passive and active responses of skeletal muscle, applied to tibialis anterior muscle of Wistar rats. We assume a Hill-type additive relation for the stored energy into passive and active contributions. The terms of the stored energy have no upfront assumed shape, nor material parameters. These terms are determined directly from experimental data in spline form solving numerically the functional equations of the tests from which experimental data is available. To characterize typical longitudinal-to-transverse behavior in rodent's muscle, experiments from Morrow et al. (J. Mech. Beh. Biomed. Mater. 2010; 3: 124-129) are employed. Then, the passive and active behaviors of Wistar rats are determined from the experiments of Calvo et al. (J. Bomech. 2010; 43:318-325) and Ramirez et al. (J. Theor. Biol. 2010; 267:546-553). The twitch shape is not assumed, but reverse-engineered from experimental data. The influence of the strain and the stimulus voltage and frequency in the active response, are also modeled. A convenient stimulus power-related variable is proposed to comprise both voltage and frequency dependencies in the active response. Then, the behavior of the resulting muscle model depends only on the muscle strain maintained during isometric tests in the muscle and the stimulus power variable, along the time from initiation of the tetanus state.

Active muscle response contributes to increased injury risk of lower extremity in occupant-knee airbag interaction.

OBJECTIVE: Recent field data analysis has demonstrated that knee airbags (KABs) can reduce occupant femur and pelvis injuries but may be insufficient to decrease leg injuries in motor vehicle crashes. An enhanced understanding of the associated injury mechanisms requires accurate assessment of physiological-based occupant parameters, some of which are difficult or impossible to obtain from experiments. This study sought to explore how active muscle response can influence the injury risk of lower extremities during KAB deployment using computational biomechanical analysis. METHODS: A full-factorial matrix, consisting of 48 finite element simulations of a 50th percentile occupant human model in a simplified vehicle interior, was designed. The matrix included 32 new cases in combination with 16 previously reported cases. The following influencing factors were taken into account: muscle activation, KAB use, KAB design, pre-impact seating position, and crash mode. Responses of 32 lower extremity muscles during emergency braking were replicated using one-dimensional elements of a Hill-type constitutive model, with the activation level determined from inverse dynamics and validated by existing volunteer tests. Dynamics of unfolding and inflating of the KABs were represented using the state-of-the-art corpuscular particle method. Abbreviated Injury Scale (AIS) 2+ injury risks of the knee-thigh-hip (KTH) complex and the tibia were assessed using axial force and resultant bending moments. With all simulation cases being taken together, a general linear model was used to assess factor significance (P <.05). RESULTS: As estimated by the regression model across all simulation cases, use of KABs significantly reduced axial femur forces by 4.74 ± 0.43 kN and AIS 2+ injury risk of KTH by 47 ± 6% (P <.05) but did not provide substantial change to injury risk of leg fractures. Muscle activation significantly increased axial force and bending moment of the femur (3.87 ± 0.38 kN and 64.3 ± 5.9 Nm), the tibia (1.49 ± 0.12 kN and 43.0 ± 6.4 Nm), and the resultant probability of AIS 2+ tibia injuries by 36 ± 6% regardless of KAB use and crash scenario. Specifically, when counting on a relative scale, muscle activation exhibited more prominent elevation of injury risk for in-position occupants than out-of-position occupants. In a representative crash scenario-that is, using a bottom-deployed KAB in a nearside oblique impact-muscle bracing of the right leg may lead to 2.6 times higher tibia fracture risk than being relaxed for an out-of-position occupant and 5.4 times higher for an in-position occupant. DISCUSSION AND CONCLUSIONS: The mechanism of higher leg injuries in the presence of KAB deployment in real-world crashes can be interpreted by the increased effective body mass, axial compression along the shafts of long bones, and altered pre-impact posture due to muscle contraction. The present analysis suggests that active muscle response can increase the risk of lower extremity injury during occupant-KAB interaction. This study demonstrated the feasibility of advanced human models to investigate the influence of physiologically based parameters on injury outcomes evidenced in field study and insight from computational examination on human variability for development of future restraint systems. Future efforts are recommended on realistic vehicle and restraint environment and advanced modeling strategies toward a full understanding of KAB efficacy.