Corrigendum to “Identifying intrinsic and reflexive contributions to low-back stabilization” [J. Biomech. 46(8) (2013) 1440–1446]

Sensory contributions to stabilization of trunk posture in the sagittal plane

Trunk stabilization is required to control posture and movement during daily activities. Various sensory modalities, such as muscle spindles, Golgi tendon organs and the vestibular system, might contribute to trunk stabilization and our aim was to assess the contribution of these modalities to trunk stabilization. In 35 healthy subjects, upper-body sway was evoked by continuous unpredictable, force-controlled perturbations to the trunk in the anterior direction. Subjects were instructed to either 'maximally resist the perturbation' or to 'relax but remain upright' with eyes closed. Frequency response functions (FRFs) of admittance, the amount of movement per unit of force applied, and reflexes, the modulation of trunk extensor activity per unit of trunk displacement, were obtained. To these FRFs, we fitted physiological models, to estimate intrinsic trunk stiffness and damping, as well as feedback gains and delays. The different model versions were compared to assess which feedback loops contribute to trunk stabilization. Intrinsic stiffness and damping and muscle spindle (short-delay) feedback alone were sufficient to accurately describe trunk stabilization, but only with unrealistically low reflex delays. Addition of muscle spindle acceleration feedback or inhibitory Golgi tendon organ feedback yielded realistic delays and improved the model fit, with a significantly better model fit with acceleration feedback. Addition of vestibular feedback did not improve the model fit. In conclusion, muscle spindle feedback and intrinsic mechanical properties are sufficient to describe trunk stabilization in the sagittal plane under small mechanical perturbations, provided that muscle spindles encode acceleration in addition to velocity and position information.

A human body model with active muscles for simulation of pretensioned restraints in autonomous braking interventions

OBJECTIVE

The aim of this work is to study driver and passenger kinematics in autonomous braking scenarios, with and without pretensioned seat belts, using a whole-body finite element (FE) human body model (HBM) with active muscles.

METHODS

Upper extremity musculature for elbow and shoulder flexion-extension feedback control was added to an HBM that was previously complemented with feedback controlled muscles for the trunk and neck. Controller gains were found using a radial basis function metamodel sampled by making 144 simulations of an 8 ms(-2) volunteer sled test. The HBM kinematics, interaction forces, and muscle activations were validated using a second volunteer data set for the passenger and driver positions, with and without 170 N seat belt pretension, in 11 ms(-2) autonomous braking deceleration. The HBM was then used for a parameter study in which seat belt pretension force and timing were varied from 170 to 570 N and from 0.25 s before to 0.15 s after deceleration onset, in an 11 ms(-2) autonomous braking scenario.

RESULTS

The model validation showed that the forward displacements and interaction forces of the HBM correlated with those of corresponding volunteer tests. Muscle activations and head rotation angles were overestimated in the HBM when compared with volunteer data. With a standard seat belt in 11 ms(-2) autonomous braking interventions, the HBM exhibited peak forward head displacements of 153 and 232 mm for the driver and passenger positions. When 570 N seat belt pretension was applied 0.15 s before deceleration onset, a reduction of peak head displacements to 60 and 75 mm was predicted.

CONCLUSIONS

Driver and passenger responses to autonomous braking with standard and pretensioned restraints were successfully modeled in a whole-body FE HBM with feedback controlled active muscles. Variations of belt pretension force level and timing revealed that belt pretension 0.15 s before deceleration onset had the largest effect in reducing forward head and torso movement caused by the autonomous brake intervention. The displacement of the head relative to the torso for the HBM is quite constant for all variations in timing and belt force; it is the reduced torso displacements that lead to reduced forward head displacements.

A method to model anticipatory postural control in driver braking events

Human body models (HBMs) for vehicle occupant simulations have recently been extended with active muscles and postural control strategies. Feedback control has been used to model occupant responses to autonomous braking interventions. However, driver postural responses during driver initiated braking differ greatly from autonomous braking. In the present study, an anticipatory postural response was hypothesized, modelled in a whole-body HBM with feedback controlled muscles, and validated using existing volunteer data. The anticipatory response was modelled as a time dependent change in the reference value for the feedback controllers, which generates correcting moments to counteract the braking deceleration. The results showed that, in 11 m/s(2) driver braking simulations, including the anticipatory postural response reduced the peak forward displacement of the head by 100mm, of the shoulder by 30 mm, while the peak head flexion rotation was reduced by 18°. The HBM kinematic response was within a one standard deviation corridor of corresponding test data from volunteers performing maximum braking. It was concluded that the hypothesized anticipatory responses can be modelled by changing the reference positions of the individual joint feedback controllers that regulate muscle activation levels. The addition of anticipatory postural control muscle activations appears to explain the difference in occupant kinematics between driver and autonomous braking. This method of modelling postural reactions can be applied to the simulation of other driver voluntary actions, such as emergency avoidance by steering.