INTRODUCTION - Injury Biomechanics and Control: Optimal Protection from Impact - page 10

Cheng et al. (2005a, 2005b) used computational techniques to investigate
the potential for the optimal control of an aircraft ejection seat cushion to
reduce a pilot's spinal injury in an ejection event. A multibody model was
used to simulate the dynamics of the biomechanical system, including the
occupant, the seat pan, and the safety devices. The peak lumbar load of
the occupant in the vertical direction was defined as the performance index
to be minimized, while the peak acceleration of the upper torso was not
allowed to exceed a prescribed tolerable value.

1.2.4 Thoracic Injury Control

Crandall, Cheng, and Pilkey (2000) used a two-mass injury model of the
thorax (Lobdell et al., 1973) to study the limiting performance of seat
belt systems for occupants in automobile frontal crashes. The correspond-
ing optimal control problem was solved numerically for a specified crash
deceleration pulse and the parameters of the model. The performance was
measured by thoracic injury criteria, which include the maximum chest
acceleration, compression, and viscous response, as well as by the maxi-
mum excursion of the occupant relative to the vehicle. It was observed that
the optimal control force produced by the seat belt was not constant during
the response time and that there was a substantial spike of the seat belt
force at the beginning of the response.
Kent et al. (2007) proposed a concept for an active control of seat belts
to mitigate the risk of thoracic injuries to automobile occupants in frontal
crashes. The concept includes the determination of an optimal open-loop
control that minimizes the peak excursion of the occupant in a vehicle,
provided that the thoracic injury criteria remain within prescribed limits,
and a feedback that sustains this control. The feedback control loop is
developed based on measuring the current seat belt force and comparing
the measured force with that prescribed by the optimal control. The seat
belt force can be regulated, for example, by retracting and releasing the
seat belts. The proposed methodology was applied to the two-mass thoracic
injury model introduced by Lobdell et al. (1973).
The influence of slack in a vehicle restraint (seat belt) system on the
reduction of risk of thoracic injuries in a frontal crash was studied by Kent,
Purtsezov, and Pilkey (2007). The slack was modeled as a time delay in
the response of the restraint system to the crash impact pulse. A limiting
performance analysis was performed to determine the theoretically optimal
control force - time profile generated by a vehicle restraint system with slack.
The maximum chest compression was minimized subject to constraints on
the chest acceleration, chest compression rate, chest viscous criterion, and
excursion of the occupant in the vehicle. The two-mass injury model due to
Lobdell et al. (1973) was used. For this model, regardless of the magnitude
of the delay caused by the slack, the seat belt control force exhibited a