3. Multi-metric landscape

Occupant injury criteria are frequently taught as a list: HIC for the head, BrIC for the brain, NIC for the neck, chest deflection and the Viscous Criterion for the thorax, femur force for the upper leg, and the tibia index for the lower leg. In real restraint and vehicle development, however, these metrics do not behave as independent pass/fail gates. They are coupled through the same physical event — the occupant's motion relative to the interior — and through the restraint hardware that shapes that motion. A change that improves one metric almost always redistributes load and kinematics into another. This chapter treats the metric set as a coupled system: what each metric physically represents, how they interact, and how to reason about tradeoffs rather than optimizing a single number.

What each metric actually measures

Each criterion is a compressed summary of a different physical insult, and the compression matters when interpreting results.

• AIS (Abbreviated Injury Scale) is an anatomical, ordinal outcome scale (1 = minor through 6 = maximal/currently untreatable), assigned after injury is identified. It is not computed from a signal; it is the ground truth against which the other metrics are correlated. AIS is the common currency that lets a head injury and a leg injury be compared, but it is not linear — the jump from AIS 2 to AIS 3 is far more consequential than AIS 1 to AIS 2.
• HIC (Head Injury Criterion) integrates resultant head center-of-mass acceleration over a chosen time window, HIC = max over t1,t2 of [(t2−t1)((1/(t2−t1))∫a dt)^2.5]. It is dominated by short, high-amplitude acceleration spikes and is largely insensitive to duration beyond the window selection.
• BrIC (Brain Injury Criterion) uses peak angular velocity components, BrIC = |ωx/ωxC| + |ωy/ωyC| + |ωz/ωzC|, capturing rotational loading that HIC misses — the mechanism behind diffuse axonal injury and subdural hematoma.
• NIC (Neck Injury Criterion) is a rear-impact neck criterion based on the relative velocity and acceleration between the head and torso at the occipital condyles, NIC = 0.2·a_rel + v_rel². It targets the shear/extension mechanism of whiplash.
• Chest deflection is the peak sternum-to-spine compression (absolute or normalized to chest depth), the primary correlate of rib fracture and thoracic organ injury in frontal loading.
• Viscous Criterion (VC) is the maximum of the product of chest compression velocity and instantaneous compression, VC = max(v(t)·C(t)), capturing rate-dependent soft-tissue injury that pure deflection underestimates.
• Femur force is the axial compressive load transmitted through the femur, associated with shaft and hip fractures; it is strongly sensitive to knee-bolster and lower-instrument-panel geometry.
• Tibia index (TI) combines axial force and bending moment at the tibia, TI = Fz/Fc + M/Mc, reflecting the combined compression-plus-bending mechanism of lower-leg fracture.

The critical observation is that these metrics respond to different parts of the same acceleration pulse and to different restraint load paths. HIC and BrIC both describe head loading but through orthogonal mechanisms (linear vs. angular); chest deflection and VC describe the same chest but through magnitude vs. rate; femur force and tibia index describe the same leg but through different load components. Treating them as a set of independent thresholds discards exactly the information that matters for design.

The coupling structure

The couplings run through three shared channels: occupant kinematics, restraint load path, and the crash pulse itself. Consider a frontal impact with a force-limiting belt and a driver airbag. Increasing belt force limit reduces chest deflection and VC by allowing more forward excursion, but that extra excursion increases head travel toward the airbag and steering wheel, which can raise HIC and, if the head is loaded off-center, BrIC. Softening the airbag reduces head acceleration but may allow greater chest loading through the belt. Adding a knee bolster reduces femur force by catching the knees earlier, but it also changes pelvis rotation and can increase chest deflection by altering the torso's coupling to the belt. Lowering the knee bolster to protect the tibia may raise femur force. Every one of these is a real, observed tradeoff, not a hypothetical.

The coupling is also temporal. The metrics are evaluated over different windows and peak at different times. HIC peaks early, during the head's contact with the airbag; chest deflection peaks slightly later as the torso loads the belt; femur force peaks when the knees reach the bolster; tibia index peaks with the lower-leg load path. A restraint that is well-tuned for the head may be mistimed for the chest, and the resulting metric set can look contradictory until the timing is examined.

Reading the landscape as a system

The figure below represents the metric set as a coupled load-path diagram. The occupant is the central node; each metric is attached to the body region it describes; the restraint and interior hardware are the shared inputs that redistribute load among regions. The arrows show the dominant coupling directions — the paths along which a change in one input propagates to multiple metrics.

Working a tradeoff: a reproducible example

To make the coupling concrete, consider a frontal sled or full-vehicle simulation of a 50th-percentile male driver with a three-point belt and driver airbag. The following is an illustrative workflow with representative parameter ranges; the numbers are teaching values, not measured results.

1. Establish the baseline. Run the model with the current belt force limit (e.g., 4 kN), airbag vent size, and knee bolster position. Extract the full time history of head resultant acceleration, head angular velocity, chest deflection, chest compression rate, femur axial force, and tibia force/moment. Compute HIC₁₅, BrIC, peak deflection, VC, peak femur force, and TI.
2. Perturb one input at a time. Raise the belt force limit to 5 kN and rerun. Expect chest deflection and VC to fall, but head forward excursion to increase. Check whether HIC and BrIC rise as the head loads the airbag harder or later.
3. Examine the time axis. Plot all metrics against time. If HIC rises while BrIC is flat, the head is being loaded more linearly (airbag contact) without more rotation. If BrIC rises while HIC is flat, the head is rotating more — often a sign of off-center airbag contact or belt-induced head rotation.
4. Adjust the coupled input. If the head metrics degrade, soften the airbag or enlarge the vent rather than lowering the belt force limit back. This decouples the head from the chest to some degree, at the cost of more head excursion.
5. Check the leg chain. If the knee bolster was moved to reduce femur force, verify that tibia index did not rise from the changed lower-leg load path, and that pelvis rotation did not increase chest deflection.

The expected pattern — not a guaranteed result — is a Pareto front: no single configuration minimizes every metric, and the design task is to find a configuration whose metric set is acceptable against the relevant AIS-correlated thresholds and regulatory or rating requirements, not to minimize any one number.

Practical judgment

Three habits make the coupled landscape tractable. First, always report the metric set together with the time histories that produced it; a peak value without its timing and load path is not interpretable. Second, when a tradeoff appears, identify which shared channel — kinematics, load path, or pulse — is responsible before changing hardware; the fix usually lives in the channel, not in the metric. Third, use AIS as the common outcome scale to weigh tradeoffs: a small increase in a metric that remains well below its AIS 2 correlate may be an acceptable price for a large reduction in a metric near an AIS 3 threshold. The landscape is a system, and the design decision is a judgment about which injuries matter most for the occupant population in question.