3. Injury metrics and criteria

Injury criteria translate the raw output of a crash simulation or physical test into a decision about tissue risk. A finite element model can report thousands of nodal stresses, but a safety engineer needs a small set of scalar metrics with defined units and accepted thresholds to answer one question: will this occupant, pedestrian, or athlete be injured? This chapter defines the principal injury metrics used for the head, neck, chest, abdomen, and extremities, states their units and reference conventions, and gives the threshold values that appear in regulations, consumer rating programs, and biomechanical literature. The emphasis is on what each metric physically represents, so that when a value exceeds a threshold you can trace it back to the underlying tissue mechanism rather than treating the number as an opaque pass/fail flag.

Head: HIC, HIP, and Rotational Metrics

The Head Injury Criterion (HIC) remains the most widely used head metric. It is computed from the resultant translational acceleration at the head center of gravity, expressed in units of g, over a time window:

HIC = max over t1,t2 of [ (t2 - t1) * ( (1/(t2-t1)) * ∫ a(t) dt )^2.5 ]
      with (t2 - t1) ≤ 36 ms  (HIC36) or ≤ 15 ms (HIC15)

HIC is dimensionless. The exponent 2.5 and the 36 ms window derive from the Wayne State tolerance curve, which relates tolerable linear acceleration to pulse duration. The commonly cited threshold is HIC = 1000 for a 36 ms window, corresponding to roughly a 16% risk of skull fracture or severe brain injury in the abbreviated injury scale (AIS) 3+ sense. HIC15 = 700 is used in several pedestrian and FMVSS 208 contexts. HIC is purely translational and is insensitive to rotation, which is why it under-predicts diffuse axonal injury in oblique impacts.

To capture rotation, the Head Impact Power (HIP) and the Brain Injury Criterion (BrIC) are used. BrIC is defined from peak angular velocity components about the three anatomical axes, each normalized by a critical value:

BrIC = (ωx / ωxc)^2 + (ωy / ωyc)^2 + (ωz / ωzc)^2
ωxc = 66.3 rad/s, ωyc = 53.1 rad/s, ωzc = 41.5 rad/s

BrIC ≥ 1 indicates a 50% risk of AIS 4+ brain injury in the reference dataset. Angular velocity is in rad/s; do not mix degrees per second into the formula. For sports and automotive applications, report both HIC and BrIC, because a low-HIC, high-rotation event can still produce concussion-level strain.

Neck: Nij and Neck Injury Criterion

The neck is loaded in four modes: tension, compression, flexion, and extension. The Nij interaction criterion combines axial force and bending moment, normalized by their respective critical values:

Nij = (Fz / Fzc) + (My / Myc)

where Fz is the axial force (N) and My the sagittal bending moment (N·m). Critical values depend on the load direction and occupant size; for a mid-size male in tension-flexion, Fzc ≈ 6806 N and Myc ≈ 310 N·m are representative. Nij ≥ 1.0 corresponds to a 22% risk of AIS 3+ neck injury. The older Neck Injury Criterion (NIC) targets whiplash and uses the relative horizontal acceleration between the top and bottom of the neck:

NIC = 0.2 * (a_rel * v_rel)   [m²/s²]

with a threshold of NIC = 15 m²/s² for soft-tissue injury. Note that NIC is a rate-based criterion and is not interchangeable with Nij; they address different injury mechanisms.

Chest: Compression, VC, and TT

Chest injury is dominated by deflection. The Chest Compression Criterion (Cmax) is the peak sternum-to-spine deflection expressed as a percentage of the initial chest depth. A Cmax of 40% is a common AIS 3+ threshold for the adult thorax. The Viscous Criterion (VC) captures the rate dependence of soft-tissue injury:

VC = max over time of [ (dD(t)/dt) * (D(t) / D0) ]   [m/s]

where D(t) is the instantaneous deflection, D0 the initial chest depth, and the product is evaluated in m/s. VC = 1.0 m/s is the AIS 3+ threshold for the chest. The Thoracic Trauma Index (TTI) is used in side impact and is computed from the lateral acceleration of the rib cage and the spine, scaled by mass and age:

TTI = 1.4 * AGE + 0.5 * (RIB_y + T12_y) * (MASS / MASS_ref)

with TTI = 85 g for a 45-year-old reference occupant as the AIS 3+ threshold. TTI is in g; the age term is in years and the mass term is dimensionless.

Abdomen and Extremities

Abdominal injury is assessed through the Abdominal Injury Criterion (AIC), which combines peak compression force and the viscous response of the abdominal wall, and through organ-specific strain in FE models. A commonly used AIS 3+ threshold is AIC = 1.0, with the force normalized to a belt-loading reference. For the extremities, the dominant metrics are bone fracture criteria: peak axial force in the femur (threshold ≈ 10 kN for AIS 3+), bending moment in the tibia, and the Knee-Thigh-Hip (KTH) force. In pedestrian legform testing, the tibia bending moment threshold is 220 N·m and the knee shear displacement threshold is 6 mm.

Units are the most common source of error in injury metric reporting. HIC is dimensionless; BrIC is dimensionless but requires rad/s; Nij is dimensionless but its inputs must be in N and N·m; VC is in m/s; TTI is in g. Always record the unit and the time window alongside the value. A HIC of 1000 computed over 15 ms is not the same as one computed over 36 ms.
Injury Metrics by Body Region — Unit and AIS 3+ Threshold REGION METRIC UNIT THRESHOLD HEAD HIC36 dimensionless 1000 HIC15 dimensionless 700 BrIC dimensionless (rad/s) 1.0 NECK Nij dimensionless (N, N·m) 1.0 NIC m²/s² 15 CHEST Cmax % chest depth 40% VC m/s 1.0 TTI g 85 ABDOMEN AIC dimensionless 1.0 EXTREMITIES Femur force / Tibia moment kN / N·m 10 / 220

Reading a Metric Set in Practice

Consider a frontal sled simulation of a mid-size male occupant. The model reports HIC36 = 820, BrIC = 0.74, Nij = 0.88, Cmax = 34%, VC = 0.82 m/s, and femur force = 8.4 kN. Each value sits below its AIS 3+ threshold, but the margin is uneven: Nij at 0.88 and VC at 0.82 are the closest to their limits, so the neck and chest are the governing regions for this design. A useful workflow is to normalize every metric by its threshold and rank the ratios. The largest ratio identifies the region that should drive restraint tuning, padding changes, or geometry revision. This normalization also makes heterogeneous units comparable without pretending that the metrics are physically equivalent.

Two cautions apply. First, thresholds are population-based probabilities, not deterministic injury boundaries; a value just below threshold still carries nonzero risk, and occupant size, age, and sex shift the critical values. Second, metrics computed from different time windows or filter classes (SAE J211 CFC 600 versus CFC 1000) are not directly comparable. Record the filter class, the time window, and the reference critical values with every reported metric so that the result can be reproduced and audited. When a metric exceeds threshold, return to the underlying tissue mechanism — skull fracture for HIC, axonal strain for BrIC, rib fracture for Cmax and VC — and confirm that the simulated load path is physically plausible before concluding that the design is unsafe.

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