3. Head injury criteria and biomechanical metrics

In automotive interior impact protection, the question "how severe is this head impact?" must be answered with numbers that regulators, test labs, and CAE engineers all interpret the same way. That shared language is built from a small family of biomechanical metrics: HIC and its time-window variants, the 3 ms clip, and the newer rotational predictors such as BrIC. Each metric encodes a different hypothesis about what actually injures brain tissue, and each has its own pass/fail threshold, sampling requirements, and failure modes. Understanding where these numbers come from — and where they break down — is essential before trusting any head impact result.

From Acceleration-Time History to HIC

Every head injury criterion begins with the same raw signal: the resultant translational acceleration a(t) measured at the head center of gravity, in units of g. The Head Injury Criterion integrates this signal over a sliding time window:

HIC = max over (t1, t2) of:
      [ (1/(t2 - t1)) * ∫ a(t) dt from t1 to t2 ]^2.5 * (t2 - t1)

where a(t) is the resultant acceleration at the head CG in g,
and (t2 - t1) is the window length in seconds.

The exponent 2.5 and the linear window term are empirical: they were fitted so that the resulting scalar correlates with skull fracture and severe brain injury observed in cadaver and animal experiments. Because the window length is a free variable, HIC is defined only once you fix it. That is exactly why the standard splits into variants.

• HIC36 — window capped at 36 ms. Historically used in FMVSS 208 and older European protocols. It tolerates longer, lower-amplitude pulses.
• HIC15 — window capped at 15 ms. Now the dominant criterion in FMVSS 208 (frontal, 700 limit) and Euro NCAP. It is more sensitive to short, sharp spikes.
• HIC (unqualified) — in most modern test standards this implicitly means HIC15. Always confirm the window before comparing values.

The practical consequence is significant. A pulse with a broad 30 ms plateau may produce HIC36 = 650 but HIC15 = 900, because the 15 ms window captures the steepest portion. Reporting "HIC = 650" without stating the window is meaningless. In CAE post-processing, the window is typically swept in 0.1 ms steps across the entire pulse; the maximum found is the reported HIC.

The 3 ms Clip: Limiting Sustained Acceleration

HIC alone does not bound peak acceleration. A very short spike can be averaged away inside a 15 ms window while still representing a violent local loading. The 3 ms clip addresses this by asking: what is the highest acceleration level that the head sustains for any continuous 3 ms? Formally, it is the maximum value of a(t) such that the acceleration remains at or above that level for at least 3 ms. Typical limits are 80 g for the head in FMVSS 208 frontal testing (and 60 g in some European and child-restraint contexts).

The 3 ms clip and HIC are complementary. HIC penalizes long, moderate pulses; the 3 ms clip penalizes short, high peaks. A restraint system that is too stiff may pass HIC but fail the 3 ms clip; one that is too soft may do the reverse. Designers therefore tune both simultaneously — for example, by adjusting airbag venting and seatbelt load limiting so that the head deceleration curve stays below 80 g for any 3 ms while the 15 ms HIC stays under 700.

Rotational Injury: BrIC and Its Relatives

Translational metrics assume that linear acceleration is the primary injury mechanism. Real-world concussion data, however, points strongly to angular kinematics — rotational acceleration and change in angular velocity — as the driver of diffuse axonal injury and concussion. This gap produced a second family of criteria.

The Brain Injury Criterion (BrIC) is defined from peak angular velocity components:

BrIC = max( |ωx| / ωxC , |ωy| / ωyC , |ωz| / ωzC )

with critical angular velocities (rad/s):
  ωxC = 66.3   (about the x-axis, sagittal plane rotation)
  ωyC = 53.1   (about the y-axis, coronal plane rotation)
  ωzC = 41.5   (about the z-axis, axial rotation)

BrIC = 1.0 corresponds approximately to a 50% risk of
moderate-to-severe concussion (AIS 2+).

BrIC is deliberately simple: it takes the worst single axis, normalized by its critical value. This makes it conservative and easy to compute from a six-degree-of-freedom head sensor or a CAE head model. It is now referenced in Euro NCAP far-side and oblique test protocols, often alongside HIC15.

Other rotational predictors exist and are worth knowing by name. HIP (Head Impact Power) combines linear and rotational terms into a single power-based scalar. DAMAGE and SIMon attempt to model strain in specific brain regions. PRA (Peak Rotational Acceleration) is sometimes reported directly in krad/s². None has displaced HIC in regulation, but BrIC has become the de facto rotational companion metric in consumer-test protocols.

How the Metrics Fit Together

The diagram below shows the signal chain from raw head acceleration to each reported metric, and the decision logic a test engineer applies when reading a result.

Reading a Result: A Worked Example

Suppose a sled test produces a head CG resultant acceleration pulse with a sharp peak of 95 g lasting 2 ms, followed by a broader plateau of 70 g lasting 12 ms. A quick manual estimate:

• 3 ms clip: the 95 g peak lasts only 2 ms, so it does not qualify. The 70 g plateau lasts 12 ms, so the 3 ms clip is approximately 70 g — below the 80 g limit.
• HIC15: the 15 ms window will capture the plateau plus part of the spike. The average over the window is roughly 72 g, giving HIC15 ≈ 72^2.5 × 0.015 ≈ 700 — right at the limit. This is a marginal case.
• BrIC: if the peak angular velocity about the z-axis reaches 38 rad/s, BrIC = 38/41.5 ≈ 0.92 — below 1.0 but close.

The engineering conclusion is not "pass" or "fail" but "marginal on two metrics." The appropriate response is to reduce the plateau amplitude slightly — for example, by increasing airbag venting or lowering the seatbelt load-limiting force — which lowers HIC15 without raising the 3 ms clip. This is the typical tuning loop in restraint system development.

Summary of Thresholds

These metrics are not competing definitions of the same thing — they are complementary probes of different injury mechanisms. A complete head protection assessment reports HIC15, the 3 ms clip, and BrIC together, with the coordinate system and filter class stated explicitly. Anything less leaves the result open to misinterpretation, and in a regulatory context, that is a failure in itself.