2. Head injury biomechanics fundamentals

Root cause analysis of head injuries in restraint-related events depends on a clear biomechanical model of what the head actually experiences. A restraint system does not "cause" a concussion directly; it changes the kinematics of the occupant's head, and those kinematics determine whether the brain tissue is loaded beyond its tolerance. This section establishes the physical quantities, threshold concepts, and tolerance criteria that later chapters will use to reconstruct real events and to judge whether a restraint design or usage pattern contributed to injury.

Kinematics: Linear and Angular Acceleration

Head injury analysis begins with the motion of the head as a rigid body. Two acceleration components matter, and they must be kept distinct throughout any investigation:

• Linear acceleration (translational), expressed in g or m/s², describes the head center of mass moving along a path. It is the dominant mechanism for focal injuries such as skull fracture and epidural hematoma, typically from direct contact.
• Angular acceleration (rotational), expressed in rad/s², describes the head rotating about its center of mass. It is the dominant mechanism for diffuse injuries such as concussion, diffuse axonal injury (DAI), and subdural hematoma, because rotation produces shear strain in brain tissue.

Sign conventions must be fixed before any reconstruction. A practical convention: define the SAE J211 / ISO 6487 head coordinate system with +x forward, +y to the occupant's left, +z upward, and positive angular velocity by the right-hand rule about each axis. State this convention explicitly in every analysis report, because a sign error in a rotational pulse can invert the inferred loading direction and mislead the root cause conclusion.

Acceleration is measured with accelerometers or calculated by differentiating velocity data. In practice, raw signals are filtered per SAE J211 Channel Frequency Class (CFC) — CFC 1000 for head acceleration in crash testing, CFC 180 or CFC 60 for lower-frequency occupant responses. Filtering is not cosmetic: an unfiltered or wrongly filtered pulse can change the computed injury criterion by tens of percent.

Impact Versus Inertial Loading

Two loading pathways must be separated in any root cause analysis:

• Contact (impact) loading — the head strikes a surface (A-pillar, side window, roof rail, airbag module, or another occupant). Contact force is localized and produces focal injury; the contact duration is short and the acceleration pulse is high-amplitude and high-frequency.
• Inertial (non-contact) loading — the head is accelerated by forces transmitted through the neck and torso, without head contact. This produces the rotational loading associated with concussion and DAI, and it is the pathway most relevant to restraint geometry, belt routing, and pretensioner/load-limiter behavior.

In a real event, both pathways usually coexist. A restraint that prevents head contact with the interior may still allow injurious rotational loading through the neck; conversely, an airbag that prevents contact can itself impart a concentrated load if the occupant is out of position. Root cause analysis must therefore ask which pathway dominated, not merely whether contact occurred.

Concussion Thresholds and Injury Tolerance Criteria

Tolerance criteria convert measured kinematics into an injury probability or a pass/fail judgment. The most widely used criteria in restraint design are summarized below. Values are representative published thresholds used for engineering judgment; they are not a substitute for the specific regulatory or customer specification applicable to a given program.

HIC is defined as:

HIC = max over t1,t2 of [ (1/(t2-t1)) * ∫ a(t) dt ]^2.5 * (t2-t1)
      where a(t) is the resultant linear acceleration at the head CG in g,
      and (t2 - t1) ≤ 15 ms for HIC15 (36 ms for HIC36).

Two practical cautions follow. First, HIC is a linear-acceleration criterion and is largely blind to rotation; a restraint that satisfies HIC can still produce injurious angular loading. Second, HIC is sensitive to the integration window and to filtering, so the same raw data can yield materially different values depending on processing choices. Always report the window length, filter class, and coordinate convention alongside the number.

From Kinematics to Restraint Design Decisions

Tolerance criteria become actionable when mapped to restraint parameters. The figure below shows how occupant and restraint variables propagate into head loading and then into the injury criteria used for judgment.

The diagram makes the central analytical point explicit: a criterion exceedance is an output, not a cause. If HIC15 is high, the analyst must determine whether the dominant contributor was a hard contact (interior stiffness, airbag module, out-of-position occupant) or a short, high-amplitude pulse transmitted through the belt and neck. If BrIC or rotational acceleration is high, the question shifts to belt geometry, pretensioner force, and whether the head was free to rotate. These are different root causes with different countermeasures.

Worked Example: Interpreting a Reconstructed Pulse

Consider a reconstructed frontal event in which the head CG resultant linear acceleration pulse is approximately triangular, peaking at 85 g and lasting 40 ms, with the peak occurring 12 ms after the pulse begins. This is an illustrative example, not a measured result.

For a triangular pulse of peak a_p and duration T, the HIC15 integral over the 15 ms window containing the peak can be approximated by taking the average acceleration over that window. If the window captures the peak and the pulse is roughly flat near the peak, the average is on the order of 70–80 g over 15 ms. Applying the HIC formula with a 15 ms window and an average of 75 g gives a HIC15 on the order of 75^2.5 × 0.015 ≈ 4,900, which is far above the 700 limit. The correct interpretation is not "the restraint failed" but "the pulse is contact-dominated and too hard"; the analyst should then examine what the head contacted and whether padding, airbag tuning, or geometry changes would soften the pulse. This kind of order-of-magnitude check is useful for screening reconstruction data before committing to detailed simulation.

What This Means for Root Cause Analysis

Three habits separate a defensible biomechanical analysis from a superficial one. First, always identify the dominant loading pathway before naming a cause. Second, report every criterion with its window, filter, coordinate convention, and data source so the number can be reproduced. Third, treat thresholds as probability statements rather than hard boundaries: a HIC of 690 is not "safe" and a HIC of 710 is not "failed" in any absolute sense — both sit near a risk curve, and the root cause conclusion should be framed in terms of which design or usage factor moved the occupant along that curve. These habits carry directly into the reconstruction and countermeasure chapters that follow.