2. Injury biomechanics fundamentals

Injury biomechanics provides the physical and physiological bridge between the mechanical loading a body region experiences during a crash and the resulting tissue damage. For crash injury risk modeling, three concepts form the working foundation: the injury mechanism (how load produces damage), the tolerance criterion (the measurable quantity and threshold that separates safe from injurious loading), and the risk function (a probabilistic mapping from that quantity to the likelihood of injury at a given severity). This chapter develops these three layers for the head, thorax, abdomen, and extremities, and shows how they are used together in simulation and test data workflows.

From Mechanism to Measurable Criterion

Every tolerance criterion exists because a specific mechanism has been identified. The mechanism tells you what to measure; the criterion tells you where the threshold lies. Confusing the two is one of the most common modeling errors — for example, applying a head acceleration threshold to a loading case whose dominant mechanism is skull fracture rather than diffuse brain injury.

Mechanisms are typically classified as:

• Compression / crush — tissue is loaded beyond its compressive strength (e.g., vertebral body fracture, pelvic crush).
• Tension / stretch — elongation beyond tissue failure strain (e.g., axonal stretch, aortic rupture).
• Shear — differential displacement across tissue layers (e.g., diffuse axonal injury, liver laceration).
• Bending / buckling — long bones and ribs under transverse load.
• Inertial / cavitation — internal motion driven by density differences (e.g., brain–skull relative motion).

In practice, a single event often combines several mechanisms, and the criterion chosen must reflect the dominant one for the injury being predicted.

Head

Head injury mechanisms split into contact (skull fracture, focal contusion) and inertial (concussion, diffuse axonal injury). The classical inertial criterion is the Head Injury Criterion (HIC), defined over a time window:

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

where a(t) is the resultant translational acceleration at the head
center of gravity, expressed in g, and (t2 - t1) ≤ 15 ms.

A HIC of 1000 corresponds to roughly a 15–20% risk of severe (AIS 3+) head injury for the 50th-percentile adult male, and this value underpins many regulatory limits. HIC captures the combined effect of acceleration magnitude and duration but ignores rotational loading, which is now recognized as the primary driver of concussion and diffuse axonal injury. Modern models therefore add rotational criteria such as BRIC (Brain Rotational Injury Criterion) or BrIC, computed from peak angular velocity and angular acceleration, and often combine them with HIC in a multivariate risk function.

For skull fracture, the relevant criterion is local: contact force or local skull deformation, with tolerance depending on impactor geometry and bone thickness. A simulation predicting head injury should therefore report both translational and rotational metrics, and state which injury type each metric addresses.

Thorax

Thoracic injury mechanisms include rib fracture from compression and bending, lung contusion from compression, and aortic rupture from shear and stretch. The most widely used criterion is the Viscous Criterion (VC), which captures the rate-dependent behavior of soft tissue:

VC = max over time of [ V(t) * C(t) ]

V(t) = instantaneous chest deflection velocity (m/s)
C(t) = instantaneous chest compression ratio = deflection / chest depth

Typical tolerance: VC = 1.0 m/s corresponds to ~25% risk
of AIS 3+ thoracic injury for the 50th-percentile male.

VC is complemented by maximum chest compression (typically 35–40% of chest depth for AIS 3+ risk) and by 3 ms clip acceleration (commonly 60 g for the chest). In finite element models, chest deflection is extracted from the simulated rib cage, and VC is computed from the deflection time history. A common pitfall is using the deflection of a single rib rather than the maximum across the chest, which underestimates risk.

Abdomen

Abdominal injury is dominated by compression and shear of solid organs (liver, spleen, kidneys) and by hollow organ rupture. Tolerance is usually expressed as abdominal compression or abdominal force, with the Abdominal Injury Criterion (AIC) combining force and deflection. For belt loading, a common criterion is peak abdominal force normalized by body mass, with tolerance around 2.5–3.0 kN for the 50th-percentile male. Because abdominal injury is highly sensitive to loading location and rate, risk functions are often stratified by loading condition (belt, airbag, steering wheel) rather than using a single global threshold.

Extremities

Extremity injuries are rarely life-threatening but carry high societal cost. The dominant mechanisms are bending and axial compression of long bones, and shear/compression at joints. Criteria are typically expressed as bone force or bending moment:

• Femur — axial compressive force, tolerance ~10 kN for the 50th-percentile male; bending moment tolerance ~300 N·m.
• Tibia — axial force and bending moment, with tolerance lower than the femur (~5–7 kN axial).
• Pelvis — force applied through the acetabulum, tolerance ~5–10 kN depending on loading direction.

In simulation, these are read directly from force transducers or from contact forces at the bone–impactor interface. Because bone strength varies strongly with age and sex, extremity risk functions are usually age- and sex-specific.

Risk Functions: From Threshold to Probability

A tolerance criterion gives a single threshold; a risk function gives a probability curve. The standard form is a cumulative normal (probit) function:

P(injury) = Φ( (x - μ) / σ )

x = the injury metric value (e.g., HIC, VC, force)
μ = the metric value at 50% risk
σ = the standard deviation of the tolerance distribution
Φ = standard normal cumulative distribution function

For example, a head risk function might use μ = 1000 and σ = 200 for HIC, giving approximately 15% risk at HIC = 800 and 50% at HIC = 1000. The choice of μ and σ must be documented, because different studies report different values depending on the population, injury definition (AIS level), and loading condition.

Putting the Layers Together

The workflow for a single body region is: identify the dominant mechanism from the loading condition, select the corresponding metric, extract that metric from the simulation or test data, and apply the calibrated risk function. The SVG below summarizes this mapping for the four regions covered in this chapter.

Practical Guidance for Modeling

When building or reviewing a crash injury model, verify the following for each body region:

1. Mechanism–metric alignment. Confirm that the metric you extract actually corresponds to the dominant mechanism for the loading case. A frontal impact with head contact and a lateral impact with head rotation require different head metrics.
2. Metric extraction consistency. Define the coordinate system and sign convention before extracting data. For chest deflection, state whether positive deflection is toward the spine or away from it, and keep this consistent between simulation and test.
3. Risk function provenance. Record the source population, injury definition (AIS level, body region), and loading condition for every μ and σ. Do not mix values from different sources without recalibration.
4. Uncertainty reporting. Report risk as a probability with its confidence interval, not as a single number. A risk of 0.22 with a 95% CI of 0.15–0.31 is more honest than 0.22 alone.

The next chapter builds on these fundamentals by introducing the data sources — cadaveric, animal, volunteer, and real-world crash data — that are used to calibrate the tolerance values and risk functions described here.