3. Human Body Models (HBMs)

Human Body Models are computational surrogates of the human body used to predict injury under mechanical loading. Unlike the ATD, which is a physical device with fixed material behavior and a single validated response corridor, an HBM is a numerical construct whose fidelity depends on three independent choices: the formulation (how the body is discretized and solved), the anatomical fidelity (how closely geometry and tissue distribution match a real human), and the material models (how tissue stress–strain behavior is represented). A model can be geometrically excellent yet predict poorly if its material models are wrong, and vice versa. This chapter explains how these three axes interact and how validation hierarchies establish credibility for injury prediction.

Finite Element vs. Multibody Formulations

The two dominant HBM formulations differ in what they can resolve and what they cost.

Multibody (MB) models represent the body as rigid segments connected by joints with defined stiffness and damping. They solve ordinary differential equations for a small number of degrees of freedom, so a full-body run completes in seconds to minutes. MB models excel at gross kinematics: occupant trajectory, belt–body interaction, head excursion, and joint-level loading. They cannot resolve stress or strain inside a tissue, so they cannot directly predict fracture or brain strain. Their injury prediction is therefore kinematic-threshold-based — for example, a head injury criterion computed from resultant head acceleration, or a chest deflection threshold derived from a spring element.

Finite element (FE) models discretize organs and skeletal structures into elements with constitutive laws. A detailed head model may contain 200,000–1,000,000 elements; a full-body FE model can exceed 2 million. They resolve local stress, strain, and strain rate, enabling tissue-level injury metrics such as maximum principal strain in brain tissue or von Mises stress in cortical bone. The cost is computational: a 150 ms frontal impact simulation may require hours on a high-performance computing cluster.

A practical hybrid strategy is common in industry: use an MB model for rapid parameter sweeps and design-space exploration, then run FE simulations on the most critical configurations. The two must be correlated at the interface — typically by matching the MB joint kinematics to the FE model's skeletal motion before comparing injury metrics.

Anatomical Fidelity and Its Consequences

Anatomical fidelity is not a single number. It decomposes into at least four measurable aspects:

• Geometric accuracy — organ volumes, cortical bone thickness, and segment lengths compared to cadaveric or imaging data. A 10% error in brain volume changes the predicted strain field because the same imposed displacement is distributed over a different mass.
• Topological accuracy — the presence and connectivity of structures such as the falx cerebri, tentorium, sulci, and white-matter tracts. These features create strain concentrations that a smooth, featureless brain model cannot reproduce.
• Anthropometric coverage — whether the model represents a 50th-percentile male, a small female, a child, or an obese occupant. Injury risk is strongly anthropometry-dependent; a model validated only for the 50th-percentile male may not be credible for a 5th-percentile female.
• Mesh quality — element aspect ratio, Jacobian, and hourglass control. Poor mesh quality produces numerical artifacts that masquerade as physical strain concentrations.

The practical consequence is that two FE models of the same nominal anatomy can differ by 30–50% in predicted peak brain strain under identical loading. This is why validation against experimental data, not geometric similarity alone, is the credibility criterion.

Material Models for Biological Tissue

Biological tissues are nonlinear, viscoelastic, anisotropic, and nearly incompressible. The material model choice determines whether the simulation captures rate dependence and large deformation correctly.

Two implementation details matter in practice. First, nearly incompressible tissue requires either a mixed formulation (displacement–pressure elements) or a bulk modulus high enough to enforce incompressibility without causing volumetric locking. Second, viscoelastic parameters fitted from one strain rate may not extrapolate to another; the Prony series must be calibrated across the rate range of interest, typically 0.1–100 s⁻¹ for impact.

Validation Hierarchies

A single whole-body validation test cannot establish credibility because it confounds many error sources. The accepted approach is a hierarchy of tests, each isolating a subset of the model's behavior.

At Level 1, coupon tests calibrate the material model in isolation. If the brain tissue model cannot reproduce a simple uniaxial compression curve, no whole-body result is credible. At Level 2, organ-level tests check whether the assembled organ behaves correctly — for example, a fluid–structure interaction brain model under rotational loading should match cadaveric strain measurements from tagged MRI. At Level 3, regional tests add boundary conditions and adjacent structures. At Level 4, the full body is loaded in a realistic occupant environment. At Level 5, the model's injury predictions are compared to field or epidemiological data.

Each level uses a different acceptance metric. A common mistake is to judge a Level 4 result against a Level 1 tolerance. The correct practice is to define, before running, the metric and corridor for each level — for example, "Level 2 brain model must match cadaveric peak principal strain within ±20% at 30 rad/s" — and to document any level that fails.

Practical Calibration Example: Brain Model Under Rotational Loading

Consider calibrating a brain FE model against a published cadaveric rotational test. The input is a measured angular velocity profile applied to the skull, typically a half-sine pulse with peak 25–35 rad/s and duration 20–30 ms. The model's skull is constrained to follow this profile; the brain deforms passively.

The observable output is the displacement field in the brain, from which maximum principal strain is computed. A validated model should reproduce the experimentally observed strain pattern: highest strains in the midbrain and corpus callosum region, with peak values in the range of 0.10–0.25 depending on loading severity. If the model predicts peak strain in the cortex instead, the material model or the falx representation is likely wrong. If peak strain is an order of magnitude too low, the brain–skull interface may be over-constrained, preventing relative motion.

Typical failure symptoms and their causes:

• Strain concentration at a single node — mesh artifact; refine locally or apply hourglass control.
• No strain variation across the brain — material model too stiff or boundary condition fully tied; check interface friction and material parameters.
• Strain rate independence — viscoelastic Prony series not active or time step too large; verify that the simulation resolves the pulse duration with at least 20 time steps.

Choosing the Right HBM for a Given Task

The formulation and fidelity level should follow the injury metric of interest. If the question is "will the occupant's head strike the B-pillar?", an MB model with a validated head trajectory is sufficient and far faster. If the question is "what is the risk of diffuse axonal injury?", an FE brain model with validated strain prediction is required. If the question is "will the rib fracture?", an FE thorax with cortical bone damage is needed. Matching the model's validated output domain to the decision being made is the central engineering judgment in HBM application.

In practice, this means maintaining a model inventory with documented validation status per body region and per loading direction. A model validated for frontal impact is not automatically valid for lateral or rear impact. The validation hierarchy is not a one-time certification; it is a living record that must be extended whenever the model is applied outside its validated envelope.