When a hit lands, the skull moves first. The brain, sitting inside it like a stiff jelly suspended in cerebrospinal fluid, lags slightly behind. In the instant between the skull moving and the brain catching up, the tissue stretches. That stretch — measured as a ratio rather than a distance — is what biomechanists call strain.
If the strain stays small, the tissue snaps back unharmed. If it crosses a tolerance threshold, the long white-matter fibres that connect one brain region to another can be damaged. That’s the proposed mechanism behind diffuse axonal injury, the kind of damage that shows up in repetitive head-impact research and in studies of professional contact-sport players.
How strain gets quantified
The headline figure researchers usually quote is Maximum Principal Strain (MPS) — the largest stretch ratio at any moment during the impact, in any direction. An MPS of 0.10 means the tissue stretched by 10 % at its worst moment. In practice the absolute maximum across all elements is sensitive to numerical artefacts in the underlying simulation, so studies typically report a high-percentile statistic instead. trace* follows that convention and predicts MPS90 — the 90th-percentile maximum principal strain — within each region.
What counts as “elevated” varies by region and by paper, but as a rough orientation:
| MPS range | Interpretation |
|---|---|
| < 0.10 | Low — typical of everyday head movement |
| 0.10–0.20 | Moderate — common in routine contact-sport play |
| > 0.20 | Elevated — associated with higher injury-risk literature |
These thresholds are not diagnoses. They are statistical bands from published cohorts.
Where the numbers come from — biomechanics models
You cannot directly measure brain strain in a living athlete. The gold standard is a finite-element brain model: a digital reconstruction of skull, brain, ventricles, and the membranes between them, broken into hundreds of thousands of tiny tetrahedra. You feed it the recorded head kinematics, and a solver computes how each tetrahedron deforms.
A handful of detailed models do this:
- Imperial College (IC) brain model (Ghajari, Hellyer & Sharp, 2017) — about 1 million elements representing 11 tissues; validated against post-mortem human-subject experiments. This is the model whose predictions the trace XGBoost was trained to imitate.*
- KTH head model (Royal Institute of Technology, Stockholm) — long-running open-source model used in many sport-injury studies.
- WHIM — Worcester Head Injury Model — high-resolution finite-element model with detailed white-matter tract atlases.
- THUMS — Total Human Model for Safety — Toyota’s whole-body model, used widely in automotive research.
The catch: running any of these models against a single recorded impact takes 5–6 hours on a high-performance compute cluster. You can do it once per study; you cannot do it for every impact in every match of every season.
Why trace* exists
trace* doesn’t run a finite-element model live. Instead, it learns from the output of one — millions of FE-simulated impacts — and trains a much faster surrogate model that takes the mouthguard kinematics and returns a per-region MPS estimate in milliseconds.
You lose a little accuracy compared to a full simulation. You gain the ability to do it at the touchline, for every impact, for every athlete, in real-time. For monitoring exposure across a season or a career, that trade is the whole point.
Sources & further reading
- Ghajari, M., Hellyer, P. & Sharp, D. (2017) — Computational modelling of traumatic brain injury predicts the location of chronic traumatic encephalopathy pathology. Brain 140 (2). — The Imperial College FE brain model trace* uses as its ground truth.
- Chan, E. Y. K., Yu, X., Qin, C. & Ghajari, M. (2025) — Balancing efficiency and accuracy. Engineering Applications of Artificial Intelligence 162, 112489.
- Kleiven, S. — Predictors for traumatic brain injuries evaluated through accident reconstructions — The KTH head model.