Why the brain does not simply follow the skull during a head impact.
A head-mounted inertial sensor can measure how the head moves. It cannot directly measure how the brain moves inside the skull. Between those two events lies a mechanical transfer system made of skull, cerebrospinal fluid, membranes, vessels, and a brain whose tissue is soft, heterogeneous, and viscoelastic. That transfer is one reason why two impacts with similar peak accelerations can produce different intracranial responses.
The simplest picture of a head impact would be a rigid skull containing a brain that moves with it. Real measurements do not support that picture. During acceleration and impact, the skull changes motion first. Brain tissue partly follows, partly lags behind, deforms, and continues moving after the skull's own motion has already changed. Cerebrospinal fluid permits relative motion, while the falx, tentorium, vessels, ventricles, and other anatomical structures constrain and redirect it.
Cadaver experiments using implanted neutral-density targets have directly measured millimetre-scale brain motion relative to the skull during impact. In living volunteers, tagged magnetic resonance imaging has shown that even mild head motion produces spatially non-uniform deformation — rotation, extension, and different loading directions engage different regions. Intracranial response is not a scaled copy of external head acceleration.
Brain tissue behaves partly like an elastic solid and partly like a viscous material. An elastic material stores deformation energy and tends to recover its shape. A viscous material dissipates energy and resists motion in a time-dependent way. Brain tissue does both, and neither behaviour is constant across all loading conditions.
Its apparent stiffness depends on how rapidly it is loaded. A deformation lasting a few milliseconds samples a different part of the tissue's mechanical response than a slower deformation lasting tens of milliseconds. Frequency matters for the same reason: higher-frequency components are generally attenuated differently from lower-frequency components, and phase relationships change with frequency. Tissue properties also vary by region, direction, strain magnitude, temperature, and experimental method.
There is no single, universal number that can be called "brain stiffness" for every impact — and no one universally accepted model that turns a measured acceleration waveform into a unique map of brain strain.
The word filter is useful if it's taken literally rather than as a figure of speech. The skull–CSF–brain system does not transmit every part of an impact waveform equally. Some components are attenuated. Some are delayed. Some excite larger-scale deformation modes that persist after the original input has already changed. The resulting deformation is spatially shaped by anatomy.
Human in-vivo studies have identified dominant deformation modes in the approximate 7–14 Hz range during mild rotation and extension. These are not universal injury frequencies and should not be turned into fixed thresholds — but they do show that the living human brain has measurable dynamic modes, and that a short external pulse can excite a longer intracranial response.
This has an immediate implication for head-impact measurement. Peak acceleration is only one description of the input. Duration, rise time, angular velocity, rotational impulse, direction, the timing between translation and rotation, and the frequency composition of the waveform can all affect how that input is transferred into the brain.
For much of the cerebrum, rotational motion is strongly associated with distortional deformation and shear. Angular velocity and the duration over which rotation develops often contain information that is lost when only peak angular acceleration is retained. Translation remains important too, especially for pressure, focal contact response, and some inferior or interface-related responses. Real impacts commonly combine both.
The practical consequence is not that one should replace linear acceleration with one rotational number. It's that the mechanical input is multidimensional. A waveform has amplitude, direction, duration, temporal structure, and coupling between its translational and rotational components. A brain with viscoelastic and anatomical structure can respond differently to different combinations of these features even when conventional peak values are similar.
The brain is not mechanically uniform. Gray matter and white matter differ in microstructure; white-matter fibres introduce directionality. The corpus callosum, brainstem, deep white matter, ventricular margins, sulci, and mesial temporal structures sit in distinct mechanical environments. The falx and tentorium constrain motion; vessels are tethered structures embedded in moving tissue; cerebrospinal-fluid spaces alter local boundary conditions.
Human imaging and modelling point toward multiple mechanical pathways rather than one generic "brain strain":
This distinction matters because an imaging abnormality is not a direct photograph of the original impact waveform. It's a later, modality-specific observation of one branch of a mechanical and biological cascade.
A sensor can measure the external input to this system, provided it is adequately coupled to the skull and its measurement limitations are understood.
Even validated finite-element head models can produce materially different strain estimates when given the same external kinematics. The result depends on anatomy, boundary conditions, and the constitutive description of brain tissue used.
The purpose of a multidimensional description of an impact is not to pretend that every waveform feature is itself a tissue variable. It's to avoid discarding potentially meaningful information before the mechanical transfer problem has even been considered.
If two events have the same peak acceleration but differ in duration, rotational impulse, loading–unloading asymmetry, frequency content, or translation–rotation organisation, a viscoelastic brain is not obliged to respond to them the same way. Conventional peak metrics can collapse mechanically different events into the same number. IFS preserves more of the structure of the forcing waveform, so those differences remain available for classification, comparison, and later modelling.
Reduced-order skull-to-brain models may eventually provide useful additional features — calibrated to estimate phase lag, attenuation, relative motion, or a chosen strain surrogate. But they should remain explicitly labelled as model-derived proxies. They are not a substitute for full finite-element modelling, and a one- or two-mode representation cannot recover arbitrary local axonal, vascular, or pressure responses.
The established evidence already justifies treating head impacts as time-dependent, multidimensional mechanical events. These questions are more speculative — interesting directions for future work, not claims.
Can a small number of calibrated modes capture enough skull-to-brain phase lag, attenuation, and recovery to add useful information to wearable-sensor analysis — without pretending to reconstruct local tissue mechanics?
Which combinations of rotation, translation, direction, duration, and frequency are sufficiently reproducible to predict broad classes of intracranial deformation across people and impact types?
Does incomplete mechanical or biological recovery change the response to the next event — and can a sequence of impacts be described more meaningfully than by counting events or summing peaks?
Football-head contact can generate a very rapid pressure disturbance before the later gross head motion is fully developed. Could that early mechanical event alter the subsequent tissue or vascular response — or is it biologically negligible once the later inertial deformation is controlled? This remains an unproven hypothesis.
These sources are sufficient for this public-facing annex; the underlying evidence base and additional methodological caveats run deeper.
The six IFS domains this annex refers back to.