Background article for impactfeaturespace.com. Narrative history; sources and limits of checking are stated in the evidence notes.
Every head impact produces linear acceleration of the head's centre of mass and angular acceleration about it, in different proportions depending on the impact direction, location and the head's coupling to the neck and body [1]. Since the 1940s the question has been which of the two, if either, accounts for which kinds of brain injury. The answer changed as experimental methods, neuropathology, regulatory practice and measurement technology changed.
This article follows that history. It is a narrative review written for a general scientific readership, not a systematic review. Several older sources were checked at the level of their bibliographic records and abstracts, and a few details come from secondary sources. The evidence notes at the end state where that applies.
Terms used in this article
Head impact: a mechanical event, for example one recorded by a sensor.
Kinematic severity: a property of the measured signal (peak acceleration, Severity Index, Head Injury Criterion). It is not a clinical severity grade.
Concussion: a clinical diagnosis. How the term developed is covered in the companion article on terminology.
Clinical severity: the Glasgow Coma Scale, duration of loss of consciousness and post-traumatic amnesia.
1940s: concussion as a consequence of head acceleration
In Oxford, Denny-Brown and Russell published a large experimental study of concussion in 1941 [2]. A contemporaneous summary distinguished "acceleration concussion," which accompanies closed head injury, from "compression concussion," which required a crushing injury or skull penetration [3]. That summary does not separate linear from rotational acceleration.
The rotational argument was made in 1943 by A. H. S. Holbourn, a research physicist, in The Lancet [4]. As later described by Kleiven, Holbourn observed shear strain patterns in two-dimensional gel models and argued that translation of the head is not injurious, whereas rotation can account for most traumatic brain injury because brain tissue is nearly incompressible [5]. Holbourn extended the argument in the British Medical Bulletin in 1945 [6].
Pudenz and Shelden placed a transparent lucite calvarium on macaques and used high-speed cinematography to record brain movement after blows and gunshot wounds to the head [7].
1950s–1960s: white matter pathology
Strich (1956) described diffuse degeneration of cerebral white matter in patients who survived severe head injury with dementia [8]. In 1961 she proposed shearing of nerve fibres as the cause of the damage [9]. Peerless and Rewcastle (1967) examined 37 patients and described axonal and small-vessel injury concentrated in the diencephalon and mesencephalon. They argued that a blow to the head imparts rotational velocity to the brain and that the resulting shear strains distort and rupture axons and vessels [10]. Adams and colleagues later analysed 45 non-missile head injury cases with diffuse axonal injury (DAI) [11].
1950s–1970s: the automotive, linear-acceleration tradition
In parallel, the Wayne State University group (Gurdjian, Lissner, Patrick and colleagues) measured acceleration and intracranial pressure in experimental head injury, with skull fracture and severe injury as the principal concern [12–14]. Acceleration–duration tolerance relations from this work are referred to as the Wayne State Tolerance Curve. Later literature describes the Severity Index (SI) and then the Head Injury Criterion (HIC) as developed from analyses of that curve [15].
Gadd (1966) proposed a weighted-impulse integration that accounted for both the intensity and duration of the acceleration pulse, replacing peak acceleration or pulse-area criteria [16]. The Severity Index is calculated as SI = ∫ a(t)2.5 dt, with acceleration a in multiples of g and time in milliseconds [16]. Versace (1971) reviewed the Severity Index, concluded that its derivation contained inconsistencies, and recommended a formula that followed the tolerance-limit data more literally. He also wrote that a more appropriate severity measure would reflect the probable degree of brain injury [17].
NHTSA's own account states that in 1972 a proposal was issued to replace the Gadd Severity Index in Federal Motor Vehicle Safety Standard 208 with the Head Injury Criterion [18]. HIC is the maximum, over any time window from t1 to t2, of (t2 − t1) multiplied by the window-averaged resultant acceleration raised to the power 2.5 [18]. The window is now limited to 36 ms (HIC36, limit 1,000) or 15 ms (HIC15, limit 700) in the current standard [19]. The exact date on which HIC replaced SI in the regulation was not established in preparing this article. In automotive regulation and testing, HIC computed from the linear acceleration of a headform has remained the principal verification measure [5].
These criteria were derived from linear acceleration of the head. They were not designed to represent rotational loading.
In sport, the NOCSAE specification for new football helmets (document ND002, version 17m19a, effective November 2019) requires that the peak Severity Index of any drop impact not exceed 1200, that the lowest-velocity (11.34 ft/s, 3.46 m/s) drop impacts not exceed 300, and that the peak Severity Index of any pneumatic ram impact not exceed 1200. It also requires that peak rotational acceleration in any ram test on the medium headform not exceed 6,000 rad/s². A 2017 revision removed the rotational acceleration pass/fail criterion for two other headform sizes [20]. The document does not state the rationale for the rotational limit. Football helmet certification therefore rests mainly on the Severity Index, with a limited rotational criterion added in recent versions.
1960s–1970s: primate experiments on rotation
Ommaya and colleagues developed primate concussion models in the 1960s [21, 22] and examined whiplash-type loading and brain damage [23]. Ommaya and Hirsch (1971) published tolerances for concussion from head impact and whiplash in primates [24]. Hirsch and Ommaya (1970) compared the significance of translational and rotational motion after impact [25], and Gennarelli, Thibault and Ommaya (1972) studied the pathophysiological responses to rotational and translational head accelerations [26].
Ommaya and Gennarelli (1974) correlated experimental and clinical observations in blunt head injury [27]. Their hypothesis, now referred to as the centripetal theory of concussion [28], holds that mechanically induced disruption progresses from the surface of the brain toward the centre with increasing severity. In Ommaya's formulation, as summarised by Kleiven, rotation can produce both focal and diffuse injuries, whereas translation is limited to focal effects [5].
1980s–1990s: direction of rotation and diffuse axonal injury
Gennarelli and colleagues (1982) accelerated the heads of 45 monkeys without impact in one of three directions. Coma duration, neurological impairment and the amount of DAI were directly related to the amount of coronal head motion. Coma lasting more than six hours occurred in 20 of 26 animals with lateral motion, which also developed DAI, and in only one animal in the sagittal or oblique groups. The authors concluded that axonal damage from coronal head acceleration is a major cause of prolonged traumatic coma [29]. This is the most cited evidence that the direction of rotation matters.
Thibault and Gennarelli (1985) summarised tolerance criteria derived from primate experiments, physical surrogates and isolated tissue elements. Under impulsive angular acceleration, the primate response ranged from mild concussion to massive diffuse white matter damage with prolonged coma [30]. Margulies and Thibault (1992) proposed a tolerance criterion for DAI in man [31].
What injures tissue is deformation
The quantity that injures tissue is deformation, not head acceleration. Direct in vivo strain measurements exist only for non-injurious loading, made with tagged MRI in volunteers [32–34]. Direction of rotation matters, but not identically across species. In primates the coronal plane gave the longest comas [29]. In swine, axial-plane rotation produced immediate prolonged coma and coronal rotation did not, while diffuse axonal injury occurred in both planes [35, 36]. The cellular and metabolic sequence that follows tissue deformation is described in the companion article on what happens inside the head in a sports concussion.
2000s: instrumented sport and the combined question
Instrumented helmets recorded head impacts in football from the early 2000s. Pellman and colleagues reconstructed professional football impacts and injuries [37]. King and colleagues (2003) asked directly whether head injury is caused by linear or angular acceleration. They noted that a helmeted head sustained the same angular acceleration as an unhelmeted head while linear acceleration fell substantially. They concluded that this was difficult to reconcile with a purely angular-acceleration hypothesis and proposed that input acceleration limits be replaced by response variables [38, 39]. Zhang, Yang and King (2004) reported that shear stress around the brainstem region was a candidate injury predictor for concussion in reconstructions of field accidents [39].
Greenwald and colleagues (2008) examined linear acceleration, rotational acceleration, impact duration and impact location in football players. They formed a composite score (weighted principal component score) by principal component analysis and compared its receiver operating characteristic curves with classical measures [40]. The head impact telemetry system used in this work estimated angular acceleration indirectly from linear accelerometer data [41].
2010s: rotational velocity, strain and risk functions
Rowson and Duma (2011) described the STAR helmet evaluation system, built on a risk function for concussion and measured on-field exposure [42]. Rowson and colleagues (2012) derived injury risk functions from rotational kinematics in football [15]. Rowson and Duma (2013) introduced the combined probability of concussion, based on peak linear and rotational acceleration. In the field dataset, the combined probability and linear acceleration alone were significantly better predictors than rotational acceleration alone, and not different from each other. In the dataset of reconstructed professional impacts, no parameter differed significantly from another [43]. The authors also stated that no federal or industry head injury standard then considered rotational acceleration [43].
Takhounts and colleagues (2013) proposed BrIC, a kinematic criterion derived from angular velocity and calibrated against brain-model strain measures. They reported that BrIC correlated best with the strain-based measures CSDM and MPS, concluded that rotational velocity rather than rotational acceleration was the relevant kinematic mechanism in their analysis, and stated that BrIC could capture injuries in situations where translational acceleration criteria such as HIC are insufficient [44].
Kleiven (2013), in a perspective article, argued from finite element analysis that the bulk modulus of brain tissue is roughly five to six orders of magnitude larger than its shear modulus, so the brain deforms predominantly in shear. He concluded that rotational kinematics should indicate traumatic brain injury risk better than linear acceleration, and that radial impacts mainly cause skull fracture [5]. Sports and automotive helmets, he noted, were then tested mainly with radial impacts, with the exception of an oblique test for motorcycle helmets that assessed external projections and surface friction [5].
What the injury endpoint is
The dependent variable in injury risk functions is a clinical label. Mild TBI case definitions varied between studies (in the WHO task force review some required neither loss of consciousness nor amnesia and some excluded imaging abnormalities) [45], recovery endpoints vary between studies [46], and under-reporting required statistical adjustment in field data [43]. Part of the limited discriminative performance of kinematic thresholds may therefore reflect endpoint heterogeneity and not only the information in the kinematic signal. This is an interpretation by the authors of this article and not a finding of the cited studies.
Current position
The linear and rotational explanations are no longer treated as exclusive alternatives. Linear acceleration remains the basis of most automotive and many helmet criteria and is associated with skull fracture and pressure-related focal injury. Rotational kinematics are associated with strain in brain tissue and with diffuse injury. In field data from football, peak linear acceleration has performed comparably to composite measures [43], and neither linear nor angular peaks alone have been established as a diagnostic threshold.
Regulatory practice has begun to change. UN Regulation No. 22 (06 series) for motorcycle helmets was adopted by the UN World Forum for Harmonization of Vehicle Regulations in June 2020 and entered into force on 3 January 2021. It added an oblique impact test [47]. According to conference papers evaluating helmets under the new regulation, the oblique tests use five impact configurations at 8.0 m/s and limit peak rotational acceleration to 10.4 krad/s² and BrIC to 0.78. Peak linear acceleration and HIC are not evaluated in the oblique test [48, 49]. The thresholds are quoted from those papers and not from the regulation text. This makes BrIC an example of a rotational criterion that has entered a regulation.
Instrumented mouthguards now measure six-degree-of-freedom kinematics directly, rather than estimating angular acceleration from linear sensors [41].
Evidence notes
These notes record the limits of the checking behind this article, so that readers can weigh the statements accordingly.
Journal, volume, page and DOI details were checked against indexed records for most references. For many older works (the 1950s–1970s primate, Wayne State and white-matter papers and the Stapp Car Crash conference papers) the checking covered the record and abstract, not the full text. Statements about these works are kept at the level of what they describe or examined.
Holbourn's argument is described as summarised by Kleiven, and not from Holbourn's text.
Pudenz and Shelden recorded brain movement after blows and gunshot wounds. The abstract does not describe the loading as rotational.
The date on which HIC replaced the Severity Index in FMVSS 208 was not established. Only the 1972 proposal is documented here.
The UN Regulation 22.06 pass/fail values come from two IRCOBI conference papers, not from the regulation text. Adoption and entry-into-force dates come from UNECE documents.
The NOCSAE values come directly from the standard (ND002-17m19a). Newer versions may exist; the current version should be checked at nocsae.org.
The author list of the instrumented mouthguard paper was not verified against the bibliographic record.
The statement that later literature describes SI and HIC as derived from the Wayne State curve relies on a secondary source.