Impact Feature Space: Representing Head-Motion Waveforms from Wearable Sensors

Impact Feature Space: Representing Head-Motion Waveforms from Wearable Sensors | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Impact Feature Space: Representing Head-Motion Waveforms from Wearable Sensors Jyrki Launes, Kati Peltonen, Matti Vartiainen, Laura Hokkanen This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9652948/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Background : Peak linear acceleration and peak rotational velocity are commonly used for describing head-motion events in sport. These kinematic measurements capture the intensity of the recorded motion but compress the full waveform to a scalar, discarding structural, temporal, and frequency-domain information. Waveform structure, temporal organisation, rotational–translational coupling, and frequency content are dimensions of the mechanical event that peak values miss. Objective : To introduce the Impact Feature Space (IFS), a multidimensional representation of head-motion waveforms in which each event is described across multiple mechanical domains, and to demonstrate empirically that IFS structural features and the peak kinematic metrics are mutually non-predictive — capturing orthogonal dimensions of the recorded motion — and that this orthogonality has discriminative properties. Methods : Head-motion events recorded during elite-level women’s ice hockey were captured using the ACT Head Impact Tracker Pro positioned over the mastoid process and expressed as measurement vectors spanning four mechanical domains. : structural waveform, translational–rotational coupling, spectral and vibration, and artefact detection. Principal component analysis was used to quantify the intrinsic dimensionality of the peak kinematic 6-variable and IFS structural 111-variable feature sets, as well as the orthogonality between them, across the full dataset of 4,402 events. . Random forest and histogram gradient boosting classifiers were then applied to a gameplay-restricted subset (n = 661 events) to illustrate the discriminative consequences of this orthogonality. Results : The peak kinematic feature set was effectively one-dimensional: two components explained 96.4% of total variance. The IFS structural feature set required 14 components to reach 80% of variance, and 55.3% of its total variance was mathematically orthogonal to the entire peak kinematic feature set. In the gameplay illustration, peak kinematic features performed at chance (ROC-AUC 53–56%), while IFS features achieved 73–74% AUC consistently using random forest and histogram gradient boosting . Conclusions : Peak kinematic metrics and IFS structural features represent two distinct and mutually non-predictive characterisations of head-motion events: the former describe intensity, the latter describe mechanical organisation. The IFS provides access to structural information that is not recoverable from peak values and offers a complementary representation for the analysis of head-motion waveforms. head impact monitoring impact biomechanics head kinematics waveform analysis feature space wearable sensors concussion head injury load monitoring repetitive head exposure ice hockey Figures Figure 1 Figure 2 1 Introduction Head impact measurement in sport studies has most commonly been performed using peak linear acceleration and peak rotational velocity measurements with wearable inertial sensors, summarising a limited set of peak kinematic measurements. These metrics originated in impact biomechanics laboratories, where they served as practical approximations of complex kinematic events and were calibrated against injury thresholds derived from cadaveric and animal studies. As field deployment of wearable sensor technology became routine, the same scalar summaries were carried forward [ 1 – 8 ], embedded in detection and reporting thresholds [ 9 ], and used as inputs to injury-risk models [ 10 – 13 ]. This history shows the practical constraints of early instrumentation as much as any theoretical commitment; the measures were adopted as convenient summary statistics and, over time, accepted as complete descriptions of the mechanical event. However, peak kinematic measurements are indicators of overall impact intensity but capture only a portion of the mechanical characteristics of head motion [ 1 – 3 , 5 , 14 ]. Biomechanical simulation and laboratory studies have demonstrated that head motion during impacts is complex, involving rapid and time-varying interactions across multiple axes of movement that are not reflected in peak values alone, and even neck musculature and anticipatory activation modulate head kinematics during impacts [ 16 , 17 ]. These modulatory effects may be better reflected in waveform structure than in peak magnitudes. The translational and rotational components of the motion evolve differently over time, the activity waveforms have structural information about the nature of the collision, and two events producing identical peak accelerations may differ in other respects. The role of rotational kinematics in the mechanics of brain injury was recognised in the foundational work of Holbourn in 1943 [ 40 ] and remains central [ 15 , 18 ]. Finite-element modelling indicates that regional brain strain responses correlate with the product of rotational acceleration magnitude and duration — effectively, rotational velocity — but not with linear acceleration independently [ 19 ]. Despite this, field monitoring continues to report peak rotational velocity as a parallel scalar alongside linear acceleration, examining each independently of the other even though both contribute to head impact kinematics and their relationship varies with impact location and direction [ 8 , 10 ]. The majority of field studies report only peak resultant kinematic magnitudes on the basis that higher values indicate greater severity, without accounting for signal characteristics such as frequency content, pulse duration, or the coupling between rotational and translational components that may influence brain injury risk [ 8 ]. The data consisting of mainly peak kinematic measurements will in this paper be referred to as traditional kinematic features. A more complete description of head-motion events therefore requires consideration of multiple signal features that together describe the mechanical organisation of the recorded motion [ 3 ]. The present study introduces the concept of an Impact Feature Space (IFS): a multidimensional representation of head-motion events in which each event is described not as a set of peak scalars but as a measurement vector whose components are derived from the recorded waveform across multiple mechanical domains. Duration, frequency composition, the temporal relationship between rotational and translational components, and the complexity of waveform shape are all derivable from the signal the device already records [ 20 – 22 ]. In impact analysis, the traditional peak kinematic measurements and IFS structural measures have fundamentally different roles. Peak kinematic measurements primarily function as indicators of event intensity, whereas the structural measures of the IFS describe the mechanical organisation of the motion itself, including temporal structure, rotational–translational relationships, and frequency characteristics [ 13 ]. We describe here the IFS concept, its four measurement domains, and the sensor placement requirements. We demonstrate that the traditional peak kinematic values cannot be used to predict IFS structural features, and IFS structural features cannot be used to predict peak kinematic values. The two representations are orthogonal in purpose and in mathematical content. We then present results in two parts. First, the primary theoretical demonstration on the full dataset of 4,402 impact events, establishing the dimensionality and orthogonality properties of the two representations. Second, an illustration using a gameplay classification task to show that the orthogonality means that IFS has discriminative potential that peak kinematic measures do not. 2 Methods 2.1 Design rationale In the dominant tradition of head-impact monitoring, events are described through measurements such as peak linear acceleration or peak rotational velocity or acceleration. These measures are well validated, widely reported, and have value as indicators of overall impact intensity. They do not, however, describe the shape of the waveform, the temporal relationship between translational and rotational motion, or the frequency composition of the signal. These structural properties are present in the time-series and can be recorded, but are discarded if the signal is reduced to a scalar maximum. The IFS uses structural information by treating each recorded event as a point in a high-dimensional measurement space rather than as a single number. The full waveform is the input; the IFS is the structured output. Because the structural properties of a waveform are not determined by its peak value — two waveforms with the same maximum can have entirely different shapes, durations, and frequency profiles — the IFS and peak metrics are expected to capture different information. This is not a design decision but a mathematical consequence of the measurement structure, and it is verified empirically in this study. The feature groupsof the IFS are defined to capture different aspects of the impact process (e.g., temporal evolution, frequency content, translational–rotational interaction) and are therefore intended to represent mechanistically distinct signal domains rather than alternative parameterizations of the same quantity. 2.2 Measurement validity and sensor placement Sensor placement is critical for signal validity in wearable head-motion measurement. A sensor mounted on a helmet records helmet motion; a sensor coupled directly to the skull records head motion. These are different physical quantities, and no analytical correction can recover what was not measured [ 4 , 24 , 25 ]. The relative motion between helmet and head is non-negligible and varies with impact magnitude, direction, helmet fit, and padding properties. During high-magnitude impacts, the helmet may lead or lag the head substantially [ 24 ], meaning that the waveform recorded by a helmet-mounted sensor bears a complex and impact-dependent relationship to actual head kinematics. For the IFS, the sensor placement requirement is particularly consequential. Waveform structure — the properties the IFS is designed to capture — is exactly what helmet coupling corrupts [ 27 , 28 ]. The IFS as defined here is therefore applicable only to sensors coupled directly to the skull; in the present study, the mastoid process was used, which provides direct skull coupling without the confound of an intervening equipment layer. 2.3 Measurement domains Four measurement domains define the space. 1. A structural waveform domain captures the internal temporal organisation of the motion signal — the presence of secondary peaks, oscillatory patterns, or irregular motion sequences that reflect how the mechanical event evolves from onset through resolution. It records whether the motion was a clean single pulse, a complex oscillatory sequence, or something in between — properties that vary with the mechanics of the contact and that are not reflected in the peak value the signal produces. 2. The translational–rotational coupling domain describes the relative contribution of rotational motion to overall head movement during the event. This domain captures how rotational and translational motion related to each other within the event — a property that varies with impact location, direction, and contact mechanics. This relationship is of particular biomechanical significance given the well-established primacy of rotational kinematics in the mechanics of brain injury in sport [ 15 , 29 ]. 3. The spectral and vibration domain describes the frequency composition of the impact waveform: short, high-frequency impulses are associated with rigid direct contacts, whereas lower-frequency, longer-duration signals tend to reflect impacts mediated by body mass or soft-tissue interactions. This domain captures what the frequency content of the waveform reveals about the physical nature of the contact in a way that no peak value can. 4. The artefact detection domain quantifies signal patterns that are characteristic of sensor disturbances rather than genuine head motion, providing a principled basis for distinguishing true impacts from spurious threshold crossings. It captures whether the signal pattern is consistent with genuine head motion at all, or whether it bears the structural hallmarks of sensor disturbance — a question that magnitude-based criteria cannot answer because artefact events and genuine impacts occupy overlapping magnitude ranges. Table 1 lists representative measures from the three primary IFS domains with a description of what each captures. The mathematical structure of IFS components is outlined in Table 1 . A discussion positioning the IFS concept within the existing head-impact monitoring literature is provided in Supplementary Appendix . Table 1 Representative measures from the three primary domains of the Impact Feature Space, with a plain-language description of what each captures. Mathematical definitions, signal formulas, and units for IFS structural variables are provided in Supplementary Appendix A. Contextual positioning of the IFS concept within the existing head-impact monitoring literature is provided in Supplementary Appendix B. Domain Measure What it captures Structural waveform Kurtosis of linear acceleration Impulsiveness of the waveform; high values indicate a sharp, brief peak; low values indicate a sustained, broadly distributed signal Skewness of linear acceleration Temporal asymmetry of waveform shape; reflects whether the signal rises and decays symmetrically or has a rapid onset with a slow decay Duration above 10% of peak Temporal persistence of the event; longer duration reflects extended mechanical loading relative to peak intensity Waveform crest factor Ratio of peak to RMS amplitude; sensitive to brief high-amplitude transients that do not reflect sustained loading VBA waveform shape index Captures the internal morphology of the vector-based acceleration signal across the event window Translational–rotational coupling Rotational-to-linear peak ratio Relative contribution of rotational to translational motion; varies with impact location, direction, and contact mechanics Peak timing offset Time difference between peak angular acceleration and peak linear acceleration; reflects whether rotational and translational components are coincident or temporally decoupled Rotational dominance index Fraction of total kinematic energy carried by the rotational component over the full event window VBA rotational path length Cumulative path length of the angular velocity vector; reflects total rotational complexity independent of peak magnitude Linear-to-rotational ratio Inverse coupling measure; captures the balance of translational versus rotational loading within the event Spectral and vibration Spectral entropy Frequency-domain complexity; high entropy reflects broad multi-frequency content characteristic of genuine body contact; low entropy reflects narrow-band signals associated with rigid contacts or sensor disturbances Dominant frequency Frequency of maximum power in the Welch power spectral estimate; distinguishes low-frequency body-mass impacts from high-frequency rigid contacts HF/LF spectral ratio Ratio of high-frequency to low-frequency power in the angular velocity spectrum; artefact events concentrate energy at high frequencies VBA vibration clearance Clearance factor of the vibration-band signal; sensitive to transient high-energy oscillations not sustained across the event window Bandpower distribution Relative energy in low (0–20 Hz), mid (20–80 Hz), and high (80–200 Hz) frequency bands; characterises the spectral profile of the contact 2.4 Measuring equipment and software ACT Head Impact Tracker Pro (Northern Sports Insight and Intelligence, Helsinki, Finland) was worn via an adjustable headband positioned over the mastoid process behind one ear. The device simultaneously measures tri-axial linear acceleration and tri-axial angular velocity at a sampling rate of 1000 Hz. Event detection was driven by a threshold crossing on the linear acceleration signal: whenever the resultant linear acceleration exceeded 10 g , the device was triggered and stored the preceeding 5 ms and subsequent 70 ms of motion data across six kinematic channels (linear acceleration and angular velocity in 3-dimensional coordinates). In the ACT system, recorded signals are not subject to data loss or channel dropout under normal operating conditions as all six channels are complete for every detected event. It continuously scans for linear acceleration and records events only when the resultant linear acceleration exceeds the 10 g detection threshold, meaning that routine head movements associated with skating, running, or other normal athletic activity do not enter the dataset [ 9 ]. The recorded event pool therefore consists of threshold-crossing events — a mixture of genuine head contacts and artefact events that cross the threshold due to equipment knocks, sensor disturbances, or high-acceleration non-contact movements. Data are transmitted via Bluetooth Low Energy to a smartphone application and stored in a cloud service, from which raw impact data can be downloaded. The software that calculates IFS components’ values is the proprietary property of the first author. Figure 1 shows a typical impact pattern recorded from live ice hockey play. 2.5 Demonstration dataset Thirty-four competitive ice-hockey players from two Finnish teams of the of the national championship league for women's ice-hockey, had 4402 recorded impacts during 19 consecutive game events in September and October 2025 using the ACT Head Impact Tracker Pro. The median peak acceleration was 187 m/s 2 (range 44–2841m/s 2 ; 75th percentile 315 m/s 2 ) in this series of recordings. Ice hockey was selected as the demonstration context because it generates a large number of threshold-crossing events across varied gameplay and non-gameplay recording periods within a single session, providing natural variation in event context. Independently derived event-context labels from the Wisehockey [ 30 ] player-tracking system, which uses dedicated puck- and player-tracking infrastructure to record player positions and states in real time, permitted validation against an external reference standard not derived from the sensor data. Based on the event-context labels, the dataset was divided into on-ice events (n = 367; recorded during active on-ice gameplay periods) and off-ice events (n = 4,035; recorded during on-bench, warm-up, intermissions, and post-game periods). The events during active gameplay (n = 661, recorded during periods 1–3 and overtime) included those recorded whilst the player was seated on the bench (n = 294) in addition to those recorded whilst they were physically on the ice (n = 367). 2.6 Signal processing and feature extraction The angular velocity signals were smoothed before computation of signal-derived variables using a fourth-order Butterworth low-pass filter; the cutoff frequency was set at 165 Hz. The analysis derives three composite scalar time-series from the six raw measurement channels. The resultant linear acceleration magnitude is defined as l(t) = √(ax²(t) + ay²(t) + az²(t)) where ax, ay, and az are the three orthogonal linear acceleration components in m/s². The resultant angular velocity magnitude is defined as ω(t) = √(ωa²(t) + ωb²(t) + ωc²(t)) where ωa, ωb, and ωc are the three orthogonal angular velocity components in rad/s. Angular acceleration magnitude is derived numerically as α(t) = dω(t)/dt using a finite-difference approximation over the 1 ms sampling interval. These three composite signals - l(t), ω(t), and α(t) - together with their component-wise counterparts, form the complete basis for all subsequent computation of signal-derived measures. Each recorded event is then represented as a point x ∈ ℝⁿ, where n is the number of computed measures and each component x i corresponds to a single derived quantity extracted from one or more of these signals across the 75 ms event window. The coordinates of x define the position of the event within the Impact Feature Space. The Impact Feature Space representation is implemented in proprietary software developed by the first author. 2.7 Statistical analysis Principal component analysis (PCA) was applied separately to the traditional kinematic feature set (6 variables: peak linear acceleration and peak angular velocity and angular acceleration at 0–20 ms and 0–75 ms windows) and the IFS structural feature set (111 variables) to quantify the intrinsic dimensionality of each representation. All variables were standardised to zero mean and unit variance before decomposition. The number of components required to explain 80% of total variance was taken as the primary dimensionality index. The proportion of IFS structural variance mathematically orthogonal to the entire traditional feature set was quantified by projecting the IFS variables onto the space spanned by all traditional principal components and computing the proportion of residual (unexplained) variance; this figure represents the fraction of IFS information that cannot be captured by any linear combination of traditional peak metrics and equally, the fraction of IFS information from which peak values cannot be predicted. These analyses were conducted on the full dataset of 4402 events. To examine event separation in the full dataset, projection onto the first two principal components of each feature space was used to assess the spatial organisation of on-ice events (n = 367; recorded during active on-ice gameplay periods) relative to all types of off-ice events (n = 4,035; recorded during on-bench, warm-up, intermissions, and post-game periods). Linear discriminant analysis (LDA) with stratified five-fold cross-validation then quantified this separation numerically, using balanced accuracy (BACC), sensitivity, and area under the receiver operating characteristic curve (ROC-AUC) as performance metrics. Mann-Whitney U tests with rank-biserial correlation effect sizes (|r_bc|) identified IFS structural measures with large and mechanically interpretable differences between on-ice and off-ice events. As a focused applied illustration of the orthogonality result, random forest (RF) and histogram gradient boosting (HGB) classifiers were applied to the subset of events recorded during active gameplay periods only (including events on-ice and on-bench during periods 1–3 and overtime; n = 661). Within this subset, the on-ice classification label partitioned events into those recorded whilst the participant was physically on the ice (n = 367) and those recorded whilst they were seated on the bench (n = 294), yielding a near-balanced binary classification problem in which both classes share the same gameplay context and both exceed the 10 g detection threshold. Bench events cannot be distinguished from ice events on the basis of timing alone — both occur within the same active play periods — and any classification performance must therefore reflect information encoded in the waveform itself rather than in when the event was recorded. The traditional feature set comprised the six raw peak kinematic measures only. IFS variables included all structural variables together with integral (area-under-curve) measures, yielding 111 IFS variables. All 111 IFS variables were entered into the classifiers without prior feature selection, dimensionality reduction, or any optimisation specific to the gameplay classification task. Three models were trained for each algorithm: traditional peak metrics only (6 variables), IFS measures only (111 variables), and all features combined (117 variables). RF models used 300 trees and the square-root feature subsampling rule with balanced class weights. HGB models used a maximum depth of 3, a learning rate of 0.05, minimum leaf size of 20, L2 regularisation of 1.0, and early stopping with a 15% validation fraction and patience of 20 rounds. All models used balanced class weights and were evaluated using stratified five-fold cross-validation. Feature importances for the combined RF model were computed using mean decrease in impurity (MDI) across all trees. Analyses were performed in Python (version 3.12) using scikit-learn (version 1.4) and SciPy (version 1.13). Effect sizes for Mann-Whitney U tests are reported as rank-biserial correlations, computed as |r_bc| = 1 − (2U / n₁n₂). 3 Results 3.1 Dimensionality and orthogonality of the traditional and IFS representations (full dataset, n = 4,402) Principal component analysis of the traditional kinematic feature set revealed that two components explained 96.4% of total variance, with the first component alone accounting for 76.3%. The IFS structural feature set required 14 components to explain 80% of total variance. The first principal component explained 25.0% of variance; the first two components together accounted for 38.3%. Of the total variance in the IFS structural feature set, 55.3% is mathematically orthogonal to the entire traditional feature set. 3.2 Event separation in the full dataset Projection onto the first two principal components of the traditional feature space showed substantial overlap between on-ice and off-ice events, with no clear spatial boundary between the two classes. Projection onto the first two IFS structural components showed a partially different organisational structure, with on-ice events occupying a more distinct region, though substantial overlap remained at the two-component level. Linear discriminant analysis with stratified five-fold cross-validation on the full dataset (n = 4,402; class imbalance 11.0:1) produced a traditional BACC of 50.0%, sensitivity of 0.0%, and ROC-AUC of 64.8%. The IFS structural feature set produced a BACC of 59.0% and ROC-AUC of 82.2%. 3.3 Structural measures distinguishing on-ice from off-ice events Mann-Whitney U tests identified IFS structural measures with large and mechanically interpretable differences between on-ice and off-ice events across the full dataset. Linear acceleration kurtosis was lower for on-ice events (medians: 6.07 vs 8.50; |r_bc| = 0.348, p < 0.001). Waveform skewness followed the same direction (medians: 1.88 vs 2.37; |r_bc| = 0.340, p < 0.001), indicating that on-ice events produced more symmetrical waveforms with less rightward asymmetry than the off-ice pool. Duration above 10% of peak was longer for on-ice events (medians: 54 ms vs 44 ms; |r_bc| = 0.208, p < 0.001). The rotational-to-linear peak ratio was higher for on-ice events (medians: 6.89 vs 4.94; |r_bc| = 0.191, p < 0.001). 3.4 Applied illustration: classifier comparison during gameplay (n = 661) Classification was evaluated on the 661 events recorded during active gameplay periods (on-ice n = 367, bench-seated n = 294). The traditional feature set (6 variables) produced BACC of 53.2% (± 3.1%) and ROC-AUC of 53.0% (RF) and 55.9% (HGB). The IFS feature set (111 variables) produced BACC of 67.4% (± 3.5%) and ROC-AUC of 74.2% (RF) and 73.2% (HGB). The combined feature set (117 variables) produced ROC-AUC of 74.0% (RF) and 73.5% (HGB) (Fig. 2 .) Feature importances from the combined RF model (mean decrease in impurity) showed that all 20 of the highest-ranked features were drawn from the IFS set; no traditional peak measure appeared among the top 20. The five highest-ranked individual variables were waveform kurtosis, vibration clearance, phase decay time, spectral entropy, and VBA rotational path length. 4 Discussion This study demonstrates that peak kinematic metrics and the Impact Feature Space represent fundamentally different characterisations of head-motion events. The dimensionality analysis shows that the traditional feature set is effectively one-dimensional, while the IFS distributes information across multiple independent components. The finding that 55.3% of IFS variance is orthogonal to the traditional feature set means that the two representations are mutually non-predictive and cannot be derived from one another. 4.1 Orthogonality and mutual non-predictability between IFS and peak metrics Even though both linear and angular measurements are included, the dimensionality analysis establishes a fundamental property of the traditional kinematic feature set. Two principal components account for 96.4% of total variance, with the first explaining 76.3%. This near-singular dimensionality reflects strong collinearity among peak magnitude measures, which function as highly correlated indices of overall event intensity. This means that the traditional feature set is one-dimensional, providing a ranking of events by intensity only. In contrast, the IFS structural feature set distributes variance across multiple components. Fourteen features are required to explain 80% of variance, with the first accounting for only 25.0% and the first two for 38.3%. This reflects the design of the IFS, in which multiple measurement capture several distinct mechanical properties and independent dimensions of mechanical variation. It should be noted that while, due to phase of software development, we used 111 variables in this analysis, the concept of IFS is not restricted to these only. The decisive result is the orthogonality between the two representations. Of the total variance in the IFS structural feature set, 55.3% is mathematically orthogonal to the traditional feature set. More than half of the information in the IFS cannot be recovered from any linear combination of traditional peak metrics, as defined within the principal component representation used here. This orthogonality is interpreted here as an empirical indicator of non-redundant information content within the chosen representation, rather than as proof of statistical independence or causal separation. The two representations are therefore mutually non-predictive, which is a structural property of what they measure, not a consequence of measurement precision. This distinction has direct practical implications. Reducing a waveform to a peak value removes information about temporal evolution, waveform structure, rotational–translational coupling, and frequency content. Events with identical peak magnitudes may differ substantially in these properties, which may carry biomechanical significance [ 8 , 13 ]. The IFS retains and represents this information by expressing each event as a multidimensional measurement vector derived from the recorded waveform. Peak measurements indicate event intensity, whereas IFS features describe the mechanical organisation of motion. These are not competing descriptions but address different questions: how intense an event was versus how it unfolded mechanically. This bidirectional non-predictability defines the IFS concept and provides the basis for interpreting all subsequent analyses. This conceptual distinction is matched by empirical evidence. Peak metrics cannot predict IFS structural features, nor can IFS features predict peak metrics as demonstrated in Results 3.1. 4.2 Dimensionality constraints and event separability The PCA projection results are consistent with the dimensionality findings. In the traditional feature space, on-ice and off-ice events overlap in the two-component projection because a representation that captures essentially one dimension of variation cannot separate classes that differ across multiple mechanical dimensions. There is no additional variance available in the traditional feature set to support separation beyond intensity. In contrast, the IFS projection shows a partially distinct organisational structure for on-ice events. The remaining overlap at the two-component level is expected: the first two IFS components capture only 38.3% of total variance, while 14 components are required to explain 80%. The discriminative structure of the IFS is therefore distributed across higher dimensions not visible in low-dimensional projections. The LDA results make this dimensionality contrast explicit. The traditional feature set achieves 50.0% balanced accuracy and zero sensitivity, reflecting the inability of a one-dimensional representation to separate classes that do not differ along its single axis. The IFS achieves 59.0% balanced accuracy and ROC-AUC of 82.2% on the same task. The larger gain in AUC reflects the ability of the IFS to provide meaningful rank-ordering across events, even when threshold-based accuracy is constrained by class imbalance. These results demonstrate that dimensionality is not a descriptive property alone but directly determines the separability that any classifier can achieve. 4.3 Feature-level differences and biomechanical interpretation The individual feature comparisons provide an opportunity for a mechanically coherent interpretation of the separation observed in the IFS. A detailed analysis is not within the scope of this study, but as an example, on-ice events exhibit lower kurtosis and skewness, indicating broader and more symmetrical waveforms compared to the sharply peaked transients characteristic of off-ice events. Duration above 10% of peak was longer for on-ice events, reflecting sustained mechanical loading, while the higher rotational-to-linear peak ratio indicates stronger coupling between rotational and translational motion. These differences are consistent with the biomechanics of head contact. Sustained impacts transmitted through body mass and tissue produce temporally extended, structurally complex signals, whereas sensor disturbances generate brief, high-amplitude transients with limited rotational coherence. Taken together, these findings suggest that the separability observed in the IFS arises from physically meaningful differences in waveform structure rather than from statistical artefacts. In other words, events that are indistinguishable in peak magnitude occupy distinct regions of the IFS because they differ in how the motion unfolds over time and across mechanical domains. 4.4 Role of rotational kinematics and translational–rotational coupling Rotational kinematics occupy a central role within the IFS, reflecting established biomechanical understanding of brain injury mechanisms. Since Holbourn’s early work [ 40 ], the sensitivity of neural tissue to rotational shear has been recognised, and finite-element modelling indicates that the majority of brain strain energy arises from rotational motion [ 19 , 33 ]. Despite this, field monitoring practice typically treats rotational velocity as a scalar reported alongside linear acceleration, without examining their relationship within each event. The translational–rotational coupling domain of the IFS captures this relationship explicitly. The relative contribution, timing, and coordination of rotational and translational motion vary systematically with impact location, direction, and contact mechanics. These distinctions are invisible when each component is reduced to an independent peak value. By representing their interaction within the waveform, the IFS provides access to mechanically meaningful differences that are directly relevant to injury mechanisms but are not recoverable from scalar metrics. 4.5 Applied classification: practical implications of orthogonality The gameplay classification demonstrates how the orthogonality between IFS features and peak metrics translates into practical discriminative performance. By restricting analysis to events recorded during active gameplay periods, where both on-ice and bench-seated (on-bench) events occur under identical temporal and recording conditions, classification must rely on waveform structure rather than contextual cues. Under these conditions, the traditional feature set performs at chance (ROC-AUC 53–56%), confirming that peak magnitude alone does not contain sufficient information to distinguish between the two event types. It should be noted that the IFS feature set was used in its entirety without task-specific feature selection or optimisation; the reported AUC of 73–74% therefore represents a conservative estimate of the discriminative potential of the IFS for this task, and targeted feature selection or dimensionality reduction would be expected to improve performance. The consistency of results across random forest and histogram gradient boosting — two methods with distinct learning strategies — confirms that the discriminative advantage of the IFS does not depend on the choice of algorithm. The combined feature set does not improve performance beyond the IFS alone, consistent with the orthogonality finding: the information captured by peak metrics does not provide independent discriminative signal once the structural dimensions of the IFS are represented. Feature importance rankings further support this interpretation, with all top-ranked variables originating from the IFS domains. 4.6 Artefact detection as an emergent property The IFS provides a principled basis for handling artefact events that does not rely on externally imposed magnitude thresholds or heuristic filtering. Because the detection threshold is defined by resultant linear acceleration, both genuine head contacts and incidental sensor disturbances enter the dataset when they exceed the same trigger criterion [ 34 ]. Conventional approaches address this by applying secondary thresholds, duration filters, or manual inspection, all of which depend on investigator-defined rules that may not generalise across devices or contexts. In the IFS, artefact character emerges from waveform structure. Sensor disturbances cross the detection threshold through mechanisms that differ systematically from genuine head contacts: their signals are shorter in duration, concentrated in narrower frequency bands, and exhibit weaker or incoherent coupling between translational and rotational components. Genuine impacts, by contrast, produce temporally sustained signals with consistent inter-axis relationships and mechanically coherent coupling patterns. These differences are expressed across the structural, spectral, and coupling domains simultaneously. Artefact events therefore occupy distinct regions of the measurement space without requiring explicit exclusion criteria. The distinction is not imposed on the data but arises from the same structural properties that define the IFS representation. 4.7 Individual variability and longitudinal implications Beyond event-level description, the IFS enables analysis at the level of the individual athlete and over time. The same peak acceleration may correspond to different mechanical events depending on factors such as head mass, neck musculature, and anticipatory activation, all of which modulate head kinematics during impact [ 16 , 17 ]. These differences are expressed in waveform structure rather than in peak magnitude. Individuals therefore exhibit characteristic distributions within the IFS, reflecting both their biomechanical properties and the patterns of contact they experience. Each athlete occupies a region of the feature space over a monitoring period, and deviations from this individual baseline may provide a more sensitive indicator of change than comparisons to population-level norms. This is particularly relevant for cumulative exposure. Repeated low-magnitude impacts may differ substantially in mechanical structure despite similar peak values [ 35 – 37 ], and aggregation based on peak magnitude alone conflates mechanically distinct events. The IFS provides a richer per-event representation that may support more informative cumulative exposure metrics, providing a new tool for studying the relationship between structural features and clinical outcomes. 4.8 Toward intracranial mechanical response modelling A natural extension of the IFS is toward modelling intracranial mechanical response. The brain does not follow skull motion rigidly; its deformation depends on the temporal profile of the kinematic input as well as its magnitude. Finite-element models and reduced-order mechanical systems treat the head kinematic signal as a time-series the shape, duration, and frequency content of which determine strain responses [ 13 , 19 , 33 ]. The structural properties captured by the IFS — including waveform duration, rise characteristics, and spectral composition — correspond directly to parameters that influence intracranial strain in these models. For example, the response of viscoelastic systems depends on input pulse shape and duration. The IFS features describe these events theoretically relevant to intracranial mechanics. Whether IFS features provide predictive value for brain strain beyond peak-based metrics remains an empirical question requiring paired kinematic and intracranial data. However, the conceptual alignment between IFS features and established biomechanical models provides a clear basis for such investigations. 4.9 Sensor placement as a prerequisite for valid waveform analysis The validity of the IFS depends critically on sensor placement. A sensor mounted on a helmet records a composite of helmet and head motion, with relative motion that varies across impacts and cannot be reconstructed analytically [ 24 , 27 ]. This limitation affects all head-impact measurement but is particularly consequential for waveform-based analysis. Peak metrics may be partially robust to moderate signal distortion because they depend on the maximum value of the signal. In contrast, waveform structure — including duration, oscillatory patterns, frequency content, and translational–rotational coupling — is directly altered by helmet motion. Applying the IFS to helmet-mounted data would therefore describe helmet dynamics rather than head motion. The IFS as defined here is thus applicable only to sensors coupled directly to the skull. This is not a matter of measurement precision but of measuring the correct physical quantity. 4.10 Limitations The demonstration dataset comprised events from two Finnish female ice-hockey teams recorded over 19 games; the generalisability of the observed IFS feature distributions to other sports, populations, and levels of play is beyond the scope of this study. The classification task distinguishes events by player location and differences in activity (playing or sitting) rather than by injury relevance, and both on-ice and bench-seated categories include many event types. The present study does not establish relationships between IFS structural features and injury outcomes. Such relationships require datasets linking head kinematics to clinical or biomechanical endpoints, including intracranial strain estimates. In addition, the IFS feature set was developed for a specific sensor system and anatomical placement; adaptation and independent validation would be required for application to other devices [ 38 , 39 ]. 4.11 Conclusion Peak metrics describe event intensity, whereas IFS structural features capture how motion unfolds over time, including waveform structure, rotational–translational coupling, and frequency content. These properties enable discrimination between events that are indistinguishable in peak magnitude and provide a basis for analysing mechanical characteristics that are otherwise lost when the waveform is reduced to a scalar. The results indicate that waveform structure constitutes a distinct and informative dimension of head-impact analysis. Incorporating this information does not extend peak-based monitoring but complements it by capturing mechanical properties that peak metrics do not represent. The Impact Feature Space therefore provides a basis for more complete description of head-motion events and a foundation for future work linking kinematic waveform features to biomechanical and clinical outcomes. Declarations Ethics approval and consent to participate The ice hockey measurements were conducted as part of the Sustainable Careers in Elite Contact Sports (SUCCESS) study, approved by the Ethics Committee of Helsinki University Hospital (HUS/5422/2024, 3 July 2024). All procedures were conducted in accordance with the principles of the Declaration of Helsinki, and informed written consent was obtained from all participants. Consent for publication Not applicable. Funding Ice hockey measurements were part of the Sustainable Careers in Elite Contact Sports (SUCCESS) study, funded by the Research Council of Finland (Academy Programme for Sport Science and Physical Activity ACTIVE), grant number 361442. Development of the IFS methodology received no specific funding. Authors’ contributions JL conceived the study, developed the IFS methodology, performed the data analysis, and drafted the manuscript. KP contributed to data collection, study design and critical revision. MV contributed to data collection, study design, and critical revision. LH contributed to study design, neuropsychological interpretation, critical revision, supervision and funding. All authors read and approved the final manuscript. Competing interests J.L. is named as an inventor on a pending patent application filed with the Finnish Patent and Registration Office concerning methods for extracting and representing waveform-derived features from wearable head-impact sensor data, including aspects of the Impact Feature Space methodology described in this manuscript. The patent application was filed before submission of the manuscript. No licensing income or commercial revenue has been received. The other authors declare no competing interests. Availability of data and materials The individual-level head-impact data are restricted because the recorded events are linked to identifiable players within the research dataset compromising participant confidentiality. The Impact Feature Space methodology and feature-extraction software are proprietary and are not publicly available at the time of submission because they are subject to intellectual property protection. 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Kinematic and biomechanical analysis of head impacts in the National Football League. Annals of Biomedical Engineering , 44(2), 454–462. https://doi.org/10.1007/s10439-015-1502-5 Camarillo, D. B., Shull, P. B., Mattson, J., Shultz, R., & Garza, D. (2013). An instrumented mouthguard for measuring linear and angular head impact kinematics in American football. Annals of Biomedical Engineering , 41(9), 1939–1949. https://doi.org/10.1007/s10439-013-0801-y Rowson, S., & Duma, S. M. (2022). A review of head injury metrics used in automotive safety and sports protective equipment. Journal of Biomechanical Engineering , 144(11), 110801. https://doi.org/10.1115/1.4054379 Joodaki, H., Bailey, A., Lessley, D., Funk, J., Sherwood, C., & Crandall, J. (2019). Relative motion between the helmet and the head in football impact test. Journal of Biomechanical Engineering , 141(8), 081006. https://doi.org/10.1115/1.4043038 Jones, B., Tooby, J., Weaving, D., Till, K., Owen, C., Begonia, M., Stokes, K. A., Rowson, S., Phillips, G., Hendricks, S., Falvey, É. C., Al-Dawoud, M., & Tierney, G. (2022). Ready for impact? A validity and feasibility study of instrumented mouthguards (iMGs). British Journal of Sports Medicine , 56(20), 1171–1179. https://doi.org/10.1136/bjsports-2022-105523 Sciacca, D., & Ionescu, A. (2025). Helmet–head decoupling in ice hockey impacts: An in-lab exploratory study using autoregressive modeling. Annals of Biomedical Engineering , 53(11), 3141–3155. https://doi.org/10.1007/s10439-025-03848-2 Luke, D., Kenny, R., Bondi, D., Clansey, A., & Wu, L. C. (2024). On-field instrumented mouthguard coupling. Journal of Biomechanics , 162, 111889. https://doi.org/10.1016/j.jbiomech.2023.111889 Clansey, A. C., Bondi, D., Kenny, R., Luke, D., Masood, Z., Gao, Y., Elez, M., Ji, S., Rauscher, A., van Donkelaar, P., & Wu, L. C. (2024). On-field head acceleration exposure measurements using instrumented mouthguards: Multi-stage screening to optimize data quality. Annals of Biomedical Engineering , 52(10), 2666–2677. https://doi.org/10.1007/s10439-024-03592-z Giza, C. C., & Hovda, D. A. (2014). The new neurometabolic cascade of concussion. Neurosurgery , 75 Suppl 4, S24–S33. https://doi.org/10.1227/NEU.0000000000000505 Wisehockey Ltd. (2025). Wisehockey real-time ice hockey analytics platform. Available from: https://wisesport.com/hockey. Accessed October 2025. Zhao, W., & Ji, S. (2017). Brain strain uncertainty due to shape variation in and simplification of head angular velocity profiles. Biomechanics and Modeling in Mechanobiology , 16(2), 449–461. https://doi.org/10.1007/s10237-016-0829-7 Bain, A. C., & Meaney, D. F. (2000). Tissue-level thresholds for axonal damage in an experimental model of central nervous system white matter injury. Journal of Biomechanical Engineering , 122(6), 615–622. https://doi.org/10.1115/1.1324667 Kleiven, S. (2007). Predictors for traumatic brain injuries evaluated through accident reconstructions. Stapp Car Crash Journal , 51, 81–114. https://doi.org/10.4271/2007-22-0003 Wang, T., Kenny, R., & Wu, L. C. (2021). Head impact sensor triggering bias introduced by linear acceleration thresholding. Annals of Biomedical Engineering , 49(12), 3189–3199. https://doi.org/10.1007/s10439-021-02868-y McKee, A. C., Stern, R. A., Nowinski, C. J., Stein, T. D., Alvarez, V. E., Daneshvar, D. H., et al. (2013). The spectrum of disease in chronic traumatic encephalopathy. Brain , 136(Pt 1), 43–64. https://doi.org/10.1093/brain/aws307 Mainwaring, L., Pennock, K. M. F., Mylabathula, S., & Alavie, B. Z. (2018). Subconcussive head impacts in sport: A systematic review of the evidence. International Journal of Psychophysiology , 132, 39–54. https://doi.org/10.1016/j.ijpsycho.2018.01.007 Caccese, J. B., Best, C., Lamond, L. C., DiFabio, M., Kaminski, T. W., Watson, D. A. N., Getchell, N., & Buckley, T. A. (2019). Effects of repetitive head impacts on a concussion assessment battery. Medicine & Science in Sports & Exercise , 51, 1355–1361. https://doi.org/10.1249/MSS.0000000000001905 Gabler, L., Patton, D., Begonia, M., Daniel, R., Rezaei, A., Huber, C., Siegmund, G., Rooks, T., & Wu, L. C. (2022). Consensus Head Acceleration Measurement Practices (CHAMP): Laboratory validation of wearable head kinematic devices. Annals of Biomedical Engineering , 50(11), 1356–1371. https://doi.org/10.1007/s10439-022-03066-0 Kuo, C., Patton, D., Rooks, T., Tierney, G., McIntosh, A., Lynall, R., Esquivel, A., Daniel, R., Kaminski, T., Mihalik, J., Dau, N., & Urban, J. (2022). On-field deployment and validation for wearable devices. Annals of Biomedical Engineering , 50(11), 1372–1388. https://doi.org/10.1007/s10439-022-03001-3 Holbourn, A. H. S. (1943). Mechanics of head injuries. The Lancet , 242(6267), 438–441. https://doi.org/10.1016/S0140-6736(00)87453-X Additional Declarations Competing interest reported. J.L. is named as an inventor on a pending patent application filed with the Finnish Patent and Registration Office concerning methods for extracting and representing waveform-derived features from wearable head-impact sensor data, including aspects of the Impact Feature Space methodology described in this manuscript. The patent application was filed before submission of the manuscript. No licensing income or commercial revenue has been received. The other authors declare no competing interests. Supplementary Files IFSSupplementv17BMC.docx AppendixStructuredSummaryStatements.docx Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-9652948","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":637928625,"identity":"5bae44e2-c485-440f-afc0-897c4fb738b5","order_by":0,"name":"Jyrki Launes","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABA0lEQVRIiWNgGAWjYBACxgYGZoYEBgsI72MDgwyQDxKR4yGgRQLCmdnAwAPVYoxTCxAwAzFECzMvSAtExBi3+hm5jw0eMEjIG9xuPvzZdocNj3w772GgiIEMTofNSDdOADrMcMOdY2nSuWfSeAwO8yUDRQxw+2VGGvMBoBbGDTdyzJhz2w7zGDDzGANF/hDUYr/hRv7nz5Zt/3nkm8Fa8NsCclgi0BYGaca2AzwMh3mM8Tus5xmzQYKBRPLMG2lmkr1tyUC/8BgDRXBrMWxPY5b8UWFj23cj+fGHn212cvL9Z4yBIgb2OLVMSACSBhjimCJwIM9/ALfkKBgFo2AUjAIwAADu7Ex+4pl4/QAAAABJRU5ErkJggg==","orcid":"","institution":"University of Helsinki","correspondingAuthor":true,"prefix":"","firstName":"Jyrki","middleName":"","lastName":"Launes","suffix":""},{"id":637928627,"identity":"a8d1743c-ad33-4538-9796-c38386fad3ba","order_by":1,"name":"Kati Peltonen","email":"","orcid":"","institution":"University of Helsinki","correspondingAuthor":false,"prefix":"","firstName":"Kati","middleName":"","lastName":"Peltonen","suffix":""},{"id":637928629,"identity":"e731de8b-7df3-499c-8ae0-289670bfcd80","order_by":2,"name":"Matti Vartiainen","email":"","orcid":"","institution":"University of Helsinki","correspondingAuthor":false,"prefix":"","firstName":"Matti","middleName":"","lastName":"Vartiainen","suffix":""},{"id":637928630,"identity":"efc8d683-2571-459d-9b2f-882639d4328a","order_by":3,"name":"Laura Hokkanen","email":"","orcid":"","institution":"University of Helsinki","correspondingAuthor":false,"prefix":"","firstName":"Laura","middleName":"","lastName":"Hokkanen","suffix":""}],"badges":[],"createdAt":"2026-05-08 10:39:49","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":true,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-9652948/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9652948/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":109068234,"identity":"43e5486e-1357-4ed3-a6a7-7df6c7d2c403","added_by":"auto","created_at":"2026-05-12 10:04:49","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":802128,"visible":true,"origin":"","legend":"\u003cp\u003eA randomly selected 412 m/s\u003csup\u003e2\u003c/sup\u003e (42 \u003cem\u003eg\u003c/em\u003e) impact during ice hockey game play recorded using the\u0026nbsp; ACT Head Impact Tracker Pro device which was worn on head band on the mastoid process. Upper panel shows a peak in linear acceleration caused by an outside force on the player’s head. Middle panel shows the resulting rotational movement which starts when linear acceleration has had time to interact with mass and continues steady for the remaining recorded period of 70 ms. Lowest panel shows angular acceleration occurring only for a brief period after the initial impact. This is a artefact-free good quality record. Please note the time scale, the 75 ms time window corresponds roughly to one frame in a video played at 13.3 Hz frame rate. Such a video would appear flickering but movement would be recognizable.\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-9652948/v1/eba596906ae18cf52e1846df.png"},{"id":109042893,"identity":"5dc8e917-70af-4ab1-9ebb-36419121f3e7","added_by":"auto","created_at":"2026-05-12 04:31:51","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":193845,"visible":true,"origin":"","legend":"\u003cp\u003eROC curves for classification of on-ice vs on-bench events during active gameplay periods (n = 661; on-ice n = 367, bench-seated n = 294). The traditional feature set comprised six raw peak kinematic measures (peak linear and angular acceleration and velocity at 0–20 ms and 0–75 ms windows); the IFS feature set comprised 111 variables including all structural, coupling, spectral, vibration, and artefact domain measures together with integral (area-under-curve) variables. Colour indicates feature set: red, traditional; blue, IFS. Line style indicates algorithm: solid, random forest (RF); dashed, histogram gradient boosting (HGB). The traditional feature set produces ROC-AUC of 53.0% (RF) and 55.9% (HGB), statistically indistinguishable from chance; the IFS feature set yields 74.2% (RF) and 73.2% (HGB). Balanced accuracy: traditional 53.2% (±3.1%), IFS 67.4% (±3.5%), five-fold cross-validation. All 20 of the highest-ranked features by mean decrease in impurity in the combined RF model were drawn from the IFS set; no traditional peak measure appeared among the top 20.\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-9652948/v1/c661b1d274d9ed5abc2d7a7f.png"},{"id":109204773,"identity":"bf135618-f4b1-423e-9474-0d75f6439e01","added_by":"auto","created_at":"2026-05-13 15:02:07","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1067713,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9652948/v1/6c3f1118-ca41-4656-906b-afa3d7012435.pdf"},{"id":109042896,"identity":"631d646e-6b2d-49c6-af29-99ef6fe9621c","added_by":"auto","created_at":"2026-05-12 04:31:51","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":10546,"visible":true,"origin":"","legend":"","description":"","filename":"IFSSupplementv17BMC.docx","url":"https://assets-eu.researchsquare.com/files/rs-9652948/v1/1af9f4d64cc9cc3fb5360ce2.docx"},{"id":109042895,"identity":"42a8ac4e-222e-4bf1-9068-054e65caf37a","added_by":"auto","created_at":"2026-05-12 04:31:51","extension":"docx","order_by":2,"title":"","display":"","copyAsset":false,"role":"supplement","size":14861,"visible":true,"origin":"","legend":"","description":"","filename":"AppendixStructuredSummaryStatements.docx","url":"https://assets-eu.researchsquare.com/files/rs-9652948/v1/93935ecd20f6a25b3cd7e335.docx"}],"financialInterests":"Competing interest reported. J.L. is named as an inventor on a pending patent application filed with the Finnish Patent and Registration Office concerning methods for extracting and representing waveform-derived features from wearable head-impact sensor data, including aspects of the Impact Feature Space methodology described in this manuscript. The patent application was filed before submission of the manuscript. No licensing income or commercial revenue has been received. The other authors declare no competing interests.","formattedTitle":"Impact Feature Space: Representing Head-Motion Waveforms from Wearable Sensors","fulltext":[{"header":"1 Introduction","content":"\u003cp\u003eHead impact measurement in sport studies has most commonly been performed using peak linear acceleration and peak rotational velocity measurements with wearable inertial sensors, summarising a limited set of peak kinematic measurements. These metrics originated in impact biomechanics laboratories, where they served as practical approximations of complex kinematic events and were calibrated against injury thresholds derived from cadaveric and animal studies. As field deployment of wearable sensor technology became routine, the same scalar summaries were carried forward [\u003cspan additionalcitationids=\"CR2 CR3 CR4 CR5 CR6 CR7\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e], embedded in detection and reporting thresholds [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e], and used as inputs to injury-risk models [\u003cspan additionalcitationids=\"CR11 CR12\" citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]. This history shows the practical constraints of early instrumentation as much as any theoretical commitment; the measures were adopted as convenient summary statistics and, over time, accepted as complete descriptions of the mechanical event. However, peak kinematic measurements are indicators of overall impact intensity but capture only a portion of the mechanical characteristics of head motion [\u003cspan additionalcitationids=\"CR2\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e, \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e, \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eBiomechanical simulation and laboratory studies have demonstrated that head motion during impacts is complex, involving rapid and time-varying interactions across multiple axes of movement that are not reflected in peak values alone, and even neck musculature and anticipatory activation modulate head kinematics during impacts [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e, \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e]. These modulatory effects may be better reflected in waveform structure than in peak magnitudes. The translational and rotational components of the motion evolve differently over time, the activity waveforms have structural information about the nature of the collision, and two events producing identical peak accelerations may differ in other respects. The role of rotational kinematics in the mechanics of brain injury was recognised in the foundational work of Holbourn in 1943 [\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e] and remains central [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e, \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]. Finite-element modelling indicates that regional brain strain responses correlate with the product of rotational acceleration magnitude and duration \u0026mdash; effectively, rotational velocity \u0026mdash; but not with linear acceleration independently [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]. Despite this, field monitoring continues to report peak rotational velocity as a parallel scalar alongside linear acceleration, examining each independently of the other even though both contribute to head impact kinematics and their relationship varies with impact location and direction [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e, \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]. The majority of field studies report only peak resultant kinematic magnitudes on the basis that higher values indicate greater severity, without accounting for signal characteristics such as frequency content, pulse duration, or the coupling between rotational and translational components that may influence brain injury risk [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. The data consisting of mainly peak kinematic measurements will in this paper be referred to as traditional kinematic features. A more complete description of head-motion events therefore requires consideration of multiple signal features that together describe the mechanical organisation of the recorded motion [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThe present study introduces the concept of an Impact Feature Space (IFS): a multidimensional representation of head-motion events in which each event is described not as a set of peak scalars but as a measurement vector whose components are derived from the recorded waveform across multiple mechanical domains. Duration, frequency composition, the temporal relationship between rotational and translational components, and the complexity of waveform shape are all derivable from the signal the device already records [\u003cspan additionalcitationids=\"CR21\" citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eIn impact analysis, the traditional peak kinematic measurements and IFS structural measures have fundamentally different roles. Peak kinematic measurements primarily function as indicators of event intensity, whereas the structural measures of the IFS describe the mechanical organisation of the motion itself, including temporal structure, rotational\u0026ndash;translational relationships, and frequency characteristics [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eWe describe here the IFS concept, its four measurement domains, and the sensor placement requirements. We demonstrate that the traditional peak kinematic values cannot be used to predict IFS structural features, and IFS structural features cannot be used to predict peak kinematic values. The two representations are orthogonal in purpose and in mathematical content. We then present results in two parts. First, the primary theoretical demonstration on the full dataset of 4,402 impact events, establishing the dimensionality and orthogonality properties of the two representations. Second, an illustration using a gameplay classification task to show that the orthogonality means that IFS has discriminative potential that peak kinematic measures do not.\u003c/p\u003e"},{"header":"2 Methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1 Design rationale\u003c/h2\u003e \u003cp\u003eIn the dominant tradition of head-impact monitoring, events are described through measurements such as peak linear acceleration or peak rotational velocity or acceleration. These measures are well validated, widely reported, and have value as indicators of overall impact intensity. They do not, however, describe the shape of the waveform, the temporal relationship between translational and rotational motion, or the frequency composition of the signal. These structural properties are present in the time-series and can be recorded, but are discarded if the signal is reduced to a scalar maximum.\u003c/p\u003e \u003cp\u003eThe IFS uses structural information by treating each recorded event as a point in a high-dimensional measurement space rather than as a single number. The full waveform is the input; the IFS is the structured output. Because the structural properties of a waveform are not determined by its peak value \u0026mdash; two waveforms with the same maximum can have entirely different shapes, durations, and frequency profiles \u0026mdash; the IFS and peak metrics are expected to capture different information. This is not a design decision but a mathematical consequence of the measurement structure, and it is verified empirically in this study.\u003c/p\u003e \u003cp\u003eThe feature groupsof the IFS are defined to capture different aspects of the impact process (e.g., temporal evolution, frequency content, translational\u0026ndash;rotational interaction) and are therefore intended to represent mechanistically distinct signal domains rather than alternative parameterizations of the same quantity.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2 Measurement validity and sensor placement\u003c/h2\u003e \u003cp\u003eSensor placement is critical for signal validity in wearable head-motion measurement. A sensor mounted on a helmet records helmet motion; a sensor coupled directly to the skull records head motion. These are different physical quantities, and no analytical correction can recover what was not measured [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e, \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e, \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e]. The relative motion between helmet and head is non-negligible and varies with impact magnitude, direction, helmet fit, and padding properties. During high-magnitude impacts, the helmet may lead or lag the head substantially [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e], meaning that the waveform recorded by a helmet-mounted sensor bears a complex and impact-dependent relationship to actual head kinematics.\u003c/p\u003e \u003cp\u003eFor the IFS, the sensor placement requirement is particularly consequential. Waveform structure \u0026mdash; the properties the IFS is designed to capture \u0026mdash; is exactly what helmet coupling corrupts [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e, \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e]. The IFS as defined here is therefore applicable only to sensors coupled directly to the skull; in the present study, the mastoid process was used, which provides direct skull coupling without the confound of an intervening equipment layer.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e2.3 Measurement domains\u003c/h2\u003e \u003cp\u003eFour measurement domains define the space. 1. \u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eA structural waveform domain\u003c/span\u003e captures the internal temporal organisation of the motion signal \u0026mdash; the presence of secondary peaks, oscillatory patterns, or irregular motion sequences that reflect how the mechanical event evolves from onset through resolution. It records whether the motion was a clean single pulse, a complex oscillatory sequence, or something in between \u0026mdash; properties that vary with the mechanics of the contact and that are not reflected in the peak value the signal produces. 2. \u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eThe translational\u0026ndash;rotational coupling domain\u003c/span\u003e describes the relative contribution of rotational motion to overall head movement during the event. This domain captures how rotational and translational motion related to each other within the event \u0026mdash; a property that varies with impact location, direction, and contact mechanics. This relationship is of particular biomechanical significance given the well-established primacy of rotational kinematics in the mechanics of brain injury in sport [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e, \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e]. 3. \u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eThe spectral and vibration domain\u003c/span\u003e describes the frequency composition of the impact waveform: short, high-frequency impulses are associated with rigid direct contacts, whereas lower-frequency, longer-duration signals tend to reflect impacts mediated by body mass or soft-tissue interactions. This domain captures what the frequency content of the waveform reveals about the physical nature of the contact in a way that no peak value can. 4. \u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eThe artefact detection domain\u003c/span\u003e quantifies signal patterns that are characteristic of sensor disturbances rather than genuine head motion, providing a principled basis for distinguishing true impacts from spurious threshold crossings. It captures whether the signal pattern is consistent with genuine head motion at all, or whether it bears the structural hallmarks of sensor disturbance \u0026mdash; a question that magnitude-based criteria cannot answer because artefact events and genuine impacts occupy overlapping magnitude ranges.\u003c/p\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e lists representative measures from the three primary IFS domains with a description of what each captures. The mathematical structure of IFS components is outlined in Table \u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. A discussion positioning the IFS concept within the existing head-impact monitoring literature is provided in Supplementary Appendix .\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eRepresentative measures from the three primary domains of the Impact Feature Space, with a plain-language description of what each captures. Mathematical definitions, signal formulas, and units for IFS structural variables are provided in Supplementary Appendix A. Contextual positioning of the IFS concept within the existing head-impact monitoring literature is provided in Supplementary Appendix B.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003e Domain\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMeasure\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eWhat it captures\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eStructural waveform\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eKurtosis of linear acceleration\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eImpulsiveness of the waveform; high values indicate a sharp, brief peak; low values indicate a sustained, broadly distributed signal\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSkewness of linear acceleration\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eTemporal asymmetry of waveform shape; reflects whether the signal rises and decays symmetrically or has a rapid onset with a slow decay\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eDuration above 10% of peak\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eTemporal persistence of the event; longer duration reflects extended mechanical loading relative to peak intensity\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eWaveform crest factor\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eRatio of peak to RMS amplitude; sensitive to brief high-amplitude transients that do not reflect sustained loading\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eVBA waveform shape index\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eCaptures the internal morphology of the vector-based acceleration signal across the event window\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTranslational\u0026ndash;rotational coupling\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eRotational-to-linear peak ratio\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eRelative contribution of rotational to translational motion; varies with impact location, direction, and contact mechanics\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePeak timing offset\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eTime difference between peak angular acceleration and peak linear acceleration; reflects whether rotational and translational components are coincident or temporally decoupled\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eRotational dominance index\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eFraction of total kinematic energy carried by the rotational component over the full event window\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eVBA rotational path length\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eCumulative path length of the angular velocity vector; reflects total rotational complexity independent of peak magnitude\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eLinear-to-rotational ratio\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eInverse coupling measure; captures the balance of translational versus rotational loading within the event\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSpectral and vibration\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSpectral entropy\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eFrequency-domain complexity; high entropy reflects broad multi-frequency content characteristic of genuine body contact; low entropy reflects narrow-band signals associated with rigid contacts or sensor disturbances\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eDominant frequency\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eFrequency of maximum power in the Welch power spectral estimate; distinguishes low-frequency body-mass impacts from high-frequency rigid contacts\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eHF/LF spectral ratio\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eRatio of high-frequency to low-frequency power in the angular velocity spectrum; artefact events concentrate energy at high frequencies\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eVBA vibration clearance\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eClearance factor of the vibration-band signal; sensitive to transient high-energy oscillations not sustained across the event window\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eBandpower distribution\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eRelative energy in low (0\u0026ndash;20 Hz), mid (20\u0026ndash;80 Hz), and high (80\u0026ndash;200 Hz) frequency bands; characterises the spectral profile of the contact\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e2.4 Measuring equipment and software\u003c/h2\u003e \u003cp\u003eACT Head Impact Tracker Pro (Northern Sports Insight and Intelligence, Helsinki, Finland) was worn via an adjustable headband positioned over the mastoid process behind one ear. The device simultaneously measures tri-axial linear acceleration and tri-axial angular velocity at a sampling rate of 1000 Hz. Event detection was driven by a threshold crossing on the linear acceleration signal: whenever the resultant linear acceleration exceeded 10 \u003cem\u003eg\u003c/em\u003e, the device was triggered and stored the preceeding 5 ms and subsequent 70 ms of motion data across six kinematic channels (linear acceleration and angular velocity in 3-dimensional coordinates). In the ACT system, recorded signals are not subject to data loss or channel dropout under normal operating conditions as all six channels are complete for every detected event. It continuously scans for linear acceleration and records events only when the resultant linear acceleration exceeds the 10 g detection threshold, meaning that routine head movements associated with skating, running, or other normal athletic activity do not enter the dataset [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]. The recorded event pool therefore consists of threshold-crossing events \u0026mdash; a mixture of genuine head contacts and artefact events that cross the threshold due to equipment knocks, sensor disturbances, or high-acceleration non-contact movements. Data are transmitted via Bluetooth Low Energy to a smartphone application and stored in a cloud service, from which raw impact data can be downloaded. The software that calculates IFS components\u0026rsquo; values is the proprietary property of the first author. Figure\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e shows a typical impact pattern recorded from live ice hockey play.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e2.5 Demonstration dataset\u003c/h2\u003e \u003cp\u003eThirty-four competitive ice-hockey players from two Finnish teams of the of the national championship league for women's ice-hockey, had 4402 recorded impacts during 19 consecutive game events in September and October 2025 using the ACT Head Impact Tracker Pro. The median peak acceleration was 187 m/s\u003csup\u003e2\u003c/sup\u003e (range 44\u0026ndash;2841m/s\u003csup\u003e2\u003c/sup\u003e; 75th percentile 315 m/s\u003csup\u003e2\u003c/sup\u003e) in this series of recordings.\u003c/p\u003e \u003cp\u003eIce hockey was selected as the demonstration context because it generates a large number of threshold-crossing events across varied gameplay and non-gameplay recording periods within a single session, providing natural variation in event context. Independently derived event-context labels from the Wisehockey [\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e] player-tracking system, which uses dedicated puck- and player-tracking infrastructure to record player positions and states in real time, permitted validation against an external reference standard not derived from the sensor data. Based on the event-context labels, the dataset was divided into on-ice events (n\u0026thinsp;=\u0026thinsp;367; recorded during active on-ice gameplay periods) and off-ice events (n\u0026thinsp;=\u0026thinsp;4,035; recorded during on-bench, warm-up, intermissions, and post-game periods). The events during active gameplay (n\u0026thinsp;=\u0026thinsp;661, recorded during periods 1\u0026ndash;3 and overtime) included those recorded whilst the player was seated on the bench (n\u0026thinsp;=\u0026thinsp;294) in addition to those recorded whilst they were physically on the ice (n\u0026thinsp;=\u0026thinsp;367).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003e2.6 Signal processing and feature extraction\u003c/h2\u003e \u003cp\u003eThe angular velocity signals were smoothed before computation of signal-derived variables using a fourth-order Butterworth low-pass filter; the cutoff frequency was set at 165 Hz.\u003c/p\u003e \u003cp\u003eThe analysis derives three composite scalar time-series from the six raw measurement channels. The resultant linear acceleration magnitude is defined as\u003c/p\u003e \u003cp\u003e \u003cem\u003el(t) = \u0026radic;(ax\u0026sup2;(t)\u0026thinsp;+\u0026thinsp;ay\u0026sup2;(t)\u0026thinsp;+\u0026thinsp;az\u0026sup2;(t))\u003c/em\u003e \u003c/p\u003e \u003cp\u003ewhere ax, ay, and az are the three orthogonal linear acceleration components in m/s\u0026sup2;. The resultant angular velocity magnitude is defined as\u003c/p\u003e \u003cp\u003e \u003cem\u003eω(t) = \u0026radic;(ωa\u0026sup2;(t) + ωb\u0026sup2;(t) + ωc\u0026sup2;(t))\u003c/em\u003e \u003c/p\u003e \u003cp\u003ewhere ωa, ωb, and ωc are the three orthogonal angular velocity components in rad/s. Angular acceleration magnitude is derived numerically as\u003c/p\u003e \u003cp\u003e \u003cem\u003eα(t) = dω(t)/dt\u003c/em\u003e \u003c/p\u003e \u003cp\u003eusing a finite-difference approximation over the 1 ms sampling interval. These three composite signals - l(t), ω(t), and α(t) - together with their component-wise counterparts, form the complete basis for all subsequent computation of signal-derived measures. Each recorded event is then represented as a point x \u0026isin; ℝⁿ, where n is the number of computed measures and each component x\u003csub\u003ei\u003c/sub\u003e corresponds to a single derived quantity extracted from one or more of these signals across the 75 ms event window. The coordinates of x define the position of the event within the Impact Feature Space. The Impact Feature Space representation is implemented in proprietary software developed by the first author.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003e2.7 Statistical analysis\u003c/h2\u003e \u003cp\u003ePrincipal component analysis (PCA) was applied separately to the traditional kinematic feature set (6 variables: peak linear acceleration and peak angular velocity and angular acceleration at 0\u0026ndash;20 ms and 0\u0026ndash;75 ms windows) and the IFS structural feature set (111 variables) to quantify the intrinsic dimensionality of each representation. All variables were standardised to zero mean and unit variance before decomposition. The number of components required to explain 80% of total variance was taken as the primary dimensionality index. The proportion of IFS structural variance mathematically orthogonal to the entire traditional feature set was quantified by projecting the IFS variables onto the space spanned by all traditional principal components and computing the proportion of residual (unexplained) variance; this figure represents the fraction of IFS information that cannot be captured by any linear combination of traditional peak metrics and equally, the fraction of IFS information from which peak values cannot be predicted. These analyses were conducted on the full dataset of 4402 events.\u003c/p\u003e \u003cp\u003eTo examine event separation in the full dataset, projection onto the first two principal components of each feature space was used to assess the spatial organisation of on-ice events (n\u0026thinsp;=\u0026thinsp;367; recorded during active on-ice gameplay periods) relative to all types of off-ice events (n\u0026thinsp;=\u0026thinsp;4,035; recorded during on-bench, warm-up, intermissions, and post-game periods). Linear discriminant analysis (LDA) with stratified five-fold cross-validation then quantified this separation numerically, using balanced accuracy (BACC), sensitivity, and area under the receiver operating characteristic curve (ROC-AUC) as performance metrics. Mann-Whitney U tests with rank-biserial correlation effect sizes (|r_bc|) identified IFS structural measures with large and mechanically interpretable differences between on-ice and off-ice events.\u003c/p\u003e \u003cp\u003eAs a focused applied illustration of the orthogonality result, random forest (RF) and histogram gradient boosting (HGB) classifiers were applied to the subset of events recorded during active gameplay periods only (including events on-ice and on-bench during periods 1\u0026ndash;3 and overtime; n\u0026thinsp;=\u0026thinsp;661). Within this subset, the on-ice classification label partitioned events into those recorded whilst the participant was physically on the ice (n\u0026thinsp;=\u0026thinsp;367) and those recorded whilst they were seated on the bench (n\u0026thinsp;=\u0026thinsp;294), yielding a near-balanced binary classification problem in which both classes share the same gameplay context and both exceed the 10 g detection threshold. Bench events cannot be distinguished from ice events on the basis of timing alone \u0026mdash; both occur within the same active play periods \u0026mdash; and any classification performance must therefore reflect information encoded in the waveform itself rather than in when the event was recorded. The traditional feature set comprised the six raw peak kinematic measures only. IFS variables included all structural variables together with integral (area-under-curve) measures, yielding 111 IFS variables. All 111 IFS variables were entered into the classifiers without prior feature selection, dimensionality reduction, or any optimisation specific to the gameplay classification task. Three models were trained for each algorithm: traditional peak metrics only (6 variables), IFS measures only (111 variables), and all features combined (117 variables). RF models used 300 trees and the square-root feature subsampling rule with balanced class weights. HGB models used a maximum depth of 3, a learning rate of 0.05, minimum leaf size of 20, L2 regularisation of 1.0, and early stopping with a 15% validation fraction and patience of 20 rounds. All models used balanced class weights and were evaluated using stratified five-fold cross-validation. Feature importances for the combined RF model were computed using mean decrease in impurity (MDI) across all trees.\u003c/p\u003e \u003cp\u003eAnalyses were performed in Python (version 3.12) using scikit-learn (version 1.4) and SciPy (version 1.13). Effect sizes for Mann-Whitney U tests are reported as rank-biserial correlations, computed as |r_bc| = 1 \u0026minus; (2U / n₁n₂).\u003c/p\u003e \u003c/div\u003e"},{"header":"3 Results","content":"\u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003e3.1 Dimensionality and orthogonality of the traditional and IFS representations (full dataset, n\u0026thinsp;=\u0026thinsp;4,402)\u003c/h2\u003e \u003cp\u003ePrincipal component analysis of the traditional kinematic feature set revealed that two components explained 96.4% of total variance, with the first component alone accounting for 76.3%. The IFS structural feature set required 14 components to explain 80% of total variance. The first principal component explained 25.0% of variance; the first two components together accounted for 38.3%. Of the total variance in the IFS structural feature set, 55.3% is mathematically orthogonal to the entire traditional feature set.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec12\" class=\"Section2\"\u003e \u003ch2\u003e3.2 Event separation in the full dataset\u003c/h2\u003e \u003cp\u003eProjection onto the first two principal components of the traditional feature space showed substantial overlap between on-ice and off-ice events, with no clear spatial boundary between the two classes. Projection onto the first two IFS structural components showed a partially different organisational structure, with on-ice events occupying a more distinct region, though substantial overlap remained at the two-component level.\u003c/p\u003e \u003cp\u003eLinear discriminant analysis with stratified five-fold cross-validation on the full dataset (n\u0026thinsp;=\u0026thinsp;4,402; class imbalance 11.0:1) produced a traditional BACC of 50.0%, sensitivity of 0.0%, and ROC-AUC of 64.8%. The IFS structural feature set produced a BACC of 59.0% and ROC-AUC of 82.2%.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec13\" class=\"Section2\"\u003e \u003ch2\u003e3.3 Structural measures distinguishing on-ice from off-ice events\u003c/h2\u003e \u003cp\u003eMann-Whitney U tests identified IFS structural measures with large and mechanically interpretable differences between on-ice and off-ice events across the full dataset. Linear acceleration kurtosis was lower for on-ice events (medians: 6.07 vs 8.50; |r_bc| = 0.348, p\u0026thinsp;\u0026lt;\u0026thinsp;0.001). Waveform skewness followed the same direction (medians: 1.88 vs 2.37; |r_bc| = 0.340, p\u0026thinsp;\u0026lt;\u0026thinsp;0.001), indicating that on-ice events produced more symmetrical waveforms with less rightward asymmetry than the off-ice pool. Duration above 10% of peak was longer for on-ice events (medians: 54 ms vs 44 ms; |r_bc| = 0.208, p\u0026thinsp;\u0026lt;\u0026thinsp;0.001). The rotational-to-linear peak ratio was higher for on-ice events (medians: 6.89 vs 4.94; |r_bc| = 0.191, p\u0026thinsp;\u0026lt;\u0026thinsp;0.001).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec14\" class=\"Section2\"\u003e \u003ch2\u003e3.4 Applied illustration: classifier comparison during gameplay (n\u0026thinsp;=\u0026thinsp;661)\u003c/h2\u003e \u003cp\u003eClassification was evaluated on the 661 events recorded during active gameplay periods (on-ice n\u0026thinsp;=\u0026thinsp;367, bench-seated n\u0026thinsp;=\u0026thinsp;294). The traditional feature set (6 variables) produced BACC of 53.2% (\u0026plusmn;\u0026thinsp;3.1%) and ROC-AUC of 53.0% (RF) and 55.9% (HGB). The IFS feature set (111 variables) produced BACC of 67.4% (\u0026plusmn;\u0026thinsp;3.5%) and ROC-AUC of 74.2% (RF) and 73.2% (HGB). The combined feature set (117 variables) produced ROC-AUC of 74.0% (RF) and 73.5% (HGB) (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e.)\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFeature importances from the combined RF model (mean decrease in impurity) showed that all 20 of the highest-ranked features were drawn from the IFS set; no traditional peak measure appeared among the top 20. The five highest-ranked individual variables were waveform kurtosis, vibration clearance, phase decay time, spectral entropy, and VBA rotational path length.\u003c/p\u003e \u003c/div\u003e"},{"header":"4 Discussion","content":"\u003cp\u003eThis study demonstrates that peak kinematic metrics and the Impact Feature Space represent fundamentally different characterisations of head-motion events. The dimensionality analysis shows that the traditional feature set is effectively one-dimensional, while the IFS distributes information across multiple independent components. The finding that 55.3% of IFS variance is orthogonal to the traditional feature set means that the two representations are mutually non-predictive and cannot be derived from one another.\u003c/p\u003e \u003cdiv id=\"Sec16\" class=\"Section2\"\u003e \u003ch2\u003e4.1 Orthogonality and mutual non-predictability between IFS and peak metrics\u003c/h2\u003e \u003cp\u003eEven though both linear and angular measurements are included, the dimensionality analysis establishes a fundamental property of the traditional kinematic feature set. Two principal components account for 96.4% of total variance, with the first explaining 76.3%. This near-singular dimensionality reflects strong collinearity among peak magnitude measures, which function as highly correlated indices of overall event intensity. This means that the traditional feature set is one-dimensional, providing a ranking of events by intensity only.\u003c/p\u003e \u003cp\u003eIn contrast, the IFS structural feature set distributes variance across multiple components. Fourteen features are required to explain 80% of variance, with the first accounting for only 25.0% and the first two for 38.3%. This reflects the design of the IFS, in which multiple measurement capture several distinct mechanical properties and independent dimensions of mechanical variation. It should be noted that while, due to phase of software development, we used 111 variables in this analysis, the concept of IFS is not restricted to these only.\u003c/p\u003e \u003cp\u003eThe decisive result is the orthogonality between the two representations. Of the total variance in the IFS structural feature set, 55.3% is mathematically orthogonal to the traditional feature set. More than half of the information in the IFS cannot be recovered from any linear combination of traditional peak metrics, as defined within the principal component representation used here. This orthogonality is interpreted here as an empirical indicator of non-redundant information content within the chosen representation, rather than as proof of statistical independence or causal separation. The two representations are therefore mutually non-predictive, which is a structural property of what they measure, not a consequence of measurement precision.\u003c/p\u003e \u003cp\u003eThis distinction has direct practical implications. Reducing a waveform to a peak value removes information about temporal evolution, waveform structure, rotational\u0026ndash;translational coupling, and frequency content. Events with identical peak magnitudes may differ substantially in these properties, which may carry biomechanical significance [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e, \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]. The IFS retains and represents this information by expressing each event as a multidimensional measurement vector derived from the recorded waveform. Peak measurements indicate event intensity, whereas IFS features describe the mechanical organisation of motion. These are not competing descriptions but address different questions: how intense an event was versus how it unfolded mechanically. This bidirectional non-predictability defines the IFS concept and provides the basis for interpreting all subsequent analyses. This conceptual distinction is matched by empirical evidence. Peak metrics cannot predict IFS structural features, nor can IFS features predict peak metrics as demonstrated in Results 3.1.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec17\" class=\"Section2\"\u003e \u003ch2\u003e4.2 Dimensionality constraints and event separability\u003c/h2\u003e \u003cp\u003eThe PCA projection results are consistent with the dimensionality findings. In the traditional feature space, on-ice and off-ice events overlap in the two-component projection because a representation that captures essentially one dimension of variation cannot separate classes that differ across multiple mechanical dimensions. There is no additional variance available in the traditional feature set to support separation beyond intensity.\u003c/p\u003e \u003cp\u003eIn contrast, the IFS projection shows a partially distinct organisational structure for on-ice events. The remaining overlap at the two-component level is expected: the first two IFS components capture only 38.3% of total variance, while 14 components are required to explain 80%. The discriminative structure of the IFS is therefore distributed across higher dimensions not visible in low-dimensional projections.\u003c/p\u003e \u003cp\u003eThe LDA results make this dimensionality contrast explicit. The traditional feature set achieves 50.0% balanced accuracy and zero sensitivity, reflecting the inability of a one-dimensional representation to separate classes that do not differ along its single axis. The IFS achieves 59.0% balanced accuracy and ROC-AUC of 82.2% on the same task. The larger gain in AUC reflects the ability of the IFS to provide meaningful rank-ordering across events, even when threshold-based accuracy is constrained by class imbalance. These results demonstrate that dimensionality is not a descriptive property alone but directly determines the separability that any classifier can achieve.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec18\" class=\"Section2\"\u003e \u003ch2\u003e4.3 Feature-level differences and biomechanical interpretation\u003c/h2\u003e \u003cp\u003eThe individual feature comparisons provide an opportunity for a mechanically coherent interpretation of the separation observed in the IFS. A detailed analysis is not within the scope of this study, but as an example, on-ice events exhibit lower kurtosis and skewness, indicating broader and more symmetrical waveforms compared to the sharply peaked transients characteristic of off-ice events. Duration above 10% of peak was longer for on-ice events, reflecting sustained mechanical loading, while the higher rotational-to-linear peak ratio indicates stronger coupling between rotational and translational motion. These differences are consistent with the biomechanics of head contact. Sustained impacts transmitted through body mass and tissue produce temporally extended, structurally complex signals, whereas sensor disturbances generate brief, high-amplitude transients with limited rotational coherence. Taken together, these findings suggest that the separability observed in the IFS arises from physically meaningful differences in waveform structure rather than from statistical artefacts. In other words, events that are indistinguishable in peak magnitude occupy distinct regions of the IFS because they differ in how the motion unfolds over time and across mechanical domains.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec19\" class=\"Section2\"\u003e \u003ch2\u003e4.4 Role of rotational kinematics and translational\u0026ndash;rotational coupling\u003c/h2\u003e \u003cp\u003eRotational kinematics occupy a central role within the IFS, reflecting established biomechanical understanding of brain injury mechanisms. Since Holbourn\u0026rsquo;s early work [\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e], the sensitivity of neural tissue to rotational shear has been recognised, and finite-element modelling indicates that the majority of brain strain energy arises from rotational motion [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e, \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e]. Despite this, field monitoring practice typically treats rotational velocity as a scalar reported alongside linear acceleration, without examining their relationship within each event.\u003c/p\u003e \u003cp\u003eThe translational\u0026ndash;rotational coupling domain of the IFS captures this relationship explicitly. The relative contribution, timing, and coordination of rotational and translational motion vary systematically with impact location, direction, and contact mechanics. These distinctions are invisible when each component is reduced to an independent peak value. By representing their interaction within the waveform, the IFS provides access to mechanically meaningful differences that are directly relevant to injury mechanisms but are not recoverable from scalar metrics.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec20\" class=\"Section2\"\u003e \u003ch2\u003e4.5 Applied classification: practical implications of orthogonality\u003c/h2\u003e \u003cp\u003eThe gameplay classification demonstrates how the orthogonality between IFS features and peak metrics translates into practical discriminative performance. By restricting analysis to events recorded during active gameplay periods, where both on-ice and bench-seated (on-bench) events occur under identical temporal and recording conditions, classification must rely on waveform structure rather than contextual cues.\u003c/p\u003e \u003cp\u003eUnder these conditions, the traditional feature set performs at chance (ROC-AUC 53\u0026ndash;56%), confirming that peak magnitude alone does not contain sufficient information to distinguish between the two event types. It should be noted that the IFS feature set was used in its entirety without task-specific feature selection or optimisation; the reported AUC of 73\u0026ndash;74% therefore represents a conservative estimate of the discriminative potential of the IFS for this task, and targeted feature selection or dimensionality reduction would be expected to improve performance. The consistency of results across random forest and histogram gradient boosting \u0026mdash; two methods with distinct learning strategies \u0026mdash; confirms that the discriminative advantage of the IFS does not depend on the choice of algorithm.\u003c/p\u003e \u003cp\u003eThe combined feature set does not improve performance beyond the IFS alone, consistent with the orthogonality finding: the information captured by peak metrics does not provide independent discriminative signal once the structural dimensions of the IFS are represented. Feature importance rankings further support this interpretation, with all top-ranked variables originating from the IFS domains.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec21\" class=\"Section2\"\u003e \u003ch2\u003e4.6 Artefact detection as an emergent property\u003c/h2\u003e \u003cp\u003eThe IFS provides a principled basis for handling artefact events that does not rely on externally imposed magnitude thresholds or heuristic filtering. Because the detection threshold is defined by resultant linear acceleration, both genuine head contacts and incidental sensor disturbances enter the dataset when they exceed the same trigger criterion [\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e]. Conventional approaches address this by applying secondary thresholds, duration filters, or manual inspection, all of which depend on investigator-defined rules that may not generalise across devices or contexts.\u003c/p\u003e \u003cp\u003eIn the IFS, artefact character emerges from waveform structure. Sensor disturbances cross the detection threshold through mechanisms that differ systematically from genuine head contacts: their signals are shorter in duration, concentrated in narrower frequency bands, and exhibit weaker or incoherent coupling between translational and rotational components. Genuine impacts, by contrast, produce temporally sustained signals with consistent inter-axis relationships and mechanically coherent coupling patterns.\u003c/p\u003e \u003cp\u003eThese differences are expressed across the structural, spectral, and coupling domains simultaneously. Artefact events therefore occupy distinct regions of the measurement space without requiring explicit exclusion criteria. The distinction is not imposed on the data but arises from the same structural properties that define the IFS representation.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec22\" class=\"Section2\"\u003e \u003ch2\u003e4.7 Individual variability and longitudinal implications\u003c/h2\u003e \u003cp\u003eBeyond event-level description, the IFS enables analysis at the level of the individual athlete and over time. The same peak acceleration may correspond to different mechanical events depending on factors such as head mass, neck musculature, and anticipatory activation, all of which modulate head kinematics during impact [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e, \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e]. These differences are expressed in waveform structure rather than in peak magnitude.\u003c/p\u003e \u003cp\u003eIndividuals therefore exhibit characteristic distributions within the IFS, reflecting both their biomechanical properties and the patterns of contact they experience. Each athlete occupies a region of the feature space over a monitoring period, and deviations from this individual baseline may provide a more sensitive indicator of change than comparisons to population-level norms. This is particularly relevant for cumulative exposure.\u003c/p\u003e \u003cp\u003eRepeated low-magnitude impacts may differ substantially in mechanical structure despite similar peak values [\u003cspan additionalcitationids=\"CR36\" citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e], and aggregation based on peak magnitude alone conflates mechanically distinct events. The IFS provides a richer per-event representation that may support more informative cumulative exposure metrics, providing a new tool for studying the relationship between structural features and clinical outcomes.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec23\" class=\"Section2\"\u003e \u003ch2\u003e4.8 Toward intracranial mechanical response modelling\u003c/h2\u003e \u003cp\u003eA natural extension of the IFS is toward modelling intracranial mechanical response. The brain does not follow skull motion rigidly; its deformation depends on the temporal profile of the kinematic input as well as its magnitude. Finite-element models and reduced-order mechanical systems treat the head kinematic signal as a time-series the shape, duration, and frequency content of which determine strain responses [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e, \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e, \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThe structural properties captured by the IFS \u0026mdash; including waveform duration, rise characteristics, and spectral composition \u0026mdash; correspond directly to parameters that influence intracranial strain in these models. For example, the response of viscoelastic systems depends on input pulse shape and duration. The IFS features describe these events theoretically relevant to intracranial mechanics. Whether IFS features provide predictive value for brain strain beyond peak-based metrics remains an empirical question requiring paired kinematic and intracranial data. However, the conceptual alignment between IFS features and established biomechanical models provides a clear basis for such investigations.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec24\" class=\"Section2\"\u003e \u003ch2\u003e4.9 Sensor placement as a prerequisite for valid waveform analysis\u003c/h2\u003e \u003cp\u003eThe validity of the IFS depends critically on sensor placement. A sensor mounted on a helmet records a composite of helmet and head motion, with relative motion that varies across impacts and cannot be reconstructed analytically [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e, \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e]. This limitation affects all head-impact measurement but is particularly consequential for waveform-based analysis. Peak metrics may be partially robust to moderate signal distortion because they depend on the maximum value of the signal. In contrast, waveform structure \u0026mdash; including duration, oscillatory patterns, frequency content, and translational\u0026ndash;rotational coupling \u0026mdash; is directly altered by helmet motion. Applying the IFS to helmet-mounted data would therefore describe helmet dynamics rather than head motion. The IFS as defined here is thus applicable only to sensors coupled directly to the skull. This is not a matter of measurement precision but of measuring the correct physical quantity.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec25\" class=\"Section2\"\u003e \u003ch2\u003e4.10 Limitations\u003c/h2\u003e \u003cp\u003eThe demonstration dataset comprised events from two Finnish female ice-hockey teams recorded over 19 games; the generalisability of the observed IFS feature distributions to other sports, populations, and levels of play is beyond the scope of this study. The classification task distinguishes events by player location and differences in activity (playing or sitting) rather than by injury relevance, and both on-ice and bench-seated categories include many event types.\u003c/p\u003e \u003cp\u003eThe present study does not establish relationships between IFS structural features and injury outcomes. Such relationships require datasets linking head kinematics to clinical or biomechanical endpoints, including intracranial strain estimates. In addition, the IFS feature set was developed for a specific sensor system and anatomical placement; adaptation and independent validation would be required for application to other devices [\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e, \u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e].\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec26\" class=\"Section2\"\u003e \u003ch2\u003e4.11 Conclusion\u003c/h2\u003e \u003cp\u003ePeak metrics describe event intensity, whereas IFS structural features capture how motion unfolds over time, including waveform structure, rotational\u0026ndash;translational coupling, and frequency content. These properties enable discrimination between events that are indistinguishable in peak magnitude and provide a basis for analysing mechanical characteristics that are otherwise lost when the waveform is reduced to a scalar.\u003c/p\u003e \u003cp\u003eThe results indicate that waveform structure constitutes a distinct and informative dimension of head-impact analysis. Incorporating this information does not extend peak-based monitoring but complements it by capturing mechanical properties that peak metrics do not represent. The Impact Feature Space therefore provides a basis for more complete description of head-motion events and a foundation for future work linking kinematic waveform features to biomechanical and clinical outcomes.\u003c/p\u003e \u003c/div\u003e"},{"header":"Declarations","content":"\u003cp\u003eEthics approval and consent to participate\u003c/p\u003e\n\u003cp\u003eThe ice hockey measurements were conducted as part of the Sustainable Careers in Elite Contact Sports (SUCCESS) study, approved by the Ethics Committee of Helsinki University Hospital (HUS/5422/2024, 3 July 2024). All procedures were conducted in accordance with the principles of the Declaration of Helsinki, and informed written consent was obtained from all participants.\u003c/p\u003e\n\u003cp\u003eConsent for publication\u003c/p\u003e\n\u003cp\u003eNot applicable.\u003c/p\u003e\n\u003cp\u003eFunding\u003c/p\u003e\n\u003cp\u003eIce hockey measurements were part of the Sustainable Careers in Elite Contact Sports (SUCCESS) study, funded by the Research Council of Finland (Academy Programme for Sport Science and Physical Activity ACTIVE), grant number 361442. Development of the IFS methodology received no specific funding.\u003c/p\u003e\n\u003cp\u003eAuthors\u0026rsquo; contributions\u003c/p\u003e\n\u003cp\u003eJL conceived the study, developed the IFS methodology, performed the data analysis, and drafted the manuscript. KP contributed to data collection, study design and critical revision. MV contributed to data collection, study design, and critical revision. LH contributed to study design, neuropsychological interpretation, critical revision, supervision and funding. All authors read and approved the final manuscript.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting interests\u003c/strong\u003e\u003cbr\u003e\u0026nbsp;J.L. is named as an inventor on a pending patent application filed with the Finnish Patent and Registration Office concerning methods for extracting and representing waveform-derived features from wearable head-impact sensor data, including aspects of the Impact Feature Space methodology described in this manuscript. The patent application was filed before submission of the manuscript. No licensing income or commercial revenue has been received. The other authors declare no competing interests.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eAvailability of data and materials\u003c/p\u003e\n\u003cp\u003eThe individual-level head-impact data are restricted because the recorded events are linked to identifiable players within the research dataset compromising participant confidentiality. \u0026nbsp;The Impact Feature Space methodology and feature-extraction software are proprietary and are not publicly available at the time of submission because they are subject to intellectual property protection.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eAcknowledgements\u003c/p\u003e\n\u003cp\u003eThe authors thank Mr Mika Hulkki of Wisehockey Oy for benevolent cooperation with real-time event tracking.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eCrisco, J. J., Chu, J. J., \u0026amp; Greenwald, R. M. (2004). 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Mechanics of head injuries. \u003cem\u003eThe Lancet\u003c/em\u003e, 242(6267), 438\u0026ndash;441. https://doi.org/10.1016/S0140-6736(00)87453-X\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":true,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"head impact monitoring, impact biomechanics, head kinematics, waveform analysis, feature space, wearable sensors, concussion, head injury load monitoring, repetitive head exposure, ice hockey","lastPublishedDoi":"10.21203/rs.3.rs-9652948/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9652948/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003e\u003cstrong\u003eBackground\u003c/strong\u003e: Peak linear acceleration and peak rotational velocity are commonly used for describing head-motion events in sport. These kinematic measurements capture the intensity of the recorded motion but compress the full waveform to a scalar, discarding structural, temporal, and frequency-domain information. Waveform structure, temporal organisation, rotational–translational coupling, and frequency content are dimensions of the mechanical event that peak values miss.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eObjective\u003c/strong\u003e: To introduce the Impact Feature Space (IFS), a multidimensional representation of head-motion waveforms in which each event is described across multiple mechanical domains, and to demonstrate empirically that IFS structural features and the peak kinematic metrics are mutually non-predictive — capturing orthogonal dimensions of the recorded motion — and that this orthogonality has discriminative properties.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eMethods\u003c/strong\u003e: Head-motion events recorded during elite-level women’s ice hockey were captured using the ACT Head Impact Tracker Pro positioned over the mastoid process and expressed as measurement vectors spanning four mechanical domains. : structural waveform, translational–rotational coupling, spectral and vibration, and artefact detection. Principal component analysis was used to quantify the intrinsic dimensionality of the peak kinematic 6-variable and IFS structural 111-variable feature sets, as well as the orthogonality between them, across the full dataset of 4,402 events. . Random forest and histogram gradient boosting classifiers were then applied to a gameplay-restricted subset (n = 661 events) to illustrate the discriminative consequences of this orthogonality.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eResults\u003c/strong\u003e: The peak kinematic feature set was effectively one-dimensional: two components explained 96.4% of total variance. The IFS structural feature set required 14 components to reach 80% of variance, and 55.3% of its total variance was mathematically orthogonal to the entire peak kinematic feature set. In the gameplay illustration, peak kinematic features performed at chance (ROC-AUC 53–56%), while IFS features achieved 73–74% AUC consistently using random forest and histogram gradient boosting .\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConclusions\u003c/strong\u003e: Peak kinematic metrics and IFS structural features represent two distinct and mutually non-predictive characterisations of head-motion events: the former describe intensity, the latter describe mechanical organisation. The IFS provides access to structural information that is not recoverable from peak values and offers a complementary representation for the analysis of head-motion waveforms.\u003c/p\u003e","manuscriptTitle":"Impact Feature Space: Representing Head-Motion Waveforms from Wearable Sensors","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-05-12 04:31:43","doi":"10.21203/rs.3.rs-9652948/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"2b038788-6181-4ac8-bcb8-063e0fa31736","owner":[],"postedDate":"May 12th, 2026","published":true,"recentEditorialEvents":[{"type":"decision","content":"Rejected","date":"2026-05-12T11:53:27+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-05-11T05:48:46+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2026-05-11T05:47:50+00:00","index":"","fulltext":""},{"type":"submitted","content":"BMC Sports Science, Medicine and Rehabilitation","date":"2026-05-08T10:23:05+00:00","index":"","fulltext":""}],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2026-05-12T13:19:49+00:00","versionOfRecord":[],"versionCreatedAt":"2026-05-12 04:31:43","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9652948","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9652948","identity":"rs-9652948","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}