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Vector field statistical analysis of kinematic and force trajectories
Open accessAbstract
When investigating the dynamics of three-dimensional multi-body biomechanical systems it is often difficult to derive spatiotemporally directed predictions regarding experimentally induced effects. A paradigm of 'non-directed' hypothesis testing has emerged in the literature as a result. Non-directed analyses typically consist of ad hoc scalar extraction, an approach which substantially simplifies the original, highly multivariate datasets (many time points, many vector components). This paper describes a commensurately multivariate method as an alternative to scalar extraction. The method, called 'statistical parametric mapping' (SPM), uses random field theory to objectively identify field regions which co-vary significantly with the experimental design. We compared SPM to scalar extraction by re-analyzing three publicly available datasets: 3D knee kinematics, a ten-muscle force system, and 3D ground reaction forces. Scalar extraction was found to bias the analyses of all three datasets by failing to consider sufficient portions of the dataset, and/or by failing to consider covariance amongst vector components. SPM overcame both problems by conducting hypothesis testing at the (massively multivariate) vector trajectory level, with random field corrections simultaneously accounting for temporal correlation and vector covariance. While SPM has been widely demonstrated to be effective for analyzing 3D scalar fields, the current results are the first to demonstrate its effectiveness for 1D vector field analysis. It was concluded that SPM offers a generalized, statistically comprehensive solution to scalar extraction's over-simplification of vector trajectories, thereby making it useful for objectively guiding analyses of complex biomechanical systems.
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“SPM has been widely validated and applied in biomechanical research, demonstrating its efficacy in detecting continuous gait differences [32,33].”
From Sagittal Plane Kinematic Deviations and Spatio-Temporal Gait Characteristics in Children with Idiopathic Toe Walking: A Comparative Analysis Using Statistical Parametric Mapping (2025) · cites this paper as [33]
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“SPM has been widely validated and applied in biomechanical research, demonstrating its efficacy in detecting continuous gait differences [32,33].”
Metadata
- Authors
- Pataky, T. C., Robinson, M. A., & Vanrenterghem, J.
- Affiliations
- Shinshu University (JP)
- Liverpool John Moores University (GB)
- Corresponding author
- Pataky, Todd C.
- Venue
- Journal of Biomechanics
- Publisher
- Elsevier BV
- Published
- 2013-09
- Volume
- 46
- Issue
- 14
- Pages
- 2394-2401
- ISSN
- 0021-9290 (ISSN-L)
- OpenAlex
- W2080500625
- Cited by
- 741
- References
- 25
- Citations by year
- 2026: 56 · 2025: 102 · 2024: 90 · 2023: 72 · 2022: 82 · 2021: 90 · 2020: 63 · 2019: 60 · 2018: 47 · 2017: 34 · 2016: 31 · 2015: 8 · 2014: 5 · 2013: 1
- FWCI
- 8.28
- Type
- journal article
- Language
- en
- Update notices
- erratum (2015-01-02)
- Open access
- green
- hdl.handle.net
- Licence
- cc-by-nc-nd
- www.elsevier.com/tdm/userlicense/1.0/ (tdm)
- Locations
- Journal of Biomechanics (publishedVersion)
- PubMed (publishedVersion)
- SOAR (Shinshu University) (submittedVersion, cc-by-nc-nd)
- Institutional Repositories DataBase (IRDB) (submittedVersion)
- Funders
- JSPS Wakate B (22700465)
- Topics
- Physical Sciences › Engineering › Biomedical Engineering › Lower Extremity Biomechanics and Pathologies
- Physical Sciences › Engineering › Biomedical Engineering › Muscle activation and electromyography studies
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Applications
- Keywords
- statistical parametric mapping, random field theory, vector field analysis, kinematic trajectories, ground reaction force, knee kinematics, temporal correlation, hypothesis testing, biomechanical systems
- MeSH terms
- Biomechanical Phenomena, Data Interpretation, Statistical, Humans, Knee, Rotation, Running, Models, Statistical, Walking, Muscle, Skeletal, Musculoskeletal Pain
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
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