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Region-of-interest analyses of onedimensional biomechanical trajectories: Bridging 0D and 1D theory, augmenting statistical power


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One-dimensional (1D) kinematic, force, and EMG trajectories are often analyzed using zero-dimensional (0D) metrics like local extrema. Recently whole-trajectory 1D methods have emerged in the literature as alternatives. Since 0D and 1D methods can yield qualitatively different results, the two approaches may appear to be theoretically distinct. The purposes of this paper were (a) to clarify that 0D and 1D approaches are actually just special cases of a more general region-of-interest (ROI) analysis framework, and (b) to demonstrate how ROIs can augment statistical power. We first simulated millions of smooth, random 1D datasets to validate theoretical predictions of the 0D, 1D and ROI approaches and to emphasize how ROIs provide a continuous bridge between 0D and 1D results. We then analyzed a variety of public datasets to demonstrate potential effects of ROIs on biomechanical conclusions. Results showed, first, that a priori ROI particulars can qualitatively affect the biomechanical conclusions that emerge from analyses and, second, that ROIs derived from exploratory/pilot analyses can detect smaller biomechanical effects than are detectable using full 1D methods. We recommend regarding ROIs, like data filtering particulars and Type I error rate, as parameters which can affect hypothesis testing results, and thus as sensitivity analysis tools to ensure arbitrary decisions do not influence scientific interpretations. Last, we describe open-source Python and MATLAB implementations of 1D ROI analysis for arbitrary experimental designs ranging from one-sample t tests to MANOVA.
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Submitted 13 July 2016
Accepted 4 October 2016
Published 2 November 2016
Corresponding author
Todd C. Pataky,
Academic editor
John Hutchinson
Additional Information and
Declarations can be found on
page 10
DOI 10.7717/peerj.2652
2016 Pataky et al.
Distributed under
Creative Commons CC-BY 4.0
Region-of-interest analyses of one-
dimensional biomechanical trajectories:
bridging 0D and 1D theory, augmenting
statistical power
Todd C. Pataky1, Mark A. Robinson2and Jos Vanrenterghem3
1Institute for Fiber Engineering, Department of Bioengineering, Shinshu University, Ueda, Nagano, Japan
2Research Institute for Sport and Exercise Sciences, Liverpool John Moores University,
Liverpool, United Kingdom
3Department of Rehabilitation Sciences, Katholieke Universiteit Leuven, Belgium
One-dimensional (1D) kinematic, force, and EMG trajectories are often analyzed
using zero-dimensional (0D) metrics like local extrema. Recently whole-trajectory 1D
methods have emerged in the literature as alternatives. Since 0D and 1D methods can
yield qualitatively different results, the two approaches may appear to be theoretically
distinct. The purposes of this paper were (a) to clarify that 0D and 1D approaches are
actually just special cases of a more general region-of-interest (ROI) analysis framework,
and (b) to demonstrate how ROIs can augment statistical power. We first simulated
millions of smooth, random 1D datasets to validate theoretical predictions of the 0D,
1D and ROI approaches and to emphasize how ROIs provide a continuous bridge
between 0D and 1D results. We then analyzed a variety of public datasets to demonstrate
potential effects of ROIs on biomechanical conclusions. Results showed, first, that
a priori ROI particulars can qualitatively affect the biomechanical conclusions that
emerge from analyses and, second, that ROIs derived from exploratory/pilot analyses
can detect smaller biomechanical effects than are detectable using full 1D methods.
We recommend regarding ROIs, like data filtering particulars and Type I error rate, as
parameters which can affect hypothesis testing results, and thus as sensitivity analysis
tools to ensure arbitrary decisions do not influence scientific interpretations. Last, we
describe open-source Python and MATLAB implementations of 1D ROI analysis for
arbitrary experimental designs ranging from one-sample ttests to MANOVA.
Subjects Animal Behavior, Bioengineering, Kinesiology, Statistics
Keywords Time series analysis, Kinematics, Constrained hypotheses, Statistical parametric
mapping, Dynamics, Random field theory, Hypothesis testing, Biomechanics, Human movement
Many biomechanical measurements may be regarded as ‘n-dimensional m-dimensional’
(nDmD) continua, where nand mare the dimensionalities of the measurement domain
and dependent variable, respectively. Common examples include: joint flexion (1D1D),
ground reaction force (1D3D), plantar pressure distribution (2D1D) and bone strain tensor
distributions (3D6D). These data are often analyzed using 0D1D metrics from regions of
How to cite this article Pataky et al. (2016), Region-of-interest analyses of one-dimensional biomechanical trajectories: bridging 0D and
1D theory, augmenting statistical power. PeerJ 4:e2652; DOI 10.7717/peerj.2652
interest (ROIs) which summarize particular continuum features. In this paper ‘ROI’ refers
to a geometrical subset of a continuum dataset, and ‘ROI analysis’ refers to the analysis
of data extracted from an ROI. More explicit definitions for these terms with literature
context are provided in Appendix A.
In n>1 datasets ROIs are often explicitly constructed based on anatomical
rationale, especially for plantar pressure (Cavanagh & Ulbrecht, 1994) and finite element
analyses (Radcliffe & Taylor, 2007). In n=1 datasets ROIs tend to be used both explicitly
(e.g., with phase labels including: ‘‘early stance,’’ ‘‘push off,’’ ‘‘swing,’’ etc.) (Blanc et al.,
1999) and implicitly (e.g., local extrema are used without explicitly labeled continuum
regions) (Cavanagh & Lafortune, 1980). Regardless, the ultimately analyzed metrics are
often n=0 scalars, so we refer to this class of methods as ‘0D.’ For simplicity the remainder
of this paper focusses on n=1 datasets and corresponding ‘1D methods’ (Appendix A).
Recently a variety of 1D methodologies have emerged in the Biomechanics literature
including functional data analysis (FDA) (Ramsay & Silverman, 2005), principal
component analysis(PCA) (Daffertshofer et al., 2004) and statistical parametric mapping
(SPM) (Pataky, Robinson & Vanrenterghem, 2013), each of which afford whole-field 1DmD
analysis. SPM in particular is ideal for ROI-related hypothesis testing because it is valid for
arbitrary 1D geometries including broken or segmented regions of arbitrary size (Pataky,
2016). FDA is less ideal because it employs continuous basis functions and not, to our
knowledge, piecewise continuous ones. PCA can easily handle arbitrary ROI data, but it is
predominantly a data reduction technique and not a hypothesis testing technique.
This paper therefore focusses on SPM, a methodology that was initially developed in the
Neuroimaging literature in the 1990s (Friston et al., 1995), that spread to Electrophysiology
through the 2000s (Kiebel & Friston, 2004;Kilner, Kiebel & Friston, 2005), and which has
more recently appeared in the Biomechanics literature (Pataky, 2012;Pataky, Robinson
& Vanrenterghem, 2013). In Neuroimaging and Electrophysiology SPM has grown into
a comprehensive suite of techniques capable of handling all aspects of n-dimensional
continuum analysis including univariate and multivariate continuum analysis, parametric
and non-parametric probability density utilization, classical and Bayesian inference, and
multi-modal analysis among other functionality (Friston et al., 2007). In the context of this
paper, SPM’s classical hypothesis testing ability is key. Briefly, and considering only 1D
data, SPM first computes a 1D test statistic continuum (often the tstatistic continuum)
from a set of experimentally measured 1D continua. This step is effectively equivalent
to 1D mean and standard deviation continuum computation, which is frequently done
in the Biomechanics literature. SPM then conducts statistical inference at a Type I error
rate of by calculating the critical test statistic value above which random test statistic
continua (generated by smooth, 1D Gaussian continua) would traverse in only (1)%
of an infinite number of identical experiments; if the experimentally observed continuum
exceeds that critical value the null hypothesis is rejected. This general approach to classical
hypothesis testing has been validated extensively in the Neuroimaging literature for 3D
(and 4D) continua (Friston et al., 1995;Friston et al., 2007) and has also been validated for
1D univariate and multivariate data (Pataky, 2016).
Pataky et al. (2016), PeerJ , DOI 10.7717/peerj.2652 2/12
Despite the validity of 1D approaches, a variety of conceptual difficulties may arise when
attempting to corroborate 0D and 1D approaches. In particular, 0D statistical results are
typically tabulated using single numbers for the test statistic and pvalues, so test statistic
continua may appear odd. Another apparent discrepancy between 0D and 1D techniques
is that the former requires continuum summary metric extraction but the latter does not,
so 0D techniques may appear to be somewhat more subjective than 1D techniques. A final
discrepancy is that 1D techniques involve multiple comparison corrections, so they may
appear to be less powerful than 0D techniques. All of these real or perceived discrepancies
could lead one to infer that 0D and 1D approaches are fundamentally different.
The primary purpose of this paper was to clarify the theoretical consistency between
0D and 1D techniques as special cases of ROI analysis. To that end we describe 1D ROI
theory then validate its predictions using numerical simulations of random datasets with
temporal scopes ranging from single points to large 1D continua. The second purpose was
to demonstrate how ROIs can be used to augment statistical power in both exploratory
and hypothesis-driven experiments. The final purpose was to introduce an open-source
software implementation of ROI analysis (in Appendix C) which emphasizes how 0D, 1D
and ROI analyses can all be executed using a common software interface.
All analyses were implemented in Python 2.7 (Van Rossum, 2014) using Canopy 1.6
(Enthought Inc., Austin, TX, USA) and spm1d (Pataky, 2012;Pataky, 2016)(http:
// All datasets described below are included in the spm1d package
and are accessible using the interface as described in Appendix D. High-level
Python and MATLAB (The MathWorks, Natick, MA, USA) interfaces for ROI analyses are
now available in spm1d as described in Appendix C.
ROI theory and validation
In classical hypothesis testing the null hypothesis is rejected if the experimentally observed
test statistic texceeds a critical threshold t, which can be computed according to:
where is the Type I error rate (usually 0.05) and P(t>t) is the probability that the test
statistic exceeds tif the null hypothesis is true.
For an ROI of size S(S0), Eq. (1) can be written as (Friston et al., 2007;Pataky, 2016):
P(tmax >t)=1exp"P0D (t>t)S
where tmax is the maximum value of the tstatistic inside the ROI, P0D(t>t) is the proba-
bility under the null hypothesis that 0D random Gaussian data will produce a tvalue greater
than t,Wis the FWHM representing trajectory smoothness (Appendix B), and is the
degrees of freedom. Note that P(tmax >t) converges to P0D(t>t) as Sapproaches zero,
and that tmust increase as Sincreases to maintain a given . In other words, the larger the
Pataky et al. (2016), PeerJ , DOI 10.7717/peerj.2652 3/12
Figure 1 Simulated datasets. Datasets A and B are identical except in Dataset B the signal at time =75%
is amplified. Three regions of interest (ROIs) are depicted, centered at time =75% and spanning time
windows of 10%, 20% and 30%, respectively.
ROI, the more likely smooth, purely random 1D Gaussian data are to produce high tvalues.
Also note that Eq. (2) can accommodate multiple ROIs using a relatively simple correction
(Friston et al., 2007).
We computed tfor a range of ROI sizes (S), smoothness values (FWHM) and sample
sizes (). ROI size was systematically varied over the full range of possibilities (i.e., from
0 to 100% trajectory length). FWHM and values were selected to span a range of
values observed in representative open-access biomechanical datasets (FWHM =[5, 50],
=[5,49])(Pataky, Vanrenterghem & Robinson, 2016).
To validate Eq. (2) for arbitrary ROI sizes we simulated 100,000 smooth, purely random
Gaussian 1D datasets using ‘rft1d’ (Pataky, 2016), and repeated for each combination of S,
FWHM and values. For each random dataset we computed tmax , thereby producing one
distribution of 100,000 tmax values for each combination of parameters. We then estimated
tfor each distribution as the 95th percentile of the distribution, then qualitatively
compared to the theoretical result (Eq. (2)).
Example ROI analyses
Simulated datasets
Datasets A and B (Fig. 1)(Pataky, Robinson & Vanrenterghem, 2013) consisted of ten
simulated, smooth, random 1D Gaussian fields to which a Gaussian pulse was added at
time =75%. The degrees of freedom and number of time nodes were =9 and Q=101,
respectively, for both datasets. The pulse was slightly larger in Dataset B than in Dataset A.
Both were analyzed using six procedures, in order of increasing conservativeness: (1) 0D
analyses on the local maxima at time =75%, (2–4) 1D ROI analysis with ROIs centered
at time =75% and with temporal sizes of ±5%, ±10% and ±15%, respectively, (5)
1D full-field analysis (i.e., with ROI size =100%), and (6) 1D full-field analysis with a
Bonferroni correction. The latter assumes independence amongst adjacent trajectory nodes
so is overly conservative for smooth data (Pataky, Robinson & Vanrenterghem, 2013).
Pataky et al. (2016), PeerJ , DOI 10.7717/peerj.2652 4/12
Figure 2 Experimental datasets; error clouds depict standard deviations. (A) Knee kinematics during
side-shuffle and v-cut maneuvers (Neptune, Wright & Van den Bogert, 1999). (B) Pilot data from N=1
subject comparing vertical ground reaction force (VGRF) in ‘‘Normal’’ vs. ‘‘Fast’’ walking (Pataky et al.,
2008). (C) Subsequent identical VGRF experiment conducted on N=6 subjects (Pataky et al., 2008).
Experimental datasets
Dataset C (Fig. 2A)(Neptune, Wright & Van den Bogert, 1999)(=7,Q=101) contained
stance-phase sagittal plane knee angles from eight participants who each performed both
side-shuffle and v-cut maneuvers. We started with 0D analysis of maximal knee flexion
(i.e., S=0), then conducted three ROI analyses with ROIs centered approximately on
maximal flexion (time =50%) and with temporal extents of 10%, 40% and 80%,
respectively. Finally, the 1D full-field ROI and Bonferroni procedures were applied as
in the simulated datasets.
Dataset D (Figs. 2B and 2C)(Pataky, Robinson & Vanrenterghem, 2013)(Q=101)
contained stance-phase body-weight-normalized vertical ground reaction forces (VGRF)
from seven subjects who each performed normal, self-paced walking and fast walking in
a randomized order. Analysis proceeded in two-stages to demonstrate how ROIs can be
used to increase analysis sensitivity in exploratory experiments (Pataky, Vanrenterghem
& Robinson, 2016, Fig.7). First, the chronologically first subject was separated as a pilot
subject (Fig. 2B). This subject’s results were examined qualitatively and were used to define
ROIs. Finally, those ROIs were used as an a priori constraint in analysis of the six remaining
subjects (Fig. 2C)(=5). Results of this ROI-driven two-stage procedure were compared
to a full-field 1D analysis.
Critical thresholds tnecessary to maintain =0.05 (Eq. (2)) increased nonlinearly as ROI
size increased and tvalues for 1D data converged to 0D tvalues as ROI size approached
zero (Fig. 3). Numerical simulations validated theoretical tvalues for arbitrary 1D field
smoothness values and arbitrary sample sizes. These results emphasize that 0D analyses are
a special case of 1D analysis for which ROI size is zero.
In Dataset A, the test statistic exceeded the critical threshold for 0D analysis and also for
a narrow ROI of 10%, but failed to reach the thresholds for wider ROIs of 20% and 30%,
and also failed to reach the full-field threshold (Fig. 4A). In contrast, Dataset B’s slightly
amplified signal at time =75% exceeded all thresholds except for the highly conservative
Pataky et al. (2016), PeerJ , DOI 10.7717/peerj.2652 5/12
Figure 3 Validation of theoretical critical thresholds for region of interest (ROI) analysis. (A) Three
different degrees of freedom () and one smoothness (FWHM) value. (B) Three different FWHM values
and one value. The analytical 0D results assume 0D Gaussian randomness and the 1D results assume
smooth 1D Gaussian randomness.
Figure 4 Simulated dataset hypothesis testing results. ‘‘SPM{t}’’ denotes the tvalue extended in time to
form a ‘statistical parametric map.’ Six critical thresholds are depicted (see text). The width of each thresh-
old depicts the temporal extent of the null hypothesis.
full-field Bonferroni correction (Fig. 4B). These results imply that small ROIs can identify
relatively small effects like in Dataset A, and that large or even full-field ROIs can identify
large effects. ROIs thus embody a trade-off between statistical power and the temporal
scope of the null hypothesis; statistical power decreases as ROI size increases and vice versa.
For Dataset C, 0D analysis conducted on maximum knee flexion passed the critical
threshold, as did a moderately broad ROI of 40% (Fig. 5). However, an ROI of 80% and
full-field analysis failed to cross the critical threshold in the vicinity of maximum flexion.
The null hypothesis was nevertheless rejected for both an ROI size of 80% and full-field
analysis, but in this case the statistical conclusion pertains to regions other than maximum
Pataky et al. (2016), PeerJ , DOI 10.7717/peerj.2652 6/12
Figure 5 Dataset C (knee flexion/extension) hypothesis testing results. ‘‘SPM{t}’’ denotes the tvalue.
Critical thresholds are presented as in Fig. 4, with both the height and temporal extent of each threshold
For Dataset D the pilot subject’s data were used to identify two relatively narrow ROIs
in the vicinity of the first local maximum and the local minimum at mid-stance (Fig. 6A).
These ROIs led to null hypothesis rejection for both ROIs in the independent six-subject
dataset (Fig. 6C). Had the ROIs not been defined the null hypothesis would not have been
rejected (Fig. 6B).
The main purpose of this paper was to clarify the theoretical consistency between ‘‘0D’’
and ‘‘1D’’ analyses, and to emphasize that both are actually just special cases of ROI
analysis. In particular, the ROI size (S) and 1D smoothness (FWHM) parameters together
construct a continuous theoretical bridge between 0D and 1D methodologies (Eq. (2),
Fig. 3). ROI-based statistical analysis of nD continua was formalized in the Neuroimaging
literature (Brett et al., 2002;Poldrack, 2006;Friston et al., 2007) where established ROI
software tools exist, including especially MarsBar (Hammers et al., 2002;Brett et al., 2002)
for SPM99 (Wellcome Trust Centre for Neuroimaging, University College London, UK).
Although ROI analyses are common in biomechanical applications like plantar pressure
analysis (Cavanagh & Ulbrecht, 1994) and finite element analysis (Radcliffe & Taylor, 2007),
statistical ROI theory has not, to our knowledge, been addressed in the Biomechanics
The key theoretical point to consider when implementing ROI analyses is that small
ROIs can more readily detect true within-region effects than large ROIs (Figs. 3 and 4).
However, ROI analysis are not necessarily more sensitive than full-field 1D analysis because
effects may exist outside the ROI (Fig. 5, narrowest ROI). An investigator must therefore
balance local signal detectability (via narrow a priori ROI definition) with full-field signal
Pataky et al. (2016), PeerJ , DOI 10.7717/peerj.2652 7/12
Figure 6 Dataset D (VGRF) sensitivity augmentation procedure and results. (A) Pilot study’s mean
inter-condition VGRF difference (see Fig. 2B) for N=1 subject along with user-defined ROIs. The ROIs
specify both the direction and temporal extent of an omnibus a priori hypothesis to be tested in an inde-
pendent experiment. (B) Experimental analysis on N=6 independent subjects using full-field inference
(i.e., had no ROIs been selected); ‘‘SPM{t}’’ denotes the tvalue. The experimental differences between
Normal and Fast are insufficiently large to reject the full-field null hypothesis (because the tvalue fails to
traverse the critical threshold—depicted in red—at =0.05). (C) Experimental analysis using ROI-based
inference: the omnibus ROI-based null hypothesis is rejected.
Pataky et al. (2016), PeerJ , DOI 10.7717/peerj.2652 8/12
detectability (via larger ROIs). In the absence of an a priori hypothesis regarding a specific
portion of the continuum it has been suggested that full-field analyses should be conducted
(Pataky, Vanrenterghem & Robinson, 2016), and this paper extends that suggestion to
include a caveat for exploratory work in a two-stage procedure involving an initial full-field
analysis on an exploratory dataset followed by more precise ROI-based testing (Fig. 6).
An apparent limitation of ROIs is that, since they can create / eradicate statistical
significance (Figs. 4 and 5), they have the potential to be abused. We don’t regard this
limitation as unique to ROI analysis because ROI size, like , can be manipulated to
artificially raise / lower critical thresholds. We would therefore recommend that, instead
of choosing a single ROI size or a single , investigators should actively manipulate
all parameters that might affect ultimate conclusions including: ROI size, , data
filtering, coordinate system definitions, etc., and then actively report the results of those
manipulations in a sensitivity analysis as has been done elsewhere (Pataky et al., 2014). If
the reported results are robust to those manipulations then one can be more confident that
the reported results are neither false positives (Pataky, Vanrenterghem & Robinson, 2016)
nor false negatives. Such manipulations may be especially important for biomechanical
datasets considering that these data can be sensitive to ROI definitions (Figs. 56), and
also considering that some controversies regarding the relative merits of 0D and ROI
vs. full-field analysis exist in other literatures (Kubicki et al., 2002;Giuliani et al., 2005;
Furutani et al., 2005;Friston et al., 2006;Saxe, Brett & Kanwisher, 2006;Snook, Plewes &
Beaulieu, 2007;Kilner, 2013).
More formally, ROI definitions and procedures should be considered from the
perspective of ‘circular analysis’ (Kriegeskorte et al., 2009), an umbrella term encompassing
bias-generating factors in scientific intepretations of processed data. In particular, the
approach we have recommended with Dataset D — ROI generation based on independent-
subject pilot studies—is analogous to ‘functional localizers’ in the Neuroimaging literature
for which substantial benefits but also substantial cicular risks exist (Friston et al., 2006;
Saxe, Brett & Kanwisher, 2006;Kilner, 2013). As a simple example of circular analysis and
its dangers consider the local maximum in Dataset A near time =15% (Fig. 4A). Defining
an ROI about this maximum after seeing this result would lead to null hypothesis rejection
even for relatively broad ROIs of 20%. This would be a circular conclusion because the
observed result has directly affected the conclusion’s assumption that the identified ROI
was not of a priori interest but is now. In contrast, the 1D (full-field) threshold correctly
fails to reject the null hypothesis; the 1D approach’s conclusion is not circular because the
a priori assumption of full-field effects was not affected by the observed result.
The literature contains a variety of recommendations regarding avoiding bias associated
with circularity in ROI analyses, and recent developments in particular show that it is
possible to use algorithmic data-driven ROI selection in an unbiased manner to increase
statistical power and also maintain control over Type I error rates (Brooks, Zoumpoulaki
& Bowman, in press). This result is limited to specific cases of experimental variance, but
may nevertheless be promising for researchers concerned regarding inadequate power in
analyses of large 1D datasets with potentially many 1D variables. Regardless, if one wishes
to conduct ROI analysis or otherwise reduce the recorded 1D dataset, they should be aware
Pataky et al. (2016), PeerJ , DOI 10.7717/peerj.2652 9/12
of circularity and how circular (il)logic can produce a vast array of biased conclusions
following dataset reduction.
A technical point not addressed in the analyses above is how to handle within-ROI
signals that extend beyond the ROI. This situation is observable in Fig. 6C, when the
test statistic value is greater than the threshold on the ROI boundaries. From a classical
hypothesis perspective the point is moot because the null hypothesis is rejected regardless
of the temporal scope of a supra-threshold signal. It has been recommended elsewhere that,
if a within-ROI signal is detected, the entire signal be reported even if it extends outside of
the ROI (Friston et al., 2007). Our recommended approach of manipulating ROI location
and size in a sensitivity analysis is consistent with that approach in that ROI boundaries
should generally be regarded as soft.
In summary, this paper has introduced and validated an ROI approach for analyzing 1D
biomechanical trajectories which clarifies the consistency between common 0D approaches
and recent 1D approaches. Since biomechanical interpretations can be sensitive not only to
ROI size but also to other data processing particulars like filtering and coordinate system
definitions, it is recommended that ROIs be used only when there is adequate a priori
justification for ignoring other regions of the 1D continuum, and that when they are used
ROI sensitivity results are also reported.
This work was supported by Wakate A Grant 15H05360 from the Japan Society for the
Promotion of Science. The funders had no role in study design, data collection and analysis,
decision to publish, or preparation of the manuscript.
Grant Disclosures
The following grant information was disclosed by the authors:
Japan Society for the Promotion of Science: 15H05360.
Competing Interests
The authors declare there are no competing interests.
Author Contributions
Todd C. Pataky conceived and designed the experiments, analyzed the data, wrote the
paper, prepared figures and/or tables, reviewed drafts of the paper.
Mark A. Robinson and Jos Vanrenterghem conceived and designed the experiments,
analyzed the data, wrote the paper, reviewed drafts of the paper.
Data Availability
The following information was supplied regarding data availability:
All raw data analyzed in this paper are available in the ‘‘spm1d’’ software package
available at:
Pataky et al. (2016), PeerJ, DOI 10.7717/peerj.2652 10/12
Supplemental Information
Supplemental information for this article can be found online at
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Appendix A Nomenclature
This Appendix proposes a set of terms and definitions for use in analyses of 1D biomechanical
continua (Table A.1) and relates these terms to analogous, established terms from the neuroimaging
literature (Table A.2). Note that the neuroimaging terminology cannot easily be used for 1D applications
because the meaning of ‘volume’ is unclear for 1D data.
Table A.1: Proposed nomenclature for statistical parametric mapping (SPM) analyses of 1D continua.
Category Term AbbreviationDescription
Point of in-
POI A single position in a 1D continuum. (e.g. time = 10%)
Region of in-
ROI A continuous portion of a 1D continuum. (e.g. time =
0D inference Inference procedures applied to 0D univariate or multi-
variate data which do not account for correlation amongst
adjacent continuum points.
1D inference Inference procedures applied to univariate or multivariate
1D data which use multiple comparisons corrections to ac-
count for correlation amongst adjacent continuum points.
RFT procedures are assumed unless otherwise stated.
Field Theory
RFT Provides analytical parametric solutions for probabilities
associated with smooth 1D Gaussian continua, and in par-
ticular the probability that small samples of 1D Gaussian
continua will produce test statistic continua that reach cer-
tain heights in particular experiments. Reference: Adler
and Taylor (2007)
Small region
SRC A multiple comparisons correction across within-ROI val-
ues using (parametric) RFT or a nonparametric alternative.
RFT is assumed unless otherwise stated.
0D analysis Analysis of univariate or multivariate 0D data using 0D
inference procedures.
1D analysis Analysis of univariate or multivariate 1D data using 1D
inference procedures
0D method A method which conducts 0D analysis of 0D data.
1D method A method which conducts 1D analysis of 1D data.
SPM A methodology for analyzing nD continua, often using clas-
sical hypothesis testing. SPM’s classical hypothesis testing
involves: (i) test statistic continuum computation from a
set of registered nD continua, (ii) continuum smoothness
estimation based on the nD gradient of the model residuals,
(iii) critical threshold computation using RFT and the esti-
mated smoothness, and (iv) probability value computation
using RFT and the estimated smoothness for threshold-
surviving clusters. Reference: Friston et al. (2007)
Region of in-
terest analy-
ROIA A set of procedures involving (i) ROI definition and (ii)
statistical analyses of ROI data.
0D metric-
based ROI
ROIA-0D ROIA which conducts 0D analysis on a 0D summary metric
(e.g. mean, median, maximum, etc.) that is meant to sum-
marize or otherwise represent all values in an ROI. ROIA-
0D with a local extremum summary metric (minimum or
maximum) is common in the Biomechanics literature.
ROIA-1D ROIA which conducts 1D analysis of an ROI’s data using a
small region correction (SRC). This is the focus of the main
manuscript. Equivalent to ‘SRC-based ROI analysis’.
Note: Bonferroni and other corrections applied across multiple continuum nodes but which do not
consider inter-node correlation are included in ‘0D inference’.
Table A.2: Relevant nomenclature from the neuroimaging literature. Terms without abbreviations do
not explicitly appear in the literature and are instead introduced here to clarify connections to the
proposed nomenclature in Table A.1.
Term Abbreviation Description
Region of interest ROI A continuous portion of an nD continuum. Also called a ‘vol-
ume of interest’ (VOI) in 3D.
Region of interest
0D analyses conducted on a 0D metric extracted from an
ROI. Reference: Brett et al. (2002). Equivalent to ‘volume of
interest (VOI) analysis’.
Small volume cor-
SVC A multiple comparisons correction across within-ROI val-
ues using (parametric) RFT or a nonparametric alterna-
tive. RFT is assumed unless otherwise stated. Ref-
erence: SPM12 Manual (FIL Methods Group, Wellcome
Trust Centre for Neuroimaging, University College London)
Appendix B Field smoothness: FWHM
The full width at half maximum (FWHM) parameter describes the smoothness of 1D random fields.
Most precisely, the FWHM specifies the breadth of a Gaussian kernel (Fig.B.1) which, when convolved
with uncorrelated (perfectly rough) Gaussian 1D data yields smooth Gaussian 1D fields (Fig.B.2).
Random field theory (RFT) (Adler and Taylor, 2007) uses the FWHM value to describe the prob-
abilistic behavior of smooth fields. The most important probability for classical hypothesis testing is
the probability that the random fields will reach a certain height (Friston et al., 2007); setting that
probability to = 0.05 yields the critical RFT thresholds depicted in Fig.3 (main manuscript).
Figure B.1: Breadth parameters for Gaussian kernels: and FWHM.
Figure B.2: One-dimensional Gaussian random fields. The FWHM parameterizes field smoothness.
The smaller the FWHM the rougher the field, and the more likely random fields are to reach a specified
height. Infinitely smooth fields (FWHM=1) are probabilistically equivalent to 0D scalars. It has been
shown that Biomechanics datasets generally tend to lie in the range FWHM = [5%, 50%], including
(processed) kinematics, force and processed EMG (Pataky et al., 2016).
Appendix C ROI analysis in Python and MATLAB
This Appendix describes the Python and MATLAB interfaces for region of interest (ROI) analysis
in spm1d ( Below Python and MATLAB code snippets are presented in green and
orange, respectively.
C.1 Example ROI analysis
In spm1d, ROI analysis can be conducted using the keyword “roi” in all statistical routines from
spm1d.stats including t tests, regression, ANOVA, etc. As an example, a two-sample t test with an
ROI spanning from time = 10% to 40% can be conducted as follows:
import numpy as np
import spm1d
#(0) Load dataset:
#(1) Define SR:
roi = np.array( [False]*101 )
roi[10:40] = True
#(2) Conduct t test:
t = spm1d.stats.ttest2(YB, YA, roi=roi)
ti = t.inference(0.05)
%(0) Load dataset:
dataset =;
[YA,YB] = deal(dataset.YA, dataset.YB);
%(1) Define ROI:
roi = false( 1, 101 );
roi(11:40) = true;
%(2) Conduct t test:
t = spm1d.stats.ttest2(YB, YA, 'roi',roi);
ti = t.inference(0.05);
C.2 Example analysis in detail
After importing the necessary packages, the next commands retrieve one of spm1d’s built-in datasets:
dataset =;
[YA,YB] = deal(dataset.YA, dataset.YB);
Here the variables YA and YB are both (JQ) arrays, where Jand Qare the number of observations
and the number of nodes in the 1D continuum, respectively. They can be visualized as follows:
from matplotlib import pyplot
pyplot.plot(YA.T, color="k")
pyplot.plot(YB.T, color="r")
plot(YA', 'color','r')
hold on
plot(YB', 'color','k')
This produces the following figure:
Figure C.1: Example dataset “SimulatedTwoLocalMax”.
In this example the ROI is specified as a binary vector of length Q, where True indicates the ROI:
roi = np.array( [False]*101 )
roi[10:40] = True
roi = false( 1, 101 );
roi(11:40) = true;
Since the boolean values False and True numerically evaluate to 0 and 1, respectively, the ROI can
be visualized using a standard plotting command (Fig.C.2a):
pyplot.plot(roi, color="b")
pyplot.ylim(-0.1, 1.1)
plot(roi, 'color', 'b')
ylim( [-0.1 1.1] )
Alternatively the ROI can be visualized using spm1d’s “plot roi” function — currently only available
in Python (Fig.C.2b):
pyplot.plot(YA.T, color="k")
pyplot.plot(YB.T, color="r")
spm1d.plot.plot_roi(roi, facecolor="b", alpha=0.3)
Figure C.2: Example ROI visualization (a) using pyplot.plot and (b) using spm1d.plot.plot roi
ROI-based statistical analysis proceeds as follows (Fig.C.3a)
t = spm1d.stats.ttest2(YB, YA, roi=roi)
ti = t.inference(0.05)
t = spm1d.stats.ttest2(YB, YA, 'roi', roi)
ti = t.inference(0.05)
To conduct the same analysis without an ROI simply drop the “roi” keyword as follows (Fig.C.3b)
t = spm1d.stats.ttest2(YB, YA)
ti = t.inference(0.05)
t = spm1d.stats.ttest2(YB, YA)
ti = t.inference(0.05)
Figure C.3: Example analysis (a) with one ROI and (b) without any ROIs. “SPM{t}” denotes the t
statistic extended in time to form a ‘statistical parametric map’.
Note the following:
When conducting ROI analysis spm1d masks portions of the t statistic curve which lie outside
the specified ROIs. This masking is replicated in the statistical continuum itself (the “z” attribute
of the spm object), as indicated below. Note: in MATLAB, masked elements “- -” are replaced
by “NaN”.
print( t.z )
[-- -- -- -- -- -- -- -- -- -- -0.22776187136870144 -0.35193394183457477
-0.4454435693960439 -0.4866562443204332 -0.45343849771681227
-0.32945352380074494 -0.10481565221034789 0.22601109469000205
0.6659607107024268 1.2186672527052544 1.8786714310449357 2.624090708123374
3.3977458417276942 4.09182563625598 4.557446151350232 4.676118446926481
4.4442233781988865 3.976243703618212 3.414764145392637 2.864043743188491
2.379655562970072 1.9818420780205368 1.6712848172222807 1.4407743903014176
1.2783724255448865 1.17159899332 1.1081081854538306 1.0770125187802424
1.0676148836585948 1.0710020774519424 -- -- -- -- -- -- -- -- -- -- -- --
-- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --
-- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --]
Critical thresholds (hashed horizontal lines in Fig.C.3) are always lower in ROI vs. non-ROI
analysis because the search volume is smaller.
When conducting ROI analysis there may be regions outside of the specified ROI which would
have reached significance had whole-field analysis been conducted (Fig.C.3b) and/or had the ROIs
been chosen dierently. This issue is discussed in the main manuscript.
C.3 Multiple ROIs in a single analysis
To conduct statistical analysis using multiple ROIs simply add multiple portions to the boolean
roi = np.array( [False]*101 )
roi[10:40] = True
roi[60:75] = True
roi = false( 1, 101 );
roi(11:40) = true;
roi(61:75) = true;
When there are multiple ROIs spm1d automatically raises the critical threshold to account for the
expanded search volume (Fig.C.4). Note that the critical threshold for two ROIs of breadths b1and b2
is not equivalent to the the critical threshold for a single ROI of breadth (b1+b2). For example, using
the two-ROIs defined above yields a critical threshold of t=3.115. If, instead a single ROI of the same
total breadth had been defined as follows:
roi = np.array( [False]*101 )
roi[10:55] = True
roi = false( 1, 101 );
roi(11:55) = true;
the critical threshold would be slightly lower: t=3.050. The reason is that within-ROI variance is
smooth (across the 1D continuum), but between-ROI variance is generally not smooth. The spm1d
software accounts for this using the Euler characteristic of the specified ROI (see Pataky 2016).
Figure C.4: Example analysis (a) with one ROI and (b) with two ROIs.
C.4 Directional ROIs
‘Directional ROIs’ can be used to simultaneously test a set of one-tailed hypotheses. As depicted
in Fig.5 (main manuscript), dierent ROIs can embody one-tailed hypotheses. Directional ROIs are
specified in spm1d as an integer vector containing the values: -1, 0 and +1 as follows:
roi = np.array( [0]*101 )
roi[10:40] = +1
roi[60:75] = -1
roi = zeros( 1, 101 );
roi(11:40) = +1;
roi(61:75) = -1;
Results for this particular set of directional ROIs as applied to the dataset above are depicted in
Fig.C.5b. Interpreting this result is somewhat complex and warrants discussion. First let us compare
this result with the case where both ROIs are positive (Fig.C.5a):
roi = np.array( [0]*101 )
roi[10:40] = +1
roi[60:75] = +1
roi = zeros( 1, 101 );
roi(11:40) = +1;
roi(61:75) = +1;
There are two results to consider:
1. Omnibus result: The omnibus result involves simultaneous testing of all ROIs. In this example
there is sucient evidence to reject the omnibus null hypothesis for both Fig.C.5a and C.5b because
the SPM{t}crosses the critical threshold in the predicted direction in both cases.
2. Individual ROI results: These results may be regarded as a post hoc qualification of the omnibus
test, much in the same way post hoc t tests work in ANOVA. In Fig.C.5a the null hypotheses are
rejected for both ROIs, but in Fig.C.5b the null hypothesis is rejected only for the first ROI.
In other words, there is sucient evidence to reject the omnibus null hypothesis for both Fig.C.5a
and Fig.C.5b. In Fig.C.5a there is sucient evidence to reject the null hypotheses pertaining to both
individual ROIs in post hoc analysis. However, in Fig.C.5a there is only sucient evidence to reject the
null hypothesis pertaining to the first ROI.
Figure C.5: Example directional ROI analysis. (a) Both ROIs are positive-directed. (b) The first and
second ROIs are positive- and negative-directed, respectively.
Appendix D Accessing datasets
All datasets analyzed in this paper are available in the spm1d software package (
and can be accessed via the interface as described below. Python and MATLAB code
snippets appear in green and orange font, respectively.
All datasets in are organized as follows:
where XXXX refers to the data modaility (e.g. univariate, one-dimensional), ZZZZ refers to the original
or appropriate statistical test (e.g. one-sample t test), and DatasetName is a unique name assigned to
each dataset, containing the main author’s family name and publication year where appropriate.
Datasets A and B (Pataky et al., 2015)
Datasets A and B contain univariate, one-dimensional data (“uv1d”), the appropriate test for both
is a one-sample t-test (“’t1”), and the dataset names are “SimulatedPataky2015a” and “Simulated-
Pataky2015b”. They can be accessed as indicated below. The YA and YB variables are both (10 x 101)
arrays, where 10 is the number of responses and 101 is the number of time nodes used to approximate
the continuum.
import spm1d
datasetA =
datasetB =
YA = datasetA.Y
YB = datasetB.Y
datasetA =;
datasetB =;
YA = datasetA.Y;
YB = datasetB.Y;
Dataset C (Neptune et al., 1999)
Dataset C contains multivariate, one-dimensional data (“mv1d”), the appropriate test is a paired
Hotellings T2test (“hotellings paired”), and the dataset name is “Neptune1999kneekin”. They can be
accessed as indicated below. The YA and YB variables are both (8 x 101 x 3), where 8 is the number
of responses, 101 is the number of time nodes, and 3 is the number of vector components. Although
these data are multivariate, in this study univariate analyses were conducted on only the first vector
component (variables yA and yB).
import spm1d
dataset =
YA,YB = dataset.YA, dataset.YB
yA,yB = YA[:,:,0], YB[:,:,0]
dataset =;
[YA,YB] = deal( dataset.YA, dataset.YB );
[YA,YB] = deal( YA(:,:,1), YB(:,:,1) );
Dataset D (Pataky et al., 2008)
Dataset D contains univariate, one-dimensional data (“uv1d”), the appropriate test is one-way
ANOVA (“anova1”), and the dataset name is “SpeedGRFcategorical”. Individual subjects’ data can
be loaded using the “subj” keyword as indicated below. The Y and A variables in each dataset are (60
x 101), and (60 x 1), respectively, where 60 is the number of responses and 101 is the number of time
nodes. Y contains the GRF data and A contains a vector of condition labels, where the labels “1”, “2”,
and “3” refer to slow, normal and fast walking, respectively. Note that 20 repetitions of each condition
were conducted and that the conditions were presented in a randomized order. In this paper only the
normal and fast conditions were considered.
The Y00 and Y01 variables are both (20 x 101) and were used in the Stage 1 analyses (Fig.6a). The
Y0 and Y1 variables are both (6 x 101) and contain within-subject mean trajectories for each of the six
subjects, and were used in the State 2 analyses (Fig.6b–c).
# load pilot subject's data:
subj0 = 0
dataset =
Y,A = dataset.Y, dataset.A
Y00 = Y[A==2]
Y01 = Y[A==3]
# load experiment subjects' data:
SUBJ = [2, 3, 4, 5, 6, 7]
Y0 = []
Y1 = []
for subj in SUBJ:
dataset =
Y,A = dataset.Y, dataset.A
Y0.append( Y[A==2].mean(axis=0) )
Y1.append( Y[A==3].mean(axis=0) )
Y0,Y1 = np.array(Y0), np.array(Y1)
% load pilot subject's data:
subj0 = 0;
dataset =;
[Y,A] = deal( dataset.Y, dataset.A );
Y00 = Y(A==2,:);
Y01 = Y(A==3,:);
% load experiment subjects' data:
SUBJ = [2 3 4 5 6 7];
Y0 = zeros(6, 101);
Y1 = zeros(6, 101);
for i = 1:6
dataset = SUBJ(i) );
[Y,A] = deal( dataset.Y, dataset.A );
Y0(i,:) = mean( Y(A==2,:), 1);
Y1(i,:) = mean( Y(A==3,:), 1);
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marsbar toolbox for spm 99. NeuroImage, 16(2):S497.
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during cutting movements. Medicine & Science in Sports & Exercise, 31(2):294–302, data: http:
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are highly sensitive to region boundary definitions. Journal of Biomechanics, 41(12):2772–2775.
Pataky, T. C., Vanrenterghem, J., and Robinson, M. A. (2015). Zero- vs. one-dimensional, paramet-
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... However, an important limitation of these measures is that they just provide a general overview of the myoelectric behaviour of the leg muscles for the full running cycle, not allowing the identification of changes at different time-points or phases during the running cycle (Pataky, Robinson, & Vanrenterghem, 2016;Robinson, Vanrenterghem, & Pataky, 2015). Therefore, it is important to employ signal-processing techniques which allow the evaluation of temporal differences in muscle activity during the entire time series of a task (e.g., full running cycle), rather than comparing ensemble averages for the full running cycle, which provides results with poor temporal resolution. ...
... A statistical-processing technique that has allowed biomechanical variables to be examined in function of the time series of a task, is statistical parametric mapping (SPM) (Pataky, 2010;Pataky et al., 2016). This technique was first described by Friston et al. (1995), and then validated by Pataky based on kinematic and kinetic data (Pataky, 2010;Pataky et al., 2016). ...
... A statistical-processing technique that has allowed biomechanical variables to be examined in function of the time series of a task, is statistical parametric mapping (SPM) (Pataky, 2010;Pataky et al., 2016). This technique was first described by Friston et al. (1995), and then validated by Pataky based on kinematic and kinetic data (Pataky, 2010;Pataky et al., 2016). SPM is based on an inferential method, where hypothesis testing is directly applied to the signal (Pataky et al., 2016). ...
The aim of this study was to apply statistical parametric mapping (SPM) to compare temporal changes in EMG amplitude between rearfoot (RF) and forefoot (FF) running techniques. Eleven recreational runners ran on a treadmill at a self-selected speed, once using a RF strike pattern and once using a FF strike pattern (randomized order). The myoelectric activity of five lower limb muscles [rectus femoris (RFe), biceps femoris (BF), tibialis anterior (TA), medial and lateral gastrocnemius (MG and LG)] was evaluated, using bipolar electromyography (EMG). EMG data from the RF and FF running techniques was then processed and posteriorly compared with SPM, dividing the analysis of the running cycle into stance and swing phases. The MG and LG muscles showed higher activation during FF running at the beginning of the stance phase and at the end of the swing phase. During the end of the swing phase the TA muscle's EMG amplitude was higher, when the RF running technique was used. A higher level of co-activation between the gastrocnemius and TA muscles was observed at the end of the swing phase during RF running. The myoelectric behaviour of the RFe and BF muscles was similar during both running techniques. These findings highlight the importance of SPM for the accurate assessment of differences in muscle activity during running and strongly suggest that these two running techniques predominately reflect adjustments of the leg and not the thigh muscles.
... Stance was defined as the period between the first and last instances of foot-to-ground contact of the instrumented leg, as detected by the vertical GRF exceeding 20 N. For each trial, ACL forces were normalized to 100% of stance, averaged for each participant, and ensemble-averaged for each footwear condition. Statistical parametric mapping (SPM) was used to analyse ACL force in a time-continuous manner [40]. The SPM analyses were implemented using open-source SPM1d software (v.M.0.4.7, ...
Full-text available
Rates of anterior cruciate ligament (ACL) rupture in young people have increased markedly over the past two decades, with females experiencing greater growth in their risk compared to males. In this study, we determined the effects of low- and high-support athletic footwear on ACL loads during a standardized drop–land–lateral jump in 23 late-/post-pubertal females. Each participant performed the task unshod, wearing low- (Zaraca, ASICS) or high- (Kayano, ASICS) support shoes (in random order), and three-dimensional body motions, ground-reaction forces, and surface electromyograms were synchronously acquired. These data were then used in a validated computational model of ACL loading. One-dimensional statistical parametric mapping paired t-tests were used to compare ACL loads between footwear conditions during the stance phase of the task. Participants generated lower ACL forces during push-off when shod (Kayano: 624 N at 71–84% of stance; Zaraca: 616 N at 68–86% of stance) compared to barefoot (770 N and 740 N, respectively). No significant differences in ACL force were observed between the task performed wearing low- compared to high-support shoes. Compared to barefoot, both shoe types significantly lowered push-off phase peak ACL forces, potentially lowering risk of ACL injury during performance of similar tasks in sport and recreation.
... Then, the para-player's joint angle-time histories were compared to the controls using one-dimensional statistical parametric mapping (SPM, one-sample t-test). SPM allowed analysis of the entire waveform over time, offering a more comprehensive analysis over extracting discrete kinematic variables at critical events such as maximum or minimum values [25]. Such waveform analysis can provide additional dynamic information that may be missed when reporting discrete variables (e.g., joint angles, ROM) alone [26]. ...
Full-text available
Background Both able-bodied and Class 7 para-table tennis players compete while standing, but do they use the same techniques to hit the ball? This case study examined the shoulder joint kinematics of a highly skilled para-table tennis player with severe leg impairment. Methods One international level Class 7 male para-table tennis player was compared with a control group of 9 male, competitive university team players. Participants performed 15 trials of forehand and 15 trials of backhand topspin drives. Shoulder abduction/adduction angles and joint range of motion (ROM) were measured using an inertial measurement system. Results The joint ROM of the para-player was comparable to the control group in the forehand [para-player 38°, controls 32 (15)°] and slightly larger in backhand [para-player 35°, controls 24 (16)°]. Waveform analysis revealed significant differences in the entire forehand drives (p < .001) and the preparation (p < .001) and follow-through phases (p = .014) of the backhand drives. Conclusions Coaches should not simply instruct para-table tennis players to replicate the characteristics of able-bodied players. Depending on the nature of the physical impairment, para-players should optimise their movement strategies for successful performance.
... Les valeurs étaient dites subnormales quand elles étaient situées entre 1 et 2 écarttypes, et anormales au-delà. Pour affiner l'analyse, la méthode SPM (Statistical Parametric Mapping) a été utilisée pour déterminer les instants du cycle de marche pour lesquels les deux populations étaient significativement différentes (Pataky et al. 2013, Pataky et al. 2016. ...
Le rachitisme hypophosphatémique lié au chromosome X (XLH) est une maladie rare touchant le système musculosquelettique et la fonction des membres inférieurs. La plupart des symptômes du XLH ont un impact fort sur le quotidien des patients mais peuvent être minimisés lors de la croissance sous l’effet d’un traitement adapté. A ce jour, seule une appréciation qualitative des symptômes physiques du XLH est possible. Cette thèse vise à définir un protocole d’évaluation quantitative du XLH et de son évolution durant la croissance pour les membres inférieurs. La première partie porte sur l’étude 3D du squelette. On y montre que la diaphyse fémorale est particulièrement touchée. En suivi on voit que les angles mécaniques se normalisent en premiers sous l’effet du traitement, le fémur et le tibia évoluant au même rythme. Une deuxième partie sur l’analyse quantifiée de la marche montre que les altérations concernent principalement le plan frontal et qu’elles sont liées aux déformations osseuses. Une dernière partie, consacrée aux muscles, met en avant une altération de la composition et une atrophie musculaire chez les patients avec XLH pouvant expliquer la faiblesse musculaire observée. En combinant ces trois examens, le protocole proposé dans cette thèse permet à la fois de quantifier les altérations du système musculosquelettique et de la marche chez des enfants avec XLH et d’améliorer notre compréhension des interactions existantes entre ces trois éléments.
... In order to analyse the effect of the groups on the characteristics of the rotational and translational behaviour over the time-series of a complete gait cycle, one-dimensional statistical parametric mapping (SPM) was performed (Pataky et al., 2016). A total of 15 one-way ANOVAs were performed. ...
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Background A comparison of natural versus replaced tibio-femoral kinematics in vivo during challenging activities of daily living can help provide a detailed understanding of the mechanisms leading to unsatisfactory results and lay the foundations for personalised implant selection and surgical implantation, but also enhance further development of implant designs towards restoring physiological knee function. The aim of this study was to directly compare in vivo tibio-femoral kinematics in natural versus replaced knees throughout complete cycles of different gait activities using dynamic videofluoroscopy. Methods Twenty-seven healthy and 30 total knee replacement subjects (GMK Sphere, GMK PS, GMK UC) were assessed during multiple complete gait cycles of level walking, downhill walking, and stair descent using dynamic videofluoroscopy. Following 2D/3D registration, tibio-femoral rotations, condylar antero-posterior translations, and the location of the centre of rotation were compared. Findings The total knee replacement groups predominantly experienced reduced tibial internal/external rotation and altered medial and lateral condylar antero-posterior translations compared to natural knees. An average medial centre of rotation was found for the natural and GMK sphere groups in all three activities, whereas the GMK PS and UC groups experienced a more central to lateral centre of rotation. Interpretation Each total knee replacement design exhibited characteristic motion patterns, with the GMK Sphere most closely replicating the medial centre of rotation found for natural knees. Despite substantial similarities between the subject groups, none of the implant geometries was able to replicate all aspects of natural tibio-femoral kinematics, indicating that different implant geometries might best address individual functional needs.
... Quasi-continuous joint and muscle forces throughout the motion were analyzed using statistical parametric mapping (SPM) repeated-measures analysis of variance, with post hoc 2-tailed SPM paired t tests (1d package, version 0.4; 31 Simulator data were collected at every 2 -5 of glenohumeral elevation; splines and up-sampling were then applied to provide compatible data densities. The glenohumeral elevation range-of-motion domains of all trials were cropped to the domain of the minimum continuous data set among specimens. ...
Background While typically favorable in outcome, anatomic total shoulder arthroplasty (aTSA) can require long-term revision. The most common cause for revision is glenoid loosening, which may result from eccentric cyclic forces and joint translations. “Rocking” of the glenoid component may be exacerbated by the joint geometry, such as glenoid inclination and version. Restoration of premorbid glenoid inclination may be preferable, although laboratory and computational models indicate that both superior and inferior inclination have benefits. This discrepancy may arise since previous studies were limited by a lack of physiologic conditions to test inclination. Therefore, a cadaveric shoulder simulator with 3D human motion was used to study joint contact and muscle forces with isolated changes in glenoid inclination. Methods Eight human cadaver shoulders were tested before and after aTSA. Scapular plane abduction kinematics from human subjects were used to drive a cadaveric shoulder simulator with 3D scapulothoracic and glenohumeral motion. Glenoid inclination was varied from -10º to +20º, while compressive, superior-inferior shear, and anterior-posterior shear forces were collected with a 6 degree of freedom loadcell during motion. Outputs also included muscle forces of the deltoid and rotator cuff. Data were evaluated with statistical parametric mapping (SPM) repeated measures analysis of variance and t-tests. Results Inferior glenoid inclination (-10°) reduced both compressive and superior-inferior shear forces versus neutral 0° inclination by up to 40%, more when compared to superior inclination (p<0.001). Superior inclinations (+10°, +20°) tended to increase deltoid and rotator cuff forces versus neutral 0° inclination or inferior inclination, on the order of 20-40% (p≤0.045). All force metrics except anterior-posterior shear were lowest for inferior inclination. Most aTSA muscle forces for neutral 0° inclination were not significantly different than native shoulders, and decreased 45% and 15% in the posterior deltoid and supraspinatus, respectively (p≤0.003). Joint translations were similar to prior reports in aTSA patients, and did not differ between any inclinations or native shoulders. Joint reaction forces were similar to those observed in human subjects with instrumented aTSA implants, providing confidence in the relative magnitude of the present results. Conclusions Inferior inclination reduces overall forces in the shoulder. Superior inclinations increased the muscle effort required for the shoulder, to achieve similar motion, thus increasing the forces exerted on the glenoid component. These results suggest that a bias in aTSA glenoid components toward inferior inclination may reduce the likelihood of glenoid loosening by reducing excessive muscle and joint contact forces.
While there is general agreement on the transverse plane knee joint motion for loaded flexion activities, its kinematics during functional movements such as level walking are discussed more controversially. One possible cause of this controversy could originate from the interpretation of kinematics based on different analysis approaches. In order to understand the impact of these approaches on the interpretation of tibio-femoral motion, a set of dynamic videofluoroscopy data presenting continuous knee bending and complete cycles of walking in ten subjects was analysed using six different kinematic analysis approaches. Use of a functional flexion axis resulted in significantly smaller ranges of condylar translation compared to anatomical axes and contact approaches. All contact points were located significantly more anteriorly than the femur fixed axes after 70° of flexion, but also during the early/mid stance and late swing phases of walking. Overall, a central to medial transverse plane centre of rotation was found for both activities using all six kinematic analysis approaches, although individual subjects exhibited lateral centres of rotation using certain approaches. The results of this study clearly show that deviations from the true functional axis of rotation result in kinematic crosstalk, suggesting that functional axes should be reported in preference to anatomical axes. Contact approaches, on the other hand, can present additional information on the local tibio-femoral contact conditions. To allow a more standardised comparison and interpretation of tibio-femoral kinematics, results should therefore be reported using at least a functionally determined axis and possibly also a contact point approach.
Vibration has the potential to compromise performance in cycling. This study aimed to investigate the effects of vibration on full-body kinematics and muscle activation time series. Nineteen male amateur cyclists (mass 74.9 ± 5.9 kg, body height 1.82 ± 0.05 m, Vo2max 57 ± 9 ml/kg/min, age 27 ± 7 years) cycled (216 ± 16 W) with (Vib) and without (NoVib) vibration. Full-body kinematics and muscle activation time series were analysed. Vibration did not affect lower extremity joint kinematics significantly. The pelvic rotated with vibration towards the posterior direction (NoVib: 22.2 ± 4.8°, Vib: 23.1 ± 4.7°, p = 0.016, d = 0.20), upper body lean (NoVib: 157.8 ± 3.0°, Vib: 158.9 ± 3.4°, p = 0.001, d = 0.35) and elbow flexion (NoVib: 27.0 ± 8.2°, Vib: 29.4 ± 9.0°, p = 0.010, d = 0.28) increased significantly with vibration. The activation of lower extremity muscles (soleus, gastrocnemius lat., tibialis ant., vastus med., rectus fem., biceps fem.) increased significantly during varying phases of the crank cycle due to vibration. Vibration increased arm and shoulder muscle (triceps brachii, deltoideus pars scapularis) activation significantly over almost the entire crank cycle. The co-contraction of knee and ankle flexors and extensors (vastus med. – gastrocnemius lat., vastus med. – biceps fem., soleus – tibialis ant.) increased significantly with vibration. In conclusion vibrations influence main tasks such as propulsion and upper body stabilization on the bicycle to a different extent. The effect of vibration on the task of propulsion is limited due to unchanged lower body kinematics and only phase-specific increases of muscular activation during the crank cycle. Additional demands on upper body stabilization are indicated by adjusted upper body kinematics and increased muscle activation of the arm and shoulder muscles during major parts of the cranking cycle.
Background Gait analysis is burdened by time and equipment costs, interpretation, and accessibility of three-dimensional motion analysis systems. Evidence suggests growing adoption of gait testing in the shift toward evidence-based medicine. Further developments addressing these barriers will aid its efficacy in clinical practice. Previous research aiming to develop gait analysis systems for kinetics estimation using the Kinect V2 have provided promising results yet modified approaches using the latest hardware may further aid kinetics estimation accuracy Research Question Can a single Azure Kinect sensor combined with a musculoskeletal modeling approach provide kinetics estimations during gait similar to those obtained from marker-based systems with embedded force platforms? Methods Ten subjects were recruited to perform three walking trials at their normal speed. Trials were recorded using an eight-camera optoelectronic system with two embedded force plates and a single Azure Kinect sensor. Marker and depth data were both used to drive a musculoskeletal model using the AnyBody Modeling System. Predicted kinetics from the Azure Kinect-driven model, including ground reaction force (GRF) and joint moments, were compared to measured values using root meansquared error (RMSE), normalized RMSE, Pearson correlation, concordance correlation, and statistical parametric mapping Results High to very high correlations were observed for anteroposterior GRF (ρ = 0.889), vertical GRF (ρ = 0.940), and sagittal hip (ρ = 0.805) and ankle (ρ =.876) moments. RMSEs were 1.2 ± 2.2 (%BW), 3.2 ± 5.7 (%BW), 0.7 ±.1.3 (%BWH), and 0.6 ± 1.0 (%BWH) Significance The proposed approach using the Azure Kinect provided higher accuracy compared to previous studies using the Kinect V2 potentially due to improved foot tracking by the Azure Kinect. Future studies should seek to optimize ground contact parameters and focus on regions of error between predicted and measured kinetics highlighted currently for further improvements in kinetic estimations.
Background In vivo measurements of tibiotalar and subtalar joint motion following TAR are unavailable. Using biplane fluoroscopy, we tested the hypothesis that the prosthetic tibiotalar joint and adjacent subtalar joint would demonstrate kinematic and range of motion differences compared to the contralateral untreated limb, and control participants. Methods Six patients of 41 identified candidates that all underwent unilateral Zimmer TAR (5.4 ± 1.9 years prior) and 6 control participants were imaged with biplane fluoroscopy during overground walking and a double heel-rise activity. Computed tomography scans were acquired; images were segmented and processed to serve as input for model-based tracking of the biplane fluoroscopy data. Measurements included tibiotalar and subtalar kinematics for the TAR, untreated contralateral, and control limbs. Statistical parametric mapping quantified differences in kinematics throughout overground walking and the double heel-rise activity. Results Patients with this TAR performed walking and heel-rise activities symmetrically with no significant kinematic differences at the tibiotalar and subtalar joints between limbs. Compared to control participants, patients exhibited reduced dorsi/plantarflexion range of motion that corresponded to decreased peak dorsiflexion, but only in the late stance phase of walking. This reduction in tibiotalar dorsi/plantarflexion range of motion in the TAR group became more apparent with double heel-rise activity. Conclusion Patients with a Zimmer TAR had symmetric kinematics during activities of walking and double heel-rise, but they did exhibit minor compensations in tibiotalar kinematics as compared to controls. Clinical Relevance The lack of significant kinematic compensation at the subtalar joint may explain why secondary subtalar osteoarthritis is reported as being relatively uncommon in patients with some TAR designs.
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In ERP and other large multidimensional neuroscience data sets, researchers often select regions of interest (ROIs) for analysis. The method of ROI selection can critically affect the conclusions of a study by causing the researcher to miss effects in the data or to detect spurious effects. In practice, to avoid inflating Type I error rate (i.e., false positives), ROIs are often based on a priori hypotheses or independent information. However, this can be insensitive to experiment-specific variations in effect location (e.g., latency shifts) reducing power to detect effects. Data-driven ROI selection, in contrast, is nonindependent and uses the data under analysis to determine ROI positions. Therefore, it has potential to select ROIs based on experiment-specific information and increase power for detecting effects. However, data-driven methods have been criticized because they can substantially inflate Type I error rate. Here, we demonstrate, using simulations of simple ERP experiments, that data-driven ROI selection can indeed be more powerful than a priori hypotheses or independent information. Furthermore, we show that data-driven ROI selection using the aggregate grand average from trials (AGAT), despite being based on the data at hand, can be safely used for ROI selection under many circumstances. However, when there is a noise difference between conditions, using the AGAT can inflate Type I error and should be avoided. We identify critical assumptions for use of the AGAT and provide a basis for researchers to use, and reviewers to assess, data-driven methods of ROI localization in ERP and other studies.
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A false positive is the mistake of inferring an effect when none exists, and although α controls the false positive (Type I error) rate in classical hypothesis testing, a given α value is accurate only if the underlying model of randomness appropriately reflects experimentally observed variance. Hypotheses pertaining to one-dimensional (1D) (e.g. time-varying) biomechanical trajectories are most often tested using a traditional zero-dimensional (0D) Gaussian model of randomness, but variance in these datasets variance is clearly 1D. The purpose of this study was to determine the likelihood that analyzing smooth 1D data with a 0D model of variance will produce false positives. We first used random field theory (RFT) to predict the probability of false positives in 0D analyses. We then validated RFT predictions via numerical simulations of smooth Gaussian 1D trajectories. Results showed that, across a range of public kinematic, force and EMG datasets, the median false positive rate was 0.382 and not the assumed α=0.05, even for a simple two-sample t test involving N=10 trajectories per group. The median false positive rates for experiments involving three-component vector trajectories was p=0.764. This rate increased to p=0.945 for two three-component vector trajectories, and to p=0.999 for six three-component vectors. This implies that experiments involving vector trajectories have a high probability of yielding 0D statistical significance when there is, in fact, no 1D effect. Either (a) explicit a priori identification of 0D metrics or (b) adoption of 1D methods can more tightly control α.
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Through topological expectations regarding smooth, thresholded n-dimensional Gaussian continua, random field theory (RFT) describes probabilities associated with both the field-wide maximum and threshold-surviving upcrossing geometry. A key application of RFT is a correction for multiple comparisons which affords field-level hypothesis testing for both univariate and multivariate fields. For unbroken isotropic fields just one parameter in addition to the mean and variance is required: the ratio of a field’s size to its smoothness. Ironically the simplest manifestation of RFT (1D unbroken fields) has rarely surfaced in the literature, even during it foundational development in the late 1970s. This Python package implements 1D RFT primarily for exploring and validating RFT expectations, but also describes how it can be applied to yield statistical inferences regarding sets of experimental 1D fields.
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Biomechanical processes are often manifested as one-dimensional (1D) trajectories. It has been shown that 1D confidence intervals (CIs) are biased when based on 0D statistical procedures, and the non-parametric 1D bootstrap CI has emerged in the Biomechanics literature as a viable solution. The primary purpose of this paper was to clarify that, for 1D biomechanics datasets, the distinction between 0D and 1D methods is much more important than the distinction between parametric and non-parametric procedures. A secondary purpose was to demonstrate that a parametric equivalent to the 1D bootstrap exists in the form of a random field theory (RFT) correction for multiple comparisons. To emphasize these points we analyzed six datasets consisting of force and kinematic trajectories in one-sample, paired, two-sample and regression designs. Results showed, first, that the 1D bootstrap and other 1D non-parametric CIs were qualitatively identical to RFT CIs, and all were very different from 0D CIs. Second, 1D parametric and 1D non-parametric hypothesis testing results were qualitatively identical for all six datasets. Last, we highlight the limitations of 1D CIs by demonstrating that they are complex, design-dependent, and thus non-generalizable. These results suggest that (i) analyses of 1D data based on 0D models of randomness are generally biased unless one explicitly identifies 0D variables before the experiment, and (ii) parametric and non-parametric 1D hypothesis testing provide an unambiguous framework for analysis when one׳s hypothesis explicitly or implicitly pertains to whole 1D trajectories. Copyright © 2015 Elsevier Ltd. All rights reserved.
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Center of pressure (COP) trajectories summarize the complex mechanical interaction between the foot and a contacted surface. Each trajectory itself is also complex, comprising hundreds of instantaneous vectors over the duration of stance phase. To simplify statistical analysis often a small number of scalars are extracted from each COP trajectory. The purpose of this paper was to demonstrate how a more objective approach to COP analysis can avoid particular sensitivities of scalar extraction analysis. A previously published dataset describing the effects of walking speed on plantar pressure (PP) distributions was re-analyzed. After spatially and temporally normalizing the data, speed effects were assessed using a vector-field paired Hotelling's T2 test. Results showed that, as walking speed increased, the COP moved increasingly posterior at heel contact, and increasingly laterally and anteriorly between ∼60-85% stance, in agreement with previous independent studies. Nevertheless, two extracted scalars disagreed with these results. Furthermore, sensitivity analysis found that a relatively small coordinate system rotation of 5.5 deg reversed the mediolateral null hypothesis rejection decision. Considering that the foot may adopt arbitrary postures in the horizontal plane, these sensitivity results suggest that non-negligible uncertainty may exist in mediolateral COP effects. As compared with COP scalar extraction, two key advantages of the vector-field approach are: (i) coordinate system independence, (ii) continuous statistical data reflecting the temporal extents of COP trajectory changes.
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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.
In an age where the amount of data collected from brain imaging is increasing constantly, it is of critical importance to analyse those data within an accepted framework to ensure proper integration and comparison of the information collected. This book describes the ideas and procedures that underlie the analysis of signals produced by the brain. The aim is to understand how the brain works, in terms of its functional architecture and dynamics. This book provides the background and methodology for the analysis of all types of brain imaging data, from functional magnetic resonance imaging to magnetoencephalography. Critically,Statistical Parametric Mappingprovides a widely accepted conceptual framework which allows treatment of all these different modalities. This rests on an understanding of the brain's functional anatomy and the way that measured signals are caused experimentally. The book takes the reader from the basic concepts underlying the analysis of neuroimaging data to cutting edge approaches that would be difficult to find in any other source. Critically, the material is presented in an incremental way so that the reader can understand the precedents for each new development. This book will be particularly useful to neuroscientists engaged in any form of brain mapping; who have to contend with the real-world problems of data analysis and understanding the techniques they are using. It is primarily a scientific treatment and a didactic introduction to the analysis of brain imaging data. It can be used as both a textbook for students and scientists starting to use the techniques, as well as a reference for practicing neuroscientists. The book also serves as a companion to the software packages that have been developed for brain imaging data analysis. * An essential reference and companion for users of the SPM software * Provides a complete description of the concepts and procedures entailed by the analysis of brain images * Offers full didactic treatment of the basic mathematics behind the analysis of brain imaging data * Stands as a compendium of all the advances in neuroimaging data analysis over the past decade * Adopts an easy to understand and incremental approach that takes the reader from basic statistics to state of the art approaches such as Variational Bayes * Structured treatment of data analysis issues that links different modalities and models * Includes a series of appendices and tutorial-style chapters that makes even the most sophisticated approaches accessible.
This article discusses the methodology and rationale for the application of plantar pressure measurement (PPM) to patients with diabetes mellitus in a clinical setting. PPM is often the only dynamic component of the examination and it provides data on the foot-ground interaction during the specific activity (walking) in which plantar ulceration usually occurs. Elevated plantar pressure has been linked both prospectively and retrospectively with plantar ulceration and it is likely that future studies will show PPM to be predictive of both the site of ulceration and the risk of ulceration. The principles of operation of a number of platforms and in-shoe devices together with methods of analysis and display are disscussed. Biomechanical factors which may lead to elevated pressure are briefly discussed and 8 case studies illustrating different facets of the use of PPM in a clinical setting are presented.