Statistical analysis of temporal kinematic waveforms

[Mark Goss-Sampson]

Hi folks
In most kinematic studies comparisons are made between data at specific events - effectively disregarding the temporal changes throughout the data - thus sacrificing temporal resolution.
I am curious if anyone has any views on different methods for statistically analysing waveform variance over time i.e. if there are statistically significant differences in specific temporal regions of either say 20 repeated trials from an individual or in a comparison of multiple waveforms in two or more conditions. I have found several methods that appear to have been utilised to a greater or lesser extent in other waveform analyses such as Coefficients of Multiple Correlation, wavelet-based functional ANOVA and Statistical Parametric Mappings.
I would be interested in hearing your views / experiences / recommendations for such analysis.

[Mark Robinson]

Re: Statistical analysis of temporal kinematic waveforms

Hi Mark,

My colleague Jos Vanrenterghem and I have been using Statistical Parametric Mapping (SPM) in the context you describe for the last couple of years. SPM, although an established technique in other fields was described in a biomechanical context by Pataky (2010). This paper shows that SPM is an n-dimensional technique that can be applied in the context of a t-test, ANOVA, regression etc. Pataky (2012) describes the free and open-source Python package for conducting SPM analyses. To date, we have used SPM in the context of linear regression (Vanrenterghem et al., 2012 - running speed vs knee loading) and ANOVA with post-hoc t-tests (De Ridder et al., In Press - 3 groups ankle instability). These analyses were able to identify specific time periods where running speed significantly predicted knee loading and where differences in multi-segment foot kinematics occurred.

Hope these references help.

Regards
Mark Robinson
Lecturer in Biomechanics
Liverpool John Moores University, UK

REFERENCES
Pataky TC. 2010. Generalized n-dimensional biomechanical field analysis using statistical parametric mapping. J Biomech 43(10):1976–1982.
Pataky TC. 2012. One-dimensional statistical parametric mapping in Python. CMBBE 15(3): 295-301.
Vanrenterghem, J., Venables, E., Pataky, T., & Robinson, M. 2012. The effect of running speed on knee mechanical loading in females during side-cutting. J Biomech, 45, 2444-2449.
De Ridder, R., Willems, T., Vanrenterghem, J., Robinson, M., Pataky, T., Roosen, T. In Press. Gait Kinematics of Subjects with Ankle Instability Using a Multisegmented Foot Model. Medicine and Science in Sports and Exercise.

[Matthew Seeley]

Re: Statistical analysis of temporal kinematic waveforms

Hi Mark,

My colleagues and I have recently been using what our statistician simply calls a functional analysis approach to consider various neuromechanical variables during different movement tasks. The approach allows us to compare different dependent variables across entire durations, rather than only at discrete time points. This approach is further described in the following article:

Hopkins, J.T., Coglianese, M.†, Glasgow, P., Reese, S., & Seeley, M.K. (2012). Alterations in evertor/invertor muscle activation and center of pressure trajectory in patients with chronic ankle instability. Journal of Electromyography and Kinesiology, 22, 280-285.

[Mark Goss-Sampson]

Re: Statistical analysis of temporal kinematic waveforms

My thanks to Mark and Matthew who have replied with some suggestions regarding this matter - any other views appreciated.

[Todd Pataky]

Re: Statistical analysis of temporal kinematic waveforms

Hi Mark,
I'm one of the authors of the papers Mark Robinson mentioned in his post above, and I'd be happy to discuss SPM if you're interested. You may also be interested in Chris Richter's work on fPCA (below). I think the best choice of method depends on your analysis goal. One of SPM's strengths is that it conducts statistical hypothesis testing directly on multiple trajectories, regarding the single trajectory as the unit of observation. I know much less about FDA and fPCA, but from what I understand their key strengths include objectively uncovering patterns in the data, in subsequently testing those patterns, and in highlighting potential areas of interest for subsequent testing.

Richter, Chris and O'Connor, Noel E. and Moran, Kieran (2012) Comparison of discrete point and continuous data analysis for identifying performance determining factors. In: 30th Conference of the International Society of Biomechanics in Sport, 2-6 July 2012, Melbourne, Australia.

[Philippe C. Dixon]

Re: Statistical analysis of temporal kinematic waveforms

Hi Mark,

Although I do not have great expertise in the methods proposed in the previous replies, I think they will address your problems adequately. You may, however, want to take a look at an other solution using Bootstrapping. This method is a little more limited, but still addresses the weakness of point-by-point analysis. I've recently used this method and found it easy to implement and interpret. The Bootstrap is well described in the biomech context in the references below:

Lenhoff MW, Santner TJ, Otis JC, Peterson MG, Williams BJ, Backus SI. Bootstrap prediction and confidence bands: a superior statistical method for analysis of gait data. Gait and Posture 1999;9:10–7

Duhamel A, Bourriez JL, Devos P, Krystkowiak P, Destee A, Derambure P, et al. Statistical tools for clinical gait analysis. Gait and Posture 2004;20:204–12

Hope that helps,
Phil

[Bruno Mazuquin]

Re: Statistical analysis of temporal kinematic waveforms

Hi everyone!

I'm really interested in studying more about statistical parametric mapping. I would be really appreciated if someone, please, indicate more references!

Bruno Mazuquin

[Todd Pataky]

Re: Statistical analysis of temporal kinematic waveforms

Hi Bruno,

I believe that the best SPM resource is the book by Karl Friston, Will Penny and others (below). It's a fantastic resource, but also unfortunately contains a lot of complexities (like 3D image processing and temporal response modeling) which aren't immediately relevant to kinematic/force trajectory analysis. You could also check out the open-source packages listed below, they contain documentation and analysis examples which might be useful. The spm1d package might be most immediately useful for kinematic/force trajectory analysis.

As far as I know biomechanics-specific papers include only those cited above.

Cheers,
Todd


Book:
Friston, K. J., Ashburner, J. T., Kiebel, S. J., Nichols, T. E., and Penny, W. D. (2007). Statistical Parametric Mapping: The Analysis of Functional Brain Images, Elsevier/Academic Press, Amsterdam.

Online resources:

http://en.wikibooks.org/wiki/SPM

Software:
SPM8: http://www.fil.ion.ucl.ac.uk/spm/
spm1D: http://www.tpataky.net/spm1d/

[Bruno Mazuquin]

Re: Statistical analysis of temporal kinematic waveforms

Thank you very much Todd!

[Paul Biggs]

Re: Statistical analysis of temporal kinematic waveforms

I'm a first year PhD student so am still learning, but Principle Component Analysis can often be used to describe about 95% variance in your waveforms with only a few components, so you are still reducing temporal resolution however each variable (principle component value) describes a proportion of the waveform.

[Chris Richter]

Re: Statistical analysis of temporal kinematic waveforms

Hey there,

For the last years, I am tackling the problems of discrete point analysis by applying continuous waveform analysis. As a result my college (Kieran Moran) and I had the idea of analyzing characterizing phases 'Analysis of Characterizing Phases (ACP)': which has been mentioned previously in this discussion.

To give you a quick overview, ACP identifies phases of variance (key-phases) of a data set: which are used for analysis. Knowing key-phases allows examining timing, magnitude and the combination of timing and magnitude to find differences between groups or correlations to a dependent variable. Key-phases can be identified by performing, for example, a fPCA, which generates principal components (PCs) that separate pattern of variation of a data set and give a clear indication about the strength of a pattern of variation at every time point. This information can be used (i) to identify and test phases over which a pattern of variation has the greatest strength and (ii) allows the extension of these phases to identify the full duration over which a pattern of variation differs.

@ Paul Biggs: I would examine PCs behind the variance level of 95%. The eigenvalue of PCs describes the influence to the data not to a dependent variable. I got a short paper accepted at the symposium of ISB 2013 which discusses that issue "Identification of an optimal principal components analysis threshold to describe jump height accurately using vertical ground reaction forces".

If you have any question please contact me.

Chris

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Tel: 00353 1 700 6830

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Recent references are:

Journal papers ---

Richter C., Marshal B., O’Connor N.E. and K. Moran (2013), Comparison of discrete point and functional data based analysis for identifying performance determining factors. Journal of applied Biomechanics: Accepted for publication (I would send it out per email if requested)

Conference proceedings ---

Richter, C., O’Connor N.E. and K. Moran (2012). Comparison of discrete point and continuous data analysis for identifying performance determining factors Symposium of the International Society of Biomechanics in Sports. Melbourne, Australia. 2012.

Chris Richter, Leonardo Gualano, Noel E. O’Connor, Kieran Moran, "Cross-comparison of the performance of discrete, phase and functional data analysis to describe a dependent variable", Symposium of the International Society of Biomechanics in Sports. Taiwan, Taipei. 2013.

Danica Mauz, Randall L. Jensen, Falk Naundorf, Chris Richter, Manfred Vieten, " Kinematic adjustments during successful and unsuccessful wolf jumps on the balance beam ", Symposium of the International Society of Biomechanics in Sports. Taiwan, Taipei. 2013.

Randall L. Jensen, William P. Ebben, Erich J. Petushek, Kieran Moran, Noel E. O’Connor, Chris Richter, "Continuous waveform analysis of force, velocity, and power adaptations to a periodized plyometric training program", Symposium of the International Society of Biomechanics in Sports. Taiwan, Taipei. 2013.

[Todd Pataky]

Re: Statistical analysis of temporal kinematic waveforms

In case anyone's interested in additional SPM details, we recently had a paper accepted which details SPM's utility for vector trajectory analysis (e.g. 3D kinematics, 3D forces):

http://www.sciencedirect.com/science/article/pii/S0021929013003564

https://www.researchgate.net/publication/255738742_Vector_field_statistical_analysis_of_kinematic_and_force_trajectories

SPM regards the entire vector trajectory as the unit of observation, making it is relatively straightforward to conduct t tests, regression, ANOVA, etc. directly on the raw (time-normalized) trajectories.

[J. Lucas McKay]

Re: Statistical analysis of temporal kinematic waveforms

Hi Mark,

I'm one of the authors on a wavelet-based functional ANOVA paper that came out in J Neurophysiol recently for comparing temporal EMG waveforms across conditions. The reference is below - is that the one you mentioned in your post? I was wondering when we put it out whether anyone would read it, given how nerdy the title is.

Anyway, I have had good luck identifying statistically-significant time-domain "contrast curves" between temporal EMG waveforms from different experimental conditions, and we are actively pursuing collaborators in order to extend the analysis to other types of data. Kinematic data is of course one of the main areas I'd like to look at. Please drop me an email at j.lucas.mckay@emory.edu if you'd like to discuss the technique further.

Best,

J. Lucas McKay

McKay JL, Welch TD, Vidakovic B, and Ting LH. Statistically significant contrasts between EMG waveforms revealed using wavelet-based functional ANOVA. J Neurophysiol 109: 591-602, 2013.