# Symbolic representation of propulsion cycles in manual wheelchair locomotion

Vanel Steve Siyou Fotso, Engelbert Mephu Nguifo, Philippe Vaslin

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Vanel Steve Siyou Fotso, Engelbert Mephu Nguifo, Philippe Vaslin. Symbolic representation of propulsion cycles in manual wheelchair locomotion. 40th Congress of the Société de Biomécanique, Oct 2015, Paris, France. pp.2058-2059. hal-05017697

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# Symbolic representation of propulsion cycles in manual wheelchair locomotion.

V.S. Siyou Fotso<sup>a, b</sup>, E. Mephu Nguifo<sup>a, b</sup>, Ph. Vaslin<sup>a, b*</sup>

<sup>a</sup> Clermont Université, Université Blaise Pascal, LIMOS, BP 10448, F-63000 Clermont-Ferrand;

<sup>b</sup> CNRS, UMR 6158, LIMOS, F-63173 Aubière.

**Keywords:** wheelchair; locomotion; cyclic time series; symbolic representation; SAX-P.

## 1. Introduction

Over the last two decades, the biomechanical analysis of manual wheelchair (MWC) locomotion has benefited from the improvement of electronics and sensors, which allowed research laboratories and manufacturers to design and build various sophisticated measurement tools like fixed laboratory ergometers (Niesing et al. 1990), wheel dynamometers (Asato et al. 1993) or full instrumented wheelchairs (Dabonneville et al. 2005). Depending on the number of sensors embedded on these devices and on the sample frequency, the volume of data recorded during experiments with these instruments may be huge, which impairs their processing and their analysis. In order to overcome these paradoxical drawbacks, there is a need for a method allowing to reduce data volume, without altering them, and to facilitate their interpretation.

In signal processing, several methods already exist that potentially could address this question: Piecewise Aggregate Approximation (PAA), Symbolic Aggregate approximation (SAX), ESAX or SAX-TD (Sun et al. 2014). These methods split a time series in successive segments of a same arbitrary length of time and compute only a few basic properties of each segment (i.e. mean, minimum and maximum values, trend) but none of them is convenient for processing cyclic time series like those recorded or computed during human locomotion (e.g. walking, running). Therefore, a new symbolic method has been designed (Siyou Fotso et al. 2015) and named SAX-P as it takes into account several properties of cyclic time series. This method has been applied to time series recorded during manual wheelchair locomotion.

## 2. Methods

### 2.1 Principles of SAX-P method

This method is based on SAX and works as follows:

- A cyclic time series is split in successive segments (e.g. propulsion cycles) using a threshold for identifying their beginnings and ends;

- Several parameters (properties) are computed on each segment: cycle time, push time, mean, median, standard deviation, minimum and maximum values, and the area under the curve of each cycle. As all these parameters have different units, they must be normalized (i.e. centred and reduced);

- Segments are then gathered in *k* clusters using a classification algorithm (*k*-means: Esling & Agon 2012) and each cluster is named by a capital letter;

- Each segment is replaced by the letter of the cluster to which it belongs, so that the initial cyclic time series is then represented by a string of characters;

- The distance between two strings, which may have different numbers of characters, is computed using the Dynamic Time Warping (DTW, Petitjean et al. 2014).

### 2.2 Application to manual wheelchair locomotion

This method has been applied to the axial moment (Mz) measured by both right and left rear wheels of an instrumented MWC (FRET-2) during five there and back 10-meter linear displacements between two cones performed by three handicapped subjects (Table 1).

<table><caption>Table 1 Subjects' characteristics.</caption><thead><tr><td>Subject</td><td>Gender</td><td>Age (year)</td><td>Height (cm)</td><td>Weight (kg)</td><td>Lesion level</td></tr></thead><tbody><tr><td>S1</td><td>Male</td><td>27</td><td>180</td><td>78</td><td>L3</td></tr><tr><td>S2</td><td>Male</td><td>67</td><td>177</td><td>75</td><td>C5</td></tr><tr><td>S3</td><td>Male</td><td>72</td><td>167</td><td>70</td><td>D5</td></tr></tbody></table>

## 3. Results and discussion

The threshold value (5 Nm) used for splitting time series of axial moments into propulsion cycles has been chosen according to the features of the recorded signals. The quality of all propulsion cycles was visually checked before computing their properties (see Methods). In the case of a propulsive moment, the area between the time series and the time axis corresponds to the angular impulse (Nms) applied by the subject on the rear wheel for moving the MWC. All propulsion cycles were then statistically distributed in five clusters (*k* = 5: A, B, C, D, E), according to their properties. The replacement of propulsion cycles by the letters of the clusters to which they belong allowed to transform the initial time series in strings of characters. The strings obtained for both right and left axial moments were then split in five runs performed by each subject (Fig. 1). The distance between the right and left sub-strings of a same run is expressed by the DTW value (Table 2).
<figure><img src="image_2.png" /><figcaption>Figure 1 Time series of the axial moment (Mz) applied on the right wheel of an instrumented MWC (FRET-2) by subject S1 during his third linear run (vertical bars delimit the propulsion cycles of this run, and capital letters indicate the clusters to which each cycle belongs).</figcaption></figure>

<table><caption>Table 2 Strings of characters obtained with SAX-P method on times series of axial moments applied by the three subjects on right and left rear wheels of FRET-2 during their third 10-m run.</caption><thead><tr><th rowspan="2">Subject</th><th colspan="3">S1</th><th colspan="2">S2</th><th colspan="2">S3</th></tr><tr><th>Right</th><th>Left</th><th>Right</th><th>Left</th><th>Right</th><th>Left</th></tr></thead><tbody><tr><td>1</td><td>B</td><td>A</td><td>C</td><td>D</td><td>C</td><td>D</td></tr><tr><td>2</td><td>B</td><td>A</td><td>B</td><td>D</td><td>D</td><td>D</td></tr><tr><td>3</td><td>A</td><td>B</td><td>B</td><td>D</td><td>B</td><td>D</td></tr><tr><td>4</td><td>A</td><td>B</td><td>D</td><td>B</td><td>D</td><td>D</td></tr><tr><td>5</td><td>A</td><td>B</td><td>D</td><td>D</td><td>D</td><td>D</td></tr><tr><td>6</td><td>B</td><td>B</td><td>D</td><td>D</td><td>D</td><td>B</td></tr><tr><td>7</td><td>B</td><td>B</td><td>B</td><td>B</td><td>D</td><td>B</td></tr><tr><td>8</td><td>D</td><td></td><td>D</td><td>D</td><td>D</td><td>B</td></tr><tr><td>9</td><td></td><td></td><td>B</td><td>D</td><td>D</td><td>B</td></tr><tr><td>10</td><td></td><td></td><td>B</td><td>D</td><td>D</td><td>B</td></tr><tr><td>11</td><td></td><td></td><td>D</td><td>D</td><td>D</td><td>D</td></tr><tr><td>12</td><td></td><td></td><td>D</td><td>D</td><td>D</td><td>D</td></tr><tr><td>13</td><td></td><td></td><td>B</td><td>D</td><td>D</td><td>D</td></tr><tr><td>14</td><td></td><td></td><td></td><td>D</td><td></td><td>D</td></tr><tr><td>15</td><td></td><td></td><td></td><td>D</td><td></td><td>E</td></tr><tr><td>DTW</td><td>181</td><td></td><td>285</td><td></td><td></td><td>128</td></tr></tbody></table>

Processing these particular time series with SAX-P greatly facilitates their analysis and their interpretation:

- At first sight (Table 2), it immediately appears that during their third run the three subjects did not exert the same number of pushes for moving FRET-2 on the same 10-m distance (S1: 8-7; S2 & S3: 13-15);

- It is also obvious that each subject did not apply the same number of pushes on each rear wheels. Moreover, although right and left pushes exerted by one subject globally belong to the same clusters, the total distance (DTW) between all these pushes can be more (S2: 285) or less (S3: 128) high. Both these observations demonstrate that the three subjects did not propel their MWC symmetrically during this run;

- Finally, the classification of subjects' pushes exhibits that those exerted by S1 were more dynamic than those exerted by S2 or S3 because they mainly belong to clusters A and B, whereas those of S2 and S3 mainly belong to clusters B and D. This latter result is

consistent with the age and the lesion level of S1 compared to those of S2 and S3 (Table 1).

## 4. Conclusions

The Symbolic Aggregate approximation method presented in this paper (SAX-P) takes into account more properties of each segment than previous methods of the same family (SAX, ESAX, SAX-TD). These properties depend on the time series and may be chosen according to their physical meaning (e.g. angular impulse).

The few results presented here show that this method largely reduces data volume and facilitates their analysis and interpretation. It should thus be useful for studying improvement of wheelchair propulsion during rehabilitation (Vegter et al. 2014), or for evaluating injury risks of different propulsion techniques (Desroches et al. 2010).

## References

Asato KT, Cooper RA, Robertson RN, Ster JF. 1993. SmartWheels: Development and testing of a system for measuring manual wheelchair propulsion dynamics. IEEE Trans Biomed Eng. 40:1320-1324.

Dabonneville M, Vaslin Ph, Kauffmann Ph, de Saint Rémy N, Couétard Y, Cid M. 2005. A self-contained wireless wheelchair ergometer designed for biomechanical measures in real life conditions. Technol. Disabil. 17, Sp. Issue 2:63-76.

Desroches G, Dumas R, Pradon D, Vaslin P, Lepoutre FX, Chèze L. 2010. Upper limb joint dynamics during manual wheelchair propulsion. Clin Biomech. 25:299-306.

Esling P, Agon C. 2012. Time-series data mining. ACM Computing Surveys. 45:1-34.

Niesing R, Eijskoot F, Kranse R, den Ouden AH, Storm J, Veeger HEJ, Woude LHV van der, Snijders CJ (1990). Computer-controlled wheelchair ergometer. Med. Biol. Eng. Comput., 28: 329-338.

Petitjean FF, Forestier G, Webb GI, Nicholson AE, Chen Y, Keogh E. 2014. Dynamic Time Warping Averaging of Time Series Allows Faster and More Accurate Classification. Proc IEEE Int Conf Data Mining. 470-479.

Siyou Fotso VS, Mephu-Nguifo E, Vaslin Ph. 2015. Symbolic representation of cyclic time series: application to biomechanics. CML Workshop, 32nd International Conference on Machine Learning (ICML), Lille (France), 6th - 11th July.

Sun Y, Li J, Liu J, Sun B, Chow Ch. 2014. An improvement of symbolic aggregate approximation distance measure for time series. Neurocomputing. 138:189-198.

Vegter Riemer JK, Lamoth CJ, de Groot S, Veeger HEJ, van der Woude LHV. 2014. Inter-Individual Differences in the initial 80 minutes of motor learning of handrim wheelchair propulsion. PLoS ONE 9(2): e89729.