*Facultad de Enfermería y Podología, Universidad de Valencia, Valencia, Spain.

Transcription

1 1 Variability of the Dynamic Stiffness of Foot Joints. Effect of Gait Speed Enrique Sanchis-Sales, PhD* Joaquín Luis Sancho-Bru Alba Roda-Sales Javier Pascual Huerta *Facultad de Enfermería y Podología, Universidad de Valencia, Valencia, Spain. Departamento de Ingeniería Mecánica y Construcción, Universitat Jaume I, Castellón, Spain. Clínica del Pie Elcano, Barakaldo, Bilbao, Spain Corresponding author: Erique Sanchis-Sales, MSci, Facultad de Enfermería y Podología, Universidad de Valencia, C/Jaume Roig s/n, 46010,Valencia, Spain. ( ensansa@uv.es) Abstract Background: Comparison of dynamic stiffness of foot joints was previously proposed to investigate pathological situations with changes in the properties of muscle and passive structures. Samples must be controlled to reduce the variability within groups being compared, which may arise from different sources, such as gait speed or foot posture index (FPI). Methods: In this work, variability in the measurement of the dynamic stiffness of ankle, midtarsal and 1

2 metatarsophalangeal joints was studied in a controlled sample of healthy adult male subjects with normal FPI, and the effect of gait speed was analyzed. In Experiment I, dynamic stiffnesses were obtained in three sessions, five trials per session, for each subject, taking the mean value across trials as representative of each session. In Experiment II, five trials were considered at slow, comfortable, and fast velocities. Results: Results showed similar inter- and intra-session errors and intra-subject errors within sessions, indicating the goodness of using five trials per session for averaging. Intra- and inter-subject variability data provided can be used to select the sample size in future comparative analyses. Significant differences with gait speed were observed in most dynamic stiffnesses considered, with a general rise when gait speed increased, especially at the midtarsal joint, this being attributed to an active modulation produced by the central nervous system. Conclusions: Differences from gait speed were higher than intra- and inter-session repeatability errors for the propulsion phases at the ankle and midtarsal joints, comparative analyses at these phases needing a more exhaustive control of gait speed to reduce the required sample size Abbreviations MT, midtarsal; MP, metatarsophalangeal; EMSP, early midstance phase; LMSP, late midstance phase; PP, propulsion phase; FPI, foot posture index; DF, dorsiflexion; PF, plantarflexion; AB, abduction; AD, adduction; IN, inversion; EV, eversion; CoP, centre of pressure; K %, dynamic stiffness at EMSP for the ankle; K %, dynamic stiffness at PP for the ankle; K!", dynamic stiffness at LMSP for the MT joint; K!", dynamic stiffness at PP for the MT joint; K!", dynamic stiffness at PP for the MP joint; RMSE, root mean squared error; SD, standard deviation. 2

3 Keywords Dynamic stiffness; foot joints; variability; gait speed. Introduction The analysis of dynamic joint stiffness has been proposed as a tool for assessing the dynamic behavior of the joints of the lower limb 1 6. Dynamic stiffness (or quasi-stiffness) is defined as the ratio between the external moment applied to the joint and the joint angle, at a specific angle, assessed while performing activities that require muscle activation, such as jumping, running or walking. This stiffness combines the effect of muscle forces, inertia and deformation of soft tissue, and has been applied to characterize the ankle behavior during different activities such as walking, running or climbing stairs 2,5,7 9. These works have shown that there are different periods within the stride phases in which moment and angle changes are linearly related, i.e., with a constant dynamic stiffness. The constant dynamic stiffnesses in these periods have been proposed for analyzing the foot joint dynamics, e.g., to study the effects of mobile-bearing total ankle replacement, to assess the treatment of patients with cerebral palsy, and to assess gait function in patients with hemiparesis 1,3,10. Recently, the authors used an adaptation of an existing multi-segment biomechanical model of the foot 11 to analyze the flexion stiffness of the foot joints during normal walking, specifically the ankle, midtarsal (MT) and metatarsophalangeal (MP) joints in normal healthy male subjects 12. Constant dynamic stiffnesses were identified during early and late midstance phases (EMSP and LMSP) and the propulsion phase (PP) at the ankle and MT joints, and only during PP at the MP joint. 3

4 The analysis of these dynamic stiffnesses of the foot joints could be used for many purposes: to help surgeons to quantify the mechanical effect of their operations (e.g., arthrodesis of foot joints), in the design of foot prostheses and orthotics, or as a basis for detecting abnormalities (e.g., differentiating between normally and abnormally tight Achilles tendons) 12. However, the results from the previous work 12 also highlighted the importance of properly controlling the samples in these studies, so as to reduce the variability of the dynamic stiffness within groups. In this sense, different previous works have failed to identify any significant differences when analyzing the effect of different parameters and situations on the dynamic stiffness of the ankle joint during gait, such as the analysis of the effect of gender and age 13, the comparison between a mobile-bearing total ankle replacement with the healthy intact ankle 10, or the comparison of the gait between patients with hemiparesis and a healthy population 3. However, the variability of the dynamic stiffness within groups in these works was high, so that the effect of the different parameters and situations might be hidden. This variability could arise from different sources. E.g., subjects are usually asked to walk at a comfortable self-selected speed, and the static foot posture index (FPI), i.e., index of pronation-supination, is not controlled, among others. In this work, quantitative values for the intra- and inter-session variabilities in the measurement of the dynamic stiffness of the ankle, MT and MP joints of the right foot are provided for a controlled sample of healthy adult male subjects with normal static FPI, along with intra- and inter-subject variability, and the effect of gait speed variation is quantified. These data may help in the selection of the sample size to be considered in comparative analyses of the dynamic stiffness between groups for clinical purposes. 88 4

5 Materials and methods Description of experiments All participants were healthy adult male subjects, right-foot dominant, with normal static FPI (and very similar in both feet), as measured by Redmon et al. 14 (see descriptive data in Table 1). All of them provided written informed consent to participate in the study, which was approved by the ethical committee of the Universitat Jaume I (Castellón, Spain). The subjects were asked to walk barefoot along a 7 m walkway, and to step on a pressure platform located in the middle of the walkway, with their right foot. The subjects faced forward while walking to avoid platform targeting, discarding those trials where they did not step on the platform with the right foot. Before data collection, the subjects walked on the walkway several times to get familiarized with the walking conditions. Experiment I was performed on five subjects to check for intra- and inter-session variability. In three different sessions (days), the subjects were asked to walk repeatedly on the walkway at a comfortable self-selected speed until having five valid trials in each session. Experiment II was performed on five subjects to quantify the effect of gait speed variation on the dynamic stiffnesses of foot joints. The subjects were asked to walk repeatedly on the walkway until having five valid trials at three different gait speeds: first, at a comfortable self-selected speed, then at a forced slower speed, and finally, at a forced faster speed. Data acquisition The kinematics of the ankle, MT and MP joints of the right foot were registered using an adaptation of the model proposed by Bruening et al. 11, as presented in Sanchis-Sales et al. 12. Segments position and orientation were tracked by an eight infrared camera motion analysis 5

6 system (Vicon Motion Systems Ltd., Oxford, UK) operating at a 100 Hz sampling rate. And joint angles were calculated, from the upright standing static reference posture, using a Cardan rotation sequence between distal and proximal segments: 1 - dorsiflexion/plantarflexion (DF/PF), 2 - abduction/adduction (AB/AD), and 3 - inversion/eversion (IN/EV) 15. All kinematic data were low-pass filtered using a 4 th -order Butterworth filter with a cut-off frequency of 10 Hz. A Podoprint pressure platform (Namrol Group, Barcelona, Spain) was synchronized with the infrared camera system, operating at a 100 Hz sampling rate, for compatibility with 3D kinematic data. The compatibility required also the spatial mapping of the location of the pressure cells to the global coordinate system used with the infrared cameras. This was accomplished by properly setting the global coordinate system during the calibration: the calibration wand was placed on the pressure platform, so that the origin of the coordinate system matched the centre of the pressure platform, and was aligned so that the X-axis and Y-axis corresponded to the mediolateral and anteroposterior axes, respectively. Then, the pressure data at each time were segmented by comparing the Y-coordinates of the contact cells at this time and those of the ankle, MT and MP joint centres for the time when the foot was fully contacting on the platform (E.g., cells with Y-coordinate between those of MT and MP joint centres were assigned to the forefoot segment). Then, at each segment, the total normal ground reaction force was calculated, along with the corresponding centre of pressure (CoP). The joint moments were then calculated as the cross product of the ground reaction forces on distal segments and the 3D distances between the CoPs and the joint centres, and expressed relative to the orientation of the local coordinate system of the proximal segment. The joint flexion moments were normalized to body-mass, consistently with previous publications 1,3,4,10,13, and were low-pass filtered using a 6

7 th -order Butterworth filter with a cut-off frequency of 50 Hz. The time spent during the stance phase was used as a quantitative index of the speed of each trial. Calculation of dynamic stiffnesses Dynamic stiffnesses were computed for each trial in experiments I and II. In accordance with the previous work 12, they were calculated at those phases with an approximate flexion moment- angle linear relationship, which corresponded, approximately, to EMSP and PP for the ankle and K % ), LMSP and PP for the MT joint (K!" and K!" ), and PP for the MP joint (K % (K!" ). These phases were identified as follows: for the ankle, EMSP goes from the local minimum dorsiflexion joint angle at the beginning of the stance phase until the inflection point in the joint angle curve occurring midway in the midstance phase; and PP goes from the global maximum dorsiflexion joint angle until the end of the stance phase. For the MT joint, LMSP goes from the inflection point in the dorsiflexion joint angle curve occurring midway in the midstance phase, until the global maximum dorsiflexion moment; and PP goes from this global maximum moment until the end of the stance phase. Finally, for the MP joint, PP goes from the inflection point in the dorsiflexion joint angle curve at the end of the midstance phase and the global maximum dorsiflexion moment. In accordance with previous works 4,12,13, dynamic stiffness for each phase was calculated from the slope of the linear regression of the joint flexion moment versus the joint flexion angle (phases trimmed by 5% at both the onset and ending of each phase). Statistical analysis Intra-session variability: intra-session repeatability errors were calculated as the root mean squared errors (RMSEs) in a set of ANOVAs on the dynamic stiffnesses from Experiment I as 7

8 dependent variables, and with the interaction subject x session as the factor. Furthermore, standard deviations (SDs) of the dynamic stiffnesses for each subject within sessions were calculated, and mean values across sessions and subjects were provided as intra-subject intrasession SDs. Inter-session variability: first, mean dynamic stiffnesses were computed across trials for each subject in each session of Experiment I. Then, inter-session repeatability errors were computed as the RMSEs in a set of ANOVAs on these mean dynamic stiffnesses as dependent variables, with the factor subject. Moreover, the SDs of these mean dynamic stiffnesses were calculated for each subject across sessions, and mean values across subjects were provided as intra-subject inter-session SDs. Inter-subject variability: mean dynamic stiffnesses across trials within sessions for each subject were also averaged across sessions of Experiment I as representatives of the overall dynamic stiffnesses for each subject. These overall values were used to calculate inter-subject means and SDs. Effect of gait speed: first, the effect of gait speed was checked by means of a set of ANOVAs on the dynamic stiffnesses from Experiment II as dependent variables, and with subject, speed (slow, comfortable and fast) and their interaction as factors. Post hoc Tukey tests were performed for a deeper understanding when significant differences were detected, and linear correlations between dynamic stiffnesses and gait speed (indirectly through the time spent in the stance phase) were checked. In order to assure that the speeds used by each subject were significantly different, an additional ANOVA was performed with the time spent in the stance phase as dependent variable and with factors speed, subject and their interaction. Furthermore, plots of 8

9 averaged joint moments versus joint angles from all of the trials and subjects for each gait speed were used for a global comparative analysis. In addition, the variability bounds arising from the differences in gait speed were quantified through the RMSEs in another set of ANOVAs on the dynamic stiffnesses averaged across trials of each subject at each speed, with a single factor subject Results Mean (SD) of the R-squared values obtained in the flexion moment-angle linear regressions when calculating K %, K %, K!", K!" and K!" were (0.0167), (0.0252), (0.0276), (0.0209) and (0.0408), respectively. Intra- and inter-session repeatability errors obtained in the ANOVAs are presented in Table 2, along with the intra- and inter-subject SDs. Inter-session repeatability errors are quite close to the intra-session ones, and intra-subject SDs within sessions are higher than those arising from different sessions. Inter-subject SDs are similar to the intra-subject SDs arising from the different repetitions within a session, with the highest SD-to-mean ratio for K % and K!". The speeds used by each subject were significantly different (p<0.05) when checked by means of an ANOVA with the time spent in the stance phase as dependent variable and with factors speed, subject and their interaction (as indicative, the average time spent in the stance phase at a comfortable speed was 0.82 s, while at lower and faster speeds they were 1.03 s and 0.74 s, respectively). Table 3 contains the results of the ANOVAs performed to check the effect of gait speed. A significant (p < 0.05) large size effect (Eta squared > 0.138) 16 was found for the gait speed on K %, K!" and K!", with statistical power higher than 97%. The Tukey post- 9

10 199 hoc analyses revealed significant differences (p < 0.05) between comfortable and slow gait 200 speeds for K % and K!", between comfortable and fast gait speeds for K % and K!", and between slow and fast gait speeds for K!" and K!". The plots of the averaged joint moments versus joint angles from all of the trials and subjects for each gait speed are shown in Figure 1, where it is possible to observe higher stiffness for higher gait speed except for K % at the ankle 17. The figure also shows a wider counterclockwise loop with gait speed at the ankle in agreement with Frigo et al. 6, and a clockwise loop at the MT and MP joints. As the interaction between subject and speed was statistically significant, a more detailed analysis was performed by subject, in which a general increase of the dynamic stiffness was observed from slow to comfortable speed for all subjects (except subject 2 for K!" and subject 5 for K % ); but when comparing comfortable to fast speed, some subjects presented an increase in the dynamics stiffness, and others presented very similar values (even a little bit smaller in some cases), especially for the ankle. Significant positive linear correlations with gait speed were found for K!" (p < 0.05) and K!" (p < 0.01). The RMSEs for K %, K %, K!", K!" and K!", aimed at quantifying the variability bounds arising from the differences in gait speed in experiment II, were , , , and N m/kg/rad, respectively. The values of these errors are similar to the intra- and inter-session repeatability errors for K %, K!" and K!", and somewhat higher than those of K % Discussion and K!". 10

11 Quantitative values for the intra- and inter-session variabilities in the measurement of the dynamic stiffness of the ankle, MT and MP joints have been provided for a controlled sample of healthy adult male subjects with normal static FPI. The similarity between intra- and intersession repeatability errors, and the fact that intra-subject SDs within sessions were higher than those arising from different sessions are good indicators that five trials is a correct selection of the number of trials within each session used for averaging. Values of intra- and inter-subject variability have also been provided. These data may help to properly select the sample size to be considered in comparative analyses of the dynamic stiffness between groups for clinical purposes. For example, the G*Power 3 program 18 can be used to check that the mean and SD 228 values obtained for K % would require 166 subjects per group to identify significant differences of 10% in dynamic stiffness between groups (p < 0.05), with a statistical power of 95%, and 43 and 8 subjects per group for differences of 20% and 50%, respectively. This helps us to understand that the number of subjects used in some previous works 3,10 may have been insufficient to identify significant differences of medium or small size effect. When planning comparative analyses of foot dynamic stiffnesses, the most demanding parameters would be K % and K!", as they have shown the highest inter-subject SD-to-mean ratios. The different analyses performed to study the effect of the gait speed have made it possible to identify that, in general, an increase in the gait speed becomes an increase in the dynamic stiffness, but especially at the MT joint. A more detailed analysis revealed that the dynamic stiffness was more affected by a change of speed from slow to comfortable than from comfortable to fast, for the conditions used in this experiment. Higher joint stiffness during faster movements was also observed at the ankle in a previous work 13 and was attributed to an active 11

12 modulation of the motor output produced by the central nervous system, so that active forces are produced by muscle contractions to shape the mechanical properties of lower limb joints. This active modulation of joint stiffness is therefore particularly important at the MT joint during gait, to prevent collapse of the medial longitudinal arch. Significant differences were observed on all dynamic stiffnesses considered, except for K % and K!", which is consistent with the fact that they have shown the highest inter-subject SD-to-mean ratios, thus requiring a wider sample to detect differences, if existing. When looking at the moment-angle curves, the ankle and MT joints exhibit a passive spring-like joint behavior. The counterclockwise loop observed at the ankle joint reveals defines an area (positive net work) that becomes wider at higher walking velocities, revealing the need for an increased active contribution of the plantarflexor muscles, in accordance with previous works 6. At the MT joint, the loop is in the clockwise direction, thereby defining an area (negative net work) that remains approximately unchanged with increasing walking speed. Therefore, it seems that the plantarflexor muscles and connective tissues at the MT joint absorb the work represented by this area by a similar amount for the different gait speeds. The MP joint behaves differently, with a more variable dynamic stiffness defining a clockwise loop (negative net work) that also remains approximately invariable with gait speed. The MP dynamic stiffness is much lower than that of the ankle or MT joints probably because of the weakness of the flexor musculature, which could favor the development of different deformities, e.g., claw toe deformity, hallux valgus, etc. The study of the MP dynamic stiffness could be particularly interesting in diabetic patients to prevent ulcers. 12

13 The effect of gait speed variation has been quantified, being similar to the intra- and inter-session repeatability errors for K %, K!" and K!", and somewhat higher than those of K % and K!". Therefore, a more exhaustive control of the gait speed during the experiments could be considered in order to reduce the sample size required in comparative analyses of the dynamic stiffnesses, especially for K % and K!", similarly to the control performed by Crenna et al. 13 at the ankle. The present study has some limitations. The pressure platform did not allow considering frictional forces when obtaining the joint moments. However, the ankle joint moments reported in this work are quite similar to those obtained in a previous work 19 that used a force platform, therefore taking into account the frictional forces. This fact seems to show that not having considered frictional forces results in a low error, so that the results reported in this study are representative of the real behaviour. Also, the dynamic stiffness behavior described herein is constrained to the dominant foot. Although no differences were found in a previous work 20 for the dynamic stiffness at the ankle between dominant and non-dominant feet, it may be interesting to check footedness-related differences for the MT and MP joints. Moreover, the sample used in experiment I limits the representativeness of the SD values reported, and the sample used to analyze the effect of gait speed on the dynamic stiffnesses was somewhat reduced to look for medium size effects, which could be the case of K % and K!". Conclusion The results of this study may serve for planning future studies aimed at investigating the dependence of the dynamic joint stiffnesses of the foot joints on different parameters, such as FPI, age, sex, or height, and in clinical studies aimed at investigating pathological situations, where changes in the rheological properties of muscle and passive structures can occur. This 13

14 information could be used to modify the dynamic joint stiffness by using orthoses, to design prostheses, or to pre-plan surgical interventions for the foot and ankle. Declaration of interest Conflicts of interest: none. Funding The authors received no financial support for the research, authorship, and/or publication of this article References 1. Davis RB, DeLuca PA. Gait characterization via dynamic joint stiffness. Gait Posture. 1996;4(3): Lark SD, Buckley JG, Bennett S, Jones D, Sargeant AJ. Joint torques and dynamic joint stiffness in elderly and young men during stepping down. Clin Biomech. 2003;18(9): Sekiguchi Y, Muraki T, Kuramatsu Y, Furusawa Y, Izumi S-I. The contribution of quasi-joint stiffness of the ankle joint to gait in patients with hemiparesis. Clin Biomech. 2012;27(5): Shamaei K, Sawicki GS, Dollar AM. Estimation of Quasi-Stiffness and Propulsive Work of the Human Ankle in the Stance Phase of Walking. PLoS One. 2013;8(3). 5. Gabriel RC, Abrantes J, Granata K, Bulas-Cruz J, Melo-Pinto P, Filipe V. Dynamic joint stiffness of the ankle during walking: gender-related differences. Phys Ther Sport. 2008;9(1): Frigo C, Crenna P, Jensen LM. Moment-angle relationship at lower limb joints during human walking at different velocities. J Electromyogr Kinesiol. 1996;6(3): Hamill J, Gruber AH, Derrick TR. Lower extremity joint stiffness characteristics during running with different footfall patterns. Eur J Sport Sci. 2014;14(2):

15 Kuitunen S, Komi P V, Kyröläinen H. Knee and ankle joint stiffness in sprint running. Med Sci Sports Exerc. 2002;34(1): Mauroy G, Schepens B, Willems PA. Leg stiffness and joint stiffness while running to and jumping over an obstacle. J Biomech. 2014;47(2): Houdijk H, Doets HC, van Middelkoop M, (Dirkjan) Veeger HEJ. Joint stiffness of the ankle during walking after successful mobile-bearing total ankle replacement. Gait Posture. 2008;27(1): Bruening DA, Cooney KM, Buczek FL. Analysis of a kinetic multi-segment foot model. Part I: Model repeatability and kinematic validity. Gait Posture. 2012;35(4): Sanchis-Sales E, Sancho-Bru JL, Roda-Sales A, Pascual-Huerta J. Dynamic Flexion Stiffness of Foot Joints During Walking. J Am Podiatr Med Assoc. 2016;106(1): Crenna P, Frigo C. Dynamics of the ankle joint analyzed through moment angle loops during human walking: Gender and age effects. Hum Mov Sci. 2011;30(6): Redmond AC, Crosbie J, Ouvrier RA. Development and validation of a novel rating system for scoring standing foot posture: the Foot Posture Index. Clin Biomech (Bristol, Avon). 2006;21(1): Grood ES, Suntay WJ. A joint coordinate system for the clinical description of three-dimensional motions: application to the knee. J Biomech Eng. 1983;105(2): Cohen J. Statistical Power Analysis for the Behavioral Sciences. 2nd ed. Hillsdale N.J.: L. Erlbaum Associates; Stefanyshyn DJ, Nigg BM. Dynamic Angular Stiffness of the Ankle Joint during Running and Sprinting. J Appl Biomech. 1998;14(3): Faul F, Erdfelder E, Lang A-G, Buchner A. G*Power 3: A flexible statistical power analysis program for the social, behavioral, and biomedical sciences. Behav Res Methods. 2007;39(2):175-15

16 doi: /bf Hunt a E, Smith RM, Torode M. Extrinsic muscle activity, foot motion and ankle joint moments during the stance phase of walking. Foot ankle Int. 2001;22(1): doi: / Atalaia T, Abrantes J, Castro-Caldas A. Footdness-related differences in dynamic joint stiffness and leg stiffness measurements. J Sci Res Reports. 2015;6(5): doi: /jsrr/2015/

17 Table 1. Mean (SD) values of the descriptive data in both experiments I and II. Age Mass Height FPI yr Kg cm Right foot Left foot Experiment I 34.0 (13.2) 85.0 (16.9) (5.4) 4.2 (0.8) 3.2 (1.9) 346 Experiment II 30.6 (16.0) 83.3 (20.3) (7.8) 3.4 (1.7) 2.4 (1.9) Table 2. Intra- and inter-session variability results obtained from experiment I Intrasession Intersession Intersubject Stiffness (N m/kg/rad) K % K % K!" K!" K!" Repeatability error Intra-subject SD Repeatability error Intra-subject SD Mean SD Ratio SD/mean

18 Table 3. Results from the ANOVAs to check the effect of gait speed with data from experiment II Source Subject x Speed Subject Speed Dependent variable Sig. Partial Eta squared Observed power K % K % K!" K!" K!" K % K % K!" K!" K!" K % K % K!" K!" K!"

19 Figure 1. Plots of the averaged joint moments versus averaged joint angles from all the trials and subjects for each gait speed in experiment II