Journal of Biomechanics 48 (2015) 1219–1223
Contents lists available at ScienceDirect
Journal of Biomechanics journal homepage: www.elsevier.com/locate/jbiomech www.JBiomech.com
Short communication
Sensor positioning and experimental constraints influence estimates of local dynamic stability during repetitive spine movements Samuel J. Howarth a,n, Ryan B. Graham b a b
Department of Graduate Education and Research Programs, Canadian Memorial Chiropractic College, Toronto, ON, Canada School of Physical Health and Education, Nipissing University, North Bay, ON, Canada
art ic l e i nf o
a b s t r a c t
Article history: Accepted 24 January 2015
Application of non-linear dynamics analyses to study human movement has increased recently, which necessitates an understanding of how dependent measures may be influenced by experimental design and setup. Quantifying local dynamic stability for a multi-articulated structure such as the spine presents the possibility for estimates to be influenced by positioning of kinematic sensors used to measure spine angular kinematics. Oftentimes researchers will also choose to constrain the spine's movement by physically restraining the pelvis and/or using targets to control movement endpoints. Ten healthy participants were recruited, and asked to perform separate trials of 35 consecutive cycles of spine flexion under both constrained and unconstrained conditions. Electromagnetic sensors that measure threedimensional angular orientations were positioned over the pelvis and the spinous processes of L3, L1, and T11. Using the pelvic sensor as a reference, each sensor location on the spine was used to obtain a different representation of the three-dimensional spine angular kinematics. Local dynamic stability of each kinematic time-series was determined by calculating the maximum finite-time Lyapunov exponent (λmax). Estimates for λmax were significantly lower (i.e. dynamically more stable) for spine kinematic data obtained from the L3 sensor than those obtained from kinematic data using either the L1 or T11 sensors. Likewise, λmax was lower when the movement was constrained. These results emphasize the importance of proper placement of instrumentation for quantifying local dynamic stability of spine kinematics and are especially relevant for repeated measures designs where data are obtained from the same individual on multiple days. & 2015 Elsevier Ltd. All rights reserved.
Keywords: Lyapunov exponents Flexion Spine Stability Non-linear dynamics
1. Introduction The prevalence of non-linear dynamics analyses to quantify local dynamic stability has recently increased in studies of human movement. Originally these analyses were applied to temporal joint and segmental angular kinematic patterns of the lower limb during gait (Dingwell et al., 2001; Bruijn et al., 2009a); however, Granata and England (2006) used a non-linear dynamics approach to quantify local dynamic stability of spine angular kinematics during cyclical trunk flexion/extension. Studies to date have investigated the effects of movement speed, fatigue, external load, and low back pain on local dynamic stability of spine angular kinematics (Granata and England, 2006; Granata and Gottipati, 2008; Graham et al., 2012a; Beaudette et al., 2013; Graham et al., 2014). While the computational algorithms for calculating local dynamic stability are identical for any time-
n Corresponding author at: Department of Graduate Education and Research Programs, Canadian Memorial Chiropractic College, 6100 Leslie Street, Toronto, Ontario, Canada, M2H3J1. Tel.: þ 1 416 482 2340x236; fax: þ 1 416 482 2560. E-mail address: [email protected] (S.J. Howarth).
http://dx.doi.org/10.1016/j.jbiomech.2015.01.036 0021-9290/& 2015 Elsevier Ltd. All rights reserved.
varying quantity, there are additional methodological considerations when applying these techniques to spine angular kinematic data. Local dynamic stability analysis of joint angular kinematics requires kinematic information from the proximal and distal segments that span the joint. For example, local dynamic stability of knee kinematics during gait is determined using the time-series of relative orientations between the femur and shank. Regarding the spine, studies have primarily focused on determining the local dynamic stability of the lumbar spine angular kinematics. Contrary to the knee joint (a single articulation between the shank and femur), the lumbar spine consists of five vertebrae and the pelvis that span five joints. To obtain three-dimensional kinematics of the lumbar spine, sensors are often positioned over the pelvis and near the level of the twelfth thoracic vertebra (Cholewicki and McGill, 1996). Since these sensors span multiple segments, the magnitudes of lumbar spine angular kinematics are directly influenced by the number of vertebral segments that are spanned. Therefore, larger angular deviations are measured when the sensors span a larger number of segments. Given that sensor placement can effectively alter the magnitude of spine angular kinematics, it is also important to know if sensor
1220
S.J. Howarth, R.B. Graham / Journal of Biomechanics 48 (2015) 1219–1223
Table 1 The average age, height, and weight of participants used in this study. Values in parentheses represent the standard error of the mean.
N Age(years) Height(m) Weight(kg)
Females
Males
Overall
5 24.6 (3.4) 1.71 (0.03) 65.4 (3.1)
5 21.2 (0.7) 1.83 (0.04) 78.5 (4.6)
10 22.9 (1.7) 1.77 (0.04) 72.0 (3.4)
placement could influence estimates of local dynamic stability of spine movement. The purpose of the current investigation was to determine the influence of sensor positioning on estimates of local dynamic stability of spine movements. In addition, this study compared estimates of local dynamic stability for spine movements both with and without the pelvis being restrained.
2.1. Participants A total of 10 participants (5 male and 5 female) were recruited for this investigation (Table 1). All participants were free from lower back pain at the time of data collection. Prior to data collection, each participant read and signed an informed consent document outlining the experimental protocols that were approved by the research ethics board at Nipissing University.
2.2. Instrumentation Spine angular kinematic data were obtained by using electromagnetic sensors that measured three-dimensional angular orientations (3D Guidance trakSTAR, Ascension Technology Corporation, Milton, VT, USA). A single sensor was placed over the pelvis. Three additional sensors were positioned over the spinous processes at the levels of the first lumbar (L1), third lumbar (L3), and eleventh thoracic (T11) vertebrae. An investigator identified each of the spinous processes by manual palpation. Angular kinematic data were digitally sampled from each of the sensors at 240 Hz.
2.3. Protocol
EN i : varðENÞ
ð2Þ
The maximum finite-time Lyapunov exponent (λmax) was then used to quantify local dynamic stability of each representation of spine movement. A brief description of the mathematical process used to calculate λmax from a time-series of angular kinematic data is presented here. Interested readers are referred elsewhere for more detailed explanations (Rosenstein et al., 1993; Dingwell and Cusumano, 2000; Granata and England, 2006; Graham et al., 2011). The 35 cycles of repetitive spine flexion were identified for each of the kinematic time-series. Each EN time-series was adjusted so that a total of 33600 (35 cycles 4 s/cycle 240 Hz) samples fell between the defined start and end points to account for potential bias that may occur due to differences in time-series duration (Bruijn et al., 2009b). The n-dimensional state space for the timeseries representing the EN angle was then reconstructed using the method of delays (Abarbanel et al., 1993). Based on previous work, a delay of 96 samples ( 10% of the average number of samples per cycle), and a reconstruction dimension of 6 were chosen (Granata and England, 2006; Graham et al., 2012a; Graham and Brown, 2012; Howarth et al., 2013). The exponential rate of divergence between initially neighboring trajectories in the reconstructed state space was used to estimate λmax. Specifically, λmax was equivalent to the slope of the linear fit 1
Δt
o ln dj ðiÞ 4 ;
ð3Þ
where y(i) is the average logarithm of divergence (dj(i)) for all pairs of nearest neighbors (j) throughout a certain number of time steps (i). The slope was determined across the first 0.5 cycles (480 samples) (Bruijn et al., 2009a, 2009b; Graham et al., 2012a, 2012b.
2.5. Statistical analysis Dependent measures of λmax and peak spine angles that were both derived from each of the time-series of spine angular kinematics were first averaged across the two trials for each of the constrained and unconstrained conditions and then analyzed with two factor (SENSOR POSITION and CONSTRAINT CONDITION) repeated measures analyses of variance. Post hoc analyses for any significant main or interaction effects were conducted using paired t-tests. Intraclass correlation coefficients (ICC2,1) were also determined between values of λmax for each of the three combinations of spine angular kinematic time series. For ICC2,1 analyses, values for λmax from both trials under each constraint condition were used. All statistical analyses were performed in SPSS (SPSS 21, SPSS Corporation, Chicago, IL, USA). The level of significance for all analyses was set to 0.05 a priori.
3. Results
Following instrumentation, participants were asked to perform repetitive spine flexion under two conditions. During the first condition the pelvis was constrained. Participants were instructed to keep their arms outstretched with their hands together and to touch targets positioned directly in front of them at shoulder height and 0.5 m anterior to the knee by flexing and extending their spine (Fig. 1A). The participant's pelvis was also restrained during this condition. For the second condition the protocol was repeated without pelvic constraint and participants were instructed to maximally flex and extend their spine. The order of the two conditions was randomly determined for each participant. All participants completed two consecutive trials of 35 consecutive cycles of forward spine flexion followed by extension to an upright posture for each condition. Thus, each participant completed a total of four trials. The rate of each spine flexion/extension cycle for all trials was controlled at 0.25 Hz by a digital metronome.
2.4. Data processing and analysis Using the pelvis sensor as a common reference for each of the three vertebral sensors, three different representations for the spine's angular positions were calculated (T11 vs. Pelvis, L1 vs. Pelvis, and L3 vs. Pelvis). In each case, threedimensional angles were extracted through Euler rotation matrices of the corresponding low back sensor relative to the pelvis using a flexion-extension (FE), lateral-bending (LB), and axial twist (AT) rotation sequence (Graham et al., 2012a). Then, in order to get an overall depiction of the spine's movement (Granata and England, 2006), the Euclidean norm (EN) of the three Euler angles for each angular representation was calculated at each sample (i) as qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi FE2i þ LB2i þ AT 2i :
EN i ¼
yðiÞ ¼
2. Methods
EN i ¼
EN angle was normalized to unit variance as
ð1Þ
Furthermore, to ensure that any observed stability differences were not simply due to magnitude effects (i.e. the T11 vs. Pelvis EN angle would be greater than the L3 vs. Pelvis EN angle because a greater number of vertebrae were spanned), each
The interaction between constraint condition and sensor placement for both peak spine angle, and λmax was not statistically significant (p¼0.371 for peak spine angle; p¼0.406 for λmax); however, there were significant main effects of both constraint condition (p¼0.017 for both peak spine angle and λmax), and sensor placement (p¼0.001 for peak spine angle; p¼0.004 for λmax). Increasing the height of sensor placement increased the peak spine angles (L3¼25.173.61; L1¼ 42.672.81; T11¼49.974.11). In particular, the peak spine angles recorded from the L3 sensor were significantly lower than those recorded from either the L1 (p¼ 0.010) or T11 (p¼ 0.006) sensors. Positioning the second sensor at L3 produced a 13% lower estimate for λmax than positioning the second sensor at either L1 (p¼0.008) or T11 (p¼0.031) (Table 2). There was no difference between λmax values determined from the sensors placed at L1 and T11 (p¼0.961). Maximum finite-time Lyapunov exponents derived from the constrained trials were 11% lower on average than those derived from the unconstrained trials (p¼ 0.017) (Table 2). Intraclass correlation coefficients for both unconstrained and constrained conditions showed the best correspondence in λmax determined from the spine angular kinematic data obtained using the L1 and T11 locations for the second sensors (ICC2,1 ¼0.789 and 0.946) (Table 3). Conversely, the lowest correspondence in λmax was observed between spine angular kinematic data obtained using the L3 and T11 (furthest separation distance) locations for the second sensors (ICC2,1 ¼0.255 and 0.559) (Table 3).
S.J. Howarth, R.B. Graham / Journal of Biomechanics 48 (2015) 1219–1223
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Fig. 1. Experimental setups for the (A.) constrained and (B.) unconstrained conditions. Note that targets were used to define the start and end positions in the constrained setup. The start and end positions were not defined in the unconstrained setup.
4. Discussion When processing biomechanical data, it is important to understand how the techniques being employed can be influenced by the experimental setup and protocols. Previous work using λmax to estimate local
dynamic stability evaluated the number of movement cycles to achieve suitable precision in the estimates, sensitivity of the technique to the number of samples in the time-series, as well as between and within day reliability (Bruijn et al., 2009b; Kyvelidou et al., 2009; Graham et al., 2012b; Dupeyron et al., 2013). The current investigation demonstrated
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S.J. Howarth, R.B. Graham / Journal of Biomechanics 48 (2015) 1219–1223
Table 2 Local dynamic stability quantified using the angular kinematic time-series for each combination of constraint condition, and sensor location. Values in parentheses represent the standard error of the mean. The asterisk denotes a statistically significant difference between the constrained and unconstrained conditions. Columns, representing the sensor locations, with the same letter were statistically similar.
Unconstrained Constrained Sensor location overall
L3
L1
T11
Condition overall*
2.00 (0.08) 1.76 (0.11) 1.88 (0.08)
2.20 (0.10) 2.06 (0.08) 2.13 (0.07)
2.25 (0.10) 2.01 (0.10) 2.13 (0.10)
2.15 (0.08) 1.94 (0.08)
A
B
B
Table 3 Intraclass correlation coefficients (ICC2,1) between estimates of local dynamic stability using each pair of spine angular kinematic time-series from the different sensor locations, and for each of the unconstrained and constrained conditions. L3 Unconstrained
Constrained
L3 L1 T11 L3 L1 T11
L1
T11
0.640
0.559 0.946
0.450
0.255 0.789
that significant discrepancies in estimates of local dynamic stability of spine movements could occur as a result of different kinematic sensor placements and experimental constraints. Recent literature has advocated using metrics derived from nonlinear dynamics analyses (e.g. λmax) within studies conducted using different pathological populations or to evaluate rehabilitation (Harbourne and Stergiou, 2009; Stergiou and Decker, 2011). As examples, λmax has been applied to center of pressure traces in developmentally delayed infants and stroke patients during rehabilitation, and to gait patterns of individuals with unilateral anterior cruciate ligament deficiency (Stergiou et al., 2004; Roerdink et al., 2006; Kyvelidou et al., 2013). Recent evidence has demonstrated that individuals with lower back pain may exhibit less stable kinematic behavior than those without lower back pain (Graham et al., 2014). If estimates of local dynamic stability are employed in a repeated measures design over multiple testing days (e.g. to track progress throughout a rehabilitation program), then it is also necessary to minimize possible discrepancies that can occur from improper replacement of kinematic sensors. Two sources that can produce discrepancies in sensor placement for spine kinematics are incorrect palpation of spinous processes, and the chosen type of sensor. For example, physiotherapists asked to identify the location for specific spinous processes were successful only 47% of the time with an average error of 18.6 mm (Harlick et al., 2007). The electromagnetic sensors used in the current investigation were approximately 20 mm wide and 8 mm tall, which made them convenient for mounting to specific anatomical landmarks. Other experimental setups using optoelectronic cameras to measure spine angular kinematics may affix an array of markers to a rigid body that is subsequently affixed to the skin or a belt at a specified vertebral level (Graham et al., 2011; Howarth and Mastragostino, 2013). These rigid bodies may span multiple vertebral levels, and could subsequently introduce error as a result of improper placement. Finally, our investigation demonstrated that constrained movements resulted in lower estimates for λmax than unconstrained movements (i.e. an improvement in local dynamic stability). Constraining
the spine's movement by physically restraining the pelvis, and using targets to direct movement endpoints is typically employed in studies that investigate function of the spine system (Cholewicki et al., 2005; Granata and England, 2006; Hodges et al., 2009; Graham et al., 2012a, 2012b; van Drunen et al., 2013); however, constraining the movement evaluates it under non-functional conditions (Delphinus and Sayers, 2013). The higher values for λmax found during the unconstrained movements were likely the result of not explicitly defining the start and end points for the movement and allowing movement in the lower limbs and pelvis. In conclusion, our investigation demonstrated that positioning of kinematic sensors and also the experimental decision to either constrain or not constrain the movement could influence estimates for local dynamic stability of spine movement. Based on the strong agreement between local dynamic stability estimates from the L1 and T11 sensors, it is likely that, in studies where reapplication of the instrumentation is necessary, replacement of sensors near the original site will generate reliable results. Nevertheless, careful placement and documentation of sensor positioning is still highly recommended to capture true differences in studies employing a repeated measures design where data is collected from each participant on multiple days. The decision to either constrain or not constrain the movement should be dependent upon the overlying purpose of the investigation. For example, if the main purpose of a study is to evaluate overall movement patterns, then it is advised that the movement is not constrained. Conversely, if the main purpose is to study the spine system in isolation, then it is likely best to apply constraints to the movement.
Conflict of interest The authors have no conflicts of interest to declare.
Acknowledgments This study was funded by the Natural Sciences and Engineering Research Council of Canada (NSERC) (RGPIN-2014–05560 [Ryan Graham]).
References Abarbanel, H.D.I., Brown, R., Sidorowich, J.J., Tsimring, L.S., 1993. The analysis of observed chaotic data in physical systems. Rev. Mod. Phys. 65, 1331–1392. Beaudette, S.M., Graham, R.B., Brown, S.H., 2013. The effect of unstable loading versus unstable support conditions on spine rotational stiffness and spine stability during repetitive lifting. J. Biomech. 47, 491–496. Bruijn, S.M., van Dieën, J.H., Meijer, O.G., Beek, P.J., 2009a. Is slow walking more stable? J. Biomech. 42, 1506–1512. Bruijn, S.M., van Dieën, J.H., Meijer, O.G., Beek, P.J., 2009b. Statistical precision and sensitivity of measures of dynamic gait stability. J. Neurosci. Methods 178, 327–333. Cholewicki, J., McGill, S.M., 1996. Mechanical stability of the in vivo lumbar spine: implications for injury and chronic low back pain. Clin. Biomech. 11, 1–15. Cholewicki, J., Silfies, S.P., Shah, R.A., Greene, H.S., Reeves, N.P., Alvi, K., Goldberg, B., 2005. Delayed trunk muscle reflex responses increase the risk of low back injuries. Spine 30, 2614–2620. Delphinus, E.M., Sayers, M.G., 2013. The interrelationship of the thorax and pelvis under varying task constraints. Ergonomics 56, 659–666. Dingwell, J.B., Cusumano, J.P., 2000. Nonlinear time series analysis of normal and pathological human walking. Chaos 10, 848–863. Dingwell, J.B., Cusumano, J.P., Cavanagh, P.R., Sternad, D., 2001. Local dynamic stability versus kinematic variability of continuous overground and treadmill walking. J. Biomech. Eng. 123, 27–32. Dupeyron, A., Rispens, S.M., Demattei, C., van Dieën, J.H., 2013. Precision of estimates of local stability of repetitive trunk movements. Eur. Spine J. 22, 2678–2685. Graham, R.B., Sadler, E.M., Stevenson, J.M., 2011. Does the personal lift-assist device affect the local dynamic stability of the spine during lifting? J. Biomech. 44, 461–466.
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Graham, R.B., Brown, S.H., 2012. A direct comparison of spine rotational stiffness and dynamic spine stability during repetitive lifting tasks. J. Biomech. 45, 1593–1600. Graham, R.B., Sadler, E.M., Stevenson, J.M., 2012a. Local dynamic stability of trunk movements during the repetitive lifting of loads. Hum. Mov. Sci. 31, 592–603. Graham, R.B., Sheppard, P.S., Almosnino, S., Stevenson, J.M., 2012b. Dynamic spinal stability and kinematic variability across automotive manufacturing work shifts and days. Int. J. Indus. Ergon. 42, 428–434. Graham, R.B., Oikawa, L.Y., Ross, G.B., 2014. Comparing the local dynamic stability of trunk movements between varsity athletes with and without non-specific low back pain. J. Biomech. 47, 1459–1464. Granata, K.P., England, S.A., 2006. Stability of dynamic trunk movement. Spine 31, E271–E276. Granata, K.P., Gottipati, P., 2008. Fatigue influences the dynamic stability of the torso. Ergonomics 51, 1258–1271. Harbourne, R.T., Stergiou, N., 2009. Movement variability and the use of nonlinear tools: Principles to guide physical therapist practice. Phys. Ther. 89, 267–282. Harlick, J.C., Milosavljevic, S., Milburn, P.D., 2007. Palpation identification of spinous processes in the lumbar spine. Man. Ther. 12, 56–62. Hodges, P., van den Hoorn, W., Dawson, A., Cholewicki, J., 2009. Changes in the mechanical properties of the trunk in low back pain may be associated with recurrence. J. Biomech. 42, 61–66. Howarth, S.J., Mastragostino, P., 2013. Use of kinetic and kinematic data to evaluate load transfer as a mechanism for flexion relaxation in the lumbar spine. J. Biomech. Eng. 135, 101004.
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Howarth, S.J., Kingston, D.C., Brown, S.H., Graham, R.B., 2013. Viscoelastic creep induced by repetitive spine flexion and its relationship to dynamic spine stability. J. Electromyogr. Kinesiol. 23, 794–800. Kyvelidou, A., Harbourne, R.T., Stuberg, W.A., Sun, J.F., Stergiou, N., 2009. Reliability of center of pressure measures for assessing the development of sitting postural control. Arch. Phys. Med. Rehabil. 90, 1176–1184. Kyvelidou, A., Harbourne, R.T., Willett, S.L., Stergiou, N., 2013. Sitting postural control in infants with typical development, motor delay, or cerebral palsy. Pediatr. Phys. Ther. 25, 46–51. Roerdink, M., De Haart, M., Daffertshofer, A., Donker, S.F., Geurts, A.C.H., Beek, P.J., 2006. Dynamical structure of center-of-pressure trajectories in patients recovering from stroke. Exp. Brain Res. 174, 256–269. Rosenstein, M.T., Collins, J.J., De Luca, C.J., 1993. A practical method for calculating largest Lyapunov exponents from small data sets. Phys. D: Nonlinear Phenom. 65, 117–134. Stergiou, N., Moraiti, C., Giakas, G., Ristanis, S., Georgoulis, A.D., 2004. The effect of the walking speed on the stability of the anterior cruciate ligament deficient knee. Clin. Biomech. 19, 957–963. Stergiou, N., Decker, L.M., 2011. Human movement variability, nonlinear dynamics, and pathology: is there a connection? Hum. Mov. Sci. 30, 869–888. van Drunen, P., Maaswinkel, E., van der Helm, F.C., van Dieën, J.H., Happee, R., 2013. Identifying intrinsic and reflexive contributions to low-back stabilization. J. Biomech. 46, 1440–1446.
Contents lists available at ScienceDirect
Journal of Biomechanics journal homepage: www.elsevier.com/locate/jbiomech www.JBiomech.com
Short communication
Sensor positioning and experimental constraints influence estimates of local dynamic stability during repetitive spine movements Samuel J. Howarth a,n, Ryan B. Graham b a b
Department of Graduate Education and Research Programs, Canadian Memorial Chiropractic College, Toronto, ON, Canada School of Physical Health and Education, Nipissing University, North Bay, ON, Canada
art ic l e i nf o
a b s t r a c t
Article history: Accepted 24 January 2015
Application of non-linear dynamics analyses to study human movement has increased recently, which necessitates an understanding of how dependent measures may be influenced by experimental design and setup. Quantifying local dynamic stability for a multi-articulated structure such as the spine presents the possibility for estimates to be influenced by positioning of kinematic sensors used to measure spine angular kinematics. Oftentimes researchers will also choose to constrain the spine's movement by physically restraining the pelvis and/or using targets to control movement endpoints. Ten healthy participants were recruited, and asked to perform separate trials of 35 consecutive cycles of spine flexion under both constrained and unconstrained conditions. Electromagnetic sensors that measure threedimensional angular orientations were positioned over the pelvis and the spinous processes of L3, L1, and T11. Using the pelvic sensor as a reference, each sensor location on the spine was used to obtain a different representation of the three-dimensional spine angular kinematics. Local dynamic stability of each kinematic time-series was determined by calculating the maximum finite-time Lyapunov exponent (λmax). Estimates for λmax were significantly lower (i.e. dynamically more stable) for spine kinematic data obtained from the L3 sensor than those obtained from kinematic data using either the L1 or T11 sensors. Likewise, λmax was lower when the movement was constrained. These results emphasize the importance of proper placement of instrumentation for quantifying local dynamic stability of spine kinematics and are especially relevant for repeated measures designs where data are obtained from the same individual on multiple days. & 2015 Elsevier Ltd. All rights reserved.
Keywords: Lyapunov exponents Flexion Spine Stability Non-linear dynamics
1. Introduction The prevalence of non-linear dynamics analyses to quantify local dynamic stability has recently increased in studies of human movement. Originally these analyses were applied to temporal joint and segmental angular kinematic patterns of the lower limb during gait (Dingwell et al., 2001; Bruijn et al., 2009a); however, Granata and England (2006) used a non-linear dynamics approach to quantify local dynamic stability of spine angular kinematics during cyclical trunk flexion/extension. Studies to date have investigated the effects of movement speed, fatigue, external load, and low back pain on local dynamic stability of spine angular kinematics (Granata and England, 2006; Granata and Gottipati, 2008; Graham et al., 2012a; Beaudette et al., 2013; Graham et al., 2014). While the computational algorithms for calculating local dynamic stability are identical for any time-
n Corresponding author at: Department of Graduate Education and Research Programs, Canadian Memorial Chiropractic College, 6100 Leslie Street, Toronto, Ontario, Canada, M2H3J1. Tel.: þ 1 416 482 2340x236; fax: þ 1 416 482 2560. E-mail address: [email protected] (S.J. Howarth).
http://dx.doi.org/10.1016/j.jbiomech.2015.01.036 0021-9290/& 2015 Elsevier Ltd. All rights reserved.
varying quantity, there are additional methodological considerations when applying these techniques to spine angular kinematic data. Local dynamic stability analysis of joint angular kinematics requires kinematic information from the proximal and distal segments that span the joint. For example, local dynamic stability of knee kinematics during gait is determined using the time-series of relative orientations between the femur and shank. Regarding the spine, studies have primarily focused on determining the local dynamic stability of the lumbar spine angular kinematics. Contrary to the knee joint (a single articulation between the shank and femur), the lumbar spine consists of five vertebrae and the pelvis that span five joints. To obtain three-dimensional kinematics of the lumbar spine, sensors are often positioned over the pelvis and near the level of the twelfth thoracic vertebra (Cholewicki and McGill, 1996). Since these sensors span multiple segments, the magnitudes of lumbar spine angular kinematics are directly influenced by the number of vertebral segments that are spanned. Therefore, larger angular deviations are measured when the sensors span a larger number of segments. Given that sensor placement can effectively alter the magnitude of spine angular kinematics, it is also important to know if sensor
1220
S.J. Howarth, R.B. Graham / Journal of Biomechanics 48 (2015) 1219–1223
Table 1 The average age, height, and weight of participants used in this study. Values in parentheses represent the standard error of the mean.
N Age(years) Height(m) Weight(kg)
Females
Males
Overall
5 24.6 (3.4) 1.71 (0.03) 65.4 (3.1)
5 21.2 (0.7) 1.83 (0.04) 78.5 (4.6)
10 22.9 (1.7) 1.77 (0.04) 72.0 (3.4)
placement could influence estimates of local dynamic stability of spine movement. The purpose of the current investigation was to determine the influence of sensor positioning on estimates of local dynamic stability of spine movements. In addition, this study compared estimates of local dynamic stability for spine movements both with and without the pelvis being restrained.
2.1. Participants A total of 10 participants (5 male and 5 female) were recruited for this investigation (Table 1). All participants were free from lower back pain at the time of data collection. Prior to data collection, each participant read and signed an informed consent document outlining the experimental protocols that were approved by the research ethics board at Nipissing University.
2.2. Instrumentation Spine angular kinematic data were obtained by using electromagnetic sensors that measured three-dimensional angular orientations (3D Guidance trakSTAR, Ascension Technology Corporation, Milton, VT, USA). A single sensor was placed over the pelvis. Three additional sensors were positioned over the spinous processes at the levels of the first lumbar (L1), third lumbar (L3), and eleventh thoracic (T11) vertebrae. An investigator identified each of the spinous processes by manual palpation. Angular kinematic data were digitally sampled from each of the sensors at 240 Hz.
2.3. Protocol
EN i : varðENÞ
ð2Þ
The maximum finite-time Lyapunov exponent (λmax) was then used to quantify local dynamic stability of each representation of spine movement. A brief description of the mathematical process used to calculate λmax from a time-series of angular kinematic data is presented here. Interested readers are referred elsewhere for more detailed explanations (Rosenstein et al., 1993; Dingwell and Cusumano, 2000; Granata and England, 2006; Graham et al., 2011). The 35 cycles of repetitive spine flexion were identified for each of the kinematic time-series. Each EN time-series was adjusted so that a total of 33600 (35 cycles 4 s/cycle 240 Hz) samples fell between the defined start and end points to account for potential bias that may occur due to differences in time-series duration (Bruijn et al., 2009b). The n-dimensional state space for the timeseries representing the EN angle was then reconstructed using the method of delays (Abarbanel et al., 1993). Based on previous work, a delay of 96 samples ( 10% of the average number of samples per cycle), and a reconstruction dimension of 6 were chosen (Granata and England, 2006; Graham et al., 2012a; Graham and Brown, 2012; Howarth et al., 2013). The exponential rate of divergence between initially neighboring trajectories in the reconstructed state space was used to estimate λmax. Specifically, λmax was equivalent to the slope of the linear fit 1
Δt
o ln dj ðiÞ 4 ;
ð3Þ
where y(i) is the average logarithm of divergence (dj(i)) for all pairs of nearest neighbors (j) throughout a certain number of time steps (i). The slope was determined across the first 0.5 cycles (480 samples) (Bruijn et al., 2009a, 2009b; Graham et al., 2012a, 2012b.
2.5. Statistical analysis Dependent measures of λmax and peak spine angles that were both derived from each of the time-series of spine angular kinematics were first averaged across the two trials for each of the constrained and unconstrained conditions and then analyzed with two factor (SENSOR POSITION and CONSTRAINT CONDITION) repeated measures analyses of variance. Post hoc analyses for any significant main or interaction effects were conducted using paired t-tests. Intraclass correlation coefficients (ICC2,1) were also determined between values of λmax for each of the three combinations of spine angular kinematic time series. For ICC2,1 analyses, values for λmax from both trials under each constraint condition were used. All statistical analyses were performed in SPSS (SPSS 21, SPSS Corporation, Chicago, IL, USA). The level of significance for all analyses was set to 0.05 a priori.
3. Results
Following instrumentation, participants were asked to perform repetitive spine flexion under two conditions. During the first condition the pelvis was constrained. Participants were instructed to keep their arms outstretched with their hands together and to touch targets positioned directly in front of them at shoulder height and 0.5 m anterior to the knee by flexing and extending their spine (Fig. 1A). The participant's pelvis was also restrained during this condition. For the second condition the protocol was repeated without pelvic constraint and participants were instructed to maximally flex and extend their spine. The order of the two conditions was randomly determined for each participant. All participants completed two consecutive trials of 35 consecutive cycles of forward spine flexion followed by extension to an upright posture for each condition. Thus, each participant completed a total of four trials. The rate of each spine flexion/extension cycle for all trials was controlled at 0.25 Hz by a digital metronome.
2.4. Data processing and analysis Using the pelvis sensor as a common reference for each of the three vertebral sensors, three different representations for the spine's angular positions were calculated (T11 vs. Pelvis, L1 vs. Pelvis, and L3 vs. Pelvis). In each case, threedimensional angles were extracted through Euler rotation matrices of the corresponding low back sensor relative to the pelvis using a flexion-extension (FE), lateral-bending (LB), and axial twist (AT) rotation sequence (Graham et al., 2012a). Then, in order to get an overall depiction of the spine's movement (Granata and England, 2006), the Euclidean norm (EN) of the three Euler angles for each angular representation was calculated at each sample (i) as qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi FE2i þ LB2i þ AT 2i :
EN i ¼
yðiÞ ¼
2. Methods
EN i ¼
EN angle was normalized to unit variance as
ð1Þ
Furthermore, to ensure that any observed stability differences were not simply due to magnitude effects (i.e. the T11 vs. Pelvis EN angle would be greater than the L3 vs. Pelvis EN angle because a greater number of vertebrae were spanned), each
The interaction between constraint condition and sensor placement for both peak spine angle, and λmax was not statistically significant (p¼0.371 for peak spine angle; p¼0.406 for λmax); however, there were significant main effects of both constraint condition (p¼0.017 for both peak spine angle and λmax), and sensor placement (p¼0.001 for peak spine angle; p¼0.004 for λmax). Increasing the height of sensor placement increased the peak spine angles (L3¼25.173.61; L1¼ 42.672.81; T11¼49.974.11). In particular, the peak spine angles recorded from the L3 sensor were significantly lower than those recorded from either the L1 (p¼ 0.010) or T11 (p¼ 0.006) sensors. Positioning the second sensor at L3 produced a 13% lower estimate for λmax than positioning the second sensor at either L1 (p¼0.008) or T11 (p¼0.031) (Table 2). There was no difference between λmax values determined from the sensors placed at L1 and T11 (p¼0.961). Maximum finite-time Lyapunov exponents derived from the constrained trials were 11% lower on average than those derived from the unconstrained trials (p¼ 0.017) (Table 2). Intraclass correlation coefficients for both unconstrained and constrained conditions showed the best correspondence in λmax determined from the spine angular kinematic data obtained using the L1 and T11 locations for the second sensors (ICC2,1 ¼0.789 and 0.946) (Table 3). Conversely, the lowest correspondence in λmax was observed between spine angular kinematic data obtained using the L3 and T11 (furthest separation distance) locations for the second sensors (ICC2,1 ¼0.255 and 0.559) (Table 3).
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Fig. 1. Experimental setups for the (A.) constrained and (B.) unconstrained conditions. Note that targets were used to define the start and end positions in the constrained setup. The start and end positions were not defined in the unconstrained setup.
4. Discussion When processing biomechanical data, it is important to understand how the techniques being employed can be influenced by the experimental setup and protocols. Previous work using λmax to estimate local
dynamic stability evaluated the number of movement cycles to achieve suitable precision in the estimates, sensitivity of the technique to the number of samples in the time-series, as well as between and within day reliability (Bruijn et al., 2009b; Kyvelidou et al., 2009; Graham et al., 2012b; Dupeyron et al., 2013). The current investigation demonstrated
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Table 2 Local dynamic stability quantified using the angular kinematic time-series for each combination of constraint condition, and sensor location. Values in parentheses represent the standard error of the mean. The asterisk denotes a statistically significant difference between the constrained and unconstrained conditions. Columns, representing the sensor locations, with the same letter were statistically similar.
Unconstrained Constrained Sensor location overall
L3
L1
T11
Condition overall*
2.00 (0.08) 1.76 (0.11) 1.88 (0.08)
2.20 (0.10) 2.06 (0.08) 2.13 (0.07)
2.25 (0.10) 2.01 (0.10) 2.13 (0.10)
2.15 (0.08) 1.94 (0.08)
A
B
B
Table 3 Intraclass correlation coefficients (ICC2,1) between estimates of local dynamic stability using each pair of spine angular kinematic time-series from the different sensor locations, and for each of the unconstrained and constrained conditions. L3 Unconstrained
Constrained
L3 L1 T11 L3 L1 T11
L1
T11
0.640
0.559 0.946
0.450
0.255 0.789
that significant discrepancies in estimates of local dynamic stability of spine movements could occur as a result of different kinematic sensor placements and experimental constraints. Recent literature has advocated using metrics derived from nonlinear dynamics analyses (e.g. λmax) within studies conducted using different pathological populations or to evaluate rehabilitation (Harbourne and Stergiou, 2009; Stergiou and Decker, 2011). As examples, λmax has been applied to center of pressure traces in developmentally delayed infants and stroke patients during rehabilitation, and to gait patterns of individuals with unilateral anterior cruciate ligament deficiency (Stergiou et al., 2004; Roerdink et al., 2006; Kyvelidou et al., 2013). Recent evidence has demonstrated that individuals with lower back pain may exhibit less stable kinematic behavior than those without lower back pain (Graham et al., 2014). If estimates of local dynamic stability are employed in a repeated measures design over multiple testing days (e.g. to track progress throughout a rehabilitation program), then it is also necessary to minimize possible discrepancies that can occur from improper replacement of kinematic sensors. Two sources that can produce discrepancies in sensor placement for spine kinematics are incorrect palpation of spinous processes, and the chosen type of sensor. For example, physiotherapists asked to identify the location for specific spinous processes were successful only 47% of the time with an average error of 18.6 mm (Harlick et al., 2007). The electromagnetic sensors used in the current investigation were approximately 20 mm wide and 8 mm tall, which made them convenient for mounting to specific anatomical landmarks. Other experimental setups using optoelectronic cameras to measure spine angular kinematics may affix an array of markers to a rigid body that is subsequently affixed to the skin or a belt at a specified vertebral level (Graham et al., 2011; Howarth and Mastragostino, 2013). These rigid bodies may span multiple vertebral levels, and could subsequently introduce error as a result of improper placement. Finally, our investigation demonstrated that constrained movements resulted in lower estimates for λmax than unconstrained movements (i.e. an improvement in local dynamic stability). Constraining
the spine's movement by physically restraining the pelvis, and using targets to direct movement endpoints is typically employed in studies that investigate function of the spine system (Cholewicki et al., 2005; Granata and England, 2006; Hodges et al., 2009; Graham et al., 2012a, 2012b; van Drunen et al., 2013); however, constraining the movement evaluates it under non-functional conditions (Delphinus and Sayers, 2013). The higher values for λmax found during the unconstrained movements were likely the result of not explicitly defining the start and end points for the movement and allowing movement in the lower limbs and pelvis. In conclusion, our investigation demonstrated that positioning of kinematic sensors and also the experimental decision to either constrain or not constrain the movement could influence estimates for local dynamic stability of spine movement. Based on the strong agreement between local dynamic stability estimates from the L1 and T11 sensors, it is likely that, in studies where reapplication of the instrumentation is necessary, replacement of sensors near the original site will generate reliable results. Nevertheless, careful placement and documentation of sensor positioning is still highly recommended to capture true differences in studies employing a repeated measures design where data is collected from each participant on multiple days. The decision to either constrain or not constrain the movement should be dependent upon the overlying purpose of the investigation. For example, if the main purpose of a study is to evaluate overall movement patterns, then it is advised that the movement is not constrained. Conversely, if the main purpose is to study the spine system in isolation, then it is likely best to apply constraints to the movement.
Conflict of interest The authors have no conflicts of interest to declare.
Acknowledgments This study was funded by the Natural Sciences and Engineering Research Council of Canada (NSERC) (RGPIN-2014–05560 [Ryan Graham]).
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