Ryan B. Graham 1 School of Physical and Health Education, Nipissing University, 100 College Drive, Box 5002, North Bay, ON P1B 8L7, Canada e-m ail: ryang@ nipissingu.ca
Stephen H. M. Brown Department of Human Health and Nutritional Sciences, University of Guelph, 50 Stone Road East, Guelph, ON N 1 G 2 W 1 , Canada e-m ail: shm brown@ uoguelph.ca
Local Dynamic Stability of Spine Muscle Activation and Stiffness Patterns During Repetitive Lifting To facilitate stable trunk kinematics, humans must generate appropriate motor patterns to effectively control muscle force and stiffness and respond to biomechanical perturba tions and/or neuromuscular control errors. Thus, it is important to understand physiolog ical variables such as muscle force and stiffness, and how these relate to the downstream production o f stable spine and trunk movements. This study was designed to assess the local dynamic stability of spine muscle activation and rotational stiffness patterns using Lyapunov analyses, and relationships to the local dynamic stability of resulting spine kinematics, during repetitive lifting and lowering at varying combinations of lifting load and rate. With an increase in the load lifted at a constant rate there was a trend for decreased local dynamic stability of spine muscle activations and the muscular contribu tions to spine rotational stiffness; although the only significant change was for the full state space muscle activation stability (p) Each of the 30 lift/lowers consisted of moving from a target at position (1) to a target at position (2) and back, to the beat of a metronome. 1210 06 -2 / Vol. 136, DECEMBER 2014
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was removed, the raw EMG data were bandpass filtered between 30 and 450 Hz, and then full-wave rectified and low-pass filtered using a second order Butterworth filter with a 2.5 Hz cutoff fre quency. These EMG signals were then normalized to maximum activation produced during the MVC trials, and down-sampled to 32 Hz to match the kinematics. Three-dimensional (3D) lumbar spine angles were calculated using Euler rotation matrices recorded from the 7 j2 sensor, with respect to the S t sensor. The data from the first five lifts within each trial were discarded to ensure steady-state motion [9,10].
Stability Modeling Muscular Contributions to Lumbar Spine Rotational Stiffness. Linear enveloped EMG signals, 2D positions (vertical and A/P) of the hand and SH relative to Si, as well as the 3D lumbar spine angles (Fig. 2) were entered into an anatomically-detailed EMG-driven bio mechanical model consisting of 58 muscle lines of action represent ing seven bilateral muscle groups crossing the L4/L5 spinal joint [5,18]. Succinctly, an estimate of the force generated by each of these muscle lines was made by Fm = NEMGm * PCSAm * om * lm * vm * G
(1)
where Fm is force in muscle m (N), NEMGm is normalized EMG signal for muscle m (% MVC), PCSA„, is physiological crosssectional area of muscle m (cm2), om is maximum stress generated by muscle m (set at 35 N/cm2), l„, is length coefficient of muscle m (unitless), vm is velocity coefficient of muscle m (unitless), and G is participant specific multiplier (unitless). The length and 12/min0%
F ig . 2
12/min 5%
velocity coefficients were solved using equations detailed by McGill and Norman [19]. Detailed descriptions of the anatomical muscle model (e.g., origin and insertion coordinates, PCSAs, etc.) have been published previously [5]. The participant specific multiplier was obtained by finding a best match in a 45 deg trunk flexion calibration trial between the experimentally determined moment (calculated from the scaled digital photograph using a 2D rigid linked-segment model (QBack, Queen’s University, Kingston, ON, Canada)), and the moment estimated by the EMG-driven model. In this way differ ences in muscle moment generating capability between individu als could be accommodated by the model. The mean (range) of multipliers calculated and used was 2.3 (1.5-3.9). The muscular contributions to lumbar spine rotational stiffness, at each instant in time, were then estimated as per [7] AxBx + A YBY — r2
(2)
where Sz is the rotational stiffness about the z-axis (F/E) of the L4/L5 joint, F is muscle force (N), l is 3D length of the muscle vector that crosses L4/L5, L is full 3D length of the muscle, r is 3D muscle moment arm, Ax , Ay = origin coordinates with respect to the L4/L5 joint at (0,0,0)m, Bx , B y are initial deflection or insertion (without deflection points) coordinates with respect to L JL 5, and q is stiffness gain relating muscle force and length to stiffness (value of 10 used). A q of 10 was used based on previous model ing work that has estimated a range from approximately 0.5-50, with a mean of approximately 10 [20,21],
12/min 10%
E x e m p la r E M G lin e a r e n v e lo p e s , 3 D a n g u la r a n d 2 D p o s it io n a l d a ta f r o m
o n e p a r t ic ip a n t d u r in g e a c h o f t h e f iv e
r e p e titiv e liftin g s c e n a r io s . E M G : T E S , L E S , M F , L D , 10 , E O , R A . A n g le s : F /E , L B = la t e r a l b e n d in g , R T = a x ia l r o t a t io n . P o s itio n s : S H , H A , A /P , l/S = in fe r io r /s u p e r io r .
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Rotational stiffness was also calculated about lateral bend Qc-axis) and axial twist (y-axis) axes by appropriate substituting of coordinates [7]. Then, in order to get an estimate of overall stiff ness, the Euclidean norm of the stiffness about all three axes was calculated at each instant in time [11] Sn onn =
+ S2y + S*
(3)
Local Dynamic Stability. The local dynamic stability of: (1) spine muscle activations and (2) the muscular contributions to spine rotational stiffness, were assessed using the maximum finite-time Lyapunov exponent, / max. Because estimates of / max may be biased by time series length [22], the data from each of the 25 lifting trials sampled at 32 Hz were normalized to 4000 samples prior to further analyses. This method maintains lift-tolift temporal variability [9].
Y(t) — [Vtes(0
F ld (f)
F les (0
VmfW
F ra (f)
V eo (0
For the local dynamic stability of spine rotational stiffness, a 6D state-space was first created using the method of delays (Fig. 3) [23] Y(t) = [r(0, r(t + Td), r(t + 2Td) , ..., r(t + (n - l)Td)]
(4)
where Y(t) is the ^-dimensional state-space, r(t) is the original time series data (Euclidean norm spine rotational stiffness data), n is the number of reconstruction dimensions, and Td is a constant time delay [23], A TA of 16 samples (10% of average lift) was used to ensure data were processed similarly [9,10], and an embedding dimension of six was chosen to match the methods used to calculate the local dynamic stability of kinematic meas ures from this dataset [11]; chosen previously using global false nearest neighbor’s analysis [24]. For the muscle activation (EMG) data, two seperate state spaces were created [14]. First, a full 14D state space was defined using the normalized linear envelopes of EMG voltage for each muscle (V), as well as their corresponding time-derivatives (F) [3]
Vio(t)
Fres(f)
F ld M
Vles (0
F mf(0
F ra (f)
F eo (0
F io (0 ]
(5)
Derivatives were included to capture the muscle activation rates of change [3], A second state space was also created using only the low back EMG signals (LES and MF), as these were the most active during the lifting task. First, the two EMG linear envelopes were combined (Eq. (6)), and then a 6D state space was created using the method of delays, as per the stiffness stability methods above.
F lowBack (0 — \Z F les (/)2 + F mf (?)2
(6)
Maximum finite-time Lyapunov exponents were then calcu lated by analyzing the exponential rate of divergence of initially neighboring trajectories in each of the three aforementioned reconstructed state spaces. This was done by estimating Amax as the slope of the linear best-fit line created by
(d)
Fig. 3 The process of state space reconstruction and local dynamic stability analysis using the spine rotational stiffness data, (a) Original 3D spine rotational stiffness data, as well as the Euclidean norm stiffness at each point in time, (b) The reconstructed dynamics in state space using a reconstruction dimension of six and a time delay of 16 samples (0.5 s). (c) Expanded view of a local region on the attractor (outlined in b), displaying the diverging Euclidean distance (dj) of nearest neighbors after an infinitesimally small perturbation, (d) Average logarithmic rate of divergence for all nearest neighbor pairs over 0.5 cycles. 121006-4 / Vol. 136, DECEMBER 2014
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>(*■) = ^ ( ln 4 ( 0 )
subject variability when computing the regression coefficients. In the present case significant mixed-model regression slopes were interpreted as being analogous to significant linear correlations between variables [26].
(7)
where (in 4 ( 0 ) represents the average logarithm of divergence,
dj{i), for all pairs of nearest neighbors, j, throughout a certain number of time steps (iAi) [25], The slope was calculated from 0 to 0.5 lifts, which provides an exponent analogous to Amax.SIride used in gait research, and controls for the differences in lifting rate across the conditions [26],
Statistical Analyses. After confirming that the Lyapunov exponents from this dataset were normally distributed using Shapiro-Wilk tests, separate repeated-measures analysis of var iances (anovas) (a = 0.05) with post hoc pairwise comparisons using Bonferroni corrections for multiple comparisons were applied to determine the effect of both load and lifting rate on each of the dependent variables: (1) local dynamic stability (Ama*) of the muscular contributions to spine rotational stiffness, (2) local dynamic stability (A^x) of the full state space muscle activation, and (3) local dynamic stability (Amax) of low back muscle activa tion (SPSS 20, IBM Corporation, Armonk, NY). Furthermore, to determine the relationship between each the different stability variables as well as the spine rotational stiffness and local dynamic stability of kinematics outputs from our previous work [11], linear mixed modelling was applied in SPSS. Linear mixed modelling is a regression technique similar to gener alized estimating equations that takes repeated measures into account, and allows for the separation of within and between
Results Effects of Load. With an increase in the load lifted at a con stant rate there was a trend for decreased local dynamic stability of spine muscle activations and muscular contributions to spine rotational stiffness (increased maximum Lyapunov exponents); although the only significant change was for the full state space muscle activation stability (p = 0.005) (Fig. 4). Post hoc pair-wise comparisons revealed that the 10% load condition was signifi cantly different (less stable) from both the 0% and 5% load condi tions (Fig. 4). These results contrast with those from our previous study [11], where an increase in load lifted at a constant rate significantly increased the local dynamic stability of spine kinematics (decreased Lyapunov exponents) and significantly increased mean, maximum, and minimum muscular contributions to spine rotational stiffness (p < 0.05) (Fig. 4). Effects of Lifting Rate. With an increase in lifting rate with a constant load there was a significant decrease in the local dynamic stability of spine muscle activations and rotational stiffness (significant increase in maximum Lyapunov exponents; p U-» w '3o5
«
C3 M &j)0-
H^ -o s P i 5Q J Z
n c S3 “ o
Journal of Biomechanical Engineering
trunk movements in space. Interestingly, we found that the dynamic stability of spine muscle activations and muscular contri butions to spine rotational stiffness were significantly and consis tently decreased with an increase lifting rate. There was also a trend for reductions in this stability with an increase in lifting load, with the only significant effect for the local dynamic stabil ity of the full trunk system muscle activation. Thus, in general, the stability of these important variables was reduced as demand was increased; the implications of this are discussed below. Under the changing rate condition (constant load), significant decreases in the local dynamic stability of muscle activations and rotational stiffness were observed (greater maximum finite-time Lyapunov exponents). Therefore, under the changing rate condi tion, participants were less able to maintain stable spine muscular activity and stiffness trajectories and profiles, despite increases in mean and maximum rotational stiffness due to increased muscular activity and movement velocity [11], Thus, under this condition, even though overall stiffness is higher, the downstream kinematic stability does not change, thus not bolstering the ability to avoid kinematic-related disturbances in a situation where this may be important (i.e., higher loading due to greater muscle activation and movement accelerations). Since muscle activation directly affects muscle force and stiffness, which in turn affect the moments and spine rotational stiffness, and subsequently kine matic stability, these findings are important to understanding injury risk during fast movements [27]. This might also explain why weak linear relationships between the rotational stiffness and local dynamic kinematic stability measures were observed in our previous work. Specifically, although overall stiffness was higher (more mechanically stable), local dynamic kinematic stability was not changed [11], possibly due to difficulties in modulating muscle activity and force with increased speed [3,26], which reduced the local dynamic stability of the muscular activity and the muscular contributions to spine rotational stiffness. Conversely, no significant differences in the local dynamic stability of spine rotational stiffness were observed with an increase in load lifted at a constant rate, although there was a trend for reduced stability with higher loads that may have become sig nificant with more participants. Concordantly, similar results were observed for the local dynamic stability of muscle activity, with the only statistically significant change occurring in the full state space local dynamic stability. Thus, it may be more difficult to continuously match task demands and maintain stable and con sistent muscle activation profiles even though muscular activity and the muscular contributions to spine rotational stiffness (mean, maximum, and minimum) are significantly increased due to augmented muscular and moment demands [5,28]. Therefore, since the differences in the local dynamic stability of the muscular contributions to spine rotational stiffness were not statistically sig nificant, this may explain why moderate to strong correlations between the spine rotational stiffness and dynamic kinematic stability estimates were observed in our previous work [11], Rota tional stiffness was higher, and the local dynamic stability of spine rotational stiffness was maintained (did not significantly change), thus creating a situation where the increased overall stiffness could correspond to a significant increase in kinematic dynamic stability. It has been well established that trunk muscle activation levels increase in response to greater challenges to the spine [29,30], Our previous study confirmed this and further demonstrated a con sequent increase in spine stiffness. This increased stiffness corre sponded to greater local dynamic kinematic stability when the spine was challenged through the lifting of different loads, but not when challenged through the lifting at different rates. Interest ingly, we also discovered in that study that kinematic stability was most closely related to a minimum level of stiffness, thereby sug gesting that, of these variables, it is the most vulnerable state of the system (state of minimum stiffness) that best corresponds to kinematic stability. Here we have expanded on this idea by dem onstrating that increased stiffness, driven by increased muscle DECEMBER
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activation, may come at a cost of reduced stability of these muscle activation and stiffness patterns. This has been reported previ ously, where muscle force variability increases with increased muscle activation, thus rendering the spine feedback control sys tem less effective e.g., Refs. [31-33]. It is possible that this impaired stiffness stability is what establishes the stiffness minimums determined previously to best correspond to kinematic stability. Linear mixed-model relationships across all of our different variables demonstrate that the local dynamic stability of both the muscular contributions to spine rotational stiffness and muscular activity were positively correlated; not surprising as the rotational stiffness data is calculated using an EMG-driven approach [10,15], Second, it can be observed that the local dynamic stability of both spine muscle activations and the muscular contributions to spine rotational stiffness were positively correlated to the local dynamic stability of kinematic outputs from our previous work during the changing rate condition. During the changing load condition, the local dynamic stability of rotational stiffness was positively correlated to local dynamic stability of kinematic outputs. Therefore, since the EMG (motor patterns) drives the kinematics [2], and because EMG and stiffness data are closely related, it appears that stable muscular activity and stiffness profiles do contribute to the production of stable kinematic pro files, at least to some degree. This is important as it suggests that training movement and muscular activation techniques may corre spond to increased stiffness stability, and subsequently improved kinematic responses to perturbations. Lastly, the full trunk system EMG stability was negatively correlated to the minimum level of stiffness under both the load and rate condition, which indicates good agreement between these two dependent measures. Although the present results help explain our previous findings and provide insight into how the human body stabilizes physiolog ical variables (muscle force and stiffness) related to the control of movement, it is important to address several limitations to the present research. We have shown that two contributing factors to the dynamic stability of human kinematics are: (1) the amount (magnitude) of spine rotational stiffness, and (2) the local dynamic stability of muscle activation, force, and stiffness. During lifting, the controlled variable may be considered the kine matic movement and stability of the torso and/or box, and the con tributing factors to this control are plant stiffness, damping, and nervous system mediated feedback control [2,34], Thus, although we have considered stiffness and feedback related factors as well as the full dynamic outputs through these two research studies, we have yet to consider the full dynamics of the control system (i.e., damping inputs) and how this interacts with the other factors. This damping effect, which could play a larger role with increased movement rate and velocity, could thus help explain our previ ously reported reduced agreement between stiffness and dynamic stability [11], and should be explored in the future. Nevertheless, the stiffness-based model does control for higher order velocityrelated effects within the muscles themselves [8,18,35], and previ ous research has suggested that muscle and joint stiffness in particular may act as important controlling factors for the nervous system [36-39]. Moreover, stiffness itself is a critical variable to study, as it is an important contributor to overall spine stability [11], modifications have been found in low back pain patients [40], and stiffness can be trained in such a population [41].
findings suggest that in addition to the total amount of rotational stiffness (mechanical stability), it is also important to consider how the human body stabilizes muscle activation and the muscu lar contributions to spine rotational stiffness to meet task demands when assessing injury risk. The findings from this study also help explain our earlier findings [11], and show that Lyapunov analyses of kinematic data do capture some relevant information regarding the mechanical effect of spine stiffness (i.e., the amount of stiff ness) as well as the local dynamic stability of these stiffness pro files (among other things). Furthermore, this analysis technique provides important insight into how the body stabilizes motor pat terns and subsequently the muscular contributions to spine rota tional stiffness over time, and also provides an effective method of assessing the fundamental physiological control of muscle force and stiffness (and the resulting effects on spine rotational stiffness), and how these subsequently affect the ability to main tain stable spine kinematics.
Acknowledgment The authors would like to thank Dr. Joan Stevenson for her mentorship and contributions to this research study. Dr. Ryan Graham was funded by a Natural Sciences and Engi neering Research Council (NSERC) of Canada Graduate Scholar ship (CGS-D2) during the completion of this study.
Nomenclature Ax, Ay = origin coordinates with respect to the L4/Ls joint Bx By = initial deflection or insertion coordinates with respect to LJL5 joint dj = divergence of nearest neighbor pairs EMG = electromyography EO = external oblique F = muscle force (N) G = participant specific multiplier 10 = internal oblique i = 3D length of muscle vector that crosses LJLS joint / = length coefficient of muscle (unitless) L = full 3D length of the muscle LD = latissimus dorsi LES = lumbar erector spinae MF = multifidus MVC = maximum voluntary contraction n = number of reconstruction dimensions PCSA = physiological cross sectional area q = stiffness gain relating muscle force to stiffness r = 3D muscle moment aim r = Euclidean norm stiffness RA = rectus abdominus Sz = rotational stiffness about axis z Td = time delay TES = thoracic erector spinae V = raw voltage V = voltage rate of change V = state space /.max = maximum finite-time Lyapunov exponent v = velocity coefficient of muscle (unitless) a = maximum muscle stress (cm2)
Conclusion In conclusion, we found that the local dynamic stability of spine muscle activations and muscular contributions to spine rotational stiffness were significantly and consistently decreased with an increased lifting rate. There was also a trend for reductions in this stability with an increase in lifting load, with the only significant effect for the local dynamic stability of the full trunk system mus cle activation. Thus, in general, the stability of these important variables was reduced as demand was increased. These novel 1 21006-8 / Vol. 136, DECEMBER 2014
References [1] Panjabi, M. M., 1992, “The Stabilizing System of the Spine. Part I. Function, Dysfunction, Adaptation, and Enhancement,” J. Spinal Disord., 5(4), pp. 383-389. [2] Reeves, N. P., Narendra, K. S., and Cholewicki, J., 2007, “Spine Stability: The Six Blind Men and the Elephant,” Clin. Biomech., 22(3), pp. 266-274. [3] Kang, H. G., and Dingwell, J. B., 2009, “Dynamics and Stability of Muscle Activations During Walking in Healthy Young and Older Adults,” J. Biomech., 42(14), pp. 2231-2237.
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[4] McGill, S. M., Grenier, S., Kavcic, N., and Cholewicki, J., 2003, “Coordination of Muscle Activity to Assure Stability of the Lumbar Spine,” J. Electromyogr. Kinesiol., 13(4), pp. 353-359. [5] Cholewicki, J., and McGill, S. M., 1996, “Mechanical Stability of the In Vivo Lumbar Spine: Implications for Injury and Chronic Low Back Pain,” Clin. Biomech., 11(1), pp. 1-15. [61 Granata, K. P., and Gottipati, P., 2008, “Fatigue Influences the Dynamic Stabil ity of the Torso,” Ergonomics, 51(8), pp. 1258-1271. [7] Potvin, J. R., and Brown, S. H. M., 2005, “An Equation to Calculate Individual Muscle Contributions to Joint Stability,” J. Biomech., 38(5), pp. 973-980. [8] Brown, S. H. M., and McGill, S. M., 2005, “Muscle Force-Stiffness Character istics Influence Joint Stability: A Spine Example,” Clin. Biomech., 20(9), pp. 917-922. [9] Granata, K. P., and England, S. A., 2006, “Stability of Dynamic Trunk Move ment,” Spine, 31(10), pp. E271-E276. [10] Graham, R. B., Sadler, E. M., and Stevenson, J. M., 2012, “Local Dynamic Stability of Trunk Movements During the Repetitive Lifting of Loads,” Hum. Mov. Sci., 31(3), pp. 592-603. [11] Graham, R. B., and Brown, S. H. M., 2012, “A Direct Comparison of Spine Rotational Stiffness and Dynamic Spine Stability During Repetitive Lifting Tasks,” J. Biomech., 45(9), pp. 1593-1600. [12] Bergmark, A., 1989, “Stability of the Lumbar Spine. A Study in Mechanical Engineering,” Acta Orthop. Scand. Suppl., 230(230), pp. 1-54. [13] Rodrick, D., and Quesada, P. M., 2013, “Non-Linear Dynamics of Lower Leg Muscle Surface Electromyogram During Repeated Plantar Flexion,” Theor. Issues Ergonomics Sci., 14(2), pp. 37-41. [14] Graham, R. B., Oikawa, L. Y., and 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(6), pp. 1459-1464. [15] McGill, S. M., 1991, “Electromyographic Activity of the Abdominal and Low Back Musculature During the Generation of Isometric and Dynamic Axial Trunk Torque: Implications for Lumbar Mechanics,” J. Orthop. Res., 9(1), pp. 91-103. [16] McGill, S. M., 1992, “A Myoelectrically Based Dynamic Three-Dimensional Model to Predict Loads on Lumbar Spine Tissues During Lateral Bending,” J. Biomech., 25(4), pp. 395-414. [17] Kingma, I., Staudenmann, D., and van Dieen, J. H., 2007, “Trunk Muscle Acti vation and Associated Lumbar Spine Joint Shear Forces Under Different Levels of External Forward Force Applied to the Trunk,” J. Electromyogr. Kinesiol., 17(1), pp. 14-24. [18] Brown, S. H. M., and McGill, S. M., 2010, “The Relationship Between Trunk Muscle Activation and Trunk Stiffness: Examining a Non-Constant Stiffness Gain,” Comput. Methods Biomech. Biomed. Eng., 13(6), pp. 829-835. [19] McGill, S. M., and Norman, R. W., 1986, “Partitioning the L4-L5 Dynamic Moment Into Disc, Ligamentous, and Muscular Components,” Spine, 11(7), pp. 666-678. [20] Cholewicki, J., and McGill, S. M., 1995, “Relationship Between Muscle Force and Stiffness in the Whole Mamallian Muscle: A Simulation Study,” ASME J. Biomech. Eng., 117(3), pp. 339-342. [21] Crisco, J. J., and Panjabi, M. M., 1991. “The Intersegmental and Multisegmental Muscles of the Lumbar Spine: A Biomechanical Model Comparing Lateral Stabilizing Potential,” Spine, 16(7), pp. 793-799.
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[22] Bruijn, S. M., van Dieen, J. H., Meijer, O. G., and Beek, P. J., 2009, “Statistical Precision and Sensitivity of Measures of Dynamic Gait Stability,” J. Neurosci. Methods, 178(2), pp. 327-333. [23] Abarbanel, H. D. I., Brown, R., Sidorowich, J. J., and Tsimring, L. S., 1993, “The Analysis of Observed Chaotic Data in Physical Systems,” Rev. Mod. Phys., 65(4), pp. 1331-1392. [24] Kennel, M. B., Brown, R., and Abarbanel, H. D. I., 1992, “Determining Embed ding Dimension for Phase-Space Reconstruction Using a Geometrical Con struction,” Phys. Rev. A, 45(6), pp. 3403-3411. [25] Rosenstein, M. T., Collins, J. J., and De Luca, C. J., 1993, “A Practical Method for Calculating Largest Lyapunov Exponents From Small Data Sets,” Phys. D, 65(1-2), pp. 117-134. [26] Bruijn, S. M., van Dieen, J. H., Meijer, O. G., and Beek, P. J., 2009, “Is Slow Walking More Stable?,” J. Biomech., 42(10), pp. 1506-1512. [27] Marras, W. S., Lavender, S. A., Ferguson, S. A., Splittstoesser, R. E., and Yang, G., 2010, “Quantitative Dynamic Measures of Physical Exposure Predict Low Back Functional Impairment,” Spine, 35(8), pp. 914—923. [28] Gardner-Morse, M. G., and Stokes, I. A., 2001, “Trunk Stiffness Increases With Steady-State Effort,” J. Biomech., 34(4), pp. 457-463. [29] Granata, K. P., and Marras, W. S., 1995, “The Influence of Trunk Muscle Coactivity on Dynamic Spinal Loads,” Spine, 20(8), pp. 913-919. [30] van Dieen, J. H., Kingma, I., and van der Bug, J. C. E., 2003, “Evidence for a Role of Antagonistic Cocontraction in Controlling Trunk Stiffness During Lifting,” J. Biomech., 36(12), pp. 1829-1836. [31] Newell, K. M., and Carlton, L. G., 1988, “Force Variability in Isometric Responses,” J. Exp. Pscyhol. Hum. Percept. Perform, 14(1), pp. 37-44. [32] Slifkin, A. B., and Newell, K. M., 2000, “Variability and Noise in Continuous Force Production.,” J. Mot. Behav., 32(2), pp. 141-150. [33] Hamilton, A. F. D. C., Jones, K. E., and Wolpert, D. M., 2004, “The Scaling of Motor Noise With Muscle Strength and Motor Unit Number in Humans,” Exp. Brain Res., 157(4), pp. 417-430. [34] Reeves, N. P., and Cholewicki, J., 2010, “Expanding Our View of the Spine System,” Eur. Spine J., 19(2), pp. 331-332. [35] Brown, S. H. M., and Potvin, J. R., 2007, “Exploring the Geometric and Mechanical Characteristics of the Spine Musculature to Provide Rotational Stiffness to Two Spine Joints in the Neutral Posture,” Hum. Mov. Sci., 26(1), pp. 113-123. [36] Houk, J. C., 1979, “Regulation of Stiffness by Skeletomotor Reflexes,” Annu Rev Physiol, 41, pp. 99-114. [37] Axelson, H. W., and Hagbarth, K. E., 2001, “Human Motor Control Consequences of Thixotropic Changes in Muscular Short-Range Stiffness,” J. Physiol., 535(1), pp. 279-288. [38] Campbell, K. S., 2010, “Short-Range Mechanical Properties of Skeletal and Cardiac Muscles,” Adv. Exp. Med. Biol., 682, pp. 223-246. [39] Stein, R., 1982, “What Muscle Variable(s) Does the Nervous System Control in Limb Movements?,” Behav. Brain Sci., 5(4), pp. 535-541. [40] Karayannis, N. V., Smeets, R. J. E. M., van den Hoorn, W., and Hodges, P. W., 2013, “Fear of Movement is Related to Trunk Stiffness in Low Back Pain,” PLoS One, 8(6), p. e67779. [41] Cacciatore, T., Gurfinkel, V., Horak, F., Cordo, P., and Ames, K., 2011, “Increased Dynamic Regulation of Postural Tone Through Alexander Tech nique Training,” Hum. Mov. Sci., 30(1), pp. 74—89.
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Stephen H. M. Brown Department of Human Health and Nutritional Sciences, University of Guelph, 50 Stone Road East, Guelph, ON N 1 G 2 W 1 , Canada e-m ail: shm brown@ uoguelph.ca
Local Dynamic Stability of Spine Muscle Activation and Stiffness Patterns During Repetitive Lifting To facilitate stable trunk kinematics, humans must generate appropriate motor patterns to effectively control muscle force and stiffness and respond to biomechanical perturba tions and/or neuromuscular control errors. Thus, it is important to understand physiolog ical variables such as muscle force and stiffness, and how these relate to the downstream production o f stable spine and trunk movements. This study was designed to assess the local dynamic stability of spine muscle activation and rotational stiffness patterns using Lyapunov analyses, and relationships to the local dynamic stability of resulting spine kinematics, during repetitive lifting and lowering at varying combinations of lifting load and rate. With an increase in the load lifted at a constant rate there was a trend for decreased local dynamic stability of spine muscle activations and the muscular contribu tions to spine rotational stiffness; although the only significant change was for the full state space muscle activation stability (p) Each of the 30 lift/lowers consisted of moving from a target at position (1) to a target at position (2) and back, to the beat of a metronome. 1210 06 -2 / Vol. 136, DECEMBER 2014
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was removed, the raw EMG data were bandpass filtered between 30 and 450 Hz, and then full-wave rectified and low-pass filtered using a second order Butterworth filter with a 2.5 Hz cutoff fre quency. These EMG signals were then normalized to maximum activation produced during the MVC trials, and down-sampled to 32 Hz to match the kinematics. Three-dimensional (3D) lumbar spine angles were calculated using Euler rotation matrices recorded from the 7 j2 sensor, with respect to the S t sensor. The data from the first five lifts within each trial were discarded to ensure steady-state motion [9,10].
Stability Modeling Muscular Contributions to Lumbar Spine Rotational Stiffness. Linear enveloped EMG signals, 2D positions (vertical and A/P) of the hand and SH relative to Si, as well as the 3D lumbar spine angles (Fig. 2) were entered into an anatomically-detailed EMG-driven bio mechanical model consisting of 58 muscle lines of action represent ing seven bilateral muscle groups crossing the L4/L5 spinal joint [5,18]. Succinctly, an estimate of the force generated by each of these muscle lines was made by Fm = NEMGm * PCSAm * om * lm * vm * G
(1)
where Fm is force in muscle m (N), NEMGm is normalized EMG signal for muscle m (% MVC), PCSA„, is physiological crosssectional area of muscle m (cm2), om is maximum stress generated by muscle m (set at 35 N/cm2), l„, is length coefficient of muscle m (unitless), vm is velocity coefficient of muscle m (unitless), and G is participant specific multiplier (unitless). The length and 12/min0%
F ig . 2
12/min 5%
velocity coefficients were solved using equations detailed by McGill and Norman [19]. Detailed descriptions of the anatomical muscle model (e.g., origin and insertion coordinates, PCSAs, etc.) have been published previously [5]. The participant specific multiplier was obtained by finding a best match in a 45 deg trunk flexion calibration trial between the experimentally determined moment (calculated from the scaled digital photograph using a 2D rigid linked-segment model (QBack, Queen’s University, Kingston, ON, Canada)), and the moment estimated by the EMG-driven model. In this way differ ences in muscle moment generating capability between individu als could be accommodated by the model. The mean (range) of multipliers calculated and used was 2.3 (1.5-3.9). The muscular contributions to lumbar spine rotational stiffness, at each instant in time, were then estimated as per [7] AxBx + A YBY — r2
(2)
where Sz is the rotational stiffness about the z-axis (F/E) of the L4/L5 joint, F is muscle force (N), l is 3D length of the muscle vector that crosses L4/L5, L is full 3D length of the muscle, r is 3D muscle moment arm, Ax , Ay = origin coordinates with respect to the L4/L5 joint at (0,0,0)m, Bx , B y are initial deflection or insertion (without deflection points) coordinates with respect to L JL 5, and q is stiffness gain relating muscle force and length to stiffness (value of 10 used). A q of 10 was used based on previous model ing work that has estimated a range from approximately 0.5-50, with a mean of approximately 10 [20,21],
12/min 10%
E x e m p la r E M G lin e a r e n v e lo p e s , 3 D a n g u la r a n d 2 D p o s it io n a l d a ta f r o m
o n e p a r t ic ip a n t d u r in g e a c h o f t h e f iv e
r e p e titiv e liftin g s c e n a r io s . E M G : T E S , L E S , M F , L D , 10 , E O , R A . A n g le s : F /E , L B = la t e r a l b e n d in g , R T = a x ia l r o t a t io n . P o s itio n s : S H , H A , A /P , l/S = in fe r io r /s u p e r io r .
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Rotational stiffness was also calculated about lateral bend Qc-axis) and axial twist (y-axis) axes by appropriate substituting of coordinates [7]. Then, in order to get an estimate of overall stiff ness, the Euclidean norm of the stiffness about all three axes was calculated at each instant in time [11] Sn onn =
+ S2y + S*
(3)
Local Dynamic Stability. The local dynamic stability of: (1) spine muscle activations and (2) the muscular contributions to spine rotational stiffness, were assessed using the maximum finite-time Lyapunov exponent, / max. Because estimates of / max may be biased by time series length [22], the data from each of the 25 lifting trials sampled at 32 Hz were normalized to 4000 samples prior to further analyses. This method maintains lift-tolift temporal variability [9].
Y(t) — [Vtes(0
F ld (f)
F les (0
VmfW
F ra (f)
V eo (0
For the local dynamic stability of spine rotational stiffness, a 6D state-space was first created using the method of delays (Fig. 3) [23] Y(t) = [r(0, r(t + Td), r(t + 2Td) , ..., r(t + (n - l)Td)]
(4)
where Y(t) is the ^-dimensional state-space, r(t) is the original time series data (Euclidean norm spine rotational stiffness data), n is the number of reconstruction dimensions, and Td is a constant time delay [23], A TA of 16 samples (10% of average lift) was used to ensure data were processed similarly [9,10], and an embedding dimension of six was chosen to match the methods used to calculate the local dynamic stability of kinematic meas ures from this dataset [11]; chosen previously using global false nearest neighbor’s analysis [24]. For the muscle activation (EMG) data, two seperate state spaces were created [14]. First, a full 14D state space was defined using the normalized linear envelopes of EMG voltage for each muscle (V), as well as their corresponding time-derivatives (F) [3]
Vio(t)
Fres(f)
F ld M
Vles (0
F mf(0
F ra (f)
F eo (0
F io (0 ]
(5)
Derivatives were included to capture the muscle activation rates of change [3], A second state space was also created using only the low back EMG signals (LES and MF), as these were the most active during the lifting task. First, the two EMG linear envelopes were combined (Eq. (6)), and then a 6D state space was created using the method of delays, as per the stiffness stability methods above.
F lowBack (0 — \Z F les (/)2 + F mf (?)2
(6)
Maximum finite-time Lyapunov exponents were then calcu lated by analyzing the exponential rate of divergence of initially neighboring trajectories in each of the three aforementioned reconstructed state spaces. This was done by estimating Amax as the slope of the linear best-fit line created by
(d)
Fig. 3 The process of state space reconstruction and local dynamic stability analysis using the spine rotational stiffness data, (a) Original 3D spine rotational stiffness data, as well as the Euclidean norm stiffness at each point in time, (b) The reconstructed dynamics in state space using a reconstruction dimension of six and a time delay of 16 samples (0.5 s). (c) Expanded view of a local region on the attractor (outlined in b), displaying the diverging Euclidean distance (dj) of nearest neighbors after an infinitesimally small perturbation, (d) Average logarithmic rate of divergence for all nearest neighbor pairs over 0.5 cycles. 121006-4 / Vol. 136, DECEMBER 2014
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>(*■) = ^ ( ln 4 ( 0 )
subject variability when computing the regression coefficients. In the present case significant mixed-model regression slopes were interpreted as being analogous to significant linear correlations between variables [26].
(7)
where (in 4 ( 0 ) represents the average logarithm of divergence,
dj{i), for all pairs of nearest neighbors, j, throughout a certain number of time steps (iAi) [25], The slope was calculated from 0 to 0.5 lifts, which provides an exponent analogous to Amax.SIride used in gait research, and controls for the differences in lifting rate across the conditions [26],
Statistical Analyses. After confirming that the Lyapunov exponents from this dataset were normally distributed using Shapiro-Wilk tests, separate repeated-measures analysis of var iances (anovas) (a = 0.05) with post hoc pairwise comparisons using Bonferroni corrections for multiple comparisons were applied to determine the effect of both load and lifting rate on each of the dependent variables: (1) local dynamic stability (Ama*) of the muscular contributions to spine rotational stiffness, (2) local dynamic stability (A^x) of the full state space muscle activation, and (3) local dynamic stability (Amax) of low back muscle activa tion (SPSS 20, IBM Corporation, Armonk, NY). Furthermore, to determine the relationship between each the different stability variables as well as the spine rotational stiffness and local dynamic stability of kinematics outputs from our previous work [11], linear mixed modelling was applied in SPSS. Linear mixed modelling is a regression technique similar to gener alized estimating equations that takes repeated measures into account, and allows for the separation of within and between
Results Effects of Load. With an increase in the load lifted at a con stant rate there was a trend for decreased local dynamic stability of spine muscle activations and muscular contributions to spine rotational stiffness (increased maximum Lyapunov exponents); although the only significant change was for the full state space muscle activation stability (p = 0.005) (Fig. 4). Post hoc pair-wise comparisons revealed that the 10% load condition was signifi cantly different (less stable) from both the 0% and 5% load condi tions (Fig. 4). These results contrast with those from our previous study [11], where an increase in load lifted at a constant rate significantly increased the local dynamic stability of spine kinematics (decreased Lyapunov exponents) and significantly increased mean, maximum, and minimum muscular contributions to spine rotational stiffness (p < 0.05) (Fig. 4). Effects of Lifting Rate. With an increase in lifting rate with a constant load there was a significant decrease in the local dynamic stability of spine muscle activations and rotational stiffness (significant increase in maximum Lyapunov exponents; p U-» w '3o5
«
C3 M &j)0-
H^ -o s P i 5Q J Z
n c S3 “ o
Journal of Biomechanical Engineering
trunk movements in space. Interestingly, we found that the dynamic stability of spine muscle activations and muscular contri butions to spine rotational stiffness were significantly and consis tently decreased with an increase lifting rate. There was also a trend for reductions in this stability with an increase in lifting load, with the only significant effect for the local dynamic stabil ity of the full trunk system muscle activation. Thus, in general, the stability of these important variables was reduced as demand was increased; the implications of this are discussed below. Under the changing rate condition (constant load), significant decreases in the local dynamic stability of muscle activations and rotational stiffness were observed (greater maximum finite-time Lyapunov exponents). Therefore, under the changing rate condi tion, participants were less able to maintain stable spine muscular activity and stiffness trajectories and profiles, despite increases in mean and maximum rotational stiffness due to increased muscular activity and movement velocity [11], Thus, under this condition, even though overall stiffness is higher, the downstream kinematic stability does not change, thus not bolstering the ability to avoid kinematic-related disturbances in a situation where this may be important (i.e., higher loading due to greater muscle activation and movement accelerations). Since muscle activation directly affects muscle force and stiffness, which in turn affect the moments and spine rotational stiffness, and subsequently kine matic stability, these findings are important to understanding injury risk during fast movements [27]. This might also explain why weak linear relationships between the rotational stiffness and local dynamic kinematic stability measures were observed in our previous work. Specifically, although overall stiffness was higher (more mechanically stable), local dynamic kinematic stability was not changed [11], possibly due to difficulties in modulating muscle activity and force with increased speed [3,26], which reduced the local dynamic stability of the muscular activity and the muscular contributions to spine rotational stiffness. Conversely, no significant differences in the local dynamic stability of spine rotational stiffness were observed with an increase in load lifted at a constant rate, although there was a trend for reduced stability with higher loads that may have become sig nificant with more participants. Concordantly, similar results were observed for the local dynamic stability of muscle activity, with the only statistically significant change occurring in the full state space local dynamic stability. Thus, it may be more difficult to continuously match task demands and maintain stable and con sistent muscle activation profiles even though muscular activity and the muscular contributions to spine rotational stiffness (mean, maximum, and minimum) are significantly increased due to augmented muscular and moment demands [5,28]. Therefore, since the differences in the local dynamic stability of the muscular contributions to spine rotational stiffness were not statistically sig nificant, this may explain why moderate to strong correlations between the spine rotational stiffness and dynamic kinematic stability estimates were observed in our previous work [11], Rota tional stiffness was higher, and the local dynamic stability of spine rotational stiffness was maintained (did not significantly change), thus creating a situation where the increased overall stiffness could correspond to a significant increase in kinematic dynamic stability. It has been well established that trunk muscle activation levels increase in response to greater challenges to the spine [29,30], Our previous study confirmed this and further demonstrated a con sequent increase in spine stiffness. This increased stiffness corre sponded to greater local dynamic kinematic stability when the spine was challenged through the lifting of different loads, but not when challenged through the lifting at different rates. Interest ingly, we also discovered in that study that kinematic stability was most closely related to a minimum level of stiffness, thereby sug gesting that, of these variables, it is the most vulnerable state of the system (state of minimum stiffness) that best corresponds to kinematic stability. Here we have expanded on this idea by dem onstrating that increased stiffness, driven by increased muscle DECEMBER
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activation, may come at a cost of reduced stability of these muscle activation and stiffness patterns. This has been reported previ ously, where muscle force variability increases with increased muscle activation, thus rendering the spine feedback control sys tem less effective e.g., Refs. [31-33]. It is possible that this impaired stiffness stability is what establishes the stiffness minimums determined previously to best correspond to kinematic stability. Linear mixed-model relationships across all of our different variables demonstrate that the local dynamic stability of both the muscular contributions to spine rotational stiffness and muscular activity were positively correlated; not surprising as the rotational stiffness data is calculated using an EMG-driven approach [10,15], Second, it can be observed that the local dynamic stability of both spine muscle activations and the muscular contributions to spine rotational stiffness were positively correlated to the local dynamic stability of kinematic outputs from our previous work during the changing rate condition. During the changing load condition, the local dynamic stability of rotational stiffness was positively correlated to local dynamic stability of kinematic outputs. Therefore, since the EMG (motor patterns) drives the kinematics [2], and because EMG and stiffness data are closely related, it appears that stable muscular activity and stiffness profiles do contribute to the production of stable kinematic pro files, at least to some degree. This is important as it suggests that training movement and muscular activation techniques may corre spond to increased stiffness stability, and subsequently improved kinematic responses to perturbations. Lastly, the full trunk system EMG stability was negatively correlated to the minimum level of stiffness under both the load and rate condition, which indicates good agreement between these two dependent measures. Although the present results help explain our previous findings and provide insight into how the human body stabilizes physiolog ical variables (muscle force and stiffness) related to the control of movement, it is important to address several limitations to the present research. We have shown that two contributing factors to the dynamic stability of human kinematics are: (1) the amount (magnitude) of spine rotational stiffness, and (2) the local dynamic stability of muscle activation, force, and stiffness. During lifting, the controlled variable may be considered the kine matic movement and stability of the torso and/or box, and the con tributing factors to this control are plant stiffness, damping, and nervous system mediated feedback control [2,34], Thus, although we have considered stiffness and feedback related factors as well as the full dynamic outputs through these two research studies, we have yet to consider the full dynamics of the control system (i.e., damping inputs) and how this interacts with the other factors. This damping effect, which could play a larger role with increased movement rate and velocity, could thus help explain our previ ously reported reduced agreement between stiffness and dynamic stability [11], and should be explored in the future. Nevertheless, the stiffness-based model does control for higher order velocityrelated effects within the muscles themselves [8,18,35], and previ ous research has suggested that muscle and joint stiffness in particular may act as important controlling factors for the nervous system [36-39]. Moreover, stiffness itself is a critical variable to study, as it is an important contributor to overall spine stability [11], modifications have been found in low back pain patients [40], and stiffness can be trained in such a population [41].
findings suggest that in addition to the total amount of rotational stiffness (mechanical stability), it is also important to consider how the human body stabilizes muscle activation and the muscu lar contributions to spine rotational stiffness to meet task demands when assessing injury risk. The findings from this study also help explain our earlier findings [11], and show that Lyapunov analyses of kinematic data do capture some relevant information regarding the mechanical effect of spine stiffness (i.e., the amount of stiff ness) as well as the local dynamic stability of these stiffness pro files (among other things). Furthermore, this analysis technique provides important insight into how the body stabilizes motor pat terns and subsequently the muscular contributions to spine rota tional stiffness over time, and also provides an effective method of assessing the fundamental physiological control of muscle force and stiffness (and the resulting effects on spine rotational stiffness), and how these subsequently affect the ability to main tain stable spine kinematics.
Acknowledgment The authors would like to thank Dr. Joan Stevenson for her mentorship and contributions to this research study. Dr. Ryan Graham was funded by a Natural Sciences and Engi neering Research Council (NSERC) of Canada Graduate Scholar ship (CGS-D2) during the completion of this study.
Nomenclature Ax, Ay = origin coordinates with respect to the L4/Ls joint Bx By = initial deflection or insertion coordinates with respect to LJL5 joint dj = divergence of nearest neighbor pairs EMG = electromyography EO = external oblique F = muscle force (N) G = participant specific multiplier 10 = internal oblique i = 3D length of muscle vector that crosses LJLS joint / = length coefficient of muscle (unitless) L = full 3D length of the muscle LD = latissimus dorsi LES = lumbar erector spinae MF = multifidus MVC = maximum voluntary contraction n = number of reconstruction dimensions PCSA = physiological cross sectional area q = stiffness gain relating muscle force to stiffness r = 3D muscle moment aim r = Euclidean norm stiffness RA = rectus abdominus Sz = rotational stiffness about axis z Td = time delay TES = thoracic erector spinae V = raw voltage V = voltage rate of change V = state space /.max = maximum finite-time Lyapunov exponent v = velocity coefficient of muscle (unitless) a = maximum muscle stress (cm2)
Conclusion In conclusion, we found that the local dynamic stability of spine muscle activations and muscular contributions to spine rotational stiffness were significantly and consistently decreased with an increased lifting rate. There was also a trend for reductions in this stability with an increase in lifting load, with the only significant effect for the local dynamic stability of the full trunk system mus cle activation. Thus, in general, the stability of these important variables was reduced as demand was increased. These novel 1 21006-8 / Vol. 136, DECEMBER 2014
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