Lower Local Dynamic Stability and Invariable Orbital Stability in the Activation of Muscle Synergies in Response to Accelerated Walking Speeds

Ali, 1999, On the local stability of limit cycles, Chaos, 9, 348, 10.1063/1.166412

Allen, 2013, The influence of merged muscle excitation modules on post-stroke hemiparetic walking performance, Clin. Biomech., 28, 697, 10.1016/j.clinbiomech.2013.06.003

Allen, 2012, Three-dimensional modular control of human walking, J. Biomech., 45, 2157, 10.1016/j.jbiomech.2012.05.037

Arellano, 2009, The independent effect of added mass on the stability of the sagittal plane leg kinematics during steady-state human walking, J. Exp. Biol., 212, 1965, 10.1242/jeb.026153

Arnold, 2013, How muscle fiber lengths and velocities affect muscle force generation as humans walk and run at different speeds, J. Exp. Biol., 216, 2150, 10.1242/jeb.075697

Balasubramanian, 2007, Relationship between step length asymmetry and walking performance in subjects with chronic hemiparesis, Arch. Phys. Med. Rehabil., 88, 43, 10.1016/j.apmr.2006.10.004

Bruijn, 2011, The validity of stability measures: a modelling approach, J. Biomech., 44, 2401, 10.1016/j.jbiomech.2011.06.031

Bruijn, 2009, Statistical precision and sensitivity of measures of dynamic gait stability, J. Neurosci. Methods, 78, 327, 10.1016/j.jneumeth.2008.12.015

Bus, 2005, A comparison of the 1-step, 2-step, and 3-step protocols for obtaining barefoot plantar pressure data in the diabetic neuropathic foot, Clin. Biomech., 20, 892, 10.1016/j.clinbiomech.2005.05.004

Cappellini, 2006, Motor patterns in human walking and running, J. Neurophysiol., 95, 3426, 10.1152/jn.00081.2006

Cavagna, 1963, External work in walking, J. Appl. Physiol, 18, 1, 10.1152/jappl.1963.18.1.1

Cheung, 2005, Central and sensory contributions to the activation and organization of muscle synergies during natural motor behaviors, J. Neurosci., 25, 6419, 10.1523/JNEUROSCI.4904-04.2005

Chvatal, 2013, Common muscle synergies for balance and walking, Front. Comput. Neurosci., 7, 48, 10.3389/fncom.2013.00048

Clark, 2010, Merging of healthy motor modules predicts reduced locomotor performance and muscle coordination complexity post-stroke, J. Neurophysiol., 103, 844, 10.1152/jn.00825.2009

Correa, 2010, Contributions of individual muscles to hip joint contact force in normal walking, J. Biomech., 43, 1618, 10.1016/j.jbiomech.2010.02.008

d'Avella, 2003, Combinations of muscle synergies in the construction of a natural motor behavior, Nat. Neurosci., 6, 300, 10.1038/nn1010

Den Otter, 2007, Abnormalities in the temporal patterning of lower extremity muscle activity in hemiparetic gait, Gait Posture, 25, 342, 10.1016/j.gaitpost.2006.04.007

Dingwell, 2000, Nonlinear time series analysis of normal and pathological human walking, Chaos, 10, 848, 10.1063/1.1324008

Dingwell, 2007, Differences between local and orbital dynamic stability during human walking, J. Biomech. Eng., 129, 586, 10.1115/1.2746383

Dingwell, 2006, Kinematic variability and local dynamic stability of upper body motions when walking at different speeds, J. Biomech., 39, 444, 10.1016/j.jbiomech.2004.12.014

Doke, 2005, Mechanics and energetics of swinging the human leg, J. Exp. Biol., 208, 439, 10.1242/jeb.01408

England, 2007, The influence of gait speed on local dynamic stability of walking, Gait Posture, 25, 172, 10.1016/j.gaitpost.2006.03.003

Fraser, 1986, Independent coordinates for strange attractors from mutual information, Phys. Rev. A Gen. Phys., 33, 1134, 10.1103/PhysRevA.33.1134

Fukunaga, 2001, In vivo behaviour of human muscle tendon during walking, Proc. Biol. Sci., 268, 229, 10.1098/rspb.2000.1361

Gottschall, 2005, Energy cost and muscular activity required for leg swing during walking, J. Appl. Physiol., 99, 23, 10.1152/japplphysiol.01190.2004

Hagio, 2015, Identification of muscle synergies associated with gait transition in humans, Front. Hum. Neurosci., 9, 48, 10.3389/fnhum.2015.00048

Hagio, 2014, The flexible recruitment of muscle synergies depends on the required force-generating capability, J. Neurophysiol., 112, 316, 10.1152/jn.00109.2014

Hausdorff, 1995, Is walking a random walk? Evidence for long-range correlations in stride interval of human gait, J. Appl. Physiol, 78, 349, 10.1152/jappl.1995.78.1.349

Hoogkamer, 2015, Toward new sensitive measures to evaluate gait stability in focal cerebellar lesion patients, Gait Posture, 41, 592, 10.1016/j.gaitpost.2015.01.004

Huang, 2017, Chaos and bifurcation control of torque- stiffness-controlled dynamic bipedal walking, IEEE Trans. Syst. Man Cybern Syst., 47, 1229, 10.1109/TSMC.2016.2569474

Huang, 2014, Torque–stiffness-controlled dynamic walking with central pattern generators, Biol. Cybern., 108, 803, 10.1007/s00422-014-0625-3

Hurmuzlu, 1994, On the measurement of dynamic stability of human locomotion, J. Biomech. Eng., 116, 30, 10.1115/1.2895701

Ivanenko, 2004, Five basic muscle activation patterns account for muscle activity during human locomotion, J. Physiol., 556, 267, 10.1113/jphysiol.2003.057174

Judge, 1996, Step length reductions in advanced age: the role of ankle and hip kinetics, J. Gerontol. A Biol. Sci. Med. Sci., 51, 303, 10.1093/gerona/51A.6.M303

Kang, 2008, Effects of walking speed, strength and range of motion on gait stability in healthy older adults, J. Biomech., 41, 2899, 10.1016/j.jbiomech.2008.08.002

Kang, 2009, Dynamics and stability of muscle activations during walking in healthy young and older adults, J. Biomech., 42, 2231, 10.1016/j.jbiomech.2009.06.038

Kennel, 1992, Determining embedding dimension for phase-space reconstruction using a geometrical construction, Phys. Rev. A, 45, 3403, 10.1103/PhysRevA.45.3403

Kerrigan, 1998, Biomechanical gait alterations independent of speed in the healthy elderly: evidence for specific limiting impairments, Arch. Phys. Med. Rehabil., 79, 317, 10.1016/S0003-9993(98)90013-2

Kibushi, 2018, Speed-dependent modulation of muscle activity based on muscle synergies during treadmill walking, Front. Hum. Neurosci., 12, 4, 10.3389/fnhum.2018.00004

Kouzaki, 2010, Steadiness in plantar flexor muscles and its relation to postural sway in young and elderly adults, Muscle Nerve, 42, 78, 10.1002/mus.21599

Kubo, 2017, Action direction of muscle synergies in voluntary multi-directional postural control, Front. Hum. Neurosci., 11, 434, 10.3389/fnhum.2017.00434

Kuo, 2002, The relative roles of feedforward and feedback in the control of rhythmic movements, Motor Control, 6, 129, 10.1123/mcj.6.2.129

Kurz, 2010, Attractor divergence as a metric for assessing walking balance, Nonlinear Dynamics Psychol. Life Sci., 14, 151

Labini, 2012, Recurrence quantification analysis of gait in normal and hypovestibular subjects, Gait Posture, 35, 48, 10.1016/j.gaitpost.2011.08.004

Lai, 2015, In vivo behavior of the human soleus muscle with increasing walking and running speeds, J. Appl. Physiol., 118, 1266, 10.1152/japplphysiol.00128.2015

Lee, 1999, Learning the parts of objects by non-negative matrix factorization, Nature, 401, 788, 10.1038/44565

Lelas, 2003, Predicting peak kinematic and kinetic parameters from gait speed, Gait Posture, 17, 106, 10.1016/S0966-6362(02)00060-7

Lichtwark, 2007, Muscle fascicle and series elastic element length changes along the length of the human gastrocnemius during walking and running, J. Biomech., 40, 157, 10.1016/j.jbiomech.2005.10.035

Liu, 2008, Muscle contributions to support and progression over a range of walking speeds, J. Biomech., 41, 3243, 10.1016/j.jbiomech.2008.07.031

Lockhart, 2008, Differentiating fall-prone and healthy adults using local dynamic stability, Ergonomics, 51, 1860, 10.1080/00140130802567079

Mbourou, 2003, Step length variability at gait initiation in elderly fallers and non-fallers, and young adults, Gerontology, 49, 21, 10.1159/000066506

McGowan, 2010, Modular control of human walking: adaptations to altered mechanical demands, J. Biomech., 43, 412, 10.1016/j.jbiomech.2009.10.009

Neptune, 2009, Modular control of human walking: a simulation study, J. Biomech., 42, 1282, 10.1016/j.jbiomech.2009.03.009

Neptune, 2008, The effect of walking speed on muscle function and mechanical energetics, Gait Posture, 28, 135, 10.1016/j.gaitpost.2007.11.004

Neumann, 2002, Kinesiology of the Musculoskeletal System: Foundation for Physical Rehabilitation

Nishida, 2017, Comparison of muscle synergies for running between different foot strike patterns, PLoS ONE, 12, e0171535, 10.1371/journal.pone.0171535

Oliveira, 2013, Fast changes in direction during human locomotion are executed by impulsive activation of motor modules, Neuroscience, 228, 283, 10.1016/j.neuroscience.2012.10.027

Pires, 2014, Joint-level mechanics of the walk-to-run transition in humans, J. Exp. Biol., 217, 3519, 10.1242/jeb.107599

Prilutsky, 2001, Swing-and support-related muscle actions differentially trigger human walk–run and run–walk transitions, J. Exp. Biol., 204, 2277, 10.1242/jeb.204.13.2277

Rosenstein, 1993, A practical method for calculating largest Lyapunov exponents from small data sets, Phys. D, 65, 117, 10.1016/0167-2789(93)90009-P

Santuz, 2018, Challenging human locomotion: stability and modular organisation in unsteady conditions, Sci. Rep., 8, 2740, 10.1038/s41598-018-21018-4

Sawers, 2015, Long-term training modifies the modular structure and organization of walking balance control, J. Neurophysiol., 114, 3359, 10.1152/jn.00758.2015

Schmitz, 2009, Differences in lower-extremity muscular activation during walking between healthy older and young adults, J. Electromyogr. Kinesiol., 19, 1085, 10.1016/j.jelekin.2008.10.008

Sinitksi, 2012, Effects of perturbation magnitude on dynamic stability when walking in destabilizing environments, J. Biomech., 45, 2084, 10.1016/j.jbiomech.2012.05.039

Srinivasan, 2006, Computer optimization of a minimal biped model discovers walking and running, Nature, 439, 72, 10.1038/nature04113

Steele, 2015, Muscle synergies and complexity of neuromuscular control during gait in cerebral palsy, Dev. Med. Child. Neurol., 57, 1176, 10.1111/dmcn.12826

Su, 2007, Dynamic stability of passive dynamic walking on an irregular surface, J. Biomech. Eng., 129, 802, 10.1115/1.2800760

Takens, 1981, Dynamical systems and turbulence, Lecture Notes in Mathematics, 366

Torres-Oviedo, 2006, Muscle synergy organization is robust across a variety of postural perturbations, J. Neurophysiol., 96, 1530, 10.1152/jn.00810.2005

Torres-Oviedo, 2007, Muscle synergies characterizing human postural responses, J. Neurophysiol., 98, 2144, 10.1152/jn.01360.2006

Tresch, 1999, The construction of movement by the spinal cord, Nat. Neurosci., 2, 162, 10.1038/5721

van Schooten, 2013, Assessing gait stability: the influence of state space reconstruction on inter-and intra-day reliability of local dynamic stability during over-ground walking, J. Biomech., 46, 137, 10.1016/j.jbiomech.2012.10.032

Warren, 2004, Temporal patterns of plantar pressures and lower-leg muscle activity during walking: effect of speed, Gait Posture, 19, 91, 10.1016/S0966-6362(03)00031-6

Winter, 1987, The Biomechanics and Motor Control of Human Gait

Yokoyama, 2016, Distinct sets of locomotor modules control the speed and modes of human locomotion, Sci. Rep., 6, 36275, 10.1038/srep36275

Zelik, 2014, Can modular strategies simplify neural control of multidirectional human locomotion?, J. Neurophysiol., 111, 1686, 10.1152/jn.00776.2013