Research Papers

Simulated Tremor Propagation in the Upper Limb: From Muscle Activity to Joint Displacement

[+] Author and Article Information
Thomas H. Corie

Mechanical Engineering,
350 EB,
Provo, UT 84602

Steven K. Charles

Mechanical Engineering and Neuroscience,
Brigham Young University,
350 EB,
Provo, UT 84602
e-mail: skcharles@byu.edu

1Corresponding author.

Manuscript received May 7, 2018; final manuscript received April 1, 2019; published online May 6, 2019. Assoc. Editor: Eric A. Kennedy.

J Biomech Eng 141(8), 081001 (May 06, 2019) (17 pages) Paper No: BIO-18-1221; doi: 10.1115/1.4043442 History: Received May 07, 2018; Revised April 01, 2019

Although tremor is the most common movement disorder, there are few noninvasive treatment options. Creating effective tremor suppression devices requires a knowledge of where tremor originates mechanically (which muscles) and how it propagates through the limb (to which degrees-of-freedom (DOF)). To simulate tremor propagation, we created a simple model of the upper limb, with tremorogenic activity in the 15 major superficial muscles as inputs and tremulous joint displacement in the seven major DOF as outputs. The model approximated the muscle excitation–contraction dynamics, musculoskeletal geometry, and mechanical impedance of the limb. From our simulations, we determined fundamental principles for tremor propagation: (1) The distribution of tremor depends strongly on musculoskeletal dynamics. (2) The spreading of tremor is due to inertial coupling (primarily) and musculoskeletal geometry (secondarily). (3) Tremorogenic activity in a given muscle causes significant tremor in only a small subset of DOF, though these affected DOF may be distant from the muscle. (4) Assuming uniform distribution of tremorogenic activity among muscles, tremor increases proximal-distally, and the contribution from muscles increases proximal-distally. (5) Although adding inertia (e.g., with weighted utensils) is often used to suppress tremor, it is possible to increase tremor by adding inertia to the wrong DOF. (6) Similarly, adding viscoelasticity to the wrong DOF can increase tremor. Based solely on the musculoskeletal system, these principles indicate that tremor treatments targeting muscles should focus first on the distal muscles, and devices targeting DOF should focus first on the distal DOF.

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Bhatia, K. P. , Bain, P. , Bajaj, N. , Elble, R. J. , Hallett, M. , Louis, E. D. , Raethjen, J. , Stamelou, M. , Testa, C. M. , and Deuschl, G. , 2018, “ Consensus Statement on the Classification of Tremors. From the Task Force on Tremor of the International Parkinson and Movement Disorder Society,” Mov. Disord., 33(1), pp. 75–87. [CrossRef] [PubMed]
Anouti, A. , and Koller, W. C. , 1995, “ Tremor Disorders. Diagnosis and Management,” West. J. Med., 162(6), pp. 510–513. [PubMed]
Gallego, J. Á. , Rocon, E. , Belda-Lois, J. M. , and Pons, J. L. , 2013, “ A Neuroprosthesis for Tremor Management Through the Control of Muscle Co-Contraction,” J. NeuroEng. Rehabil., 10(1), p. 36. [CrossRef] [PubMed]
Deuschl, G. , Bain, P. , and Brin, M. , 2008, “ Consensus Statement of the Movement Disorder Society on Tremor,” Mov. Disord., 13(S3), pp. 2–23. [CrossRef]
Louis, E. D. , and Ferreira, J. J. , 2010, “ How Common Is the Most Common Adult Movement Disorder? Update on the Worldwide Prevalence of Essential Tremor,” Mov. Disord., 25(5), pp. 534–541. [CrossRef] [PubMed]
Louis, E. D. , and Ottman, R. , 2014, “ How Many People in the USA Have Essential Tremor?, Deriving a Population Estimate Based Epidemiological Data,” Tremor Other Hyperkinetic Mov., 4, p. 259.
Koller, W. , Biary, N. , and Cone, S. , 1986, “ Disability in Essential Tremor: Effect of Treatment,“ (in Eng),” Neurology, 36(7), pp. 1001–1004. [CrossRef] [PubMed]
Tröster, A. I. , Pahwa, R. , Fields, J. A. , Tanner, C. M. , and Lyons, K. E. , 2005, “ Quality of Life in Essential Tremor Questionnaire (QUEST): Development and Initial Validation,” Parkinsonism Relat. Disord., 11(6), pp. 367–373. [CrossRef] [PubMed]
Louis, E. D. , Rohl, B. , and Rice, C. , 2015, “ Defining the Treatment Gap: What Essential Tremor Patients Want That They Are Not Getting,” Tremor Other Hyperkinetic Mov., 5, p. 331.
Zesiewicz, T. A. , Elble, R. , Louis, E. D. , Hauser, R. A. , Sullivan, K. L. , Dewey, R. B. , Ondo, W. G. , Gronseth, G. S. , and Weiner, W. J. , and., 2005, “ Practice Parameter: Therapies for Essential Tremor,” Neurology, 64(12), pp. 2008–2020. [CrossRef] [PubMed]
Deuschl, G. , Raethjen, J. , Hellriegel, H. , and Elble, R. , 2011, “ Treatment of Patients With Essential Tremor,” Lancet Neurol., 10(2), pp. 148–161. [CrossRef] [PubMed]
Louis, E. D. , Rios, E. , and Henchcliffe, C. , 2010, “ How Are We Doing With the Treatment of Essential Tremor (ET)?, Persistence ET Patients Medication: Data From 528 Patients Three Settings,” Eur. J. Neurol., 17(6), pp. 882–884. [CrossRef] [PubMed]
Diaz, N. L. , and Louis, E. D. , 2010, “ Survey of Medication Usage Patterns Among Essential Tremor Patients: Movement Disorder Specialists vs. general Neurologists,” Parkinsonism Relat. Disord., 16(9), pp. 604–607. [CrossRef] [PubMed]
Schneider, S. A. , and Deuschl, G. , 2014, “ The Treatment of Tremor,” Neurotherapeutics, 11(1), pp. 128–138. [CrossRef] [PubMed]
Flora, E. D. , Perera, C. L. , Cameron, A. L. , and Maddern, G. J. , 2010, “ Deep Brain Stimulation for Essential Tremor: A Systematic Review,” Mov. Disord., 25(11), pp. 1550–1559. [CrossRef] [PubMed]
Wharen, R. E. , Okun, M. S. , Guthrie, B. L. , Uitti, R. J. , Larson, P. , Foote, K. , Walker, H. , Marshall, F. J. , Schwalb, J. , Ford, B. , Jankovic, J. , Simpson, R. , Dashtipour, K. , Phibbs, F. , Neimat, J. S. , Stewart, R. M. , Peichel, D. , Pahwa, R. , Ostrem, J. L. , and SJM DBS ET Study Group, 2017, “ Thalamic DBS With a Constant-Current Device in Essential Tremor: A Controlled Clinical Trial,” Parkinsonism Relat. Disord., 40, pp. 18–26. [PubMed]
Dembek, T. A. , Barbe, M. T. , Åström, M. , Hoevels, M. , Visser-Vandewalle, V. , Fink, G. R. , and Timmermann, L. , 2017, “ Probabilistic Mapping of Deep Brain Stimulation Effects in Essential Tremor,” NeuroImage: Clin., 13, pp. 164–173. [CrossRef] [PubMed]
Pahwa, R. , Lyons, K. E. , Wilkinson, S. B. , Simpson, R. K. , Ondo, W. G. , Tarsy, D. , Norregaard, T. , Hubble, J. P. , Smith, D. A. , Hauser, R. A. , and Jankovic, J. , 2006, “ Long-Term Evaluation of Deep Brain Stimulation of the Thalamus,” J. Neurosurg., 104(4), pp. 506–512. [CrossRef] [PubMed]
Ramirez-Zamora, A. , Boggs, H. , and Pilitsis, J. G. , 2016, “ Reduction in DBS Frequency Improves Balance Difficulties After Thalamic DBS for Essential Tremor,” J. Neurol. Sci., 367, pp. 122–127. [CrossRef] [PubMed]
Blomstedt, P. , and Hariz, M. I. , 2006, “ Are Complications Less Common in Deep Brain Stimulation Than in Ablative Procedures for Movement Disorders?,” Stereotactic Funct. Neurosurg., 84(2–3), pp. 72–81. [CrossRef]
Shih, L. C. , LaFaver, K. , Lim, C. , Papavassiliou, E. , and Tarsy, D. , 2013, “ Loss of Benefit in VIM Thalamic Deep Brain Stimulation (DBS) for Essential Tremor (ET): How Prevalent Is It?,” Parkinsonism Relat. Disord., 19(7), pp. 676–679. [CrossRef] [PubMed]
Sydow, O. , Thobois, S. , Alesch, F. , and Speelman, J. D. , 2003, “ Multicentre European Study of Thalamic Stimulation in Essential Tremor: A Six Year Follow Up,” J. Neurol., Neurosurg., Psychiatry, 74(10), pp. 1387–1391. [CrossRef]
Baizabal-Carvallo, J. F. , Kagnoff, M. N. , Jimenez-Shahed, J. , Fekete, R. , and Jankovic, J. , 2014, “ The Safety and Efficacy of Thalamic Deep Brain Stimulation in Essential Tremor: 10 Years and Beyond,” J. Neurol., Neurosurg. Psychiatry, 85(5), pp. 567–572. [CrossRef]
Kestenbaum, M. , Ford, B. , and Louis, E. D. , 2015, “ Estimating the Proportion of Essential Tremor and Parkinson's Disease Patients Undergoing Deep Brain Stimulation Surgery: Five‐Year Data From Columbia University Medical Center (2009–2014),” Mov. Disord. Clin. Pract., 2(4), pp. 384–387. [CrossRef] [PubMed]
Davidson, A. D. , and Charles, S. K. , 2017, “ Fundamental Principles of Tremor Propagation in the Upper Limb,” Ann. Biomed. Eng., 45(4), pp. 1133–1147. [CrossRef] [PubMed]
Samotus, O. , Rahimi, F. , Lee, J. , and Jog, M. , 2016, “ Functional Ability Improved in Essential Tremor by IncobotulinumtoxinA Injections Using Kinematically Determined Biomechanical Patterns—A New Future,” PLoS One, 11(4), p. e0153739. [CrossRef] [PubMed]
Samotus, O. , Lee, J. , and Jog, M. , 2017, “ Long-Term Tremor Therapy for Parkinson and Essential Tremor With Sensor-Guided Botulinum Toxin Type a Injections,” PLoS One, 12(6), p. e0178670. [CrossRef] [PubMed]
Dosen, S. , Muceli, S. , Dideriksen, J. L. , Romero, J. P. , Rocon, E. , Pons, J. , and Farina, D. , 2015, “ Online Tremor Suppression Using Electromyography and Low-Level Electrical Stimulation,” IEEE Trans. Neural Syst. Rehabil. Eng., 23(3), pp. 385–395. [CrossRef] [PubMed]
Freeman, C. T. , Sampson, P. , Burridge, J. H. , and Hughes, A. M. , 2015, “ Repetitive Control of Functional Electrical Stimulation for Induced Tremor Suppression,” Mechatronics, 32, pp. 79–87 (in English). [CrossRef]
Manesk, L. P. , Jorgovanović, N. , Ilić, V. , Došen, S. , Keller, T. , and Popović, M. B. , 2011, “ Electrical Stimulation for the Suppression of Pathological Tremor,” Medical Biol. Eng. Comput., 49(10), pp. 1187–1193 (in English). [CrossRef]
Prochazka, A. , Elek, J. , and Javidan, M. , 1992, “ Attenuation of Pathological Tremors by Functional Electrical-Stimulation—1: Method,” Ann. Biomed. Eng., 20(2), pp. 205–224. [CrossRef] [PubMed]
Winter, D. A. , 2009, Biomechanics and Motor Control of Human Movement, Wiley, Hoboken, NJ.
Burdet, E. , 2013, Human Robotics, The MIT Press, Cambridge, MA.
Haruno, M. , and Wolpert, D. M. , 2005, “ Optimal Control of Redundant Muscles in Step-Tracking Wrist Movements,” J. Neurophysiol., 94(6), pp. 4244–4255. [CrossRef] [PubMed]
Saul, K. R. , Hu, X. , Goehler, C. M. , Vidt, M. E. , Daly, M. , Velisar, A. , and Murray, W. M. , 2015, “ Benchmarking of Dynamic Simulation Predictions in Two Software Platforms Using an Upper Limb Musculoskeletal Model,” Comput. Methods Biomech. Biomed. Eng., 18(13), pp. 1445–1458. [CrossRef]
Holzbaur, K. R. S. , Murray, W. M. , Gold, G. E. , and Delp, S. L. , 2007, “ Upper Limb Muscle Volumes in Adult Subjects,” J. Biomech., 40(4), pp. 742–749. [CrossRef] [PubMed]
Holzbaur, K. R. , Delp, S. L. , Gold, G. E. , and Murray, W. M. , 2007, “ Moment-Generating Capacity of Upper Limb Muscles in Healthy Adults,” J. Biomech., 40(11), pp. 2442–2449. [CrossRef] [PubMed]
Holzbaur, K. R. S. , Murray, W. M. , and Delp, S. L. , 2005, “ A Model of the Upper Extremity for Simulating Musculoskeletal Surgery and Analyzing Neuromuscular Control,” Ann. Biomed. Eng., 33(6), pp. 829–840. [CrossRef] [PubMed]
Wu, G. , van der Helm, F. C. T. , (DirkJan) Veeger, H. E. J. , Makhsous, M. , Van Roy, P. , Anglin, C. , Nagels, J. , Karduna, A. R. , McQuade, K. , Wang, X. , Werner, F. W. , and Buchholz, B. , 2005, “ ISB Recommendation on Definitions of Joint Coordinate Systems of Various Joints for the Reporting of Human Joint Motion—Part II: Shoulder, Elbow, Wrist and Hand,” J. Biomech., 38(5), pp. 981–992. [CrossRef] [PubMed]
Formica, D. , Charles, S. K. , Zollo, L. , Guglielmelli, E. , Hogan, N. , and Krebs, H. I. , 2012, “ The Passive Stiffness of the Wrist and Forearm,” J. Neurophysiol., 108(4), pp. 1158–1166. [CrossRef] [PubMed]
Drake, W. B. , and Charles, S. K. , 2014, “ Passive Stiffness of Coupled Wrist and Forearm Rotations,” Ann. Biomed. Eng., 42(9), pp. 1853–1866. [CrossRef] [PubMed]
Pando, A. L. , Lee, H. , Drake, W. B. , Hogan, N. , and Charles, S. K. , 2014, “ Position-Dependent Characterization of Passive Wrist Stiffness,” IEEE Trans. Bio-Med. Eng., 61(8), pp. 2235–2244 (in English). [CrossRef]
de Leva, P. , 1996, “ Adjustments to Zatsiorsky-Seluyanov's Segment Inertia Parameters,” J. Biomech., 29(9), pp. 1223–1230. [CrossRef] [PubMed]
Corke, P. , 2017, Robotics, Vision and Control: Fundamental Algorithms in MATLAB® Second, Completely Revised, Extended and Updated Edition, Springer International Publishing, Berlin.
Matsumoto, Y. , Seki, M. , Ando, T. , Kobayashi, Y. , Iijima, H. , Nagaoka, M. , and Fujie, G. M. , 2012, “ Analysis of EMG Signals of Patients With Essential Tremor Focusing on the Change of Tremor Frequency,” Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), San Diego, CA, Aug. 28–Sept. 1, pp. 2244–2250.
He, F. , Sarrigiannis, P. G. , Billings, S. A. , Wei, H. , Rowe, J. , Romanowski, C. , Hoggard, N. , Hadjivassilliou, M. , Rao, D. G. , Grünewald, R. , Khan, A. , and Yianni, J. , 2016, “ Nonlinear Interactions in the Thalamocortical Loop in Essential Tremor: A Model-Based Frequency Domain Analysis,” Neuroscience, 324, pp. 377–389. [CrossRef] [PubMed]
Grimaldi, G. , and Manto, M. , 2008, “ Tremor: From Pathogenesis to Treatment,” Synth. Lectures Biomed. Eng., 3(1), pp. 1–212. [CrossRef]
Nisticò, R. , Pirritano, D. , Salsone, M. , Novellino, F. , Del Giudice, F. , Morelli, M. , Trotta, M. , Bilotti, M. , Condino, F. , Cherubini, A. , Valentino, P. , and Quattrone, A. , 2011, “ Synchronous Pattern Distinguishes Resting Tremor Associated With Essential Tremor From Rest Tremor of Parkinson's Disease,” Parkinsonism Relat. Disord., 17(1), pp. 30–33. [CrossRef] [PubMed]
Milanov, I. , 2001, “ Electromyographic Differentiation of Tremors,” Clin. Neurophysiol., 112(9), pp. 1626–1632. [CrossRef] [PubMed]
Palm, W. J. , 2014, System Dynamics, 3rd ed., McGraw-Hill, New York.
Matsumoto, Y. , Seki, M. , Nakashima, Y. , Ando, T. , Kobayashi, Y. , Iijima, H. , Nagaoka, M. , and Masakatsu, G. , 2017, “ Algorithm to Demodulate an Electromyogram Signal Modulated by Essential Tremor,” Robomech J., 4(1), p. 15. [CrossRef]
Parkinson, M. , 2014, “ Anthropometric Data Explorer,” Penn State University Open Design Lab, State College, PA, accessed Feb. 18, 2014, http://tools.openlab.psu.edu/tools/explorer.php
Gallego, J. A. , Dideriksen, J. L. , Holobar, A. , Ibanez, J. , Glaser, V. , Romero, J. P. , Benito-Leon, J. , Pons, J. L. , Rocon, E. , and Farina, D. , 2015, “ The Phase Difference Between Neural Drives to Antagonist Muscles in Essential Tremor Is Associated With the Relative Strength of Supraspinal and Afferent Input,” J. Neurosci., 35(23), pp. 8925–8937. [CrossRef] [PubMed]
Britton, T. C. , Thompson, P. D. , Day, B. L. , Rothwell, J. C. , Findley, L. J. , and Marsden, C. D. , 1994, “ Rapid Wrist Movements in Patients With Essential Tremor. The Critical Role of the Second Agonist Burst,” Brain: J. Neurol., 117(1), pp. 39–47. [CrossRef]
Pedrosa, D. J. , Quatuor, E.-L. , Reck, C. , Pauls, K. A. M. , Huber, C. A. , Visser-Vandewalle, V. , and Timmermann, L. , 2014, “ Thalamomuscular Coherence in Essential Tremor: Hen or Egg in the Emergence of Tremor?,” J. Neurosci., 34(43), p. 14475. [CrossRef] [PubMed]
Dideriksen, J. L. , Enoka, R. M. , and Farina, D. , 2011, “ A Model of the Surface Electromyogram in Pathological Tremor,” IEEE Trans. Biomed. Eng., 58(8), pp. 2178–2185. [CrossRef]
Belda-Lois, J. M. , Martinez-Reyero, A. I. , Castillo, A. , Rocon, E. , Pons, J. L. , Loureiro, R. , Manto, M. , Normie, L. , and Soede, M. , 2007, “ Controllable Mechanical Tremor Reduction.Assessment of Two Orthoses,” Technol. Disability, 19(4), pp. 169–178.
Rocon, E. , Belda-Lois, J. M. , Ruiz, A. F. , Manto, M. , Moreno, J. C. , and Pons, J. L. , 2007, “ Design and Validation of a Rehabilitation Robotic Exoskeleton for Tremor Assessment and Suppression,” IEEE Trans. Neural Syst. Rehabil. Eng., 15(3), pp. 367–378. [CrossRef] [PubMed]
Baruh, H. , 2014, Applied Dynamics, CRC Press, Boca Raton, FL.


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Fig. 1

Model of upper limb neuromusculoskeletal dynamics used to simulate tremor propagation. The excitation-contraction dynamics of muscle low-pass filters muscle activity into muscle force; the musculoskeletal geometry of the limb mixes force from various muscles into joint torques; and the mechanical impedance filters and mixes joint torques, resulting in joint displacement. t1 and t2 are time constants representing the dynamics of muscle excitation and contraction, respectively; C is the gain between muscle activity and muscle force; M is a matrix of moment arms; I, D, and K are matrices representing the coupled joint inertia, damping, and stiffness, respectively.

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Fig. 2

Methodological details. (a) input muscle activity was approximated by triangular waves, based on experimentally observed sEMG in tremor patients. Shown are detrended, rectified, and low-pass filtered sEMG signals from pectoralis major (solid gray) and lateral deltoid (dashed gray) muscles from a subject with severe tremor, compared to triangular waves (black), (b) Magnitude ratio of first submodel (excitation–contraction dynamics, with default values and C=1), along with the Fourier transforms of the input signal, u (5 Hz triangle wave of width 110 ms), and the output, f, (c) The dynamics of the first submodel (muscle excitation–contraction dynamics) are illustrated by the submodel's impulse response, which represents a muscle twitch (simulated using default values and C=1), (d) Postures included in our simulation. Posture 1 is the default posture. Postures 2–4 were used in the sensitivity analysis. Posture 2: hand in front of mouth, representing feeding and grooming activities; Posture 3: hand in workspace in front of abdomen, representing many activities of daily living; and Posture 4: arm somewhat outstretched, representing reaching. Joint angles for each posture are given in Ref. [25].

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Fig. 3

Progression through the model, from input in a single muscle (triceps longus; 5 Hz triangle wave with of width 110 ms) to muscle force in that same muscle, joint torque in the DOF crossed by that muscle, and joint displacement in all DOFs (DOF colors indicated at the bottom of the figure). Both the transient and steady-state responses are visible.

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Fig. 4

Impulse responses of all 105 input–output relationships, organized into subplots by input muscle (listed in each subplot) and color-coded by output DOF (color code listed below figure)

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Fig. 5

Settling times of the impulse responses of the 105 input–output relationships shown in Fig. 4, showing the trend that settling times decrease proximal-distally for both inputs (muscles) and outputs (DOF). The settling time was defined as the time required for the impulse response to remain within 2% of its steady-state value.

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Fig. 6

Magnitude ratios of all 105 input–output relationships in the tremor band (4–12 Hz), organized by input muscle (listed in each subplot) and color coded by output DOF (color code listed below figure). The units of the magnitude ratio are the units of the output displacement (rad) divided by the units of the input muscle activity (arbitrary units).

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Fig. 7

Phasor plot of the frequency response at 8 Hz (middle of the tremor band), grouped by output DOF (listed above each subplot) and color coded by input muscle. The numeric value on each subplot indicates the radius of the outer circle (in rad/a.u.; see caption of Fig. 6).

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Fig. 8

Magnitude ratios for all 105 input–output relationships at 8 Hz (middle of tremor band), showing that the distal DOFs exhibit the most tremor, and that most of this tremor comes from the distal muscles (and, for FPS, from the biceps muscles). This trend was largely consistent throughout the tremor band. The last column shows the mean magnitude ratio for each row. The units of the magnitude ratio are rad/a.u. (see caption of Fig. 6).

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Fig. 9

Coupling analysis. Each subplot shows the magnitude ratio at 8 Hz (middle of tremor band) for a given input muscle (listed in each subplot), listed by output DOF (horizontal axis) for the default model (solid blue circles), a model with coupling due to inertia but not moment arms (I, empty red circles), and a model with coupling due to moment arms but not inertia (M, empty yellow circles). For the majority of input–output cases, spreading due to inertia only (red) is more similar to the full model than spreading due to moment arms only (yellow), indicating that inertia spreads tremor more than musculoskeletal geometry (i.e., moment arms). The units of the magnitude ratio are rad/a.u. (see caption of Fig. 6).

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Fig. 10

Results of sensitivity analysis: (a) Effect of varying muscle time constants t1 and t2, (b) effect of changing moment arms from default model (50th percentile male) to 10th or 90th percentile male. The line of the 10th percentile male is nearly indistinguishable from the 50th percentile male. (c) Changes to total summed magnitude ratio at 8 Hz for each DOF for different postures. The units of the magnitude ratio are rad/a.u. (see caption of Fig. 6).



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