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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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Figures

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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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