Computational Models of Populations of Motor Neurons

Jakob L. Dideriksen and Dario Farina

Department of Neurorehabiliation Engineering, Bernstein Focus Neurotechnology Göttingen,

Bernstein Center for Computational Neuroscience, Universitätsmedizin Göttingen, Göttingen, Germany

1 OBJECTIVES

In this paper, we will provide examples of how

computational models of motor neuron and muscle

activity can support basic and applied research on

human movement. Both examples focus on

pathological tremor. Tremor is a rhythmic,

involuntary oscillation of a limb and it is the most

prevalent movement disorder, symptomatic to e.g.

Parkinson’s Disease (Wenning et al., 2005). Tremor

implies a serious worsening of the quality of life,

also because the effect of the current treatments is

variable(Rascol et al., 2000).

First, we show how models can be applied in the

development of a rehabilitation device for

suppressing pathological tremor (Objective 1). The

proposed tremor rehabilitation system relied on

modulation of spinal neuron excitability of the

tremorogenic motor neurons using homonymous

excitation and reciprocal inhibition evoked by

electrical stimulation of peripheral type Ia nerves.

Successful implementation of this strategy implied

robust and precise on-line analysis of tremor

(Objective 1A) and stimulation parameter selection

(Objective 1B). Here, the Iterated Hilbert Transform

(IHT) applied to the surface EMG signals were

selected for tremor analysis (Dideriksen et al.,

2011).

Next, we demonstrate how models can enhance

the understanding of the underlying physiological

mechanisms of tremor (Objective 2), especially

aspects that cannotbe easily assessed experimentally.

Specifically, here we will address the contribution of

afferent feedback in tremor, which has been debated

in the literature (Rack and Ross 1986).

2 METHODS

The neuromechanical models applied to address the

two objectives consisted of a number of sub-models

and shared the same basic structure; however, the

level of model complexity required for addressing

each of the objectives determined how the various

sub-models were implemented.

2.1 Neuromechanical Models

The model was designed to reflect the characteristics

of an antagonist muscle pair acting on one limb in

one degree of freedom and consisted of a number of

sub-models interacting via one or more variables.

First, the activity of the motor neuron population

(spike trains) was determined based on the synaptic

input it received. Each motor neuron innervated a set

of muscle fibers (the motor unit). Each motor unit

was assigned a set of parameters describing its

contractile properties. Along with these properties,

the discharge rate determined the motor unit force.

The force of the muscles (the sum of the force

generated by all motor units) evoked the movement

of the limb. Proprioceptive activity was determined

by limb dynamics (muscle spindle; type Ia) and

muscle forces (Golgi tendon organs; type Ib) and

provided afferent feedback to the motor neurons.

Tremor was simulated by imposing a sine wave to

the motor neuron input.

For Objective 1A, a model of the motor unit

population and the force it generates was adopted

(Fuglevand et al., 1993), while the afferent feedback

was simulated as compound signals (Prochazka and

Gorassini, 1998). A model of the surface motor unit

action potentials(Farina et al., 2004) was used to

simulate the surfaceEMG signal (based on the motor

unit spike trains), that was used for tremor

estimation. For Objective 1B and 2 a more detailed

description of the single neuron behaviour (Cisi and

Kohn, 2008), a more advanced mechanical model

(Oguztoreli and Stein, 1982), as well as models

allowing the afferent feedback to be described as

spike trains (Mileusnic and Loeb, 2006) were

applied. In this way, simulation of axon action

potentials generated by surface stimulation was

made possible.

L. Dideriksen J. and Farina D..

Computational Models of Populations of Motor Neurons.

 2013 SCITEPRESS (Science and Technology Publications, Lda.)

2.1.1 Model Validation

The validation for the model used for Objective 1A

relied on its ability to generate patterns of motor unit

spike trains, as observed in tremor. The key feature

for Objectives 1B and 2 were the capability of the

model to reflect the true spinal connectivity. For this

reason, experimentally used protocols for H-reflex

recruitment curves and estimation of reciprocal

inhibition strength were simulated.

2.1.2 Simulations

For Objective 1Athe surface EMG signal was

simulated in a variety of conditions, including

different contraction levels (0-20% MVC), tremor

frequencies (4-12 Hz), and tremor intensities.

Tremor identification was assessed by comparison

with the imposed neural oscillations. For Objective

1B stimulation amplitude, frequency, and timing

were varied. Tremor suppression was evaluated by

the integral power of the limb movement spectrum

with and without stimulation. For Objective 2,

simulations were carried out with and without

afferent feedback and the power spectra of the

neural drive in each situation were compared.

3 RESULTS

The motor unit inter-spike interval histograms in

simulated tremor were in agreement to those

experimentally observed previously (Christakos et

al., 2009) and the simulated H-reflex recruitment

curves and the strength of the reciprocal inhibition

were comparable to previous experimental results

(Wargon et al., 2006) (not shown).

3.1 Tremor Identification

Figure 1 shows an example of the simulated surface

EMG signal during an 8-Hz tremor. Furthermore,

the oscillations imposed on the motor neuron

population (Figure 1B, black line) are shown,

superimposed with the estimation of the

tremorogenic input signal obtained from the surface

EMG using the IHT algorithm. The two signals were

similar, except the delay, caused by the delays of the

nervous system. Across all simulated conditions, the

estimation of the tremor amplitude was correlated

with the imposed amplitude (r

=0.52), and the

RMSE in estimation of frequency was 2.6 Hz,

mostly due to errors at high frequencies in

conditions with low tremor. This efficiency was

maintained in windows down to 500 ms, showing

the capability of the algorithm to drive tremor

suppression on-line (Dideriksen et al., 2011).

Figure 1: Simulated surface EMG (A) and imposed and

estimated tremor (black, grey respectively; B).

Figure 2: Simulated tremor with and without afferent

stimulation (grey box; A). Power spectrum (B) indicates

tremor suppression (grey line).

3.2 Tremor Suppression

Figure 2 depictsthe simulated tremor suppression

approach applied in a 2-s window during 5-Hz

tremor. The tremor amplitude was decreased by

63%, as also shown in the power spectrum

represented in the lower panel. The optimal

suppression was obtained at 60 Hz stimulation at an

intensity recruiting 22% of all Ia axons and no motor

neuron axons. Stimulation efficiency was highly

sensitive to the timing of the stimulation bursts with

respect to the imposed oscillations. Optimally a 15-

ms delay should be used, while deviations of more

than 25 ms involved tremor amplification, implying

the need for accurate tremor estimation algorithms.

3.3 Afferent Contribution to Tremor

Figure 3 shows the power spectra of the motor

neuron population output in simulations performed

with and without afferent feedback. At 6 Hz, the

afferent feedback enhanced the oscillations by up to

80%, while afferent feedback reduced tremor at 2 Hz

by 40%. This difference can be explained by the

neural delays. At low frequencies, the afferent

feedback arrives at the motor neuron almost exactly

out of phase with the imposed oscillations, and vice

versa at higher frequencies, due to faster

contractions. This observation may explain the

common occurrence of tremor in the 4-6 Hz range.

Figure 3: Power spectra of neural drive in simulations with

(grey) and without (black) afferent feedback with 6 Hz (A)

and 2 Hz (B) imposed.

4 DISCUSSION

Two examples of applications of neuromechanical

models were given, each highlighting different

advantages of using simulations to support

experimental tests. The first example demonstrated

how models can be applied to test the robustness of

rehabilitation techniques when experimental data is

sparse and when full parameter sensitivity analysis

in patients is not feasible. Last, the sensitivity of

internal physiological parameters on the motor

output was assessed, for neuromuscular properties

that cannot be measured experimentally.

ACKNOWLEDGEMENTS

This work was supported by the EU project

NEUROTREMOR (contract FP7-ICT-2011-7-

287739)

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