Discussion

The main findings o f the study were that voluntary isometric contractions are

characterised by the presence o f signal dependent noise (SDN) that has a relatively

constant CV over a wide range o f force output. This noise is not a result o f peripheral

neuromuscular noise as it was not present in the NMES condition. Instead the structure

o f the SDN is a characteristic o f the process of graded voluntary contractions, whether

those occur in isolation or on top of an NMES induced contraction. This feature o f SDN

in isometric contractions was captured in a model o f the motor-unit pool where it was

found that the presence o f SDN depended on the range o f motor-unit forces, the

distribution o f recruitment thresholds and orderly recruitment. The magnitude o f the

noise was closely correlated with the variability in the discharge o f motor neurons, but

this variability in and o f itself did not generate the SDN.

Voluntary contractions and force variability

The relationship between motor-output variability and the magnitude o f the

force output has been previously investigated for both discrete and continuous force

production protocols (Schmidt et al., 1979; Enoka et al., 1999; Slifkin and Newell,

The sources of signal dependent noise during isometric force production: Discussion

output increased monotonically with an increase in mean force output, similar to what

we have reported here. None o f these previous studies were particularly concerned with

the exact structure o f SDN as it relates to the optimisation of motor planning.

It has been previously shown that the increased variability in force that

accompanies aging is likely due to an increased variability in the discharge rates o f

motor neurons (Laidlaw et al., 2000). These authors also showed that elderly subjects

had a higher frequency o f double discharges that would also increase the force

variability. While we did not examine the effects o f double discharges, it was clear

from our modelling results that the variability o f motor neuron ISIs had a strong effect

on the magnitude o f the variability at a given force level without affecting the

underlying structure o f the SDN (Fig 6B). Thus our results support their conclusion that

an increase in the variability o f motor neuron ISIs will give rise to an increase in force

output variability.

These authors also pointed out that isometric contractions o f the first dorsal

interosseus are characterised by a coefficient o f variation (CV) that is higher for lower

forces before reaching a plateau o f about 0.02 - 0.05 at a contraction level of 10% MVC

(Enoka et al., 1999; Laidlaw et al., 2000). There was some evidence for a similar

monotonically decreasing CV in our experimental data, however we did not sample the

forces below a target value o f 20% MVC and thus cannot comment further. However,

the modelling results presented in Fig 5D can be directly compared to the previous

experimental evidence for an initially high CV that decreases to a plateau. This feature

o f the CV was particularly susceptible to changes in recruitment order, so while in the

control condition with orderly recruitment there was some evidence for a decreasing

CV, this became particularly evident in the random and reversed recruitment schemes.

The sources of signal dependent noise during isometric force production: Discussion

give rise to the enhancement o f CV at low force levels in old subjects (Laidlaw et ah,

2000).

Another factor affecting the overall magnitude o f force variability at a given

mean force level is the synchronization of motor neuron discharges (Datta and

Stephens, 1990; Semmler and Nordstrom, 1998; Yao et ah, 2000; Semmler et ah, 2001).

Our simulations revealed the presence o f SDN in the motor output in the absence o f

synchronization and therefore it seems that while synchronization will affect the

magnitude o f the variability (Yao et ah, 2000; Semmler et ah, 2001), it is likely to do so

without changing the overall pattern o f the SDN. It could be postulated that if

synchronization o f motor neuron discharges within a pool changed with the overall

level o f excitatory drive, then this too could be an important factor contributing to the

presence o f SDN. However it remains to be empirically determined whether

synchronization varies as a function o f excitatory drive.

NMES condition

The main purpose o f this condition was to determine if peripheral

neuromuscular noise contributed to the pattern o f SDN. The classical descriptions of

muscle force output in response to electrical stimulation were concerned primarily with

the mean force output in response to a particular stimulus paradigm (Rack and

Westbury, 1969). While it was clear from this earlier work that staggered stimulation o f

groups o f motor units could produce a smoother force output compared to synchronous

stimulation, force variability at different levels o f mean force was not examined. We

found that the variability o f the force output in all but one case was not related to the

mean force output. In the single case that did show a significant relationship, the

The sources of signal dependent noise during isometric force production: Discussion

SDN. Thus we conclude that the mechanics o f muscular contraction, that is the

neuromuscular junction and muscle fibres, while they may contribute some fixed

amount o f noise, do not contribute to SDN.

Twitches, threshold and recruitment order

The simulation results showed that the pattern o f increased force variability with

increases in mean force, which characterises SDN, depended on the large range o f

twitch forces, the distribution of recruitment thresholds and the orderly recruitment o f

motor-units in a pool, i.e. the underlying physiology o f the motor-unit pool. A motor-

unit pool composed of units with the same twitch amplitude did not generate SDN, nor

did a pool in which all motor-units had the same recruitment threshold (Fig 4F & G).

Even given a motor-unit pool with a broad distribution o f twitch amplitudes and

recruitment thresholds, it was necessary to recruit these in an orderly fashion to

reproduce the pattern o f SDN seen in the experimental data.

While recruitment studies on human motor units have emphasized the

importance o f orderly recruitment during isometric contractions, it is also clear that

there is some noise in the overall orderly recruitment pattern (Milner-Brown et al.,

1973; Desmedt and Godaux, 1977). This noise is mainly apparent in the lower

threshold units where the differences between recruitment thresholds are small.

Additionally, recent experimental data in the cat and subsequent theoretical analysis has

emphasized that fluctuation o f spike threshold likely contributes to experimental

observations o f variability in motor neuron spike trains and low levels o f synchrony

between motor neurons commonly reported in human motor unit studies (Powers and

The sources of signal dependent noise during isometric force production: Discussion

concerned with variation in threshold between spikes, it indicates that recruitment

threshold for a motor neuron is not static but likely exhibits some variability.

One o f the key factors determining the force output o f a motor unit, and

therefore the range o f twitch forces in a motor-unit pool, is the innervation number. It

has been empirically determined and theoretically estimated that the innervation

numbers and resulting motor unit force outputs in human muscle are not homogenously

distributed (Garnett et al., 1979; Thomas et al., 1990; Enoka and Fuglevand, 2001).

Instead the distribution o f motor units according to force is skewed with a majority o f

motor units producing small forces. Theoretical studies have concluded that the optimal

distribution o f motor-unit forces depends on the probability distribution function (pdf)

o f the forces generated by the muscle. If this p df is monotonically decreasing, then an

optimal distribution o f twitch/tetanic force outputs for a fixed number o f motor-units, N,

and a constant value o f MVC will also be monotonically decreasing. That is, if the

muscle produces small force outputs more frequently than large force outputs, it will be

optimal to have a greater number o f small than large twitch motor-units (Senn et al.,

1997; Tax and Denier van der Gon, 1991). In addition such a distribution o f motor unit

forces is optimal from an information theoretical point o f view in a motor unit pool that

regulates force by pure recruitment modulation (Senn et al., 1997).

It is also interesting to contrast the mechanism converting Poisson spike trains in

motor neurons into SDN in motor output, with the mechanism converting Poisson firing

in the sensory system into W eber’s law. As demonstrated above, the conditions

required for SDN in the motor system are a range o f twitch forces and recruitment

thresholds, together with orderly motor unit recruitment. In the retina, W eber’s law for

luminance arises due to adaptation o f the receptors to the overall light level (Laughlin,

The sources of signal dependent noise during isometric force production: Discussion

an orderly fashion with stimulus intensity. Though motor SDN arises only from the

behaviour o f a whole pool o f units, while sensory SDN can arise in a single cell, it

seems that the mechanism o f varying thresholds has similarities between these two

situations.

Optimization of motor output

There have been many post hoc explanations for the benefit of orderly

recruitment as well as much experimental work designed to determine the physiological

explanation for orderly recruitment first enunciated by Henneman (Hennemann, 1957;

Binder and Mendell, 1990). As argued by Senn et al. (1997), orderly recruitment

according to the size o f motor unit force output minimizes the error between the input,

modelled as required force, and the force output. We have shown that the sequela o f

this pattern o f recruitment is SDN in the force output.

We have shown a particular pattern o f SDN, one with a constant coefficient of

variation over a wide range o f force output. There are two reasons for emphasizing this

particular pattern o f SDN. Firstly the experimental data support this pattern o f SDN;

the mean power in SD = a mean* was 1.05 ± 0.48 (± SD, Table 1). Secondly the value

o f the power has significant effects on the type o f control strategy used in the TOPS

model (Harris and Wolpert, 1998). As detailed in the Introduction, if the power were

0.5, i.e. SDN with a constant FANO factor, then the optimal control strategy for

minimizing end-point errors would be bang-off-bang control (Harris and Wolpert,

unpublished simulations). Conversely, with a power o f I.O, i.e. SDN with a constant

coefficient o f variation, the optimal strategy is one generating a continuous motor

command and the output trajectories match experimental observations (Harris and

The sources of signal dependent noise during isometric force production: Discussion

shown in Figure 3-8D and highlighted in some experimental studies (Enoka et ah, 1999;

Laidlaw et ah, 2000), on the TOPS model have yet to be evaluated.

Thus it would appear that the cost o f optimisation o f the force output at the level

of a single muscle is SDN in the force output. The CNS accounts for the SDN in

planning movements so that the optimal trajectory is constrained by this feature o f the

The Scaling of Motor Noise with Muscle Strength and Motor Unit number: Abstract

In document The role of noise in sensorimotor control (Page 88-95)