Rethinking force steadiness: a new perspective

A fundamental aspect of research in motor control is understanding the fluctuating nature of the motor output and its implications for functional performance. This type of work can be traced back to the pioneering study by Fullerton and Cattell in 1892 (1) showing that motor variability impairs our ability to perceive light weights. In the 1970s, researchers initiated the use of a constant isometric force task to determine the physiological mechanisms responsible for this variability (2). However, the Enoka work in the early 1990s, showing increased force variability in older adults (3), marked a pivotal turning point in the field’s interest and inspired significant scientific exploration of the functional implications of force variability. Over the last three decades, the examination of force variability during submaximal isometric contractions has been instrumental in understanding motor deficits associated with human development (4–6) and neurological disorders like Parkinson’s disease and essential tremor (7). Also, force variability has been used to decode the effects of stress (8), fatigue (9), and visual feedback (10–12) on motor control across diverse groups. The physiological roots of force variability have captivated scientific interest for over 130 years and remain debated to this date (13–16). Regardless of its functional implications and physiological roots, exacerbated force variability during constant isometric contractions is often used synonymously with lower force steadiness (referred here as force unsteadiness), implying movement control deficits (5).

Here, we Introduce a fresh perspective on “force unsteadiness,” challenging the status quo and arguing that our current metrics [coefficient of variation of force (CVF)], which quantifies force variability, might just be scratching the surface of understanding force unsteadiness and consequently movement control. We posit that the CVF does not robustly capture force unsteadiness. Movement unsteadiness is calculated by the change in limb acceleration (a) quantified with the first derivative of a (da/dt; jerk, j) or the second derivative of a (d²a/dt²; snap, s) (17, 18). We define force unsteadiness as the change in force fluctuations, which differs from the currently used metric (CVF). We propose to quantify force unsteadiness, as the root mean square (magnitude) of the first-time derivative of force (dF/dt; Eq. 1), recently termed “yank” (19).

$$\mathrm{Force}\hspace{0.17em}\mathrm{Unsteadiness}=\sqrt{\frac{1}{n}{\displaystyle \sum }_i{\left(\frac{\mathrm{dF}}{\mathrm{d}t}\right)}_i^2}$$ (1)

WHY DO METRICS OF FORCE VARIABILITY FALL SHORT IN ACCURATELY CAPTURING FORCE UNSTEADINESS?

The output of biological systems, including the force (F) output during constant isometric contractions, comprises different frequency oscillations. During movements, unsteadiness is more influenced by higher-frequency oscillations (see Experimental Example below). Quantifying movement unsteadiness necessitates the use of higher-order derivatives to understand the change in the movement output (18). Here, we propose the same process for the force output during constant contractions. It is well established that force variability strongly relates to lower frequency oscillations (<1 Hz; 15, 20–22), as it is demonstrated in Fig. 1. Interestingly, individuals with pronounced movement unsteadiness, such as those with pathological tremor, exhibit greater oscillations from 3 to 8 Hz (7). In line with the physical law a = A(2πf)² (where A is amplitude and f is frequency), the net force applied to the limb and the consequent changes in limb a (or force from F = ma) are more pronounced with higher frequency oscillations (Fig. 1). Low-frequency oscillations lead to gradual limb a (or F) changes, whereas high-frequency oscillations induce more frequent limb a (or F) changes (23). This results in a net force surge, undermining force steadiness and the smoothness of the force output. Thus, we propose that force variability and force unsteadiness are separate concepts. Specifically, metrics of variability, such as the CVF, quantify the deviation from the average force, whereas metrics of unsteadiness quantify the smoothness of the force output.

Figure 1.

Force variability and force unsteadiness. Example of sustained isometric force task using the abduction of the index finger model (left). Finger force fluctuations (blue line for a healthy control subject and red line for an individual with essential tremor) above and below the mean exerted force (green line). The force fluctuations comprise different oscillations. Force variability is primarily affected by oscillations below 1 Hz (orange line), whereas finger unsteadiness (dF/dt; yank) is primarily affected by higher-frequency oscillations, such as tremor (4–8 Hz; seen as a faster fluctuation for the individual with ET). Although the individual with ET exhibited slightly greater (37%) force variability [as quantified with the coefficient of variation of force (CVF)] than the healthy control individual, the change in force fluctuations (quantified with dF/dt; yank) was ∼250% greater for the individual with ET, highlighting the impact of higher-frequency force oscillations to force unsteadiness. Thus, force unsteadiness is captured by the magnitude of change in force fluctuations (quantified with dF/dt; yank) and not by the magnitude of force fluctuations (quantified with the CVF). ET, essential tremor.

In certain situations, metrics of force variability (e.g., CVF) might mirror the proposed metrics of force unsteadiness (Eq. 1), suggesting that a group or condition does not have deficits in unsteadiness and can exert a smooth force output. Such finding will reflect the group’s inability to modulate low-frequency force oscillations caused by slower processes like breathing (24) and visuomotor adjustments (20, 25). To pinpoint the origins of force fluctuations, decomposing the force output into its oscillatory components is essential. For a general assessment of force steadiness, existing metrics like the CVF are inadequate, as they only capture unsteadiness linked to force variability, ignoring the smoothness of the force trajectory. Our proposed metric (Eq. 1) offers greater precision than the CVF, as it incorporates both variability and smoothness of the force output. Below, we illustrate this distinction between CVF and unsteadiness through experimental and simulated examples.

Experimental Example

The impact of power in higher-frequency oscillations on force steadiness can be illustrated by the pronounced instability observed in individuals with tremor (Fig. 1). Individuals with essential tremor (ET) experience significant movement unsteadiness due to amplified 4- to 8-Hz oscillations, severely hindering basic activities of daily living like eating, dressing, and writing. In Fig. 1, we provide data from one individual with ET and one age- and sex-matched healthy control. Even though the amplified force oscillations from 4 to 8 Hz minimally increase the overall force fluctuations (and thus CVF), power in these oscillations dramatically increases the magnitude of dF/dt (>250%). This example, therefore, hints that force unsteadiness, at least as experienced by patients with tremor , may be reflected in the amplitude of the change in force fluctuations but not the CVF during a constant isometric force task.

Simulated Example

To confirm the contribution of faster oscillations to force unsteadiness, we simulated force signals from experimental data with distinct oscillations. We compared two signals, one mimicking oscillations seen in patients with tremor and one mimicking oscillations seen in healthy individuals. Both signals combined a dominant 0.5-Hz oscillation (tremor, 62%; healthy, 75% of total power) with a 0.75-Hz oscillation (tremor, 21%; healthy, 22% of total power) and a minor 5-Hz oscillation (tremor, 17%; healthy, 3% of total power). The power in the 5-Hz oscillation represented increased tremor intensity. Comparing signals with 3% and 17% 5-Hz contributions, we observed a mild (∼13%) decrease in the CVF, but a dramatic increase in the magnitude of dF/dt (100%). This stark contrast underscores how the CVF can significantly underrepresent force unsteadiness, which is more accurately reflected in the magnitude of the change in force fluctuations (see Eq. 1).

In conclusion, we assert the distinct nature of CVF and force unsteadiness, emphasizing the importance of distinguishing between these two concepts. This is exemplified through experimental (see Fig. 1) and simulated evidence (see above), highlighting the fact that the CVF, a metric of force variability, does not always equal force unsteadiness. We propose that the change in force fluctuations (yank; Eq. 1) provides a more appropriate metric of force unsteadiness. We posit that this metric will be a stronger predictor of movement unsteadiness than the CVF and future studies should test this hypothesis. If the interest is to understand the underlying physiological mechanisms that control the force output, we advise a methodical decomposition of the force output into its frequency components.

GRANTS

This work was funded by National Institutes of Health Grant NS119849.

DISCLOSURES

No conflicts of interest, financial or otherwise, are declared by the authors.

AUTHOR CONTRIBUTIONS

B.Y. and E.A.C. conceived and designed research; performed experiments; analyzed data; interpreted results of experiments; prepared figures; drafted manuscript; edited and revised manuscript; approved final version of manuscript.