Purpose We employed an optimization method for the approximate entropy (ApEn) parameters (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">$m$</EquationSource> <EquationSource Format="MATHML"><math> <mi>m</mi> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$r$</EquationSource> <EquationSource Format="MATHML"><math> <mi>r</mi> </math></EquationSource> </InlineEquation>) to evaluate the influence of changes in contraction intensity, visual feedback conditions, and joint angles in force ApEn during an isometric force-matching task. Methods Seventeen participants performed an index finger abduction isometric force task in six contraction intensities (5–75% of maximum voluntary contraction, MVC), with and without visual feedback of the force, and in three different metacarpophalangeal (MCP) joint angles. Force variability, complexity (ApEn), and power spectrum density (PSD) were assessed, and a correlation analysis was performed between these variables. Results The best ApEn (<InlineEquation ID="IEq3"> <EquationSource Format="TEX">$m$</EquationSource> <EquationSource Format="MATHML"><math> <mi>m</mi> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$r$</EquationSource> <EquationSource Format="MATHML"><math> <mi>r</mi> </math></EquationSource> </InlineEquation>) pair for muscle force analysis was <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$m=2$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>m</mi> <mo>=</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$r=0.20\times$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>r</mi> <mo>=</mo> <mn>0.20</mn> <mo>×</mo> </mrow> </math></EquationSource> </InlineEquation> force standard deviation (SD). Visual feedback influenced the ApEn; however, the comparison between experimental conditions (force intensity and joint angle) was similar. Both the force ApEn and the coefficient of variation (CoV) were reduced as a function of contraction intensity and without visual feedback. Conversely, the force SD and the PSD in the low-frequency band increased with contraction intensity and the absence of visual feedback. The changes in the MCP joint angle affected the MVC values and force CoV, with no significant effect on the force ApEn. The PSD in the low-frequency band (< 5 Hz) showed a strong negative correlation with force ApEn in both visual feedback conditions. Conclusion ApEn is influenced by force level and visual feedback, and it is strongly correlated with low-frequency force oscillations, which are related to the muscle’s common drive.

Reassessment of isometric muscle force complexity under different contraction intensities, joint angles, and visual feedback conditions

期刊论文
发表日期：

2025年7月1日

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Ellen Pereira Zambalde,
Carina Marconi Germer,
Ricardo Gonçalves Molinari,
Francesco Negro,
Jakob Dideriksen,
Leonardo Abdala Elias

摘要

Purpose

We employed an optimization method for the approximate entropy (ApEn) parameters ( $m$ $m$ , $r$ $r$ ) to evaluate the influence of changes in contraction intensity, visual feedback conditions, and joint angles in force ApEn during an isometric force-matching task.

Methods

Seventeen participants performed an index finger abduction isometric force task in six contraction intensities (5–75% of maximum voluntary contraction, MVC), with and without visual feedback of the force, and in three different metacarpophalangeal (MCP) joint angles. Force variability, complexity (ApEn), and power spectrum density (PSD) were assessed, and a correlation analysis was performed between these variables.

Results

The best ApEn ( $m$ $m$ , $r$ $r$ ) pair for muscle force analysis was $m=2$ $m = 2$ and $r=0.20\times$ $r = 0.20 \times$ force standard deviation (SD). Visual feedback influenced the ApEn; however, the comparison between experimental conditions (force intensity and joint angle) was similar. Both the force ApEn and the coefficient of variation (CoV) were reduced as a function of contraction intensity and without visual feedback. Conversely, the force SD and the PSD in the low-frequency band increased with contraction intensity and the absence of visual feedback. The changes in the MCP joint angle affected the MVC values and force CoV, with no significant effect on the force ApEn. The PSD in the low-frequency band (< 5 Hz) showed a strong negative correlation with force ApEn in both visual feedback conditions.

Conclusion

ApEn is influenced by force level and visual feedback, and it is strongly correlated with low-frequency force oscillations, which are related to the muscle’s common drive.