[Paper Review] The comparison of Higuchi fractal dimension and Sample Entropy analysis of sEMG: effects of muscle contraction intensity and TMS

Milena Čukić, Mirjana M. Platiša+3 more|arXiv (Cornell University)|Mar 28, 2018

Muscle activation and electromyography studies33 references3 citations

TL;DR

This study compares Higuchi fractal dimension (HFD) and sample entropy (SampEn) in quantifying surface electromyography (sEMG) signal complexity during varying muscle contraction intensities and after single-pulse transcranial magnetic stimulation (spTMS). Results show that both measures respond differently to contraction intensity and neural perturbation, with SampEn better capturing low-frequency dynamics and HFD more sensitive to high-frequency components, indicating that combining both metrics provides a more comprehensive assessment of sEMG complexity than either alone.

ABSTRACT

The aim of the study was to examine how the complexity of surface electromyogram (sEMG) signal, estimated by Higuchi fractal dimension (HFD) and Sample Entropy (SampEn), change depending on muscle contraction intensity and external perturbation of the corticospinal activity during muscle contraction induced by single-pulse Transcranial Magnetic Stimulation (spTMS). HFD and SampEn were computed from sEMG signal recorded at three various levels of voluntary contraction before and after spTMS. After spTMS, both HFD and SampEn decreased at medium compared to the mild contraction. SampEn increased, while HFD did not change significantly at strong compared to medium contraction. spTMS significantly decreased both parameters at all contraction levels. When same parameters were computed from the mathematically generated sine-wave calibration curves, the results show that SampEn has better accuracy at lower (0-40 Hz) and HFD at higher (60-120 Hz) frequencies. Changes in the sEMG complexity associated with increased muscle contraction intensity cannot be accurately depicted by a single complexity measure. Examination of sEMG should entail both SampEn and HFD as they provide complementary information about different frequency components of sEMG. Further studies are needed to explain the implication of changes in nonlinear parameters and their relation to underlying sEMG physiological processes.

Motivation & Objective

• To evaluate how Higuchi fractal dimension (HFD) and sample entropy (SampEn) respond to changes in muscle contraction intensity in sEMG signals.
• To investigate the effects of single-pulse transcranial magnetic stimulation (spTMS) on sEMG complexity as measured by HFD and SampEn.
• To compare the accuracy of HFD and SampEn in detecting signal complexity across different frequency bands using synthetic sine-wave signals.
• To determine whether a single complexity measure can adequately represent sEMG dynamics across varying physiological conditions.
• To advocate for the combined use of HFD and SampEn to capture complementary aspects of sEMG signal complexity.

Proposed method

• Higuchi fractal dimension (HFD) was computed from sEMG signals recorded at three voluntary contraction levels: mild, medium, and strong.
• Sample entropy (SampEn) was calculated using standard algorithms with a fixed embedding dimension and tolerance parameter.
• sEMG signals were recorded before and after single-pulse transcranial magnetic stimulation (spTMS) to assess cortical perturbation effects.
• Sine-wave calibration signals were generated across frequency bands (0–40 Hz and 60–120 Hz) to test the accuracy of HFD and SampEn in detecting complexity.
• Statistical comparisons were performed across contraction levels and time points (pre- and post-spTMS) to assess changes in HFD and SampEn.
• The study used a within-subject design with multiple sEMG recordings from participants under controlled contraction and stimulation conditions.

Experimental results

Research questions

• RQ1 How do Higuchi fractal dimension (HFD) and sample entropy (SampEn) change with increasing muscle contraction intensity in sEMG signals?
• RQ2 How does single-pulse transcranial magnetic stimulation (spTMS) affect HFD and SampEn in sEMG signals across different contraction levels?
• RQ3 Which complexity measure—HFD or SampEn—better captures low-frequency (0–40 Hz) dynamics in sEMG signals?
• RQ4 Which complexity measure—HFD or SampEn—better captures high-frequency (60–120 Hz) dynamics in sEMG signals?
• RQ5 Can a single nonlinear complexity measure fully represent the dynamic changes in sEMG during varying motor output and cortical perturbation?

Key findings

• After spTMS, both HFD and SampEn significantly decreased at medium contraction intensity compared to mild contraction.
• At strong contraction, SampEn increased compared to medium contraction, while HFD did not show a significant change.
• spTMS induced a significant reduction in both HFD and SampEn across all contraction levels, indicating a general suppression of signal complexity.
• In synthetic sine-wave signals, SampEn demonstrated better accuracy in detecting complexity at low frequencies (0–40 Hz), whereas HFD showed higher accuracy at high frequencies (60–120 Hz).
• The results indicate that HFD and SampEn respond differently to changes in muscle activity and neural perturbation, reflecting complementary sensitivity to distinct frequency components of sEMG.
• The study concludes that relying on a single complexity measure may misrepresent sEMG dynamics, and that combining HFD and SampEn provides a more comprehensive assessment of signal complexity.