Lempel-Ziv complexity of simultaneous surface electromyography and magnetomyography during muscle fatigue

This study demonstrates that Lempel-Ziv complexity metrics effectively capture fatigue-related changes in neuromuscular signal organization beyond conventional amplitude and spectral features, revealing both shared and modality-specific dynamics between simultaneous surface electromyography and optically pumped magnetometer-based magnetomyography recordings.

The Gist

The Big Picture: Listening to Tired Muscles

Imagine your muscles are a busy orchestra. When you are fresh, the musicians (your nerve cells and muscle fibers) are playing a complex, chaotic, and lively jazz improvisation. Everyone is doing their own thing, creating a rich, "complex" sound.

But as you hold a heavy weight for a long time, the musicians get tired. They stop improvising and start playing the same simple, repetitive beat over and over again. The music becomes boring and predictable. In the world of science, this loss of "complexity" is a sign of fatigue.

This paper asks a simple question: Can we hear this change in the music using two different microphones?

1. Microphone A (sEMG): The traditional skin sensor that picks up electrical signals (like hearing the voltage).
2. Microphone B (OPM-MMG): A brand-new, high-tech magnetic sensor that picks up the magnetic fields generated by the muscles (like hearing the magnetic "hum").

The researchers wanted to know if the new magnetic microphone hears the same "tiredness" as the old electrical one, and if we can use a special math trick called Lempel-Ziv (LZ) complexity to measure exactly how "boring" the muscle music has become.

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The Experiment: The Arm Workout

The scientists put sensors on the biceps of healthy volunteers and asked them to do two different tasks:

• The Long Haul: Hold a light weight (20% of their max strength) for 20 minutes.
• The Sprint: Hold a heavy weight (60% of their max strength) for 3 minutes.

While they held the weights, the sensors recorded the muscle activity the whole time.

The Three Things They Measured

To understand the fatigue, they looked at three different "stats" for the muscle signals:

1. The Volume (RMS): As muscles get tired, they have to work harder to keep the weight up. It's like turning up the volume on a speaker. The signal gets louder.
2. The Pitch (Median Frequency): Tired muscle fibers conduct signals slower. It's like a guitar string going slack; the sound gets deeper and lower.
3. The Complexity (Lempel-Ziv): This is the star of the show. They used a math formula to measure how "random" or "repetitive" the signal is.
   • Fresh Muscle: High complexity (lots of variety, like a jazz solo).
   • Tired Muscle: Low complexity (very repetitive, like a metronome).

The Findings: What Did They Discover?

1. Both Microphones Heard the Same Fatigue

The most important finding is that the new magnetic sensor (OPM) and the old electrical sensor (sEMG) agreed perfectly. As the muscles got tired:

• The volume went up.
• The pitch went down.
• The complexity went down.

This is great news! It means the new magnetic sensors are a valid way to study muscles, not just a fancy gimmick. They hear the same story as the traditional sensors.

2. Complexity Tells a Secret Story

The researchers ran a special test to see if the drop in complexity was just because the volume went up or the pitch went down.

• The Result: No! Even after accounting for volume and pitch, the complexity still dropped on its own.
• The Analogy: Imagine a song getting quieter and slower. You might expect it to sound simpler. But this study found that the song was becoming even simpler than just the volume and speed changes could explain. It was becoming more "robotic." This suggests that complexity measures something unique about how the brain and muscles are coordinating, something the old "volume and pitch" metrics missed.

3. The "Heavy vs. Light" Difference

Here is where the two microphones disagreed slightly:

• The Electrical Sensor (sEMG): When the volunteers lifted the heavy weight, the signal was naturally more complex (more chaotic) than when they lifted the light weight.
• The Magnetic Sensor (OPM): It didn't seem to care as much about the weight difference. The complexity looked the same whether the weight was light or heavy.

Why? The authors suspect the magnetic sensors might be a bit "blurry" right now. They might not be sensitive enough to catch the subtle differences in how hard the muscle is working, whereas the electrical sensors are very sharp at detecting those differences.

The Takeaway

Think of this study as a test drive for a new car (the magnetic sensor).

• Verdict: The new car drives just as well as the old one for the main job (detecting fatigue).
• Bonus: The new car has a special dashboard (Complexity) that tells you things the old car's dashboard missed.
• Caveat: The new car's speedometer (sensitivity to weight) isn't quite as accurate as the old one yet, but it's getting there.

In short: We can now use these new, wearable magnetic sensors to watch muscles get tired, and by using "complexity" math, we can understand the fatigue in a deeper, more detailed way than ever before. This could help athletes train better or help doctors monitor patients with muscle diseases more accurately.

Technical Summary

1. Problem Statement

Muscle fatigue is a multifactorial process involving changes in motor unit recruitment, firing rates, and conduction velocities. Traditionally, fatigue is monitored using surface electromyography (sEMG) by tracking amplitude increases (Root Mean Square, RMS) and spectral shifts toward lower frequencies (Median Frequency). However, these conventional metrics may not fully capture the temporal organization and structural complexity of neuromuscular signals.

While Optically Pumped Magnetometers (OPM) have emerged as a promising tool for recording magnetomyography (MMG) to complement sEMG, it remains unclear whether complexity-based metrics (specifically Lempel-Ziv complexity) derived from magnetic recordings behave similarly to those from electrical recordings. Furthermore, it is unknown if complexity metrics provide unique information beyond standard amplitude and spectral features, and how these metrics vary across different contraction intensities.

2. Methodology

Experimental Design:

• Participants: Healthy young adults (12 in the 20% MVC group; 6 in the 60% MVC group).
• Task: Sustained isometric elbow flexion of the biceps brachii.
  • Condition A: 20% Maximal Voluntary Contraction (MVC) for 20 minutes.
  • Condition B: 60% MVC for 3 minutes.
• Simultaneous Recording:
  • sEMG: Bipolar configuration using Ag/AgCl electrodes.
  • OPM-MMG: Single-channel Optically Pumped Magnetometer (QuSpin QZFM-gen-1.5) placed over the muscle belly inside a magnetically shielded room.
  • Sampling: Both signals sampled at ~2344 Hz, later resampled to 1000 Hz.

Signal Processing:

• Preprocessing: High-pass (30 Hz) and low-pass (200 Hz) filtering; notch filtering for powerline harmonics; artifact removal via visual inspection.
• Windowing: Data divided into non-overlapping 5-second windows.
• Feature Extraction (per window):
  1. Lempel-Ziv (LZ) Complexity: Calculated on a binarized signal (thresholded at the median) to quantify the degree of regularity/repetition. Normalized by $T/\log_2(T)$.
  2. Median Frequency: Derived from Welch's power spectral density.
  3. Root Mean Square (RMS): Amplitude measure.

Statistical Analysis:

• Correlation Matrices: Pearson correlations computed between Time, LZ, Median Frequency, and RMS for both modalities and intensities.
• Multiple Linear Regression: To isolate unique contributions, LZ was regressed against Time, Median Frequency, and RMS (and vice versa) to determine if complexity changes are independent of spectral/amplitude shifts.
• Linear Mixed-Effects Models: Used to compare trajectories between 20% and 60% MVC, testing for main effects of protocol, time, and their interaction.
• Correction: False Discovery Rate (FDR) applied for multiple comparisons.

3. Key Contributions

1. First Direct Comparison of Complexity in MMG vs. sEMG: The study establishes that OPM-based MMG captures fatigue-related complexity dynamics (LZ decline) that are highly consistent with sEMG.
2. Independence of Complexity Metrics: Demonstrates that the decline in LZ complexity during fatigue is not fully explained by concurrent changes in amplitude (RMS) or spectral content (Median Frequency), suggesting complexity captures a distinct aspect of neuromuscular signal organization.
3. Modality-Specific Intensity Effects: Reveals a divergence between modalities regarding contraction intensity: sEMG shows intensity-dependent complexity changes (higher complexity at 60% MVC), whereas OPM-MMG does not show this modulation.

4. Key Results

Temporal Evolution of Fatigue Markers:

• Consistent Trends: Across both 20% and 60% MVC, and in both sEMG and MMG, fatigue manifested as:
  • Increasing RMS (Amplitude).
  • Decreasing Median Frequency (Spectral slowing).
  • Decreasing LZ Complexity (Increased signal regularity/repetition).
• Correlation: LZ complexity was strongly correlated with both Median Frequency and RMS, confirming that these features evolve together during fatigue.

Partial Contributions (Regression Analysis):

• Time as an Independent Predictor: Even after controlling for Median Frequency and RMS, Time remained a significant negative predictor of LZ complexity in both modalities.
  • Interpretation: The progressive loss of signal complexity is a distinct phenomenon that cannot be solely attributed to spectral compression or amplitude increases. It reflects a fundamental reorganization of neuromuscular output.
• Modality Similarity: Both sEMG and OPM-MMG showed similar regression coefficients, indicating that magnetic recordings capture the same underlying fatigue-induced structural changes as electrical recordings.

Intensity-Dependent Effects:

• sEMG: Showed significantly higher LZ complexity and Median Frequency at 60% MVC compared to 20% MVC. The rate of complexity decline was also steeper at 60% MVC.
• OPM-MMG: Did not show significant differences in LZ complexity or Median Frequency between the 20% and 60% MVC protocols.
• RMS: No significant intensity-dependent differences were found in RMS for either modality.

5. Significance and Implications

• Validation of OPM-MMG: The study validates OPM-based MMG as a viable tool for assessing neuromuscular fatigue using advanced complexity metrics, not just conventional spectral features. This supports the use of wearable magnetic sensors in clinical and rehabilitation settings.
• Beyond Conventional Metrics: The findings suggest that complexity-based metrics (like LZ) offer a "third dimension" of analysis. They capture temporal signal organization that is distinct from amplitude and frequency, potentially offering earlier or more sensitive detection of fatigue mechanisms (e.g., motor unit synchronization changes).
• Physiological Insight: The decline in complexity likely reflects a transition from a variable, stochastic neuromuscular drive to a more rigid, repetitive pattern as the system fatigues. This may be driven by both peripheral factors (conduction velocity slowing) and central factors (reduced recruitment variability).
• Technical Limitations & Future Directions: The lack of intensity-dependent modulation in MMG suggests current OPM systems may have limitations (e.g., bandwidth, sensor orientation sensitivity) compared to sEMG. Future work requires higher-density sensor arrays and motor-unit-level decomposition to disentangle central vs. peripheral contributions to signal complexity.

In conclusion, this paper provides a methodological foundation for using multimodal (sEMG + OPM-MMG) complexity analysis to characterize neuromuscular fatigue, highlighting that while the modalities are broadly comparable, they possess distinct sensitivities to contraction intensity.