⚡ electrical engineering

Heart Artifact Removal in Electrohysterography Measurements Using Algebraic Differentiators

This paper presents a causal FIR filter-based method using algebraic differentiators to effectively remove ECG artifacts from electrohysterography signals without auxiliary references, while preserving signal integrity and suppressing noise.

Original authors: Amine Othmane, Maria Camila Bustos Vivas, Johannes Steuer, Jana Hutter

Published 2026-03-20

📖 4 min read☕ Coffee break read

CC BY 4.0

Original authors: Amine Othmane, Maria Camila Bustos Vivas, Johannes Steuer, Jana Hutter

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine your body is a busy city with many different "radio stations" broadcasting signals at the same time.

The Uterus is a quiet, rhythmic drumbeat (the signal doctors want to hear to check on pregnancy or menstrual health).
The Heart is a very loud, powerful siren that goes off every second.
Muscles and Bowels are like construction crews making random, messy noise.

When doctors try to listen to the quiet uterine drumbeat using sensors on the belly (a technique called Electrohysterography or EHG), the loud heart siren drowns it out. It's like trying to hear a whisper in a room where someone is blasting a fire alarm.

The Problem: How to turn down the siren without muting the drum?

For a long time, doctors have tried to fix this with a few different tools, but they all had flaws:

The "Cut and Paste" method: They tried to guess where the heartbeats were, cut them out, and paste a smooth line over the gap. But this often distorted the real uterine signal, like editing a song and accidentally chopping out the singer's voice.
The "Reference" method: They asked for a second sensor on the chest to record the heart separately. But this is annoying for patients and doesn't always work perfectly.
The "Math Magic" method: They used complex computer programs (Machine Learning) that needed thousands of hours of training data and were hard to understand.

The Solution: The "Algebraic Differentiator" (The Smart Filter)

This paper introduces a new, clever tool from the world of control theory called an Algebraic Differentiator. Think of this tool as a super-sensitive motion detector.

Here is how it works, using a simple analogy:

1. The "Speed Camera" Analogy
Imagine you are watching a parade.

The Heartbeats are like a race car zooming past. They happen very fast and suddenly.
The Uterine signals are like a slow-moving float. They change gradually.
The Noise is like wind blowing leaves around.

If you just look at the parade (the raw signal), the race car and the float are mixed together. But, if you put on "Speed Goggles" (the algebraic differentiator) that only show you how fast things are changing, the slow-moving float disappears (because it's not changing speed much), and the wind leaves are just a blur. The race car, however, looks like a massive, sharp spike because it changed speed instantly.

2. The "Noise Cancelling" Trick
The researchers designed this "Speed Goggle" with very specific settings.

It ignores the slow drifts (like breathing or posture changes).
It ignores the hum of the electrical outlet (50Hz power line noise).
It only highlights the sharp, sudden spikes of the heart.

3. The "Teamwork" Check (Cross-Channel Clustering)
Sometimes, a muscle twitch might look like a heart spike in just one sensor. To avoid mistakes, the system looks at all the sensors at once.

If a spike happens in only one sensor, it's probably a local muscle twitch (an artifact).
If a spike happens in almost all sensors at almost the exact same time (within a few milliseconds), the system knows, "Aha! This is the heart!" because the heart's signal travels through the whole body.

4. The "Surgical Removal"
Once the system identifies the heart spikes, it doesn't just delete them. It calculates exactly how big they were and subtracts them from the original signal, leaving the uterine drumbeat perfectly intact.

What Did They Find?

The researchers tested this on real people (a man and a woman).

The Result: The method successfully removed the heart noise without needing a chest sensor.
The Catch: It works best when the sensors are a bit far from the uterus. If a sensor is right on top of the uterus, the uterine signal itself can sometimes look "spiky" to the filter, making it a little harder to separate. But for most placements, it worked beautifully.

Why Does This Matter?

This is a big deal because:

No Extra Sensors: You don't need to strap a heart monitor to the patient's chest.
No Training Data: It doesn't need a supercomputer to learn how to work; the math is built-in.
Real-Time: It's fast enough to be used while the patient is being monitored, not just after the fact.

In short, the authors built a smart, mathematical filter that acts like a bouncer at a club. It knows exactly what the "Heart" looks like, kicks it out, and lets the "Uterus" party inside without any disturbance.

1. Problem Statement

Electrohysterography (EHG) is a non-invasive technique used to monitor uterine electrical activity (myometrial contractions) for pregnancy monitoring, preterm labor detection, and menstrual cycle analysis. However, surface EHG recordings are heavily contaminated by physiological artifacts, most notably the Electrocardiogram (ECG) from the maternal heart.

Challenge: ECG signals often have large amplitudes that obscure the weaker uterine signals.
Limitations of Existing Methods:
- QRS Interpolation: Risks distorting the underlying neural signal dynamics.
- Adaptive Filtering: Requires auxiliary ECG reference channels, which are often unavailable or impractical.
- Template Subtraction: Assumes stationary ECG morphology; fails when waveforms vary, leaving residual artifacts.
- Wavelet/ML Methods: Require high computational resources, extensive training data, or lack interpretability.
Goal: Develop a method to remove cardiac artifacts from multichannel EHG signals without auxiliary ECG references, preserving the integrity of the uterine signal, and suitable for real-time processing.

2. Methodology

The proposed solution utilizes Algebraic Differentiators, a control-theoretic tool for model-free derivative estimation, adapted for signal processing.

A. Signal Modeling

The observed signal $x_i(t)$ in channel $i$ is modeled as a superposition of:

Impulsive Events: Discrete physiological events (heartbeats, uterine bursts, bowel movements) modeled as Dirac delta distributions convolved with propagation delays.
Baseline: Slow-varying components (respiratory drift, posture) assumed to be locally smooth and differentiable.
Interference: Deterministic powerline noise (50 Hz and harmonics) and additive measurement noise.

The core assumption is temporal scale separation: Cardiac R-waves are extremely short (10–20 ms) compared to baseline variations (seconds), allowing them to be treated as instantaneous impulses relative to the baseline.

B. Algebraic Differentiator Design

The method employs an $n$ -th order algebraic differentiator to transform the signal.

Mechanism: The signal is convolved with the $n$ -th derivative of a causal kernel $g(t)$ constructed from weighted Jacobi polynomials.
Effect:
- Baseline Suppression: High-order differentiation ( $n$ ) attenuates slow-varying baseline components (respiration, drift).
- Impulse Enhancement: The impulsive cardiac events are transformed into characteristic shifted kernel signatures, dominating the derivative signal.
- Noise/Interference Rejection: The kernel parameters are tuned to create zeros in the frequency response at the powerline frequency (50 Hz) and its harmonics, while managing noise amplification.

C. Pulse Detection and Clustering Algorithm

Derivative Calculation: Compute the $n$ -th order derivative of the raw signal.
Thresholding: Identify candidate pulse start times where the magnitude of the derivative exceeds a percentile-based threshold.
Cross-Channel Clustering:
- Cardiac pulses propagate across all electrodes with small, consistent inter-channel delays (spatial coherence).
- Localized artifacts (bowel, motion) affect only a subset of channels.
- The algorithm groups detections from all channels within a short temporal window ( $\Delta t_{beat}$ ). A group is classified as a cardiac beat only if it appears in a sufficient percentage ( $\rho$ ) of channels.
Reconstruction:
- Estimate the amplitude of each detected cardiac pulse using Least Squares.
- Reconstruct the cardiac artifact component and subtract it from the filtered (differentiator output) signal.
- This process removes the ECG, powerline noise, and baseline drift while preserving the uterine signal.

3. Key Contributions

Distributional Signal Model: A formal model representing physiological events as impulsive trains against a smooth baseline, justifying the use of differentiation for separation.
Systematic Artifact Removal: A method using algebraic differentiators with explicit parameter design to simultaneously suppress powerline interference, attenuate baseline drift, and maximize Signal-to-Noise Ratio (SNR).
Reference-Free Detection: A cross-channel clustering algorithm that distinguishes cardiac pulses from localized artifacts using spatial coherence, eliminating the need for an auxiliary ECG reference channel.
Computational Efficiency: The method is implemented as a causal Finite Impulse Response (FIR) filter, requiring no training data and offering low computational complexity suitable for real-time applications.

4. Experimental Results

The method was validated on multichannel EHG recordings from two subjects: one non-pregnant female and one healthy male (to isolate uterine-specific components).

Performance on Male Subject (No Uterine Signal):
- The method successfully removed ECG artifacts while preserving the signal structure.
- SNR Improvement: Achieved output SNR gains of 5.14 dB and 7.42 dB for different channels compared to the raw signal.
- Comparison: Outperformed or matched Template Subtraction (TS) without introducing the residual artifacts common in TS when waveforms vary.
Performance on Female Subject (Near Uterus):
- Limitation Identified: For electrodes placed very close to the uterus, the method showed reduced effectiveness (SNR: -2.15 dB).
- Reason: Slow-varying uterine contractions violate the assumption that the baseline derivative is zero ( $\hat{x}^{(n)}_{i,base} \approx 0$ ). The differentiator erroneously interprets these slow uterine components as artifacts.
Spatial Coherence Validation:
- Estimated inter-channel delays for cardiac pulses ranged from -11.6 ms to 3.0 ms.
- The tight interquartile range (1–2 ms) and calculated conduction velocity (3–7 m/s) confirmed the validity of the spatial coherence assumption used for clustering.

5. Significance and Conclusion

This work presents a robust, model-free, and reference-free approach to ECG artifact removal in EHG. By leveraging control-theoretic algebraic differentiators, it effectively isolates impulsive cardiac events from complex physiological backgrounds.

Advantages: Low computational load, no training data required, and effective suppression of powerline noise.
Clinical Impact: Enables cleaner monitoring of uterine activity, which is crucial for diagnosing conditions like adenomyosis and endometriosis, and for monitoring preterm labor.
Future Work: The authors suggest extending the signal model to handle non-zero baseline derivatives (to better accommodate electrodes near the uterus) and conducting quantitative benchmarking on larger patient cohorts.

In summary, the paper demonstrates that algebraic differentiators provide a mathematically rigorous and practically efficient solution for a persistent challenge in biomedical signal processing, offering a viable alternative to traditional template-based or machine learning approaches.