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A Kalman Filter-Based Framework for Granger Causality Assessment: Application in Tracking Maternal-Fetal Heart Rate
IEEE Transactions on Bio-Medical Engineering
|July 6, 2026
Summary
This study introduces a new Kalman filter-based method to analyze nonstationary Granger causality between fetal and maternal heart rates. The novel approach identifies brief coupling episodes missed by traditional methods, revealing dynamic interactions during pregnancy and labor.
Area of Science:
- Biomedical Engineering
- Physiological Signal Processing
- Maternal-Fetal Medicine
Background:
- Fetal and maternal heart rates (FHR and MHR) are key indicators of well-being during labor.
- Assessing directed coupling between FHR and MHR reveals crucial interactions.
- Nonstationary coupling, influenced by labor dynamics, challenges traditional analysis tools.
Purpose of the Study:
- To develop and evaluate a Kalman filter-based, time-varying autoregressive framework for nonstationary Granger causality (GC) assessment.
- To analyze maternal-fetal heart rate coupling during pregnancy and labor.
- To identify transient coupling episodes missed by stationary methods.
Main Methods:
- Introduced a Kalman filter (KF)-based, time-varying autoregressive (TVAR) framework for nonstationary GC.
- Modeled autoregressive coefficients as latent states in a linear state-space model, tracked recursively by an optimized KF.
- Calculated time-varying GC by comparing prediction errors with and without the other signal's history.
Main Results:
- The KF-TVAR GC method successfully identified brief, statistically significant MHR-FHR coupling episodes.
- Stationary GC methods failed to localize these transient coupling events.
- Maternal-to-fetal coupling was generally stronger in late pregnancy, shifting to fetal-to-maternal during labor.
Conclusions:
- The proposed KF-TVAR framework provides a robust method for analyzing nonstationary physiological signals like FHR and MHR.
- This approach offers a significant advancement over traditional stationary methods for detecting dynamic interactions.
- The findings highlight shifts in maternal-fetal heart rate coupling dynamics throughout pregnancy and labor.
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