Persistent Entropy Relates Rest-Activity During Pregnancy to Unfavorable Health Outcomes in Maternal and Newborn Health

This repository contains the thesis and supporting code for the Master’s thesis submitted by Sashiel Vagus to San Diego State University in Spring 2024, in partial fulfillment of the requirements for the degree Master of Science in Applied Mathematics, with a concentration in Dynamical Systems.

Full Thesis: PersistenceEntropy_PregnancyOutcomes_Thesis.pdf
Main Notebook: Rips_dim1_extended.ipynb

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Project Summary

This thesis applies topological data analysis (TDA) — specifically persistent entropy — to actigraphy data collected from pregnant women during gestation weeks 22 and 32. Persistent entropy quantifies disorder in temporal patterns and is used here to assess correlations between rest-activity rhythms and maternal and newborn health outcomes.

Key findings show that:

• High persistent entropy (>8.22) at gestation week 22 was associated with increased pregnancy complications.
• Greater day-to-day variability in entropy was linked to more frequent adverse outcomes.
• Women with high BMI and high entropy were most likely to experience complications.

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Methodology

• Data: Actigraphy wrist-worn device (30-sec epoch) from G22 (n=41) and G32 (n=44)
• Processing Steps:
  1. Resample actigraphy point clouds using Greedy Permutation
  2. Apply Vietoris–Rips filtration via ripser
  3. Compute persistence diagrams (dimension 0)
  4. Calculate entropy using persim and numpy
  5. Compare across groups using Mann-Whitney U and Fisher tests

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Technologies Used

• Python 3.8+
• Libraries:
  • ripser, persim, scikit-tda
  • numpy, pandas, matplotlib

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Results

• Women with entropy values above 8.22 were significantly more likely to have pregnancy complications.
• The variability in entropy across days was also strongly associated with maternal or newborn complications.
• Persistent entropy captures latent structure in actigraphy data missed by standard statistical measures.

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Thesis Committee

• Chair: Dr. Uduak George (Mathematics & Statistics)
• Committee Members:
  • Dr. Jérôme Gilles (Mathematics & Statistics)
  • Dr. Emily Schmied (Public Health)
• Data Provider: Dr. Theresa Casey (Purdue University)

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Citation

Vagus, S. (2024). Persistence Entropy Relates Rest-Activity During Pregnancy to Unfavorable Health Outcomes in Maternal and Newborn Health (Master’s thesis, San Diego State University).

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Contact

Sashiel Vagus
Email: svagus2@sdsu.edu
GitHub: @sashielvagus

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License

This repository is shared for academic, educational, and research purposes. For reuse or collaboration, please contact the author.