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    Women's Health

    (M-495) Mathematical Analysis of Postpartum Uterine Involution as Applied to IUD Insertion Timing Based on Expulsion Risks

    Thursday, October 12, 2023
    9:30 AM – 10:30 AM PDT
    Location: Exhibit Hall - Row M - Poster # 495

      Presenting Author(s)

    • Sophia Mains (she/her/hers)

      Undergraduate Biomedical Engineering student
      Stevens Institute of Technology
      Hoboken, New Jersey, United States

    • LS

      Lauren Smith

      Undergraduate Biomedical Engineering Student
      Stevens Institute of Technology, United States

    Introduction::

    This study investigates the risk of intrauterine device (IUD) expulsion in postpartum women. A cohort of 326,658 women who had IUD insertion after childbirth was monitored to assess expulsion frequency. Results indicate that postpartum women face over five times the risk of expulsion compared to non-postpartum women. IUDs offer highly effective and cost-effective contraception, filling a crucial gap in women's healthcare. They are particularly suitable for postpartum women who cannot take birth control pills due to lactation.


    The World Health Organization recommends immediate IUD insertion after placental delivery as a safe and effective method to prevent unintended pregnancies during the postpartum period. However, there are concerns regarding the increased risk of spontaneous expulsion associated with immediate insertion.


    During the postpartum period, the uterus undergoes significant anatomical changes that contribute to the high expulsion rate. A study revealed rapid uterine size reduction in the initial 30 days, followed by a slower decrease to 82% of the original size after 60 days. These changes contribute to the elevated risk of IUD expulsion in postpartum women compared to non-postpartum women.


    Understanding the forces exerted on the uterine walls is crucial for comprehending IUD expulsion. To determine the optimal timing for IUD insertion and mitigate expulsion risk, this study reviews uterine involution in women with different delivery types and birth orders. By considering these variables, a revised timeline for safer postpartum IUD insertion will be provided, benefiting healthcare practitioners and improving contraceptive outcomes for postpartum women.



    Materials and Methods::

    This analysis investigates the forces involved in intrauterine device (IUD) expulsion and their relationship to the dimensions of the postpartum uterus. The study assumes that the IUD exerts identical frictional forces on both sides of the uterus, forming 5-85-90 triangles at the point of contact. The summation of forces in the y-direction is calculated based on the frictional forces and their angles. To prevent IUD expulsion, the sum of these forces must be less than or equal to the force required for expulsion, which ranges from 1 to 5.8 Newtons.


    The study analyzes the changing dimensions of the uterus during the postpartum period using data from literature. By calculating the cross-sectional area of the uterus over time, the force exerted by the IUD on the uterine walls is modeled. A constant stress value of .012 MPa is assumed for the uterus.


    Using this mathematical model, the study determines the specific day during the postpartum period when the force reaches the thresholds of 1 Newton and 5.8 Newtons. These thresholds indicate the safest range of dates for IUD insertion after childbirth. Two analyses are conducted, one comparing vaginal birth to cesarean section birth and another comparing first-time mothers (primipara) to those having their second child (multipara). Understanding these relationships between uterine involution and the forces exerted by the IUD provides insights into the optimal timing for postpartum IUD insertion. 



    Results, Conclusions, and Discussions::

    The data from this mathematical analysis reveals that the uterus does not regain its control shape and IUD force until over one year after childbirth, despite rapid uterine involution in the first thirty days of the postpartum period. The study suggests that for vaginal delivery, cesarean delivery, primipara, and multipara, IUD insertion can be considered after days 15, 16, 19, or 27, respectively. However, women in these categories are not risk-free from IUD expulsion due to pregnancy until day 444, 756, 1123, or 2177, respectively. These results indicate that the current practice of inserting IUDs ten minutes after delivery, as recommended by the WHO and the ACOG, is not suitable, particularly for multipara women.


    Despite the type of delivery method and the multiplicity of births, several factors impact the invention of the uterus including age, lifestyle, choice of breastfeeding, health factors, and previous miscarriages. Evidently, one IUD insertion time does not fit every woman. In the future, more testing at a greater frequency is needed on the uterine tissues and forces postpartum to validate the results. Decreasing the risk of expulsion is particularly relevant to underrepresented communities where delivery may be the only opportunity for a healthy woman to receive health care and gain access to a form of birth control.


    Several assumptions were made in this analysis. The triangular shape of the uterus was assumed for calculating the cross-sectional area over time, and the IUD angle of five degrees was estimated. It was assumed that the uterus followed a consistent involution trend throughout the calculation. Additionally, the stress value for uterine soft tissue was based on measurements from mice, and it was assumed to remain constant during postpartum, disregarding potential variations. The changing collagen content in the uterus during postpartum, which can impact IUD expulsion, was not considered due to limited data.


    In conclusion, the current design and timing of insertion of IUDs is not suitable for postpartum women. A differently shaped IUD or a new method of birth control should be administered to postpartum women.



    Acknowledgements (Optional): : The research team would like to thank Dr. Sally Shady for her advisory and the Stevens Institute of Technology Department of Biomedical Engineering.

    References (Optional): :


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