SIAM News Blog

Modeling the Biofluids of Reproduction

By Lina Sorg

Fluid dynamics of the reproductive system can be modeled with mathematics. Image credit: Lisa Fauci, AN16 presentation.
Lisa Fauci of Tulane University is this year’s recipient of the distinguished AWM-SIAM Sonia Kovalevsky Lecture prize, given annually to highlight significant contributions of women to applied or computational mathematics. She discussed her work in a prize lecture, “Biofluids of Reproduction: Oscillators, Viscoelastic Networks and Sticky Situations,” at the SIAM Annual meeting. Fauci spoke about the use of computational fluid dynamics frameworks and fluid structure interactions as tools to study sperm motility in the human reproductive system, the mechanics of cilia and flagella, and the dynamics of embryo transfer.

Fertilization in mammals involves coordination among movement of spermatozoa, uterus and oviduct contraction, and the beating of cilia. “There is no better illustration of complex fluid-structure interactions than mammalian reproduction,” Fauci said. Elastic structures generate forces that drive fluid motion, and fluid dynamics in the environment determine the structures’ configuration and arrangement. For example, for sperm flagella to successfully move into the oviduct, uterine peristalsis and flagellar and ciliary beating must occur. Sperm may also need to change their oscillation patterns to escape potential adherence to oviduct epithilia; otherwise they risk getting caught in the mucosal folds. 

Nearly planar swimming of sperm. Image credit: Lisa Fauci, AN16 presentation.
Sperm are considered hyperactive when their flagella maintain an asymmetrical, high-amplitude beating pattern. Fauci summarized the functional implications of a hyperactive waveform, including moving interfaces, complicated geometries, and Non-Newtonian fluids. Sperm motility is characterized by sinusoidal waves, which Fauci demonstrated with a video clip featuring their eel-like movements.  

She then posed a series of questions to the full lecture hall that included the following: (1) what are the biochemical pathways that initiate hyperactivation? (2) How do these biochemical signals change the internal force-generating mechanisms? (3) What are the complications?  Fauci also addressed the many choices accompanying development of a mathematical model, including the decision to model in two or three dimensions.  “Life is 3D, but perhaps we could learn something from 2D models” Fauci said. Thus, even though the waveform is planar, the fluid mechanics are three-dimensional and hence can be studied in two dimensions.  

Modeling fluid mechanics of sperm and ovum. Image credit: Lisa Fauci, AN16 presentation.

Lastly, Fauci described a model simulating the process of human reproduction, where the fetus is manifested as a rigid cylinder and the uterus as a flexible tube. This is then used to measure the fluid dynamics forces, as very little information is known about the forces a fetus experiences during birth. She concluded with a humorous motivation for those in the field. "For the fluid mechanists in the audience, forget the baby,” she said, “this is an interesting fluid mechanics problem!” Pausing, she added cheekily,” I didn't really mean forget the baby.” 

   Lina Sorg is the associate editor of SIAM News


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