CAREER: Numerical Methods and Biomechanical Models for Sperm Motility

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Mammalian sperm must navigate the female reproductive tract, swimming a distance greater than 1000 times their own length to reach and fertilize the egg. In order to aid in the treatment of reduced sperm motility, it is important to understand interactions of the sperm flagellum with different regions of the reproductive tract. In particular, fluid flow helps bring the egg to the uterus (in the opposite direction of sperm progression). Recent experiments have shown that a large percentage of sperm exhibit positive rheotaxis, the ability to reorient and swim against a background flow. Additionally, sperm will bind and unbind to the oviductal wall and the role of a background flow on sperm detachment is not known. The main scientific goals of this project include further analyzing existing experimental data (through image processing techniques) and developing new computational models to understand the clinical importance of migration through the female reproductive tract and sperm binding and detachment from walls in a background flow. Several new computational modeling frameworks will be developed to allow simulations of sperm in the presence of a background flow and a wall. The PI will provide interdisciplinary training for several students (undergraduate and graduate) as well as one postdoc in the areas of computational biofluids, image processing of experimental movies, and model development. In addition, the PI will work to develop image processing and modeling modules to be used in area High Schools and at summer programs for High School students at WPI. The sperm flagellum is an elastic structure that propagates waves of bending along its length to propel itself through the female reproductive tract. Understanding the behavior of the interaction between sperm, dynamic elastic structures, and their surrounding fluid will shed light onto the biophysics of their 3-dimensional motion and will help determine the clinical importance of migration through the female reproductive tract in a background flow. Models will be able to delineate the importance of factors such as sperm rolling, types of flagellar waveforms, biochemistry, and fluid viscosity for forward progression of the sperm. In this project, the PI will model the sperm flagellum as a Kirchhoff rod that is able to bend and twist. The rod is able to achieve both planar and nonplanar waveforms and the rotation of the rod can be captured via an orthonormal triad associated with each material point along the centerline of the flagellum. Through this work the PI will focus on the following objectives: (1) Understand the types of emergent waveforms and trajectories of sperm in a background flow at different viscosities; (2) Determine if rolling is due to calcium mediated changes in flagellar waveforms, background flow, wall interactions, or hydrodynamic interactions with other sperm; (3) Investigate the role of background fluid flow on attachment/detachment of sperm to walls; (4) Extend current numerical methods. The PI's research will lead to the development of two new numerical methods to study interactions near a wall and increase accuracy of force calculations through parametric representations of the structure. These newly developed methods can also be used for other slender elastic structures such as cilia and bacterial flagella.