Fondecyt Postdoctoral No3100072: Computational modeling of peristaltic pumping in 3D.

AM2V Members: Erwin Hernández, Vivian Aranda
Start Date: - End Date:
Status: in progress

The fluid movement inside the uterus and the fallopian tubes directly affect the movement of the ovum and the sperm and therefore its effect in the reproductive process is evident. It is of great interest to have mathematical models that recreate reality, and to be able to perform computational experiments which can help us to obtain answers to problems that cannot be solved through experimentation on living beings.

The main goal of this research is to improve and extend models of peristalsis in two dimensions for the uterus transport phenomenon and in three dimensions for the fallopian tube transport phenomenon using the method of Regularized Stokeslets, including new situations.

We will extend the method to the non-axisymmetric case and will make careful parameter studies of the effects of non-axisymmetric waves on fluid pumping efficiency, and study the effects on the meanflow when pressure gradients are imposed.

We will also simulate the evolution of an ovum with volume within the peristaltic tube. This ovum will be represented by an immersed elastic structure fully coupled to the Stokes fluid, and its structure will evolve along a geometric path which contains nodes joined by springs representing the ovum membrane.

We will study the effects of a tube that has variable elastic or pumping properties. This is a step in the direction of recreating different aspects of reality, because this can represent cases where, for instance, a portion of the tube (uterus) has scar tissue and cannot contract. In the same direction we would like to extend these models to include the interaction of the peristaltic tubes with immersed representations of swimming spermatozoa. It is relevant to emphasize that spermatozoa have their own motility system, which is not the case for the ovum.

Finally, through the mathematical and numerical analysis of the regularized Stokeslet method, in these situations, we look a more efficient implementation of the algorithm.

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