Theoretical study of spermatozoa sorting by dielectrophoresis or magnetophoresis with supervised learning

Assisted reproduction currently accounts for over one in every hundred births in developed countries. The chances of successful conception are closely related to the morphology of sperm used. Despite well-established microfluidic sorting techniques, and reliable mathematical models to quantify the swimming of microorganisms, research on sperm sorting via dielectrophoresis or magnetophoresis lacks theoretical and statistical support. In this thesis, the kinematics of sperm subjected to an external electric or magnetic field is investigated to provide a theoretical framework for computing the resultant velocity. The flagellum waveform is prescribed analytically, and subsequently solved from force and moment balance. The hydrodynamic force acting on the sperm is computed using Resistive Force Theory as well as Slender Body Theory, and the resulting velocity is compared qualitatively and quantitatively. As normal and abnormal sperm cells have different morphological parameters, their velocities under the influence of dielectrophoresis or magnetophoresis are altered to varying extents. This effect is more prominent in a viscoelastic Oldroyd-B fluid than in a Newtonian fluid medium. To account for the natural variations in sperm morphology and beating characteristics, pseudo-random data are generated from a normal distribution. The crosssection of the microchannel is assumed to be much larger than the sperm, such that boundary effects can be ignored. A large number of velocity computations is performed to obtain statistically meaningful results. The difference in velocity distribution between normal and abnormal sperm cells can be widened using an external field to double the proportion of normal ones, with at least half the number of normal spermatozoa in the original sample retained. This sorting has potential to improve the probability of success for intrauterine insemination, given that pregnancy rates are similar as long as the percentage of normal cells exceed a minimum threshold, even if the initial motile sperm count is under a million. Supervised learning is proposed to reduce the computational costs by making predictions after a subset of the data is computed and used for training. By fitting the model to a tenth of the sample size required for statistical convergence, predicted results are precise and accurate to a handful of percentage points. This framework can be adopted to shortlist feasible designs of microfluidic devices before fabrication, as well as assess a wider variety of scenarios in preliminary hypotheses.Doctor of Philosoph