Optimisation and properties of gamete transport

• Main Author: Wakeley, Paul William
• Published: University of Birmingham 2009
• Subjects: 510; QA Mathematics
• Online Access: https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.532315

We consider a series of problems from the field of biological fluid mechanics, in particular the properties and optimisation of human sperm motility, and the fluid flow in the oviduct. As an initial approach, we consider and refine a sinusoidal planar model by introducing a new envelope function with parameters to specify the distal component of the beat pattern and to account for non-constant wavenumber; we investigate the properties of beat pattern configurations such as predicted cell velocity, power consumption and efficiency. The modelling of self-propelled flagellated micro-organisms at low Reynolds number is achieved using the powerful singularity method and slender-body theory. Results using the modified envelope parameter model agree qualitatively with experimental data to show that a balance between velocity, drag and power consumption is a factor in determining a beat pattern configuration. Limitations of the model are discussed including the underlying assumption that the beat pattern is a modified sinusoidal wave which limits the range of permissible patterns. A new method for specifying beat pattern configurations is developed arising from analysis of experimental data using the shear-angle. The resulting two parameter model encompasses a wide range of beat pattern observed in human sperm in vitro. The two parameter model is considered and various modes of efficient beating are illustrated. By considering the bending moment density (which scales with viscosity) we offer an explanation for the viscosity-dependent modulation of human sperm beat. Further extensions and applications of the new model are proposed.