Modelling of energy expended by free swimming spermatozoa in temperature-dependent viscous semen.

Derived models of fertilization kinetics have relied upon estimates of the swimming velocity of spermatozoa from the insemination site to a fallopian tube. However, limited derivations are available describing the probability and energy expended when spermatozoa collide with one another. An analytic approach of spermatozoon motion in a linear viscoelastic fluid is adopted to simplify the derivation. The complex kinematics of motion of an inextensible flagellum is modelled as planar flagellar wave of small amplitude. In humans, a temperature difference is expected between the cooler tubal isthmus and the warmer tubal ampulla. Thus, fluidic characteristics of semen such as viscosity can vary along the female reproductive tract. The results suggest that the probability of spermatozoa colliding in relatively lower viscous semen increases by 64.87% for a 0.5 degrees C surge in temperature. Moreover, this increases for a denser concentration of spermatozoa due to the limited semen volume available to manoeuvre. In addition, the propulsive forces and shear stress were 39.35% lower in less viscous semen due to an increase in temperature of only 0.5 degrees C. Hence, the described derivations herein can assist in the understanding of work done by a normal motile spermatozoon in a pool of semen.