Biomechanics of the self-propulsion of spermatozoa through porous medium in human cervical canal

The present prospective theoretical investigation concerns biomechanics of the self-propulsion of spermatozoa through cervical mucus that fills the pore spaces of porous medium in the human cervical canal. Modeling of the proposed mathematical model yields two linear partial differential equations. Resulting partial differential equations are solved analytically. Expressions for pressure gradient, propulsive velocity, mucus velocity, and time mean flow rate are analyzed for embedded parameters. Pumping characteristics are also explored. Analysis delineated maximal propulsive velocity of the spermatozoa in the absence of traveling waves along walls of the cervical canal. Pressure rise facilitates the motion of spermatozoa to fertilize an egg whereas the pressure drop inverts the direction of spermatozoa toward the vagina and controls the fertility. It is evident that the inclusion of porous medium reduces velocity of the spermatozoa while it causes enhancement in velocity of the cervical mucus and amplitude of the pressure gradient wave. Pumping rate is minimal in retrograde region whereas it is found to be maximal in augmented region in the absence of porous medium. Comparison of the current analysis with the experimental and theocratical literature is also made.