In order to image sperm cells moving, one needs to capture the right dilution of solution such that the sperm can move freely. Also, the coverslip needs to be placed so that it does not impede cell movement.

The scalebar in the images represents 50 microns.

Using ImageJ we defined a region of interest where we observed measurable movement. We picked a specific cell and measured its movement from frame to frame. Our frame-by-frame measuring stick can be seen in the following movies as a white line.

Now that we know the movement (i.e. displacement), knowing the time between each frame in the movie we were able to calculate the velocity of the sperm under observation. Shown below are the magnitude of velocity traces for the sperm that we observed in the movies above (5-7).

From the above plots it can be seen that the velocity appears to vary quite significantly (standard deviations are very large), this can be attributed to the fact that the observed sperm halt momentarily during the movie. Comparing these velocities to those found in the literature for sperm: Van der Berghl, Marc et al. (Human Reproduction. 13, 11 [November 1998]: 3103-3107.) found that the straight line velocity ranged between 0 to 35 micrometers/second, Katz, D.F. & H.M. Dott. (Journal of Reproductive Fertility. 45, 2 [November 1975]: 263-72) found the mean veloctiy of sperm to be in the range of 68 to 162 micrometers/second.

So we are in the right ball park!

To consider the drag and energy required by the sperm cell to swim we need to establish the dominant forces in this fluid flow regime. This can be done using the dimensionless parameter known as the Reynolds number, which is defined as:

where rho is the density of the fluid, V is the characteristic velocity, D the characteristic diameter and mu is the dynamic viscosity of the fluid. So for a sperm cell: the fluid is water and for this analysis we shall assume a characteristic velocity of 55 micrometers/second and a characteristic length of 4 micrometers (approximate diamter), the Reynolds number is approximately 10^(-4)

This means that the viscous forces dominate (and the inertial forces are negligible) - this is Stokes flow. For this regime the drag force is given by:


where C_{D} is the drag coefficient, U is the velocity and A is the cross sectional area. For the purpose of this analysis we are going to approximate the sperm cell as a slender tube of diameter 4 micrometers and length 40 micrometers. Computing the drag coefficient is a rather involved process: for the derivation please read section 4.6 of "Introduction to Mathematical Biology" by Rubinow (1975) or Keller and Rubinow (J. Fluid Mech. 75:705-714 [1975]) or the more fundamental paper by Cox entitled "The motion of long slender bodies in a viscous fluid" (J. Fluid Mech. 44:791-810 [1970]). The derived result is that the drag coefficient for such a body is given by:

So for the sperm cell the drag force is approximately:

Power is given by:

The amount of energy released by the hydrolysis of one ATP molecule: ~10^(-19)J. So bearing in mind that an efficiency of 30-50% is extremely good for most systems the above estimate for power equates to about one ATP molecule being hydrolysed in the sperm cell per second. Gut feeling indicates that this is rather low estimate but the order of magnitude seems ok...