Simplified Mathematical Model to Evaluate Sperm Concentration in Kremer'S Capillary Tube Test: A Preliminary Study Report

Summary 

Objective

The in vitro cervical mucus penetration assay, which is rarely used now, plays a role in basic research and is used to determine the clinical importance of cervical hostility and immunologic causes of infertility. Sperm concentration observed in a capillary tube test, where mucus-filled cylindrical tubes are placed with an end immersed in a semen reservoir mounted on a glass slide, indicates general sperm function and has a prognostic value for subsequent in vivo pregnancy. Because cylindrical tubes are optically inferior and may hinder the counting of sperm, the assessment of the efficiency of sperm penetration into cervical mucus is a time-consuming procedure and requires complex calculations. The present study investigated the feasibility of applying a simplified calculation model to estimate sperm concentration using the results of a capillary tube test. The postulated equation (sperm concentration ! N × 10³/0.339 sperm/mL) was derived from a mathematical model of definite integrals used to calculate the volume of intersection between two cylinders.

Materials and Methods

Semen samples from 46 male subjects were allowed to penetrate mid-cycle human cervical mucus contained in cylindrical tubes and incubated at 37° C for 60 minutes. Assessments of sperm concentration in the mucus column were performed using the postulated equation and a control method whereby the total number of sperm was assessed after extracting all contents from the capillary.

Results

Estimates of sperm concentration obtained using the postulated equation (149.2 ± 30.0 × 10³/mL) were similar and correlated with those obtained using the control method (166.3 ± 29.9 × 10³/mL; r = 0.79; p < 0.05). The mean difference in sperm concentration was not significant (17.2 ± 19.2 × 10³/mL).

Conclusion

The strong correlation of sperm concentrations between these two methods suggests that the postulated equation may provide a simplified calculation model to indicate penetration efficiency in the capillary tube test.

Key Words:  capillary tube test , cervical mucus penetration , fertility investigation

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