A collective tracking method for preliminary sperm analysis

Abstract

Background: Total motile sperm count (TMSC) and curvilinear velocity (VCL) are two important parameters in preliminary semen analysis for male infertility. Traditionally, both parameters are evaluated manually by embryologists or automatically using an expensive computer-assisted sperm analysis (CASA) instrument. The latter applies a point-tracking method using an image processing technique to detect, recognize and classify each of the target objects, individually, which is complicated. However, as semen is dense, manual counting is exhausting while CASA suffers from severe overlapping and heavy computation.

Methods: We proposed a simple frame-differencing method that tracks motile sperms collectively and treats their overlapping with a statistical occupation probability without heavy computation. The proposed method leads to an overall image of all of the differential footprint trajectories (DFTs) of all motile sperms and thus the overall area of the DFTs in a real-time manner. Accordingly, a theoretical DFT model was also developed to formulate the overall DFT area of a group of moving beads as a function of time as well as the total number and average speed of the beads. Then, using the least square fitting method, we obtained the optimal values of the TMSC and the average VCL that yielded the best fit for the theoretical DFT area to the measured DFT area.

Results: The proposed method was used to evaluate the TMSC and the VCL of 20 semen samples. The maximum TMSC evaluated using the method is more than 980 sperms per video frame. The Pearson correlation coefficient (PCC) between the two series of TMSC obtained using the method and the CASA instrument is 0.946. The PCC between the two series of VCL obtained using the method and CASA is 0.771. As a consequence, the proposed method is as accurate as the CASA method in TMSC and VCL evaluations.

Conclusion: In comparison with the individual point-tracking techniques, the collective DFT tracking method is relatively simple in computation without complicated image processing. Therefore, incorporating the proposed method into a cell phone equipped with a microscopic lens can facilitate the design of a simple sperm analyzer for clinical or household use without advance dilution.

Keywords: Computer-assisted sperm analyzer (CASA); Curvilinear velocity (VCL); Frame differencing; Object tracking; Total motile sperm count (TMSC).

Fig. 1

Results of the second type of simulation conducted using the 123 synthetic bead samples at 41 settings of $N_{\text{set}}$ and ${\delta }_{\text{set}}=0$. a Total numbers $N_{\text{DFT}}$ and $N_{\text{CASA}}$ versus the preset $N_{\text{set}}$ ranging from 1 to 3500. b Average speeds $v_{\text{ave}\_\text{DFT}}$ and $v_{\text{ave}\_\text{CASA}}$ versus the preset $v_{\text{set}}$. Red points: $N_{\text{DFT}}$ and $v_{\text{ave}\_\text{DFT}}$ evaluated using the DFT method. Blue points: $N_{\text{CASA}}$ and $v_{\text{ave}\_\text{CASA}}$ measured using the CASA instrument. Green points: preset $N_{\text{set}}$ and $v_{\text{set}}=60\mathrm{\mu }\text{m/s}$

Fig. 2

Results of the experiment conducted using 20 semen samples. a Total numbers $N_{\text{DFT}}$ and $N_{\text{CASA}}$ versus the manual count $N_{\text{manual}}$ that serves as the gold standard. b Average speeds $v_{\text{ave}\_\text{DFT}}$ and $v_{\text{ave}\_\text{CASA}}$ versus the serial number of the 20 semen samples. Green points: the manual counts $N_{\text{manual}}$. Dark red points: $N_{\text{DFT}}$ and $v_{\text{ave}\_\text{DFT}}$ evaluated using the DFT method. Violet points: $N_{\text{CASA}}$ and $v_{\text{ave}\_\text{CASA}}$ measured using the CASA instrument

Fig. 3

The computation times of the DFT method and the CASA instrument as a function of the total numbers of synthetic beads and sperms. Each point represents the average computation time ± standard deviations of three times of evaluations. The red points and dark red points denote the computation times of the DFT method for the synthetic beads and sperms, respectively. The blue and violet points denote the computation times of the CASA instrument for the synthetic beads and sperms, respectively

Fig. 4

Typical color-coded DFT images of three semen samples of different concentrations for 10 s under a $10\times$ objective lens. Each trajectory in the images represents a motile sperm. a TMSC = 12, b TMSC = 45 and c TMSC = 100

Fig. 5

One-dimensional DFT of a single moving square. a The video frames of a moving square of width d at a constant speed v. b The differential footprint images of the square in different colors. c The color-coded DFT images of the square. d A turning point in the plot of the DFT area $a_1\left(t_i\right)$ as a function of time $t_i$

Fig. 6

Concept of the effective footprint area of each bead in the presence of bead overlapping. a Effective footprint of a single bead from a move. b Effective footprint area occupied by two beads. c Effective footprint area occupied by three beads. The effective footprint areas of the respective beads are different