2.1.

Hardware and Optical Design

A single-point gradient trap was generated using an $\mathrm{Nd}:\mathrm{Y}\mathrm{V}{\mathrm{O}}_4$ continuous-wave $1064\mathrm{nm}$ wavelength laser (Spectra Physics, Model BL-106C, Mountain View, CA) coupled into a Zeiss Axiovert S100 microscope and a $40\times$ , phase III, NA 1.3 oil immersion objective (Zeiss, Thornwood, NY), which is also used for imaging as previously published.¹⁰ The optical design is shown in Fig. 1 . Laser light is reflected off two dielectric mirrors to orient the beam parallel to the table and along the optical axis of the microscope. The beam is expanded by two lenses (plano-concave lens, $f=-25.5\mathrm{mm}$ at $\lambda =1064\mathrm{nm}$ , and plano-convex lens, $f=76.2\mathrm{mm}$ at $\lambda =1064\mathrm{nm}$ ) in order to fill the objective’s back aperture. A third lens (biconvex lens, $f=200\mathrm{mm}$ ) focuses the beam onto the side port of the dual video adaptor to ensure the beam is collimated at the objective’s back aperture.¹¹ The dual video adaptor contains a filter cube with a dichroic that allows laser light entering the side port to be transmitted to the microscope while reflecting visible light to the camera attached to the top port for imaging. A filter (Chroma Technology Corp., Model D535/40M, Rockingham, VT) is placed in the filter cube to block back reflections of IR laser light while allowing visible light to pass. The laser trap remains stationary near the center of the field of view. In order to trap a sperm, the microscope stage is moved to bring the sperm to the laser trap location. The laser trap location is determined prior to each experiment by trapping $10\text{-}\mu \mathrm{m}$ -diameter polystyrene beads suspended in water within a $35\text{-}\mathrm{mm}$ -diameter glass bottom Petri dish. The trap depth within the sample is kept to approximately $5\mu \mathrm{m}$ (approximately one sperm head diameter) above the cover glass. This ensures that the trap geometry is not sensitive to spherical aberrations from the surrounding media. A removable polarizer is used only for power decay experiments (experiment 3) to control laser power. Laser power in the specimen plane is attenuated by rotating the polarizer, which is mounted in a stepper-motor-controlled rotating mount (Newport Corporation, Model PR50PP, Irvine, CA). The mount is controlled by a custom program that allows the experimenter to set the power decay rate (rotation rate of polarizer) and record power decay parameters once the sperm escapes the trap. The specimen is imaged at $30\text{frames}\text{per}\text{second}$ by a CCD camera (Sony, Model XC—75, New York, NY), coupled to a variable zoom lens system (0.33–1.6 X magnification) to demagnify the field of view. Analog output (RS-170 format) from the CCD is wired into the video-in port of a digital camcorder to record sperm swimming for off-line analysis.

Fig. 1

Optical schematic: Layout of microscope path and optical tweezers.

2.2.

Specimen

Semen samples collected from several dogs were pooled and cryopreserved according to a published protocol.^{12, 13} Semen samples were also collected from two dogs, different than the dogs used in the pooled sperm samples, and cryopreserved individually (dog 1: labeled 04-060, dog 2: labeled 05-037). Dog 2’s semen sample was subdivided into two samples in order to test for experimental errors in sperm preparation from one day to the next. For each experiment, a sperm sample is thawed in a water bath $(37°\mathrm{C})$ for approximately one to two minutes, and its contents are transferred to an Eppindorf centrifuge tube. The sample is centrifuged at $2000\mathrm{rpm}$ for $10\text{minutes}$ (centrifuge tip radius is $8.23\mathrm{cm}$ ). The supernatant is removed and the remaining sperm pellet is resuspended in $1\mathrm{mL}$ of prewarmed media [ $1\mathrm{mg}$ of bovine serum albumin (BSA) per $1\mathrm{mL}$ of Biggers, Whittens, and Whittingham (BWW), osmolarity of $270–300\mathrm{mmol}∕\mathrm{kg}$ water, pH of 7.2–7.4¹⁴]. Final dilutions of 30,000 sperm per mL of media are used in the experiments. The specimen is loaded into a rose chamber and mounted into a microscope stage holder.¹⁵ The sample is kept at room temperature. To quantify the effects of temperature, control experiments were conducted using an air curtain incubator (NEVTEK, ASI 400 Air Stream Incubator, Burnsville, VA) to achieve $37°\mathrm{C}$ at the specimen.

2.3.

Experiment 1—Trap Duration

The goal of this experiment is to determine if the duration a sperm is exposed to the laser trap has a significant effect on sperm motility. The effects are tested on sperm from two dog sperm samples pooled together. Laser trapping power is held constant at $420\mathrm{mW}$ in the specimen plane for durations of 15, 10, and $5\text{seconds}$ . (Laser power is measured using a photodiode just after the oil immersed objective to define the power in the focal plane.) Curvilinear velocity (VCL, $\mu \mathrm{m}∕\sec$ ) is measured prior to and post trapping for three to five seconds. VCL is the average velocity of the point-to-point trajectory, measured using custom software that tracks the sperm.¹⁶ The ratio of VCL after trapping to VCL before trapping is calculated to measure changes in swimming speed as a result of the laser trap. The Student’s t-test¹⁷ was used to compare the ratios of sperm held at $15\sec$ , $10\sec$ , and $5\sec$ after data were found to be normally distributed by the Lilliefors test.¹⁷

2.4.

Experiment 2—Trapping Power

The goal of this experiment is to determine if the laser trapping power has a significant effect on sperm motility. The laser trap duration is held constant at $5\sec$ . The effects are tested on sperm from the same pooled dog sperm sample as in the trapping duration experiment. Sperm are trapped at $420\mathrm{mW}$ , $350\mathrm{mW}$ , $300\mathrm{mW}$ , and $250\mathrm{mW}$ laser power in the specimen plane. The VCL is measured prior to and post trapping as in experiment 1. The Student’s t-test¹⁷ is used to compare the ratios of sperm held at $420\mathrm{mW}$ , $350\mathrm{mW}$ , $300\mathrm{mW}$ , and $250\mathrm{mW}$ after data were found to be normally distributed using the Lilliefors test.¹⁷

2.5.

Experiment 3—Correlation of Swimming Force and Swimming Speed

The rotation rate of the motorized mount that holds the polarizer is programmed to produce a linear power decay from maximum (100%) to minimum $(\approx 0\%)$ in $10\sec$ . A maximum trapping power of $366\mathrm{mW}$ in the specimen plane was used in these experiments. Studies were conducted on sperm samples pooled from four dogs (different than those used in the trap duration and trapping power experiments) as well as on sperm samples from individual dogs that were not pooled.

A sperm of interest is observed for three to six seconds before and after trapping. Once a sperm is trapped, the user initializes the power decay within one second. The moment the sperm escapes the trap, the user halts the power decay, and the escape power is recorded by the computer. Recorded video segments pre- and post-trapping are analyzed by the custom software to calculate the VCL, straight-line velocity (VSL), total distance traveled, and ratio of displacement to total distance traveled. Video of the sperm are independently analyzed by three fertility experts, each blind of the VCL and VSL, who assign each sperm an SOP score (based on the 1–5 scale). Sperm that appear to be swimming in a circular path (those with no forward progression) are given an SOP score of 2 regardless of swimming speed. These sperm were eliminated from the dataset.

The data from the pooled dog sperm sample is organized into a matrix with each row representing a single sperm and each column containing the nonsubjective measurements: (1) VCL pre-trapping; (2) escape laser power (Pesc); (3) swimming displacement pre-trapping; (4) curvilinear distance traveled pre-trapping; and (5) ratio of displacement to total distance traveled. Principal components analysis (PCA) of the data matrix was performed in order to seek hidden relationships between the five measurements.¹⁸ In PCA, the data matrix is linearly mapped into principal component (PC) space after standardizing each column by the estimate of its standard deviation. The data are transformed by

A supervised classifier using modified SOP scores for training was implemented to determine the most probable hyperplane(s) for separating classes of sperm in PC space. The SOP scores were modified since the number of separable sperm classes was not found to be necessarily equal to the number of SOP classifications, likely due to the subjectivity of the SOP scoring system. Instead, the number of sperm classes was determined by the number of statistically separable groups within the SOP scoring system, as assessed by the Wilcoxon paired-sample test.¹⁷ The supervised classifier returns the misclassification error rate, which is the percentage of observations in the dataset that are reclassified with respect to the modified SOP scores. Classified data are remapped into the original data space to understand the physical implications of the determined classes. VCL is plotted against Pesc for each class, and robust linear fitting is applied to seek a trend within each sperm class.

The trained classifier was tested with naïve data consisting of two individual, as opposed to pooled, dog sperm samples (exclusive from the pooled sperm sample set). The classifier first maps the naïve data into PC space using PC weights calculated from the pooled dog. The data are then classified using the pooled data as a training set. Linear regressions of Pesc vs. VCL are fit to each resulting class of sperm. This procedure is also used to test the effects of sample temperature by analyzing individual dog sperm samples at room temperature (approximately $25°\mathrm{C}$ ) and at $37°\mathrm{C}$ .

3.1.

Experiment 1—Trap Duration

A total of 179 dog sperm were trapped and analyzed: $N_{15\sec }=53$ sperm ( $⟨\mathrm{VCL}\text{pre}\text{-}\text{trap}⟩=102\mu \mathrm{m}∕\sec$ , range $[60.7–151]\mu \mathrm{m}∕\sec$ ), $N_{10\sec }=77$ ( $⟨\mathrm{VCL}\text{pre}\text{-}\text{trap}⟩=110\mu \mathrm{m}∕\sec$ , range $[37.4–200]\mu \mathrm{m}∕\sec$ ), and $N_{5\sec }=49$ ( $⟨\mathrm{VCL}\text{pre}\text{-}\text{trap}⟩=104\mu \mathrm{m}∕\sec$ , range $[39.8–174]\mu \mathrm{m}∕\sec$ ). Average velocity ratios of VCL post-trapping to VCL pre-trapping for various trap durations were determined (Table 1 ). Figure 2 plots sperm velocity ratios for the three trapping durations. The ratio of “1” is emphasized in order to distinguish the sperm that swam out of the trap at a higher velocity than before trapping from those that swam out of the trap at a lower velocity. The results of the Student’s t-test that compare the means of the sperm velocity ratios are also listed in Fig. 2. A trap duration of $15\sec$ resulted in a greater decrease in VCL than $10\text{-}\sec$ or $5\text{-}\sec$ durations (at $420\mathrm{mW}$ laser power). Average VCL decrease for trap durations of $10\sec$ and $5\sec$ were negligible and statistically equivalent.

Fig. 2

Experiment 1—Effects of Trap Duration: VCL ratios for the three trap durations tested ( $15\sec$ , $10\sec$ , $5\sec$ ) at constant power $\left(420\mathrm{mW}\right)$ . The less time sperm are exposed to the trap, the closer the VCL ratio is to unity (less effect on sperm motility). The results of the Student’s t-test ( $P$ -values) are listed.

Table 1

Effect of Laser Trap Duration and Laser Power of on Sperm Motility

3.2.

Experiment 2—Trapping Power

A total of 195 dog sperm were trapped and analyzed: $N_{420\mathrm{mW}}=49$ ( $⟨\mathrm{VCL}\text{pre}\text{-}\text{trap}⟩=104\mu \mathrm{m}∕\sec$ , range $[39.8–174]\mu \mathrm{m}∕\sec$ ), $N_{350\mathrm{mW}}=49$ ( $⟨\mathrm{VCL}\text{pre}\text{-}\text{trap}⟩=108\mu \mathrm{m}∕\sec$ , range $[41.7–185]\mu \mathrm{m}∕\sec$ ), $N_{300\mathrm{mW}}=51$ ( $⟨\mathrm{VCL}\text{pre}\text{-}\text{trap}⟩=78.2\mu \mathrm{m}∕\sec$ , range $[85.5–140]\mu \mathrm{m}∕\sec$ ), and $N_{250\mathrm{mW}}=46$ ( $⟨\mathrm{VCL}\text{pre}\text{-}\text{trap}⟩=91.6\mu \mathrm{m}∕\sec$ , range $[42.0–165]\mu \mathrm{m}∕\sec$ ). Average velocity ratios for various trapping powers are listed in Table 1. Figure 3 plots sperm velocity ratios for all four trapping powers. The data at all four trapping powers were found to be statistically equivalent $(P>0.05)$ , and the average decrease in VCL post-trapping is considered negligible. Thus, a $10\text{-}\sec$ power decay beginning at $420\mathrm{mW}$ or less should not significantly affect sperm motility.

Fig. 3

Experiment 2—Effects of Trapping Power: VCL ratios for the four trapping powers tested ( $420\mathrm{mW}$ , $350\mathrm{mW}$ , $300\mathrm{mW}$ , $250\mathrm{mW}$ ). All VCL ratios are close to unity.

3.3.

Experiment 3—Correlation of Swimming Force to Swimming Speed

Figure 4 demonstrates the subjective nature of SOP scores. Pesc (mW) is plotted against VCL $(\mu \mathrm{m}∕\sec )$ for the pooled dog sperm dataset (excluding circle swimmers). The data are labeled according to the SOP scores assigned by each of the three qualified sperm scoring experts. Variability in assigned SOP score is evident. As expected, a linear relationship between swimming force and Pesc was found with $R^2\approx 0.9$ using a robust linear regression. However, doing so is contrary to a qualitative analysis of the data that suggests there may be intrinsic groupings, each with their own Pesc to VCL relationship. For example, potential groupings could be a high escape power group and a low escape power group or a slow group and a fast group with high Pesc outliers.

Fig. 4

Experiment 3—Discrepancy between SOP score assignment between individuals: Pesc vs. VCL for the pooled dog sperm sample with scores assigned by scorers #1, #2, and #3 (left to right).

PC analysis consolidated 73% of the variation in the data to within the first two principal components. Table 2 lists the percent variability accounted for by each PC as well as the PC weights. Figure 5 plots PC1 vs. PC2 for the pooled sperm data.

Fig. 5

Experiment 3—Data Variation Maximization: Pooled dog sperm data set in PC space—optimum group division shown for two classes. Scorer #1 plotted as circles, scorer #2 plotted as dots, both showing SOP $2^{*}$ group in green and SOP $3^{*}$ group in black.

Table 2

Principal Component Analysis

To test uniqueness of the SOP scores, Wilcoxon paired-sample tests¹⁷ for equal median (5% significance level) were performed on Pesc distributions of sperm grouped by SOP score, for each scorer. Table 3 summarizes the number of significantly separable groups each scorer distinguished. Two of the three scorers uniquely distinguished at most two groups of sperm, consisting of “slower” and “faster” swimmers. For the purpose of classification in PC space, modified SOP scores were constructed based on these findings: $“\text{slower}”=\mathrm{SOP}{2}^{*}$ and $“\text{faster}”=\mathrm{SOP}{3}^{*}$ (Table 3 maps SOP scores to modified SOP scores for each scorer).

Table 3

Defining Sperm Classes

Figure 5 plots the pooled dog sperm data in PC space labeled by their modified SOP scores for scorers #1 and #2. As can be seen, the region of support lies nearly along a straight line. A supervised classifier with a linear hyperplane was found to yield the lowest misclassification error rate (7.44%). A classifier based on scorer #3 had a misclassification error rate of 28.05% (not shown). Subsequent data analysis is based only on classifiers trained from scorers #1 and #2.

Figure 6 plots the data of Fig. 4 labeled by classifier output. Linear regressions with robust fitting for each group (SOP $2^{*}$ , SOP $3^{*}$ ) are shown for scorer #1. Table 4 lists the slopes $\left(m\right)$ , $y$ -intercepts, and $R^2$ -values for linear regressions applied to the original dataset and applied to the classified groups, by scorer. Regressions were compared using the Student’s t-test.¹⁷ Regression parameters of the original data were statistically different from the SOP $2^{*}$ and SOP $3^{*}$ groups, casting doubt on the validity of regressing the entire dataset. Interestingly, SOP $2^{*}$ slopes showed little to no relationship between Pesc and VCL (mean value was 0 or 0.02 for scorers #1 and #2, respectively). Both scorers revealed an SOP $3^{*}$ group with equivalent nonzero slopes. This suggests the SOP $3^{*}$ group has a linear Pesc to VCL dependence.

Fig. 6

Experiment 3—Classified data with regressions: Pesc vs. VCL for pooled dog sperm sample is plotted according to the reclassification for scorer #1 with robust linear regressions applied to each sperm class.

Table 4

Unclassified vs. Classified Data

Of interest are the outlying sperm that escape the trap at higher powers than the majority of the sperm analyzed. They were neither identifiable by their SOP score (see Fig. 4), nor as an independent group using PCA and supervised classification. One possibility is that these outlier sperm are all from one specific dog within the pooled sample which has stronger-swimming sperm. This theory is tested by repeating the experiment using the single-dog sperm samples. Figure 7 plots Pesc vs. VCL for the individual dog sperm samples (dog 1 and dog 2 tested on separate days) superimposed with the pooled dog sample data. Both individual dog sperm samples exhibit two groups of sperm, slower and faster swimming, as well as outlying sperm that escape the trap at higher trapping powers. Using the Wilcoxon rank sum test, VCL and Pesc of dog 2 were found to have equal medians $(P>0.05)$ between days one and two.

Fig. 7

Experiment 3—Comparison of individual samples with pooled samples: Pesc vs. VCL for individual dog sperm samples referenced with pooled dog sample. Dog 1 in triangles, dog 2 (day 1) in pluses, dog 2 (day 2) in asterisks, and pooled dog in x’s.

The individual dog sperm data were transformed into PC space by the PC weights calculated with the pooled dog sperm data. Subsequent classification (trained on the pooled dog data) had a misclassification error rate of 1.36%. Linear regression of the SOP $2^{*}$ group shows a near-zero slope while regression of the SOP $3^{*}$ group finds a linear increase in swimming force with swimming speed. Table 4 summarized the regression results.

Sperm velocity distributions were found to be of equal median $(P>0.05)$ for a sample analyzed at room temperature and at $37°\mathrm{C}$ . Regressions fit to escape power vs. VCL are found to be statistically equivalent $(P>0.05)$ .