Preparing and incubating sperm suspension

Frozen sperm specimens of a Warmblood stallion were obtained from the Center for Equine Health at the University of California, Davis. Before freezing, fresh semen specimens were first diluted to a concentration of 50 million sperms per ml with equine semen extender (E-Z Mixin BFT, Animal Reproduction Systems) and then were centrifuged at 400 G for 15 min. After centrifugation the pellet was re-suspended in freezing extender (E-Z Freezin Equine Semen Extender, Animal Reproduction Systems) with a final concentration of 400 million sperms per ml. The processed sperms specimens were packaged in 0.5 ml straws and frozen in a programmable freezer. When the straws had reached −150°C they were plunged in liquid nitrogen for storage.

To prepare the horse sperm suspension for imaging, the frozen specimens were first thawed at 38°C water bath for 30 sec and then rehydrated for 15 min by mixing with equine semen extender (BotuSemen, Nidacon, Sweden) by a ratio of 1:1. After rehydration, gradient density centrifugation with isotonic density medium (Equipure, Nidacon, Sweden, 200 g for 30 min) was used to concentrate the motile sperms within the semen specimens. The centrifuged sperm pellet was re-suspended with the same equine semen extender at a concentration of ~1 million sperms per ml (>50% motile) and then incubated for another 30 min. Right before lensfree on-chip imaging experiments, ~25 μL of the sperm suspension was put into a disposable observation chamber prepared by taping a laser-cut Acetal film (~0.15 mm thick) between two pieces of No. 1 cover slips.

The methods and related procedures for preparing and incubating human sperm suspensions have been explained in detail in our previous work23.

Dual-view and dual-wavelength lensfree on-chip holographic imaging and tracking set-up

A dual-view and dual-wavelength lensfree on-chip holographic imaging setup, as illustrated in Fig. 2, was utilized to record the 3D movement of sperms. Two partially-coherent light sources (LED-coupled multimode fibers, core size: 400 μm) illuminated the observation chambers from two different angles with two different wavelengths (vertical one: 625 nm; oblique one at 45°: 470 nm; bandwidth ~20 nm). When recording the 3D movement of sperms, the observation chamber was placed directly on the top of the protection glass of our CMOS (Complementary Metal-Oxide-Semiconductor) image sensor (Aptina MT9P031STC, 5 megapixels, 2.2 μm pixel size, monochrome; see Fig. 2(b)). The power of this image sensor chip was cut off between video acquisition sessions to maintain the temperature of the sperm observation chamber at ~37–39°C.

The frame rate of the computational imaging system used in this manuscript was raised to 143 FPS to oversample the faster beating of horse sperms (beat-cross-frequency, BCF: ~30 Hz), whereas it was operated at ~92 FPS for imaging of human sperms23. Such high frame rates reduced the imaging area of individual regions-of-interest (ROIs) that the CMOS image sensor chip can record at its full speed. Therefore, the whole field of view (FOV) of the image sensor was digitally divided into 16 (for human sperms) or 50 (for horse sperms) ROIs, which were sequentially recorded for continuous intervals of e.g., 0.7–7.0 seconds each. Further details of the human sperm imaging and tracking experiments can be found in Ref. 23. For horse samples, scanning over 50 such ROIs (with >5,000 lensfree holographic frames) and recording the 3D trajectories of >1,000 sperms took approximately 30 min for each semen sample. At the same time, the exposure time of the imaging system was also shortened to ~3 ms to avoid motion blur in recording the high-speed movement of horse sperms (which exhibit a typical instantaneous speed of e.g., ~150 μm/sec).

Reconstructing the 3D trajectories of sperms

For horse sperms, due to the high density of dead sperms and undissolved extender solute in the suspension liquid, each lensfree holographic frame was subtracted from a stationary image to remove the holograms of non-moving objects within the ROI. This stationary image was generated by averaging 100 consecutive lensfree frames that are nearest to the processing frame in the video sequence of the same ROI. These digital background cleaning steps were not needed and were not used for human sperm data.

The 3D trajectories of mobile sperms inside the FOV of the image sensor were then reconstructed following the procedures detailed in our previous work23. The vertical and oblique lensfree projections of each sperm head were digitally reconstructed on all the possible depth (i.e., z) planes individually. Once passed the morphological screening process, the centroid positions of both the vertical and the oblique head projections were calculated by their centers-of-gravity within their corresponding reconstructed amplitude images. The x and y coordinates of the sperms were taken directly from the centroid positions of the vertical head projections, while the z (depth) coordinates of the sperms were calculated by dividing the distance between their vertical and oblique projection centroids with the tangent of the oblique illumination angle in water. A space-time matrix containing the spatial and temporal coordinates of all the sperms within the observation volume was generated by repeating the same 3D localization procedures depicted above on all the holographic frames. Finally, the 3D trajectory of each sperm was constructed by linking the detected points across the recorded frames by a Brownian-statistics-based algorithm44. Note that the shapes of the sperm heads are assumed to be either spherical or ellipsoidal so that the orientation of the heads will not create a systematic error in the centroid-based position estimation. For tracking of sperms with deformed heads (see, e.g., images in References 45 and 46), processing techniques reported in Ref. 47 can potentially be used to minimize such errors and improve the reliability of our lensfree 3D tracking technique for deformed sperms.

Definitions of sperms' 3D dynamic swimming parameters

To quantify the 3D dynamics of sperm motion, we extracted a series of parameters from individual reconstructed sperm trajectories. All the parameters reported for horse sperms in this work were extracted from either 0.7 sec-long trajectories (~100 lensfree frames at 143 FPS) or track segments of such length that were digitally cropped from longer trajectories (e.g., ~4–7 sec long). For human sperms, however, these parameters were extracted from 1.1 sec-long tracks (~100 lensfree frames at 92 FPS). Similar to our previous work23, a digital “straightening” process was performed to compensate the curvature in sperm's forward motion before extracting these dynamical parameters. The definitions of parameters such as straight-line velocity (VSL), curvilinear velocity (VCL), linearity (LIN), amplitude of lateral head displacement (ALH) have been described in detail in our previous work23. Here we elaborate on the definition of the dynamical parameters that were newly introduced in this work:

Rate of twisting (RTW) represents the rotation speed (units: rad/sec) of the head beating plane for a sperm swimming in a ribbon pattern. It is defined as the angular frequency of the linear function that best fits the time evolution of the osculating plane angle for a track segment. The osculating plane angle on each position along the track segment is calculated by finding the most frequent angle of the lateral displacements occurring in the adjacent beating cycle, whose duration is defined by 2/BCF.

Twisting stability (TWS) is defined as the ratio between the accumulated angle change of the osculating plane and the averaged error to the best-fit linear function in the osculating plane angle. Both the angle change accumulation and the error averaging (by taking root mean square) were performed across the whole duration of each track segment. TWS represents how much a track segment is confined to a twisted ribbon (see, e.g., the magenta ribbon surfaces in Fig. 3 (b) and (e)). The value of TWS is reported in logarithm to the base 10. For example, a track segment with 10 radians of accumulated osculating plane angle change and 1 radians of mean linear-fit error would have a TWS of 1.

Digital classification of sperm trajectories

The 3D swimming patterns of sperms were classified based on the dynamic parameters defined in the previous section. Note that all the horse sperm trajectories with VCL smaller than 60 μm/sec and VSL smaller than 20 μm/sec are considered as immotile and are excluded from the reported statistics. The following are the specific criteria that we have used in this work to distinguish different categories of horse sperm trajectories:

Ribbon trajectory: TWS ≥ 1.2.

Hyperactivated trajectory: VCL ≥ 180 μm/sec and ALH ≥ 12 μm (following the definition used in Ref. 48).

Hyper-ribbon trajectory: A hyperactivated trajectory that also forms a ribbon (TWS ≥ 1.2).

Because human sperm trajectories were recorded at a lower frame rate (92 FPS instead of 143 FPS), the criteria for categorizing these trajectories for human sperms were modified as such:

Immotile trajectory: VCL < 30 μm/sec.

Ribbon trajectory: TWS ≥ 1.3.

Hyperactivated trajectory: VCL ≥ 150 μm/sec; LIN ≤ 0.5 and ALH ≥ 7 μm (following the definition used in Ref. 49).

The other criteria remained the same as the ones used for horse sperms.

Automated processing of 3D sperm trajectory data

Data processing procedures, including the reconstruction of lensfree holographic images, the localization of sperms' 3D centroids, the linking and resolution of sperms' 3D spatio-temporal trajectories and the classification of their 3D swimming patterns were all performed with a fully-automated custom-designed Matlab program. The typical computation time for automatic processing of e.g., ~5,000 lensfree images from a single semen sample is ~4 hours (using Matlab R2011a running on a PC with an eight-core Intel Core i7-930 2.80 GHz processor).