High-throughput lensfree 3D tracking of human sperms reveals rare statistics of helical trajectories.
ABSTRACT Dynamic tracking of human sperms across a large volume is a challenging task. To provide a high-throughput solution to this important need, here we describe a lensfree on-chip imaging technique that can track the three-dimensional (3D) trajectories of > 1,500 individual human sperms within an observation volume of approximately 8-17 mm(3). This computational imaging platform relies on holographic lensfree shadows of sperms that are simultaneously acquired at two different wavelengths, emanating from two partially-coherent sources that are placed at 45° with respect to each other. This multiangle and multicolor illumination scheme permits us to dynamically track the 3D motion of human sperms across a field-of-view of > 17 mm(2) and depth-of-field of approximately 0.5-1 mm with submicron positioning accuracy. The large statistics provided by this lensfree imaging platform revealed that only approximately 4-5% of the motile human sperms swim along well-defined helices and that this percentage can be significantly suppressed under seminal plasma. Furthermore, among these observed helical human sperms, a significant majority (approximately 90%) preferred right-handed helices over left-handed ones, with a helix radius of approximately 0.5-3 μm, a helical rotation speed of approximately 3-20 rotations/s and a linear speed of approximately 20-100 μm/s. This high-throughput 3D imaging platform could in general be quite valuable for observing the statistical swimming patterns of various other microorganisms, leading to new insights in their 3D motion and the underlying biophysics.
Conference Paper: Lensfree computational imaging[Show abstract] [Hide abstract]
ABSTRACT: We review our progress on the development of computational lensfree on-chip microscopy and tomography techniques for biomedical imaging, microanalysis and telemedicine applications.SPIE Optical Metrology 2013; 05/2013
Conference Paper: Head tracking and flagellum tracing for sperm motility analysis[Show abstract] [Hide abstract]
ABSTRACT: Sperm quality assessment plays an essential role in human fertility and animal breeding. Manual analysis is time-consuming and subject to intra- and inter-observer variability. To automate the analysis process, as well as to offer a means of statistical analysis that may not be achieved by visual inspection, we present a computational framework that tracks the heads and traces the tails for analyzing sperm motility, one of the most important attributes in semen quality evaluation. Our framework consists of 3 modules: head detection, head tracking, and flagellum tracing. The head detection module detects the sperm heads from the image data, and the detected heads are the inputs to the head tracking module for obtaining the head trajectories. Finally, a flagellum tracing algorithm is proposed to obtain the flagellar beat patterns. Our framework aims at providing both the head trajectories and the flagellar beat patterns for quantitatively assessing sperm motility. This distinguishes our work from other existing methods that analyze sperm motility based merely on the head trajectories. We validate our framework using two confo-cal microscopy image sequences of ram semen samples that were imaged at two different conditions, at which the sperms behave differently. The results show the effectiveness of our framework.2014 IEEE 11th International Symposium on Biomedical Imaging (ISBI 2014); 04/2014
Conference Paper: Simple and effective one-time password authentication scheme[Show abstract] [Hide abstract]
ABSTRACT: Analyzed some shortages of the existing one-time password (OTP) authentication schemes, a new OTP authentication scheme is designed. This scheme used the SM2 cryptographic algorithm and Hash function to ensure data transmission security, provided the mutual authentication between client and server, resisted different kinds of attacks, and protected the user's identity information effectively. Analysis showed that compared with the existing schemes, the new designed scheme had higher security, small system overhead and easy to implement.2013 2nd International Symposium on Instrumentation & Measurement, Sensor Network and Automation (IMSNA); 12/2013
High-throughput lensfree 3D tracking of human
sperms reveals rare statistics of helical trajectories
Ting-Wei Sua,b, Liang Xuea,b,c, and Aydogan Ozcana,b,d,e,1
aElectrical Engineering Department, University of California, Los Angeles, CA 90095;
dCalifornia NanoSystems Institute, University of California, Los Angeles, CA 90095; and
University of California, Los Angeles, CA 90095
bBioengineering Department, University of California, Los Angeles,
cDepartment of Information Physics and Engineering, Nanjing University of Science and Technology, Nanjing, Jiangsu 210094, China;
eDepartment of Surgery, David Geffen School of Medicine,
Edited by Wallace F. Marshall, UCSF, San Francisco, CA, and accepted by the Editorial Board August 16, 2012 (received for review July 21, 2012)
Dynamic tracking of human sperms across a large volume is a chal-
lenging task. To provide a high-throughput solution to this impor-
tant need, here we describe a lensfree on-chip imaging technique
that can track the three-dimensional (3D) trajectories of >1,500
individual human sperms within an observation volume of ap-
proximately 8–17 mm3. This computational imaging platform relies
on holographic lensfree shadows of sperms that are simulta-
neously acquired at two different wavelengths, emanating from
two partially-coherent sources that are placed at 45° with respect
to each other. This multiangle and multicolor illumination scheme
permits us to dynamically track the 3D motion of human sperms
across a field-of-view of >17 mm2and depth-of-field of approxi-
mately 0.5–1 mm with submicron positioning accuracy. The large
statistics provided by this lensfree imaging platform revealed that
only approximately 4–5% of the motile human sperms swim along
well-defined helices and that this percentage can be significantly
suppressed under seminal plasma. Furthermore, among these ob-
served helical human sperms, a significant majority (approximately
90%) preferred right-handed helices over left-handed ones, with a
helix radius of approximately 0.5–3 μm, a helical rotation speed of
approximately 3–20 rotations∕s and a linear speed of approxi-
mately 20–100 μm∕s. This high-throughput 3D imaging platform
could in general be quite valuable for observing the statistical
swimming patterns of various other microorganisms, leading to
new insights in their 3D motion and the underlying biophysics.
human sperm imaging ∣ sperm tracking ∣ digital holography ∣
imaging volume of optical microscopes that are based on conven-
since the sperm head is small (approximately 3–4 μm) demanding a
relatively high-magnification objective lens, and moves rather fast
(20–100 μm∕s) which makes it difficult to track their 3D swimming
patterns as they quickly move out of the observation volume of an
objective lens. Partly due to this low throughput and the limited
spatial and temporal sampling windows that conventional micro-
scopes provide, natural 3D swimming patterns of human sperms and
were obtained using lens-based conventional microscopes either
measured the 2D trajectories of the human sperms along a focal
plane, or reported on sperms of other species such as sea urchin,
which were significantly easier to resolve under a microscope since
their 3D rotation diameter is larger (>13 μm) together with a lower
rotation frequency compared to human sperms.
Here we report a new technique that is based on lensfree
holographic imaging on a chip to dynamically track the 3D tra-
jectories of human sperms across a large volume of approximately
8–17 mm3(Fig. 1) with submicron positioning accuracy. This
platform can track >1;500 individual human sperms over several
hours, obtaining massive amounts of statistics about their 3D
swimming patterns across 10–20 s for each continuous pattern.
bserving three-dimensional (3D) trajectories of sperms is
in general a challenging task. This is partially due to limited
The large pool of statistics provided by this lensfree computa-
tional imaging platform enabled us to observe, for the first time,
the helical trajectories of human sperms, exhibiting a tight helix
radius of approximately 0.5–3 μm, a helical rotation speed of
approximately 3–20 rotations∕s and a linear speed of approxi-
mately 20–100 μm∕s. Furthermore, this platform revealed that
only approximately 4–5% of the motile humansperms swim along
well-defined helices, and that this percentage of helical sperms
can be considerably suppressed using seminal plasma. Quite in-
terestingly, we also observed that a significant majority (approxi-
mately 90%) of these rare helical sperms preferred right-handed
helices over left-handed ones, which is an observation that is
enabled by the large spatial and temporal measurement windows
that our on-chip imaging platform provides.
Compared to earlier reports that also used holographic ima-
ging techniques (20–28) to track sperms or other microorganisms,
our approach is lensfree (Fig. 1) and therefore exhibits a signifi-
cantly larger imaging field-of-view of >17 mm2together with unit
fringe magnification, while still achieving submicron positioning
accuracy that is necessary to observe human sperms’ tight helical
paths. Furthermore, instead of using a laser source with high
degree of coherence, we use partially-coherent illumination (both
spatially and temporally) at two different wavelengths emanating
from two light-emitting-diodes (LEDs) that are placed at 45°
with respect to each other. This partially-coherent multiangle
illumination at two different wavelengths (blue and red) signifi-
cantly suppresses speckle and multiple-reflection interference
noise terms as well as cross-interference among sperms’ diffrac-
tion patterns, which make it feasible to track >1;500 sperms with
submicron positioning accuracy. Our results on human sperms
demonstrate the unique capabilities of this high-throughput on-
chip imaging platform by resolving the tight and rapidly evolving
rare helical trajectories of motile sperms. Finally, the same tech-
nique might in general be widely applicable for observing the
statistical swimming patterns of various other microorganisms,
leading to new insights in their 3D motion and the underlying
Human sperms exhibit a large variation in their 3D swimming
patterns, and therefore using our dual-view lensfree holographic
imaging platform (Fig. 1) we initially grouped these swimming
patterns into four major categories as exemplified in Fig. 2
(typical, helical, hyperactivated, and hyperhelical; Table S1 and
Methods). The “typical” trajectory shown in Fig. 2A (Movie S1)
Author contributions: T.-W.S. and A.O. designed research; T.-W.S., L.X., and A.O.
performed research; T.-W.S. analyzed data; and T.-W.S. and A.O. wrote the paper.
The authors declare no conflict of interest.
This article is a PNAS Direct Submission. W.F.M. is a guest editor invited by the Editorial
1To whom correspondence should be addressed. E-mail: email@example.com.
This article contains supporting information online at www.pnas.org/lookup/suppl/
16018–16022 ∣ PNAS ∣ October 2, 2012 ∣ vol. 109 ∣ no. 40www.pnas.org/cgi/doi/10.1073/pnas.1212506109
is the most prevalent swimming pattern observed among human
sperms (>90%), in which the sperm head moves forward swiftly
(as fast as 140 μm∕s) along a slightly curved axis with a small
lateral displacement (approximately 4 μm side-to-side). In this
category (i.e., typical), although the lateral displacement exhibits
a certain degree of periodicity, the sperm head changes its direc-
tion arbitrarily in 3D space (Fig. 2A and Fig. S1 A, C, and D).
However, when these typical trajectories are located near the
chamber boundaries, some of them also exhibit lateral displace-
ments that are better confined to a two-dimensional plane, which
is not necessarily parallel to the boundary (Fig. S1B).
In the second category of swimming patterns that human
sperms exhibit, we observed helical trajectories (approximately
(Movie S2), which show the sperm head moving forward with very
stable revolutions around a central axis, creating a well-defined
helix. Not only is this helical trajectory (Fig. 2B) quite tight with
an average helix radius of approximately 1.6 μm and a rotation
speed of approximately 10 rotations∕s, but also it moves rather
fast, traveling more than 30–40 μm in depth-of-field (i.e., the z
direction) within approximately 1 s, making it rather challenging
to observe with a typical objective lens due to its limited depth-
of-field and observation volume. In contrast to typical swimming
patterns, we observed that the structure of these helical patterns
did not alter much when the sperm head was near the boundaries
of the observation chamber (Fig. S2).
In our third category, we observed hyperactivated 3D swim-
ming patterns (<3% of motile human sperms, Table S1) that
exhibit quite different movement compared to the previous two
pattern types (Fig. 2C and Movie S3). The most noticeable
change in a hyperactivated pattern is the decrease of its forward
movement, despite the fact that the instantaneous speed of
hyperactivated sperms (>150 μm∕sec) is usually 2X faster than
the instantaneous speed of typical or “helical” sperms. Most of
the track length of a hyperactivated human sperm is consumed
by the increased lateral movement, which has a size of >7 μm
from one side to the other (Fig. 2C). This hyperactivated swim-
ming pattern can be also divided into two subcategories, similar
to 2D observations (5): (i) transitional hyperactivation, where the
sperm still moves forward with a “meander” track (Fig. 2C and
Fig. S3 A and C); and (ii) “star-spin” hyperactivation (mostly ob-
served near the chamber boundaries), where the sperm bounces
around vigorously but totally loses its forward movement as illu-
strated in Fig. S3B. Similar to the typical swimming patterns,
many of the sperms in transitional hyperactivation category show
quasi-2D lateral displacement near the chamber boundaries
(compare Fig. S3 A and C, where the latter is much better con-
fined to a plane).
In the final category of human sperm swimming patterns,
we observed hyperhelical patterns (Fig. 2D, Fig. S3 D–F, and
Movie S4), which can be considered as a combination of transi-
tional hyperactivation and regular helical trajectories, exhibiting
enlarged and slightly more unstable revolutions around a helix
axis with a sustained forward movement. This swimming pattern
was significantly rare, constituting only <0.5% of motile human
sperms (Table S1). No major difference in swimming patterns
was observed between the hyperhelical trajectories located in free
3D volume and the ones located near the chamber boundaries.
An important feature of the presented lensfree on-chip ima-
ging approach is that it can track 3D trajectories of >1;500
human sperms over a large sample volume, which enables us
diagram of the imaging system. Two partially-coherent light sources (red and
blueLEDs at 625nm and470 nm, respectively) are butt-coupledto multimode
fibers (0.4 mm core diameter each) to simultaneously illuminate the sperms
at two different angles (red at 0° and blue at 45°). A CMOS sensor chip re-
cords the dual-view lensfree holograms that encode the position information
of each sperm. The 3D location of each sperm is determined by the centroids
of its head images reconstructed in the vertical (red) and oblique (blue) chan-
nels. This schematic diagram is not drawn to scale. (B) The reconstructed 3D
sperm trajectories. 1,575 human sperms inside a volume of 7.9 μL were
tracked at a frame rate of 92 FPS. The time position of each track point is
encoded by its color (see the color bar).
Dual-view lensfree 3D tracking of human sperms. (A) The schematic
typical pattern. (B) The helical pattern. (C) The hyperactivated pattern.
(D) The hyperhelical pattern. The inset in each panel represents the front
view of the straightened trajectory of the sperm (Methods). The arrows in-
dicate the directions of the sperms’ forward movement. The time position of
each track point is encoded by its color (see the color bar). The helices shown
in (B) and (D) are both right-handed. See Movies S1–S4 for the time evolution
of the sperm trajectories shown in (A–D), respectively. Some other examples
of human sperm trajectories are also provided in Figs. S1–S4.
Four major categories of human sperm swimming patterns. (A) The
Su et al.PNAS
October 2, 2012
to observe the transitions among different swimming patterns
across a time window of approximately 10–20 s for each contin-
uous sperm trajectory. Fig. 3, Fig. S4, and Movie S5 illustrate
some examples of such swimming pattern transitions acquired
using our lensfree imaging platform. Based on our measurement
results, Table S2 summarizes the statistics of such transitions
among different swimming patterns observed in human semen
samples. These results reveal that most of the observed helical
and hyperactivated trajectories quickly switch back to typical
swimming patterns (approximately 64% for helical trajectories
and approximately 58% for hyperactivated trajectories).
Our human sperm tracking experiments can be further sum-
marized in Fig. 4, where we quantify various parameters of 3D
swimming patterns, curvilinear velocity (VCL), straight-line
velocity (VSL), amplitude of lateral head displacement (ALH),
beat-cross frequency (BCF), linearity (SI Text), and compare
them to the statistical behavior of only the helical human sperms,
which constitute <5% of the motile sperms. The mean values of
these swimming parameters and their standard deviations are also
listed in Tables S3 and S4. Based on these results, it is rather inter-
esting to note that a significant majority (approximately 90%)
of helical human sperms in baseline medium prefer right-handed
helixes over left-handed ones (Fig. 4F), exhibiting a tight helix
radius of 0.5–3 μm and a rotation speed of 3–20 revolutions∕s.
To shed more light on this observation (i.e., the preference of
right-handed helices), we performed an additional experiment
(Fig. 5) to measure the percentage of helical trajectories as a
function of time after the sperms were removed from seminal
plasma and were placed into baseline medium (SI Text). The re-
sults of this time-traced experiment revealed that, after removal
of the seminal plasma, the percentage of right-handed helical
sperms significantly increased within approximately 2–3 h of
incubation in baseline medium, reaching approximately 4–5% of
motile human sperms (Fig. 5), which is also consistent with our
previous observations in Fig. 4 and Table S1. On the other hand,
the same experiment did not reveal any major changes in the left-
handed helical sperm percentage as a function of time, which
remained to be <0.5% even after >3 h of incubation in baseline
medium, as illustrated in Fig. 5.
These results also suggest that seminal plasma significantly
suppresses helical trajectories of human sperms, while human
tubal fluid initiates them. An experimental comparison of how
different concentrations of seminal plasma affect the 3D swim-
ming patterns of human sperms (in specific helical and hyper-
activated trajectories) is also provided in Fig. 6, which once again
confirmed the suppressing effect of seminal plasma on helical
trajectories (after >2 h of incubation time, SI Text). Another
important observation is that the helical trajectories, compared
to the hyperactivated ones, were more difficult to suppress by in-
creasing the percentage of seminal plasma in medium (Fig. 6),
suggesting that these two swimming patterns might be regulated
through different mechanisms.
We should emphasize that to obtain large numbers of statistics
regarding the swimming patterns of human sperms one would
need a high-throughput imaging platform with submicron 3D
tracking accuracy and sub-12-ms temporal resolution to clearly
swimming patterns of a human sperm. (A), (C), and (D) illustrate digitally ex-
tracted segments (approximately 1 s long each) of the whole sperm trajectory
shown in (B). See Movie S5 for the time evolution of this trajectory. More
sample trajectories with different pattern transitions are also provided in
Fig. S4. The inset in each panel is the front view of the straightened trajectory
of the sperm. The time position of each track point is encoded by its color (see
the color bar).
A 10.9-s long trajectory showing the transitions between different
1,069 helical trajectories. Color bar represents the relative density of data
points in each graph. Magenta lines enclose 90% of the motile/helical tracks
presented in each panel. A helix with RPS > 0 (RPS < 0) is defined as right-
handed (left-handed). VSL: straight-line velocity. VCL: curvilinear velocity.
ALH: amplitude of lateral head displacement. BCF: beat-cross frequency. RPS:
rotation speed. The unit r∕s: revolutions per second. These measurements
were made in baseline medium (artificial HTF) after >2 h of incubation as
described in SI Text.
Dynamic swimming parameters of 24,090 motile human sperms and
artificial human tubal fluid (HTF). After approximately 2–3 h of incubation
in HTF, the percentage of right-handed helical trajectories significantly
increased to approximately 4–5% of motile human sperms, while the percen-
tage of left-handed ones did not show a major change, remaining <0.5% of
Time evolution of helical sperm trajectories after resuspension in
www.pnas.org/cgi/doi/10.1073/pnas.1212506109Su et al.
resolve different patterns, especially the helical patterns, which
exhibit a tight helix radius of approximately 0.5–3 μm with a fast
rotation speed that might reach 15–20 rotations∕s. Conventional
microscopes equipped with high-magnification objective lenses
and high-frame-rate cameras can only meet these requirements
for imaging sperms along a 2D plane, which can infer limited in-
formation on their natural 3D motion (1–16). Estimation of the
3D trajectories of sperms from their 2D observations can also be
feasible in some cases by assuming a known swimming pattern
(15, 29). However, such approaches in general would not be able
to infer the details and quantify the fine parameters of 3D sperm
trajectories due to lack of position information along the third
dimension. A 2D vs. 3D comparison of human sperm trajectories
is provided in Fig. S5 to better illustrate that different swimming
patterns of human sperms can look very similar in 2D observation
while their 3D patterns are vastly different.
More advanced microscopy configurations (17–19) or holo-
graphic imaging schemes (20–28) have also been used to resolve
3D trajectories of sperms of other species. However, these pre-
vious approaches have not reported submicron 3D localization
accuracy throughout a large observation volume of ≥1 μL. The
dual-view partially-coherent holographic on-chip imaging techni-
que described in this article uses a lensfree hologram recording
configuration to image a large field-of-view of 17 mm2and
utilizes a multicolor illumination scheme to achieve submicron
localization accuracy for tracking human sperms within a volume
of 8–17 μL. This high-throughput platform provides unique
opportunities to observe the swimming patterns of human sperms
and reveal their rare statistics for helical or hyperhelical trajec-
tories, as summarized in Results.
In general, human sperm trajectories reconstructed by our 3D
tracking technique are consistent with previous observations
made by conventional lens-based 2D microscopy tools (1, 3–7,
12, 13). Most sperms swim forward with quasiperiodic small
lateral displacements, while some sperms move with enlarged
lateral displacement (transitional hyperactivation), and some
other sperms display the “star-spin” movement (complete hyper-
activation). In addition to this, the extra depth information pro-
vided by our lensfree imaging technique enabled us to reconstruct
the complete 3D trajectories of human sperms, isolating the he-
lical motion from planar or other types of swimming patterns.
Furthermore, our approach also permits investigation of
sperms’ 3D distribution inside an observation chamber, shedding
more light on the effect of surface boundaries on 3D swimming
patterns of human sperms. Similar to what was reported previ-
ously for chambers that are deeper than a sperm’s body length
(9, 30–33), we also observed the accumulation of human sperms
on the inner surfaces of our observation chambers. Although such
accumulation happens on both the top andbottom surfaces for all
four swimming patterns (Fig. 2), the presence of the surface
boundaries, as described in Results, only modifies the typical and
hyperactivated patterns but not the helical ones. Note that in our
experiments, we used plain glass surfaces without siliconization.
With different surface treatment methods, our platform can also
be used to study how the surface properties can affectthe statistics
of sperm movement.
Compared to the swimming patterns of sea urchin sperms,
which have also been extensively studied (2, 8–11, 15–19, 29, 31,
34, 35), human sperms exhibit some distinct features in their 3D
swimming behavior. First, motile human sperms, just like other
mammaliansperms (36),occasionally display hyperactivatedswim-
ming patterns; however, sea urchin sperms do not exhibit hyper-
activation. Second, when swimming near a surface, sea urchin
sperms tend to follow circular swimming paths with a strongly
preferred handedness (9, 11, 31, 34, 35), whereas human sperms
do not exhibit such behavior. Third, helical trajectories of human
sperms can be observed both in free 3D volume and near solid
surfaces; however, sea urchin sperms only display helical move-
of human sperms, compared to sea urchin sperms (19), exhibit sig-
nificantly smaller helix radii (1.6 ? 0.5 μm vs. 6.8 ? 1.1 μm) and
faster rotation speeds (6.8 ? 4.6 r∕s vs. 4.0 ? 0.8 r∕s), making
them much more challenging to resolve in 3D.
Although we have reported large statistics on 3D trajectories
of >24;000 human sperms revealing several important obser-
vations that have so far been hidden due to limited capabilities
of existing optical imaging platforms, most of the regulating
mechanisms behind these observations still remain unclear. For
example, in our experiments seminal plasma suppressed the
percentage of helical sperm trajectories as illustrated in Fig. 6.
This observation could be due to (i) the higher viscosity of semi-
nal plasma; or (ii) its chemical composition. The effect of medium
viscosity to make helical movement un-sustainable is also sup-
ported by previous studies, where high viscosity is shown to re-
duce the amplitude of sperms’ lateral head displacement (12).
However, the time lag (Fig. 5) between the removal of human
sperms from seminal plasma and the appearance of helical tra-
jectories suggests that there should be some other biochemical
factors involved that delay the activation of this helical move-
ment. By imaging human sperms in media with various activating
or suppressing constituents, our 3D tracking platform can be used
to better investigate the underlying mechanisms regulating such
helical or hyperhelical patterns. Along the same lines, this lens-
free sperm imaging platform can also provide a high-throughput
tool to rapidly quantify the impact of various stimuli and drugs
on the 3D swimming patterns of sperms.
3D Tracking of Human Sperms. The lensfree holographic frames recorded by
the dual-view and dual-color lensfree holographic imaging setup (SI Text)
were first individually reconstructed on all the possible object planes (with
25 μm vertical spacing) within the observation chamber, for both the vertical
red illumination and the oblique blue illumination. This digital reconstruction
process for each illumination wavelength followsthe iterative phase recovery
method that is detailed in our previous work (37). The digital separation of
sperm head’s vertical and oblique lensfree projections is discussed in SI Text,
Fig. S6 and Movie S6. In each reconstructed lensfree frame, possible sperm
candidates were segmented by thresholding the amplitude image for both
color channels. Detection artifacts were filtered out with a series of morpho-
logical criteria, such as peak value, area, and eccentricity (38). Once con-
firmed as the projection of a sperm, the 2D centroid position of each sperm
projection in both color channels was calculated by its center-of-gravity (38)
based on the square of its reconstructed amplitude profile. At the same time,
the focal distance of each vertical projection (which was estimated as the
distance with the highest contrast in its reconstructed 2D image stack)
was taken as the “coarse” vertical (i.e., z) distance of the sperm from the
Complementary Metal—Oxide—Semiconductor sensor chip. This initial esti-
mate has a lower depth accuracy of approximately 5–10 μm and is just used
to search for the corresponding projection of each sperm in the oblique
illumination channel. The 2D centroid position of the sperm head projection
in the vertical channel was directly used as the sperm’s x-y coordinate. The
precise z coordinate of the sperm was then calculated by dividing the dis-
tance between its vertical and oblique projection centroids with the tangent
(B) trajectories as a function of increased seminal plasma concentration in
culture media. Each of the mean ? SD bars in (A) and (B) was based on 14
measurements of two specimens (seven with each) obtained from different
Quenching of human sperms’ helical (A) and hyperactivated
Su et al.PNAS
October 2, 2012
of the oblique illumination angle in water (Fig. 1A). Refer to SI Text and
Fig. S7 for quantification of our submicron localization accuracy.
The same 3D localization procedures outlined above for human sperms
were repeated for each recorded lensfree holographic frame to generate
a 3D-t (i.e., space-time) matrix, which contains the spatial and temporal co-
ordinates of all the sperm head positions detectedin our observation volume.
The trajectory of each sperm as a function of time was then constructed by
linking up the nearest detected points (39) across the reconstructed 3D am-
plitude frames. To improve our tracking accuracy, we also used a Brownian-
statistics-basedalgorithm(40) forbetter handlingnoise inour measurements.
Digital Classification of the Reconstructed Sperm Trajectories. The 3D swim-
ming patterns of human sperms were categorized based on several dynamic
parameters extracted from their reconstructed 3D-t trajectories, such as cur-
vilinear velocity, linearity, lateral displacement, and number of stable turns
(rotations) (SI Text). All the parameter extraction performed in this work was
based on either 1.1 s-long trajectories (approximately 100 frames at 92 FPS)
or track segments of such length that were digitally extracted from longer
trajectories (10–20 s long).
Before automatically extracting these dynamic parameters for each sperm
within our observation volume, the reconstructed 3D trajectory segments
need to go through a digital “straightening” process to compensate the cur-
vature in their 3D motion. To this end, a 3D parabolic curve model was used
to fit the curved moving axis of each segment by minimizing the square of
the distance between all the position points and the fitted axis (where the
distance was created by the sperm’s lateral displacement). All the position
points were then reassigned laterally onto a plane moving along the axial
direction according to their relative position to the fitted axis (Fig. S8 A–C).
After this digital straightening step, the moving axis of each segment became
a straight line and the position points evolved laterally around the fitted axis.
The lateral coordinates of the position points (the Xrand Yrin Fig. S8 B
and C) were then used to calculate the instantaneous radius and the angle
of the trajectory points (Fig. S8 D and E), where the instantaneous angle was
further unwrapped to eliminate possible 2π phase jumps and fitted with a
linear function to estimate its rotation speed.
Note that in this work we considered all the human sperm trajectories
with a VCL that is smaller than 30 μm∕s as immotile (41). The motile sperm
trajectories that cannot be classified as helical, hyperactivated, or hyperhe-
lical are then classified as typical trajectories. For distinguishing helical,
hyperactivated and hyperhelical 3D sperm trajectories from typical ones,
the following criteria have been used:
Helical trajectory—Number of stable turns, NST ≥ 2.0.
Hyperactivated trajectory—VCL needs to be larger than 150 μm∕s; the
linearity needs to be smaller than 0.5; and ALH needs to be larger than
Hyperhelical trajectory—All the requirements for both helical and hyper-
activated trajectories need to be satisfied.
Because of the fact that the fitting of helices requires more than two
stable turns and that the hyperactivated sperms can change their swimming
patterns back and forth within a few seconds (5), longer sperm trajectories
are digitally divided into track segments that are each approximately 1.1 s
long, which is long enough for fitting a helix but short enough for minimiz-
ing swimming pattern transitions within each segment.
ACKNOWLEDGMENTS. We thank Drs. Christina Wang and Andrew Leung
(Harbor-UCLA Medical Center, Torrance, CA, USA) for their valuable discus-
sions and help on processing semen specimens. A.O. acknowledges the
support of Army Research Office Young Investigator Award, National Science
Foundation CAREER Award, the Office of Naval Research Young Investigator
Award, and the National Institutes of Health Director’s New Innovator Award
DP2OD006427 from the Office of The Director, National Institutes of Health.
1. Phillips DM (1972) Comparative analysis of mammalian sperm motility. J Cell Biol
2. Rikmenspoel R (1978) Movement of Sea Urchin Sperm Flagella. J Cell Biol 76:310–322.
3. Serres C, Feneux D, Jouannet P, David G (1984) Influence of the flagellar wave devel-
opment and propagation on the human sperm movement in seminal plasma. Gamete
4. Ishijima S, Oshio S, Mohri H (1986) Flagellar movement of human spermatozoa.
Gamete Res 13:185–197.
5. Mortimer ST, Swan MA (1995) Variable kinematics of capacitating human spermato-
zoa. Hum Reprod 10:3178–3182.
6. Mortimer ST (2000) CASA—Practical aspects. J Androl 21:515–524.
7. Mortimer ST, Schëväert D, Swan MA, Mortimer D (1997) Quantitative observations of
flagellar motility of capacitating human spermatozoa. Hum Reprod 12:1006–1012.
8. Woolley DM, Vernon GG (2001) A study of helical and planar waves on sea urchin
sperm flagella, with a theory of how they are generated. J Exp Biol 204:1333–1345.
9. Woolley DM (2003) Motility of spermatozoa at surfaces. Reprod 126:259–270.
10. Kaupp UB, et al. (2003) The signal flow and motor response controling chemotaxis of
sea urchin sperm. Nat Cell Biol 5:109–117.
11. Riedel IH, Kruse K, Howard J (2005) A self-organized vortex array of hydrodynamically
entrained sperm cells. Science 309:300–303.
12. Smith DJ, Gaffney EA, Gadêlha H, Kapur N, Kirkman‐Brown JC (2009) Bend propaga-
tion in the flagella of migrating human sperm, and its modulation by viscosity. Cell
Motil Cytoskeleton 66:220–236.
13. Gillies EA, Cannon RM, Green RB, Pacey AA (2009) Hydrodynamic propulsionof human
sperm. J Fluid Mech 625:445–474.
14. Friedrich BM, Riedel-Kruse IH, Howard J, Jülicher F (2010) High-precision tracking of
sperm swimming fine structure provides strong test of resistive force theory. J Exp Biol
15. Gurarie E, Grünbaum D, Nishizaki M (2011) Estimating 3D movements from 2D obser-
vations using a continuous model of helical swimming. Bull Math Biol 73:1358–1377.
16. Ishijima S (2012) Mechanical constraint converts planar waves into helices on tunicate
and sea urchin sperm flagella. Cell Struct Funct 37:13–19.
17. Crenshaw HC (1996) A new look at locomotion in microorganisms: Rotating and trans-
lating. Am Zool 36:608–618.
18. Crenshaw HC, Ciampaglio CN, McHenry M (2000) Analysis of the three-dimensional
trajectories of organisms: Estimates of velocity, curvature and torsion from positional
information. J Exp Biol 203:961–982.
19. CorkidiG, TaboadaB, WoodCD, GuerreroA,DarszonA (2008) Trackingsperminthree-
dimensions. Biochem Biophys Res Commun 373:125–129.
20. Xu W, Jericho MH, Meinertzhagen IA, Kreuzer HJ (2001) Digital in-line holography for
biological applications. Proc Natl Acad Sci USA 98:11301–11305.
21. Malkiel E, Sheng J, Katz J, Strickler JR (2003) The three-dimensional flow field gener-
ated by a feeding calanoid copepod measured using digital holography. J Exp Biol
22. Jericho SK, Garcia-Sucerquia J, Xu W, Jericho MH, Kreuzer HJ (2006) Submersible
digital in-line holographic microscope. Rev Sci Instrum 77:043706.
23. Lewis NI, et al. (2006) Swimming speed of three species of Alexandrium (Dinophyceae)
as determined by digital in-line holography. Phycologia 45:61–70.
24. Heydt M, et al. (2007) Digital in-line holography as a three-dimensional tool to study
motile marine organisms during their exploration of surfaces. J Adhes 83:417–430.
25. Sheng J, et al. (2007) Digital holographic microscopy reveals prey-induced changes
in swimming behavior of predatory dinoflagellates. Proc Natl Acad Sci USA
26. Frentz Z, Kuehn S, Hekstra D, Leibler S (2010) Microbial population dynamics by digital
in-line holographic microscopy. Rev Sci Instrum 81:084301.
27. Sohn M, et al. (2011) Determination of the swimming trajectory and speed of chain-
forming dinoflagellate Cochlodinium polykrikoides with digital holographic particle
tracking velocimetry. Mar Biol 158:561–570.
28. Lee SJ, Seo KW, Choi YS, Sohn MH (2011) Three-dimensional motion measurements
of free-swimming microorganisms using digital holographic microscopy. Meas Sci
29. Guerrero A, et al. (2011) Strategies for locating the female gamete: The importance
of measuring sperm trajectories in three spatial dimensions. Mol Hum Reprod
30. Winet H, Bernstein GS, Head J (1984) Observations on the response of human sper-
matozoa to gravity, boundaries and fluid shear. J Reprod Fertil 70:511–523.
31. Cosson J, Huitorel P, Gagnon C (2003) How spermatozoa come to be confined to
surfaces. Cell Motil Cytoskeleton 54:56–63.
32. Smith DJ, Gaffney EA, Blake JR, Kirkman-Brown JC (2009) Human sperm accumulation
near surfaces: A simulation study. J Fluid Mech 621:289–320.
33. Elgeti J, Kaupp UB, Gompper G (2010) Hydrodynamics of sperm cells near surfaces.
Biophys J 99:1018–1026.
34. Ishijima S, Hamaguchi Y (1992) Relationship between direction of rolling and yawing
of golden hamster and sea urchin spermatozoa. Cell Struct Funct 17:319–323.
35. Ishijima S, Hamaguchi Y (1993) Calcium ion regulation of chirality of beating flagellum
of reactivated sea urchin spermatozoa. Biophys J 65:1445–1448.
36. Ho HC, Suarez SS (2001) Hyperactivation of mammalian spermatozoa: Function and
regulation. Reprod 122:519–526.
37. Isikman SO, et al. (2011) Lens-free optical tomographic microscope with a large ima-
ging volume on a chip. Proc Natl Acad Sci USA, Available at: http://www.pnas.org/
content/early/2011/04/15/1015638108.abstract [Accessed December 4, 2011].
38. Su T-W, et al. (2010) Multi-angle lensless digital holography for depth resolved ima-
ging on a chip. Opt Express 18:9690–9711.
39. Su T-W, Erlinger A, Tseng D, Ozcan A (2010) Compact and light-weight automated se-
men analysis platform using lensfree on-chip microscopy. Anal Chem 82:8307–8312.
40. Crocker JC, Grier DG (1996) Methods of digital video microscopy for colloidal studies.
J Colloid Interface Sci 179:298–310.
41. World Health Organization (1999) WHO Laboratory Manual for the Examination of
Human Semen and Sperm-Cervical Mucus Interaction (Cambridge University Press,
Cambridge, UK), 4th Ed.
www.pnas.org/cgi/doi/10.1073/pnas.1212506109 Su et al.