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Applied and Environmental Microbiology, May 2000, p. 2238-2242, Vol. 66, No. 5
0099-2240/00/$04.00+0
Copyright © 2000, American Society for Microbiology. All rights reserved.
A New System for Three-Dimensional Tracking of
Motile Microorganisms
Roland
Thar,*
Nicholas
Blackburn, and
Michael
Kühl
Marine Biological Laboratory, University of
Copenhagen, 3000 Helsingør, Denmark
Received 22 December 1999/Accepted 7 March 2000
 |
ABSTRACT |
A new three-dimensional (3D)-tracking system with optimized
dark-field illumination is presented. It allows simultaneous 3D tracking of several free-swimming microorganisms with diameters of >10
µm. Resolution limits and illumination efficiencies for different
size classes of microorganisms are treated analytically. First
applications for 3D tracking of protists are demonstrated.
| |
TEXT |
Many microorganisms react to
environmental stimuli, such as chemicals, gravity, magnetic fields, or
light. By changing their motility behavior, they are able to position
themselves in regions best suited to their physiology. Studies of
microbial motility and sensory behavior are thus important for
understanding the role of motile microorganisms in microbial ecosystems
and give important clues to the structure and ecology of
microenvironments (2, 5, 7, 11).
For quantitative investigations of motility, cell tracking systems are
advantageous. Most systems described in the literature are based on
standard microscopes (1). Their optics are optimized for
high resolution, yielding a limited depth of field. Consequently, a
cell can be tracked only during the time it spends in the focal plane.
Thin test chambers (e.g., a flat microcapillary) are often used for
limiting the space available for the microorganisms to a
two-dimensional (2D) plane. The microorganisms are then forced to stay
in the focal plane, but interactions between the borders of the test
chamber and the microorganism can significantly influence their moving
patterns. This is especially the case for microorganisms driven by long
flagella (8). The optimization of optics for high resolution
is not necessarily the best optical configuration for a tracking
system, in which only their position is of interest.
Most tracking systems in use are 2D-tracking systems. Usually, a video
camera connected to a microscope records pictures of moving
microorganisms at a rate of 25 or 30 Hz. While such a setup is suitable
for studies of motile microorganisms naturally restricted to 2D
surfaces (e.g., gliding motility [10]), it has several disadvantages for observations of microorganisms with truly 3D moving
patterns, like those of swimming protozoa (7) and bacteria (4). Their tracks appear as projections with loss of
information, such as velocity and direction.
The solution to this problem is to apply true 3D imaging. Common
techniques like confocal laser scanning microscopy are much too slow
for tracking fast microorganisms, which can swim at 1,000 µm
s
1 (9). A setup for 3D tracking of single
bacteria was presented by Berg (3). It consisted of a
standard video microscope, in which the observation chamber could be
moved by solenoids in all directions. A regulatory circuit ensured that
the observed bacterium stayed in the center of the focal plane. The 3D
position of the observed bacterium was recorded every 1/12 s. However,
this approach is inherently limited to tracking one cell at a time.
Here we present a video-based 3D-tracking system for microorganisms
with a diameter of >10 µm. The tracking system is independent of
mechanical devices and provides the possibility of tracking many cells
simultaneously. In order to increase the contrast, a dark-field
illumination was applied, which was optimized for high illumination
efficiency for minimizing any influence on the sample. Nonactinic
near-infrared illumination was used, which allowed investigations of
photosensory behavior.
Description of the setup.
The 3D-tracking system is based on
simultaneous observation of a cubic volume with two video cameras
positioned at 90° relative to each other, i.e., one camera recording
projections onto the (x,z) plane while the other
recorded projections onto the (y,z) plane, where
(x,y,z) are Cartesian coordinates
inside the cubic volume. By analyzing both (time-synchronized) video
recordings, 3D tracks of the observed microorganisms can be reconstructed.
The complete setup is shown in Fig. 1.
For illumination, we used an infrared diode laser (785-nm wavelength, 3 mW; RS Components, Copenhagen, Denmark). A combination of two achromat
lenses (20- and 120-mm focal lengths) expands the beam by a factor of
six to a diameter of 15 mm. A pinhole with a 30-µm diameter was
positioned in the common focal point of the lenses, serving as a
spatial filter improving the collimation of the final beam. The beam
splitter and mirrors in the light path provided two illumination beams perpendicular to each other. The sample under investigation was placed
at the crossing point of the two illumination beams. Two standard
monochrome charged-coupled device (CCD) cameras (kamPro02; EHD, Damme,
Germany) were used, which are also sensitive in the near-infrared
range. The optical path belonging to one of the cameras was redirected
by an additional mirror for compacting the overall dimensions.
Interference band pass filters (780-nm wavelength, 10-nm bandwidth)
were placed directly in front of the CCD detectors in order to exclude
ambient light or light fields used for investigations of photosensory
behavior. The complete setup was built on an optical bench (Microbench;
Linos Photonics, Göttingen, Germany).
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FIG. 1.
Optical setup for 3D tracking of microorganisms. The
paths of the illumination laser beam are shown as shaded areas. Rays
coming from a microorganism in the sample chamber are shown as broken
lines.
|
|
The illumination light hitting the microorganisms is scattered, and
this scattered light is used for observing them. Microorganisms
are
typically 1 to 100 µm in diameter. In this region, light scattering
of roughly spherical-shaped particles can be approximated by the
Mie
theory (
6,
13). For the size class between 1 and 5 µm,
light is scattered almost equally in all directions. The illumination
efficiency for this size class cannot be improved over common
illumination techniques in microscopy. However, for the size class
of 5 to 100 µm, an improvement is possible, because forward scattering
increases with particle diameter. In order to utilize forward
scattered
light for the observation of microorganisms in dark-field
illumination,
the optics have to be almost in line with the direction
of the
illumination light. To accommodate this, the configuration
shown in
Fig.
2 was chosen. Only the setup for one
camera is shown.
The expanded laser beam illuminated the microorganisms
in the
cuvette. The scattered light was imaged by a lens onto the CCD
detector of the camera. The original laser beam was removed at
the
focal point of the lens by a thin wire with a 300-µm diameter.
This
configuration ensured a long working distance, which made
the observed
sample easily accessible.
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FIG. 2.
Optical configuration of the imaging optics used in the
3D-tracking system. Only the optics belonging to one camera are
shown.
|
|
The depth of field was regulated by placing an iris diaphragm of radius
r at the focal point of the lens close to the wire.
The
positioning of the diaphragm at this point (also called "telecentric
configuration") has several advantages. It ensures that the forward
scattered light from an object can always reach the detector,
even if
the object is not positioned on the optical axis. Consequently,
no
fading occurs at the borders of the image. Furthermore, the
sample
volume is projected onto the detector plane without metric
distortions.
Standard imaging normally yields spatially distorted
images if the
focal length of the lens is short. It should be
noted that the
telecentric configuration limits the cross-section
of the observed
volume to the area of the lens. This does not,
however, cause practical
problems for dimensions less than 10
mm.
A large depth of field inherently means a loss in spatial resolution.
Consequently, the optimal optical configuration has
to be a compromise
between depth of field and resolution. The
resolution limit
(
ares) known for classical microscopes with
parallel illumination (
12) is given by
|
(1)
|
where
is the wavelength of the laser light and
NA
is the numerical aperture, defined by
|
(2)
|
where
n is the refractive index of the medium between
the object and the lens and
is the maximum acceptance angle of the
optics, which is limited by the diaphragm in the focal point behind
the
lens (Fig.
2). In our case the medium was air, so the refractive
index
n is 1 and will be omitted in the
following.
In Fig.
2, two point objects, M1 and M2, are shown on the optical axis.
The observed volume is the height of the field of
view times the depth
of field squared. The point object M1, positioned
at the center of the
observed volume, is in focus on the CCD detector
such that
|
(3)
|
where
f is the focal length of the lens,
g
is the distance between M1 and the lens, and
b is the
distance between the lens
and the projected image on the CCD detector.
The magnification
V is given by
|
(4)
|
where
d is the distance between diaphragm and the CCD
detector and
is the maximum angle between a ray from object M1 and
the optical axis at the CCD detector. The second point object
M2,
positioned at the border of the observed volume on the optical
axis at
a distance of
g to M1, was imaged at a distance of
b plus
b to the lens. In the following we
assume
g 
g, so
|
(5)
|
where the angles
' and
' belonging to object M2 correspond
to the angles
and
belonging to object M1. It can be seen
from
equations 4 and 5 that the object M2 will produce a circle
with a
radius
a
g such that
|
(6)
|
on the detector plane. For a given depth of field
(
DOF), this radius is largest at the point
aDOF as follows:
|
(7)
|
A compromise between resolution and depth of field occurs as
follows:
|
(8)
|
For a desired depth of field, combining equations 1, 7, and 8 yields the optimum numerical aperture as follows:
|
(9)
|
The numerical aperture of the described optical setup is
determined by the aperture of the diaphragm. From equations 4 and
5, the radius
r of this aperture is as follows:
|
(10)
|
The actual resolution limit
a for a given depth of
field can be calculated by combining equations 1 and 9 as follows:
|
(11)
|
Finally, the magnification is determined by the dimensions of the
CCD detector in the cameras. As one camera's width of field
should
equal the other's depth of field (i.e., the cross-section
of the
sample volume is
DOF2, as illustrated in Fig.
2), the magnification
V is such that
|
(12)
|
where
D is the width of the CCD
detector.
Typical values for depth of field in applications of the 3D-tracking
system would be 1, 5, or 10 mm. If an illumination wavelength
of
780 nm is used, this would imply a resolution limit
a of
20, 44, or 62 µm, respectively (equation 11). This resolution
limit
does not mean that objects with a smaller diameter cannot
be detected
(see below). The limit defines the minimum distance
at which two
objects can be separated. However, the resolution
of the positional
information of an object itself is in principle
not limited by this.
Here the limitation is given by the pixel
resolution of the CCD
detector. If the CCD detector has
N pixels
in width, then
the positional resolution limit
x is calculated
as
follows:
|
(13)
|
Typical CCD detectors have at least 500 pixels in width. If we
again assume a depth of field of 1, 5, or 10 mm, this would
yield a
positional resolution limit of 2, 10, or 20 µm,
respectively.
Illumination efficiency.
The light scattering of roughly
spherical-shaped microorganisms with diameters of 1 to 100 µm can be
approximated by Mie scattering. The scattering functions,
(
), of spheres with diameters of 1, 10, and 100 µm
were calculated numerically, where is the scattering angle. The
step size of for the calculation was 0.1°. We assumed no
absorption and an optical wavelength of 780 nm. The relative refractive
index n was chosen to be 1.04, which was shown to be a good
approximation for the refractive index of microorganisms relative to
that of water (13). The scattering function (6) is related to the total cross section, 
, as follows:
|
(14)
|
The fraction of the scattered light, which reaches the detector,
is limited by the numerical aperture (
NA = sin
) of
the
optical system; it can be shown that the part of the scattered
light removed by the wire can be neglected. The cross section,
det, of this part is calculated as follows:
|
(15)
|
The illumination efficiency,
e(), is calculated as
follows:
|
(16)
|
The illumination efficiency for the three different sizes of
spheres is shown in Fig.
3 as a function
of the numerical aperture
(
NA). Only
NA values of
<0.05 are shown, as this is the interesting
region for large depths of
field. A sphere with a 100-µm diameter
can be detected at very high
efficiency. With an
NA value of >0.02
(corresponding to a
depth of field of 4 mm), more than 40% of
the scattered light reaches
the CCD detector. This is due to the
pronounced forward scattering in
this case. The efficiency drops
to about 10 and 0.1% for 10- and
1-µm-diameter spheres, respectively.
For microorganisms with
diameters of >10 µm, the proposed illumination
method is much more
efficient than standard dark-field illumination
in microscopes, in
which the forward scattered light is not exploited.
Microorganisms with
diameters comparable to the wavelength of
the illumination light do not
show pronounced forward scattering,
and the illumination efficiency
drops significantly. In practice,
this limits our setup to observation
of microorganisms with diameters
of >10 µm. Smaller objects could be
only detected with a much
higher numerical aperture. But, this is
generally not compatible
with the need for a large depth of field for
the 3D-tracking system.
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FIG. 3.
Illumination efficiency as a function of the numerical
aperture (NA). The three lines represent calculations for
three model microorganisms of different diameters, as indicated in the
legend.
|
|
The tracking system.
Video sequences were recorded on two
separate video recorders, each connected to one of the two cameras. The
light source was momentarily switched off at the start of a recording
session to form a reference point for time synchronization.
Alternatively, it is possible to make do with one recorder by combining
half of the image from each camera into a single video channel (the images appear side by side) by using an editing box. We used digital tape recorders and transferred recorded video sequences to a computer via a standardized serial connector (IEEE 1394-FireWire) at 25 frames
s1 (PAL format). This technology is readily available at
low cost. Digital video sequences were stored with QuickTime, which
makes them compatible with most computer platforms.
Automatic tracking was performed for each of the two sequences
representing the (
x,
z) plane and the
(
y,
z) plane, in turn.
The tracking software
(LabTrack; DiMedia, Kvistgård, Denmark)
is based on an algorithm which
analyzes sequences one frame at
a time while building tracks. Each
video frame is thresholded
and analyzed for objects. The algorithm
searches around the end
of each existing track, and any objects in
proximity become candidates
for continuing those tracks. The best
candidate is chosen based
on velocity and trajectory. Any object not
associated with a track
becomes the start of a new track. Tracking
accuracy can be controlled
by adjusting criteria, such as search
radius, object size, velocity,
and duration. The system can track
several hundred objects simultaneously
and has proved to be quite
robust for tracking motile cells ranging
in size from small bacteria to
large ciliates (
5,
7).
3D tracks were constructed from the two sets of 2D tracks, one of the
(
x,
z) plane and the other of the
(
y,
z) plane. A track
in the
(
x,
z) plane was taken to match a track in the
(
y,
z) plane
if the average difference in their
common coordinate,
z, averaged
over time in overlapping
segments, was below a defined threshold
level.
A program for visualization of the obtained 3D tracks was written. The
tracks are shown as either 3D projections or red-green
images, which
show real 3D impressions if viewed through red-green
glasses. The
tracks can be freely rotated and viewed from all
directions.
Additionally, an option for animation exists, in which
single cells are
represented by moving points on the screen. The
program is available
from the corresponding
author.
Applications for 3D tracking of protists.
The complete
tracking system was tested with three different cultures of protists:
Euglena gracilis, Strombidium sulcatum, and
Oxhyrris marina. Three milliliters of the liquid cultures was filled into a standard glass cuvette (10 by 10 by 40 mm) with four
optically clear walls. The cuvette was placed on a Peltier element (10 by 10 mm, I = 1 A, MI 1060 T; RS Components) in order to prevent
thermal convection in the cuvette. A steady-state temperature gradient
was established after 30 min, with temperatures of 15°C at the bottom
and 18°C at the top.
In Fig.
4, the 3D track of one swimming
S. sulcatum cell is shown as projections onto the
(
x,
z) plane and the (
y,
z)
plane.
The duration of the shown track is 4.0 s. The helical
swimming
pattern of the ciliate can be seen combined with a gradual
change
in direction.
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FIG. 4.
Projections of the 3D track of one S. sulcatum cell onto the (x,z) and the
(y,z) planes. The time duration of the shown
track is 4.0 s.
|
|
The 3D tracks obtained from all three cultures are shown in Fig.
5 as 3D projections. The circles indicate
the positions of
the microorganisms at successive time steps of
0.04 s. The depth
information is indicated by the diameters of the
circles. The
S. sulcatum track (Fig.
5a) is the same as in
Fig.
4. The 3D projection
gives a good impression of its complex 3D
swimming pattern. Tracks
of two
E. gracilis cells are shown
in Fig.
5b. In this case, the
cuvette was additionally illuminated by a
standard incandescent
bulb (60 W) producing a scalar irradiance of 25 µmol photons s
1 m
2. Tumbling of
E. gracilis cells could be induced by switching
off the illumination
for 1 s, resulting in a change of swimming
direction. The tracks
consist of several straight-line parts interrupted
by the tumbling. The
last example (Fig.
5c) shows tracks of six
O. marina cells
swimming simultaneously in the observed volume.
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FIG. 5.
3D projections of tracks belonging to different
microorganisms: E. gracilis (a), S. sulcatum (b),
and O. marina (c). The circles indicate the positions of the
microorganisms at successive time steps of 0.04 s. The depth
information is indicated by the diameters of the circles.
|
|
These first applications illustrate how this system can be used in
future studies of microbial motility. Attractant chemical
sources can
be easily added into the cuvette, thus allowing detailed
3D studies of
chemotactic behavior of protists. The cuvette can
be illuminated by
well-defined light fields (e.g., fiber optics),
thus allowing studies
of photosensory behavior. The possibility
to track several
microorganisms simultaneously allows studies
of interactions between
motile microorganisms, like swarming behavior
or predator-prey
interactions.
| |
ACKNOWLEDGMENTS |
This study was supported by grants from the European Commission
(MAS3-CT98-5054), the Swedish Foundation for International Cooperation
in Research and Higher Education (STINT), and the Danish Natural
Science Research Council (9700549).
We thank Tom Fenchel and Per Juel Hansen for providing cultures of
S. sulcatum and O. marina.
| |
FOOTNOTES |
*
Corresponding author. Mailing address: Marine
Biological Laboratory, University of Copenhagen, Strandpromenaden 5, 3000 Helsingør, Denmark. Phone: 45 49 21 16 33 320/261. Fax: 45 49 26 11 65. E-mail: roland.thar{at}gmx.net.
| |
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Applied and Environmental Microbiology, May 2000, p. 2238-2242, Vol. 66, No. 5
0099-2240/00/$04.00+0
Copyright © 2000, American Society for Microbiology. All rights reserved.
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