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Study of the Line Optical Tweezers Characteristics Using a Novel Method and Establishing a
Model for Cell Sorting
View the table of contents for this issue, or go to the journal homepage for more 2009 Jpn. J. Appl. Phys. 48 072502
(http://iopscience.iop.org/1347-4065/48/7R/072502)
Study of the Line Optical Tweezers Characteristics Using a Novel Method
and Establishing a Model for Cell Sorting
Ho-Chien Linand Long Hsu
Institute and Department of Electrophysics, National Chiao-Tung University, 1001 Ta Hsueh Road, Hsinchu, Taiwan 30010, R.O.C. Received December 30, 2008; accepted April 13, 2009; published online July 21, 2009
Optical tweezers have become a powerful tool in cellular and molecule biology. Line optical tweezers enhanced its function in cell sorting. This study presents the line trap model, based on the ray-optics model, and demonstrates its accuracy for the line optical tweezers. The line optical tweezers system is established to produce the optical intensity distribution of a line pattern and to trap the micro-sized beads. The main parameter, optical intensity distribution, is used to calculate the trapping force distribution in the model. The two forces, trapping force and water dragging force, and the equation of motion is used to simulate the trajectory of micro-sized beads as they pass through the line pattern in flowing water in the microchannel. The trajectory is analyzed to determine the effective separation distance between the micro-sized beads or cells. The method will be applied in biological and medical detection. #2009 The Japan Society of Applied Physics
DOI: 10.1143/JJAP.48.072502
1. Introduction
The miniaturization of cell separation techniques is a much-sought breakthrough in the development of the microfluidic lab-on-a-chip. Currently available standard cell sorting and screening systems involve flow cytometry and a micro-channel chip, both of which have several limitations. Following many trials, the combination of the non-mechan-ical optnon-mechan-ical manipulation of optnon-mechan-ical tweezers and the microfluidic lab-on-a-chip may provide a new solution.
The cell sorting apparatus most frequently utilized today exploits optical and electronic detection associated with flow cytometry to detect specific cells rapidly. However, the large-sized and expensive flow cytometry is a drawback. In contrast, a microchannel chip is miniature and inexpensive. It exploits the characteristics of the microchannel chip to guide and differentiate among cells of different sizes. It comprises the microstructure and the dielectrophoresis (DEP). Although a microchannel chip is a tool of cell sorting, it has some limitations. First, the procedure is only applicable to fixed-sized cells and cannot be extended to apply to individual sample cells. Once the size, location and pattern of the structure fabricated on the chip have been set, neither the microstructure nor the electrode on the chip can be altered, despite the consistency between the cell and the sample cell size. Next, the electrode plates are normally placed at the bottom of the microchannel because an effective trapping domain of an electrode is only around 100 mm wide; therefore, a microchannel with a deeper domain is ineffective. Because of these unsolved problems, a microchannel chip has not been extensively applied.
Unlike a microchannel chip, optical tweezers perform not mechanical but optical trapping. They do not raise the difficulties of the microchannel encounters. Optical tweezers are a photonic device that exploits a focused laser beam to provide a trapping force. They function like a ‘‘hand’’ with which to trap and manipulate single cells or molecules under the microscope. Although an optical tweezers trap the micro-sized bead which effective trapping domain is only around 100 mm long, similar to that of a microchannel chip, the trapping point can be freely controlled in a microchannel of a large area. This feature enables trapped cells to be guided
in the microchannel. The advantages of optical tweezers somewhat eliminate the limitations and drawbacks of microchannel chips. With a combination of microfluidic lab-on-a-chip, optical tweezers have been established to be powerful tools in the miniaturization of cell separation techniques.
This study proposes the model and the line optical tweezers system in which cells of various sizes are effectively separated in a microchannel. Since their inven-tion by Ashkin et al.,1)optical tweezers have opened up new areas of the study in cellular and molecular biology, because their ability to trap and manipulate single cells or mole-cules.2–7)Reicherter and Curtis further constructed a system of holographic optical tweezers (HOT) by combining the programmable phase modulator (PPM) with traditional optical tweezers.8,9)The HOT system enables many particles or cells to be manipulated simultaneously. Restated, it extends the application of optical tweezers from the generation of one trap to the generation of multiple traps simultaneously.10) Based on HOT and the PPM, Tseng developed the line trap by arranging multiple traps in a line.11) He also introduced the possibility of guiding and separating differently sized particles using the line trap. Grier focused on the relationship between phase modulation and optical intensity distribution of holographic line traps.12,13) This work presents the line trap model and demonstrates its accuracy. The model is utilized to analyze the functions of line optical tweezers, including trapping, guiding and separation. The micro-sized bead/cell separa-tion was determined as a funcsepara-tion of velocity of flowing water and the included angle between the line pattern and direction of flow.
2. Model
This section proposes model of a line optical tweezers and experimentally demonstrates the accuracy of the model. The model was used to calculate the distribution of the trapping force when the micro-sized bead was trapped in the line optical tweezers for all of the line patterns produced by the PPM. Next, numerical simulation was used to calculate the trajectories of two micro-sized beads of different sizes under the influence of the different resultant forces that comprise the water dragging force and the trapping force. From the trajectories, the separation distance d of the two
sized beads was calculated. Based on the model, this distance was used to determine the separation efficiency. Finally, the separation conditions of water flowing velocity vw and included angle w between the line pattern and
direction of flow were determined.
To calculate the trapping force distribution of the trapped micro-sized beads, the interaction of the micro-sized beads immersed in an aqueous solution with line optical tweezers was considered. The five known parameters were the refractive index of the aqueous solution ns, the refractive
index of a micro-sized bead nB, the radius RBof the beads,
the mass M of the beads, and the laser wavelength . The center of the trapped micro-sized bead was designated the origin OBwith coordinats (xo, yo, zo), the length of the line
pattern was L and the total laser power of the line pattern was P. This model assumes that the line pattern is formed from many individual trapping points. Then, based on Ashkin’s Single Trap Ray-Optics model, the trapping force distribution at each trapping point is individually calculated and then summed to determine the trapping force distribu-tion of the line-trap model.
Figure 1 shows the line pattern at z ¼ 0 which comprises m individual trapping points is established first. The coordinate of each trapping point k is (xk, yk, 0), where
1 k m. Next, each trapping point is assumed to have a laser power Pk that differs from each of the others, for a
total power (P ¼Pmk¼1Pk). Additionally, since each
trap-ping point corresponds to one-trap optical tweezers, on a simulated objective can be assumed to be located on the top of each trapping point. Each laser power Pk is that of a
parallel incident laser beam. When all the corresponding incident laser beams converge, they meet at focal points in the focal plane, which later become a line pattern. The specification of these virtual objectives is assumed to be identical to that of the experimental objectives. The focus is defined as fobj and the radius of the entrance pupil is
Robj. Accordingly, the coordinate of any center of the
objectives is Ok, with coordinate (xk, yk, fobj). To simulate
the focusing of a laser beam, each beam is divided into j rays, for convenience of tracing. Since each trapping
point corresponds to its own laser beam, the laser power of any ray i at any trapping point k is Pki¼Pk=j, where
1 i j.
In ray tracing, on the objective of a virtual microscope, the i-th ray of the k-th laser beam was assumed to be emitted at an angle of inclination !ki from point Aki, with coordinate
(xAki, yAki, fobj) to one of the points Bki, on the surface of
the micro-sized bead, and then to refract into the bead. Geometry is used to obtain the coordinate of Bki and the
coordinate of the incident ray that is closest to the center of the bead, Cki(xCki, yCki, zCki). xCki¼ xoþyotan ’ki zo tan kicos ’ki 1 þ tan2’ kiþ 1 tan kicos ’ki 2; ð1Þ yCki¼ykþ ðxCkixkÞ tan ’ki; ð2Þ and zCki¼ ðxCkixkÞ tan kicos ’ki ; ð3Þ which ’ki¼tan1 yAkiyk xAkixk ; ð4Þ
is the angle between x-axis and vector Ok to vector Aki,
!ki¼tan1 rki fobj ; ð5Þ and rki¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðxAkixkÞ 2þ ðy AkiykÞ 2 q ; ð6Þ
is the distance between Akito Ok; accordingly, the incident
angle kiand the refraction angle ’kiat point Bkifor this ray
can be obtained: ki¼sin1 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðxoxCkiÞ 2þ ðy oyCkiÞ 2þ ðz ozCkiÞ 2 p RB ; ð7Þ ’ki¼sin1 nssin ki nB : ð8Þ x y z ki
Aki: (xAki, yAki, -fobj)
Bki
(xCki, yCki, zCki) : Cki
OB: (xo, yo, zo) (xm, ym, 0) (x1, y1, 0) ki fSki P1 Pki O1: (x1, y1, -fobj) fobj ki ki rki Ok: (xk, yk, -fobj) Robj Gki θ (xk, yk, 0) Pk ϕki fSki φki Virtual Objectives ω rki Robj f
Fig. 1. A schematic drawing of the interaction between the line optical tweezers and the micro-sized bead. The line pattern at z ¼ 0 which comprises m individual trapping points. Each trapping point corresponds to one-trap optical tweezers. The scattering force fGk iand the gradient
force fSk i exerted by each one-trap optical tweezers on the micro-sized bead was calculated.
Consider both s- and p-polarizations under the influence of electric field; the ray in position Bki, the reflectance Rkiand
transmittance Tkican be expressed as
Rki¼ nscos kinBcos ’ki nscos kiþnBcos ’ki 2 for s-polorization nscos ’kinBcos ki nscos ’kiþnBcos ki 2 for p-polorization 8 > > > < > > > : ; ð9Þ and Tki¼ nBcos ’ki nscos ki 2nscos ki nscos kiþnBcos ’ki 2 for s-polorization nBcos ’ki nscos ki 2n scos ’ki nscos ’kiþnBcos ki 2 for p-polorization 8 > > > > > > > > < > > > > > > > > : : ð10Þ
According to Ashkin’s RO model, each incident ray that passes through the micro-sized bead exerts two main forces that are mutually perpendicular: one is a scattering force, which acts parallel to the incident ray, and the other is gradient force, which acts perpendicular to the incident ray.14,15)The method of the RO model is then applied to the line trap model. As shown in Fig. 1, when the i-th ray of the k-th laser beam passes through the micro-sized bead, the exerted scattering force fSki and gradient force fGki can be
expressed as fSki ¼ nsPki c 1 þ Rkicos 2ki T 2 ki½sinð2ki2’kiÞ þRkicos 2ki 1 þ R2 kiþ2Rkicos 2’ki ; ð11Þ and fGki ¼ nsPki c Rkisin 2ki T 2 ki½sinð2ki2’kiÞ þRkisin 2ki 1 þ R2 kiþ2Rkicos 2’ki ; ð12Þ where c is velocity of light in vacuum.
To calculate the resultant forces associated with the total number of incident rays on the micro-sized bead, the resultant forces, scattering force and gradient force, are first converted into three resultant force components along the xyz-axes: fxki¼ rkicos ’ki ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi rki2þfobj2 p fSki fobjcos ’ki ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi rki2þfobj2 p fGki; ð13Þ fyki¼ rkisin ’ki ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi rki2þfobj2 p fSki fobjsin ’ki ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi rki2þfobj2 p fGki; ð14Þ and fzki¼ fobj ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi rki2þfobj2 p fSki rki ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi rki2þfobj2 p fGki: ð15Þ
Adding all of the components of the trapping force exerted by each ray on the micro-sized bead at all of the trapping points, yields the components of each axial trapping force FLine in the line trap:
FLine;xðxo; yo; zoÞ ¼ Xm k¼1 Xj i¼1 fxki ! ; ð16Þ FLine;yðxo; yo; zoÞ ¼ Xm k¼1 Xj i¼1 fyki ! ; ð17Þ and FLine;zðxo; yo; zoÞ ¼ Xm k¼1 Xj i¼1 fzki ! ; ð18Þ
where (xo, yo, zo) is the center position of the micro-sized
bead, m is the total number of trapping points, and j is the total number of rays on a trapping point, respectively. After the trapping force distribution where the line trap was used to hold on the micro-sized bead was determined, the trajectory of the micro-sized bead was simulated using its motion equation. Given the velocity of the flowing water, vw
and the line trap in the microchannel, two forces, the water dragging force Fd and the trapping force FLineðxo; yo; zoÞare
expected to act on the micro-sized bead simultaneously. These two forces and the equation of motion of the trapped micro-sized bead are
Md
2r
dt2 ¼FdðrÞ þ FLineðrÞ; ð19Þ
where M denotes the mass of a micro-sized bead, r ¼ rðxo; yo; zoÞ is the vector of the center of the micro-sized
bead, and t is time. Here the water dragging force Fd is
FdðrÞ ¼ 6RB vw
dr dt
; ð20Þ
where is the fluid viscosity, and RB is the radius of the
sized bead. Based on the assumption that the micro-sized bead reaches its terminal velocity, its acceleration will be zero. Therefore, eq. (19) is modified to
dr
dt ¼vw FLineðrÞ
6RB
: ð21Þ
Next, the finite-difference time-domain (FDTD)16) and eq. (21), adopted to carry out a numerical analysis and obtain the trajectory rðtÞ of the micro-sized bead under the influence of the water dragging force Fd and the trapping
force FLinein the line pattern. Equation (21) can be rewritten
as following based on the FDTD; rn¼ vw
FLineðrnÞ
6RB
t; ð22Þ
where rn¼rnrn1is the change in position of a moving
micro-sized bead by unit time t. Equation (22) yields the trajectory of any each micro-sized bead in the line pattern with various included angles.
The trajectories of two beads of different sizes and the difference between the vertical distances d1 and d2
associ-ated with the oblique displacements are compared. This difference is the separation (d ¼ d1d2) of the two beads
in the line trap, and is used to determine separation efficiency. The water flow velocity vw and the included
angle w between the line pattern and the flowing direction
are separation condition. 3. Experimental Procedure
3.1 Setup
experiment are those used in the HOT system. Basically, they comprise a traditional single trap optical tweezers apparatus and an inserted reflection PPM (Hamamatsu X8267), as displayed in Fig. 2. Notably, the PPM should be inserted in the equivalent front focal plane of the microscope, such that the modulated phase pattern, adjusted by PPM, can generate a line pattern via a Fourier transform in the rear focal sample plane of the microscope.
To utilize fully the phase-modulation of a laser beam by PPM, a two-lens (L1and L2) laser beam expander is adapted
to extend the cross-sectional area of a diode laser beam ( at 1064 nm) to fill the receiving area of the PPM. After the modulated laser beam has been refracted, it passes through the two lenses of the telescope (L3 and L4) to reduce
cross-sectional area of a laser beam to fill the entrance pupil of the objectives. Then, the narrowed laser beam passes through a dichroic mirror into the objective (Olympus 100X, numer-ical aperture = 1.25, oil), producing a line pattern in the sample plane. The sample plane was moved by manipulating the actuator. To observe the experiment and analyze the image, a rear lighting source behind the sample plane was turned on, such that lens L5 could project the image in the
sample plane onto the charge coupled device (CCD) camera.
3.2 Methods
The model has the following three main parameters; (i) the optical intensity distribution of the line pattern, (ii) the radius of a micro-sized polystyrene bead and (iii) the total power of the line pattern. Among these, the first parameter is the most complex. In this experiment, a line pattern was created by using the line optical tweezers system, as presented in Fig. 2. Next, the image processing method was used to analyze the optical intensity distribution and determine the first parameter. The other two parameters were taken directly from the known parameters that were also used in the model.
Figure 3(a) displays a partial two-dimensional image of a phase-modulated line pattern that was captured by a CCD camera with a resolution of 720 480 pixels. The image processing LabVIEW Software IMAQ was adopted to analyze the distribution of all of the gray-level values of
the pixel in the image. To determine all of the gray-level values of the pixels corresponding total power P of the laser beam, the respective corresponding power Pk of the
gray-level value of each pixel was determined. To simplify a two-dimensional (2D) line pattern into a one-two-dimensional (1D) line pattern, the power of all the longitudinal pixels that have the same coordinator as the transverse pixels was summed. Therefore, a line pattern with an equivalent 1D optical intensity distribution was evaluated and the first parameter was determined, as displayed in Fig. 3(b).
In this simulated example, the total laser power P was 100 mW; the laser wavelength was 1064 nm; the length of the line pattern was approximately 22.5 mm, and the total number of pixels was 278. For simplification, each pixel was treated as a trapping point, such that the total number of trapping points m ¼ 278. The refraction index of the aqueous solution ns was 1.33, and that a micro-sized
polystyrene bead nB was 1.57. Finally, a micro-sized
polystyrene bead of radius rB1 is 3 mm, commonly adopted
in experiments, were selected. The above parameters were used in the model and the trapping force distribution exerted by the line optical tweezers on the micro-sized bead was calculated.
To confirm the accuracy of the model, the actual distribution of the horizontal and vertical trapping forces exerted by the line optical tweezers on the micro-sized bead was calculated experimentally. Then, the experimental data concerning the distribution were compared with the distri-bution predicted by the model. The water-dragging-force and image processing methods were used to determine the trapping force distribution of the micro-sized bead that was trapped by the line optical tweezers. In the absence of flow, the attraction of the trapping force caused the micro-sized bead, close to the area of the line pattern, eventually to rest at the location in the line pattern, which was the balance point for the micro-sized bead, which the trapping force on the bead was zero. When the sample plane was moved at constant velocity by manipulating the actuator, an additional water drag force was generated, causing the bead to move toward new balance point and the trapping force was offset. Increasing the velocity of the sample plane in the horizontal Laser M L2 CCD L1 L3 L4 M M PPM Objective Mirror L5 M M λat 1064 nm PPM PPM Phase pattern Telescope
Intensity line pattern
Dichroic mirror Sample plane Illumination light Beam expander
Fig. 2. A schematic diagram of the line optical tweezers setup: a traditional optical tweezers apparatus and the PPM.
(b) 22.5 µm Pixel [ # ] 250 200 150 100 50 0 (a) 0.0003 0.00025 0.0002 0.00015 0.00005 0.0001
Relative Optical Intensity [a.u.]
Fig. 3. (a) 2D image of a line pattern and (b) its equivalent 1D optical intensity distribution.
and vertical directions of the line pattern, the micro-sized bead to move toward the new balance points until it escaped from the line trap, as observed on the video-recording. Next, an image processing method was used to locate the new balance points of each micro-sized bead for each water flow velocity. According to eq. (20), not only the water dragging force was measured but also the trapping force values were obtained in real time. Accordingly, a relationship between trapping force and the position of the micro-sized bead was demonstrated. To test the accuracy of the model, the result was compared with the predicted trapping force distribution. Finally, numerical simulation was used to calculate the trajectory and separation between the two micro-sized beads of different sizes as they flowed into the line pattern. Changing the included angle w for the single water flow
velocity vw enabled each separation distance d ¼ d1d2
between the two micro-sized beads up to the maximum dmax to be determined.
4. Results
The results of this experimental study demonstrated that the line trap model had been successfully tested. Figure 4 plots the horizontal trapping force distribution in the trapped micro-sized bead with a radius of 3 mm in the line pattern. The left and right of Fig. 4 is a partial enlarged view which shows the force balance positions. The solid curve represents the values FLine;xðxÞjy¼0 predicted by the model, while the
spots represent the experimental data. The experimental data are close to the predicted values with errors of between 0.9 and 7.1%. The predicted and experimental result also include two force balance positions (xjFLine;x¼0) of the trapped
micro-sized bead in the identical line pattern [Fig. 3(a)]. These two positions were x1¼ 5:37 mm and x2¼3:32 mm
(predicted), and x3¼ 5:14 mm and x4¼3:11 mm
(exper-imental). Since the force balance positions were the locations where the line optical tweezers most easily trapped the micro-sized beads, the vertical trapping force distribu-tions, FLine;yðyÞjx¼x1 and FLine;yðyÞjx¼x2, on the y-axis, shown
in Figs. 5(a) and 5(b), were obtained. The experimental data are close to the predicted values with errors of between 1.2%
and 10.5%. Both figures clearly indicate that the theoretical modeling (solid cure) was consistent with the experimental results (spots). Therefore, the accuracy of this model was quantitatively examined.
Then, the above results were applied to simulate the trajectory of the two known micro-sized beads as they passed through the line pattern. The trajectory is analyzed to determine the separation distance between the micro-sized beads. Based on the trajectories, Fig. 6 presents the separation distance d under water flow velocity vw¼
250 mm/s; the total laser power P was 100 mW, and included angle wfrom 0 to 80. As the included angle wincreased
from 0 to 45, the separation did not increase significantly.
However, as the included angle increased further, the separation distance d increased rapidly. The angle of 49, d > 6:0 mm, was the threshold included angle
w-thfor
the effective separation between the large bead from the small bead. It is defined as the separation distance exceeds the diameter of the large bead. It is easy to separate large bead from small bead. The maximum separation distance, dmax¼ 11:83 mm, between the two micro-sized beads was
reached when the included angle was 64. Therefore, 64 is
the optimal included angle of separation. As the included angles increased beyond this value, the separation distance began to decrease gradually. The gray area of Fig. 6 is a domain of effective separation and the included angle form 49 to 80. The left of Fig. 6 is a diagram which shows the x1 x3 x4 x2 FLine ,x |y=0 [pN] x [µm] 15 0 5 10 -15 -10 -5 -2 6 4 2 0 -6 -4 -8 8 x1 x3 x4 x2
Fig. 4. Horizontal trapping force distribution for the bead of radius 3 mm. The solid curve is the model predicted value, FLine;xðx Þjy ¼0, and
x1¼ 5:37 mm and x2¼3:32 mm are the force balance positions. The
spots are the experimental data, also x3¼ 5:14 mm and x4¼3:11 mm
are the force balance positions. The force balance positions are clear shown in the partial enlarged view.
3 0 1 2 -3 -2 -1 15 0 5 10 -15 -10 -5 y [µm] FLine ,y |x= x1 [pN] (a) (b) 3 0 1 2 -3 -2 -1 15 0 5 10 -15 -10 -5 y [µm] FLine ,y |x= x2 [pN]
Fig. 5. The vertical trapping force distribution. (a) The force balance position is x1; (b) the force balance position is x2, they were easy to
measure the trapping force experimentally. The solid curve was the theoretical modeling and the spots are experimental data. The errors were 1.2 –10.5%.
relationship between trajectory and separation distance. The two known micro-sized beads followed the same start and moved to the line pattern. The dashed curve represents the trajectory of the large bead rB1with a radius of 3 mm and the
solid curve represents that of the small bead rB2with a radius
of 1.5 mm. The d1 and d2 were vertical distances of oblique
displacement in the trajectory. The difference between d1
and d2 was separation distance. The separation distance
corresponds to the included angle. The optimal separation distance was as an example, the others were identical method of the numerical simulation.
5. Discussion
In the process of beads separation, this line pattern has a threshold included angle of effective separation w-th and
an included angle of maximum separation w-opt, clearly
presented in Fig. 6. The trapping force and the water dragging force were compared to determine a threshold included angle of effective separation. To take an example, as presented in Fig. 7, both the trapping force and the water dragging force were calculated and perpendicular to the direction of the line pattern. The solid curve (FLine;yðxÞjrB1)
and the dashed curve (FLine;yðxÞjrB2) represent the maximum
trapping force distribution for the large (rB1) and small (rB2)
beads, respectively, whereas the solid line (FdjrB1, w¼30
and 45) and the dashed line (F
djrB2, w¼30 and 45
)
represent the water dragging force, for the same water flow velocity and included angles of 30 and 45, on the large and
small beads in the line pattern. When the included angle of the line pattern is 30, the trapping force on the two beads in the linear trapping scope exceeds the water dragging force. Consequently, both beads moved along, and did not escape until the end of the line pattern (T1 and T2). The separation
distance, d2-1¼x2x1, was small. When the included
angle in the line pattern became 45, the trapping force is
less than the water dragging force at T3 in Fig. 7, the small
bead could no longer resist the water dragging force and escaped from the line pattern. However, at the same included
angle of 45, the trapping force still exceeded the water
dragging force, the large bead remained on the line pattern until it was beyond the influence of the trapping force (T4).
The separation distance, d3-4¼x3x4, was large. Based
on the separation distance, the included angle of 45 can be
used to distinguish the large from the small bead. Therefore, the water dragging force and the distribution of the trapping forces of the line pattern at different included angle affects the separation between the micro-sized beads. Additionally, when the line pattern reaches a specific (threshold) included angle at a given water flowing velocity, a difference exists the effective separations between the micro-sized beads, as shown in Fig. 6.
The simulation and the experimental results show that the optical intensity distribution of the line pattern determines not only the distribution of the trapping force but the trajectory and the separation between the micro-sized beads. Therefore, designing a line pattern with suitable intensity could help effectively to extend the optimum separation conditions. Then, this scheme may be applied to biological and medical detections.
6. Conclusions
This study presented the line optical tweezers system, and a model thereof, and simulates the separation between differ-ently micro-sized beads to determine separation condition. According to the model, four main factors determine the separation: optical intensity distribution of a line pattern, radius of micro-sized beads, flow velocity and included angle. A comparison the measurements of force verified that the model was precise to predict the trapping force of the trapped micro-size beads in the line optical trapping. The
∆ d [µ m] θw[º] ∆dth≡ 2 rB1 θw-th 80 40 20 30 50 60 70 θw-opt 0 4 12 8 6 2 10 ∆dmax 10 20 25 vw rB1rB2 0 -2 -6 -10 -14 θw-max=64° y [µ m] d 1 d2 15 5 ∆dmax = 11.83µm x [µm] Line pattern
Fig. 6. The separation distance d under water flow velocity vw¼250 mm/s; the total laser power P was 100 mW: The included
angle 49, the separation distance d exceeds the diameter of the
large bead, is threshold included angle. The included angle is 64, the
maximum separation distance is 11.83 mm. The gray area is a domain of effective separation. The left is a diagram which shows the relationship between trajectory and separation distance. The separa-tion distance d ¼ d1d2. -10 0 5 10 15 -15 -5 FLine, y (x)| rB1 FLine, y (x)| rB2 T3 x [µm] FLine, y[pN] ∆d3-4 Fd|rB2, θw=30° T4 T1 T2 ∆d2-1 Fd|rB1, θw=30° Fd|rB2, θw=45° Fd|rB1, θw=45° 2.5 15 12.5 10 7.5 5 x4 x3x1x2
Fig. 7. Compare trapping force (curve) with water dragging force (line), understanding the effective separation. The Ti ji¼1{ 4is trapping
force (dashed curve) less than water dragging force (dashed line), the beads escaped from these position. When the include angle wis 30,
the beads moved along, and did not escape until the end of the line pattern. The large and small beads escaped from T1 and T2
respectively. The separation distance d2-1was x2x1. The include
angle wis 45, the large and small beads escaped from T3and T4
respectively. The separation distance d3-4was x3x4. Compare the
separation distance, a clear separation in the included angle 45.
Accordingly, when the line pattern reaches a specific (threshold) included angle, a difference exists the effective separations between the micro-sized beads.
model and the equation of motion were used to simulate the trajectory of differently sized micro-sized beads on the line pattern and to determine optimal and effective separation. Therefore, the simulation calculations support the design and manipulation of the line optical trapping.
For practical applications, a microchannel chip based on simulated parameters was designed by modeling a simulated sample that was both before and after testing. Combining the line optical tweezers with a designed microchannel chip will enable a fast, precise, and effective sorting and screening method for the chip to be implement-ed, supporting further quantitative analysis. Restatimplement-ed, this study has provided a novel biological detection method and a powerful tool in the miniaturization of cells/beads separation techniques.
Acknowledgements
The authors would like to thank the National Science Council of the Republic of China, Taiwan, for financially supporting this research under Contract No. NSC96-2120-M-009-003. Ted Knoy is appreciated for his editorial assistance.
1) A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu:Opt. Lett. 11 (1986) 288.
2) A. Ashkin and J. M. Dziedzic:Science 235 (1987) 1517.
3) S. C. Grover, A. G. Skirtach, R. C. Gauthier, and C. P. Grover: J. Biomed. Opt. 6 (2001) 14.
4) Y. Wakamoto, I. Inoue, H. Moriguchi, and K. Yasuda:Fresen. J. Anal. Chem. 371 (2001) 276.
5) M. Ozkan, M. Wang, C. Ozkan, R. Flynn, A. Birkbeck, and S. Esener: Biomed. Microdevices 5 (2003) 61.
6) M. Ozkan, T. Pisanic, J. Scheel, C. Barlow, S. Esener, and S. N. Bhatia:Langmuir 19 (2003) 1532.
7) A. D. Mehta, M. Rief, J. A. Spudich, D. A. Smith, and R. M. Simmons:Science 283 (1999) 1689.
8) M. Reicherter, T. Haist, E. U. Wagemann, and H. J. Tiziani:Opt. Lett. 24(1999) 608.
9) J. Liesener, M. Reicherter, T. Haist, and H. J. Tiziani:Opt. Commun. 185(2000) 77.
10) J. E. Curtis, B. A. Koss, and D. G. Grier:Opt. Commum. 207 (2002) 169.
11) S. Tseng, S. Chi, and L. Hsu:Proc. SPIE 5514 (2004) 687. 12) Y. Roichman and D. G. Grier:Opt. Lett. 31 (2006) 1675.
13) Y. Roichman, I. Cholis, and D. G. Grier:Opt. Express 14 (2006) 10907.
14) A. Ashkin:Phys. Rev. Lett. 24 (1970) 156. 15) A. Ashkin:Biophys. J. 61 (1992) 569.
