paper

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paper

16th Int Symp on Applications of Laser Techniques to Fluid Mechanics
Lisbon, Portugal, 09-12 July, 2012
Time Series Volumetric Velocity Measurement in Aneurysm Models
by Shadow Imaged Stereo Streak PTV
Genshi Moriya1, Rie Yasui1, and Koichi Hishida1
1: Dept. of System Design Engineering, Keio University, Yokohama, Japan, [email protected]
Abstract The internal flow of an aneurysm changes temporally and spatially by heartbeat and its complex
form; accordingly time series volumetric velocity measurement has been required. In the present study, we
have developed time series 3-dimentional and 3-component (3D - 3C) velocity vector measurement using
shadow imaged stereo streak PTV (Particle Tracking Velocimetry) and applied this system to aneurysm
models. The present system realizes voluminous illumination using LED lights and records particle shadow
images. The ghost particle is unactual particle which occurs in the process of 3-dimentional reconstruction
and it is connected directly with incorrect velocity vectors in volumetric measurement. Generally, this
problem has been conventionally solved using three or more than three cameras and various thresholds. In
the present study, we have adopted a technique which is able to remove all ghost particles with only two
cameras. The technique can estimate the depth of particle position using a defocus of particle images and we
defined it as DI (Defocusing Index) quantitatively.
As the result of applying this system to the aneurysm model with the curved wall, we have obtained
following results. The measuring volume size was about 7.0 mm × 6.9 mm × 6.8 mm and velocity
fluctuation was from 0.5 mm/s to 18.9 mm/s. Moreover, this system could accurately measure the small and
large eddy changing spatiotemporally. From these results, it is concluded that shadow imaged streak stereo
PTV is applicable to the milli-scale flows like an aneurysm.
1. Introduction
A prophylaxis and treatment of subarachnoid hemorrhage have spurred a great deal of research.
It has been found that a rupture of an aneurysm are associated with the internal flow structure of it,
and a visualization of internal flow has been required. In the prior studies, 2-dimentional vectors
were measured by PTV with one camera in the aneurysm model (T.-M. Liou and S.-N. Liou 2010).
Because the internal flow of the aneurysm changes temporally and spatially by heartbeat and its
complex form, in order to elucidate the flow structure, it is necessary to estimate the time series 3dimentional 3-compornent (3D3C) vectors. In volumetric measurement system, back flow of the
cylinder was measured by 3D-PTV with three cameras (Kieft et al, 2002) and by tomographic PIV
(Particle Image Velocimetry) with four cameras (Sacrano and Poelma,2009). In the present study,
we have developed shadow imaged streak PTV which enable the time series volumetric velocity
measurement with only two cameras by simple experimental setup. Figure 1 shows the optical
system of shadow imaged streak PTV. The model was irradiated with LED lights and overlapping
area of it becomes measuring volume. Generally, the voluminous illumination is realized using
Laser and scattered light of particle is recorded, but in this study we realized voluminous
illumination using LED lights and record particle shadow imaged.
The ghost particle is unactual particle which occurs in the process of 3-dimentional
reconstruction and it is connected directly with incorrect vectors in volumetric measurment. In
tomographic PTV, J. Kitzhofer, C. Brücker (2010) removed ghost particles using three cameras,
particle size and intensity threshold. In the present study, in order to remove ghost particles, we
have developed the method which can estimate the particle depth positions using defocus of particle
shadow images. The defocus of particle shadow images was defined as DI (Defocusing Index)
quantitatively.
The followings indicate the condensed processes of shadow imaged stereo streak PTV.
(1) LED lights irradiate the aneurysm model three-dimensionally. Shadow images of particles are
recorded by two cameras in longer time of exposure.
(2) Recorded images are processed dynamic thresholding binarization, and centroids of particles are
detected.
-1-
(3) 2-dimentional vectors are resolved using streak PTV.
(4) 3-dimentionals positions are reconstructed using mapping function.
(5) Ghost particles are removed using DI.
(6) 3D3C-vectors are resolved through the use of 3-dimentional distance of particles.
In this paper, we applied the present system to two types of aneurysm model; one is a
rectangular model, and another is a cylindrical model with curved wall. In either model, the
Reynolds numbers were about 150. To begin with we measured internal flow of rectangular model
and analyzed the captured time series 3D3C particle motions. Moreover, in a cylindrical model with
curved wall, we compensated the distorted shadow images using mapping function and measured
time series 3D3C vectors.
Aneurysm model
LED
LED
Measuring volume
Tracer particle
CCD camera (Left)
CCD camera (Right)
Recorded camera image
Fig . 1 Optical system of shadow imaged stereo streak PTV
2. Measurement System
2.1 Optical System
Figure 2 shows the block diagram of the present measuring system. The voluminous
illumination is realized using LED lights. As shown in Fig .2, measuring volume is formed as an
overlapping area of two LED lights. The particle shadow images are recorded with the system
consisting of two CCD cameras (Imperx 2M30H-L, 1092 × 1012 pixels 32 fps, exposure time 31
ms) with an angular displacement of roughly 90°. The cameras are equipped with telecentric lenses
by Edmund Optics. Two cameras are synchronized by pulse generator and measuring volume is
constantly irradiated by LEDs.
Power
supply
Timing chart
LED
LED
LED
Concave lens
LED
z
Left camera
y
Convex lens
Measuring volume
x
Right camera
CCD camera (Left)
CCD camera (Right)
PC
Pulse
generator
Fig .2 Block diagram of shadow imaged streak PTV
-2-
2.2 Measurement algorism
Figure 3 indicates the measurement algorithm of this system. The followings show the
processes of measurement algorithm.
(1) Background noises of recorded shadow images are rejected, and the center location of particle
shadow images are detected by dynamic thresholding binarization (Ohmi et al, 2000).
(2) 2-dimentional vectors are detected by means of streak-PTV.
(3) 3-dimentional positions of the particles are reconstructed using mapping function and 3D3C
vectors are detected from particle positions at each time.
(4) Ghost particles are removed using DI.
The following section will show the detailed processing of this algorithm
Camera 1
Camera 2
Reduction of background noise
Streak PTV
Dynamic threshoulding binalization
PIV
Detection of the 2-dimensional vector
Reconstruction of 3-dimensional particle
positions
Elimination of the ghost particle
Calculation of 3D3C velocity vector
Fig .3 Flow chart of proposed algorithm of 3-dimentional particle position and velocity detection.
2.3 Streak PTV method
We have adopted streak PTV and the algorism of the method is shown in Fig .4. Shadow
images are recorded in longer exposure time in streak PTV. It enables to determine 2-dimensional
vectors effectively because it records particle locus having velocity information. The following is
the procedures of Streak PTV.
(1) Rough movement of particles ΔL, within interrogation window is calculated by PIV (Particle
image velocimetry).
(2) A reference window is arranged ΔL away from the center of particle and aspect ratio of window
size is changed in proportion to particle streak size.
(3) The movement of each particle between two times is calculated by the position difference of
same particles between t1 and t2. 2-dimentional vectors are determined by movement of
particles.
Streak PTV has fast processing speed and low incorrect vectors in comparison with general
PTV because smaller reference window can be set than that of general PTV.
-3-
Interrogation window
Refference window
: Movement
Particle (t2)
Particle (t1)
t1
Movement (t1)
t2
Exposure time
Fig .4 Algorithm of detection of particle position in each time by streak PTV
2.4 Detection of particle position in 2-dimensional camera plane
An important point for measuring accurate velocity data in PTV is to detect particle positions
precisely. In general, single thresholding binarization that sorts the image intensity by one fixed
threshold value or a correlation method that selects particles fitted to an estimated pattern are
widely used for gray scale images to detect particle area. Because illumination distributions of
particle shadow images are changed by a distance from focal plane and particle motions, the single
thresholding binarization and the correlation method are not suitable. In this study, the dynamic
thresholding binarization was employed, which enables to select various threshold values for each
particle. As a result, the factor which decreases the detection accuracy due to various shadow
intensity profiles is overcome. Particle area is detected by this method with changing threshold
value,Θ. by the following equation (2). Y and Z are coordinates in camera image, Θ(Y,Z) is the
threshold value at (Y, Z), Iavgn is averaged intensity of field (Fig .5), coefficients, i, and, j, are
described as equation (3), (4), respectively.
Θ(Y ,Z ) = (1 − i )(1 − j ) I avg1 + i (1 − j ) I avg 2 + ijI avg 3 + j (1 − i ) I avg 4
(2)
i = (Y − Y1 )(Y2 − Y1 )
j = (Z − Z1 )(Z2 − Z1 )
(3)
(4)
As compared with single thresholding binarization, this method enables to detect particles
having dissimilar luminance distribution. (Fig .6)
Iavg1
Iavg2
(Y1, Z1)
(Y2, Z1)
Divided Field
Bubble image
Particle
image
Center point
of Divided field
Detection
(Yn, Zm) Center coordinates
of Divided field
Θ(Y,Z)
Iavg1
Iavg2
(Y1, Z2)
(Y2, Z2)
Iavg1
Averaged intensity
of Divided field
Θ(Y,Z)
The
The thresholding
thresolding
at
, Z)coordinates
coordinates
at (Y
(Y,Z)
Fig .5 Schematic illustration of bilinear
interpolation
Detection
Dynamic thresholding
binarization
Single thresholding
binarization
Fig .6 Comparison of detected particles
by single thresholding binarization and
dynamic thresholding binarization
-4-
2.5 Evaluation of actual particle position
This section describes removing technique of ghost particle images. Ghost particles are
unactual particles which occur in the process of 3-dimentional reconstruction. Understandably, it is
necessary to remove them because an occurrence of ghost particles is connected directly with
incorrect vectors. In this study, we use the defocus of particle shadow images for removing ghost
particles. Particle images are recorded clearly near the focal plane, and the more it departs from the
focal plane, the more it becomes dim (Fig. 7). Thus, the depth of a particle can be estimated using
the defocus of particle images. We quantitatively defined it as DI (Defocusing Index) which uses
the slope of particle intensity.
Figure 7 shows the derivation method of DI and relation between luminance distribution and
distance from the focal plane. As shown in Fig .7, the area 5 × 15 pixels are extracted on the base of
the particle centroid, and the intensity of this area is averaged in Z directions. Irregular noise of the
particle shadow image can be eliminated by averaging the intensity. After averaging the intensity,
DI is derived as length in Y direction which has more than 80 degrees of intensity angle in Y
directions. Naturally, the more a particle departs from the focal point, the bigger DI is. Figure 8
gives the experimentally measured relation between DI and distance from the focal plane. The
distance from a focal plane l, can be estimated by means of Fig .8 and ghost particles can be
removed by estimating the distance from the focal plane.
When two prospective particles on the right side camera image are detected for one particle on
the left side camera, the x position of pair particles were estimated by Fig .8. Then the distance
between the x position calculated by stereo view and that by DI was least, they were determined as
the pair of particles (Fig .9). It is possible to remove all of the detected ghost particles by using this
technique.
Fig .7 Relation between shadow image intensity and calculation of DI of particle image
-5-
Distance from focal
plane
[mm] [mm]
焦点から
の距離
Focal plane
5
4
3
2
1
0
Focal plane
l: Distance from focal plane
Detected particle position
Ghost particle
Camera 1 plane
Camera 2 plane
5 7.5
00 2.5
5 10
15 10
20
DI [-]
Fig .8 Relation between DI
and distance from focus plane, l
Fig .9
Removal method of ghost particles
2.6 Reconstruction of particle position and velocity-vector
2.6.1 Mapping function
Two models have been measured in the proposed experiments: One is a rectangular model, and
another is a cylindrical model with curved wall. In cylindrical model, recorded images are distorted
by difference of refractive index between fluid and wall material. Figure 10 shows the results of ray
tracing in case of radiating LED light to curved wall and the 3-dimentional reconstruction. Working
fluid is water and wall material is PDMS (polydimethylsiloxane). As shown in Fig .10, it was found
that the gap between actual particle and reconstructed particle occurs by difference of refractive
index. This problem has been solved by equalizing the refractive index. It is necessary to use
particular fluid with equal refractive index of wall materials. In this study, we used mapping
function which is able to pretermit the distortion of images using coordinate transformation without
equalizing the refractive index. Mapping function can match camera coordinates and nature
coordinate. It is described in equation (6), where y, z, are approximates nature coordinates, Y, Z, are
camera coordinates, yn, zn, are positions on the calibration plate in natural coordinates, ai, bi are
coefficients calculated beforehand and n is the sample number.
90 mm
LED
20 mm
LED
20 mm
Gap
Telecentric Camera
lens
plane
Actual particle
particle
Actual
Water
PDMS
Air
Telecentric
lens
Reconstructed
Reconstructedparticle
particle
from
fromcamera
cameraview
image
Ray-tracing line
Ray-tracing
line
Extension line
Extention
linefrom
from
Camera image
image
camera
Camera
plane
Fig .10 Illustration of gap occurrence between actual grid position and reconstructed grid position
(width = 20 mm, length = 20 mm, cylinder diameter = 15 mm)
-6-
⎛ y1
⎜
⎜ y2
⎜ 
⎜
⎜ y16
⎜ 
⎜
⎜y
⎝ n
z1 ⎞ ⎛1
⎟ ⎜
z 2 ⎟ ⎜1
 ⎟ ⎜
⎟=⎜
z16 ⎟ ⎜1
⎜
 ⎟⎟ ⎜ 
zn ⎟⎠ ⎜⎝1
Y1
Y2
Y12
Y22
Y13
Y23
2
16
3
16
Y1Z1
Y2 Z 2


Y16 Y

Yn
 Y13 Z13
 Y23 Z 23
Yn2
Z1
Z2
Z12
Z 22


3
16
Z16

Z162

 Yn3 Z n3
Zn
Z n2
3
16
Y
Y16 Z16  Y Z

Yn3
Yn Z v
Z13 ⎞
⎟
Z 23 ⎟⎛ a1 b1 ⎞
⎟
⎟⎜ a
b2 ⎟
⎜
2
⎟
 ⎟
Z163 ⎟⎜ 
⎜
⎟
⎟⎜
⎟
a
b
⎟⎝ 16 16 ⎠
Z n3 ⎟⎠
(6)
Because distortion of particle images change with particle depth positions, it is necessary to
derive mapping functions each depth coordinate. Figure 11 shows the matching result of camera
coordinates and nature coordinates in the cylindrical model. After inserting the calibration plate in
the cylindrical model (Fig .11 (a)), calibration plate is displaced to y-axial direction and derive
mapping functions at each y-axial position. Figure 11 (b) gives the before correction and (c) shows
the after correction using mapping function. The points of identical color, red circle and red dash
line mean the lattice point positions of the calibration plate at each y-axial positon, real particle position and
moving path of identical particle respectively. By the difference of reflective index, shadow images are
distorted and its deformation is different at each particle position (Fig .11 (b)). As Fig .11 (c), it is
found that the deformation of image is compensated using matching function.
Moving path of identical particle (c)
(b)
Displace the calibration
plate to y-axial direction
z
[mm]
y
x
y
7.0
7.0
6.0
6.0
5.0
5.0
[mm]
(a)
4.0
3.0
Moving path of identical particle
4.0
3.0
2.0
2.0
1.0
1.0
0.0
0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0
0.0
0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0
[mm]
x
[mm]
Reconstructed particle position
Real particle position
Fig .11 Mattching result of camera coordinate: a Arrangement of calibration plate, b Before correction of
particle positions, c After correction of particle positions using mapping function
2.6.2 Calculation of 3-component velocity-vector
Figure 12 indicates the derivation method of 3D particle positions and 3D3C vectors. The
method of determining it is as follows.
(1)Each depth of the particle position is determined using mapping function.
(2)As illustrated in Fig .12, the plotted particle positions are connected. It seems that true particle
position is on this line.
(3)This line is determined in each camera. The intersection of lines is considered as the 3dimentional particle position. In Streak-PTV, 2-dimensional particle position (Y, Z) and 2component velocity-vector (V, W) are determined. Thus, 3D3C vectors can be determined from
3-dimentional movement of identical particle for each instant of time.
-7-
Candidate particle
position
z
Detected particle
position
z
3D3C vector
Y
y
Y
y
Z
Z
Camera image
Left Camera
x
x
Right Camera
Fig .12 Determining the 3D particle positions and 3D3C vectors
2.6.3 Uncertainty of velocity vectors
For evaluation of accuracy of velocity vectors, we used a x, y, z stage and calibration plate
having lattice points (Fig .13). Lattice points are located at interval of 1.0 mm and its diameter is
250 µm. After inserting the calibration plate in the cylindrical model, we moved it 100 µm to x, y, z
direction respectively using xyz stage and reconstruct the lattice point as particles. We compared
reconstructed movement of lattice points and real movement, and calculated the relative error of
measured value and its standard deviation (Table. 1).
250 µm
Fig .13 Calibration plate
Table. 1 Result of accuracy verification
Real displacement
Averaged relative
Standard deviation
error [%]
[µm]
[µm]
x = 100
-5.8
2.6
y = 100
-4.7
1.9
z = 100
+3.4
1.2
As shown in Table. 2, averaged relative error is about ±5 % and standard deviation is about 2 or
so. It can be seen that there are little difference in the accuracy of x, y and z direction and depth
component of velocity in x direction is measured accurately.
-8-
3. Experimental Setup
We applied shadow imaged stereo PTV to the two types of aneurysm model. First model is a
rectangular model having flat wall surface (Fig .14), and Second model is the cylindrical model
(Fig .15). In the rectangular model, the model is located on the square channel (10 mm × 10 mm)
and has a 9 mm hole between aneurysm model and square channel. In the cylindrical model, it is
located on the columnar channel (9 mm) whose diameter is 12 mm and has a 7 mm hole. In either
model, water mixed tracer particles (80 µm) is flowed by a pump and the Reynolds number of the
channel flow is about 150. Table 2 shows the performance of CCD camera and telecentric lens.
10 mm
y
x
9 mm
z
10 mm
ϕ=9
9 mm
10 mm
12 mm
z
y
x
mm
ϕ = 7 mm
Fig .14 3-dimentional view of rectangular model Fig .15 3-dimentional view of cylindrical model
Table. 2 Performance of CCD camera and telecentric lens
CCD camera(ImperX 2m30H-L)
Telecentric lens(Edmund Mitsutoyo)
Gradation
8 bit
Magnification
5×
Max flame rate
32 Hz
NA
0.11
Spatial resolution
1920×1080 pixels
Field of view
1.28 mm
Pixel size
7.4 µm×7.4 µm
Resolution
2.5 µm
4. Results and Discussion
4.1 Rectangular model
The velocity measurement result of the rectangular model is shown in Fig .16. The central
coordinates of inflow entrance is (2.0, 0, 0) and reconstructed measuring volume size is about 8.0
mm × 10.2 mm × 6.9 mm. Velocity turbulence which is from 0.7 mm/s to 19.5 mm/s can be
measured and the time resolution is 32 ms.
As shown in Fig .16, we found that shadow imaged PTV can measure the small eddy changing
timely and spatially. Moreover, large eddy that flows along the wall, and various small eddies in the
central part were observed. This result shows that the stagnant flow circulates in the central part of
the model. Figure 17 shows the y-z cross section of Fig .16 in each x coordinates. As the result of
Fig .17, it was found that the eddy of aneurysm flows counterclockwise against channel flow and
the velocity near the wall is faster than the center flow. It seems that the reason of this phenomenon
is caused by the main stream in square channel. These results are qualitatively consistent with past
studies which measure the 2-dimentional vectors of the aneurysm model.
-9-
12 steps
14 steps
1.8mm
1.2mm
0.8mm
32ms
V[mm/s]
0.5mm
18.0
16.0
1.0mm
7.0
20.0
6.0
1.0mm
14.0
12.0
20 steps
10.0
5.0
1.0mm
4.0
3.0
2.0
8.0
6.0
4.0
1.0
0.8mm
0
0.8mm
2.0
0.0
Fig .16 Measurement result of rectangular model (3D view)
Inflow entrance
Fig .17 Measurement result of rectangular model (2D view)
- 10 -
4.2 Cylindrical model
0.3mm
0.4 mm
Figure 18 indicates the measurement result of the cylindrical model. The reconstructed
measuring volume size was about 7.0 mm × 6.9 mm × 6.8 mm. Velocity fluctuation which is from
0.5 mm/s to 18.9 mm/s could be measured. As the result of the cylindrical model, it was found that
large eddy and rapid vector near the inflow entrance is observed. Enlarged view of Fig .18 shows
the shadow imaged stereo PTV can track time series 3D3C particle motion. As compared with
rectangular model, the stagnant flow in the central part of the model could not be observed and
almost all stream flowed abreast of the wall. This result shows the cylindrical model with smooth
wall is hard to be unstable flow as compared to the rectangular model.
These measurement results prove that the proposed system is possible to measure time series
volumetric vectors in a curved model.
0.5 mm
0.6 mm
0.4mm
0.3mm
V[mm/s]
20.0
18.0
6.0
16.0
5.0
14.0
4.0
12.0
0.9 mm
7.0
3.0
2.0
8.0
-4.0
1.0
0.0-3.0
10.0
6.0
-2.0
-1.0
4.0
0.0
2.0
1.0
3.0
4.0
0.4 mm
0.6 mm
2.0
0.0
Fig .18 Measurement result of cylindrical model
5. Conclusions
We have developed shadow imaged stereo streak PTV and applied this system to aneurysm
models. The present measuring system is able to reconstruct time series 3-dimentional and 3compornent particle motions with only two cameras due to removing ghost particles using
defocusing index. As a measurement results, we obtained following conclusions.
(1) The measurement result of the rectangular model shows that the developed system enables to
trace 3-dimentional particle motion in time-series. The reconstructed measuring volume size is
about 8.0 mm × 10.2 mm × 6.9 mm and this system is able to apply to milli-scale flows.
(2) As the result of the cylindrical model, we could measure the large eddy and small eddy in timeseries. The reconstructed measurement area size was about 7.0 mm × 6.9 mm × 6.8 mm.
- 11 -
Velocity fluctuation which is from 0.5 mm/s to 18.9 mm/s could be measured. As compared with
the rectangular model, the stagnant flow in the central part of the model cannot be observed.
This result shows the cylindrical model with smooth wall is hard to be unstable flow as
compared to the rectangular model.
Acknowledgements
This work was subsidized by Grant-in-Aid for Scientific Research (S) (No. 21226006) of Japan
Society for the Promotion of Science.
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- 12 -

paper

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