Biomedical Engineering Reference
In-Depth Information
Δϕ
(rad)
10
(A)
(B)
Data
Fit
8
8
(
x
0
,
y
0
)
6
6
4
2
4
2
5µm
0
0
5
10
15
20
25
0
x
(µm)
Δϕ
(rad)
Δϕ
(rad)
Δϕ
(rad)
14
12
10
8
6
4
2
0
14
12
10
8
6
4
2
0
14
12
10
8
6
4
2
0
(C)
(D)
(E)
30
30
30
24
24
24
36
36
36
18
30
18
30
18
30
24
24
24
12
12
12
y
(µm)
18
y
(µm)
18
y
(µm)
18
6
12
x
(µm)
6
12
x
(µm)
6
12
x
(µm)
6
6
6
0
0
0
Figure 6.6
Refractive index determination of a suspended cell. (A) Quantitative digital holographic phase
contrast image of a spherical trypsinized pancreatic tumor cell located at x
0
, y
0
; (B) phase data
Δϕ
along the cross-section marked by the dashed line in (A) and the fitted data corresponding to
Eq. (6.7)
; (C) rendered pseudo-3D plot of the phase distribution in (A) that is used for the
determination of the integral refractive index; (D) rendered pseudo-3D plot of data that is
obtained by line-wise fitting of
Eq. (6.7)
; (E) rendered pseudo-3D plot of the phase difference
data between (C) and (D)
[52]
.
here
n
cell
5
1.372
6
0.002, is used for further analysis. The uncertainty for
n
cell
can be
estimated by the standard deviation obtained from all line fits. The average cell radius is
obtained by the determination of
R
5
R
x
(
y
5
y
0
)
R
fit,max
from all fitted lines (for
Figure 6.6
:
R
fit,max
5
10.2
6
0.1
m). The uncertainty for
R
is obtained from the standard
deviation of
6
5 neighboring lines to the central line at
R
5
R
fit,max
.
Figure 6.6E
shows a
pseudo-3D plot of the absolute values of the phase difference between the measured phase
contrast data in
Figure 6.6C
and the fitted data in
Figure 6.6D
(mean value
5
0.3 rad) which
indicates a homogeneous distribution of the fitting errors.
μ
The application of the method for the refractive index determination of living cells is
illustrated by the analysis of different human pancreatic tumor cell types (PaTu 8988 T
(
N
5
28), PaTu 8988 S (
N
5
15), and PaTu 8988 T pLXIN E-cadherin (
N
5
20)). The cells
were investigated in cell culture medium (Dulbecco's modified Eagle's medium) in
comparison to a human liver tumor cell line (HepG2,
N
5
55; for details, see Ref.
[52]
).
The cells were trypsinized, and for each cell line the parameters
n
cell
and
R
fit,max
were
determined with
n
medium
5
1.337
6
0.001 as described above. For data evaluation, only cells
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