Biomedical Engineering Reference
In-Depth Information
6.4 Refractive Index Determination of Cells in Suspension
The cellular refractive index represents an important parameter in quantitative phase imaging
of living cells. The cellular refractive index influences the visibility of cells and subcellular
structures in the quantitative phase images and limits of the accuracy for the determination of
the thickness of transparent samples
[29]
. In addition, the determination of the cellular
refractive indices are useful for the utilization with optical tweezers and related optical
manipulation systems as the individual cellular refractive index values influence the resulting
optical forces
[66,67]
and to analyze intracellular (protein) concentrations
[68]
.Althoughin
many cases a high measurement accuracy can be achieved, the refractive index determination
of adherent cells with quantitative phase imaging methods, as described, for example, in Refs.
[29,69
71]
, can be time consuming or it requires special experimental equipment. In
contrast, quantitative phase imaging methods for the determination of the integral refractive
index of suspended cells can be carried out without further sample preparation
[52,72,73]
.In
addition, the multifocus feature of DHM enables an increased data acquisition as several
suspended cells that may be located laterally separated in different focal planes can be
recorded simultaneously. Here, the determination of the integral refractive index of suspended
cells is illustrated by a method in which a sphere model is fitted line by line to the DHM
phase data. For sharply focused spherical cells in suspension, located at
x
5
x
0
,
y
5
y
0
,and
with radius
R
, the cell thickness
d
cell
(
x
,
y
)isasfollows:
(
q
R
2
2
2
2
2
#
R
2
2
U
2
ðx
2
x
0
Þ
2
ðy
2
y
0
Þ
for
ðx
2
x
0
Þ
1
ðy
2
y
0
Þ
d
cell
ðx
;
yÞ
5
(6.6)
2
2
.
R
2
0
for
ðx
2
x
0
Þ
1
ðy
2
y
0
Þ
Insertion of
Eq. (6.4)
in
Eq. (6.6)
gives
8
<
q
R
2
4
π
λ
U
2
2
2
2
2
ðx
2
x
0
Þ
2
ðy
2
y
0
Þ
U
ðn
cell
2
n
medium
Þ
ðx
2
x
0
Þ
1
ðy
2
y
0
Þ
#
R
2
for
Δϕ
cell
ðx
;
yÞ
5
:
2
2
.
R
2
0
for
ðx
2
x
0
Þ
1
ðy
2
y
0
Þ
(6.7)
with the unknown parameters
n
cell
,
R
,
x
0
, and
y
0
. In order to obtain the parameters
n
cell
,
R
,
x
0
, and
y
0
,
Eq. (6.7)
can be fitted iteratively to the measured phase data of spherical cells in
suspension, for example, with the Gauss
Newton method
[52,74]
.
Figure 6.6A
shows the phase contrast image of a suspended cell, coded to 256 gray levels.
The data
Δϕ
cell
(
x
,
y
) for the fitting process is selected by a threshold value that specifies the
phase noise in the area around the cell. In
Figure 6.6B
, the fit of
Eq. (6.7)
to the phase data
along dashed line in
Figure 6.6A
is depicted.
Figure 6.6C and D
show in comparison
pseudo-3D plots of the phase distribution in
Figure 6.6A
and the result of line-by-line
fitting of
Eq. (6.7)
to the measurement data. The mean value of the cell refractive index,
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