Wavelet analysis for polarization maps of networks formed by liquid biological crystals in blood plasma: statistical and fractal approaches
Considered in this paper are the possibilities of local wavelet analysis for polarization-inhomogeneous images inherent to blood plasma of healthy and oncologically ill patients. Determined is the set of statistical, correlation and fractal parameters for distributions of wavelet coefficients tha...
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irk-123456789-1182352017-05-30T03:02:55Z Wavelet analysis for polarization maps of networks formed by liquid biological crystals in blood plasma: statistical and fractal approaches Bachinsky, V.T. Ushenko, Yu.O. Tomka, Yu.Ya. Dubolazov, O.V. Balanets’ka, V.O. Karachevtsev, A.V. Considered in this paper are the possibilities of local wavelet analysis for polarization-inhomogeneous images inherent to blood plasma of healthy and oncologically ill patients. Determined is the set of statistical, correlation and fractal parameters for distributions of wavelet coefficients that characterize different scales of polarization maps inherent to polycrystalline networks of amino-acids in blood plasma. Established are criteria for differentiation of processes that provide transformation of birefringent optically-anisotropic structures in blood plasma for various scales of their geometrical dimensions. 2010 Article Wavelet analysis for polarization maps of networks formed by liquid biological crystals in blood plasma: statistical and fractal approaches/ V.T. Bachinsky, Yu.O. Ushenko, Yu.Ya. Tomka, O.V. Dubolazov, V.O. Balanets’ka, A.V. Karachevtsev // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2010. — Т. 13, № 2. — С. 189-201. — Бібліогр.: 33 назв. — англ. 1560-8034 PACS 61.43.Hv, 87.64.-t http://dspace.nbuv.gov.ua/handle/123456789/118235 en Semiconductor Physics Quantum Electronics & Optoelectronics Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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English |
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Considered in this paper are the possibilities of local wavelet analysis for
polarization-inhomogeneous images inherent to blood plasma of healthy and
oncologically ill patients. Determined is the set of statistical, correlation and fractal
parameters for distributions of wavelet coefficients that characterize different scales of
polarization maps inherent to polycrystalline networks of amino-acids in blood plasma.
Established are criteria for differentiation of processes that provide transformation of
birefringent optically-anisotropic structures in blood plasma for various scales of their
geometrical dimensions. |
| format |
Article |
| author |
Bachinsky, V.T. Ushenko, Yu.O. Tomka, Yu.Ya. Dubolazov, O.V. Balanets’ka, V.O. Karachevtsev, A.V. |
| spellingShingle |
Bachinsky, V.T. Ushenko, Yu.O. Tomka, Yu.Ya. Dubolazov, O.V. Balanets’ka, V.O. Karachevtsev, A.V. Wavelet analysis for polarization maps of networks formed by liquid biological crystals in blood plasma: statistical and fractal approaches Semiconductor Physics Quantum Electronics & Optoelectronics |
| author_facet |
Bachinsky, V.T. Ushenko, Yu.O. Tomka, Yu.Ya. Dubolazov, O.V. Balanets’ka, V.O. Karachevtsev, A.V. |
| author_sort |
Bachinsky, V.T. |
| title |
Wavelet analysis for polarization maps of networks formed by liquid biological crystals in blood plasma: statistical and fractal approaches |
| title_short |
Wavelet analysis for polarization maps of networks formed by liquid biological crystals in blood plasma: statistical and fractal approaches |
| title_full |
Wavelet analysis for polarization maps of networks formed by liquid biological crystals in blood plasma: statistical and fractal approaches |
| title_fullStr |
Wavelet analysis for polarization maps of networks formed by liquid biological crystals in blood plasma: statistical and fractal approaches |
| title_full_unstemmed |
Wavelet analysis for polarization maps of networks formed by liquid biological crystals in blood plasma: statistical and fractal approaches |
| title_sort |
wavelet analysis for polarization maps of networks formed by liquid biological crystals in blood plasma: statistical and fractal approaches |
| publisher |
Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
| publishDate |
2010 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/118235 |
| citation_txt |
Wavelet analysis for polarization maps of networks
formed by liquid biological crystals in blood plasma:
statistical and fractal approaches/ V.T. Bachinsky, Yu.O. Ushenko, Yu.Ya. Tomka, O.V. Dubolazov, V.O. Balanets’ka, A.V. Karachevtsev // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2010. — Т. 13, № 2. — С. 189-201. — Бібліогр.: 33 назв. — англ. |
| series |
Semiconductor Physics Quantum Electronics & Optoelectronics |
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Semiconductor Physics, Quantum Electronics & Optoelectronics, 2010. V. 13, N 2. P. 189-201.
© 2010, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
189
PACS 61.43.Hv, 87.64.-t
Wavelet analysis for polarization maps of networks
formed by liquid biological crystals in blood plasma:
statistical and fractal approaches
V.T. Bachinsky, Yu.O. Ushenko, Yu.Ya. Tomka, O.V. Dubolazov,
V.O. Balanets’ka, A.V. Karachevtsev
Yuri Fedkovych Chernivtsi National University,
2 Kotsybynsky str., 58012 Chernivtsi, Ukraine
Abstract. Considered in this paper are the possibilities of local wavelet analysis for
polarization-inhomogeneous images inherent to blood plasma of healthy and
oncologically ill patients. Determined is the set of statistical, correlation and fractal
parameters for distributions of wavelet coefficients that characterize different scales of
polarization maps inherent to polycrystalline networks of amino-acids in blood plasma.
Established are criteria for differentiation of processes that provide transformation of
birefringent optically-anisotropic structures in blood plasma for various scales of their
geometrical dimensions.
Keywords: wavelet analysis, polarization, crystal, birefringence, statistical moment,
correlation function, fractal.
Manuscript received 10.02.10; accepted for publication 25.03.10; published online 30.04.10.
1. Introduction
Among many directions of optical diagnostics of organic
phase-inhomogeneous objects, a new technique – laser
polarimetry [1 - 33] – has been formed within recent 10
years. It enables to obtain information about optical
anisotropy of phase-inhomogeneous objects in the form
of coordinate distributions of the biological tissues (BT)
azimuths and ellipticities of their object field
polarization.
Specifically, the above mentioned model was used
for finding and substantiating the interrelations between
the ensemble of statistic moments of the 1st to 4th orders
that characterize the orientation-phase structure
(distribution of optical axes and phase shifts for
directions of protein fibril networks) of birefringent BT
architectonics and that of 2D distributions of azimuths
and ellipticities of their laser images [1]. It was
determined [14 - 16] that the 3rd and the 4th statistic
moments for coordinate distributions of ellipticities are
the most sensitive to the change (caused by dystrophic
and oncological processes) of optical anisotropy inherent
to protein crystals. On this basis, the criteria for early
diagnostics of muscle dystrophy, pre-cancer states of
connective tissue, collagenosis, etc. were determined.
However, application of statistical analysis to
coordinate distributions for azimuths and ellipticities of
polarization in BT laser images does not enable to
estimate local changes in the structure of optically
anisotropic networks formed from protein crystals. On
the other hand, in many cases the study of biological
liquids (blood, urine, bile, synovial liquid, etc.) is more
topical and accessible from the clinical viewpoint than
the study of BT. Thereof, the task to develop new
approaches to a local analysis of polarization-
inhomogeneous images of biological liquids seems
rather reasonable.
Our work is aimed at studying capabilities of the
wavelet analysis [17, 18] in determination of statistical
(statistical moments of the first to fourth orders) as well
as fractal (fractal dimensionalities) parameters that
characterize distributions of wavelet coefficients for
images of blood plasma for diagnostics of oncological
processes in a human organism.
2. Polarizaton modeling of properties inherent to
networks of biological liquid crystals in blood plasma
As a base for analyses of processes providing formation
of polarization-inhomogeneous images of blood plasma,
we use the optical model developed in [1]:
• optical properties of blood plasma are
determined as those of a two-component amorphous-
crystalline structure;
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2010. V. 13, N 2. P. 189-201.
© 2010, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
190
• crystalline component is an architectonic net
consisting of amino-acid liquid crystals;
• optically, the amino-acid liquid crystals possess
the properties of uniaxial birefringent crystals.
Polarization properties of local optically coaxial
crystalline amino acid can be described with the
following Mueller operator { }uz [14, 27, 33]
{ }
444342
343332
242322
0
0
0
0001
zzz
zzz
zzz
z u = , (1)
where
( )
( )
⎪
⎪
⎪
⎪
⎩
⎪
⎪
⎪
⎪
⎨
⎧
δ=
δρ±=
δρ±=
δρ+ρ=
δ−ρρ=
δρ+ρ=
=δρ
.cos
,sin2sin
,sin2cos
,cos2cos2sin
,cos12sin2cos
,cos2sin2cos
,
44
42,24
43,34
22
33
32,23
22
22
z
z
z
z
z
z
zik (2)
Here, ρ is the direction of optical axis,
ndΔ= λ
πδ 2 – phase shift introduced between the
orthogonal components of the amplitude of laser wave
with the length λ passing through the liquid crystal with
the linear size of its geometrical section d and
birefringence index nΔ .
Mueller matrix ikf elements of liquid-crystal
network are determined by the following algorithm
( )[ ]∑
=
=
N
u
uikik zf
1
,δρ , (3)
where N is a finite number of liquid crystals.
The classical definition of the Mueller matrix { }F
for biological objects consists not only in the fact that it
describes optical properties of their optically anisotropic
component, but also in the fact that such mathematical
operator completely characterizes the processes of
transformation of the Stokes vector S by phase-
inhomogeneous layers [2 – 6, 19, 25]
{ } 0SFS =∗ . (4)
Here, ∗SS ,0 are the Stokes vectors of illuminating
and object beams.
For a more general state of elliptically polarized
wave, the Stokes vector looks as follows [1]
⎟
⎟
⎟
⎟
⎟
⎠
⎞
⎜
⎜
⎜
⎜
⎜
⎝
⎛
β
βα
βα
=
0
00
00
0
2sin
2cos2sin
2cos2cos
1
S , (5)
where 00 ,βα are the azimuth and ellipticity of an
electromagnetic wave.
Taking into account the expressions (2) to (5), the
Stokes vector ∗S can be written in a complete form as
.
2sin
2cos2sin
2cos2cos
1
2sin2cos2sin2cos2cos
2sin2cos2sin2cos2cos
2sin2cos2sin2cos2cos
1
1
04400430042
03400330032
02400230022
4
3
2
⎟⎟
⎟
⎟
⎟
⎠
⎞
⎜⎜
⎜
⎜
⎜
⎝
⎛
β
βα
βα
=
=
⎟
⎟
⎟
⎟
⎟
⎠
⎞
⎜
⎜
⎜
⎜
⎜
⎝
⎛
β+βα+βα
β+βα+βα
β+βα+βα
=
=
⎟
⎟
⎟
⎟
⎟
⎠
⎞
⎜
⎜
⎜
⎜
⎜
⎝
⎛
=∗
fff
fff
fff
S
S
S
S
(6)
Being based on (6), we obtain expressions for
determining the azimuth α and ellipticity β of the
object electromagnetic field polarization
( )[ ]00
2
3 ,,,5.0 βαδρ≡⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
=α ikfG
S
Sarctg ; (7)
( ) ( )[ ]004 ,,,arcsin5.0 βαδρ≡=β ikfQS . (8)
It follows from the analysis of relations (7) and (8)
that the state of polarization ( βα , ) of each point
( yxr ,≡ ) of the BT image is determined by
corresponding local orientation-phase ( δρ , ) parameters
of crystalline network.
In other words, on the terms of coordinate
heterogeneity of distributions ( )rρ and ( )rδ in the
plane of the BT layer a certain polarizationally
inhomogeneous image is formed with distributions
( )rα and ( )rβ called as polarization maps (PM) [1, 20
- 32].
3. Wavelet approach to the analysis of distributions
for azimuths and ellipticity of polarization of laser
images inherent to blood plasma
If a prototype function is taken as a specific wavelet
function possessing a finite base both in coordinate and
frequency spaces, then one can expand into series [17,
18] the one-dimensional distribution of azimuths ( )xα
or ellipticity ( )xβ for polarization
( )
( ) ∑
∞
−∞=
Ψ=
⎭
⎬
⎫
⎩
⎨
⎧
ba
abab xC
x
x
,
)(
β
α
, (9)
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2010. V. 13, N 2. P. 189-201.
© 2010, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
191
where )()( baxxab −Ψ=Ψ is a base function formed
from the function-prototype by shifting b and scaling a,
while the coefficients of this expansion are determined
as follows
( )
( )∫ Ψ
⎭
⎬
⎫
⎩
⎨
⎧
= dxx
x
x
C abab )(
β
α
. (10)
The result of this wavelet transformation for the
one-dimensional distribution of polarization parameters
is a two-dimensional array of the coefficients ),( baWα
and ),( baWβ that are defined by the following relation
dx
a
bxf
a
baW ∫
+∞
∞−
−
Ψ⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
β
α
= )(1),( 2/1 . (11)
In our work, as a wavelet function we have used
the so-called MHAT function, i.e. the second derivative
of the Gauss function. It has been shown that MHAT
wavelet possesses a narrow energy spectrum and two
moments (zero and first) that are equal to zero. It
satisfies the analysis of complex signals rather well. The
mathematical expression for the MHAT wavelet is of the
following form
2/22/
2
2 22
)1()( xx exe
dx
dx −− −==Ψ . (12)
To estimate ),...2,1,(; mbaW =βα distributions for
various scales a of the wavelet functionΨ , we
calculated the set of their statistical moments of the first
to fourth orders 4;3;2;1=jM [1, 14]
∑
=
=
m
i
iW
m
M
1
1
1 , ∑
=
=
m
i
iW
m
M
1
2
2
1 ,
∑
=
=
m
i
iW
mM
M
1
3
3
2
3
11
, ∑
=
=
m
i
iW
mM
M
1
4
2
2
4 .11 (13)
To calculate autocorrelation functions
),...2,1,(; mbaW =βα related with wavelet coefficients
for distributions of azimuths and ellipticity of laser image
polarization, we used the following expression [1, 19]
( ) ( )[ ] ( )[ ]dxxxaWmxaW
N
xK
x
x
∫ Δ−÷==Δ
→ 00
;1;1lim .
(14)
Here, ( )xΔ is the step of changing the coordinate
(b) for one-dimensional distributions of azimuths α and
ellipticity β of polarization.
The fractal analysis of ),...2,1,(; mbaW =βα
distributions was performed using calculation of
logarithmic dependences ( ) 1loglog −− dWJ for power
spectra ( )WJ [1, 19]
( ) ∫
+∞
∞−
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
= νπν
β
α
dWWJ ba 2cos, , (15)
where 1−= dν are spatial frequencies determined by
geometrical sizes ( d ) of structural elements of the
Mueller-matrix images for a biological layer.
The dependences ( ) )log(log 1−− dWJ are
approximated using the least-squares method by the
curves ( )ηΦ , the straight parts of which are used to
determine the slope angles η and to calculate the value
of fractal dimensionality D via the relation [20]
η−= tgD 3 . (16)
Classification of ),...2,1,(; mbaW =βα distributions
is performed using the following criteria offered in [21,
22]:
• these distributions are fractal, on the condition that
the slope angle has a constant value const=η in
the dependence ( )ηΦ within 2 or 3 decades in
changing sizes d ;
• the distributions are multi-fractal, on the condition
of availability of several constant values for slope
angles in ( )ηΦ ;
• the distributions are random, if there is no stable
slope angle in ( )ηΦ over the whole range of
changing sizes d .
4. Optical scheme of the polarimeter and technique of
polarimetric investigations
Fig. 1 shows the traditional optical scheme of a
polarimeter for measuring the set of coordinate
distributions for azimuths and ellipticity of polarization
of laser images inherent to human blood plasma [23].
Illumination was made with a collimated beam
(radius r = 10 mm) of He-Ne laser 1 (λ = 0.6328 μm).
Using the polarization illuminator (quarter-wave plates
3,5 and polarizer 4) we formed respective states for
polarization of illuminating beam: 1 - 00 ; 2 - 090 ; 3 -
045 ; 4 - ⊗ (right circulation).
The image of blood plasma layer was formed
within the light-sensitive area ( pixpix 600800 × ) of
CCD camera 10 by using the micro-objective 7.
For each separate pixel, we determined four
parameters of the Stokes vector
.
;
;
;
4
135453
9002
9001
⊕⊗ −=
−=
−=
+=
IIS
IIS
IIS
IIS
(17)
Here, 13545900 ;;; IIII are the intensities of
linearly (with the azimuths 0000 135;45;90;0 ) as well
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2010. V. 13, N 2. P. 189-201.
© 2010, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
192
Fig. 1. Optical scheme of the polarimeter. 1 – He-Ne laser; 2 –collimator; 3 – stationary quarter-wave plate; 5, 8 – movable
quarter-wave plates; 4, 9 – polarizer and analyzer, respectively; 6 – object under investigation; 7 – micro-objective; 10 – CCD
camera; 11 – personal computer.
as left- ⊕I and right- ⊗I circularly polarized radiation
transmitted by the system of the quarter-wave 8 –
polarizer 9.
The values of azimuth and ellipticity of
polarization were calculated using the following
algorithms
( ) ( )
( )
( ) ( )
( )⎪
⎪
⎩
⎪⎪
⎨
⎧
⎥⎦
⎤
⎢⎣
⎡
×
×=×β
⎥⎦
⎤
⎢⎣
⎡
×
×=×α
.arcsin5,0
;5,0
1
4
2
3
nmS
nmSnm
nmS
nmSarctgnm
(18)
The coordinate sets of values
⎟⎟
⎟
⎟
⎟
⎠
⎞
⎜⎜
⎜
⎜
⎜
⎝
⎛
α
mnm
n
rr
rr
..
..
..
..
1
111
and
⎟⎟
⎟
⎟
⎟
⎠
⎞
⎜⎜
⎜
⎜
⎜
⎝
⎛
β
mnm
n
rr
rr
..
..
..
..
1
111
we shall name as polarization
maps.
5. Brief characteristic of the objects under
investigation
The main optically anisotropic elements of blood plasma
are albumin and globulin that form networks of liquid
crystals in the process of crystallization. The structure of
these networks is superposition of albumin crystals with
spatially ordered directions of optical axes and spatially
disordered globulin crystals.
The above model assumptions can be qualitatively
illustrated by the results of comparative investigation of
structures in laser images of blood plasma taken from
healthy and sick patients (Fig. 2) obtained for various
values of angles 00 90;0=Θ between the transmission
planes of the polarizer 4 and analyzer 9 (Fig. 1).
As seen from these images, the blood plasma of a
healthy patient is characterized with domination of a
large-scale network consisting of albumin crystals with
ordered directions of their optical axes. In the laser
images of the blood plasma taken from a patient with
cervical carcinoma, one can observe domination of
small-scale disordered networks consisting of albumin
crystals.
6. Polarization maps for laser images of human blood
plasma
Figs 3 and 4 illustrate coordinate distributions of
azimuths ( )nm×α (Fig. 3a, e); ellipticity ( )nm×β
(Fig. 4а, e) of polarization; histograms of distributions
for their values ( )αh (Fig. 3b, f) and ( )βh (Fig. 4b, f);
Fig. 2. Polarization images of liquid-crystalline optically
anisotropic network inside blood plasma of healthy (a), (b)
and sick (c), (d) patients.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2010. V. 13, N 2. P. 189-201.
© 2010, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
193
autocorrelation functions ( )xK Δ for ( )nm×α
distributions (Fig. 3c, g) and ( )nm×β (Fig. 4c, g), as
well as logarithmic dependences ( ) 1loglog −− dJ α
(Fig. 3d, h) and ( ) 1loglog −− dJ β (Fig. 4d, h) for
polarization maps of blood plasma taken from healthy
(Fig. 3) and sick (Fig. 4) patients.
The analysis of coordinate distributions for
azimuths ( )nm×α (Fig. 3а, e) and ellipticity ( )nm×β
(Fig. 4а, e) has shown that they contain two components:
- large-scale (100 to 300 μm) parts with
homogeneous polarization (images of the optically
isotropic component in human blood plasma) that
coincides with that of laser beam 0
0 0==∗ αα ;
-
- polarization-inhomogeneous parts
( ) ( ) constyxconstyx =ΔΔ=ΔΔ ,;, βα - laser images of
elements (2 to 50 μm) of albumin and globulin
crystalline network.
Quantitatively this structure of polarization maps
for blood plasma of both types can be illustrated with
histograms ( )αh and ( )βh that are dependences
symmetrical relatively to the main extrema at
00 0;0 == βα .
Summarized in Table 1 are the values and ranges
for statistical moments of the first to fourth orders that
characterize distributions ( )nm×α and ( )nm×β
within the limits of two groups of healthy ( 21=q ) and
oncologically sick ( 19=q ) patients.
Fig. 3. Polarization maps for azimuths ( )nm×α (а), (e), their statistical (b), (f), correlation (c), (g), and fractal (d), (h) parameters
of blood plasma taken from healthy (fragments (a) to (d)) and oncologically sick (fragments (e) to (h)) patients.
Fig. 4. Polarization maps for ellipticity ( )nm×β (а), (e), their statistical (b), (f), correlation (c), (g), and fractal (d), (h) parameters
of blood plasma taken from healthy (fragments (a) to (d)) and oncologically sick (fragments (e) to (h)) patients.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2010. V. 13, N 2. P. 189-201.
© 2010, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
194
Our comparative analysis of the data obtained did
not reveal sufficiently reliable criteria (within the
framework of statistical approach) for differentiation of
coordinate structure in polarization maps for blood
plasma of both types. The values and ranges for
changing the whole set of statistical moments 4;3;2;1=jM
related to distributions of azimuths α and β ellipticity
of polarization are superimposed.
Correlation and fractal analyses of polarization
maps describing blood plasma taken from healthy and
oncologically sick patients revealed a fractal structure
inherent to coordinate distributions of azimuths
( )nm×α and ellipticity ( )nm×β of polarization
within the range of mean (50 to 200 µm) and large (200
to 2000 µm) geometrical sizes of amino acid biological
crystals. The approximating curves ( )ηΦ for
dependences ( ) 1loglog −− dJ α (Fig. 3d, h) and
( ) 1loglog −− dJ β (Fig. 4d, h) are characterized with
stable values of slope angles
( )
⎪⎩
⎪
⎨
⎧
==
==
→αη ∗
α
∗
α
αα
;32,2;83,2
;81,1;03,2
)2()1(
)1()1(
DD
DD
and
( )
⎪⎩
⎪
⎨
⎧
==
==
→βη ∗
β
∗
β
ββ
.53,1;68,2
;01,2;67,2
)2()2(
)1()1(
DD
DD
.
In the field of small geometric sizes (2 to 50 µm) of
the polycrystalline network inherent to amino acids in
human blood plasma for the patient with cervical
carcinoma, the values of fractal dimensionalities ∗
αD
and ∗
βD for distributions of polarization parameters
become indefinite. ( )ηαΦ and ( )ηβΦ dependences
within this range of sizes inherent to amino acid crystals
are curve without any definite slope angle -
( ) constm ≠μη 50...2 .
In our opinion, this “destruction” of self-similarity
for the distributions ( )nm×α and ( )nm×β in
polarization maps inherent to blood plasma of
oncologically sick patient is related with formation of a
network of small-scale globulin crystals (Fig. 2c, d). By
other words, to determine a set of objective criteria for
differentiation of polycrystalline networks of both types,
one needs a more detailed analysis of polarization
distributions just for these scales of geometrical sizes of
biological crystals.
Table 1. Statistical moments of the first to fourth orders for distributions of polarization parameters in laser images of
human blood plasma in different physiological states of patients
jM Norm ( 21=q ) Oncology ( 19=q ) ( )βjM Norm ( 21=q ) Oncology ( 19=q )
( )α1M 0.02 ± 0.004 0.01 ± 0.003 ( )β1M 0.49 ± 0.053 0.52 ± 0.061
( )α2M 0.07 ± 0.009 0.08 ± 0.01 ( )β2M 0.04 ± 0.006 0.03 ± 0.005
( )α3M 0.08 ± 0.008 0.06 ± 0.007 ( )β3M 0.91± 0.11 0.84 ± 0.095
( )α4M 3.95± 0.44 3.27 ± 0.39 ( )β4M 3.06± 0.35 2.89 ± 0.33
Fig. 5. Distributions of wavelet coefficients ( )kmkbaW ÷= 1;min of the polarization map for azimuths α (m×n) of
polarization inherent to blood plasma of a healthy patient for various lines 420;240;2=k of ССD camera.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2010. V. 13, N 2. P. 189-201.
© 2010, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
195
7. Wavelet analysis of polarization distributions of
laser images for polycrystalline networks in blood
plasma
The locally-scaled analysis of coordinate distributions
( )nm×α and ( )nm×β for laser images of blood
plasma is provided using linear nkkmk ÷=1;,...,1
scanning by the MHAT wavelet with the step pixb 1=
and window width 1 µm ≤ amin ≤ 70 µm. The result of
this scanning can be represented (see relation (11)) as a
two-dimensional set of wavelet coefficients
( ) ( )
( ) ( )⎟
⎟
⎟
⎟
⎟
⎠
⎞
⎜⎜
⎜
⎜
⎜
⎝
⎛
=
=
=
mbaWbaW
mbaWbaW
W ba
,..,
....
....
..,
max1max
min1min
,
for each k - th
Fig. 6. Distributions of wavelet coefficients ( )kmkbaW ÷= 1;min of the polarization map for ellipticity ( )nm×β of
polarization observed in blood plasma of a healthy patient.
Fig. 7. Statistical (left column), correlation (central column) and fractal (right column) parameters of distributions inherent to
wavelet coefficients ( ) ( )[ ]kmkbmmmaW ÷== 1;30;10;2min μμμ describing the polarization map for )( nm×α azimuths
of a healthy patient’s blood plasma.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2010. V. 13, N 2. P. 189-201.
© 2010, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
196
line of pixels (Figs 5 and 6) in the light-sensitive area of
CCD 10 (Fig. 1).
Thus, the obtained set of wavelet coefficients
( )kmkbaW ÷= 1;min should be averaged using the
following algorithm
( )
( )
( )
( )
( )
( )
( )
( )
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎠
⎞
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎝
⎛
=
===
=
===
=
∑∑
∑∑
==
==
.
,
,..;
,
,
....
....
;
,
..;
,
,
1
1max
max
1
1max
1max
1
1min
min
1
1min
1min
,
m
mbaW
mbaW
m
baW
baW
m
mbaW
mbaW
m
baW
baW
W
m
j
j
m
j
j
m
j
j
m
j
j
ba
.
(19)
The algorithm (19) is an analog of two-dimensional
wavelet transformation that characterizes coordinate
distributions for azimuths )( nm×α (Fig. 3a, e) and
ellipticity )( nm×β (Fig. 4a, e) of polarization observed
in laser images within the range of small scales
1 µm ≤ amin ≤ 70 µm in polycrystalline structures of
blood plasma.
Shown in Figs 7 and 8 are the results of
experimental investigations of statistical (statistical
moments of the 1-st to 4-th orders ( )baj WM ,4;3;2;1= ,
correlation (autocorrelation functions ( )baWK , ) and
fractal (logarithmic dependences of the power spectra
( ) 1
, loglog −− dWJ ba ) parameters that characterize the
distributions ( )kmkbaW ÷= 1;min for three scales
mamama μμμ 30;10;2 minminmin === of the MHAT
wavelet for polarization maps )( nm×α and
)( nm×β describing blood plasma of a healthy patient.
As seen from the data obtained, the distributions
for wavelet coefficients
( ) ( )[ ]kmkbmmmaW ÷== 1;30;10;2min μμμ of
polarization maps ( )nm×α and )( nm×β for the
polycrystalline network of amino acids from healthy
patient’s blood plasma, which is ordered along directions
of optical axis (Fig. 2a, b), are individual for each scale
( )mmma μμμ 30;10;2min = of the MHAT wavelet.
Our statistical analysis (Figs 7 and 8, left columns)
of the distributions ( ) ( )[ ]( )αμμμ kmkbmmmaW ÷== 1;30;10;2min
and ( ) ( )[ ]( )βμμμ kmkbmmmaW ÷== 1;30;10;2min revealed
different dynamics for changing the values 4;3;2;1=jM
with increasing the scale mina of the MHAT wavelet.
The ranges of changes in statistical moments of the 1-st
to 4-th orders lie within the limits of 623 ÷=M and
1134 ÷=M times, respectively. The found tendency is
indicative of transformation observed for distributions of
wavelet coefficients from practically random
( 04;32;1 →MM ff ) up to the stochastic ones
Fig. 8. Statistical (left column), correlation (central column) and fractal (right column) parameters of distributions inherent
to wavelet coefficients ( ) ( )[ ]kmkbmmmaW ÷== 1;30;10;2min μμμ describing the polarization map for ellipticity
)( nm×β of a healthy patient’s blood plasma.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2010. V. 13, N 2. P. 189-201.
© 2010, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
197
( 2;14;3 MM ff ) [1].
This fact is also confirmed by the dependences
(Figs 7 and 8, central columns) of the autocorrelation
functions ( ) ( )[ ]( ){ }αμμμ kmkbmmmaWK ÷== 1;30;10;2min and
( ) ( )[ ]( ){ }βμμμ kmkbmmmaWK ÷== 1;30;10;2min for the
distributions of wavelet coefficients, as they are
superposition of two components, namely: statistical that
drops monotonically, and the oscillating one that is
caused by periodical coordinate changes in these
distributions.
The revealed features of statistical and coordinate
structures in distributions of wavelet coefficients for
polarization maps describing healthy patient’s blood
plasma are related, in our opinion, with a different
degree of self-similarity in distributions of optical axis
directions ρ and phase shifts δ in polycrystalline
structures at different scales of analysis
( )mmma μμμ 30;10;2min = of the MHAT wavelet. So,
for small scales ( )ma μ2min = , a dominant contribution
to formation of the coordinate distributions ( )nm×α
and ( )nm×β is caused by chaotically oriented globulin
crystals. Therefore, just the random component
dominates in the respective distributions for wavelet
coefficients ( ) ( )[ ]( )αμ kmkbmaW ÷== 1;2min
and
( ) ( )[ ]( )βμ kmkbmaW ÷== 1;2min .
When the scale grows ( )mma μμ 30;10min = , also
growing is the contribution to formation of distributions
for polarization parameters of the set oriented along
directions of optical axes of albumin crystals. From the
statistical viewpoint, this process should be observed in
the growth of statistical moments of the 3-rd and 4-th
orders that characterize the distributions
( ) ( )[ ]( )αμμ kmkbmmaW ÷== 1;30;10min and
( ) ( )[ ]( )βμμ kmkbmmaW ÷== 1;30;10min , as well as in formation
of oscillations of autocorrelation dependences
( ){ }αWK and ( ){ }βWK .
Besides, some stable slope η of approximating
curves ( )ηΦ for ma μ2min = in the logarithmic
dependences ( )( ) 1
, loglog −− dWJ ba α and
( )( ) 1
, loglog −− dWJ ba β is absent. The growth in the
scale ( )mma μμ 30;10min = of the MHAT wavelet can
be observed in transformation of the random curves
( )ηΦ into polygonal lines (Figs 7 and 8, right columns).
In other words, the random distributions
( ) ( )[ ]( )αμ kmkbmaW ÷== 1;2min and ( ) ( )[ ]( )βμ kmkbmaW ÷== 1;2min
are transformed into the multi-fractal ones.
Shown in Figs 9 and 10 are the series of
distributions for wavelet coefficients
Fig. 9. Statistical (left column), correlation (central column) and fractal (right column) parameters of distributions of wavelet
coefficients ( ) ( )[ ]kmkbmmmaW ÷== 1;30;10;2min μμμ for polarization maps of azimuths )( nm×α inherent to
blood plasma of a patient with cervical carcinoma.
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© 2010, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
198
( ) ( )[ ]( )αμμμ kmkbmmmaW ÷== 1;30;10;2min and
( ) ( )[ ]( )βμμμ kmkbmmmaW ÷== 1;30;10;2min (left columns),
autocorrelation functions ( ){ }αWK and ( ){ }βWK
(central columns) as well as logarithmic dependences
( )( ) 1
, loglog −− dWJ ba α and ( )( ) 1
, loglog −− dWJ ba β
(right columns) that characterize polarization maps
( )nm×α of ( )nm×β polycrystalline networks
inherent to amino acids in blood plasma of a patient with
cervical carcinoma in the first stage.
Our analysis of the data obtained for statistical,
correlation and fractal parameters that characterize sets
of wavelet coefficients for various scales of MHAT
functions for distributions of azimuths )( nm×α and
ellipticity )( nm×β of laser images of the albumin-
globulin polycrystalline network in blood plasma of a
patient with cervical carcinoma enabled us to find:
1) Weak changes (within 10 to 15%) of the values
of statistical moments 4;3;2;1=jM that characterize the
distributions ( ) ( )[ ]( )αμ kmkbmaW ÷== 1;2min and
( ) ( )[ ]( )βμ kmkbmaW ÷== 1;2min on the scales ma μ2min = of
the MHAT wavelet as compared with analogous
statistical parameters determined for polarization maps
of healthy patient’s blood plasma.
2) An essential decrease of statistical moments of
the 3-rd (2.7 to 3.5 times) and 4-th (3.4 to 5.7 times)
orders for the distributions
( ) ( )[ ]( )α÷=μμ= kmkbmmaW 1;30;10min
and
( ) ( )[ ]( )βμμ kmkbmmaW ÷== 1;30;10min determined on larger
scales mma μμ 30;10min = of the MHAT wavelet.
3) A faster drop in the autocorrelation
dependences ( ){ }αWK and ( ){ }βWK as well as
decrease in their fluctuation amplitudes.
4) The absence of any stable slope of the
approximating curves ( )ηΦ for the logarithmic
dependences ( )( ) 1
, loglog −− dWJ ba α and
( )( ) 1
, loglog −− dWJ ba β determined on all the scales of
the MHAT wavelet.
The above mentioned differences between
statistical moments, autocorrelation functions and
logarithmic dependences that characterize the
distributions ( ) ( )[ ]( )αμμ kmkbmmaW ÷== 1;30;10min and
( ) ( )[ ]( )βμμ kmkbmmaW ÷== 1;30;10min can be related with
growth of the albumin concentration in blood plasma of
a patient with the oncological process. This biochemical
process results in growth of the birefringence coefficient
for partial albumin crystals disordered as to directions of
Fig. 10. Statistical (left column), correlation (central column) and fractal (right column) parameters of distributions of wavelet
coefficients ( ) ( )[ ]kmkbmmmaW ÷== 1;30;10;2min μμμ for polarization maps of ellipticity )( nm×β inherent to
blood plasma of a patient with cervical carcinoma.
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© 2010, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
199
their optical axes. And this transformation of the
polycrystalline structure begins from small sizes
( mmd μμ 501 ÷= ) of structural elements in the
polycrystalline network. From the viewpoint of
polarization, these processes become apparent via
formation of random distributions for azimuths
( )nm×α and ellipticity ( )nm×β (Figs 3(e) and 4(e))
in respective blood plasma laser images obtained in the
case of an oncologically sick patient. It results in
decrease of the values inherent to statistical moments of
the 3-rd and 4-th orders that characterize the
distributions ( ) ( )[ ]( )αμμμ kmkbmmmaW ÷== 1;30;10;2min and
( ) ( )[ ]( )βμμμ kmkbmmmaW ÷== 1;30;10;2min on all the scales
mina of the MHAT wavelet (Figs 7 to 10, left columns).
Due to the same reason, autocorrelation functions
experience faster drop of their intrinsic values (Figs 7 to
10, central columns), while the approximating curves
( )ηΦ for the logarithmic dependences
( )( ) 1loglog −− dWJ α and ( )( ) 1loglog −− dWJ β are
characterized with the absence of a stable slope angle
(Figs 7 to 10, right columns).
Possibilities to diagnose pathological processes in a
human organism by using the wavelet analysis of
polarization maps for azimuths and ellipticity of laser
images describing blood plasma have been illustrated in
Table 2, where the values of statistical moments that
characterize distributions on three scales mina of the
MHAT wavelet for two groups of healthy (21 samples)
and sick (19 samples) patients are summarized.
Conclusion
Thus, we have demonstrated diagnostic efficiency of the
wavelet analysis applied to coordinate distributions for
azimuths and ellipticity of polarization in laser images
inherent to amino acid polycrystalline networks in blood
plasma of patients with oncological changes in woman’s
genital organs.
References
1. Gang Yao. Two-dimensional depth-resolved
Mueller matrix characterization of biological tissue
by optical coherence tomography / Gang Yao,
Lihong V. Wang // Opt. Lett. – 1999. – Vol. 24. –
P. 537-539.
2. Wang X. Monte Carlo model and single-scattering
approximation of polarized light propagation in
turbid media containing glucose / X. Wang, G.
Yao, L. - H. Wang // Appl. Opt. – 2002. – Vol. 41.
– P. 792–801.
Table 2. Statistical moments of the 1-st to 4-th orders for distributions of wavelet coefficients related to polarization
maps for azimuths ( )nm×α and ellipticity ( )nm×β of laser images describing blood plasma of a healthy patient
and that oncologically sick.
( )nm×α
21=q
( )nm×β
19=q
m
a
μ
,min jM
Norm Cancer Norm Cancer
1M 0.53 ± 0.059 0.58 ± 0.064 0.22± 0.028 0.25 ± 0.032
2M 0.21 ± 0.023 0.19 ± 0.022 0.07± 0.008 0.06 ± 0.007
3M 0.09 ± 0.0095 0.07 ± 0.008 0.13± 0.014 0.11 ± 0.012
2
4M 0.12 ± 0.013 0.09 ± 0.0097 0.08± 0.009 0.06 ± 0.0065
1M 0.66 ± 0.071 0.62 ± 0.065 0.33± 0.038 0.31 ± 0.034
2M 0.09 ± 0.1 0.12 ± 0.014 0.08 ± 0.0085 0.09± 0.0095
3M 0.18 ± 0.021 0.07 ± 0.0085 0.36± 0.043 0.12 ± 0.015
10
4M 0.36 ± 0.043 0.11 ± 0.013 0.43± 0.052 0.08 ± 0.009
1M 0.72 ± 0.076 0.74 ± 0.081 0.48± 0.054 0.44 ± 0.052
2M 0.12 ± 0.015 0.1 ± 0.0098 0.09 ± 0.11 0.11 ± 0.015
3M 0.54 ± 0.061 0.18 ± 0.022 0.45± 0.056 0.14 ± 0.018
30
4M 1.32 ± 0.17 0.26 ± 0.029 0.87 ± 0.95 0.15 ± 0.017
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2010. V. 13, N 2. P. 189-201.
© 2010, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
200
3. Wang X. Propagation of polarized light in
birefringent turbid media: a Monte Carlo study / X.
Wang, L. - H. Wang // J. Biomed. Opt. – 2002. –
Vol. 7. – P. 279-290.
4. Shuliang Jiao. Depth-resolved two-dimensional
Stokes vectors of backscattered light and Mueller
matrices of biological tissue measured with optical
coherence tomography / Shuliang Jiao, Gang Yao,
Lihong V. Wang // Appl. Opt. – 2000. – Vol. 39. –
P. 6318-6324.
5. Shuliang Jiao. Two-dimensional depth-resolved
Mueller matrix of biological tissue measured with
double-beam polarization-sensitive optical
coherence tomography / Shuliang Jiao, Lihong V.
Wang // Opt. Lett. – 2002. – Vol. 27. – P. 101-103.
6. Wang X. Polarized light propagation through the
scattering media: time-resolved Monte Carlo and
experiments / X. Wang, L. - H. Wang, C. - W. Sun,
C. C. Yang // J. Biomed. Opt. – 2003. – Vol. 8. – P.
608-617.
7. Demos S. G. Optical polarization imaging / S. G.
Demos, R. R. Alfano // Appl. Opt. – 1997. –Vol.
36. – P. 150-155.
8. Ducros M. G. Polarization sensitive optical
coherence tomography of the rabbit eye / M. G.
Ducros, J. F. de Boer, H. E. Huang, L. C. Chao, Z.
P.Chen, J. S. Nelson, T. E. Milner, H. G. Rylander
// IEEE J. Select. Top. Quant. Electron. – 1999. –
Vol. 5. – P. 1159-1167.
9. de Boer Johannes F. Two-dimensional
birefringence imaging in biological tissue using
polarization-sensitive optical coherence
tomography / Johannes F. de Boer, Thomas E.
Milner, Martin J. van Gemert, John S. Nelson, John
S // Proc. SPIE. – 1998. – Vol. 3196. – P. 32-37.
10. J. F. de Boer. Determination of the depth-resolved
Stokes parameters of light backscattered from
turbid media by use of polarization-sensitive
optical coherence tomography / J. F. de Boer, T. E.
Milner, J. S. Nelson // Opt. Lett. – 1999. – Vol. 24.
– P. 300-302.
11. Handbook of Optical Coherence Tomography;
edited by B.E. Bouma and G.J. Tearney //
Polarization-sensitive optical coherence
tomography / J. F. de Boer, T. E. Milner, M. G.
Ducros, S. M. Srinivas and J. S. Nelson. – Marcel
Dekker Inc.: New York, 2002. – P. 237-274.
12. Everett M. J. Birefringence characterization of
biological tissue by use of optical coherence
tomography / M. J. Everett, K. Shoenenberger, B.
W. Colston, L. B. Da Silva // Opt. Lett. – 1998. –
Vol. 23. – P. 228-230.
13. Alexander G. Ushenko and Vasilii P. Pishak,
“Laser Polarimetry of Biological Tissue: Principles
and Applications”, in Handbook of Coherent-
Domain Optical Methods: Biomedical Diagnostics,
Environmental and Material Science, Vol. 1, pp.
93-138, edited by Valery V. Tuchin, Kluwer
Academic Publishers, 2004.
14. A.G. Ushenko, “Stokes-correlometry of
biotissues,” Laser Physics, vol. 10(5), pp.1286-
1292, 2000.
15. A.G. Ushenko, “The Vector Structure of Laser
Biospeckle Fields and Polarization Diagnostics of
Collagen Skin Structures,” Laser Physics, vol.
10(5), pp. 1143-1149, 2000.
16. A.G. Ushenko, I. Z.Misevich, V. Istratiy, I.
Bachyns’ka, A. P. Peresunko, Omar Kamal
Numan, and T. G. Moiysuk, “Evolution of Statistic
Moments of 2D-Distributions of Biological Liquid
Crystal Net Mueller Matrix Elements in the Process
of Their Birefringent Structure
Changes,” Advances in Optical Technologies, vol.
2010, Article ID 423145, 2010.
17. O. V. Dubolazov, A. G. Ushenko, V. T.
Bachynsky, A. P. Peresunko, and O. Ya.
Vanchulyak, “On the Feasibilities of Using the
Wavelet Analysis of Mueller Matrix Images of
Biological Crystals,” Advances in Optical
Technologies, vol. 2010, Article ID 162832, 2010.
18. O.V. Angelsky, A.G. Ushenko, Ye.G. Ushenko, “2-
D Stokes Polarimetry of Biospeckle Tissues Images
in Pre-Clinic Diagnostics of Their Pre-Cancer
States,” Journal of Holography and Speckle, vol.
2(1), pp.26-33, 2005.
19. A.G. Ushenko, “Laser diagnostics of biofractals,”
Quantum Electronics, vol. 29(12), pp. 1078–1084,
1999.
20. O.V. Angel'skii, A.G. Ushenko, A.D. Arkhelyuk,
S.B. Ermolenko, D.N. Burkovets, “Structure of
matrices for the transformation of laser radiation by
biofractals,” Quantum Electronics, vol. 29(12), pp.
1074-1077, 1999.
21. O.V. Angel'skii, A.G. Ushenko A.D. Arheluk, S.B.
Ermolenko, D. N. Burkovets, “Scattering of Laser
Radiation by Multifractal Biological Structures,”
Optics and Spectroscopy, vol. 88(3), pp. 444-448,
2000.
22. A.G. Ushenko, “Polarization Structure of
Biospeckles and the Depolarization of Laser
Radiation,” Optics and Spectroscopy, vol. 89(4),
pp. 597-601, 2000.
23. A.G. Ushenko, “Laser polarimetry of polarization-
phase statistical moments of the object field of
optically anisotropic scattering layers,” Optics and
Spectroscopy, vol. 91(2), pp. 313-316 2001.
24. A.G. Ushenko, “Polarization contrast enhancement
of images of biological tissues under the conditions
of multiple scattering,” Optics and Spectroscopy,
vol. 91(6), pp. 937-940, 2001.
25. A.G. Ushenko, “Laser probing of biological tissues
and the polarization selection of their images,”
Optics and Spectroscopy, vol. 91(6), pp.932-936,
2001.
26. A.G. Ushenko, “Correlation processing and
wavelet analysis of polarization images of
biological tissues,” Optics and Spectroscopy, vol.
91(5), pp.773-778, 2002.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2010. V. 13, N 2. P. 189-201.
© 2010, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
201
27. A.G. Ushenko, “Polarization correlometry of
angular structure in the microrelief pattern or rough
surfaces,” Optics and spectroscopy, vol. 92(2),
pp.227-229, 2002.
28. Oleg V. Angelsky, Alexander G. Ushenko, and
Yevheniya G. Ushenko, “Complex degree of
mutual polarization of biological tissue coherent
images for the diagnostics of their physiological
state,” J. Biomed. Opt., vol. 10(6), 060502, 2005.
29. Oleg V. Angelsky, Alexander G. Ushenko,
Yevheniya G. Ushenko, Yuriy Y. Tomka, “Pola-
rization singularities of biological tissues images,”
J. Biomed. Opt., vol. 11(5), 054030, 2006.
30. Alexander G. Ushenko, “Polarization structure of
laser scattering fields,” Optical Engineering, vol.
34(4), pp. 1088-1093, 1995.
31. A.G. Ushenko, M.T. Strinadko, S.B. Yermolenko,
M.A Neduzhko, “High resolution polarization
interferometry in surface and layer diagnostics,”
International journal of optoelectronics, vol. 4(6),
pp. 563–574, 1989.
32. O. V. Angelsky, A. G. Ushenko, and Ye. G.
Ushenko, “Investigation of the correlation structure
of biological tissue polarization images during the
diagnostics of their oncological changes,” Phys.
Med. Biol., vol. 50, pp. 4811-4822, 2005.
33. O.G. Ushenko, S.G. Guminetsky, A.V. Motrich,
“Optical properties of urine, blood plasma and
pulmonary condensate of the patients with
pulmovnary form of tuberculosis,” Fotoelektronika,
vol.16, pp. 133-139, 2007.
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