Mueller-matrix diagnostics of optical properties inherent to polycrystalline networks of human blood plasma
This work is aimed at studying the possibilities of Mueller-matrix diagnostics applied to optically anisotropic birefringent polycrystalline networks inherent to amino acids in human blood plasma. Determined here are interrelations between statistical moments of the first to fourth orders as well as...
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
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| Cite this: | Mueller-matrix diagnostics of optical properties inherent to polycrystalline networks of human blood plasma/ Yu.A. Ushenko, O.I. Olar, A.V. Dubolazov, V.O. Balanetskaya, V.P. Unguryan, N.I. Zabolotna, B.P. Oleinichenko // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2011. — Т. 14, № 1. — С. 98-105. — Бібліогр.: 39 назв. — англ. |
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nasplib_isofts_kiev_ua-123456789-1176502025-06-03T16:28:46Z Mueller-matrix diagnostics of optical properties inherent to polycrystalline networks of human blood plasma Ushenko, Yu.A. Olar, O.I. Dubolazov, A.V. Balanetskaya, V.O. Unguryan, V.P. Zabolotna, N.I. Oleinichenko, B.P. This work is aimed at studying the possibilities of Mueller-matrix diagnostics applied to optically anisotropic birefringent polycrystalline networks inherent to amino acids in human blood plasma. Determined here are interrelations between statistical moments of the first to fourth orders as well as fractal dimensionalities that characterize coordinate distributions of blood plasma Mueller-matrix elements and the physiological state of a human organism. 2011 Article Mueller-matrix diagnostics of optical properties inherent to polycrystalline networks of human blood plasma/ Yu.A. Ushenko, O.I. Olar, A.V. Dubolazov, V.O. Balanetskaya, V.P. Unguryan, N.I. Zabolotna, B.P. Oleinichenko // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2011. — Т. 14, № 1. — С. 98-105. — Бібліогр.: 39 назв. — англ. 1560-8034 PACS 78.20.Fm, 87.64.-t https://nasplib.isofts.kiev.ua/handle/123456789/117650 en Semiconductor Physics Quantum Electronics & Optoelectronics application/pdf Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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This work is aimed at studying the possibilities of Mueller-matrix diagnostics applied to optically anisotropic birefringent polycrystalline networks inherent to amino acids in human blood plasma. Determined here are interrelations between statistical moments of the first to fourth orders as well as fractal dimensionalities that characterize coordinate distributions of blood plasma Mueller-matrix elements and the physiological state of a human organism. |
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Ushenko, Yu.A. Olar, O.I. Dubolazov, A.V. Balanetskaya, V.O. Unguryan, V.P. Zabolotna, N.I. Oleinichenko, B.P. |
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Ushenko, Yu.A. Olar, O.I. Dubolazov, A.V. Balanetskaya, V.O. Unguryan, V.P. Zabolotna, N.I. Oleinichenko, B.P. Mueller-matrix diagnostics of optical properties inherent to polycrystalline networks of human blood plasma Semiconductor Physics Quantum Electronics & Optoelectronics |
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Ushenko, Yu.A. Olar, O.I. Dubolazov, A.V. Balanetskaya, V.O. Unguryan, V.P. Zabolotna, N.I. Oleinichenko, B.P. |
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Ushenko, Yu.A. |
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Mueller-matrix diagnostics of optical properties inherent to polycrystalline networks of human blood plasma |
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Mueller-matrix diagnostics of optical properties inherent to polycrystalline networks of human blood plasma |
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Mueller-matrix diagnostics of optical properties inherent to polycrystalline networks of human blood plasma |
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Mueller-matrix diagnostics of optical properties inherent to polycrystalline networks of human blood plasma |
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Mueller-matrix diagnostics of optical properties inherent to polycrystalline networks of human blood plasma |
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mueller-matrix diagnostics of optical properties inherent to polycrystalline networks of human blood plasma |
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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2011 |
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Mueller-matrix diagnostics of optical properties inherent to polycrystalline networks of human blood plasma/ Yu.A. Ushenko, O.I. Olar, A.V. Dubolazov, V.O. Balanetskaya, V.P. Unguryan, N.I. Zabolotna, B.P. Oleinichenko // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2011. — Т. 14, № 1. — С. 98-105. — Бібліогр.: 39 назв. — англ. |
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Semiconductor Physics Quantum Electronics & Optoelectronics |
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Semiconductor Physics, Quantum Electronics & Optoelectronics, 2011. V. 14, N 1. P. 98-105.
PACS 78.20.Fm, 87.64.-t
Mueller-matrix diagnostics of optical properties inherent
to polycrystalline networks of human blood plasma
Yu.A. Ushenko1, O.I. Olar2, A.V. Dubolazov3, V.O. Balanetskaya3, V.P. Unguryan4,
N.I. Zabolotna5, B.P. Oleinichenko6
1Chernivtsi National University, Department for Correlation Optics, 2, Kotsyubinsky vul.,
58012 Chernivtsi, Ukraine, yuriyu@gmail.com
2Bukovina State Medical University, Department of Biophysics and
Medical Informatics, 2, Teatralnaya Sq., 58012 Chernivtsi, Ukraine.
3Chernivtsi National University, Department for Optics and Spectroscopy,
2, Kotsyubinsky vul., 58012 Chernivtsi, Ukraine.
4Bukovina State Medical University, Department for Oncology,
2, Teatralnaya ploshchad, 58012 Chernivtsi, Ukraine.
5Vinnytsa National Technical University, Department for Laser and Optoelectronic Technique,
95, Khmelnitskoye shosse, 21021 Vinnytsa, Ukraine.
6Medical Center “Medivin”, 95, Khmelnitskoye shosse, 21021 Vinnytsa, Ukraine.
Abstract. This work is aimed at studying the possibilities of Mueller-matrix diagnostics
applied to optically anisotropic birefringent polycrystalline networks inherent to amino
acids in human blood plasma. Determined here are interrelations between statistical
moments of the first to fourth orders as well as fractal dimensionalities that characterize
coordinate distributions of blood plasma Mueller-matrix elements and the physiological
state of a human organism.
Keywords: polarization, Mueller matrix, optical anisotropy, birefringence, statistical
moments, fractal, blood plasma.
Manuscript received 07.10.10; accepted for publication 02.12.10; published online 28.02.11.
1. Introduction
Among the diversity of directions for optical diagnostics
of the structure typical for phase-inhomogeneous layers,
Mueller-matrix polarimetry of optical anisotropy
observed in human biological tissues (BT) is rather
developed [1 – 39].
The main result of this diagnostics lies in
determination of the set of interrelations between
statistical as well as fractal parameters of coordinate
distributions for matrix elements and an optical-
geometrical structure of BT birefringent component [1 –
6, 9, 11, 12, 14, 38]. It serves as a basis to develop the
methods for early diagnostics of pathological changes in
skin derma, epithelial and connective tissue of woman
reproductive organs etc. [11, 14, 21 – 27, 35, 36].
At the same time, one of the lacks of this optical-
medical technology is the traumatic biopsy operation.
Therefore, it seems topical to spread Mueller-matrix
diagnostics over a wide and accessible circle of
biological objects. These are various biological liquids,
namely: blood, urine, bile, joint fluid, etc.
Our work is aimed at development of the Mueller
matrix method for diagnostics of optically anisotropic
structure typical for blood plasma proteins, as it is
topical to determine statistical and fractal criteria of
transformations in amino acid polycrystalline networks,
which are caused by pathological changes in human
organism.
2. Mueller-matrix modeling the polarization
properties of polycrystalline protein networks in
blood plasma
Our analysis of optical properties inherent to
polycrystalline protein networks created by blood
plasma amino acids is based on the following model [5,
6, 15, 23, 28, 29]:
• blood plasma is considered as a two-component
isotropic-anisotropic structure;
• а optically anisotropic component is
represented by the protein fraction consisting of
optically single-axis birefringent crystals of amino acids
albumin and globulin;
• polarization properties of these biological
crystals are characterized with the Mueller matrix
© 2011, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
98
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2011. V. 14, N 1. P. 98-105.
{ }
444342
343332
242322
0
0
0
0001
zzz
zzz
zzz
z u = , (1)
where
( )
( )
⎪
⎪
⎪
⎪
⎩
⎪
⎪
⎪
⎪
⎨
⎧
δ=
δρ±=
δρ±=
δρ+ρ=
δ−ρρ=
δρ+ρ=
=
.cos
,sin2sin
,sin2cos
,cos2cos2sin
,cos12sin2cos
,cos2sin2cos
44
42,24
43,34
22
33
32,23
22
22
z
z
z
z
z
z
z uik (2)
Here, is the direction of the optical axis; ρ
ndΔλ
π=δ 2 – phase shift between orthogonal
components of the amplitude, - wavelength, -
geometric distance, - index of birefringence;
λ d
nΔ
• Mueller matrix elements for the planar
network layer (N) of crystalline amino acids are
determined by superposition of partial matrix operators
(relation (1))
ikR
( )∑
=
=
N
u
uikik zR
1
, (3)
• Mueller matrix of multilayer ( )
polycrystalline network is determined with the product
of partial matrix operators (relation (3))
n
{ } { } { } { } { }121... RRRRP nn −= , (4)
To simplify (without any losses of fullness) our
consideration, let us use the approximation of two-layer
polycrystalline protein network
{ } { } { } { }{ }XYRRP ≡= 12 . (5)
In a detailed look, the expression (5) can be written
as
⎪
⎪
⎪
⎪
⎪
⎪
⎩
⎪
⎪
⎪
⎪
⎪
⎪
⎨
⎧
++=
++=
++=
++=
++=
++=
++=
++=
++=
=
.
,
,
,
,
,
,
,
,
44443443244244
42443243224242
44243423242224
43443343234243
44343433243234
43343333233233
42343233223232
43243323232223
42243223222222
xyxyxyp
xyxyxyp
xyxyxyp
xyxyxyp
xyxyxyp
xyxyxyp
xyxyxyp
xyxyxyp
xyxyxyp
pik
(6)
Our analysis of relations (1), (2), (5) and (6) shows
that the exact solution of the inverse problem – revealing
the changes in the structure of polycrystalline protein
networks in separate layers by using available
information on matrix elements , - is incorrect from
the mathematical viewpoint and ambiguous from the
physical one.
ikp
Thus, it seems topical to use the statistical and
fractal approaches to the analysis of distributions
inherent to Mueller matrix elements in optically
anisotropic polycrystalline protein component of blood
plasma.
3. Statistical and fractal analyses of Mueller-matrix
images for networks of biological crystals
Coordinate distributions of Mueller matrix elements
in blood plasma were estimated within the frameworks
of statistical and fractal approaches.
ikp
The statistical moments of the first to fourth orders
that characterize the distributions were
calculated using the following relations [5, 8]
),( yxpik
;1
1
1
j
N
j
ikp
Q
M ∑
=
= ;)(1
1
2
2 ∑
=
=
N
j
jikp
Q
M
∑
=
=
N
j
jikp
QM
M
1
3
3
2
3 ;)(11
∑
=
=
N
j
jikp
QM
M
1
4
2
2
4 )(11 , (7)
where is the number of pixels in CCD camera. !Q
The fractal analysis of distributions was
made by finding the logarithmic dependences
),( yxpik
( ) )log(log 1−− dpJ ik for the power spectra ( )ikpJ [5,
15]
( ) ∫
+∞
∞−
νπν= dppJ ikik 2cos , (8)
where are spatial frequencies determined by the
range of changing the sizes of structural elements in
the polycrystalline network.
1−=ν d
d
The dependences were
approximated using the least-squares method to the
curves
( ) )log(log 1−− dpJ ik
( )ηΦ , straight parts of which allow determining
the slope angles η and respective fractal
dimensionalities [5, 15]
η−= tgD 3 . (9)
Classification of coordinate distributions
was performed in accord with the following criteria:
),( yxpik
• are fractal or self-similar, if η = const
within the limits of 2 or 3 decades for changing the
geometric sizes ;
),( yxpik
d
• are multifractal when several constant
slope angles
),( yxpik
const;...2;1 =η =j are available:
• are statistical or random, if ),( yxpik const≠η
over all the interval for changing . d
© 2011, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
99
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2011. V. 14, N 1. P. 98-105.
4. Scheme and method of measurements
Shown in Fig. 1 is the traditional optical scheme of the
polarimeter used for measuring the coordinate
distributions of Mueller matrix elements or Mueller-
matrix images (MMI) [5].
Illumination of blood plasma samples was made
with a parallel ( ) weakly intense (W = 5.0
mW) beam of He-Ne laser (λ = 0.6328 µm). The
polarization illuminator consists of quarter-wave plates
3, 5 and the polarizer 4, which provides formation of the
laser beam with an arbitrary azimuth and ellipticity of
polarization.
mμ×= 3102ЁЄ
The studied human blood plasma sample was
sequentially probed with the laser beam possessing the
following types of polarization: linear with the azimuths
0°, 90°, +45° and right circular (⊗). Using the micro-
objective 7, the polarization images were projected onto
the plane of the sensitive area ( pixels)
of CCD camera 10. The analysis of images of human
blood plasma was made using the analyzer 9 and
quarter-wave plate 8.
600800×=× nm
Our calculation of Mueller matrix elements for the
studied samples was performed in accord with the
following algorithm [5]
;
;
);(5,0
);(5,0
11114
11
45
113
90
1
0
112
90
1
0
111
pSp
pSp
SSp
SSp
−=
−=
−=
+=
⊗
(10)
;
;
);(5,0
);(5,0
21224
21
45
223
90
2
0
222
90
2
0
221
pSp
pSp
SSp
SSp
−=
−=
−=
+=
⊗
;
;
);(5,0
);(5,0
31334
31
45
333
90
3
0
332
90
3
0
331
pSp
pSp
SSp
SSp
−=
−=
−=
+=
⊗ .
;
);(5,0
);(5,0
41444
41
45
443
90
4
0
442
90
4
0
441
pSp
pSp
SSp
SSp
−=
−=
−=
+=
⊗
Here, are the Stokes vector parameters. ⊕
=
;90;45;0
4;3;2;1jS
5. Brief characterization of the investigated objects
As objects of investigation, we chose the samples of
blood plasma for two groups of patients: healthy woman
and that with cancer of mammary gland (Figs 1c and
1d). The respective polycrystalline networks for blood
plasma amino acids are illustrated with a set of laser
images obtained in co-axial ( ) and crossed
( ) transmission planes of the polarizer 4 and
analyzer 9 (Fig. 1).
00=Θ
090=Θ
Our comparative analysis of these laser images
found out different coordinate structures for albumin and
globulin networks. In the optically anisotropic
component of healthy woman blood plasma, one can
observe albumin crystals spatially-ordered along several
directions (Figs 1a and 1b). While blood plasma of the
patient with the oncologic process contains mainly
globulin crystals disordered as to directions of optical
axes (Figs 1c and 1d).
6. Diagnostic possibilities for statistical and fractal
analyses of Mueller-matrix images obtained for
human blood plasma
The subject of our statistical and fractal analyses was
three types of Mueller-matrix images ( nmpik )× for
human blood plasma.
The first one is the coordinate distributions of
diagonal elements in the Mueller matrix ( )nmp ×33;22 ,
which characterize the degree of transformation of the
laser wave polarization azimuth by amino acid crystals,
optical axes of which are oriented along two mutually
orthogonal directions (00 900 ↔=ρ ( )nmp ×22 ) and
© 2011, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
Fig. 1. Optical scheme of the polarimeter: 1 – He-Ne laser; 2 – collimator; 3 – stationary quarter-wave plate; 5, 8 –
mechanically movable quarter-wave plates; 4, 9 – polarizer and analyzer, respectively; 6 – studied object; 7 – micro-
objective; 10 – CCD camera; 11 – personal computer. See explanation in the text.
100
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2011. V. 14, N 1. P. 98-105.
© 2011, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
)00 13545 ↔=ρ ( ), respectively. In this
sense, these matrix elements will be named as the
“orientational” ones.
( nmp ×33
The second type is coordinate distributions for the
diagonal matrix element ( )nmp ×44 , the value of which
is determined by phase shifts between orthogonal
components for the laser wave amplitude that artise as a
consequence of birefruingence caused by crystalline
amino acids. In this sense, this element of the Mueller
matrix will be named as “phase” one.
The third type is coordinate distributions of off-
diagonal elements in the Mueller matrix
, which characterize mechanisms of
mutual transformations of linear polarization into a
elliptic one, and vice versa. These matrix elements will
be named as the “orientational-phase” ones.
( nmp ×34;24;23 )
)
Shown in Fig. 2 are the results of investigations of
the following MMI structures observed for blood plasma
of the healthy patient: coordinate ( ( nmpik × , left
column), statistical (histograms and statistical
moments of the first and fourth orders , central
column) as well as fractal (logarithmic dependences
, right column).
( ikph )
) )
nmp ×33;22
4;3;2;1=jM
( ) )log(log 1−− dpJ ik
Our analysis of the obtained data enabled us to
reveal:
“Orientational” matrix elements ( )nmp ×33;22
Histograms and are characterized with
pronounced main extremes. Formation of these extremes
may be related with superposition of matrix elements
) (relations (3)), values of which are
determined by albumin crystals ordered relatively two or
three separated directions of optical axes (relations (2),
Figs 1a and 1b).
( 22ph ( 33ph
(
The most pronounced differentiation of the
coordinate distributions for matrix elements ( )nmp ×22
and of the polycrystalline network in blood
plasma can be realized using the statistical moments of
the third and fourth orders. Differences between the
values
( nmp ×33 )
( )33;223 pM and ( )33;224 pM in these
distributions can reach 4 and 2.5 times, respectively
(Fig. 2, central column).
Our analysis of the dependences
; ( ) )log(log 1
22
−− dpJ ( ) )log(log 1
33
−− dpJ allowed us
to reveal stability in the values of slope angles η within
the range of changes in geometric sizes of amino acid
crystals from 50 up to 1000 µm (Fig. 2, right column).
This result is indicative of the fractal structure inherent
to the distributions of , which can be related
with an order of optical axis directions for albumin
crystals. By contrast, disorder in globulin crystal
orientations within the range of lower geometric sizes
(d = 2…50 µm) causes randomness in coordinate
distributions of
d
( nmZ ×33;22 )
ρ
( )nmp ×33;22 . Quantitatively, this fact is
expressed through the absence of any stable slope angle
for the dependences ( ) ;loglog 1
22
−− dpJ
( ) 1
33 loglog −− dpJ .
“Phase” matrix elements ( )nmp ×44
The histogram ( )44ph for the distribution of values
inherent to the “phase” matrix element for blood plasma
of healthy woman is characterized by a wide range of
changes in values caused by variations of geometric
sizes (d = 1…1000 µm) of albumin and globulin crystals
(relation (2)).
44p
The coordinate distribution of ( nmp )×44 is
multifractal, since the curves approximating the
logarithmic dependences are
polygonal lines with several slope angles (Fig. 2, right
column).
( )ηΦ
( ) 1
44 loglog −− dZJ
η
The found multifractality of the distribution
corresponding to the “phase” matrix element ( )nmp ×44
of blood plasma is apparently caused by multiple
changes ( ;...2;1;0,2 =π+δ=δ kk ) in phase shifts δ ,
which is related with different scales of geometric sizes
inherent to albumin (50…1000 µm) and globulin
(1…50 µm) crystals.
“Orientational -phase” matrix elements ( )nmp ×34;24;23
The histograms ( )23ph , ( )24ph and for the
distributions
( 34ph )
( )nmp ×34;24;23 are practically
“equiprobable”. Here, we do not take into account the
main extreme ( ) 034;24;23 →ph , formation of which is
caused by the influence of optically isotropic component
in blood plasma.
The wide range of changes in local extremes
( ) 034;24;23 ≠ph can be related with a simultaneous
influence of both optical axis orientation and phase
shift
ρ
δ (relations (2) and (3)) for local crystals in
albumin-globulin blood plasma network on formation of
the value of “orientational-phase” matrix elements.
It was ascertained that differentiation of optical
properties inherent to these networks can be efficiently
performed using determination of the fourth order
statistical moments for elements of
MMI, because differences between values reach 3
times.
( nmp ×34;24;23 )
4M
Our analysis of the power spectra ( )34;24;23pJ
found multifractality of distributions for matrix elements
( )nmp ×34;24;23 corresponding to healthy woman blood
plasma. It was ascertained that elements ( nmp ×34;24;23 )
101
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2011. V. 14, N 1. P. 98-105.
Fig. 2. Statistical and fractal structure of blood plasma MMI for a healthy patient.
in MMI are characterized with individual sets of fractal
dimensionalities (Fig. 2, right column).
Shown in Fig. 3 is the set of statistical ( ( )ikph ;
) and fractal ( )
parameters that characterize elements in
MMI of polycrystalline networks of amino acids in
blood plasma of the patient with mammary gland cancer.
4;3;2;1=jM ( ) qik FdpJ ;loglog 1−−
( nmpik ×
The analysis of MMI for the respective blood
plasma samples found essential transformation of
histograms ( )ikph .
The histograms ( )22ph and are
characterized with redistribution of extremes, which can
be related with changes in orientations of optical axes
( 33ph )
( )nm×ρ and phase shift values in the albumin-
globulin network of blood plasma (Fig. 3, central
column). From the biochemical viewpoint, this process
is caused by growth of the globulin concentration in
( nm×δ
)
)
© 2011, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
102
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2011. V. 14, N 1. P. 98-105.
blood plasma. As a result, we deal with disordering the
directions of optical axes inherent to globulin crystals
and growth of their birefringence. Therefore, the range
of changes in values of “orientational” matrix elements
is expanded, and the main extremes33;22p ( )122 →ph ,
are “shifted” (relations (2), (3)). ( 133 →ph
© 2011, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
)
Changes in birefringence of blood plasma
polycrystalline network observed in the samples taken
from patients with mammary gland cancer are also
pronounced in formation of practically equiprobable
distributions of “phase” and “orientational-phase”
matrix elements.
44p
34;24;23p
The analysis of the power spectra ( )ikpJ for
pathologically changed blood plasma found the tendency
to growth of the amount of fractal dimensionalities for
coordinate distributions of “orientational” ( )nmp ×33;22 ,
“orientational-phase” and “phase”
elements (Fig. 3, right column).
( nmp ×34;24;23 )
)( nmp ×44
With the aim to determine the quantitative Mueller-
matrix statistical and fractal criteria for differentiation of
polycrystalline protein networks of amino acids, we have
investigated blood plasma samples taken from two
groups of patients, namely: healthy ones (21 persons)
and those sick of cancer (19 persons).
Summarized in Table 1 are the statistical moments
from the first to fourth orders that characterize
coordinate distributions of “orientational” ,
“orientational-phase” and “phase”
elements of the Mueller matrix corresponding to blood
plasma of both groups.
33;22p
34;24;23p 44p
Our comparative analysis of the values and ranges
for changes of statistical parameters Mj found for blood
plasma of healthy patients and those sick of cancer
enabled us to reveal the following features:
• asymmetry values for the distributions of
“orientational” matrix elements
3M
( )nmp ×33;22
describing blood plasma of oncologically sick
patients decrease by 1.4 to 5 and 1.8 to 7.5 times,
respectively;
• excess for the coordinate distribution of the
“phase” element
4M
( )nmp ×44 corresponding to
pathologically changed polycrystalline protein
network of amino acids in blood plasma is 20-fold
decreased;
• decrease of the values inherent to statistical
moments of the third and fourth orders in the
coordinate distributions of “orientational-phase”
elements in the Mueller matrix ( )nmp ×34;24;23
reaches 4.3 to 5 and 7 to 20 times, respectively.
Table 1. Statistical moments for distributions of pik(m×n)
pik M Norm Mammary gland
j cancer
M1 0.73 ± 0.087 0.7 4 2 ± 0.08
M2 0.06 ± 0.008 0.07 ± 0.009
M3 1.68 ± 0.23 0.31 ± 0.037
p22
M4 3.25 ± 0.44 0.47 ± 0.054
M1 0.76 ± 0.088 0.78 ± 0.084
M2 0.04 ± 0.006 0.06 ± 0.008
M3 0.43 ± 0.057 0.32 ± 0.039
p33
M4 2.42 ± 0.31 1.32 ± 0.18
M1 0.17 ± 0.022 0.32 ± 0.041
M2 0.12 ± 0.018 0.14 ± 0.018
M3 0.23 ± 0.033 0.28 ± 0.036
p44
M4 2.09 ± 0.27 0.11 ± 0.015
M1 0.19 ± 0.024 0.16 ± 0.021
M2 0.05 ± 0.007 0.03 ± 0.004
M3 0.87 ± 0.093 0.16 ± 0.022
p23
M4 7.27 ± 0.96 0.35 ± 0.045
M1 0.21 ± 0.028 0.17 ± 0.024
M2 0.06 ± 0.008 0.03 ± 0.005
M3 0.99 ± 0.11 0.13 ± 0.017
p24
M4 2.58 ± 0.32 2.72 ± 0.33
M1 0.15 ± 0.019 0.34 ± 0.042
M2 0.10 ± 0.012 0.11 ± 0.015
M3 0.96 ± 0.099 0.19 ± 0.025
p34
M4 2.34 ± 0.28 0.25 ± 0.029
hus, just the statistical moments of higher orders
are t
the values of fractal
dime
T
he most sensitive to changes in optically isotropic
structure of blood plasma.
Table 2 illustrates
nsionalities for ( )nmpik × elements in MMI of
blood plasma in both g
The comparative analy
roups.
sis of the obtained data
indic
ormation of fractal distributions for
•
hus, it can be contended that biochemical changes
in th
ates:
• transf
“orientational” moments into the multifractal ones;
15% to 25% growth of the value and amount of
fractal dimensionalities qF for distributions of
“orientational-phase” and “phase” elements.
T
e blood plasma structure are clearly pronounced in
changes of statistical and fractal parameters
characterizing the set of MMI elements ( )nmpik × and
can be applied as new criteria for diagno man
pathological states.
stics of hu
103
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2011. V. 14, N 1. P. 98-105.
Table 2. Fractal dimensionalities for distributions of the
Mueller matrix elements
Zik Dq Norm Mammary gland
cancer
D1 2.12 ± 0.14 2.17 ± 0.18
D2 - 1.86 ± 0.15 Z22
D3 - 2.01 ± 0.21
D1 2.09 ± 0.12 2.14 ± 0.14
D2 - 1.94 ± 0.13 Z33
D3 - 2.03 ± 0.19
D1 1.98 ± 0.127 2.07 ± 0.21
D2 1.76 ± 0.19 1.83 ± 0.17 Z44
D3 - 2.31 ± 0.24
D1 2.07 ± 0.19 2.12 ± 0.18
D2 2.18 ± 0.13 2.27 ± 0.19 Z23
D3 - 1.83 ± 0.13
D1 1.83 ± 0.18 1.97 ± 0.21
D2 2.05 ± 0.26 2.11 ± 0.14 Z34
D3 - 1.81 ± 0.16
© 2011, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
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