Azimuthally invariant phase tomography of optically anisotropic sections of biological tissues
Considered in this work is the theoretical background of the azimuthally stable method of Jones matrix mapping applied to histological sections of uterine neck biopsy based on spatial-frequency selection of the mechanisms responsible for linear and circular birefringence. The comparative results of...
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2015
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irk-123456789-1218072017-06-19T03:02:42Z Azimuthally invariant phase tomography of optically anisotropic sections of biological tissues Sidor, M.I. Karachevtsev, A.O. Prysyazhnyuk, V.P. Considered in this work is the theoretical background of the azimuthally stable method of Jones matrix mapping applied to histological sections of uterine neck biopsy based on spatial-frequency selection of the mechanisms responsible for linear and circular birefringence. The comparative results of measuring the coordinate distributions of the complex degree of mutual anisotropy formed by fibrillar networks of myosin and collagen fibrils of uterine neck tissue being in different pathological states – pre-cancer (dysplasia) and cancer (adenocarcinoma) – have been shown. The values and ranges of the change in the statistical (moments of the 1st to 4 th orders) parameters of the complex degree of mutual anisotropy of coordinate distributions have been studied. The objective criteria for diagnostics of pathology and differentiation of its severity degree have been determined. 2015 Article Azimuthally invariant phase tomography of optically anisotropic sections of biological tissues / M.I. Sidor, A.O. Karachevtsev, V.P. Prysyazhnyuk // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2015. — Т. 18, № 2. — С. 147-151. — Бібліогр.: 19 назв. — англ. 1560-8034 DOI: 10.15407/spqeo18.02.147 PACS 87.50.wp, 87.57.-s, 87.64.-t, 87.85.Pq http://dspace.nbuv.gov.ua/handle/123456789/121807 en Semiconductor Physics Quantum Electronics & Optoelectronics Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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Considered in this work is the theoretical background of the azimuthally stable method of Jones matrix mapping applied to histological sections of uterine neck biopsy based on spatial-frequency selection of the mechanisms responsible for linear and circular birefringence. The comparative results of measuring the coordinate distributions of the complex degree of mutual anisotropy formed by fibrillar networks of myosin and collagen fibrils of uterine neck tissue being in different pathological states – pre-cancer (dysplasia) and cancer (adenocarcinoma) – have been shown. The values and ranges of the change in the statistical (moments of the 1st to 4 th orders) parameters of the complex degree of mutual anisotropy of coordinate distributions have been studied. The objective criteria for diagnostics of pathology and differentiation of its severity degree have been determined. |
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Sidor, M.I. Karachevtsev, A.O. Prysyazhnyuk, V.P. |
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Sidor, M.I. Karachevtsev, A.O. Prysyazhnyuk, V.P. Azimuthally invariant phase tomography of optically anisotropic sections of biological tissues Semiconductor Physics Quantum Electronics & Optoelectronics |
| author_facet |
Sidor, M.I. Karachevtsev, A.O. Prysyazhnyuk, V.P. |
| author_sort |
Sidor, M.I. |
| title |
Azimuthally invariant phase tomography of optically anisotropic sections of biological tissues |
| title_short |
Azimuthally invariant phase tomography of optically anisotropic sections of biological tissues |
| title_full |
Azimuthally invariant phase tomography of optically anisotropic sections of biological tissues |
| title_fullStr |
Azimuthally invariant phase tomography of optically anisotropic sections of biological tissues |
| title_full_unstemmed |
Azimuthally invariant phase tomography of optically anisotropic sections of biological tissues |
| title_sort |
azimuthally invariant phase tomography of optically anisotropic sections of biological tissues |
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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2015 |
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http://dspace.nbuv.gov.ua/handle/123456789/121807 |
| citation_txt |
Azimuthally invariant phase tomography of optically anisotropic sections of biological tissues / M.I. Sidor, A.O. Karachevtsev, V.P. Prysyazhnyuk // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2015. — Т. 18, № 2. — С. 147-151. — Бібліогр.: 19 назв. — англ. |
| series |
Semiconductor Physics Quantum Electronics & Optoelectronics |
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| first_indexed |
2025-07-08T20:33:15Z |
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2025-07-08T20:33:15Z |
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| fulltext |
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2015. V. 18, N 2. P. 147-151.
doi: 10.15407/spqeo18.02.147
© 2015, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
147
PACS 87.50.wp, 87.57.-s, 87.64.-t, 87.85.Pq
Azimuthally invariant phase tomography of optically anisotropic
sections of biological tissues
M.I. Sidor
1
, A.O. Karachevtsev
1
, V.P. Prysyazhnyuk
2
1
Chernivtsi National University, Optics and Publishing Department
2, Kotsyubinsky str., 58012 Chernivtsi, Ukraine
2
Bukovinian State Medical University, 58000 Chernivtsi, Ukraine
E-mail: a.dubolazov@chnu.edu.ua
Abstract. Considered in this work is the theoretical background of the azimuthally stable
method of Jones matrix mapping applied to histological sections of uterine neck biopsy
based on spatial-frequency selection of the mechanisms responsible for linear and
circular birefringence. The comparative results of measuring the coordinate distributions
of the complex degree of mutual anisotropy formed by fibrillar networks of myosin and
collagen fibrils of uterine neck tissue being in different pathological states – pre-cancer
(dysplasia) and cancer (adenocarcinoma) – have been shown. The values and ranges of
the change in the statistical (moments of the 1
st
to 4
th
orders) parameters of the complex
degree of mutual anisotropy of coordinate distributions have been studied. The objective
criteria for diagnostics of pathology and differentiation of its severity degree have been
determined.
Keywords: phase tomography, biological tissues, birefringence.
Manuscript received 10.11.14; revised version received 27.02.15; accepted for
publication 27.05.15; published online 08.06.15.
1. Introduction
Historically, the optical methods for diagnostics of
biological objects may be separated into two groups:
the spectrophotometric methods [1-3] that are based
on analysis of spatial or time changes of the radiation
field intensity scattered by biological tissues;
polarizing methods that are based on the usage of
the coherency matrix of complex amplitude.
The correlation methods are based on analysis of
the correlation degree of the parallel polarization
components of light fluctuation in different points of the
object field [4, 5].
For the complex azimuthally stable analysis of
polarizationally heterogeneous laser radiation fields, a
new approach was suggested in [6], based on
generalization of the coherence matrix by the
polarization coherence matrix for two points.
In [7], to characterize the consistency between the
polarization states of the object field in the points with
the respective intensities, a new azimuthally stable
parameter – the complex degree of mutual polarization
(CDMP) – was introduced.
This work is aimed at the development and
justification of the method of “point-to-point” Jones
matrix mapping and spatial-frequency filtering
manifestations of optical anisotropy of benign
histological sections (dysplasia – precancerous) and
malignant (adenocarcinoma – cancer) tissue of the
uterine wall.
2. Brief theory
The analysis of processes responsible for amplitude-
phase modulation of laser radiation by such an object is
based on the following assumptions [8]:
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2015. V. 18, N 2. P. 147-151.
doi: 10.15407/spqeo18.02.147
© 2015, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
148
uterine neck (UN) consists of two optically
anisotropic layers of muscle (myometrium) and
connective (endometrium) tissues;
superficial optically anisotropic component of
endometrium is formed by disordered by the
directions of optical axes collagen fibers (l ~
5…25 μm, L ≈ l) with prevailing circular
birefringence;
subsurface optically anisotropic network of
myometrium is formed by large-scale (range of cross
sizes l ~ 50…200 μm) threadlike (L >> l) myosin
fibrils with prevailing (due to the order in package
that determines the directions of optical axes of
partial biological crystals) linear birefringence;
polarization properties of the points of this fibrillar
network are characterized by the generalized matrix
of optical anisotropy D
AQD , (1)
where Q – Jones matrix of linear birefringence, A –
Jones matrix of circular birefringence or optical activity [9]:
ii
ii
Q
expsincosexp1cossin
exp1cossinexpcossin
22
22
,
(2)
cossin
sincos
A , (3)
where ρ – direction of optical axis, nl
2
– value
of phase shift between orthogonal components of the
amplitude of laser waves with the wavelength λ that
passed the geometrical path l through the biological
crystal with linear birefringence Δn, θ – rotation angle of
the polarization plane of the laser wave caused by
circular birefringence.
In the framework of the “two-point” approach [4-
7], by analogy with the parameter CDMP 21,rrV , we
can introduce the Jones matrix correlation parameter
21,rrW – the complex degree of mutual anisotropy
(CDMA).
It directly characterizes the measure or degree of
consistency in linear and circular birefringence points of
surface and subsurface tissue.
21
2
2122212121122111
21
,,,,
,
rIrI
rrdrrdrrdrrd
rrW
,
(4)
Here, 21,rrdik are the generalized matrix elements
of the following form
,,
,,
,,
,,
2221222122
2211212121
2121122112
2111112111
rdrdrrd
rdrdrrd
rdrdrrd
rdrdrrd
(5)
where dik – complex elements of Jones matrix.
Let us determine the spatial-frequency filtering for
separation of the coordinate distributions of CDMA
formed by various components of the diagnosed UN
layer with linear and circular birefringence. From the
viewpoint of medicine, the task of “optical selection” of
polarization manifestations of linear (ρ, δ) and circular
(θ) birefringence in the network of protein fibrils typical
for UN myometrium and endometrium layers is topical
for diagnostics and differentiation of the severity degree
of the pathological process. The main idea of this
approach is that the spatial-frequency structure of
Fourier form of the laser image obtained for the tissue of
the uterine wall is different for its large-scale (myosin)
and small-scale (collagen) protein structures. Proceeding
from this, using spatial-frequency filtration, it is possible
to isolate either low-frequency (with linear
birefringence) or high-frequency (with circular
birefringence) components that by means of Fourier
conversion can be transformed into respective
“separated” laser images [10]. If we locate the vignetting
(transparent ,H opaque ,1H )
diaphragm in the central part of Fourier plane, then by
means of reverse Fourier transform the low- and high-
frequency components can be restored
.,,,,
,,,,,,ˆ
1 URU
URU
Here,
f
x
and
f
y
. Тhus, it enables to determine the coordinate
distributions of the Jones matrix elements of linear
UFqik
ˆ, and circular UFaik
birefringence according to the classical technique [9]. As
a result, we obtain analytical expressions of the CDMA
parameter for various types of optically anisotropic
layers of UN:
21
2
2122212121122111
21
,,,,
~,,,
rIrI
rrqrrqrrqrrq
rrW
,
(6)
21
2
2122212121122111
21
,,,,
~,,
rIrI
rrarrarrarra
rrW
.
(7)
3. Experimental results and discussion
In the experimental part of the research, the following
algorithm was used:
3.1. Determination of statistically reliable representative
selection of patients with the known (referent) diagnosis
As objects of investigation, two groups of optically thin
(extinction coefficient τ ≈ 0.087…0.093) histological
sections of UN tissue biopsy for two groups of patients
with the following diagnoses were prepared according to
the standard technique on the freezing microtome:
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2015. V. 18, N 2. P. 147-151.
doi: 10.15407/spqeo18.02.147
© 2015, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
149
Fig. 1. Optical Stokes polarimeter with using space-frequency filtering, where: 1 – He-Ne laser; 2 – collimator; 3 – fixed
quarter-wave plate; 5, 10 – mechanically movable quarter-wave disc; 4, 11 – polarizer and analyzer, respectively; 6 – the object
of investigation; 7, 9 – object lens; 8 – low- and high-pass filter, 12 – CCD camera; 13 – PC.
Fig. 2. Low-frequency (linear birefringence of the myometrium) distributions of CDMA of the uterine wall histological
sections.
group 1 – pre-cancer (dysplasia) state,
group 2 – cancer.
The diagnoses of pre-cancer (group 1) and cancer
patients (group 2) were determined using the gold
standard method – biopsy of surgically removed tumor.
The previously examined donors were included into test
group (group 1). By means of software product Statmate
for 95% confidence interval ( 05.0p ), a reliable
quantity of patients was determined: n = 45.
The magnitude of the representative sample was
tested by cross-validation. It was established that the
average value of the standard deviation values of the
statistical moments Zi =1;2;3;4 do not exceed 0.025, which
corresponds to a statistically valid confidence interval
05.0p .
3.2. Jones matrix mapping with the spatial and
frequency selective coordinate distributions of CDMA of
endometrial histological sections
The series of Figs. 2 and 3 presents the results of Jones
matrix mapping the low-frequency (linear birefringence
of the myometrium) and high-frequency (circular
birefringence of the endometrium) distributions of
CDMA of the uterine wall histological sections.
3.3. Statistical intergroup analysis
For possible clinical application of both methods, the
following values were determined for each group of
samples [11, 12]:
average (within group 1 and group 2) values of
statistical moments qZi 4;3;2;1 , their standard
deviations and histograms iZN (Table 1).
traditional for probative medicine operational
characteristics – sensitivity %100
ba
a
Se
,
specificity %100
dc
c
Sp
and balanced accuracy
2
SpSe
Ac
, where a and b are the numbers of
correct and wrong diagnoses within the group 2; c
and d – the same ones within the group 1 (Table 2).
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2015. V. 18, N 2. P. 147-151.
doi: 10.15407/spqeo18.02.147
© 2015, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
150
Fig. 3. High frequency (circular birefringence of the endometrium) distributions of CDMA of the uterine wall histological
sections.
The comparative analysis of the data obtained
(Table 1) showed that the differences between the values
of average qZ i 4;3;2;1 moments of all orders are
statistically reliable.
Table 2 presents the parameters of the information
value obtained using the azimuthally stable method of
Jones matrix mapping optical anisotropy of histological
sections of the uterine wall biopsies of various
pathologies.
Table 1. Parameters of statistical structure of CDMA
coordinate distributions.
Para-
meters
Wρ,δ (m×n) Wθ (m×n)
Dysplasia
n1 = 45
Cancer
n2 = 45
Dysplasia
n1 = 45
Cancer
n2 = 45
Z1 0.35±0.11 0.44±0.12 0.05±0.009 0.07±0.004
Z2 0.19±0.041 0.27±0.062 0.07±0.002 0.1±0.043
Z3 1.15±0.11 0.87±0.16 0.23±0.057 0.28±0.054
Z4 0.82±0.21 0.57±0.15 1.65±0.12 1.25±0.11
Table 2. Operational characteristics of the method of Jones
matrix mapping the optical anisotropy of histological
sections taken from the uterine wall biopsy.
Parameters Zi Wρ,δ Wθ
Se (Zi)
Z1 59.7% 83.4%
Z2 62% 81.2%
Z3 90.5% 62.4%
Z4 94.2% 66.9%
Sp (Zi)
Z1 54.9% 79.8%
Z2 58.6% 74.6%
Z3 88.9% 55.6%
Z4 91.1% 57.8%
Ac (Zi)
Z1 53.25% 82.1%
Z2 58.8% 76.9%
Z3 91% 62%
Z4 93.2% 65.35%
The obtained results enable us to state a rather high
level of accuracy of azimuthally stable Jones matrix
mapping. According to the criteria of probative medicine
[4, 5, 14-19], the parameters %80~R are of good
quality, while %90~,R are of high quality.
3.4. Prospects of clinical application
The suggested method can be used to differentiate the
temporal changes of the morphological structure of fetal
tissues, as based on objective analysis of the orientation
(Table 3) and crystalline (Table 4) structure of optically
anisotropic networks.
Table 3. Statistical parameters Zi =1;2;3;4 that characterize
the coordinate distributions of orientation parameter
Wρ,δ (m×n) histological sections of fetal tissue in different
periods.
Para-
meters
5
months
6
months
7
months
8
months
9
months
10
months
Z1 0.08 0.09 0.1 0.11 0.12 0.13
Z2 0.29 0.24 0.21 0.18 0.15 0.13
Z3 0.12 0.18 0.22 0.27 0.34 0.37
Z4 0.69 0.77 0.88 1.06 1.24 1.42
Table 4. Statistical parameters Zi =1;2;3;4 that characterized
the coordinate distributions of crystallization parameter of
histological sections of fetal tissue in different periods.
Para-
meters
5
months
6
months
7
months
8
months
9
months
10
months
Z1 0.04 0.05 0.07 0.08 0.09 0.11
Z2 0.11 0.14 0.16 0.18 0.21 0.24
Z3 0.21 0.32 0.39 0.44 0.53 0.68
Z4 0.43 0.53 0.57 0.64 0.71 0.79
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2015. V. 18, N 2. P. 147-151.
doi: 10.15407/spqeo18.02.147
© 2015, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
151
4. Conclusion
The comparative investigations of the effectiveness of
the developed techniques of spatial-frequency Fourier
polarimetry of CDMA in the diagnostics of the
pathological state of the UN tissue and differentiation of
its severity degree have been carried out.
The criteria of differentiation between the UN
dysplasia and cancer on the basis of the statistical
(statistical moments of the 1
st
to 4
th
orders) analyses of
the spatial-frequency filtered distributions of CDMA of
protein networks with linear and circular birefringence
have been offered.
The method can be used for time monitoring of
changes in the orientational structure of crystalline fetal
tissues.
Acknowledgement
This work was supported by the grants № 0113U003239
and № 0112U002336 from the Ukrainian Foundation for
Basic Researches.
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