The Method of Determining Conductibility for Coronary Vessels by Termography
The purpose of this study is to evaluate the conductibity of coronary vessels for the study of blood flow in the surface layer of the myoc ardium during warming up and cooling of the heart in conditions of cardiopulmonary bypass. Results. The numerical value of the quantitative criterion obtained is...
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| Zitieren: | The Method of Determining Conductibility for Coronary Vessels by Termography / V.V. Shlykov, V.B. Maksymenko // Cybernetics and computer engineering. — 2019. — № 2 (196). — С. 59-79. — Бібліогр.: 26 назв. — англ. |
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| author | Shlykov, V.V. Maksymenko, V.B. |
| author_facet | Shlykov, V.V. Maksymenko, V.B. |
| citation_txt | The Method of Determining Conductibility for Coronary Vessels by Termography / V.V. Shlykov, V.B. Maksymenko // Cybernetics and computer engineering. — 2019. — № 2 (196). — С. 59-79. — Бібліогр.: 26 назв. — англ. |
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| description | The purpose of this study is to evaluate the conductibity of coronary vessels for the study of blood flow in the surface layer of the myoc ardium during warming up and cooling of the heart in conditions of cardiopulmonary bypass. Results. The numerical value of the quantitative criterion obtained is calculated by determining the difference in temperature between the blood and the myocardium, calculated as the difference between the geometric areas under the temperature distribution curves in the temperature field equation for the constant and the current fluxing temperature. The contouring method for determining the conductibity of coronary vessels allows to select areas on the surface of the myocardium, in which the change in temperature significantly lags behind the average temperature on the surface during warming or cooling of the heart, which indirectly allows evaluating the state of small coronary vessels in the myocardium.
Метою дослідження є оцінювання провідності коронарних судин для дослідження кровоплину у поверхневому шарі міокарда під час зігрівання та охолодження серця в умовах штучного кровообігу. Результати.Числове значення кількісного критерію отримано шляхом визначення різниці температур між кров'ю і міокардом, яке обчислюють як різницю геометричних площ під кривими розподілу температур у рівнянні температурного поля для постійного і поточного температурного напору. Метод контурування для визначення провідності коронарних судин дає змогу виділити ділянки на поверхні міокарда, в яких зміна температури значно відстає від середньої температури на поверхні під час зігрівання або охолодження серця, що уможливлює оцінювання стану дрібних коронарних судин в міокарді.
Целью исследования является оценка проводимости коронарных сосудов для исследования кровотока в поверхностном слое миокарда во время согревания и охлаждения сердца в условиях искусственного кровообращения. Результаты. Получено числовое значение количественного критерия, который рассчитывается путем определения разницы температур между кровью и миокардом, что косвенно позволяет оценивать состояние мелких коронарных сосудов в миокарде.
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ISSN 2663-2586 (Online), ISSN 2663-2578 (Print). Cyb. and comp. eng. 2019. № 2 (196)
Medical
and Biological Cybernetics
DOI: https:// 10.15407/kvt196.02.059
UDC 577.169; 616.1 – 616.7
SHLYKOV V.V.1, PhD, Associate professor
Department of Biomedical Engineering
e-mail: v.shlykov@kpi.ua
MAKSYMENKO V.B.2, DSc (Medicine), Professor
Deputy Director for Research
e-mail: maksymenko.vitaliy@gmail.com
1 National Technical University of Ukraine
“Igor Sikorsky Kyiv Polytechnic Institute”
37, Peremogy av., Kyiv, Ukraine, 03056
2 Amosov National Institute of Cardiovascular Surgery
6, Amosov st., Kyiv, Ukraine, 03038
THE METHOD OF DETERMINING CONDUCTIBILITY FOR CORONARY
VESSELS BY TERMOGRAPHY
Introduction. The character of the distribution of temperature in the heart is determined by
the process of heat exchange between the myocardium and coronary vessels, as well as the
state of microhemodynamics of the coronary vessels of the heart. For quantitative estimation
of changes in temperature distribution on the surface of the heart, the algorithm for calculat-
ing a quantitative criterion, that may be an objective marker for effective protection of the
heart and brain, is proposed. The method of determining the conductibity of coronary vessels
is implemented on the basis of the algorithm for determining the thermal contours, calculated
from the gradients of the temperature field on the image of the heart in the infrared spectrum.
The improvement of the previously developed method for determining the thermal contours
on the basis of Canny's algorithm consists of the transition from qualitative to quantitative
assessment of the rate of change in temperature on the surface of the myocardium.
The purpose of this study is to evaluate the conductibity of coronary vessels for the
study of blood flow in the surface layer of the myocardium during warming up and cooling of
the heart in conditions of cardiopulmonary bypass.
Results. The numerical value of the quantitative criterion obtained is calculated by de-
termining the difference in temperature between the blood and the myocardium, calculated as
the difference between the geometric areas under the temperature distribution curves in the
temperature field equation for the constant and the current fluxing temperature. The contour-
ing method for determining the conductibity of coronary vessels allows to select areas on the
surface of the myocardium, in which the change in temperature significantly lags behind the
average temperature on the surface during warming or cooling of the heart, which indirectly
allows evaluating the state of small coronary vessels in the myocardium.
© SHLYKOV V.V., MAKSYMENKO V.B., 2019
59
Shlykov V.V., Maksymenko V.B.
ISSN 2663-2586 (Online), ISSN 2663-2578 (Print). Cyb. and comp. eng. 2019. № 2 (196) 60
Conclusions. The method for determining the conductivity of coronary vessels for the study
of blood flow in the surface layer of the myocardium is proposed, which allowed to allocation
contours of sites on the surface of the myocardium with uneven distribution of temperature during
warming up and cooling of the heart. Scientific novelty of the method consists of the allocation of
thermal contours of sites in which the temperature change significantly lags behind the average
temperature on the surface during warming up or cooling of the heart.
Keywords: mathematical modelling, the algorithm of detector Canny, heart temperature,
temperature profiles, hypothermia, hyperthermia, cardiopulmonary bypass.
INTRODUCTION
During controlled cooling and warming on thermography images, the uneven distribu-
tion of temperature in tissues is become visible. In inflammatory processes in the
myocardium, areas of hyperthermia that correspond to the area of infiltration, that
indicate a difference in temperature with adjacent tissues are determined. In chronic
inflammation, the temperature difference is 0,7–1°C, with acute illness 1–1,5°C, and
in the destructive process reaches 1,5–2°C [1, 2]. When the blood temperature changes
in the circulatory circuit, the body temperature of the patient also changes. Moreover,
the temperature difference between the blood in the contour and the patient's body
should not differ by more than 15°C [3, 4].
The temperature field recorded by the thermographic system reflects the
unique morphological and biophysical characteristics of the myocardium [19].
The main reason for violations of local temperature in the heart is the microcir-
culation in the tissues of the myocardium due to inflammatory processes. The
regulation of temperature in the myocardium is mainly carried out by changing
the lumen of the coronary vessels [20, 21]. When cooling the heart, there is a
slowing of blood flow and narrowing of the surface vessels. In another situation,
with warming the heart, blood flow is redistributed to the surface of the vessels,
which facilitates the removal of heat into the external operating field. In this case
there is a so-called transverse temperature gradient that is the difference in tem-
perature between the surface and deep layers of tissue of the myocardium.
TASKS OF THE RESEARCH
Analytical studies of temperature distribution on the surface of the heart are
based on the developed model of the system of myocardium- coronary vessels
[5, 6], the model of heat exchange for the process of cooling the blood and heart,
and the model of heat flux propagation in the myocardium in the process of hy-
pothermia and hyperthermia [7, 8], for calculating which used the methods of
theoretical and mathematical physics (solving the boundary value of thermal
conductibility) with the involvement of experimental data on the distribution of
thermal fields in areas of temperature anomalies on the surface of the heart and
methods of the statistical analysis and processing of experimental data [22–24].
The development of the method of contouring temperature inhomogeneities
for determining the conductivity of coronary vessels on the basis of the algo-
rithm of detector Canny is a promising task for the implementation of informa-
tion technology for non-invasive control of heart temperature during conduction
of thermography studies in cardiology.
The Method of Determining Conductibility for Coronary Vessels by Termography
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The introduction of the method for assessing the conductibility of coronary
vessels in cardiac surgery will allow in the long run non-invasively control the
blood temperature in blood vessels and determine the efficiency of the operation
of distal septum vessels after coronary bypass surgery in conditions of controlled
cooling and warming during cardiopulmonary bypass.
THE PURPOSE OF THERMAL CONDUCTIBILITY STUDY
The purpose of study is to evaluate the conductibility of coronary vessels for the
study of blood flow in the surface layer of the myocardium during warming up
and cooling of the heart in conditions of cardiopulmonary bypass.The develop-
ment of the method for contouring temperature inhomogeneities is associated
with obtaining information on the state of the blood supply to the myocardium
by separating the geometric boundaries between the cooled and warmed areas of
the heart by using the algorithm of Canny’s detecting and Gaussian filters for the
video frames of the thermograms.
METHODS AND MEASURES OF THE RESEARCH
The temperature between the myocardium and the blood in the circuit of artifi-
cial blood circulation, which is cooled and warmed up in the heat exchanger, is
measured using the thermograph FLIR ThermaCAM E300 having a temperature
sensitivity of 0,1°C and a measurement error of ±1% of the range of measure-
ments. The technical capabilities of the thermograph allow to determine the min-
imum difference in temperature between the heart and blood in the circuit of
cardiopulmonary bypass from 0,5°C to 10°C.
The contouring method for determining the conductibility of coronary ves-
sels is realized on the basis of the contours algorithm of Canny detector that
allows to distinguish the contours of the boundaries between different sections of
the thermograms and divide them [9]. According to the algorithm, the selection
of Canny detector is modified to study temperature gradients on the surface of
the myocardium for analysis the stream of video data in the form of frames of
thermograms that is recorded by the thermal imager and stored in the database of
thermography images.
Clinical researches and researches on the basis of the method of mathemati-
cal modeling were conducted for estimation of efficiency of work of the algo-
rithm of allocation of contours on the images of open heart.
RESEARCH OF TEMPERATURE GRADIENTS ON THE HEART SURFACE
For determine temperature gradients in conditions of cardiopulmonary bypass, it
is necessary to control the temperature difference between coronary vessels and
myocardium. The temperature difference at a distance from the vessel wall can
be found from the equation for the amount of heat mQ that is transmitted to the
myocardium through the surface of the vessel over an area of time τ [10–13]:
( ) ,m c m cQ q S T T Sλτ τ
δ
= ⋅ ⋅ = − ⋅ ⋅
(1)
Shlykov V.V., Maksymenko V.B.
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where q — the density of the heat flow through the surface of the vessel, 2W m ,
cS — the surface area of the vessel, 2m , δ — the distance from the vessel
wall, m , cT – blood temperature in the vessel, oC , mT — the temperature of the
tissue of myocardium, oC .
From the equation we find the temperature difference between the vessel
and the myocardium:
.c mT T T qδ
λ
Δ = − =
(2)
The ratioδ λ characterizes the thermal conductibility of the myocardium,
and the value determines the full temperature pressure from the vessels to the
myocardium. For the current temperature of the blood iTΔ , that cools or warms
up to a temperature iT , it is possible to write the expression:
,i i m
TT T T T l
δ
Δ
Δ = − = Δ −
(3)
where l — the distance from the vessel wall, through which the heat travels
from the vessel to the depth of the myocardium, m .
The ratio iT TΔ Δ is a dimensionless excess temperature that characterizes
the temperature distribution from the vessel wall to the blood in the tissue of
myocardium:
1 .
i
T l
T
θ
δ
Δ
= = −
Δ
(4)
This expression is a temperature field equation in the assumption that the
coefficient of thermal conductibility for the myocardium is a constant value. For
determine the conditions for blood supply to the heart in small coronary vessels,
it is advisable to estimate the change in the value i mS S , which is the ratio of the
warmed area of the myocardium to the total surface area mS at the same time
intervals tΔ during hyperthermia:
1 ,i
i m
ST
T S
θ Δ
= = −
Δ
(5)
where mS — total area of the surface of the myocardium, 2m , iS — surface area
of the myocardium, through which the process of heat transfer occurs, 2m .
With the thickness of the atrial walls 2–3 mm and the thickness of the walls
of the left ventricle of the heart11–14 mm , which has the greatest thickness of the
myocardium, the dependence of the coefficient of thermal conductibility on
temperature ( )Tλ has a virtually linear character [25, 26]:
( ) ( )1 ,mT bTλ λ= + (6)
The Method of Determining Conductibility for Coronary Vessels by Termography
ISSN 2663-2586 (Online), ISSN 2663-2578 (Print). Cyb. and comp. eng. 2019. № 2 (196) 63
where mλ — the value of the coefficient of thermal conductibility of the myo-
cardium for the temperature 0,0 oT C= at the cooling of the heart, ( )W m K⋅ ,
b — the empirical coefficient of the temperature curve.
For the arithmetic mean temperature at the area of myocardium — coronary
vessels, the expression for the coefficient of thermal conductivity has the form:
( ) ( )1 1 .
2 2m c m m
b bT T T Tλ λ λ⎡ ⎤ ⎡ ⎤= + − = + Δ⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦
(7)
In this case, the expression for the density of the heat flux q on the surface
of the myocardium is as follows:
( ) ( ) ( ) ( )1 .
2
m
c m c m c m
T bq T T T T T T
λ λ
δ δ
⎡ ⎤= − = − + −⎢ ⎥⎣ ⎦
(8)
From this equation we find that the temperature difference TΔ in the layer
of the myocardium is a nonlinear function, even for linear dependence of the
coefficient of thermal conductivity of the myocardium ( )Tλ :
2
1 2 1 .
m
qT
b bb
δ
λ
Δ = − −
(9)
If the heat flow from the vessels is transmitted to the myocardium due to
heat transfer from the blood in the vessels, the specific heat flux is determined
from the Newton-Richman equation [10]:
( ) ( ) ( ) ,С
c m c i m
T
q T T T T
λ
α
δ
= − = −
(10)
where cα — the value of the coefficient of heat transfer in the blood vessels.
Substituting the value of the heat flux in the expression for the temperature
field, we obtain the dependence for the relation i mS S :
2
1 1 21 1 .i c
m i i i m i
S T
S T b T b T b T
αδ
λ
⎛ ⎞Δ
= − = + − −⎜ ⎟Δ Δ Δ Δ⎝ ⎠
(11)
Thus, the resulting dimensionless value i mF S S= is determined by the rate of
change in blood temperature in the vessels – the thermal conductibility of the
blood Сλ , the thermal conductibility of the myocardium mλ , the difference in tem-
perature between the blood and the myocardium iTΔ , as well as the sign and numeri-
cal values of the coefficientb for the temperature curve. The deviation of the values
of the ratio F from the linear dependence for the temperature field equation θ char-
acterizes the uneven distribution of the temperature in the myocardium owing to the
different rate of heat propagation in the medium (Fig. 1):
Shlykov V.V., Maksymenko V.B.
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Fig. 1. Curves of temperature distribution in the layer of the
myocardium for the temperature field equation
The relative deviation FΔ from the linear dependence in the temperature
field equation for the current temperature flux is calculated as the difference
between the areas under the temperature distribution curves:
( )1 1.F i iF θΔ = − ⋅ < (12)
where iθ — the current value of the ratio iT TΔ Δ , iF — the current value of the
ratio i mS S .
Obviously, in other equal conditions, the temperature in the myocar-
dium iTΔ varies so rapidly, the greater the density of the heat flux through the
surface iS , therefore, the current value of the ratio i mF S S= should approach the
value 1iF → .
CONTOURING METHOD FOR DETERMINING CONDUCTIBILITYOF CORONARY VESSELS
In accordance with the contouring method of temperature inhomogeneities for
the selection of Canny contours, modified to study the gradients of temperature
on the surface of the myocardium, the stream of video data in the form of ther-
mogram frames is recorded by the thermal imager and stored in the thermo-
graphic image database.
The first stage of treating the thermograms of the heart is the selection on the
thermograms of temperature profiles, converted at the signal level. This procedure is
carried out by applying threshold filtering. Since the level of thermal interference
makes an error in determining the levels of temperature profiles that leads to distor-
tion of the useful signal the interface of the Canny detector
[14, 15] is used. The Canny boundary detector is a one-dimensional operator, which
provides an optimal match between localization of thermal inhomogeneity and con-
tour allocation. As criteria of optimality use to such criteria as probability of detec-
0 iF 1
iθ
1
i mS S
iT TΔ Δ
The Method of Determining Conductibility for Coronary Vessels by Termography
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tion, high accuracy of localization, unambiguous response to one selection contours.
The operator Canny maximizes the sum of two criterias: the probability of passage
or false detection of the boundary, and the determination of the distance between the
true and the isolated edges of the thermal heterogeneity. The first criterion leads to a
reduction in the likelihood of the re-identification of the same edge heterogeneity.
The second criterion allows you to determine the contrast margin and outline lines
for the boundaries in the image using a certain threshold value, which use to com-
pares the length of the gradient vector.
The algorithm for the operation for the circuit of Canny detector includes
the following steps (Fig. 2):
1. Thermography image frames ( , )I x y are divided into segments for which
the processing and detection of contours within each segment are performed:
1
( , ) ( , )
N
k
k
I x y I x y
=
= Δ Δ∑ ,
(13)
where N — the number of segments of the representation of the image,
( , )I x y — the intensity of the pixels of the thermographic image, ( , )kI x yΔ Δ —
the segmentation of the image along the coordinates x and y .
2. The low frequency Gaussian Filtering. The each image segment is
smoothed with use to Gaussian convolution:
2 2
2 2
1( , , ) exp
2 2
x yG x y σ
πσ σ
⎛ ⎞+
= ⎜ ⎟⎜ ⎟
⎝ ⎠
,
(14)
where σ — the degree of smoothing parameter.
3. Calculation of the gradient of the intensity of the pixels of the image in
the vertical (axis x ) ( )g x and horizontal (axis y ) ( )g y directions with the help
of the operators of the first derivative. Definition of the gradient module:
2 2( , ) ( ) ( )kE x y g x g y= + . (15)
3. Clarification of the contours found in the previous step is accomplished
by resetting the gradient values ( , )kE x y for those elements of the image that are
not actually in the maximum of the gradient. The analysis starts from the point
of maximum, that has a gradient value more than 1T and lasts as long as the local
maximum value does not become less than the threshold 2 1T T< :
( )
1
1
( , ), ,
( , )
0, , .
k
k
E x y T T
E x y
T T
≥⎧
= ⎨ ∈ −∞⎩
(16)
4. The resulting image is subjected to threshold processing using two tem-
perature thresholds 1T and 2T , moreover 1 2T T> . Pixels of an image having an
intensity value greater then, are defined as strong ( , )kp x y+ , and pixels whose
values fall into an interval [ ]1 2,T T are defined as weak ( , )kp x y− pixels:
Shlykov V.V., Maksymenko V.B.
ISSN 2663-2586 (Online), ISSN 2663-2578 (Print). Cyb. and comp. eng. 2019. № 2 (196) 66
( )
[ ]
2
1 2
( , ), , ,
( , )
( , ), , .
k
k
k
p x y T T
p x y
p x y T T T
+
−
⎧ ∈ ∞⎪= ⎨
∈⎪⎩
(17)
5. Selecting the maximum response. For each image frame, the maximum re-
sponse is determined as the value of the gradient module, which determines the affin-
ity of the temperature profile to the given segment of the thermography image:
( , ) ( , )k
k N
E x y max E x y
→
=
. (18)
The algorithm for forming the contour ends with a morphological operation,
in which the weak pixels are added to the strong pixels. Smoothing values of
pixel intensity ( , )kI x y increases the resistance of the Canny detector:
( )
[ ]
( )
2
1 2
1
( , ) ( , ), , ,
( , ) ( , ), , ,
0, , .
k k
k k
p x y p x y T T
I x y p x y T T T
T T
+ −
−
⎧ + ∈ ∞
⎪⎪= ∈⎨
⎪ ∈ −∞⎪⎩
(19)
According to the algorithm of the work of the Canny's limit detector, pixels
of images are assigned to pixels of the boundary, which give the local maximum
of the gradient in the direction of the temperature change vector. As a result,
pixels marked white will be considered as a potential limit, all others will be
excluded and marked with black. Pixels located in the immediate proximity to
one of the vertical and horizontal directions are defined as the resulting contour
of the boundary, and pixels lying alone or away from the boundary are removed.
In order to evaluate the efficiency of the algorithm for selecting the contours
for open heart images in the presence of an additive obstacle, research was car-
ried out using the mathematical modeling method. For this purpose, the model
images of the area of the myocardium, containing an additive obstruction in the
form of normal "white noise" with a given peak signal to noise ratio, were syn-
thesized. The received noisy images were digitally processed according to the
developed algorithm circuit of the Canny's detector at various values of the de-
tector parameters, including the parameterσ characterizing the Gaussian linear
filter, the values of the temperature thresholds 1T and 2T that determining the
conditions for the segmentation of the images.
From the results of the numerical experiment it is clear that the procedure
for determining the binary areas provides for the exclusion of false contours only
when carefully selecting the parameter σ for filtering the original image. There-
fore, the value of this parameter, which specifies the degree of image smoothing
to filter interference, was selected experimentally and consisted of values:
The Method of Determining Conductibility for Coronary Vessels by Termography
ISSN 2663-2586 (Online), ISSN 2663-2578 (Print). Cyb. and comp. eng. 2019. № 2 (196) 67
Fig. 2. Algorithm of the Canny's detector using the Gaussian filter, threshold filtering
and smoothing values of the intensity of the pixels
Contour formation on the
thermography im-
age 1( , ),kE x y T T≥
Segmentation of ther-
mography image
on N video
frames
( , ), 1, ,k kI x NyΔ =Δ K
Capture the
thermographic video
( , )I x y%
Capture the ther-
mography video
( , )I x y
to the grayscale
Application of Gaussian LF
filtering
( )2( , , ) ( , ),kG x y F I x yσ σ= Δ Δ
Calculation of the intensity
gradient ( )g x in the direction
of the axis x
Calculation of the intensity
gradient ( )g y in the direction
of the axis y
Definition of the gradient inten-
sity module
2 2( , ) ( ) ( )kE x y g x g y= +
Determination of the maxi-
mum gradient
( , ) ( , )max k
k N
E x y max E x y
→
=
Determination of temperature
thresholds 1T and 2T , for
1 2T T>
Refinement of contours by
gradient profile
( )
1
1
( , ), ,
( , )
0, , .
k
k
E x y T T
E x y
T T
≥⎧
= ⎨ ∈ −∞⎩
Determine the strengths and
weak of the pixels
( )
[ ]
2
1 2
( , ), , ,
( , )
( , ), , .
k
k
k
p x y T T
p x y
p x y T T T
+
−
⎧ ∈ ∞⎪= ⎨
∈⎪⎩
Smoothing values of the inten-
sity of the pixels
( )
[ ]
( )
2
1 2
1
( , ) ( , ), , ,
( , ), , ,
0, , .
k k
k
p x y p x y T T
p x y T T T
T T
+ −
−
+ ∈ ∞
∈
∈ −∞
Morphological operation of
contour display
( , ) ( , ) ( , ),k k kI x y p x y p x y+ −= +
for ( )2 , .T T∈ ∞
1 2T T≤
1 2T T>
Shlykov V.V., Maksymenko V.B.
ISSN 2663-2586 (Online), ISSN 2663-2578 (Print). Cyb. and comp. eng. 2019. № 2 (196) 68
1,4σ = for threshold [ ] 0 0
1 2, 14 ,18T T С С⎡ ⎤= ⎣ ⎦ with hypothermia,
2,0σ = for threshold [ ] 0 0
1 2, 32 ,36T T С С⎡ ⎤= ⎣ ⎦ with hyperthermia.
Thus, the Canny's limit detector determines how fast the brightness of the
image changes at each point of the thermograms, which makes it possible to
determine the boundaries of temperature heterogeneity and its orientation.
CLINICAL STUDIES
The clinical investigations of the method for conduction of coronary vessels
were carried out at the clinical base of the Amosov National Institute of Cardio-
vascular Surgeryof NAMS of Ukraine to improve the efficiency of noninvasive
control of human heart temperature in conditions of artificial blood circulation in
the department of surgical treatment of aortic pathologies in sixteen open heart
operations and in the department of surgical treatment of acquired heart defects
in twelve open heart operations.
In clinical studies, the process of warming up and cooling myocardium is
carried out through the cannulas, which are installed in the anterior part of the
aorta in the region of the top of the heart. The cannula is installed in the branch
of the right ventricular artery for pumping a cardioplegic solution along the right
coronary artery, and the cannula is installed on the surface of the aortic bulb for
pumping the solution along the left coronary artery.
The clinical studies on isolated heart show the feasibility of using the me-
thod of determining the conductibility of coronary vessels on the basis of non-
invasive heart temperature control for assessing the conditions of blood supply
to the vessels of the myocardium (Fig. 3).
When cooling the heart (Fig. 3 a), the coronary vessels are clearly distin-
guished at the temperature difference between the tissues of the myocardium and
the solution 6°C and more (to a temperature of 10°C). Accordingly, when warm-
ing the heart (Fig. 3 b), the coronary vessels are released at a temperature differ-
ence of 9°C or more (up to 12°C). The initial temperature of the myocardium at
the beginning of the cooling process was not less than 21–22°C, and at the be-
ginning of the warming - no more than 25–26°C.
The assessment of the dynamics of temperature changes for the distribution
of temperature in the myocardium can be performed for a sequence of thermo-
grams of the heart that are performed for the state of hypothermia and hyper-
thermia in conditions of cardiopulmonary bypass (Fig. 4).
The application of the developed mathematical model of heat exchange for
the surface layer of the myocardium [16 – 18] allows us to determine the boun-
daries between the warmed and cooled sections of the myocardium during hypo-
thermia or hyperthermia of the heart. When cooling the heart (Fig. 4a) and
warming the heart (Fig. 4b), the boundaries between the warmed and cooled
areas are allocated due to the presence of a gradient on the surface of the myo-
cardium at temperatures between 0.5°C and 4°C and more.
The Method of Determining Conductibility for Coronary Vessels by Termography
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26°C
25°C
35°C
37°C
a
b
Fig. 3. Application of the thermographic method of contouring
to determine the conductivity of coronary vessels: a — for
cooled heart; b — for a warmed heart
During hypothermia (Fig. 5), the area of the warm part of the myocardium
decreases by compressing the cooling circuit gipoS and, accordingly, increasing
the area of the cooled area relative to the external cooling circuit limit oS . The
dynamics of temperature changes on the surface of the heart causes an increase
in the magnitude of the ratio i mS S and brings it closer to the value 1iF → .
During hyperthermia (Fig. 6) there is a decrease in the area of the chilled
area of the myocardium by compressing the warming contour giperS and, accord-
ingly, increasing the area of the warmed area relative to the external warming
circuit limit gipoS . The dynamics of temperature changes on the surface of the
heart causes an increase in the magnitude of the ratio oS and brings it closer
to the value 1iF → .
At the final stage of the processes of hypothermia and hyperthermia, the
value gipo gipo oF S S= is less than 1.3 times the value giper giper oF S S= , respec-
tively, which is expressed in a more uniform warming of the studied area of the
heart with hyperthermia in comparison with the process of its cooling under
hypothermia in conditions of cardiopulmonary bypass.
12°C
22°C
21°C
15°C
Shlykov V.V., Maksymenko V.B.
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а
b
Fig. 4. Thermograms of the heart for the state of
hypothermia and hyperthermia: a — for a cooled
heart; b — for a warmed heart
The developed method for determining the conductibility of coronary ves-
sels provides the reliability of non-invasive control of open heart temperature,
which is determined by the temperature sensitivity of 0,1°C of the thermometer
FLIR ThermaCAM E300 and the measurement error ±1% of the range.In addi-
tion, the use of needle heaters and sensors in the oesophagus does not allow to
determine the temperature of the inner wall of the myocardium without the in-
troduction of invasive sensors in the opening between the aorta and the left ven-
tricle, which is an additional factor for injury.
31°C
23°C
27°C
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Fig. 5. Work of the Canny detector algorithm for hypothermia of the heart
gipoS
oS
23°C
27°C
Shlykov V.V., Maksymenko V.B.
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Fig. 6. Work of the Canny detector algorithm for hyperthermia of the heart
RESULTS
For compare the temperature data, that is measured using invasive needle sen-
sors and the thermography method, the determination of regression dependence
for the calculation of the dynamic changes in temperature, determined in real
time. As a data examination class ( 1С ), the temperature value measured with the
needle sensors ( )MEDT tΔ is used. The investigated class ( 2С ) contains calculated
temperature differences on the surface of the myocardium ( )FLIRT tΔ , which are
recorded during hypothermia and hyperthermia using the thermography.
The level of confidence in the obtained temperature data, measured by
thermography means and needle sensors, reflects the value of confidence inter-
vals. The obtained confidence intervals can be considered as an interval of val-
ues of the parameters, which does not contradict the true value of temperature. In
determining the Euclidean distance by the K −mean method, the number of ob-
servations corresponding to the number of temperature measurements 10k = is
taken into account. The calculated Euclidean distance between the center of
giperS oS
33°C
31°C
The Method of Determining Conductibility for Coronary Vessels by Termography
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gravity of the examination class ( 1C ) and the studies class ( 2C ) is researched
that equals ( )1 2, 6,69d c c = . The resulting value of the confidence interval is less
than 15% shows the closeness between the data in the classes.
The reliability of determining the coefficient of correlation ( )1 2,r c c depends on
the number of measurements of temperature and the number of degrees of freedom
2k n= − . The value of the t-criterion for assessing the statistical significance of the
correlation relationship between the samples is determined by the formula:
( )
( )
( )
2
1 2
2
1 2
,
1 ,
r c c
t r n k
r c c
= −
− ,
(20)
where n — the number of temperature measurements, k — the number of de-
grees of freedom for pair regression.
The results of the regression analysis of the temperature measurement data
are to determine the correlation coefficient ( )1 2, 0,739r c c = and the regression
equation on the basis of comparison of data ,i ix y in the classes 1C and 2C to the
studies (Table 1).
The critical value of Student's t-criterion is located 2,306critt = for the sam-
ple 10n = size and the number of degrees of freedom 2k = at the level of signifi-
cance 0,05p < .The calculated t-criterion ( ) 3,102t r = for a specific correlation
coefficient ( )1 2,r c c is greater than the critical value ( ) critt r t> , hence the relation-
ship between data in classes 1C and 2C , is statistically significant. The resulting
regression equation 0,3829 0, 2137y x= + (Fig. 7) has a large angle of inclination of
the data interrelation 0,3829 and linear dependence, and allows you to perform the
conversion of temperature readings, measured with the help of needle sensors, to the
temperature values obtained using the thermography method.
Table 1. Results of regression analysis of temperature control data for the method of
determining the conductibility of coronary vessels
Evaluation criterion The value of the coeffi-
cient
• Correlation coefficient ( )1 2,r c c 0,739
• t-criterion value ( )t r 3,102
• Regression equation 0,3829 0, 2137y x= + 0,383
Shlykov V.V., Maksymenko V.B.
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Fig. 7. Regression equation based on the comparison of data xi, yi in classes:
x — data of the examination class C1 of heat sensor, ΔTMED(t), °С, y — class
data C2 for thermographic studies, ΔTFLIRt), °С.
The proposed algorithm for obtaining contours of areas with nonhomogene-
ous temperature distribution on the surface of the heart, realized on the basis of
the contours algorithm of Canny detector, allows receiving additional informa-
tion on the state of the blood supply of the myocardium by using the Gaussian
filter, and on the basis of the informative temperature profiles on thermographic
images, separating the geometric boundaries between the cooled and warmed up
areas of the myocardium by using the algorithm of Canny detecting for the video
frames of thermograms.
The obtained regression dependences have the correlation coefficient of
0.75, that allows to perform the conversion of heart temperature readings, which
are measured with the help of needle heaters in the temperature values, obtained
using the thermography method. The reliability of the method for determining
the conductibility of coronary vessels for the detection of myocardial areas with
the ischemic regions with dimensions less than 2×2 mm can be increased by
using modern medical thermographs with a sensitivity of 0,02°С and a meas-
urement error of ±0,5% of the range.
Thus, the use of the thermography method for determining the conductibil-
ity of coronary vessels in comparison with the use of needle heaters for the
evaluation of microhemodynamics of coronary vessels can significantly in-
crease the reliability of heart temperature control due to the possibility of ob-
taining additional information for the permissible difference in temperature on
the surface of the myocardium during hypothermia and hyperthermia.
0.0
1.2
0.2
0.4
0.6
0.8
1.0
0.4 0.8 x , °С 0.0
( )y x , °С
The Method of Determining Conductibility for Coronary Vessels by Termography
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CONCLUSIONS
Thus, the method of contouring the cooled and warmed areas of the myocardium
to determine the conductibility of coronary vessels using thermographic instru-
ments for measuring the temperature of the heart, and an improved of the algo-
rithm of detector Canny using the Gaussian filter, allows us to assess the con-
ductibility of coronary vessels for the study of blood flow in the surface layer of
the myocardium during warming up and cooling of the heart in conditions of
cardiopulmonary bypass.
The application of the thermography method for determining the conducti-
bility of coronary vessels in comparison with the use of needle heaters for the
evaluation of microhemodynamics of coronary vessels provides non-invasive
control of heart temperature and the possibility of obtaining additional informa-
tion on the permissible difference in temperature on the surface of the myocar-
dium during hypothermia and hyperthermia.
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sky Kyiv Polytechnic Institute, 2017. 93p. (in Ukranian)
Received 29.03.2019
ЛИТЕРАТУРА
1. Nicholas A., Diakides В., Joseph D., Bronzino А. Medical Infrared imaging RC Press
Taylor Group LLC, London. 2008. 451р.
2. Kotovskyi V.,Shlykov V., Vi?niakovc N., And?ela?e?ok. The IR-thermal imaging method for
evaluation of the status of myocardial coronary vessels under the condition of artificial blood
circulation. Technology and Health Care. vol. Pre-press, no. Pre-press. 2018. P. 1–6.
3. Maksymenko V., Danilova V., Shlykov V. The discrete model for the system of the myocar-
dium and coronary vessels. 3rd Conference "Approximation Methods for Molecular Modelling
and Diagnosis Tools" (26-30th of Jan., 2017, Kyiv). Kyiv, 2017. P. 3. (in Ukranian)
4. Shlykov V., Danilova V., Maksymenko V. Heat transfer model based on thermographic im-
aging of the heart in open chest conditions. 17th European Congress on Extracorporeal Circu-
lation Technology. (14-17th of June, 2017, Marseille). Marseille, 2017. P. 57.
5. Maksymenko V., Danilova V., Shlykov V. The Discrete Model for the System of the
Myocardium and Coronary Vessels. Наукові вісті НТУУ "КПІ". No 1 (2017). C 54 –
60. (in Ukranian)
6. Shlykov V., Danilova V., Maksymenko V. The Model of the Myocardium in the MSC
Sinda System. Cardiology and Cardiovascular Research. Vol. 1, Issue 2. 2017. P. 18–22.
7. Shlykov V., Danilova V., Maksymenko V. Numerical model for heat transfer based on
thermographic imaging of the heart. Стандартизація, сертифікація, якість. Вип.
№4(107) 2017. C 62 – 68. (in Ukranian)
8. Shlykov V., Danilova V., Maksymenko V., Sychyk M. Application of Model of Heat
Exchange for Myocardium Provided Stationary Convection Laminar Flow Journal of
Cardiology & Current Research. 2017. P. 311–313.
9. Chen J. S., Huertas A., Medioni G. Fast convolution with Laplacian-of-Gaussian masks
IEEE Transactions of Pattern Analysis and Machine Intelligence. 1987. Vol. 9, Issue 4.
P. 584–590. doi: 10.1109/tpami.1987.4767946
10. John H. Lienhard IV and John H. Lienhard V A Heat Transfer Textbook – 4th ed. Cam-
bridge, MA: Phlogiston Press. 2017. 768 P.
The Method of Determining Conductibility for Coronary Vessels by Termography
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11. MSC Sinda 2017 User’s Guide. Docs ID DOC11364 MSC Software Corporation. 2017. 451 P.
12. Kelly T. Thermal Analysis Kit III Manual. K&K Associates, Version 97.003. 1997. 23 P.
13. Thermal Network Modeling Handbook. K&K Associates, Developers of Thermal Analy-
sis Kit, Version 97.003. 2000. 29 P.
14. Sharif, M., Mohsin S. Single Image Face Recognition Using Laplacian of Gaussian and
Discrete Cosine Transforms. The International Arab Journal of Information Texnology.
2012. Vol. 9, Issue 6. P. 562–570.
15. Canny J. A computational approach to edge detection. IEEE Transactions on pattern
analysis and machine intelligence. 1986. Vol. 8, Issue 6. P. 679–698. doi:
10.1109/tpami.1986.4767851
16. Khudetskyy I.U., Danilova V.A., Shlykov V.V. Use of Thermal Imaging for Control of the
Process Hypothermia Cardiac. The Polish Journal of Applied Sciences. 2015. P. 93–96
17. Kotovskiy, V. I., Shlykov, V. V., Danilova, V. A. The Method of Processing Thermo-
graphic Images for the Open Heart. Young Scientist USA. Vol. 7. 2017. P. 1.3–3.3
18. Shlykov V. The propagation of the temperature wave in myocardium. «EUREKA: Phys-
ics and Engineering». №2 (2018) P. 52–62.
19. Bin Jing, Haiyun Li. A Novel Thermal Measurement for Heart Rate. Journal of Com-
puters. Vol. 8, No. 9, September. Academy Publisher, 2013. pp. 2163–2166. URL:
https://pdfs.semanticscholar.org/6c24/5901e748c240f7f82ff42d726db2573c3262.pdf
(Last accessed: 01.06.2019).
20. Buckberg G.D., Brazier J.R., Nelson R.L., et al. Studies of the effects of hypothermia on
regional myocardial blood flow and metabolism during cardiopulmonary bypass. I. The
adequately perfused beating, fibrillating, and arrested heart. J Thorac Cardiovasc Surg
1977; 73: 87–94.
21. Love T. J. Thermography as an indicator of blood perfusion. Annals of the New York
Academy of Sciences. 1980.V. 335. № 1. P. 429–437.
22. Gonzalez R. C., Woods R.E. Digital Image Processing Prentice Hall, 2002. URL:
http://users.dcc.uchile.cl/~jsaavedr/libros/dip_gw.pdf (Last accessed: 01.06.2019)
23. Stoica P., Moses R. Spectral analysis of signals. Prentice Hall, New Jersey, 2004. URL:
http://user.it.uu.se/~ps/SAS-new.pdf (Last accessed: 01.06.2019)
24. Pavlidis T. Algorithms and Graphics and Image Processing. N.Y.: Springer, 1982. 320 P. 25.
25. Чепурний М.М., Резидент Н.В. Тепломасообмін в прикладах і задачах: навчальний
посібник Вінниця: ВНТУ. 2011. 128 с. (in Ukranian)
26. Гільчук А.В., ХалатовА.А.Теорія теплопровідності: навчальний посібник Київ:
КПІ ім. Ігоря Сікорського, 2017. 93с. (inUkranian)
Отримано 29.03.2019
Shlykov V.V., Maksymenko V.B.
ISSN 2663-2586 (Online), ISSN 2663-2578 (Print). Cyb. and comp. eng. 2019. № 2 (196) 78
Шликов В.В.1, канд.техн.наук, доцент,
доцент кафедри біомедичної інженерії
Київського політехнічного інституту ім. Ігоря Сікорського
e-mail: v.shlykov@kpi.ua
Максименко В.Б.2, д-р.мед.наук, професор,
заст.директора з наукової роботи
e-mail: maksymenko.vitaliy@gmail.com
1 Національний технічний університет України "Київський політехнічний інститут
імені Ігоря Сікорського"
пр. Перемоги, 37, Київ, Україна, 03056
2 Національний інститут серцево-судинної хірургії імeні М.М. Амосова
вул. Амосова, 6, Київ, Україна, 03038
МЕТОД ВИЗНАЧЕННЯ ПРОВІДНОСТІ
КОРОНАРНИХ СУДИН ЗАСОБАМИ ТЕРМОГРАФІЇ
Вступ. Характер розподілу температури в серці визначається процесом теплообміну
між міокардом і коронарними судинами, а також станом мікрогемодинаміки коронар-
ного русла серця. Для кількісного оцінювання нерівномірності розподілу температури
на поверхні серця запропоновано алгоритм розрахунку кількісного критерію, що може
бути об'єктивним маркером ефективного захисту серця і мозку. Метод визначення
провідності коронарних судин реалізовано на основі алгоритму визначення теплових
контурів, що обчислюються за градієнтами температурного поля на зображенні серця в
інфрачервоному спектрі. Вдосконалення розробленого раніше методу визначення теп-
лових контурів на основі алгоритму Канні полягає в переході від якісного до кількісно-
го оцінювання швидкості зміни температури на поверхні міокарда.
Метою дослідження є оцінювання провідності коронарних судин для досліджен-
ня кровоплину у поверхневому шарі міокарда під час зігрівання та охолодження серця
в умовах штучного кровообігу.
Результати.Числове значення кількісного критерію отримано шляхом визначення різ-
ниці температур між кров'ю і міокардом, яке обчислюють як різницю геометричних площ під
кривими розподілу температур у рівнянні температурного поля для постійного і поточного
температурного напору. Метод контурування для визначення провідності коронарних судин
дає змогу виділити ділянки на поверхні міокарда, в яких зміна температури значно відстає від
середньої температури на поверхні під час зігрівання або охолодження серця, що уможлив-
лює оцінювання стану дрібних коронарних судин в міокарді.
Ключові слова: математичне моделювання, алгоритм детектування Канні, темпера-
тура серця, температурні профілі, гіпотермія, гіпертермія, штучний кровообіг.
The Method of Determining Conductibility for Coronary Vessels by Termography
ISSN 2663-2586 (Online), ISSN 2663-2578 (Print). Cyb. and comp. eng. 2019. № 2 (196) 79
Шлыков В.В.1, канд.техн.наук, доцент,
доцент кафедры биомедицинской инженерии
Киевского политехнического института им. Игоря Сикорского
e-mail: v.shlykov@kpi.ua
Максименко В.Б.2, д-р.мед.наук, професор,
зам. директора по научной роботе
e-mail: maksymenko.vitaliy@gmail.com
1 Национальный технический университет Украины
"Киевский политехнический институт имени Игоря Сикорского"
пр. Победы, 37, Киев, Украина, 03056
2 Национальный институт сердечно-сосудистой хирургии
имeни М.М. Амосова
ул. Амосова, 6, Киев, Украина, 03038
МЕТОД ОПРЕДЕЛЕНИЯ ПРОВОДИМОСТИ КОРОНАРНЫХ СОСУДОВ
СРЕДСТВАМИ ТЕРМОГРАФИИ
Введение. Для количественной оценки неравномерности распределения температуры
на поверхности сердца предложен алгоритм расчета количественного критерия, кото-
рый может являться объективным маркером эффективной защиты сердца и мозга.
Метод определения проводимости коронарных сосудов реализован на основе алгорит-
ма Канни для определения тепловых контуров, которые вычисляются по градиентам
температурного поля на изображении сердца в инфракрасном спектре.
Целью исследования является оценка проводимости коронарных сосудов для
исследования кровотока в поверхностном слое миокарда во время согревания и охлаж-
дения сердца в условиях искусственного кровообращения.
Результаты. Получено числовое значение количественного критерия, который
рассчитывается путем определения разницы температур между кровью и миокардом,
что косвенно позволяет оценивать состояние мелких коронарных сосудов в миокарде.
Ключевые слова: математическое моделирование, температура сердца, темпера-
турные профили, гипотермия, гипертермия, искусственное кровообращение.
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| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 2663-2578 |
| language | English |
| last_indexed | 2025-12-07T17:39:19Z |
| publishDate | 2019 |
| publisher | Міжнародний науково-навчальний центр інформаційних технологій і систем НАН України та МОН України |
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| spelling | Shlykov, V.V. Maksymenko, V.B. 2019-12-20T18:41:12Z 2019-12-20T18:41:12Z 2019 The Method of Determining Conductibility for Coronary Vessels by Termography / V.V. Shlykov, V.B. Maksymenko // Cybernetics and computer engineering. — 2019. — № 2 (196). — С. 59-79. — Бібліогр.: 26 назв. — англ. 2663-2578 DOI: https:// 10.15407/kvt196.02.059 https://nasplib.isofts.kiev.ua/handle/123456789/161749 577.169; 616.1 – 616.7 The purpose of this study is to evaluate the conductibity of coronary vessels for the study of blood flow in the surface layer of the myoc ardium during warming up and cooling of the heart in conditions of cardiopulmonary bypass. Results. The numerical value of the quantitative criterion obtained is calculated by determining the difference in temperature between the blood and the myocardium, calculated as the difference between the geometric areas under the temperature distribution curves in the temperature field equation for the constant and the current fluxing temperature. The contouring method for determining the conductibity of coronary vessels allows to select areas on the surface of the myocardium, in which the change in temperature significantly lags behind the average temperature on the surface during warming or cooling of the heart, which indirectly allows evaluating the state of small coronary vessels in the myocardium. Метою дослідження є оцінювання провідності коронарних судин для дослідження кровоплину у поверхневому шарі міокарда під час зігрівання та охолодження серця в умовах штучного кровообігу. Результати.Числове значення кількісного критерію отримано шляхом визначення різниці температур між кров'ю і міокардом, яке обчислюють як різницю геометричних площ під кривими розподілу температур у рівнянні температурного поля для постійного і поточного температурного напору. Метод контурування для визначення провідності коронарних судин дає змогу виділити ділянки на поверхні міокарда, в яких зміна температури значно відстає від середньої температури на поверхні під час зігрівання або охолодження серця, що уможливлює оцінювання стану дрібних коронарних судин в міокарді. Целью исследования является оценка проводимости коронарных сосудов для исследования кровотока в поверхностном слое миокарда во время согревания и охлаждения сердца в условиях искусственного кровообращения. Результаты. Получено числовое значение количественного критерия, который рассчитывается путем определения разницы температур между кровью и миокардом, что косвенно позволяет оценивать состояние мелких коронарных сосудов в миокарде. en Міжнародний науково-навчальний центр інформаційних технологій і систем НАН України та МОН України Кибернетика и вычислительная техника Medical and Biological Cybernetics The Method of Determining Conductibility for Coronary Vessels by Termography Метод визначення провідності коронарних судин засобами термографії Метод определения проводимости коронарных сосудов средствами термографии Article published earlier |
| spellingShingle | The Method of Determining Conductibility for Coronary Vessels by Termography Shlykov, V.V. Maksymenko, V.B. Medical and Biological Cybernetics |
| title | The Method of Determining Conductibility for Coronary Vessels by Termography |
| title_alt | Метод визначення провідності коронарних судин засобами термографії Метод определения проводимости коронарных сосудов средствами термографии |
| title_full | The Method of Determining Conductibility for Coronary Vessels by Termography |
| title_fullStr | The Method of Determining Conductibility for Coronary Vessels by Termography |
| title_full_unstemmed | The Method of Determining Conductibility for Coronary Vessels by Termography |
| title_short | The Method of Determining Conductibility for Coronary Vessels by Termography |
| title_sort | method of determining conductibility for coronary vessels by termography |
| topic | Medical and Biological Cybernetics |
| topic_facet | Medical and Biological Cybernetics |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/161749 |
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