Mathematical methods of motion correction in radionuclide studies
Detection and correction of patient motion during the acquisition of diagnostic data is an important step in the processing of radionuclide studies, since even a small shift of the patient’s body at this moment can affect to the accuracy of diagnostics results. Motion correction in single photon emi...
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irk-123456789-1117792017-01-15T03:02:55Z Mathematical methods of motion correction in radionuclide studies Ovsyannikov, D.A. Kotina, E.D. Shirokolobov, A.Yu. Динамика пучков Detection and correction of patient motion during the acquisition of diagnostic data is an important step in the processing of radionuclide studies, since even a small shift of the patient’s body at this moment can affect to the accuracy of diagnostics results. Motion correction in single photon emission computed tomography (SPECT) and dynamic scintigraphy are considered. Mathematical methods of motion correction based on the use of cross-correlation function are implemented. Важливим етапом при обробці радіонуклідних досліджень є виявлення і корекція руху пацієнта під час збору діагностичних даних, оскільки навіть невелике зміщення пацієнта або досліджуваного органу в цей момент може вплинути на достовірність результатів діагностики. Корекція руху розглядається для двох режимів збору даних: однофотонної емісійної комп'ютерної томографії (ОФЕКТ) і динамічної сцинтиграфії. Реалізовано математичні методи корекції з використанням функції взаємної кореляції. Важным этапом при обработке радионуклидных исследований является обнаружение и коррекция движения пациента во время сбора диагностических данных, поскольку даже небольшое смещение пациента или исследуемого органа в этот момент может повлиять на достоверность результатов диагностики. Коррекция движения рассматривается для двух режимов сбора данных: однофотонной эмиссионной компьютерной томографии и динамической сцинтиграфии. Реализованы математические методы коррекции с использованием функции взаимной корреляции. 2013 Article Mathematical methods of motion correction in radionuclide studies / D.A. Ovsyannikov, E.D. Kotina, A.Yu. Shirokolobov // Вопросы атомной науки и техники. — 2013. — № 6. — С. 137-140. — Бібліогр.: 17 назв. — англ. 1562-6016 PACS: 87.15.A http://dspace.nbuv.gov.ua/handle/123456789/111779 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Динамика пучков Динамика пучков |
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Динамика пучков Динамика пучков Ovsyannikov, D.A. Kotina, E.D. Shirokolobov, A.Yu. Mathematical methods of motion correction in radionuclide studies Вопросы атомной науки и техники |
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Detection and correction of patient motion during the acquisition of diagnostic data is an important step in the processing of radionuclide studies, since even a small shift of the patient’s body at this moment can affect to the accuracy of diagnostics results. Motion correction in single photon emission computed tomography (SPECT) and dynamic scintigraphy are considered. Mathematical methods of motion correction based on the use of cross-correlation function are implemented. |
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Article |
| author |
Ovsyannikov, D.A. Kotina, E.D. Shirokolobov, A.Yu. |
| author_facet |
Ovsyannikov, D.A. Kotina, E.D. Shirokolobov, A.Yu. |
| author_sort |
Ovsyannikov, D.A. |
| title |
Mathematical methods of motion correction in radionuclide studies |
| title_short |
Mathematical methods of motion correction in radionuclide studies |
| title_full |
Mathematical methods of motion correction in radionuclide studies |
| title_fullStr |
Mathematical methods of motion correction in radionuclide studies |
| title_full_unstemmed |
Mathematical methods of motion correction in radionuclide studies |
| title_sort |
mathematical methods of motion correction in radionuclide studies |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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2013 |
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Динамика пучков |
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http://dspace.nbuv.gov.ua/handle/123456789/111779 |
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Mathematical methods of motion correction in radionuclide studies / D.A. Ovsyannikov, E.D. Kotina, A.Yu. Shirokolobov // Вопросы атомной науки и техники. — 2013. — № 6. — С. 137-140. — Бібліогр.: 17 назв. — англ. |
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| fulltext |
ISSN 1562-6016. ВАНТ. 2013. №6(88) 137
MATHEMATICAL METHODS OF MOTION CORRECTION
IN RADIONUCLIDE STUDIES
D.A. Ovsyannikov, E.D. Kotina, A.Yu. Shirokolobov
Saint-Petersburg State University, Saint-Petersburg, Russia
E-mail: a.shirokolobov@gmail.com
Detection and correction of patient motion during the acquisition of diagnostic data is an important step in the
processing of radionuclide studies, since even a small shift of the patient’s body at this moment can affect to the
accuracy of diagnostics results. Motion correction in single photon emission computed tomography (SPECT) and
dynamic scintigraphy are considered. Mathematical methods of motion correction based on the use of cross-
correlation function are implemented.
PACS: 87.15.A
INTRODUCTION
Motion correction problems exist for diagnostic
studies [5], as well as for planning radiation therapy [4].
Radionuclide diagnostics is one of the modern radiology
methods for the estimation of the functional status of the
various organs and body systems. This method is based
on the injection of the indicator quantities of radioiso-
topes in the target organs and body systems. The meth-
od of the radioisotopes visualization includes a number
of methods for obtaining images showing distribution of
the labeled radionuclides substances in the body. These
substances are called radiopharmaceuticals and they are
designed for monitoring and evaluation of the physio-
logical functions of organs [9, 11].
Detection and correction of the patient motion are
one of the most important steps of the processing of
radionuclide studies. Even small displacement of the
patient or of the target organ during the process of data
collection may affect accuracy of diagnostic results [2,
5, 13, 15, 17]. It is impossible to avoid the position
changing of the patient or its target organs during data
acquisition.
1. MOTION CORRECTION IN SPECT
1.1. PROBLEM STATEMENT
The camera turns around patient, during the data col-
lection of the single photon emission computed tomog-
raphy (SPECT) [1, 6]. This fact must be taken into ac-
count for motion correction.
Let’s introduce two coordinate systems (Fig. 1). The
moving system of coordinates ),( yx , associated with
the detector, which rotates in a circular orbit around the
center of fixed coordinate system )',','( zyx . This
system is associated with the gamma camera gantry.
Let’s the point 'P has coordinates )',','( zyx , in
the fixed coordinate system, i.e. )',','('' zyxPP .
The point P is its projection into the plane ),( yx . The
coordinates of the point P are ),( yx , i.e.
),( yxPP . The relationship between the points P
and 'P will be defined as follows:
,
'
)sin(
zy
Ax
where )'/'( xyarctg ; – viewing angle;
22 '' yxA .
Let’s consider relative motion of a point in the pro-
jection coordinates between two consecutive frames
.0
,)cos(
y
Ax
(1)
We can see, that in the case of absence of motion the
trajectory of the point projection )',','( zyx must be
sinusoidal relative to the axis x and the line relative to
the axis y .
Fig. 1. The coordinate systems. The yellow color defines
the moving system and the fixed system is defined by the
red color
The transverse motion is the position displacement
of the examined organ parallel to the plane )','( yx ,
and a longitudinal one parallel to the axis )'(z .
The method of the cross-correlation function is used
for the determination and subsequent motion correction.
1.2. THE MOTION CORRECTION BASED
ON THE METHOD
OF THE CROSS-CORRELATION FUNCTION
This method is based on the analysis of cross-
correlation function defined for successive planar imag-
es. Discrete cross-correlation function )(sF between
the two one-dimensional data sequences A and B may
be written as
ISSN 1562-6016. ВАНТ. 2013. №6(88) 138
,)()()(
1
m
p
spBpAsF
where m dimension of sequences, Zs dis-
placement of one sequence relative to the other,
NKKsK , maximum displacement,
0)( spB , if 1sp or msp .
Let’s the initial data of tomographic studies are N
projection images of size nn pixels. Thus, we have a
set of matrices njiNkjiPk ,1,,,1),,( , the ele-
ments of which are the values of density distribution of
the radiopharmaceutical at the points ),( ii yx .
We use total profiles of data set for the analysis of
the projection images [3]. We obtain these profiles from
the planar images for each of the angles of observation:
,,1,,1,),(
1
NknjjiPC
n
i
kjk
,,1,,1,),(
1
NknijiPD
n
j
kik
where jkC and ikD total profiles along the x and
y axes respectively.
We consider the correlation between the two planar
images. Thus, the cross-correlation functions for two
successive planar images with indices k and 1k
have the forms
,,,
1
1, NKKsKCCfx
n
j
ksjjkk
(2)
,,,
1
1, NKKsKDDfy
n
i
ksiikk (3)
where 01,ksjC , if 1sj or nsj , and
01,ksiD , if 1si or nsi .
Formulas (2) and (3) represent a view of the cross-
correlations function relative to the x and y profiles
respectively.
1.3. SOFTWARE IMPLEMENTATION
The sinogram and linogram [10] are built for the
visual detection of displacement along the x and y
axes respectively.
It is necessary to determine the area of interest, be-
fore we start detecting the motion, with the purpose to
increase the ratio signal-to-noise [16].
The final value of the frame displacement is deter-
mined by the parabolic approximation of the cross-
correlation at the point where it reaches its maximum
value and the two neighboring.
As mentioned above, a major problem of the trans-
verse motion determining is that the motion is supposed
to exist in advance. The reason of this motion is the ro-
tation of the camera around the patient. For the solving
this problem, we define the difference function along
the x-axis, and then this function is approximated by the
method of least squares polynomial of order 4, and the
difference of these functions is taken.
Software module of motion correction is implement-
ed on C# (Fig. 2).
Fig. 2. The main window of the program module
The window of the module has an initial group of
frames and frames after the correction presented in ani-
mation mode, sinogram (Fig. 3), linogram (Fig. 4),
function of the difference value of frame relative to the
x and y axes.
Area of interest corresponds to the area between the
upper and lower sliders. The central slider determines
the level for which the sinogram is built.
Fig. 3. Sinogram before (left) and after (right)
correction
Fig. 4. Linogram before (left) and after (right)
correction
We take the first frame, made by the detector, as the
standard frame. Standard frame is a frame with respect
to which the motion is considered. We consider the mo-
tion for each of the two groups of frames for two detec-
tors separately.
Fig. 5. The dependence of displacement value along the
y axis on the frame number
ISSN 1562-6016. ВАНТ. 2013. №6(88) 139
In Fig. 5, we show an example of dependence of
displacement value along the y axis on the frame num-
ber.
All the figures presented here relate to the same
study. For example, the linogram before the correction
and function graph, shown in Fig. 5, and linogram after
correction demonstrate detection and subsequent motion
compensation.
2. MOTION CORRECTION IN PLANAR
DYNAMIC SCANNING
2.1. PROBLEM STATEMENT
During the data collecting in the mode of planar dy-
namic scanning detector is stationary. A sequence of
planar images with a fixed exposure is formed for each
detector. We can observe the dynamic distribution of
the radiopharmaceutical in the system of the body.
The obtained data is a set of planar images, which
are projections of three-dimensional density distribution
of the radiopharmaceuticals on the detector plane. This
mode is used in the diagnostics of diseases of the kid-
neys, liver, gall bladder, brain, etc.
Let’s the initial data of the radionuclide studies are
projection images of size nn pixels. Suppose that,
there is a contour G on some frame, this contour re-
stricts certain region of interest (ROI). The frame with
this contour is called a standard. We detect the motion
of the ROI on the other frames, relative to the standard
frame.
Let’s display the contour in the reference frame, in
all other frames and state the problem of motion correc-
tion as the task of determination of the displacement
vector contour bounding the region of interest.
Thus, it is required to find the displacement vector
Nkyxs kkk ,1),,( for the each contour. Here
kk yx , are shifts of the contour on the k frame along
the x and y axes, respectively.
2.2. SOFTWARE IMPLEMENTATION
The problem is solved in two stages. At the first
stage, as in the previous section, the method of cross-
correlation function is used. As a second stage of the
correction contour position we use a method based on
finding the center of gravity of a plane figure, bounded
by contour.
The point of origin is a point with coordinates
)0,0( in the above notation. Relative to the point of
origin the radius vector is determined.
Before the start of the motion correction set the start
time of visualization i.e. frames number in which the
object is visualized. It is necessary because the radio-
pharmaceutical, which was administered to patient not
immediately comes to the organ under investigation.
We obtain a great number of the images after data
collection. So for clarity we draw the plots of depending
function of the total counts within the selected region of
interest from the frame number. The corresponding
linogram are constructed for the visual detection of
shifts along the x and y axes.
Fig. 6. The dependence of total counts of ROI from the
frame number. A: Before motion correction.
B: After motion correction
The example of dependence of total counts of ROI
from the frame number before and after the motion cor-
rection are shown in Fig. 6.
The graph of Fig. 6,B displays the real distribution
of the radiopharmaceutical per frame in the ROI after
motion correction.
We can note also that the use of the approaches de-
scribed in [7, 8, 12, 14] can be helpful for the motion
correction as well. These approaches are based on the
determination of the velocity field and can be used for
the solving of motion correction problems for dynamic
and tomographic studies.
CONCLUSIONS
In this paper the algorithms of motion correction
based on the method of cross-correlation function are
developed and implemented. The results showed that
this methods can be used for the motion correction in
radionuclide studies.
ACKNOWLEDGEMENTS
This work was supported by St. Petersburg State
University, scientific project No. 9.39.1065.2012 and
scientific project No. 9.38.673.2013.
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Article received 11.10.2013
МАТЕМАТИЧЕСКИЕ МЕТОДЫ КОРРЕКЦИИ ДВИЖЕНИЯ В РАДИОНУКЛИДНЫХ
ИССЛЕДОВАНИЯХ
Д.А. Овсянников, Е.Д. Котина, А.Ю. Широколобов
Важным этапом при обработке радионуклидных исследований является обнаружение и коррекция дви-
жения пациента во время сбора диагностических данных, поскольку даже небольшое смещение пациента
или исследуемого органа в этот момент может повлиять на достоверность результатов диагностики. Кор-
рекция движения рассматривается для двух режимов сбора данных: однофотонной эмиссионной компью-
терной томографии и динамической сцинтиграфии. Реализованы математические методы коррекции с ис-
пользованием функции взаимной корреляции.
МАТЕМАТИЧНІ МЕТОДИ КОРЕКЦІЇ РУХУ В РАДІОНУКЛІДНИХ ДОСЛІДЖЕННЯХ
Д.О. Овсянников, О.Д. Котіна, А.Ю. Широколобов
Важливим етапом при обробці радіонуклідних досліджень є виявлення і корекція руху пацієнта під час
збору діагностичних даних, оскільки навіть невелике зміщення пацієнта або досліджуваного органу в цей
момент може вплинути на достовірність результатів діагностики. Корекція руху розглядається для двох ре-
жимів збору даних: однофотонної емісійної комп'ютерної томографії (ОФЕКТ) і динамічної сцинтиграфії.
Реалізовано математичні методи корекції з використанням функції взаємної кореляції.
|