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Файл:Ординатура / Хирургия / Библиотека им академика М.И. Перельмана / Книга_5255_Библиотеки_им_академика_М_И_Перельмана
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422
Background Subtraction in Nuclear Medicine
It can be recapitulated that in nuclear medicine imaging the counts recorded over an
organ originate from three different sources:
The true activity in target tissues, which represents the true function of the organ.
The circulating activity in blood vessels of the target and non-target tissues.
The diffused activity from blood vessels into the extravascular space (i.e. interstitial
fluid and from there into the non-target tissues).
Mathematically the relationship between these three component and recorded activity
can written as:
R(t) = T(t) + E(t) + I(t) (1)
Where R(t), T(t), E(t) and I(t) are recorded counts, true counts, counts due to extravascular
and intravascular activity respectively. All these components vary with time ‘t’ in the equation.
One can also write the above equation in terms of the frame numbers in dynamic acquisition
as:
R(i) = T(i) + E(i) + I(i)
Where ‘i’ is the frame number with a given time duration. As it has already been
mentioned that the background causes error in quantification therefore the data has to be
corrected for these unwanted components. There are some prescribed mathematical procedures
for subtraction of background from the data, which will be discussed in brief here.
Methods of background subtraction
Following methods are commonly used for background subtraction in nuclear medicine.
Conventional method
Patlak/Rutland method
Linear regression method
Modified linear regression method
Multiple regression method
Conventional method
Static images: Traditionally background subtraction of an image is carried out by drawing a
region of interest (ROI) somewhere around the target organ over the image. Then the computer
adds up the values of all picture elements (pixel counts) over the ROI and divides it by the
number of pixels in that area to calculate the average counts per pixel. This average value
then is subtracted from each pixel value in the image (or a part of image) to obtain background
corrected image. This is the basic principle of image background correction though it may
not be correct to subtract same value from different pixels. Background subtraction in static
images has very limited application in nuclear medicine (e.g. some internal dosimetry
procedures). The negative values if obtained during subtraction are made zero to avoid
misinterpretation.
GSPant\Newbook\Final-2008\27-chp\422
Background Subtraction in Nuclear Medicine
423
Dynamic images: In dynamic studies more images are acquired at different times so the
background subtraction cannot be straightforward. In dynamic studies, usually the boundaries
of the organs are defined on an image. The values of all pixel counts over the ROI are added
up in each and every serial image separately and then put in a one-dimensional array. This
array represents the variation in the organ counts with time within its field of view. Since
the recorded counts are proportional to the concentration of radioisotope in the tissues, the
array represents the change in concentration of radiopharmaceutical in the organ of interest
with respect to time (activity versus time). The graphical illustrations of such arrays are
called time-activity curves. The same procedure can be repeated for any area of the image
including the background area to obtain background time-activity curve. The curve derived
from the selected background region then is divided by its area to obtain the counts per unit
area and multiplied by the area of the organ region. This curve is then subtracted from the
time-activity curve of organ to obtain the background free organ time-activity curve. The
procedure may be formulized as:
N
R(i) = T(i) –
o
× EI(i) (2)
N
b
Where R(i) and T(i) are organ time-activity curve after and before background subtraction
respectively, No and Nb are number of pixels in organ and background ROIs respectively,
EI(i) is the background time-activity curve which includes both intra and extravascular
activity and (i) is the frame number of given temporal length. This type of background
subtraction is very commonly used in nuclear medicine especially in renal dynamic studies
and is called conventional method.
Though very simple, straightforward and widely used, the method has some limitations
due to the following incorporated assumptions:
The ratio of intravascular to extravascular activity in background ROI is equal to
that in target ROI.
The above ratio is constant during the period of acquisition.
The absolute value of both background components (intra and extra vascular) in
background and target ROIs are the same.
Apparently these assumptions are hardly valid. The ratio of intravascular to extravascular
activity in the background ROI will vary with its position in the image, the physio-pathological
condition of the patient and quality and quantity of administrated radiopharmaceutical.
Further, the relative position of the target organ and the vascular organs such as the liver and
spleen varies from patient to patient. Therefore it is very difficult to determine preset
positions for drawing background regions, which can work satisfactorily in all similar studies.
A lot of work has been done to define a suitable position for background ROI in renal
studies but not without controversies. Various workers have proposed different regions,
which attempt to reproduce the ratio of intravascular to extravascular activity over the
GSPant\Newbook\Final-2008\27-chp\423
424
Background Subtraction in Nuclear Medicine
organs. Kenny et al. used a background region between the kidneys for calculation of kidney
transit times (1). O’Reilly et al. used a region above the kidneys (2). Gates in 1984 used a
region below the kidney (3). Cosgriff et al. (4) recommended a background region between
and around the kidneys but rejected regions below the kidney. Peters et al (5) compared
different location around the kidney for drawing the background region. They found that the
area determined by the difference between the renal region and a peri-renal region with 2
pixels outside the kidney region along the horizontal and 1 pixel outside along the vertical
border to be the optimum location for the purpose. Piepsz et al (6) compared three regions
and concluded that no single background region can accurately represent both interstitial
and vascular components of the renal curve (Figure 1).
Figure 1. Difference method of drawing background ROI
For partial compensation of the above said problem some workers add an additional
factor to the formula. This factor allows for constant differences between the content of
background region and the true background. Therefore equation-1 becomes
N
R(i) = T(i) – K ×
o
× EI(i) (3)
N
b
In equation-3, K represents compensation/scaling factor. But unfortunately there have
not been an agreement about the value of scaling factor. Different workers have used different
values for this factor. Gates (3) and O’Reilly et al (2) assumed the value to be one. Kenny
et al (1) assumed the value to be less than 1 but Peters et al (5) used more than one. Martel
and Tindal (7) reported the value of this scaling factor to be 0.87 + 0.72.
It can be said that the choice of a suitable background region for any given study is more
of an art than a science (8). Conventional method of background subtraction in its simple or
modified form has its own merits and demerits. Generally the consensus approach seems to
be to find a position for background region that works empirically for the type of study
concerned or to find more realistic models for background subtraction.
GSPant\Newbook\Final-2008\27-chp\424
Background Subtraction in Nuclear Medicine
z
z
z
425
Patlak/Rutland method
Patlak and Rutland developed this method independently. Gjedde (9) applied it for the
measurement of the uptake rate of compounds in the brain. However Rutland (10) had
independently applied the method for analysis of renogram
Theory: During the first few minutes of a dynamic study the activity that enters the
organ under study outweighs the amount that leaves the organ. In many situations the
difference is large enough to ignore the out flow and to consider the organ as a reservoir. In
such circumstances the organ activity can be regarded as accumulation of input stream flow.
A simple mathematical equation can be used to explain the relationship between organ
activity T(t or i) and input stream flow I(t or i):
i i
T(t) =
Where ‘t’ represents the time, and ‘i’, in dynamic study corresponds to the frame number
in the serial images and represented by a point in the time activity curves. This equation is
valid for a short period of time, before significant excretion starts from the organ that is
from time t = 0 to t = the minimum transit time of the organ. Minimum transit time
depends upon the type of radiopharmaceutical and physiological condition of the organ.
I t dt T i I i dt
( ) ( ) ( )
0 0
(4)
In nuclear medicine, radiopharmaceuticals are usually administrated intravenously and
the blood circulation carries it to the tissues. The blood circulation therefore performs two
distinct actions in imaging. It supplies the input of the organ and simultaneously produces
intravascular background. This is due to the fact that not all the offered activity is taken up
by the organs and a part of it remains in the blood. The extraction efficiency of the organs
is always less than 100%. Moreover part of the activity from the organs diffuses and goes
back into the blood. Therefore we can assume that at any instant the rate of input supply to
the organ and the amount of intravascular activity are proportional to concentration of
the activity in the blood. This assumption is quite valid in a small volume of tissues but
proportionality changes from point to point. In a large volume of a tissue the assumption
may not truly remain valid but the approximation is usually acceptable. The error caused by
this approximation is normally less than other errors in the procedure of background
subtraction. Commonly the time activity curve recorded over the cardiac blood pool is used
to represent the blood activity and an area of minimum perfusion is selected for the
extravascular background activity. With the help of equation-4 and equation-1, one can
write:
i
I t dt E t I t
R(t) =
( ) ( ) ( )
0
(5)
GSPant\Newbook\Final-2008\27-chp\425
426
L
N
O
Q
Where R(t) is the recorded counts over the organ ROI, I(t) is recorded counts over the
cardiac pool ROI, E(t) is the recorded counts over a soft tissue ROI with minimum perfusion
and , and are scaling factors. These scales are necessary because the recorded counts
are just proportional to the amount of activity in the tissues and not equal to them. In other
words a time–activity curve shows the relative function of an organ and not the absolute
one. The factors and are the scaling factors for subtraction of extravascular and
intravascular background respectively. The factor has a special meaning. If the I(t) represents
the supplied activity to organ then factor would be the extraction efficiency of that organ.
In renal dynamic studies extraction efficiency corresponds to glomerular filtration rate (GFR).
Unfortunately the absolute value of I(t) has no meaning therefore the factor is just
proportional to the extraction efficiency but not equal to it. Many attempt have been made
for calibration of renogram and blood pool time activity curve to calculate as an approximate
value of GFR (11).
Since nuclear medicine raw data are always in discrete form the integral symbol has to
be replaced with sigma and the equation-5 can be written as:
n
I i E i I i
( ) ( ) ( )
R(i) =
Where (i) refers the frame number and n is the frame number that corresponds to the
minimum transit time of the organ. Dividing both sides by R(t) and rearranging the equation:
i
–0
Background Subtraction in Nuclear Medicine
(6)
n
I i
( )
M
=
M
i
M
R i
I i
( )
( )
M
M
Ideal background subtraction means to solve this equation for and . These values then
can be used as scaling factors for extravascular and intravascular time-activity curves for
performing background subtraction. Some workers (12) have used the factor for calculation
of zero excretion curve. The discrete form of equation-4 gives:
n
T(i) =
I i
i
0
Therefore multiplication of by integral of cardiac curve produces a rising curve, which
would be obtained if there would be no excretion from the kidney. Comparison of zero
excretion curve with background subtracted renogram may give some idea about the excretion
efficiency of the kidney and can be used for quantitation of excretion efficiency.
Certainly the practical usefulness of these procedures depends on the solution of equation-
7. Since we do not have direct mathematical equation for R(t), I(t) and E(t), an analytical
P
E i
+
( )
(7)
I i
( )
P
0
P
I i
( )
P
P
( )
(8)
GSPant\Newbook\Final-2008\27-chp\426
Background Subtraction in Nuclear Medicine
L
N
O
Q
solution is almost impossible. However, a numerical method may be used for calculation of
the desired parameters. The following three general methods are normally used to calculate t.
427
Figure 2: Zero excretion curves may be used to find out percentage of activity excreted out of the
kidneys at a given point of time
Linear regression method
If the organ of interest is very well perfused the intravascular background dominates the
extravascular activity and extravascular component can be neglected if compared to the
intravascular component (assuming a zero value for ). Equation-7 may then be reduced to a
linear equation as:
n
I i
( )
M
=
M
i
M
R i
I i
( )
( )
M
M
Then a linear regression technique can be used to solve the equation for and .
Rutland (10) used this technique in probe renography for subtraction of intravascular
background and Gjedde (13) applied it for the measurement of D-glucose uptake from blood
to the brain. Usually a ROI over the cardiac pool is used to represent the blood activity.
GSPant\Newbook\Final-2008\27-chp\427
P
P
0
+ (9)
P
I i
( )
P
P
428
L
N
O
Q
Modified linear regression method
Assuming a zero value for b may cause significant overestimation in the calculation of
and . Some users assumed a fixed nonzero value for the in order to compensate this error.
This assumption keeps the linearity form of the equation if it is rearranged as:
n
R i E i
( ) ( )
I i
( )
=
M
M
M
M
Again the linear regression technique can be used to solve the equation for and but
the results will be more correct than using previous method. Rutland (14) experimentally
determined the value of = 0.6 and used a sub-renal area for extravascular time-activity
ROI. He normalized the background time-activity curve to the size of renal area and then
multiplied it by factor and solved equation-10 using linear regression technique. The
accuracy of this method depends on how accurate the value of is presumed. With a
reasonable approximation the time activity curve recorded over the cardiac ROI and a soft
tissue ROI (around the target organ) may be used to represent intravascular and extravascular
background respectively. Background region in renography is usually outlined below the
kidney except in the transplant studies where a contralaleral region is used to calculate
background activity.
M
i
P
I i
( )
P
0
+ (10)
P
I i
( )
P
P
Background Subtraction in Nuclear Medicine
Multiple regression method
Equation-7 has two variables and it looks quite attractive to use a multiple regression
technique for solving the equation for , and simultaneously. Middleton et al (12) used
the technique for background subtraction in
cardiac region was used for extra and intravascular ROIs respectively. They compared the
technique with linear regression and concluded that multiple regression is more reproducible
and less operator dependent than the linear regression. Despite its conceptual elegance this
technique has never found wide spread application.
Comparison of these three techniques in renal dynamic study using simulated curves and
real patient data has showed that linear regression method overestimates renal function
particularly in poorly functioning kidneys and modified regression method produces the
most accurate and reproducible results (7). But the results of multiple regression were
inferior and less reproducible. These results are quite justifiable. The theory can predict the
over estimation of linear regression method and many investigators quantified this error.
Obviously the modified regression method can improve the result by subtracting a fixed
value from the organ curve. We believe that the multiple regression technique is inapplicable
for equation-7. The essential condition for using multiple regression is to assume that the
variables on right side of the equation are totally independent. This assumption is certainly
GSPant\Newbook\Final-2008\27-chp\428
99m
Tc-DTPA renography. A sub-renal and
Background Subtraction in Nuclear Medicine
429
not valid for background subtraction. Extravascular background depends upon the blood
supply and therefore can not be independent of the intravascular activity. This dependency
makes the result of regression very unstable and a little change in the raw data (e.g. by
filtration of data) may significantly alter the results leading to unacceptable reproducibility.
All these three method assume that the extra and intravascular time-activity curves are
quite pure and uncontaminated. This is not a valid assumption. Both curves are mutually
contaminated. Bell and Peters (15) showed that there is a significant amount of extravascular
(chest wall) background in the cardiac time activity curve, which may cause up to 17%
overestimation in calculation of glomerular filtration rate. Certainly the extravascular curve
is also contaminated by intravascular activity but the extent depends upon the location of
ROI drawn. Less vascular areas are better for drawing the ROIs.
Validity of all these methods to a great extent depends on how many data points are used
for regression. In renal dynamic study the minimum transit time of normal kidney can be
less than 120 seconds. If we assume the framed duration of 20 seconds the total number of
available data points will be 6. Due to the theoretical and practical problems usually the first
two or three points of the data are very erroneous and should not be used for calculation.
Therefore the number of useful data points will be 3 or 4. This is not usually sufficient for
efficient calculation. Decreasing the frame duration does not solve the problem as it decreases
the signal to noise ratio and increases the uncertainty in each individual data point.
One of the problems with these methods, which have not been considered before, is the
time delay between the curves. The activity does not reach the organ, blood pool and
background region at the same time. If the blood pool is recorded over the cardiac region
there will be approximately 5 seconds delay for the activity to reach the kidney and more
than that to reach the peripheral tissues. This delay demolishes the information contained in
equation-7 during the first few seconds of the study. This fact can visually be perceived
using graphical representation of equation-10 using real data. The first two or three points
usually have quite different trend than those from the point three onwards. There is no such
distortion with simulated data. This distortion may be augmented if the image acquisition
does not start at right time.
The information density of the image and the amount of scattered radiation have
hampering effects on the results. In obese patients the results are usually not satisfactory
due to the high scattered radiation and low count density. Scattered counts degrade the
spatial resolution of the image and consequently the resolution of time-activity curve. The
absolute value of scattered counts has no relation with the amount of activity in the tissue,
therefore if it is high may invalidate the linear relationship between recorded counts and
activity in the tissue. This assumption is quite necessary for all types of quantitation. Low
count density lowers the signal to noise ratio especially in small ROIs. Background regions
drawn are usually very small. For cardiac ROI it may not be a problem where the count
density is high. Over the extravascular regions the count density is low and if the size of
GSPant\Newbook\Final-2008\27-chp\429
430
Background Subtraction in Nuclear Medicine
ROI selected is very small the curve will be very noisy. This noisy curve not only hampers
the regression but also lowers the signal to noise ratio in the organ curve after background
subtraction.
References
1. Kenny RW, Ackery DM, Fleming JS, Goddard BA, Grant RW. Deconvolution analysis of the
scintillation camera renogram. Br J Radiol 1975; 48(570): 481-6.
2. O’Reilly PH, Shields RG, Testa HJ. Nuclear Medicine in Urology and Nephrology 2nd edn, London,
1986.
3. Gates GF. Computation of glomerular filtration rate with 99mTc-DTPA: an in-house computer program.
J Nucl Med 1984; 25(5): 613-18.
4. Cosgriff PS. Region of interest, ROI, analysis—confidence in derived parameters. Nucl Med Commun
1985; 6(5): 305-9.
5. Peters AM, George P, Ballardie F, Gordon I, Todd-Pokropek A. Appropriate selection of background
for 99mTc-DTPA renography. Nucl Med Commun 1988; 9(12): 973-85.
6. Piepsz A, Dobbeleir A, Ham HR. Effect of background correction on separate Technetium-99m-
DTPA renal clearance. J Nucl Med 1990; 31(4): 430-435.
7. Martel AL, Tindal WB. Background subtraction in
region: a comparison of methods. Nucl Med Commun 1994; 15(8): 636-42.
8. Lawson RS. Application of mathematical methods in dynamic nuclear medicine studies. Phys Med
Biol 1999; 44(4): R57-98.
9. Gjedde A. High- and low-affinity transport of D-glucose from blood to brain. J Neurochem 1981;
36(4): 1463-71.
10. Rutland MD. A single injection technique for subtraction of blood background in
renograms. Br J Radiol 1979; 52(2): 134-7.
11. Inoue Y, Ohtake T, Homma Y, Yoshikawa K, Nishikawa J, Sasaki Y. Evaluation of glomerular filtration
rate by camera-based method in both children and adults. J Nucl Med 1998; 39(10): 1784-8.
12. Middleton GW, Thomson WH, Davies IH, Morgan A. A multiple regression analysis for accurate
background subtraction in 99mTc-DTPA renography. J Nucl Med 1989; 10(5): 315-324.
13. Gjedde A. Origins of the Patlak plot. Nucl Med Commun 1995; 16(11): 979-80.
14. Rutland MD. A comprehensive analysis of renal DTPA studies. I. Theory and normal values. Nucl
Med Commun 1985; 6(1): 11-20.
15. Bell SD, Peters AM. Extravascular chest wall Technetium-99m diethylene triamine penta-acetic acid:
implications for the measurement of renal function during renography. Eur J Nucl Med 1991; 18(2):
87-90.
99m
Tc-DTPA renography using multiple background
131
I-hippuran
GSPant\Newbook\Final-2008\27-chp\430
Deconvolution Analysis
Tc DTPA Tc MAG I OIH
I OIH
and Renal Transit Time Parameters
H. Rajabi and G.S. Pant
The fast progress in computer technology has made the science of medical imaging a
real diagnostic tool for human diseases. Nuclear medicine is one of the imaging modalities,
which has been utilizing the computer technology in image acquisition, processing and
quantitation. Quantitative measurement of image data has become an easy and routine task
in nuclear medicine investigations. The modern high speed computer systems have created
opportunities to use very sophisticated and lengthy procedure for better and objective
evaluation of image data.
The dynamic renal radionuclide study (renography) is one of the most important
investigations in today’s clinical nuclear medicine. Though the use of computer has made
dramatic changes in acquisition and processing of the data, the interpretation of the result
is still rather subjective.
In renography the patient is positioned posteriorly in front of the camera collimator face
so that both kidneys are covered within the useful field of view of the detector. The
99 99 131
radiopharmaceutical
intravenously and data are acquired in the form of sequential digital images. The images are
stored as a matrix of binary digits in the computer memory and can easily be retrieved and
displayed on a monitor. The kidney boundaries are defined with the help of special software.
The values of all picture-elements (pixel counts) over the kidney regions (region of interest)
are added up in each and every serial image and are put in a one dimensional array. This
array represents the change in concentration of radiopharmaceutical in the kidney with
respect to time (activity versus time). The illustration of the array (time activity curve) is
termed as a renogram and the process is called renography.
m m
, 3,
or
123
is administered
Renography is now a well established, simple, rapid and non-invasive method for
evaluation of relative (split) kidney function. The object of renography is to study the transit
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