Добавил:
Sekretar
kiopkiopkiop18@yandex.ru
t.me/Prokururor I Вовсе не секретарь, но почту проверяю
Опубликованный материал нарушает ваши авторские права? Сообщите нам.
Вуз:
Предмет:
Файл:Ординатура / Хирургия / Библиотека им академика М.И. Перельмана / Книга_5545_Библиотеки_им_академика_М_И_Перельмана.pdf
Digital Computer inNuclear
Medicine
Digital computers were introduced in nuclear medicine practice in the mid-1960s,
but did not become an integral part in both imaging and nonimaging applications
until the mid-1970s. In imaging modalities, the computers are used to quantify the
distribution of radiopharmaceuticals in an object both spatially and temporally.
Both data acquisition and image processing in scintigraphy are accomplished by
digital computers. In nonimaging applications, patient scheduling, archiving, inventory of supplies, management of budget, record keeping, and health physics are just
a few examples of what is accomplished with the help of digital computers.
Computational capabilities have advanced tremendously over the years and are still
evolving, and the utility of a computer is limited only by the limitations of hardware
and software.
11
11.1 Basics ofaComputer
The basic elements of a computer are a central processing unit (CPU), main memory, external storage and input/output (I/O) devices, which are connected to one
another by pathways called buses. The main memory stores all program instructions
and acquired data, while the CPU executes all instructions given in a program.
External storage includes oppy disks, CD-ROMs, DVD-ROMs, and hard drives.
I/O devices include peripherals, such as keyboards, mice, video monitors, and printers, whose functions are to communicate with the computer for input of the acquired
data and output of the processed data. A typical setup of a computer is illustrated in
Fig.11.1.
The signals, i.e., electrical pulses from a scintillation camera, are obtained in
analog form and are digitized by the digital computers for further processing and
storage. Digital computers operate with binary numbers using only two digits, 0 and
1, as opposed to 10 digits 0–9in the decimal system. The basic unit of the binary
system is a bit (binary digit) that is either 0 or 1. The binary numbers are expressed
© The Author(s), under exclusive license to Springer Science+Business Media, LLC,
part of Springer Nature 2025
G. B. Saha, Physics and Radiobiology of Nuclear Medicine,
https://doi.org/10.1007/978-1-0716-4816-2_11
155
156
Video
monitor
Video
interface
Main Computer
Memory
Bus (Data & Control signals)
11 Digital Computer inNuclear Medicine
Floppy
Hard drive
CD-ROM
Laser disk
CPU
I/O
interface
Interface
Network
Fig. 11.1 Basic components of a computer
Serial
interface
Keyboard
mouse
Parallel
interface
Printer
by placing 0’s and 1’s in a row, e.g., 10101, which are equal to a sum of a series of
powers of two, as opposed to decimal numbers that are expressed in powers of 10.
Thus, the binary number 10101 (1×24+0×23+1×22+0×21+1×20) is equal
to the decimal number 21, which is given as 2×101+1×100 in the decimal system.
The bits, 1 and 0, are represented by the “on” or “off” states of many transistor
components present in the computer memory. A two-bit number can be expressed in
22, or four, ways (00, 01, 10, 11) corresponding to decimal numbers, 0, 1, 2, 3; a
three-bit number can be expressed in 23, or eight, ways (000, 001, 010, 011, 100,
101, 110, 111) corresponding to decimal numbers 0, 1, 2,…7, and an n-bit number
can be expressed in 2n ways corresponding to decimal numbers from 0 to 2n−1. In
computer nomenclature, a byte of memory is equal to eight bits that can store up to
28, i.e., 0–255, units of information. Similarly, a word of memory consists of 16 bits
or two bytes and can store up to 216, i.e., 0–65,535, units of information. In newer
computers, a word can consist of 32 or 64 bits, allowing more counts to be stored
in memory.
11.1.1 Central Processing Unit
The CPU, also called the microprocessor, performs all control, logic, and arithmetic
operations in a computer. A computer program is a set of sequential instructions for
the computer to perform with essential data inserted whenever appropriate. The
CPU retrieves the instructions and data from memory storage, executes the instructions sequentially, and displays or stores the results in appropriate locations. Transfer
11.1 Basics of a Computer
157
of data from one location to another is performed by the CPU using buses, which
are essentially a set of electrical connections.
How fast a program is executed depends on the speed of the computer operation,
which increases with the faster electrical components of the CPU.The efciency of
the computer operation is further increased by using parallel transfer of data (where
many transfers are performed simultaneously) rather than serial transfer (where
only one transfer is carried out at a time). Many CPUs are connected in parallel in
GPUs (graphic processing unit) in the memory of the computer to increase its speed
and capacity.
11.1.2 Computer Memory
The memory of a computer is a section assigned for temporary storage of data during the operation of a program. The program instructions and processed data are all
stored in the computer memory with the help of the CPU.When the CPU sends data
to the memory, it writes the data into the memory. If the CPU retrieves data from the
memory, it is then said to read the data from the memory. The memory can be of two
types: random access memory (RAM) and read-only memory (ROM). RAM has the
advantage of both write and read capacity; however, the data stored in it is lost when
the computer is shutoff or the electrical power is lost. With larger RAMs, computation time becomes shorter. Built into the CPU is another smaller, temporary memory called cache memory, to store frequently used data and instructions to speed up
access. On the other hand, data stored in ROMs such as CD-ROMs, DVD-ROMs,
etc. cannot be erased by electrical shutdown or computer shutoff.
11.1.3 External Storage Device
Floppy disks, hard disk drives (HDD), solid state drive (SDD), CD-ROMs, DVDROMs, magnetic tapes, and optical (laser) disks are varieties of external storage
devices that are commonly used for the storage of programs and data. Each of them
has variable storage space. In the past, hard drives were installed in virtually all
personal computers for internal storage of programs and data. Currently these are
being replaced with SSD for better efciency in read/write processes. Network
servers can be used for the storage of massive data, which can be shared by many
authorized individuals.
Floppy disks are commonly used for storing data externally as backup copies,
although in some applications programs and data can be stored for input into the
computer for execution. While internal or external hard drives have the storage
capacity of hundreds of gigabytes, oppy disks can only store up to a few megabytes and are getting out of use. Currently, CD-ROMs are available with capacities
of 650–700MB and DVD-ROMs with 4.7–9GB.Magnetic tapes and laser optical
disks have large storage space in compact form and can be utilized primarily for the
archiving of patient data that can be retrieved for future reference.
158
11 Digital Computer inNuclear Medicine
However, the use of CD-ROM or DVD-ROM are outdated except in personal
computers due to huge demand for storage of data by enterprises and cloud storage
is becoming the preferred choice. Cloud storage has added a new dimension to storage technology providing the scope of remotely storing a massive amount of data
for a long term. Data centers have been established for this purpose by large enterprises like Google, Amazon, Microsoft and they charge a fee for storage. Access and
retrieval of data is done via the internet. Since articial intelligence (AI) needs a
massive amount of data and hence the large storage, cloud storage is an ideal solution to meet the demand of AI.Also for AI usage, high-performance SSDs and inmemory storage (RAM) are quite popular.
11.1.4 Input/Output Device
Input/output (I/O) devices are essential for input of the initial data and for output of
the processed data. Input and output of data are carried out by the use of acquisition
and video interfaces via serial or parallel buses. The keyboard and the mouse are the
most common input devices used in computers, although joysticks, light pens, and
trackballs are occasionally used as input devices. While the keyboard is essential for
the input of alphanumeric data such as patient identication, date, time, and operator’s name, the mouse and trackballs are used to select items from the menu. Light
pens, a mouse, and touch screens are often used for the selection of regions of interest (ROI) in an image.
Common output devices include display screens (video monitors) for texts,
images, or graphics, and printers for printing. Display screens normally have a capability of a gray scale or a color scale for comparison between the intensities or
amplitudes of different regions of the image.
11.1.5 Operation ofaComputer
A computer operates according to instructions provided by an operator. These
instructions are given in the form of one or more programs. A collection of programs is called the software, which is developed by specialists according to the
specic needs for a project. The most essential program for the operation of a computer is the so-called operating system (OS) such as Windows, Unix, and Linux.
The utility of the OS is to facilitate communication the between the computer and
operator’s instructions. The operating system transfers the program instructions
from the input device to the memory, commands the CPU to carry out the specic
instruction, and returns the data to the output devices. Other utilities of this system
include le transfer from one location to another, storing data in the external storage
device, and displaying the data.
Data must be provided as input to the computer for processing, and in nuclear
medicine they are available in the form of counts or voltage pulses obtained from
scintigraphic studies. Data are processed according to instructions in the software
11.1 Basics of a Computer
program, and the processed data are then stored in computer memory or external
storage spaces or displayed on video monitors. The time to complete a task by the
computer depends on a number of factors, such as the speed of the CPU, the size of
the RAM, serial or parallel processing of data, and the data transfer rates of the I/O
devices. The faster CPU, the larger size of RAM, and the parallel buses provide
speedy computation.
159
11.1.6 Digitization ofAnalog Data
In nuclear medicine, signals from a gamma camera are acquired in analog form,
which are digitized before storing and further processing by the computer.
Conversion of analog signals to discrete digital values is performed by the socalled analog-to-digital converters (ADCs) and the process is called
digitization.
While analog signals are continuous in time, digital signals consist of a xed
number of bits produced by the ADC by sampling a selected number of time points
in the analog signal. ADCs are available as 8-, 10-, 12-, or 16-bit, depending on the
number of bits they produce in the digital signal from the analog signal. While the
analog signals can be distorted by the electronic noise, there is some inherent loss
of signal information as a result of digitization, i.e., due to different time-point
selections during the analog-to-digital conversion. This arises from the fact that
there is a likelihood of a small fraction of the signal being lost during the conversion
of a continuous analog signal to discrete digital values. However, higher bit ADCs
minimize this loss by producing a large number of bits from each analog signal. The
faster ADCs can handle higher count rates. The slower ADCs increase the dead time
of the system and hence are good for low count rates only.
11.1.7 Digital-to-Analog Conversion
For video displays, data must be in the analog form, and therefore digitized data
must be converted back to analog data. This is performed by units, called the
digital- to- analog converters (DACs), similar to the ADCs. DACs are connected to
the computer via video interface cards, and the speed of digital-to-analog conversion depends on the speed of various electrical components included in its
operation.
11.1.8 Digital Image
Digital images are characterized by two quantities: matrix size and pixel depth. The
computer memory approximates the area of the detector in a gamma camera as a
square matrix of a denite size that can range from 32× 32 to 1024 ×1024 with
1024 (1K) to 1,048,576 (1M) picture elements, called pixels, respectively. The size
160
d zNFOV/
< /3
11 Digital Computer inNuclear Medicine
of a matrix is selected by the operator, depending on the type of task to be performed, and is approximated to the eld of view (FOV). Each pixel corresponds to
a specic location in the detector. As discussed in Chap. 9, the X- and Y-pulses are
obtained in the analog form from the photomultiplier (PM) tube, which originates
from the interaction of γ-rays in the detector. The X- and Y-analog pulses are digitized by the ADC and stored in the appropriate pixel of the matrix. How many
counts can be stored in a pixel depends on the depth of the pixel, which is represented by a byte or a word. Thus, a 1-byte pixel could record up to 28, or 256, events,
whereas a 1-word pixel could store up to 216, or 65,536, events.
The pixel size, which depends on the choice of the matrix size for a study, is an
important factor that affects the spatial resolution of a digital image. The eld of
view is approximated to the matrix size; therefore, the pixel size is calculated by
dividing the FOV by the number of pixels across the matrix. Thus, if an image of
250×250mm FOV is obtained in a matrix of 128×128 mm, the pixel size would
be 250/128≈2mm. If the matrix size is changed to 64× 64, then the pixel size
would be ~4mm. Often, a zoom factor is applied during data acquisition to improve
spatial resolution because it reduces the pixel size. Overall, the pixel size d can be
calculated as
(11.1)
where z is the zoom factor (1.2, 2.0, etc.) and N is the number of pixels across the
matrix. The use of a zoom factor of, say, 2, reduces the pixel size by half, improving
the spatial resolution, but counts per pixel are reduced, thus increasing the noise on
the image (see later).
The choice of pixel size and zoom factor is limited by the spatial resolution of the
imaging device, particularly in tomographic systems. Ideally, the pixel size should
be less than 1/3 of the expected spatial resolution of the SPECT system, measured
at the center of rotation. That is,
d FWHM
(11.2)
where FWHM is the full width at half maximum of the line spread function of the
imaging system. If the expected system resolution is 12.9mm, then the pixel size in
the matrix should be less than 4.3mm. Pixel size larger than this limit would degrade
the image.
For a typical SPECT gamma camera, the FOV size is 400–500mm across and
the spatial resolution is of the order of 12mm. Thus, the pixel size in a 64×64
matrix is 400/64 or 500/64=6.25 or 7mm, which is nearly equal to or less than
the 1/3 of the spatial resolution of the SPECT system. Thus, a 64× 64 matrix
should be good enough for most SPECT imaging. Using a 128×128 matrix (pixel
size is 3.13 mm, which is much less than 1/3 of the system resolution) would
improve the spatial resolution signicantly. However, as mentioned before, the
counts in each pixel would be reduced by 1/4, as the total counts are distributed
over four times the pixels, compared to a 64×64 matrix. Thus, the noise increases
in the image, and so the signal-to-noise ratio decreases, causing degradation in
image contrast.
11.2 Application ofComputer inNuclear Medicine
161
11.2 Application ofComputer inNuclear Medicine
11.2.1 Digital Data Acquisition
The X- and Y-signals obtained in scintigraphic studies in nuclear medicine are digitized by ADCs in the computer and stored in one of two ways: (a) frame mode and
(b) list mode. In both modes, a technique of magnication or zooming can be
applied, whereby the pixel size is decreased by a zoom factor. Zoom factors typically vary from 1 to 4in increments of 0.25.
Data acquisition in the frame mode is the most common practice in nuclear medicine and widely used in static, gated, dynamic, and single-photon emission computed tomography (SPECT) studies. In this mode, a matrix is chosen that
approximates the entire area of the detector so that a position (X, Y) in the detector
corresponds to a pixel position in the matrix. Digitized signals (X, Y) are stored in
the corresponding (X, Y) positions (pixel) of the matrix of choice in the computer.
Every time a new X, Y signal arrives, it is added to the (X, Y) pixel (Fig.11.2a). In
this mode, one must specify the size and depth of the matrix, the number of frames
per study, and the duration of collection of data per frame or total counts to be collected. Data acquisition continues until a preselected time or total count is reached.
This mode provides instant images for storage and display.
In the list mode, digitized X- and Y-signals are coded with “time marks” as they
are received in sequence in time, and are stored as individual events in the order
they occur (Fig.11.2b). After the data acquisition is completed, the data can be
sorted to form images in a variety of ways to suit a specic need. Data can be
manipulated by changing the matrix size and the time of acquisition per frame.
Also, physiologic markers, such as the start of a cardiac cycle (e.g., the start of the
R-wave) in the gated cardiac studies, can be incorporated in the list mode acquisition. Since the data are listed sequentially without overlapping each other, the bad
signals from an arrhythmic cardiac cycle can be discarded, as found appropriate, in
the postacquisition reformatting. Although the list mode acquisition provides wide
exibility, its major disadvantages are larger memory space and longer processing
time required, and unavailability of images during or immediately after the completion of the study.
11.2.2 Static Study
A static study is the collection of data in one view of a region of interest in an object
for a preset time or preset total counts. Data are acquired in the frame mode, and
normally, the matrix size is specied before starting the study. The choice of a
matrix size depends on the eld of view of the imaging system and the pixel size to
give the desired image resolution. For all practical purposes, a pixel size of 2–3mm
is considered appropriate for good image resolution. Thus, for large FOV scintillation cameras (>400mm), one would need a 256×256 matrix to obtain the above
pixel size. Because of the high count densities in static views, data acquisition in
162
Detector
a
-ray interaction
b
Detector
Y-signal
X-signal
11 Digital Computer inNuclear Medicine
Digitized
Y-signal
ADC
Y-signal
X-signal
ADC
Dig
Y-s
X-s
X
0
Y
0
X-signal
clock
-ray interaction
tim
t
0
X
m
t
1
X
t
2
X
Fig. 11.2 Data acquisition in the frame mode and the list mode
byte mode may overow in individual pixels, and, therefore, the word mode is usually employed.
Digital images essentially represent the count density in regions of interest in an
object. How many counts should be acquired in an image? It depends on how small
a region in an image is to be identied and its apparent contrast with the surrounding
background. Large and high-contrast objects are easily detectable at low count densities, whereas small and low-contrast objects are difcult to delineate from the
statistical noise. Count density should be optimum for desirable contrast.
t
0
Y
1
2
3
1
t
1
Y
2
t
2
X
3
11.2.3 Dynamic Study
In dynamic studies, a series of images are collected and each image (frame) is
acquired over a certain period of time selected by the operator. While the patient’s
E
AA
d
100
11.2 Application ofComputer inNuclear Medicine
163
position cannot be changed during the image acquisition, the matrix size and the
frame rate (time of acquisition) can be changed. The frame rate can vary from many
frames per second to a single frame per hour. The acquisition of image data is buffered such that while one frame is being collected, the previous frame is stored in the
external storage device (e.g., disk). Data in dynamic studies can be collected in a
sequence of several phases, e.g., 1frame per second for 1min, then 1frame/min for
5min, followed by 1frame/10 min for 2h. The choice of frame rate for a given
study depends on the kinetics of the radiotracer through the organ of interest.
The common matrix size used in dynamic studies is 64 × 64 or 128 × 128,
although some loss of spatial resolution is expected with these matrices. However,
256×256 or larger matrices require a larger memory size. Since counts collected
per frame are low in number, the data are collected in byte mode, which obviates the
need for a large memory space, and normally does not allow pixel counts to exceed
255 with little chance of counts overow.
11.2.4 Gated Study
The gated study was introduced in the mid-1970s to determine the ejection fraction
of the heart by acquiring two images, one at end diastole and the other at end systole. It was later substituted by continuous acquisition of data in multiple sequential
images (multiple gated acquisition, MUGA) in each cardiac cycle by gating between
successive cycles.
In the MUGA study, the data are acquired in synchronization with the R-wave of
the cardiac cycle. The normal heartbeat is about 1beat/s, and the R-R interval is
therefore about 1s, i.e., 1000ms. First, the R-R interval is divided into several segments or frames (16–32 segments), depending on the number of frames one chooses
to obtain. For example, with a choice of 20 frames in the R-R interval, each frame
will be 50ms long. In actual data collection, rst the counts are acquired in frame 1
for 50ms, followed by the collection of counts in frame 2 for another 50ms, and so
on. After completion of counting in all 20 frames, a new R-wave is detected, and the
above sequence of counting continues until sufcient counts have been accumulated
in each frame. Assuming a count rate of 10,000–20,000 counts/s in a typical cardiac
study, each 50-ms frame would accumulate counts of the order of 500–1000.
Normally, 64×64 or larger matrices are used for the gated study. A typical plot of
the time-activity curve (TAC) is shown in Fig.11.3, from which the ejection fraction
(EF) of the heart is calculated as
ds
A
(11.3)
where A
F%
and As are the end-diastolic and end-systolic activities.
d
The heartbeat must be regular for the above method to work well. If the heartbeat
is irregular, such as in cardiac arrhythmia, the R-R interval is sufciently altered and
the data becomes corrupted from R-wave to R-wave. Modern acquisition programs
164
Fig. 11.3 The timeactivity curve obtained in a
gated study using segments
of a QRS cardiac cycle
11 Digital Computer inNuclear Medicine
have been devised to reject the bad heartbeat cycle. Using the list mode acquisition,
bad heart beat data can be sorted out and rejected in postacquisition reformatting.
SPECT is routinely used in nuclear medicine for various organ imaging, particularly cardiac imaging. The gated SPECT study is also employed for the cardiac
studies using the typical 20 frames in each R-R interval.
11.2.5 Reconstruction ofImage
In planar imaging, the acquired data are displayed in a two-dimensional image without further processing. In tomographic imaging, data are acquired in different angular projections around the patient. The data of each projection are processed further
using the methods described in Chap. 12 to reconstruct the images at different
depths of the patient’s organ in 3-D directions. All reconstruction methods are
accomplished by the use of modern computers.
11.2.6 Fusion andSubtraction ofImage
It has been a common practice to superimpose image data from one modality onto
another for better delineation of lesions on the images. For example, computed
tomography (CT) or magnetic resonance imaging (MRI) anatomical images of an
organ are fused with the corresponding functional images obtained by SPECT or
PET to match the functional abnormalities with the anatomical defects. Computers
are well utilized to perform these superimpositions of images.
Another important utility of the computer is the subtraction of background activity from an image or one set of images from another set. An example of the latter is
to subtract the interictal images obtained in epilepsy patients using
99m
Tc-ethyl