PROTECTION 389
Point C: Exposure -HVLs is at 1 m, which we will assume is the pa
0.14 R/wk-0 tient's surface. This is a reasonably accurate
0.07 -1 assumption because most films are taken
0.35 -2 from a distance of 40 in. We will estimate
an average field size of 14 x 14 in. (196
0.17 -3
0.10 -approx. 3.3 HVLs in.2). There are approximately 6.5 cm2/in.2
(2.54 x 2.54 em), so our field will be 1270
0.085 -4 cm2 (6.5 cm2/in.2 x 196 in.2). We will also
Lead: 0.27 x 3.3 = 0.89 mm assume one right angle scattering:
Concrete: 0.8 x 3.3 = 2.6 in.
The barrier thicknesses are different for EE8 = W· · T · 1/d2 • 1/1000 · F/400
the two methods (tables and HVLs), but E8 = 1.4 · 400 · 1 · 1/22 · 1/1000 · 1270/400
this is not important because our purpose
here is to explain principles. Also, the dif Es = 0.45 R/wk
ferences emphasize the fact that radiation
protection is not a precise science. Using the HVL method to reduce this ex
Secondary Barriers. Wall A protects a posure to the permissible level of 0.1 R/wk:
radiologist's office and will require a sec
ondary barrier. It is a controlled area with The HVL at 125 kVp is 0.27 mm
of lead and 0.8 inch of concrete.
a maximum permissible exposure of 0.1 R/
Point A: Exposure -HVLs
wk, and because it is a controlled area, its
occupancy factor is l . For convenience, we 0.45 R/wk-0
will calculate the exposures for both leak
0.225 -1
age and scatter radiation at a distance of 2
m as shown in Figure 21-5. 0.113 -2
Precalculated Tables. Table 21-12 gives 0.10 -2.3 HVLs
0.056 -3
both primary and secondary barrier re
quirements. We simply multiply the work Lead: 0.27 x 2.3 = 0.62 mm
Concrete: 0.8 x 2.3 = 1.8 in.
load (W), use (U), and occupancy (T) fac
tors (WUT), and find the barrier thickness Half-Value Layer Methodfor Leakage Ra
for the appropriate distance:
diation. We will assume that 6 rnA is the
W · U T = mA · min/wk
400 · 1 = 400 mA · min/wk maximum continuous exposure the tube
will tolerate without ove.£_heating. To de
termine the R/mA · min (EL), we divide the
0.1 R/hour permissible leakage exposure
by 60 min/hour and 6 rnA · min/min:
Converting the distance of 2 m into feet, (0.1 + 60) + 6 = 0.00028 RimA · min
we get a little over 6 ft. At 125 kVp, the
The weekly leakage exposure at point A
secondary barrier thickness for a con will be
trolled area is 0.55 mm of lead for 5 ft and EL = EL . w . T . 1/d2
0.40 mm for 7ft. We will need a thickness
between these two, say 0.5 mm, and this v,;zEL = 0.00028 · 400 · 1 · = 0.028 R/wk
would handle both the leakage and scatter An exposure of 0.028 R/wk is less than the
radiation. In other words, we would be fin permissible level for a controlled area, so
no barrier is required for leakage radia
ished. But we will go on to make the cal tion. The total secondary barrier would be
culations for scatter and leakage radiation the 0.62 mm of lead required for scatter
separately using half-value layers. radiation.
Half-Value Layer Method for Scatter Ra SHIELDING REQUIREMENTS FOR
RADIOGRAPHIC FILM
diation. The workload will be the same as
A secondary objective of radiation pro
it was for the primary barrier: 400 rnA · tection is "to prevent damage or impair-
min/wk at 125 kVp. The occupancy factor
is 1 because it is a controlled area. The
exposure is 1.4 R/mA · min. This exposure
390 PROTECTION
ment of function of radio-sensitive film or "workload"; in the amount of time that the
equipment."4 We will limit our discussion beam is directed at a particular area, called
the "use factor"; and in the amount of time
to x-ray film. "An exposure of 1 milliroent that an area is occupied, the "occupancy
gen (mR) over a portion of a film may pro factor." Distance attenuates the beam by
duce undesirable shadows."4 For protec the familiar inverse square law. If time and
distance fail to bring exposures to permis
tion purposes, an exposure of 0.2 mR is sible levels, then the third method, a bar
rier, is required. Barriers are usually con
considered safe . This is the maximum per structed of either sheet lead or concrete,
missible exposure that the film should re depending on which is cheaper.
ceive during its entire storage life.
Protection must be provided against
Protective barrier calculations for film three types of radiation: the primary, or
are exactly the same as those for controlled useful beam; scatter radiation; and leakage
and uncontrolled areas, with one excep radiation. The latter two together are
tion. The permissible exposure for the film called "stray" radiation. If the useful beam
varies with storage life. For one week of can be directed at a wall, the wall must be
storage, the customary time interval for a primary barrier. If the useful beam can
protection calculations, the permissible not be directed at a wall, it is a secondary
barrier and need only protect from stray
level is 0.2 mR. For monthly storage (4 radiation. Primary barriers serve a dual
function as both primary and secondary
weeks), the film is only permitted a weekly barriers.
exposure of 0.05 mR (0.2 mR .;- 4 weeks) . The exposure from the primary beam
can be calculated by multiplying the work
The number of HVLs of lead and concrete load, use factor, occupancy factor, and in
must be sufficient to bring exposures to the verse square of the distance by an R output
appropriate level. Barrier thicknesses can
also be determined from a table similar to at 1 m for each rnA of workload. If this
Table 21-12. exposure, expressed in R/wk, exceeds per
missible levels, then a barrier is required.
SUMMARY Barrier thicknesses can be calculated in two
Man has lived with, and tolerated, nat ways: 1) with precalculated tables or 2) with
ural radiation since the beginning of time.
Evidence is accumulating, however, that HVLs of lead or concrete. A secondary bar
small doses of radiation can cause both mu rier protects against stray radiation and is
tations and neoplasms. No one knows just only required when the useful beam cannot
how much radiation is tolerable. The ef be directed at a particular wall. Secondary
fective dose equivalent (HE) attempts to re barriers protect against scatter and leakage
late exposure to risk. The National Council radiation. For scatter radiation, the expo
on Radiation Protection's recommenda sure is assumed to be attenuated by a factor
tions are designed to protect both the gen
eral public and radiation worker. Many of of 1000 (i.e., reduced to 0.001 at a distance
the recommendations have been turned of 1 m for each right angle scattering), and
into laws. The most important recommen
dations are those involving maximum per it is also assumed that its quality does not
change. A correction factor is added for
missible doses, which are currently 5 rem/
year for a radiation worker and 0.5 rem/ field size and the use factor is always 1,
year for the occasionally exposed individ because scatter and leakage radiation go in
ual. Three parameters are available to re all directions. Otherwise, the calculation is
duce radiation exposures: time, distance, the same as for the primary beam. The R
and barriers. Time plays its role in three
ways: in the amount of time that the ma output at 1 m for each rnA · min of work
chine is turned "on" at a particular current,
expressed as rnA · min/wk, and called the load is multiplied by the workload, occu-
PROTECTION 391
pancy factor, and inverse square of the dis REFERENCES
tance, a conversion factor for field size, and
0.001 for a right angle scattering. l. Buschong, S.C.: The Development of Radiation
Protection in Diagnostic Radiology. Cleveland,
The exposure from leakage is based on
CRC Press, 1973.
the law that the maximum radiation level 2. Dalrymple, G.V., Gaulden, M.E., Kollmorgen,
at 1 m is 0.1 R/hour, or 0.00167 R/min.
G.M., and V ogel, H.G., Jr.: Medical Radiation
This exposure must be converted to RimA Biology. Philadelphia. W.B. Saunders, 1973.
3. Hall, E.J.: Radiobiology for the Radiologist. Hag
· min. The maximum operating rnA for erstown, MD, Harper & Row, 1973.
continuous exposure at maximum kVp is 4. Medical X-Ray and Gamma-Ray Protection for
Energies up to 10 MeV-Structural Shielding De
determined from anode heat rating charts,
and it is usually about 5 rnA. The conver sign and Evaluation. Washington, D.C., National
sion to RimA · min is accomplished by di Council on Radiation Protection and Measure
viding the 0.00167 R/min by the maximum ments, NCRP Report No. 49, 1976.
continuous rnA. This exposure at 1 m is 5. Ionizing Radiation Exposure of the Population
multiplied by the occupancy factor and in of the United States. National Council on Radi
ation Protection and Measurements, 7910 Wood
verse square of distance to determine the mont Ave, Bethesda, MD 28814. NCRP Report
No. 93, 1987.
leakage exposure at the point in question. 6. Pizzarello, D.J., and Witcofski, R.L.: Basic Radia
If the barrier requirements for scatter and tion Biology. 2nd Ed. Philadelphia, Lea &
leakage differ by more than 3 HVLs, the Febiger, 1975 .
larger suffices; if less than 3 HVLs, add 1 7. Schultz, R.J.: Primer of Radiation Protection. 2nd
HVL to the larger. Ed. New York, GAF Corporation. X-Ray Prod
ucts Division, 1969.
8. Recommendations on Limits for Exposure to
Ionizing Radiation. National Council on Radia
tion Protection and Measurements, 7910 Wood
mont Ave, Bethesda, MD 28814. NCRP Report
No. 91, 1987.
CHAPTER
22 Digital Radiography
The field of digital radiography has de to be a fairly conventional fluoroscopic
veloped to its present state by the imple unit, with an added digital image process
mentation of largely conventional radio ing unit.
graphic techniques using digital electronic
apparatus. No unfamiliar basic physics Fluoroscopy Unit
principles need to be introduced in de Figure 22-1 shows a fluoroscopic unit
scribing the operation of digital radio
graphic systems currently in use. Most suitable for digital applications, and obvi
techniques (including intravenous injec ously it is only the block diagram of a con
tion for arteriography) have already been ventional unit with several minor addi
used with film-screen systems, so there is tions. Digital applications, however, place
considerable common ground between some special demands on a fluoroscopy
digital radiography and the more familiar unit.
film-screen techniques. We will emphasize
these sometimes striking similarities be Mask Subtraction Application. For in
tween digital radiography and more con stance, consider intravenous injection an-
ventional radiography. In addition, the dis
cussion of digital techniques offers an 0 Light Diaphragm
opportunity to demonstrate clearly some
fundamental limits on radiographic imag c�======AP = T=IE=N=T====��
ing systems. The main topic remaining is
an extension of the understanding of com
puter image manipulations as discussed for
computed tomography (CT), without hav
ing to consider the complicated reconstruc
tion mathematics. Finally, because there
are so many promising areas for develop
ment in this field, we will take a brief look
at some current research.
A DIGITAL FLUOROSCOPY SYSTEM Figure 22-1 Block diagram of a fluoroscopic
unit
The most common type of digital radi
ography system at present is digital fluo
roscopy (DF). Such a system can be used to
demonstrate most digital radiography
principles, so we will begin with a general
system description that will be of subse
quent use. At the block diagram level, the
design of a DF system can be considered
392
DIGITAL RADIOGRAPHY 393
giography, in which subtracted images are of higher quality than normally needed for
displayed on a 512 X 512 pixel matrix . We routine fluoroscopy.
will call this technique "mask subtraction ."
Currently it is the most commonly used X-Ray Generator and X-Ray Tube. The
technique in digital radiography, and it is principal function of the generator is to
one of the methods of performing digital provide very repeatable exposures. A
subtraction angiography. Digital subtrac small difference in the x-ray tube current
tion angiography (DSA) is the generic or kilovoltage supplied by the generator
term for any digital radiographic method for two exposures in a series will result in
of implementing subtraction angiog an improper mask subtraction of the
raphy. We will discuss several other meth images of unchanged areas of the body.
ods later. This improper subtraction may obscure
the visualization of the actual structures of
Mask subtraction is the DSA technique interest (such as opacified vessels), which
that most closely resembles film-screen an have very small subject contrast differences
giography. The patient is prepared and a on the two images. The digital image proc
catheter is placed under fluoroscopic con essing unit generally has some control over
trol. The patient is then injected, either in the generator. In the case of mask subtrac
travenously or intra-arterially, with an tion, this control can be limited to the ini
x-ray contrast material that contains a high tiation and termination of the individual
atomic number element such as iodine . In exposures in a series. The generator con
dividual x-ray exposures are made at a typ nections required for this type of control
ical rate of one exposure/second or more. are usually rather simple, and are similar
The exposure series begins before the con to those needed for rapid film changers.
trast material is expected to arrive in the
vessels of interest, and extends past the An x-ray tube similar in design to one
time when the contrast material is expected that might be used in film angiography is
to have cleared the vessels. Each individual appropriate for most DF applications. The
pulsed exposure forms a single image primary beam magnification and x-ray
within the series. A precontrast mask and tube loading parameters in typical digital
a contrast-containing image are roughly angiographic procedures are quite similar
equivalent to an angiographic film pair. to those encountered in film angiographic
The subtraction of the mask image from procedures, so specially designed x-ray
the contrast-containing image is the basis tubes are currently unnecessary. In the spe
of this mask subtraction technique. If a pe cific application of the mask subtraction ex
ripheral venous injection is used, the con ample, a 512- X 512-pixel image matrix
trast material reaching the arteries is so was specified. This places resolution limi
diluted that only small attenuation differ tations on the final image that make the
ences- exist between contrast- and non-con use of very small focal spots (such as those
trast-filled arteries. The x-ray exposures used in magnification radiography) unnec
needed for producing acceptable images in essary. We will discuss these resolution lim
this situation are similar to those used for itations shortly. In fact, very small focal
serial photospot camera images, or per spots are undesirable for this application
haps even higher. because of the x-ray tube heat loading re
quirements.
A good x-ray generator and x-ray tube
of conventional design are probably ade Image Intensifier. A high quality image
quate for the mask subtraction procedure, intensifier is needed for digital applica
but an excellent image intensifier is re tions, but all the necessary image intensi
quired, and the television system must be fier (II) characteristics are also desirable for
some more conventional applications . A
very high contrast ratio is needed, which
394 DIGITAL RADIOGRAPHY
mandates use of a recently designed II. In will collect a large fraction of the light from
the case of our 512- X 512-pixel matrix, the II output phosphor for fluoroscopic
however, high spatial resolution is not images, and about 1% of that fraction for
needed for the II, so a thick input phos the serial images. In actuality, a combina
phor can be used for high x-ray detection tion of different sizes of light diaphragms
efficiency. The power supply for the II and different electronic video gains may be
must be quite stable, because small changes employed. There is also some advantage in
in accelerating potential for the electrons using a light diaphragm that is adjustable
can produce changes in the brightness gain over a range for serial exposures, because
of the II. The power supply fluctuations this increases the flexibility of the system.
are more likely to occur at radiographic
tube current levels than at fluoroscopic Television Image Chain. The second
tube current levels because of loading of component of a type not normally found
the generator. The resulting change in II in fluoroscopic systems for nondigital use
intensity might not be detectable in pho is a special TV chain, one of the most crit
tospot or cine images, but two images from ical components in the entire DF system.
a digital series may not subtract properly. The II tube absorbs a certain fraction of
the incident x-ray photons and produces a
Light Diaphragm. To this point, all com quantity of light proportional to the num
ponents have been of a type that might be ber of incident x-ray photons. The basic
found in routine use for fluoroscopy or function of the TV chain is to produce an
photospot imaging. For instance, we might electronic video signal from this light. The
have chosen a modern three-phase twelve size of this signal should be directly pro
pulse generator, angiographic x-ray tube, portional to the number of x-ray photons
and high-contrast II from those available that exit the patient. Eventually this video
for other uses. The selection of compo signal will be fed to the digital image proc
nents that would not be part of the system essing unit, where it will be digitized. At
were it not for our mask subtraction ap present, a TV camera tube with a lead ox·
plication begins with the light diaphragm. ide vidicon target (plumbicon) is favored.
A plumbicon tube of this type has low lag
The light diaphragm is used to control and has a video output that is directly pro
the amount of light from the II that portional to the light input.
reaches the TV camera tube, exactly as in
the case of changing photographic f stops. As noted in Chapter 12, a TV camera
In a typical procedure, the patient first un with high lag will produce a smeared ghost
dergoes some fluoroscopy with an x-ray that follows a rapidly moving object on the
tube current of about 2 rnA at some given TV image. A ghost is objectionable in any
kVp. Subsequently, the patient undergoes procedure. The most desirable type of TV
a serial digital procedure in which 200 rnA camera tube (all other factors being equal)
may be used to reduce quantum mottle. Let would be one in which the image on the
us choose light diaphragm sizes so that the input phosphor is completely erased dur
amount of light reaching the TV camera ing the readout of each frame. In the case
tube for a single television frame will be of images for digital subtraction, a tube
approximately the same in either the fluor with excessive lag can cause a situation in
oscopic or the serial portion of the study. which the "current" frame actually has re
If we do not make the right choice, we will sidual information that properly belongs in
either saturate the TV camera tube with the past. A TV camera tube with low lag
light during our high rnA serial exposures, is desirable, especially in dynamic studies
or we will use only a small portion of the in which rapid image changes are encoun
TV camera tube's range for display of tered.
fluoroscopic images. In this example we
Perhaps the most important property
DIGITAL RADIOGRAPHY 395
that the TV chain must possess is ex which is to change to a different x-ray ex
tremely low electronic noise. In fluoros posure and TV scanning mode.
copy at 2 to 3 rnA, there is so much quan
tum mottle in the image that relatively high The pulsed progressive readout method
electronic noise can be tolerated. As we involves two steps for obtaining a single TV
shall see later, however, the combination of frame image. First, TV camera scanning is
a much larger number of x-ray photons halted and an exposure is made. Second,
and working with subtracted images re the TV camera target is operated in a pro
quires use of a different (and expensive) gressive scan mode, which means that
TV camera tube to avoid having electronic every line is read out in order, rather than
noise obscure low-contrast structures. in a field-interlaced fashion. Now we only
need to ensure that each exposure in a se
Television Scan Modes. Another fea ries is reproducible. The exposure may be
ture that is sometimes desirable for digital of any duration up to several seconds, and
fluoroscopy is a choice of television scan all the dose is used to form the image. Be
modes. Most television systems operate in cause this mode must allow time between
an interlaced mode. In the United States, frames for the exposures (and perhaps also
each 262.5-line field is scanned in 1160 sec, for "scrubbing" any residual image off the
so that the entire 525-line frame is scanned camera target), framing rates are some
in 1/30 sec. This scan choice is adequate to what slower than in the interlaced mode.
avoid the perception of flicker, but it does There is no reason why continuous pro
have drawbacks for some digital applica gressive framing cannot be employed, but
tions. As normally employed, the TV tube the same stabilization time penalty de
scans continuously. When an x-ray expo scribed for interlaced scanning will be ap
sure begins, first the generator and all plicable.
other components must become stable,
during which time the TV system con Another method of scanning the televi
tinues to scan. In digital mask subtraction sion target that would be unsatisfactory for
these stabilization frames must be dis real-time visual presentation is a slow scan
carded for several reasons. For instance, mode. This method is currently being used
during the time the exposure is increasing, for implementing fairly large (1024- X
there would be no brightness in the first 1024-pixel) digital fluoroscopic matrices.
portion of the TV frame and considerable Implementing a 1024 X 1024 matrix on a
brightness in the last portion of the frame. 1050-line television system running in in
This would produce objectionable flicker terlaced mode at 30 frames per second
between the two fields of the frame and, would require an increase in the band
for most of the frame, the TV camera tube width of the television system to four times
would not be operating in its optimum that for a 525-line system (see Chap. 12 for
brightness region. Another reason for dis an explanation of television band width).
carding the early frames is the very severe If we do not insist on 30 frames per second,
demands that would be placed on all com each TV line can be scanned twice as long
ponents. Each component would have to as in the 525-line system (thus doubling
reach exactly the same operating point in horizontal resolution), and twice as many
the same amount of time for each exposure lines can be scanned (doubling vertical res
to ensure good subtraction. The net result olution) without increasing the video band
of throwing away some TV frames is that width. This limits the framing rate (7.5
the patient may be given some unnecessary frames per second) to one fourth of "real
x-ray exposure. There are a number of so time" (30 frames per second). There are
lutions to this particular problem, one of two advantages over the 30-frames-per
second approach. First, the television chain
electronics and the digitizer section can
396 DIGITAL RADIOGRAPHY
have the same band width as a 525-line images for later recall, 3) displaying digital
system, which significantly simplifies sys
images on a TV monitor and photograph
tem design. Second, at high band width,
electronic noise is significantly increased, ing these images, and 4) manipulating dig
which is avoided by slow scan. Naturally, ital images (e.g., averaging, subtracting,
the television camera tube must be inher changing contrast scales).
ently capable of higher spatial resolution
than that needed for a 525-line system. Basic Operation. A rough description of
Also, there are some sources of electronic
noise that are worse at the higher resolu the functions of the individual blocks in
tion and that are not helped by the use of Figure 22-2 seems to be in order before
slow scan techniques. discussing them individually in more de
tail. The central control computer is in
Digital Image Processor charge of all the other components of the
image processor (and, we hope, is abso
A typical digital image processor for DF lutely subservient to us). Suppose we tell
is shown in Figure 22-2. This block dia the computer to run a series of a certain
gram is a functional one, because different number of exposures and to store each
image processor units may have different image of the series in digital form for later
physical configurations. Therefore, unlike use. During the run the computer is to use
the fluoroscopic unit, we may not be able the first image as a mask and is to display
to indicate a particular component and say each subsequent image in subtracted form.
that it corresponds to a particular block of We set exposure techniques on the gen
our diagram. Nevertheless, all DF image erator and instruct the computer to begin.
processors are intended to have the same The computer informs the generator when
basic functions, and the same basic prin to start and to stop each exposure. It sets
up the digitizer (analog-to-digital con
ciples apply. Their major functions are 1) verter) to convert an entire TV frame into
a digital image, and starts the digitizer at
digitizing TV frames and processing them the appropriate time. Meanwhile, the com
into digital images, 2) storing the digital puter has instructed the arithmetic unit on
Video AID Digital Digital Display
Converter Arithmetic Image Sec tion
____ ,.. (Digitizer) Memory
Unit I
X-Ray �G :Video
Control '
Signals Computer
(Controller) EJ
I
t I
'
Digital
Disk Mul tiformat
Camera
Storage
Figure 22-2 Block diagram of a digital image processor unit
DIGITAL RADIOGRAPHY 397
what to do with the first digitized image, grammer may be required to implement
which is simply to place the image in ap the task. On the other hand, we shall see
propriate form and to store it in a partic that high calculation speeds are required
ular block of image memory. The com for even routine operations. A general pur
puter tells the digital disc where that pose computer capable of such speeds can
particular block is located in image mem be very large and expensive. It makes sense
ory, how big the image is, and when to start to have less expensive specialized machine
storing the image. Similar instructions are cretins that do very simply routine tasks at
given to the display section. the required speeds, provided that the sys
tem as a whole is able to do the entire job.
To handle the second exposure, the con New applications may not be easily imple
trol computer issues the same commands mented, however, if the system is too in
as before to all components except the ar flexible. The present trend seems to be use
ithmetic unit and display section. The ar of a flexible but not extremely fast general
ithmetic unit must handle the incoming purpose computer for control and com
digitized data, and stores this "raw" data in plex tasks, and use of a set of fairly flexible
a block of image memory that the digital subordinate units for fast or more mun
disk will access . Simultaneously, the arith dane work.
metic unit must access the previously
stored first image (the mask), subtract the Analog-to-Digital Conversion. The an
mask from the incoming second image, alog-to-digital converter (ADC) converts
and store the result in a third block of the video images from the TV chain into
image memory that the display section can digital form. Figure 22-3A is a photograph
access. The computer has already set the of a displayed video image of a skull. The
display section for contrast levels appro format is a frame consisting of 525 TV lines
priate for subtracted images and has told
the display section which block of image B -1.0
memory to show. For the third and sub
sequent exposures, the computer has no rJ>
new tasks to perform. It only has to pay rJ>
attention to coordinating the subordinate Q)
activities until the run is complete or until c: Q)
we abort the run from the generator. 0
��
Note that in our system the control com -0.5 .E
puter only tells its subordinates what to do 0> 0
and coordinates their actions, a strictly >
managerial task. As previously indicated,
the block diagram is functional rather than Q)
physical. The actual computer that is in 0>
corporated may be very primitive and with 0
out much control, so that the subordinates
operate very much in a preset fashion. E
Conversely, the computer may be quite
complex and take over most of the menial Figure 22-3 A TV frame of the image of a
tasks from the subordinates. Both ap
proaches have some merit. A complex gen skull phantom (A) and the video signal from one
eral purpose computer can be very flexible line of the frame (B)
and perform virtually any current or fu
ture task that may be required for digital
fluoroscopy. Of course, an ingenious pro-
398 DIGITAL RADIOGRAPHY
from two interlaced fields. If we consider number of line pairs that can be displayed
only one of the horizontal TV lines on a 512- X 512-pixel matrix. To define a
through the center of the image from the single pair of lines aligned along the ver
II, the electronic video signal that defines tical dimension, at least two pixels in the
the line for the monitor will resemble that horizontal dimension are required, one for
shown in Figure 22-3B. The video signal the bright line and one for the dark line of
has a voltage that varies during the scan the pair. Thus, the 512 horizontal pixels
from left to right along the line. The volt can define (at most) 256 line pairs. This
age is initially low, indicating a dark region limitation can be applied to the size of the
on the camera input face. The voltage then image represented by the matrix, which is
rises sharply in a brighter region, drops roughly the II input mode size (Fig. 22-4).
again in a darker region, and so forth. The If the II image represents about 12.5 em
size of the voltage at any point along the (about 5 in.) in diameter, then 125 mm into
scan should directly represent the number 250 line pairs gives us a limit on system
of x-ray photons that struck the corre resolution of 2 line pairs per mm, assuming
sponding point on the II input phosphor. no primary beam magnification. So, even
The time required to scan along the line with a small field of view, a 512- x 512-
from left to right is a little over 60 fLSec for pixel matrix will be expected to be the most
standard TV in this country. important limiting factor on resolution,
given reasonable focal spot sizes and pri
The only portion of the video frame that
needs to be digitized is the portion that mary beam magnifications. The limitation
contains the II image. To digitize the cen becomes more severe for larger II input
tral TV line, the digitizer notes the start of sizes. With an II operating in a 25-cm
the line, waits an appropriate amount of
time until the first point on the edge of the (about 10 in.) mode under the same con
II is expected, and then measures the volt ditions, resolution would be limited to
age. The measurement is simply a number about 1 line pair per mm at the II input
that the digitizer sends along to the waiting face. Similarly, displaying a 50-cm diame
arithmetic unit. The digitizer immediately ter image of a chest would result in maxi
grabs the next point along the line, meas mum resolution of only 0.5 line pair per
ures its voltage, and passes this second mm. Naturally, if the matrix size IS m-
number to the arithmetic unit. After all 512
points along this line have been digitized, 4 512 X 512 Pixel
the digitizer sits back and waits for the next Image
line to come along. When the digitizer has
performed the same operation on 512 ap -E 3
propriate lines of the 525 available, the en .E E
tire frame has been digitized. The video :i Q..).
image has been converted into digital form,
and the digitizer can wait for the next TV c:: a.
frame. Digitizers are seldom given awards 0 (/)
for high intelligence. 2
- ...
Matrix Size. In the above example, each :J 0
a.
television frame has the image from the II 0(/) cQ:):
digitized into a 512- X 512-pixel matrix. It Q)
0.::
is important to note that the choice of ma
trix size limits the spatial resolution that 1 1.5 2
Primary Magnification
can be achieved by the system. This is anal
ogous to matrix size in CT. Consider the Figure 22-4 Resolution limits imposed by a
512 x 512 pixel matrix
DIGITAL RADIOGRAPHY 399
creased to 1024 x 1024, the limitations im (3), 100 (4), 101 (5), 110 (6), 111 (7), 1000
posed by matrix size will not be as great, (8), 1001 (9), 1010 (10), 1011 (11), 1100
and system resolution will be potentially (12), and so forth. With one binary digit,
double. or bit, any whole number from 0 through
Binary Number System. We need to di 1 may be counted only two discrete values.
Two bits allow the representation of 00 (0),
gress for a moment to review the binary 01 (1), 10 (pronounced one-oh, not ten;
number system. Those who speculate on decimal 2), and 11 (pronounced one-one;
such things suggest that the decimal num
ber system is one inevitable counting decimal 3), a total of four discrete values.
method for beings with ten fingers, and
that a being with eight fingers (or their We note that 22 is 4. Three binary digits
equivalents) would probably have an octal allow eight discrete values, or 23• We would
number system; perhaps the argument is correctly expect that with n binary bits,
valid. But humans are beginning to use a some 2n discrete values could be counted.
binary as well as a decimal system because Most DF display units handle individual
of computers. The validity of this state pixels with eight-bit accuracy for displayed
ment can be checked easily by asking a brightness (we will discuss the brightness
bright 10-year-old. scale later). An individual pixel can there
fore have any brightness value from 0
Table 22-1 compares the binary and through 255 decimal, a total of 28 (decimal
decimal number systems. A binary (base 2) 256) possible brightness values. The bot
"digit" can assume only one of two values, tom of Table 22-1 provides an example of
rather than one of ten as for a decimal (base how to calculate the decimal value of a bi
10) digit. So, binary counting (with the dec nary number. The decimal representation
imal counterpart in parentheses) is in the of the number 26 can be interpreted to
following sequence: 0 (0), 1 (1), 10 (2), 11 mean that the value of the least significant
Table 22-1. Comparison of Number Systems
Allowed values of a single DECIMAL BINARY
digit counting sequence
0, 1' 2, 3, 4, 5, 6, 7, 8, 9 0, 1
0 0
1 1
2 10
3 11
100
4
255 11111111
256 100000000
Calculation of 1023 1111111111
decimal values
103 102 101 10o 0 00
0026 (0 X 2s) + (1 X 2•) + (1 X 23) +
(0 X 103) + (0 X 102) + (0 X 22) + (1 X 2') + (0 X 2o)
(2 X 101) + (6 X 10D) = (decimal 16 + 8 + 0 + 2 + 0)
= 0 + 0 + 20 + 6 = (decimal 26)
= 26
400 DIGITAL RADIOGRAPHY
digit (6) is multiplied by 10° (note that 1Oo Digitization Accuracy. There are many
= 1). The second significant digit (2) is different types of digitizers. The actual
multiplied by 101 (10). The third significant principles of operation of each type are
digit (not stated, but actually 0) is multi rather simple, but it does not seem worth
plied by 102 (100), and so forth. The actual while describing the operation of any of
number is the sum of the values repre them. What counts in this case is the result.
sented by each digit (0 + 0 + 20 + 6 = A comparison of analog video voltage and
26). The decimal representation of a binary digitized values is shown in Figure 22-5.
number may be calculated in the same fash The analog video indicates that a smooth
ion, except that the digits are multiplied by variation in brightness occurs from com
powers of 2 rather than by powers of 10. pletely dark at left to maximum brightness
For the binary number 011010 (pro at right. (There would actually be some ir
nounced oh-one-one-oh-one-oh), the value regularities caused by noise.) The digitized
of the least significant digit is 0 X 2o. The
value of the second digit is 1 x 21, and so values of brightness represent the output
forth. The result is 0 + 16 + 8 + 2 + 0 of a two-bit digitizer, so there are only two
= 26. binary digits of precision. The values that
the digitizer will obtain are .00 (at the left),
Digital information is any information then .01, .10, and finally .11 (at the right).
that is represented in discrete units. An Three-bit digitization would provide a
alog information is any information that stairway with smaller steps and less error,
is represented in continuous, rather than and four bits would be still better. As more
discrete, fashion. The common meaning bits of digitization are added, eventually
of the term "digital" is beginning to drift the steps become so small that the changes
toward a usage associated only with elec between steps are almost completely hid
tronics, computers, and the binary number den in the electronic noise from the video
system. We wish to use the perhaps out chain.
moded meaning, however, to indicate the
difference between analog and digital in The statistical fluctuations in the number
formation. A video signal is a:n analog volt of x-rays that strike a small area of the II
age representation of the quantity of light input screen can also be considered to be
that strikes the input face of a TV camera a source of noise, as will be discussed a little
tube. If this voltage analog of light intensity later. Noise limits the accuracy of the
has a total range between 0 and 1 V, then image, and an appropriate digitizer will
any quantity of light from zero intensity to add very little to the inaccuracy. An ap
some maximum intensity can be repre propriate digitizer will have enough bits so
sented exactly (ignoring such things as elec that noise hides the steps (typically about
tronic noise for illustration purposes). On ten bits). A very large number of bits, how-
the other hand, if a decimal digital system
with two digits is chosen to represent the .111 [7,..-··· V i d e,.-···'•-' o
amount of light, only discrete values be
tween .00 and .99 (a total of 100 values) <f) .11 0 Digital
are possible. The error caused by using dig
ital representation can be as great as 0.005. <f) .101 pL' JpL•'' ]
The 0.005 is 0.5% of the maximum value. Q)
The error as a percentage of the true value
can be greater than this. For instance, a .;£:: .100
value of 0.0151 would be represented as
.02, an error of more than 30% of the true 0>
value. ... .011
(l) .010
.001 ,'
.000 .,_·- ·__,'' '--- ---------
Figure 22-5 Comparison of analog video volt
age and digitized values
DIGITAL RADIOGRAPHY 401
ever, will add essentially nothing to the relative exposure. The brightness scale un
overall accuracy. It is easier and frequently der discussion is quite similar to the density
much cheaper to build digitizers, arith scale of film-screen systems. In fact, we will
metic processors, and other system com use brightness as being almost synonymous
ponents if they only have to manipulate a with film density. (Many authors speak of
small number of bits at a time. The argu a "gray scale," which is the same as our
ment extends to image memory and to dig "brightness scale.") This is one of many in
ital disc storage, because useless bits are as stances in which there is a striking parallel
expensive to store as significant ones. between digital and film-screen images.
DIGITIZED IMAGE In the film H & D curves of Figure 22-7
(same as Fig. 11-15), the relationship is
There are many tradeoffs that must be
made in the formation of any radiographic density versus log relative exposure. A long
image, and this is particularly apparent in contrast scale is achieved in the broad lat
a digital fluoroscopic image. X-ray and itude film B, while A has a much smaller
video chain equipment must be chosen latitude in its exposure range. Of course,
with the digital application in mind, and all the short latitude film will result in higher
the conventional tradeoffs regarding such contrast within the exposure range in
factors as patient dose and spatial resolu
tion are still present. The equipment cho which its H & D curve is steepest. A given
sen and the image manipulations em
ployed will have great influence on the change in log relative exposure anywhere
diagnostic usefulness of the final image, within this more or less straight line portion
but there is very little that is fundamentally of the curve will give about the same
different between a digital radiographic change in density. The size of the change
image and a film radiographic image. In will be small for film B, indicating low con
general, the choices made in conventional trast, and will be large for film A, indicating
film radiography and in digital radiogra high contrast. An increase in speed would
phy will have similar consequences.
be seen over film A if an H & D curve of
Brightness Versus Log Relative
Exposure Scale similar shape were drawn to the left of the
We have been careful so far to maintain H & D curve for film A.
a linear relationship between the number
of x-rays exiting the patient and the mag Windowing. The analogy becomes more
nitude of the digital value that is measured. exact if we digress for a moment to discuss
If the image is displayed on a monitor, as windowing. The selection of window
widths and levels is familiar from the dis
illustrated in Figure 22-6A, adding a given
cussion of CT displays, and serves the same
number of x-rays adds a constant amount fundamental purpose in digital radiogra
of brightness to the image. At present, al
most all digital fluoroscopic images are phy. As shown in Figure 22-8, if the orig
changed from this linear relationship to a
logarithmic one. In the logarithmic rela inal digitized image were displayed follow
tionship, increasing log relative exposure ing logarithmic conversion, a broad
by a given amount will increase brightness latitude of log relative exposure values
by a constant amount (Fig. 22-6B). This could be seen (solid line). The windowing
type of relationship is a familiar one. Spe operation selects only a certain range of log
relative exposure values to display, and
cifically, the H & D curves of film-screen uses the full brightness scale of the TV
monitor to display only that selected range
systems are plotted as density versus log
of log relative exposures (dashed line). A
narrow log relative exposure range, or win
dow, is roughly analogous to use of a high
contrast film. Moving the window to the left
has the same general effect as choosing a
faster film. In principle, it is possible for
402 DIGITAL RADIOGRAPHY
B.
-------- y ----------
A. -----6--8--------- :
I
I
I
I
II
H 6iogE=.3
���]_-_----: I [;�r--: : 6E =32
II I ---- 1-: 6\ogE= .3 I
: : 6E= 1 I
:I-I:M=10 I I
I1 II I
II II I
I I
I :-: 6E=10 I
I
I I
I I
I
3.3.3 .6 .9 1.2 1.5 1.8 2.1 24 27
Log Relative Exposure
0 40 60 80 100 .5 1 2 4 8 16 32 64 128 256
Relative Exposure Exposure
Figure 22-6 Comparison of a linear brightness scale (A) with a logarithmic brightness scale (B)
the digital system to produce almost any in the brightness curve to cause us diffi
shape of response curve, or to mimic the culty.
shape of an H & D curve almost exactly
A brightness scale is analogous to the
if that seems desirable. The implication is density scale for a film H & D curve. Stating
that we are making a single exposure and
then changing the brightness of each point that a point on a TV monitor has a certain
in the image to make the image appear brightness level is akin to stating that a par
different. The fact that it is possible to ticular point on a film has a certain density.
make images with film-screen systems with The brightness scale is not defined as rig
idly as the density scale for a particular
different H & D curves causes no concep film, of course. The brightness scale may
tual difficulty, so we will not allow a change be changed according to the DF user's pref-
AB
2.0 2.0 ---------------------
>
E-
-
V)
z
UJ
0
0.25
0.3 0.9 1.5 2.1 2.7 0.3 0.9 1.5 2.1 2.7
LOG RELATIVE EXPOSURE
Figure 22-7 Film H & D curves
DIGITAL RADIOGRAPHY 403
II Figure 22-9A is a photograph of a phan
I
Windowed-/ tom that will help to illustrate several points
I in the following discussion. The phantom
I consists of a step wedge of tissue-equivalent
II Total material, with crossing bars of bonelike ma
terial in its base. A shelf on top of the phan
IJ) tom makes it easy to add small structures
IJ) I
Q) I for later subtraction. Figure 22-9B is an
c:
image of this phantom made on a DF sys
1:
_Q' tem. Figure 22-9C is an image of only a
...
small region of the phantom from the up
ID per right quadrant made with the ftuoro
collimator jaws closed down to define only
I a small area. The image of this region will
be used frequently, generally in conjunc
Log Relative ElC.posure tion with subtraction, and with photo
graphic enlargement to show detaiL
Figure 22-8 The selection of a window to dis
play a smaller exposure latitude Figure 22-10 presents two subtracted
erence. Conceptually, we might speak of a digital fluoroscopic images for comparison
of linear and logarithmic conversions. The
given structure as having a density of 2 on
subtracted image of Figure 22-10A was
radiographic film. Equivalently, the same formed by a three-step process: (1) a mask
structure might have a brightness of 200, image was obtained using logarithmic con
for example, on a DF image. version; (2) a second image with some
The importance of this analogy is that
added "vessels" was obtained in an identical
most manipulations being performed in
DF have the same basic effect as those done fashion; and (3) a subtraction of the two
with film. Thus, knowledge of film-screen
radiographic imaging can be used directly, images was performed. This is the actual
rather than considering a digital system as method used to implement the mask sub
performing some new magic. Now we can traction technique described previously.
return to a discussion of why the transfor The subtracted image is displayed using a
mation to a logarithmic scale is usefuL rather narrow window (read "high-contrast
film" if you wish) to enhance contrast.
Logarithmic Transformation. On a film There is no apparent difference in the ves
sel brightness (read "film density differ
radiograph a vessel of a given size will ap ence") between thin and thick phantom
pear at about the same contrast with its regions. (The differences in quantum mot
background, regardless of where on the tle will be discussed later.) The image of
image the vessel appears. Without worry
ing about whether this is the most satisfac Figure 22-10B was made in the same way,
tory situation, we can note that most DF
images are displayed with similar charac except that no logarithmic conversion was
performed on the mask or second original
teristics. Logarithmic transformation en image. The difference in vessel brightness
sures that equal absorber thickness
changes will result in approximately between thick and thin body regions is ob
equal brightness changes, whether in thin viOus.
or thick body parts. The consequence of
Figure 22-11 offers a numerical illustra
linear and logarithmic brightness relation
ships will be illustrated with the aid of sub tion for the difference in appearances of
tracted DF images from a phantom, and
an example will be offered to explain the the images in Figure 22-10. A phantom
relationships.
with two different thickness parts has two
vessels of equal size that can be filled with
radiographic contrast material (Fig.
404 DIGITAL RADIOGRAPHY
Fig. 22-9 A phantom for tests of a
DF unit
Figure 22-10 Subtracted images using logarithmic conversion (A) and no logarithmic conversion
(B)
DIGITAL RADIOGRAPHY 405
A
8 1000
800
�.":OvEQc';:)0:>: QJQV0c_:l::
500 500-400=100
�0 >0- 400
..�o, aX:, :
OL________J
E
::J
z
c I 1000 =:log (1000)-log (800)= 0.1
500 :=log (500)-log (400)= 0.1
"2'0
.'.E"=,: QVc':l 100 L_______,
c: 0
�OQJ_::
� >-
oo
J�;aX::
E
::J
z
Figure 22-11 Phantom (A) used for numerical illustration of linear subtraction (B) versus log
arithmic subtraction (C)
22-llA). Either vessel will absorb about the linear relationship, after subtraction, is that
the vessel within the thin part appears to
same fraction of the x-ray beam that strikes have been denser than the vessel in the
thick part. The logarithmic relationship of
it. But, as seen in Figure 22-11B (a linear
Figure 22-11C makes equal fractional
relationship), the difference in the absolute
number of photons transmitted by the con changes in the number of x-ray photons
trast-filled vessels is greater for the thin result in equal brightness changes. The
than for the thick part. The result of the
406 DIGITAL RADIOGRAPHY
same percentage change, therefore, what analog level to assign to what digital
whether for a large number of photons (the value . Thus, it is easy to change window
thin phantom region) or for a small num levels and widths, or to make other changes
ber of photons (the thick region), will pro in the shape of the display response curve
vide the same apparent vessel density after (nominally brightness versus log exposure)
subtraction. without altering the values stored in mem
ory.
Subsequently, we will see that some other
sources of image degradation may make Image Noise
some modification of the strictly logarith
mic shape advisable, but the assumption of Our ability to measure any quantity in
a logarithmic conversion will be adequate the real world is ultimately limited by noise .
for our present purpose . The statement sounds something like, "If
nothing else kills you, a meteor will." Un
There are many ways in which the in fortunately, noise is an important problem
dividual pixel brightness values can be con throughout imaging. This is especially true
verted from a linear exposure relationship in the case of radiographic imaging, in
to a logarithmic exposure relationship. which x-ray photon statistics are always a
The exact method, provided that the end problem. The addition of electronic image
result is obtained in a reliable manner, does chain noise further complicates matters for
not really matter. There is one interesting digital radiography. The quantum noise in
method that illustrates a common type of digital subtraction angiographic images is
computer data manipulation. Before the particularly prominent, as is true for
advent of the hand calculator, we used tab images from CT and nuclear medicine.
ulated values instead of calculating trigo
nometric and logarithmic functions. Of Most important sources of noise in ra
course, there is a way to calculate the value diographic imaging are random in nature.
of a logarithm from scratch, but none of By comparison, an image basically consists
us could remember many details beyond of a distribution of densities or brightness
the fact that it was not too much fun. A variations arranged in some set spatial pat
logarithmic table for looking up two deci tern. Random noise, as the name implies,
does not have a set spatial pattern. Math
mal digits of precision would only need l 00 ematically, random noise and all that it pro
entries (102 = 100). A typical DF system duces can be described statistically. An ex
panded discussion of some statistics of
might digitize to ten bits (binary digits) of random noise seems to be in order here .
precision, and thus would need a table with (The authors reluctantly concede that a
love of statistics is not necessarily prima fa
only a little over 1000 entries (210 = 1024). cie evidence of mental instability.) Our em
phasis is practical, and the discussion is
The advantages are the same for the ma mandated by recent developments in med
chine as for a human: simplicity and speed. ical imaging. We will present an example
Computers take advantage of tables quite of DF images degraded by different
a bit in the "calculation" of values from data amounts of noise, followed by several ex
with limited precision. All that is necessary amples explaining different aspects of
is for the arithmetic processor to look up noise degradation effects.
the logarithmic value of pixel brightness
furnished by the digitizer, and to store that The major sources of random noise in
value in its image memory. If we do not
like a logarithmic transformation, we can a digital fluoroscopic image are electronic
put anything we want into the table and noise from the television chain and quan·
the machine will never know the differ tum noise from statistical fluctuations in
ence. Note that when it is time to convert x-ray photon density. The digital portion
from digital pixel values back into analog
video levels, an appropriate table can tell
DIGITAL RADIOGRAPHY 407
of the system should not further degrade that dose, and the image in Figure 22-12C
the image by the addition of still more has 16 times the dose of Figure 22-12A.
Note how smaller detail becomes visible on
noise. A well-designed digital system can the subtracted images as dose is increased.
meet this responsibility, so there is nothing Figure 22-12D is the same as Figure
inherent in digital radiography that nec 22-12C, except that the window has been
narrowed to increase contrast and to show
essarily leads to more noisy images. more clearly that even the smallest vessel
Quantum Mottle. Quantum mottle, is now visible. The visual prominence of
noise increases as the display window is
caused by the statistical fluctuations in the narrowed.
number of photons that exit the patient, is
Standard Deviation. One x-ray exposure
ultimately a limiting factor for all x-ray is not identical to a second x-ray exposure,
imaging. If quantum mottle is regarded as even though the same x-ray tube, genera
fluctuations in the brightness or density of tor, kVp, rnA, and time are used. Also, the
the image, the effects of the mottle become number of photons incident on different
a bit easier to describe. The concept is il areas of the patient is not identical for a
lustrated in Figure 22-12. Figure 22-12A, single exposure, simply because the pro
B, and C are the mask-subtracted images duction of x-rays is a random statistical
of simulated blood vessels superimposed process. The concept of standard deviation
on the region of the phantom shown in (SD) was introduced in Chapter 14. The
Figure 22-9C. Each image is heavily dom standard deviation (SD) for x-ray photon
inated by quantum mottle, and electronic statistics can be calculated by
noise is negligible. Subtracted images
shown in Figure 22-12A, B, and Care dis SD = VN
played using the same window width and
level. The image in Figure 22-12A was where N is the number of photons in
made with each individual unsubtracted volved. For instance, suppose that an aver-
frame taken at fluoroscopic dose levels
(about 0.1 mAs at 80 kVp). The image in
Figure 22-12B represents about four times
Figure 22-12 The effect of quantum mottle on mask-subtracted images. Images have relative
exposures of l (A), 4 (B), and 16 (C). The image in D is the same as in C, but is windowed to
enhance contrast
408 DIGITAL RADIOGRAPHY
age of 10,000 photons per mm2 exit a that the nodule has been added are very
poor. According to Table 22-2 (column 3),
phantom and are incident on the face of statistical fluctuation causes 1/3 of all the
an II during the time of one TV frame.
(An actual pulsed DF image might contain 1-mm2 areas of the TV screen to have more
100,000 photons/mm2 or more. We are us than 10,100 or less than 9900 incident pho
ing 10,000 photons/mm2 to simplify arith tons. About 1/6 of the areas that are the
metic.) The standard deviation in 10,000 same size as the added nodule will actually
be darker than the area beneath the nodule
photons is SD = \110,000 = 100. The cal (column 4). We must also keep in mind
culation is simple, but the practical mean that, for a given TV frame, the added ob
ing of standard deviation requires more ex ject may produce more or less actual sub
planation. ject contrast with its surroundings. The
average fraction of the photons absorbed
The statistics of random processes allows is equal to the average subject contrast
us to calculate the probability of occurrence (1%), because 100/10000 = 0.01, or 1%.
of certain situations. Table 22-2 presents
some probabilities based on standard de In fact, the number of photons beneath the
viations. The first line of Table 22-2 in object (average of 10,000 - 100 = 9900)
dicates that, about two out of three times, will be between 9800 and 10,000 photons
a particular value will be within 1 SD of the only about 2/3 of the time. The situation
average value. For the case in point, a par improves rapidly with increasing x-ray ab
ticular 1-mm2 area on the face of the II will sorption.
be expected to have between 9,900 and
10,100 photons incident on it about two out Subject Contrast. Higher subject con
of every three TV frames, if there is no
change in the phantom or x-ray beam pa trast lessens the importance of noise. A
rameters. Another valid interpretation is 1-mm2 nodule that absorbs 2% of the pho
that, for a phantom of uniform thickness, tons incident on it (2% average subject
about two out of every three randomly cho contrast) will exhibit an average of two
sen 1-mm2 areas of the II will have between standard deviations difference (200 pho
9900 and 10,100 incident photons. tons, or 2% of 10,000) with its surround
ings (Fig. 22-13C). About 19 out of 20
Suppose that a nodule with a 1-mm2 1-mm2 areas will be within two standard
cross-sectional area absorbs about 1% of deviations of the average of 10,000 pho
the photons that strike it (Fig. 22-13A). tons. Only one area in 40 will be less than
This is the same as saying that the average 9800 photons (i. e., 2 SD below the average,
line 2 of Table 22-2). There are so many
subject contrast between this nodule and 1-mm2 areas on the II face that the addition
its surroundings is 1%. The addition of the of a l-mm2 nodule with 2% subject contrast
nodule to the phantom will result in the
absorption of 100 of the 10,000 photons still cannot be reliably detected, using our
10,000 photons per mm2 example.
that would otherwise strike the II face, on
the average (Fig. 22-13B). Our chances of A nodule that has an average subject con
trast of 4% has a very good statistical
examining one TV frame and detecting chance of being detected reliably in this
Table 22-2. Some Probabilities Based on Standard Deviations
NUMBER OF WITHIN AVERAGE FRACTION OF READINGS BELOW
STANDARD DEVIATIONS OUTSIDE
1/6
1 2/3 1/3 1/40
3/2,000
2 19/20 1/20 3/100,000
3 997/1,000 3/1,000
4 99,994/100,000 6/100,000
DIGITAL RADIOGRAPHY 409
+ 2SD • 10,200
+1 SD 10,1 00
Average Nodule Absorbs 10,000
-1 SD 9,900
-2 SD 1 SD on Average 9,800
+2 SD •
+1 SD
Average Nodule Absorbs
-1 SD 2 SD on Average
-2 SD
+2 SD +
+1 SD
Average Nodule Absorbs
-1 SD
-2 SD 4 SO on Average
-3 SD
-4 SD
Figure 22-13 Increasing subject contrast with a constant noise level
situation (Fig. 22-13D). A 4% contrast posure reduces quantum mottle. Figure
level represents 400 photons, or 4 SD. Only 22-14 illustrates quantum mottle at differ
three 1-mm2 areas of 100,000 such areas ent exposure levels. Figure 22-14A cor
will have less than 9600 photons. There responds to the situation in Figure 22-13B.
fore, the chance that statistical fluctuations Suppose that exposure (in milliampere sec
will mimic a 4% contrast 1-mm2 nodule is onds) is increased fourfold. In the example
only three per 100,000 in our example us just discussed, with 1% subject contrast for
ing 10,000 photons per mm2• a nodule of 1-mm2 area, quadrupling the
exposure increases the number of photons
Increasing Exposure. Increasing ex-
410 DIGITAL RADIOGRAPHY
+2% Average= 10,000 % SO= 1%
+1%
Average
-1%
-2% B. Average=40,000 %SD=0.5%
+2%
+1%
Average
-1%
-2%
+2% C. Average= 160,000 %SD=0.25%
+1%
Average
-1%
-2%
Figure 22-14 Constant subject contrast with a decreasing noise level (increasing dose)
per square millimeter from 10,000 (where interest. The standard deviation of 40,000
the SD was 100) to 40,000/mm2• Figure is only 200, which means that the number
22-14B shows this increased number of of standard deviations represented by the
photons. The standard deviation of 40,000 1% contrast level is 400/200 = 2 (Fig.
22-11B). Increasing the mAs fourfold in
photons is SD = V40,000 = 200. Another creases the number of photons by four
way to calculate this is to note that the new (from 10,000/mm2 to 40,000/mm2), which
increases the number of photons absorbed
SD = Y4 X 10,000 = V4 X Y10,000 = by four times (from 100 to 400) but only
V4 X 100 = 2 X 100. The obvious ex
increases the standard deviation by V4 =
tension of this is to increase mAs by 16 2 times. Statistical fluctuations (quantum
times (Fig. 22-14C). Thus, the SD =
mottle) now represent a smaller percentage
v'I6 X V10,000 = 4 X 100 = 400.
of the total number of photons (200/
There appears to be a problem here. We 40,000, or 0.5%), and are therefore less
know that increased dose means less quan likely to be confused with the nodule (1%
tum mottle, yet the number of photons in average subject contrast). For simplicity, we
one standard deviation is larger for larger will regard this as being equivalent to re
doses. The solution to the quandary is to ducing quantum mottle to half of its pre
consider the average number of photons vious level. Figure 22-14C represents 16
removed by the nodule. Because 1% of times the dose of Figure 22-14A. The
40,000 photons is 400 photons, a 1% con quantum mottle is reduced to one fourth
trast level represents 400 photons when
there are 40,000 photons in the region of (i.e., 1/v'I6) of the original value. Increas-
DIGITAL RADIOGRAPHY 411
ing the dose M times reduces quantum mm2 in the regions that contain no contrast
mottle by v'M times. material, and SD = v'20,000 = v'2 X 100.
Noise and Observer Performance. In Only one of the original images contains
practice the relationship of image statistics
to the performance of an observer is qual contrast material. If the contrast-contain
itative rather than quantitative. Improving ing object absorbs 1% of the incident x-ray
statistics in a particular imaging situation photons (in compliance with our first ex
does improve visibility to the point where ample), an average of 100 photons will rep
other imaging limitations such as resolu resent the subject contrast in the final
tion become more important. It may be image. The statistical fluctuations are
possible to state that increasing dose will
improve the visibility of small low-contrast higher (v'2 X 100 = 141) than for a single
objects in DSA images of a particular body
region. It would not be valid to declare that frame, y et the contrast-containing struc
mammograms are "better" than chest ra ture is represented by the same number of
diographs because the former has more photons as in a single frame. The noise in
photons. Direct comparisons are valid only subtracted images is worse than in either
when such parameters as background the mask or in the contrast-containing
structures, size of image features, and con image.
trasts are reasonably similar. For instance,
we can legitimately compare the effects of Noise and Object Size. The importance
increasing contrast with the effects of in
creasing dose in DSA images. Reducing of quantum mottle tends to be much
noise (quantum mottle, in this case) by half
(by increasing dose by four times) has the greater for small objects than for large
same effect on detection probabilities as ones. In the example of a l-mm2 lesion,
doubling subject contrast. In fact, a sub
tracted image of the high-dose example us which absorbs 1% of the 10,000 incident
ing a narrow window would be virtually photons, we noted that there is about one
indistinguishable from a subtracted image
of the high subject contrast example using chance in six that any randomly chosen l
a broader window.
mm2 area of the image could be mistaken
Noise and Subtracted Images. At first for the lesion itself. The situation with a 4-
glance the quantification of the effects of mm2 lesion is much better. Quantum mot
noise on subtracted images seems to be a tle is much less significant for detecting
more difficult concept. One simple consid large structures than for detecting small
eration, however, allows us to describe ones because the larger structures have
noise in subtracted images in a very both higher inherent subject contrasts and
straightforward way. The key is to consider cover larger areas. The diameter is dou
the total number of photons within the re bled, so the area is four times that of the
gion of interest for both the mask and the
contrast-containing frame. Again, using l-mm2 lesion and attenuation is twice as
10,000 photons per mm2 within a single
frame for an example, a subtracted image great. The x-ray attenuation of the 4-mm2
requires at least two frames, one for the lesion is 2%, and there are about 40,000
mask and one for the contrast-containing photons within the area; thus, an average
image. The final subtracted image is of 800 photons is absorbed. The SD of
formed by using about 20,000 photons per 40,000 is only 200, so the lesion should pro
duce an average difference with its sur
roundings of about four standard devia
tions (800/200 = 4). The probability of
occurrence of statistical fluctuations with
four standard deviations is much less than
for one standard deviation, as previously
noted. Table 22-2 indicates that only about
three lesion-sized areas out of 100,000 will
be expected to have statistical fluctuations
that could cause an incorrect identification
412 DIGITAL RADIOGRAPHY
of quantum mottle as being the 4-mm2 le clueing the quantum noise to a small frac
sion in this case. In a clinical situation ob
server performance would be improved, tion of the 0.4% level will produce little
but not nearly as much as these simple sta improvement in image quality.
tistics would suggest.
A better TV chain might have random
Independent Noise Sources. Every
noise at a midbrightness level with a
source of image noise contributes to
image degradation to some extent. For the % SDTV of around 0.2%. Under the same
most common types of random noise, the
total degradation can be calculated by us exposure conditions, % SDc
V(0.2)2 + (0.4)2 = 0.45%. The image is
ing the percentage standard deviations of
the individual noise sources . For our pur dominated by quantum noise, and the sys
poses, the percentage standard deviation
tem is good enough to make efficient use
(% SD) can be defined as the percentage
of patient dose. Note that for very low ex
fluctuation in the brightness (or density) of
an image. For instance, the percentage posures per frame such as are typically seen
standard deviation caused by x-ray photon
in routine fluoroscopy (about 0.1 mAs per
statistics with 10,000 photons is 1% ( 100 is
1% of 10,000). In the case of DF, the major frame), the quantum noise will be much
noise sources are random electronic noise worse than for pulsed DF exposures (per
from the TV system (% SDTV) and quan haps 10 mAs per frame), and even the
tum statistical fluctuations in the number "poor" TV system might be perfectly ad
of detected x-rays (% SDQ). An equation equate.
for calculating the composite percentage Frame Integration. Another common
standard deviation (% SDc) for this situa method of reducing the noise in DF images
tion is is to average or to add together several
frames, sometimes called frame integra
tion. Frame integration reduces the effect
(�)of all types of random noise. The compos-
ite % SDc is reduced by where M
%SOc = V(%SDrvF + (% SDaF is the number of frames averaged together.
The specific equation is not of much inter
The result is that the % SD (the magnitude est to us. Whether M frames are averaged
together or the dose per frame is incre2tsed
of image fluctuations) is greater than would by M, the final image represents the same
be seen as a result of either of the two noise number of x-ray photons. The difference
sources operating alone. This is consistent is that increasing the dose per frame re
with our overall convention of considering duces only the x-ray quantum noise ef
noise as fluctuations in the final image. fects, but integrating frames reduces both
electronic and quantum noise effects. Ex
A poor TV system for DF use might have posure levels and TV chain quality deter
random noise at a midbrightness level with mine whether this distinction is important.
On the practical side, averaging also has
a % SDTV of 1%. This is the percentage the advantage of reducing the importance
of the x-ray exposure used during the sta
fluctuation in the image that would be pro bilization time (if any). Of course, frame
duced by electronic noise alone. If the integration has the disadvantage of longer
quantum noise at some x-ray exposure exposure times.
level has a % SDQ of around 0.4%, then X-Ray Scatter
% SDc = V( 1)2 + (0.4)2 = 1.077%. The
X-ray scatter produces the same funda
composite image noise in this case is only mental types of degradation in digital ra-
a little worse than that of the TV chain
alone. One common method of reducing
the noise in DF images is to increase the
exposure per frame. That clearly will do
no significant good here, because even re-
DIGITAL RADIOGRAPHY 413
diographic applications as in any other ra concentrate on the second and third ef
diographic applications. Some potentially fects.
valuable techniques in digital radiography,
however, impose severe demands on an Figure 22-15 illustrates the effect of
imaging system. Therefore, effects that scatter on contrast in different thickness
were not especially significant in past ap body regions for subtracted images. The
plications now become more limiting. Scat region of the phantom in Figure 22-15A
ter has three major effects that degrade has tight collimation to define a very small
images: x-ray field and thereby to reduce scatter.
Figure 22-15B was made with a wider col
1. Scatter reduces radiographic con limator opening and was then photograph
trast. ically cropped to show the same region.
The unsubtracted image in Figure 22-15C
2. Scatter causes small structures with is darkest in regions of greatest thickness,
equal attenuation to appear to have as has been our custom to this point. The
different contrasts with their sur simulated vessels produce less contrast in
roundings, depending on whether thick body part areas than vessels in the
the structures are in thin or thick
body regions, even after logarithmic �t in region. The effect occurs because scat
conversion.
ter tends to appear as the addition of a
3. Scatter raises the patient dose re uniform x-ray background all across the
quired to obtain a given x-ray photon image. The explanation of the effect re
statistical confidence level. quires an examination of the logarithmic
conversion that was performed during the
The action of scattered x-ray photons in collection of these images.
reducing subject contrast has been dis
cussed in Chapters 8 and 14, so we will Scatter was not discussed in the section
on logarithmic conversion. We implicitly
assumed that a structure that attenuated
Figure 22-15 Effect of scatter on contrast. (A), Low scatter. (B), High scatter. (C), Unsubtracted
image is shown for comparison
414 DIGITAL RADIOGRAPHY
some fixed fraction of the number of in removal of a larger number of photons
cident photons would remove that fixed from the thinner area.
fraction of the number of photons from
the final image. Unfortunately, that as The most obvious potential solution to
sumption is not valid. Figure 22-16 shows force thin and thick body parts to display
the situation when a uniform background true attenuation is to subtract out the scat
of scattered x-ray photons is added to Fig ter. Unfortunately, the amount of scatter
ure 22-11B. Recall that the transformation depends on such x-ray beam parameters as
of Figure 22-11B to a logarithmic scale kVp and field size. Scatter also depends on
produced Figure 22-11C, in which each the composition, thickness, and location of
opacified vessel caused a change of 0.1 with the structure being imaged. Finally, scatter
respect to local background. The familiar is not really uniform across the entire
effect of the addition of scatter is that con image. It is not feasible, therefore, to cor
trast is reduced. This can be seen by using rect an image completely for scatter by sim
a calculator, and noting that in the thick ply subtracting the same fixed fraction of
body region of Figure 22-16, log 2000 - photons from every image. In practice, an
log 1800 = 0.046 instead of 0.1 Another attempt to correct for scatter partially is
effect of scatter is that the vessels in thin often employed with DSA images. A mod
and thick regions no longer produce the ification to the "logarithmic table" (or an
same contrast change. Note that log 1500 equivalent method) is commonly em
- log 1400 = 0.03, which is less than the ployed.
change produced by the vessel in the thin
region (0.046). In other words, when equal Scatter also makes quantum noise worse,
amounts of scatter are added to all parts which leads to the discussion of the third
of an image, the removal of a small number major effect. Our well-worn example of
of photons from the thick area will not pro 10,000 photons per mm2 (primary) will
duce as large a percentage difference as the serve one last time. If 30,000 photons per
mm2 of scatter are added (not unreasona
2000- ble), the quantum noise in the image is
1800- caused by 40,000 photons per mm2 (i.e.,
primary plus scatter), but the useful image
1500- is still formed by using only 10,000 photons
1400-
per mm2 (primary only). Small low-contrast
Figure 22-16 Effect of a constant scatter back objects still attenuate the same number of
ground on thin and thick body regions primary x-ray photons. The vessel that at
tenuates 1% still removes about 100 pho
tons. The standard deviation with scatter
is 200, and without scatter it is only 100.
Thus, quantum noise is worse by a factor
of two in this case with scatter present.
Even if it were feasible simply to subtract
scatter after it was detected, the discussion
of subtracted images suggests that the
worsening of quantum noise by scatter
would still persist.
Other solutions are feasible. Increasing
dose by four times will reduce quantum
noise by \14, or twice. This means that
160,000 photons per mm2 (scatter plus pri
mary) will give the same statistical confi-
DIGITAL RADIOGRAPHY 415
dence level in the final image as for 10,000 image contrast is somewhat reduced. Veil
ing glare, however, does not significantly
photons per mm2 without scatter. Increas affect x-ray photon statistics. Thus, images
ing dose is not only bad for the patient, but with and without veiling glare will need
about the same patient dose for equivalent
the II-TV chain would have to handle 16 confidence levels, based on x-ray photon
statistics alone.
times as many x rays. The TV chain would
also need better noise characteristics to DIGITAL SUBTRACTION
handle the smaller percentage contrast dif TECHNIQUES
ferences without degradation of the image.
We have defined digital subtraction an
Note the implication that less dose is re giography (DSA) as the generic term for
quired for images with an x-ray grid as op any digital radiographic method of imple
posed to images without a grid for the same menting subtraction angiography. Many
low-contrast detectability. This option is techniques may be applied to DSA: we will
not easily implemented with film-screen ra
diography because enough x-rays must be discuss four. These are ( 1) mask subtrac
absorbed to expose the film to usable den
sities. tion (previously described), (2) dual energy
The best solution to all problems caused subtraction, (3) time interval differencing,
by scatter is to eliminate all scatter com and (4) temporal filtering. Each technique
pletely, if possible. X-ray grids and primary
beam magnification help to some extent. is mentioned under several names in the
Another particularly effective method of current literature, so our choice of termi
eliminating scatter will be discussed in a nology is somewhat arbitrary. Mask sub
later section. traction is by far the most common at pres
ent, but each of the other three techniques
Veiling Glare is beginning to see clinical use. The field
of digital radiography is advancing rapidly,
There are other effects that also contrib and any or all of these specific techniques
ute to a reduction in image contrast. For may be supplanted before they are widely
instance, image intensifiers reduce image used.
contrast because of light scatter and other
Mask Subtraction
phenomena within the II (see Chap. 13).
The general method by which mask sub
"Veiling glare" is a term used in optics to traction is implemented was described at
describe the light that is scattered and re the beginning of this chapter. We have
flected within a lens system. For conven since noted a number of limits on radio
ience, consider image veiling glare to con graphic imaging systems in general, and a
sist of all those processes except x-ray few that apply specifically to digital radio
scatter that produce a similar result in a DF graphic systems.
system. The II contributes most of this veil
ing glare, and the remainder is contributed The image spatial resolution at present
by the optical coupling to the TV chain and tends to be limited by the digital matrix
even the TV chain itself. Veiling glare be sizes used. The ability to resolve low subject
comes worse at larger field sizes. The ef contrast objects is limited by the number of
fects of veiling glare on the image are sim x-ray photons used (quantum mottle) and
ilar in some respects to those of x-ray by the electronic noise of the video chain.
scatter. The addition of a background Quantum mottle may be reduced by in
brightness to the image provides the same creasing the x-ray tube rnA, thereby in
problem of thickness-dependent contrast creasing the number of x-ray photons in
levels following simple logarithmic conver each frame. Frame averaging is often em
sion. The correction of an image for veiling ployed to reduce the effects of video chain
glare is similarly difficult, and of course
416 DIGITAL RADIOGRAPHY
noise (as well as quantum noise) in forming to give the desired density range for a par
a single image in the series. Scattered x rays ticular patient, so our example is not very
and image veiling glare also reduce con practical. In principle, though, this could
trast and cause other problems. Patient mo be done. The difference in log relative ex
tion between the time the mask is taken and posures between thin and thick body parts
the time the contrast-containing image is is 0.8 for the low kVp but, as a result of
taken is a severe problem that does not the choice of a low-contrast film for low
have any optimal solution at present. The kVp (and our judicious tinkering with
discussion of partial solutions to this mo x-ray technique factors), the thinnest soft
tion artifact problem will be deferred for tissue part is displayed at the same density
now. (2.5) as on the high-contrast film used in
the high-kVp image. The thickest part is
Dual Energy Subtraction also displayed at the same density (1.0) on
both images.
Another technique for performing DSA
is dual energy subtraction, a method that Recall that successively adding equal
does not require the acquisition of images thicknesses of tissue will cause equal
before and after the arrival of contrast ma changes in density within the straight line
terial. I n dual energy subtraction, two portion of the H & D curve. This means
images are taken within a very short pe that an intermediate soft tissue thickness
riod, during which time there is no change will also give the same film density (1.75)
in the patient. These two images are ob on either the high- or low-kVp image. The
tained by making exposures with different net result is that the high-kVp image (re
x-ray energy spectra as would be obtained, corded on high-contrast film) may be sub
for instance, from a high-kVp exposure tracted from the low-kVp image (recorded
and a low-kVp exposure. on low-contrast film), and soft tissue struc
tures will cancel. What about bone?
Film-Screen Method. We will first offer
an idealized example of dual energy sub It is no surprise that the differential at
traction using a film-screen system. This tenuation between bone and soft tissue at
example will illustrate the basic principle low kVp is much greater than their differ
of how to eliminate soft tissue, leaving only ential attenuation at high kVp, a point
bone. Figure 22-17A shows the exposures made in Chapter 5. Perhaps the best prac
transmitted through different thicknesses tical example is high-kVp versus low-kVp
of soft tissue at high kVp, and the resulting chest films. The bone contrast in the high
densities recorded on a high-contrast film kVp films is reduced much more than is
screen system. The x-ray attenuation is low the soft tissue contrast. For review, bone
at high kVp, and the difference in log rel has the higher atomic number, and thus
ative exposure values between the thinnest has a lot more attenuation because of the
body part and the thickest body part is 0.5 photoelectric effect. Because the photo
(log relative exposures of 1.7 - 1.2 = 0.5). electric attenuation drops off very rapidly
The high-contrast film records soft tissue as kVp is increased, bone attenuation
over a density range of 1.5 (densities of 2.5 changes much more than soft tissue atten
- 1.0 = 1.5). Figure 22-17B shows the uation. Figure 22-18 has the same soft tis
exposures transmitted through the same sue thicknesses as the previous figure, but
soft tissue thicknesses at low kVp (and a small bone has been added to the object.
higher mAs). Low kVp inherently provides In the regions that do not contain bone,
higher subject contrast than high kVp, so soft tissues still cancel, but bone attenuation
a low-contrast film was chosen to record the has changed more than has soft tissue at
low-kVp image. The low kVp and mAs tenuation. Regions that contain bone will
would have to be adjusted experimentally not cancel completely. Thus, the final
DIGITAL RADIOGRAPHY 417
B.
A. Low kVp with
3.5 Low Contrast Film
High kVp with Thin Part
3.0 High Contrast Film
--------------------
Thin Part
2.5
� 2.0 ----------
V>
c:
Q)
0 1.5
Thick Part Thick Part
1.0
.5
I 1I .9 1.5 2.1 2.7 3.3
.3 .9 1.5 2.1 2.7 3.3 .3
Log Relative Exposure
Figure 22-17 Film in A was selected to have soft tissue contrasts at high kVp equivalent to
contrasts of film in B at low kVp
image consists of only bone plus the inev The basic principle is the same, so consider
itable noise. If soft tissue film contrasts are the example just presented using film
made equivalent between low- and high screen subtraction. Figure 22-19A corre
kVp images, bone contrasts will not be sponds closely to Figure 22-18A. The same
equivalent.
three thicknesses of soft tissue and the
Digital Method. The dual energy sub
traction operation can be implemented in same added bone, kVp, and so forth are
practice using digital image processing.
illustrated. The digital brightness scale has
been modified so that the windowed digital
A. B.
3.5
Low kVp with
High kVp with Low Contrast Film
3.0 High Contrast Film
2.5
"'2.0
V>
�c: 1.5
1.0
.5
.3 .9 1.5 2.1 2.7 3.3 .3 .9 1.5 2.1 2.7 3.3
Log Relative Exposure
Figure 22-18 Dual energy subtraction principle. Bone contrasts change more with kVp than do
soft tissue contrasts
418 DIGITAL RADIOGRAPHY
A. B.
300 High kVp with High Contrast (Narro w ) Low kVp with Low Contrast (Broad)
Digital Window Digital Window
250 Thin Part
Thin Part+ Bone
</)
Thick Part
� 200 Thick Part
+Bone
c:
1:
·� 150
m
100
50
.3 .9 1.5 2.1 2.7 3.3 .3 .9 1.5 2.1 2.7 3.3
Log Relative Exposure
Figure 22-19 Dual energy subtraction by setting appropriate windows on a digital radiographic
system
line and straight line portion of the film H sure), and can be readily modified for the
& D curve would superimpose. Similarly, patient's requirements. A set of windows
appropriate for the subtraction of bone
the low-kVp digital window depicted in rather than soft tissue can obviously be
used if desirable for a particular problem.
Figure 22-19B and the film H & D curve A single high-kVp and low-kVp image pair
in Figure 22-18B are essentially identical. can yield chest images of either bone only,
The brightness levels of thick (50), thin soft tissue only, or both. It should be noted
(250), and intermediate (175) soft tissue that our use of display windows is for ex
planation, and that the technique is imple
regions that contain no bone are the same mented by hardware performing function
either on the narrow window (high display ally equivalent operations internally.
contrast), high-kVp image, or on the broad Problems of Dual Energy Subtraction.
window (low display contrast), low-kVp
There are inevitably some disadvantages
image. Soft tissues will cancel except for attached to this approach to imaging. All
noise. As before, the final image will consist the problems associated with radiographic
imaging in general and with DSA in par
of bone only. The small bone reduces ticular are still present, except perhaps for
anatomic motion. There are also some spe
brightness by 20 whether in thick (100 - cial problems unique to the use of dual en
80 = 20), thin, or intermediate regions of ergy subtraction.
the low-kVp image. But the same bone only First, the high-kVp image still has some
bone within it. When the soft tissue den
reduces the brightness by 10 in the high sities are eliminated by subtracting win
dowed high- and low-kVp images, some of
kVp image. the bone density is also reduced. This im
plies that to obtain the same contrast dif
Implementing dual energy subtraction ferences as with a mask subtraction tech-
by film-screen systems is very difficult. The
advantage of the digital approach is flexi
bility. The beam energies and x-ray doses
can be chosen with comparatively little con
cern for whether a good subtraction will
result. The "windows" are chosen after the
images are acquired (conceptually equiva
lent to choosing film types before expo-
DIGITAL RADIOGRAPHY 419
nique, more display contrast enhancement ditional beam hardening effect. Unchang
would be necessary with the dual energy ing structures still cancel without leaving
scheme. As always, enhancing display con residual images. The situation with dual
trast also increases the visibility of noise. energy subtraction is more complex be
More patient dose is required to suppress cause of the two beam energies employed.
the visibility of this quantum mottle for If each beam exhibited exactly the same
dual energy subtraction. amount of beam hardening in each region
of the body, proper subtraction of bone
�econd, a more complex x-ray machine and soft tissue would not be significantly
affected. The broad range of thicknesses
is indicated. An x-ray generator capable of of soft tissue and bone, however, affect the
switching kVp and mAs rapidly is needed two beams differently. A final image that
to overcome problems with anatomic mo should contain soft tissue structures only
tion. Also, bone contrast in the subtracted may in fact have significant amounts of re
image is greatest with two x-ray beams of sidual bony structures that were improp
greatly different energy spectra. The en erly subtracted.
ergy spectra can be varied even more by
several methods. For instance, very differ Finally, three different beam spectra are
ent peak voltages can be employed, and required to handle three substances with
extra filtration can be added to the higher greatly differing atomic numbers. This
kVp beam. The additional filtration adds might be termed "three-energy subtrac
some load to the x-ray tube that would not tion." The reason that three images at dif
otherwise be necessary. Some mechanism ferent beam energies are necessary can be
for rapidly changing filters between ex understood by some simple algebra. Each
posures is also necessary. pixel in a single image has information
about unknown thicknesses of soft tissue,
Third, we actually made an invalid as bone, and contrast material. Each of the
sumption in our example. A polychromatic three energies gives up independent (i.e.,
x-ray beam is in fact hardened as it tra different) information about the thickness
verses the body. Beam hardening is the within that pixel. So, we have three un
term used to describe the preferential re known thicknesses and three equations
moval of the lower energy x rays as the that can be used to solve for the unknowns.
beam traverses a thick body structure (see For most angiography work using energy
subtraction techniques alone, three expo
Chap. 5). The main cause of beam hard sures would be necessary to yield a sub
tracted image of iodine only. The iodine
ening is the photoelectric effect, which contrast would be even lower than for a
drops off rapidly at higher photon ener dual energy subtraction, and the third
gies. The net effect is that the effective en image would contribute still more quantum
ergy of the beam increases as it passes noise. The display window would need to
through thick body parts. Note that the be narrowed even more than for the dual
photoelectric effect is greater in higher energy subtraction technique. The in
atomic number materials, so higher atomic creased quantum mottle in the contrast-en
number materials have a greater beam hanced final images would become more
hardening effect. Also, higher kVp x-ray prominent. Three exposures per image
beams will have different beam hardening implies an increase in dose over the two
as compared to lower kVp beams. Beam exposures per image used for dual energy
hardening does not cause much of a prob subtraction.
lem in the simple mask subtraction tech
nique, because only one x-ray beam energy Other Dual Energy Subtraction Methods
is employed. The amount of beam hard
ening caused by bone and soft tissue is the K-Edge Subtraction. A technique called
same for each image, and small quantities
of contrast material have only a small ad- "K-edge subtraction;' using film-screen sys-
420 DIGITAL RADIOGRAPHY
terns, received considerable research inter strahlung spectrum to be filtered. As can
est several years ago. Interest waned partly
because of the difficulty of using film as the be seen from Figure 22-20B, the K-edge
recording medium. The technique was
named because of the K-shell absorption photoelectric absorption of cerium begins
edge seen on a photoelectric attenuation
at about 40 keV (binding energy of ce
curve. Figure 22-20 summarizes a method
rium's K-shell electrons). A thick filter of
of using K-edge absorption x-ray filters to cerium inserted into the beam will remove
improve dual energy subtraction for con
trast materials such as iodine. One of the most of the x rays above 40 keV by the
two images should have the highest possi
ble iodine x-ray contrast, and the other K-shell photoelectric effect. Many x rays in
image should have little or no iodine x-ray
contrast. the range of 30 to 40 keV will get through
Iodine attenuates diagnostic x-rays al the filter. The x-ray spectrum through this
most entirely by the photoelectric effect. filter will have its highest intensity just
One method for achieving high iodine sub above the K-shell binding energy of iodine
ject contrast is removal of all x-rays from
the beam except those that lie just above (Fig. 22-20C). This spectrum is nearly
the K-shell binding energy of iodine (about
33 keV). An x-ray filter made of the rare ideal for providing the highest possible
earth named cerium can do this quite well. x-ray subject contrast for iodine. This is the
advantage of K-edge filtration, whether or
Figure 22-20A shows the x-ray tube brems- not the technique is to be used with dual
energy subtraction.
A. Unfiltered X-Ray
Spectrum The image to be subtracted (roughly
::: equivalent to a mask) should have little or
no iodine subject contrast. The appropri
·v; ate x-ray spectrum should contain few
x rays that could be absorbed by iodine
c
(Fig. 22-20D). If a thick iodine filter is
cQ:J
placed in the beam, then almost all the
B. Filter Attenuation
x rays that could be absorbed by iodine
E \•••• �••-Iodine Curves have been absorbed before reaching the
tEf '•,'•\, \ : ... iodine within the patient. The resulting
image will have very low iodine subject
� ··-.��:r·'·.·�....�. 1':�'.·-.-�tI:-·.·.··�C·�er;:i-.u,..�....··..·.··.�.�.::-.�.� contrast.
:i.
X-Ray Spectrum The K-edge subtraction to form the final
5 Filtered by Cerium image is still a type of dual energy sub
c. traction, and is accomplished by a method
similar to that previously described. The
::: problems with dual energy subtraction
images, including incomplete bone-soft tis
·v; sue cancellation with only two beam spec
tra, are still present, but the very high and
�c very low subject contrast iodine images
make most of those problems somewhat
c less important. The exception is that the
technique is most effective with thick filters
D. X-Ray Spectrum that remove most of the original beam in
Filtered by Iodine tensity, and the high mAs required as a
::: result makes x-ray tube load problems
much worse. There are other problems, in
·v; cluding those regarding patient dose and
c choice of materials for the most efficient
cQJ filters, which we will not discuss.
20 Hybrid Subtraction. Another promising
Energy (keV) use for dual energy subtraction techniques
Figure 22-20 K-edge filtration
DIGITAL RADIOGRAPHY 421
is hybrid subtraction. A simple mask sub sible in some instances to obtain the same
traction technique is combined with dual diagnostic information in three exposures
energy subtraction (thus "hybrid"). The with a three-energy technique that would
technique is designed for the situation in require about 20 exposures in temporal
which anatomic motion is expected to be a mask subtraction. Finally, there is the
problem. The data are collected much as promise of obtaining subtraction images of
in simple mask subtraction, with images be contrast material for such procedures as
ing collected at about 1-sec intervals over laminography and cholecystography
the course of the passage of contrast ma where the time span between pre-contrast
terial through the vessels. The difference and post-contrast images is long.
is that where each single image of the series
is collected for mask subtraction, a high Time Interval Differencing
kVp/low-kVp image pair is collected for hy
brid subtraction. If there is no patient mo Time interval differencing (TID) is an
tion, the low-kVp image series can be used other digital subtraction technique, and it
as if a simple mask subtraction had actually has seen some application in cardiology.
occurred. The technique is closely related to simple
mask subtraction. In simple mask subtrac
Very little patient motion can be toler tion an early image is chosen as the mask,
ated in simple mask subtraction between and this single mask is subtracted from
the time the mask is taken and the time the each succeeding image of the series to form
contrast material arrives in the vessels of the series of subtracted images. In the TID
interest. The soft tissues (large structures technique, a new mask is chosen for each
without sharp edges) cancel properly if pa subtraction.
tient motion is not too great, but bone
edges cause severe artifact problems. Con For simplicity, assume that images are
sider the subtracted images to consist of collected and stored at the rate of 30
only two atomic number materials, iodine images per second for several seconds.
and bone. The hybrid subtraction tech Choose image 1 as the first mask, and sub
nique produces two sets of subtracted tract the mask from image 7 (0.2 sec later
images, one from the low-kVp and the in time) to form the first subtracted image.
other from the high-kVp series that were Next, choose image 2 as the second mask,
collected simultaneously. The same bone and subtract from image 8 (again, 0.2-sec
and iodine structures are present on both time interval) to form the second sub
sets. Dual energy subtraction can now be tracted image. The third subtracted image
used to eliminate bone, leaving only iodine. is a subtraction of image 3 from image 9,
The final image will have lower contrast and so on. Each subtracted image is the
and more noise than if the dual energy difference between images separated by
operation had proved unnecessary, but the some fixed interval of time. The successive
critical diagnostic information may be subtracted images are frequently displayed
saved. in a rapid sequence that is repeated to show
dynamic function.
Dual energy and three-energy subtrac
tion techniques have so much promise that Each individual image of the series might
they may be successful in spite of their ob have rather poor statistics that can be im
vious problems. First, the elimination of ei proved by frame integration at the expense
ther bone or soft tissue by dual energy sub of increased blurring caused by anatomic
traction may be worthwhile, especially in motion. For four-frame integration,
chest radiography. Second, hybrid subtrac images 1, 2, 3, and 4 are added together
tion may be helpful in imaging situations to form the first mask. Frames 7, 8, 9, and
10 are added together, and the first mask
in which normal anatomic motion is ex is subtracted from the result to form the
pected, as well as in the case of the un first subtracted image. The second sub
cooperative patient. Third, it may be pos- tracted image uses frames 2, 3, 4, and 5 as
422 DIGITAL RADIOGRAPHY
the mask, subtracted from the sum of ing which time individual frames are col
frames 8, 9, 10, and 11. This particular lected and stored at 30 frames per second.
TID technique involves adding a number Now for the final step. One obvious ap
of images to form a mask that represents proach is to choose either an early or a late
information about one time period, and frame with no contrast material present as
subtracting the mask from the sum of an a mask, and to subtract later frames from
other group of images that represents in the mask as was done for simple mask sub
formation about another time period. In traction. Unfortunately, the low rnA leads
principle this is very similar to another dig to very high quantum noise in single
ital subtraction technique called temporal frames. Another almost equally obvious
filtering. approach is to add together several of the
early frames and several of the late frames
Temporal Filtering to form the mask. An equal number of
frames that contain contrast can be added
Time interval differencing can actually together to form a contrast-containing
be considered to be a temporal filtering image. DSA is now accomplished by sub
technique. The word "temporal" means of traction of the low-noise mask from the
or limited by time, and clearly applies. We low-noise contrast-containing image.
will not attempt a mathematical description
of filtering either here or later in the ex In other words, individual images (single
amples of spatial filters. The description of TV frames) are added together or sub
the TID filtering operation is sufficient to tracted from each other to form a com
explain the principle for present purposes. posite image. The exact time of arrival of
A set of final data (images) was formed the contrast material is sometimes difficult
from a set of original data (also images) by to predict in reality, so the manual selection
applying a consistent set of rules. Each suc of the most appropriate frames to use for
cessive final image was formed in exactly the individual steps could be quite time
the same fashion, except for a shift along consuming. Perhaps it would be better to
the time axis of the data. This operation of allow the computer to do the selection
adding and subtracting part of a set of data using some consistent set of rules, and then
together according to a set of rules to get to generate a large number of individual
one answer, and then shifting and repeat composite DSA images so that the best may
ing to get the next answer, is a filtering be chosen. We now have a filter for doing
operation. DSA. Again, this filter generates one final
image by adding and subtracting some of
Time interval differencing is not usually the original images together, and then
regarded as a filtering technique, but of shifting and repeating to form the next
course it is actually a valid example. Tem image. Obviously a temporal filter of al
poral filtering is very general, and there are most any shape can be selected. The one
temporal filters that can be used to perform used in this example was chosen for sim
DSA (sometimes the awesome term "tem plicity of didactic explanation, and is not
poral filter" is even used). A simple ex the optimal shape for the application.
ample will show the general operation.
One advantage of the temporal filtering
The passage of contrast material approach is that less severe demands are
through an artery following intravenous placed on the video image chain than for
injection will result in a contrast dilution simple mask subtraction, because the x-ray
curve with the general shape shown in Fig tube can be operated at much lower tube
ure 22-21. Suppose that we wish to use our current values. Typically, mask subtraction
knowledge regarding the curve to perform requires around ten times the tube current
DSA. The first step is to inject a bolus of needed by temporal filtering for compa
contrast material intravenously. A second rable contrast detectability. An obvious dis
step might be to operate the x-ray tube in advantage is that a large number of indi-
a continuous fashion at 10 to 20 rnA, dur-
DIGITAL RADIOGRAPHY 423
2% -Iodine Concentration
in Vessel
c::
Bolus
.Q Injection
- •
-0...
�(.) 1%
c::
8
Image No.: 1 2 3 4 5 6 7 8 9 10 11 12 13 14
������t;:d OJ 0 rn [i] [1] 0 rn !Il � @J llil [g) @1 �
Ly..-1 J L..J-
I, l ¥ ,
Subtract Subt ract
d I IA d
•
D Final Image
Figure 22-21 Principle of temporal filtering
vidual frames must be handled for will be made here to survey the rapidly
temporal filtering. growing field of digital x-ray image proc
essing, but some discussion of present tech
Comparisons of patient dose and the niques and areas receiving attention is ap
sensitivity of the system to artifacts caused propriate. Our examples will be linked to
by patient motion are difficult to make at simple illustrations of a few general types
the present stage of development. Both pa of manipulations, rather than to specific
tient dose and anatomic motion sensitivity complex (and changeable) processing op
are highly dependent on the way in which erations now in use.
the techniques are implemented.
There are many ways to classify types of
DIGITAL IMAGE PROCESSING image manipulations (image processing
operations). Engineers tend to classify on
The field of image processing has re the basis of the type of mathematical op
ceived much attention since about the mid- eration that is implemented. We will clas
1970s. Much of the impetus for this atten sify them on the basis of the fundamental
tion has come from the space program. purpose of the manipulation.
The startling images from satellites are typ
ically manipulated by digital image proc First, there are manipulations that are
essing techniques prior to being photo intended to correct a deficiency in the
graphed for presentation to the public. imaging system or to place the information
Clearly, it is possible to manipulate medical in a form more suitable for later process
images by computer in a manner analogous ing. This might be termed "preprocessing,"
to the way in which these satellite images and it is usually performed during or im
are manipulated. Nuclear medicine images mediately after data collection. Second,
in particular have had increasingly sophis preprocessed images may be further ma
ticated digital processing techniques ap nipulated by such methods as subtraction
plied to them for years. At this point, dig to form viewable images of the type desired
ital x-ray image processing must be for a particular application. Enough ex
regarded as being in its infancy. No attempt amples of these manipulations have been
424 DIGITAL RADIOGRAPHY
given in the discussion of DSA methods to ful features of logarithmic conversion is
illustrate this point. Third, there are ma that equal-sized vessels appear equally
nipulations employed to enhance the visi dense after the later subtraction.
l;>ility of certain types of structures or cer
tain features of images. Finally, certain An operation that would be immediately
manipulations are not intended to result in useful is the correction of images for x-ray
an improved visible image at all, but rather scatter and image system veiling glare.
are aimed at allowing the computer to ex Such corrections are needed to increase the
tract information such as projected crop utility of numerical densitometry tech
yields in Canada, volcanic activity on Ju niques (to be mentioned shortly). In an
piter's moons, or the probability that a pa other area, the II-TV system introduces ge
tient has cardiac insufficiency. A single type ometric distortion in the image. This
of mathematical operation may find appli geometric distortion causes few problems
cation in all four of these types of image in simple image viewing, but makes exact
manipulations. Similarly, a single applica evaluation of spatial relationships some
tion may require all four general types of what difficult. Generally, the specific op
image processing. erations employed for preprocessing are
not intended to compensate for all prob
For instance, several processing steps are lems in the original data exactly. The com
applied in the mask subtraction technique mon approach is to use approximate meth
of DSA. The individual images are first ods to attack only those problems most
preprocessed by a logarithmic or similar important to the application. Something
conversion. Next, individual images are similar to logarithmic conversion is very
subtracted from each other to remove important for DSA, and scatter and veiling
structures that are not of interest. A narrow glare corrections would be helpful, but ge
display window is then selected to increase ometric corrections would be superfluous
displayed vessel contrast. The first of these for most DSA applications.
manipulations falls most conveniently into
the preprocessing category. Subtraction Image Enhancement
provides a viewable image suitable for the For our purposes, image enhancement
application (DSA), our second category. operations are performed at the viewer's
The increase of displayed contrast by win option after the basic image of a particular
dowing is an example of image enhance type has been formed. This might be
ment. Numerous researchers are working termed "postprocessing of images." There
on methods for extracting numerical in are so many image enhancement methods
formation regarding blood flow from DSA available that books on the subject survey
images, which would fall into our fourth only a small fraction of the available tech
general category. Obviously, categorization niques, and are obsolete before they are
of image processing operations by in published. Three postprocessing opera
tended purpose of the operation is some tions that are common in digital radiog
what arbitrary, because an argumentative raphy are mask reregistration, noise
person could successfully place a given ma smoothing, and edge enhancement. A
nipulation into some category other than common feature of these three operations
the one which we have chosen. (and enhancement operations in general)
is that "enhancement" is actually the sup
Image Correction and Preprocessing pression of information that the viewer
deems to be unnecessary for a particular
In general, preprocessing of images is problem.
done to increase the value or accuracy of
the data for later processing steps. The util Mask Reregistration. Mask reregistra
ity of a preprocessing step is very depend tion is sometimes useful when there is pa
ent on the later use to be made of the tient motion between the time the mask is
images. For instance, one of the most use- taken and the time that contrast material
DIGITAL RADIOGRAPHY 425
arrives in the vessel of interest. The prob The reregistration of the mask may be
lem is illustrated in Figure 22-22, in which accomplished either manually (viewer-con
portions of the two digital images are trolled) or automatically (computer-con
shown. Each pixel is represented by a num
ber (brightness level) in a digital matrix. trolled). Manual reregistration is similar to
Bony structures within the patient that
should subtract on the two images are not alignment of the films. The viewer rotates
recorded in the same position on the mask
frame as the same structure on the con the mask and translates it vertically or
trast-containing frame. The subtracted
horizontally while viewing the subtracted
image of Figure 22-22A shows the misreg
image until a satisfactory subtraction is ob
istered bony edges that produce motion ar
tifacts whose magnitudes are greater than tained. Automatic reregistration depends
the magnitudes of the contrast-containing
vessels of interest. The same problem oc on computer calculations, and may be done
curs in film-screen subtraction angiog
raphy, in which the mask and contrast-con in several ways. One method is first to cal
taining image are aligned by eye until the
"best" subtraction is obtained. This may be culate the sum of the "absolute values" of
considered to be a form of manual rereg
istration, and is successful when patient all pixels in a subtracted image. The ab
motion is moderate. A similar approach
will work for DSA. When the reregistered solute value of a negative number ( - 5, for
mask is subtracted from the contrast-con
instance) is just the number without the
taining image, Figure 22-22B does not
negative sign (5), and is the same as the
contain the motion artifact. The aim is to
throw away the information represented absolute value of the same positive number.
by the motion artifact.
The sum of the absolute values of 5 and
-
+5 is 10.
Now an observation can be made. The
contrast material is present on a subtracted
image whether the mask is properly reg
istered or not. In the case in which the
image is properly registered, the only
image features present are contrast and
noise. Misregistration adds such factors as
bony edges to the subtracted images, and
the sum mentioned above should be higher
Figure 22-22 Mask reregistration. (A) Poor registration. (B) Good registration of mask and
contrast-containing image
426 DIGITAL RADIOGRAPHY
than for a properly registered mask. The Rows: Columns: 3
computer can therefore try numerous po I I2 3
sitions for reregistration, calculate the sum
of absolute pixel values for each, and pick 01
the reregistration position for which the
sum is a minimum. Under good conditions, 22 5 4
this minimum sum position will produce
acceptable subtracted images. 38 3 1
etc.
There are numerous situations in which
mask reregistration will be of limited value. Figure 22-23 Smoothing noise by blurring an
The patient is three-dimensional, and image
mask reregistration operations are effec
tive only for motions confined to a plane. adjacent pixels (rows 2, 3, and 4 of the orig
Upper structures project onto different
lower structures when the patient rolls onto inal) to form the first pixel in the second
one side as compared to being flat on his row. The final image is a blurred version
back. Reregistration cannot exactly com of the original. The visual prominence of
pensate for this type of motion. The mo noise has been suppressed through the
tion of structures within the patient (es process of averaging noise within small
pecially bowel gas and larynx) also changes areas, but the disadvantage is that resolu
the relative positions of prominent struc tion is decreased.
tures, and again reregistration cannot com
pensate exactly. In the case of automatic The operation just described is a filtra
reregistration, there are numerous situa tion operation. A final image was gener
tions in which the minimum sum position ated by applying a consistent mathematical
of the mask (or some other calculation cri operation to the original image to form the
terion) is not the position that even the first pixel, and then shifting and repeating
most forgiving viewer would judge to be to form subsequent pixels. The operation
optimum for subtraction. of the filter suppressed small structures
(high spatial frequencies) and had little ef
Noise Smoothing. Noise smoothing is an fect on large structures (low spatial fre
quencies). This type of operation is some
attempt to decrease the visual prominence times called "low-pass spatial filtering,"
of noise so that low-contrast objects of mod indicating that low spatial frequencies are
erate to large size may be better appreci passed and high spatial frequencies are fil
ated. All methods of smoothing x-ray tered out. For general information, the
quantum noise sacrifice some resolution in specific mathematical operation described
the process of smoothing the image. One in the preceding paragraph is a convolu
tion. We note in passing that the literature
method is illustrated in Figure 22-23. The contains references to "spatial domain" fil
tering (of which the above is an example)
technique operates by reducing the statis and "frequency domain" or "Fourier" fil
tical fluctuations in each pixel by averaging tering as mathematical approaches. The
the pixel with its closest neighbors. The specific mathematical approach is largely a
first pixel in the smoothed image is formed
by averaging the nine nearest neighbors in
the upper left corner of the original image
(rows 1, 2, and 3). The second pixel in the
smoothed image is formed by shifting one
column to the right in the original image
and averaging, and the process continues
until the entire first row has been formed.
The second and subsequent rows are
formed similarly. One shifts down a row in
the original image and averages the nine
DIGITAL RADIOGRAPHY 427
matter of computational convenience, be cific mathematical operations could be
cause a given filter can generally be imple used to perform exactly the same overall
mented either by Fourier methods or by operation.
spatial domain methods. With that, we put
the mathematics of filters to rest. Information Extraction
Edge Enhancement. Edge enhancement A most promising area in digital radi
is intended to increase the visibility of small ography is the extraction of numerical or
structures with moderate to high contrast. graphic information from images. The ex
The basic goal is to discard most of the traction of such information from nuclear
information about the large structures and medicine images is now routine in some
keep the information that relates to small applications. Many nuclear medicine blood
structures. The appearance of a xerora flow measurements and similar dynamic
diograph is very familiar to most radiolo techniques can be implemented using DF
gists. The principal features of the xero images. The development of useful meth
radiograph that distinguish it from film ods for extracting information from DF
radiographs and DF images are that the images is still in its infancy at present.
xeroradiograph has a very broad latitude
but still shows edges at high contrast. Prob It might be useful to have a technique
lems with the xeroradiograph are that the that could accurately measure both the
necessary patient exposure becomes sig quantity of contrast material contained
nificantly higher as the kVp is increased. within some organ and the way in which
Also, once xeroradiography is chosen, it the quantity of contrast changes with time.
becomes difficult to display these images as A DSA series of images contains the
the more conventional film radiographs. needed information. A somewhat trivial
For these and other reasons, xeroradiog technique (not workable as described here)
raphy is not widely used for general radi begins when a viewer circles the region of
ographic applications. interest on one of the images. The bright
ness level in any given pixel in the sub
If a conventional radiograph could be tracted image is directly proportional to the
processed into an image that resembled a quantity of contrast material in the patient
xeroradiograph in appearance, then it volume imaged onto the pixel for the ide
might be possible to have the advantages alized case (ignore scatter, veiling glare, ge
of both methods readily available. The ometric image distortion, and magnifica
combination of the blurred (low-pass fil tion). The total quantity of contrast within
tered) imagejust described and the original the region of interest could be calculated
image contain everything necessary to im by simply adding together the contribu
plement edge enhancement and mimic a tions from all the individual pixels. Suc
xeroradiograph. The low-pass filter con cessive images of the same region of inter
tains only the information about large est could be processed in the same way to
structures and has low noise, while the orig produce the information needed for a
inal image contains additional information graph of time versus total contrast mate
about the edges plus noise. The subtraction rial. Unfortunately, all the factors that were
of the low-pass filtered image from the ignored are important to the accuracy of
original yields an image in which edges and the results. The person charged with the
small structures remain. Edge enhance resolution of these technical problems may
ment is accomplished by suppressing in have an easy task as compared to the per
formation regarding large structures. Un son who is responsible for evaluating the
fortunately, noise is also prominent in this technique for efficacy.
edge-enhanced image. The final image has
effectively been high-pass filtered, and the
operation is sometimes referred to as a
blurred mask subtraction. Many other spe-
428 DIGITAL RADIOGRAPHY
FUTURE EQUIPMENT that would strike other regions of the
DEVELOPMENTS image receptor. A long x-ray exposure is
used, during which the beam-defining col
Alternate Image Receptor Systems limator slit and the scatter rejection post
patient slit are swept in synchrony from the
At present, digital radiography is almost head to the foot of the patient.
synonymous with digital fluoroscopy in
clinical use. A large fraction of DF systems The single most important reason for the
are installed on C-arm units, and almost all development of slit radiography is the very
are limited to use in one room or in two high scatter-rejection characteristics of the
closely adjacent rooms. The average DF technique. Figure 22-24 compares scatter
unit utilizes a 9-in. II and is capable of gen rejection for a slit radiography system and
erating digital images on a 512- x 512- a two-dimensional film-screen imaging sys
pixel matrix. Most manufacturers now tem with a grid. The only radiation reach
offer 1024 X 1024 matrices as options, and ing the image receptor during the expo
12- to 14-in. lis are available for C-arm use. sure for slit radiography is that portion of
Both the large matrices and the large lis the primary radiation that does not un
are expensive. In addition to limitations on dergo any interactions within the patient,
field of view and matrix-imposed resolu and radiation that is scattered over very
tion, we have discussed sources of image small angles. Radiation scattered over wide
degradation inherent in conventional x-ray enough angles to miss the postpatient slit
lis and in TV video cameras and chains. and almost all multiple scattered radiation
are absorbed before reaching the image re
There are many alternatives to the con ceptor. The gridded system also rejects sin
ventional II-TV-based imaging chain. gly scattered photons, although perhaps
These have been investigated for many somewhat less efficiently than for slit ra
years, but digital x-ray imaging lends new diography. Also, multiple scattered pho
urgency to the search for new imaging sys tons may reach the image receptor. The
tems. Image receptor systems for three importance of scatter for radiographic
areas of application are receiving most of imaging in general, and digital radiogra
the research attention. The first is slit ra phy in particular, has been discussed in de
diography using linear detector systems. tail. Scatter rejection increases contrast, in
The second is two-dimensional detectors creases dose efficiency by reducing x-ray
for replacement of film-screen cassettes. quantum requirements, and provides a
The third area now uses automatic film final image that reflects true attenuation in
changers. We are short on crystal balls, so thin or thick regions more accurately.
each example offered has been chosen to
illustrate a diversity of approaches rather A. B.
than to predict an ultimate winner of the "-slit
technologic sweepstakes for that area.
Figure 22-24 Comparison of scatter rejection
One-Dimensional Image Receptors. for a grid (A) and for slit radiography (B)
Most radiographic imaging utilizes two
dimensional image receptor systems. An
entire volume of the patient is projected
onto the two-dimensional receptor (typi
cally a film-screen cassette or II) during a
single exposure to form the final image. In
a technique called "slit radiography," the
x-ray beam is collimated into a fan-shaped
beam so that a thin line is defined on the
final image. Postpatient collimation is used
to define further the line of the final image
that is being formed, and to reject scatter
DIGITAL RADIOGRAPHY 429
Detector systems commonly in use for ing. Also, much more time is required to
x-ray CT may be considered to be one obtain an image. Inaccuracy in collimating
dimensional. Experiments with slit radio the beam and in moving the beam-defining
graphic techniques were done with some slit increases patient dose. Some of the most
of the earliest CT scanners. Many modern valuable types of dynamic digital subtrac
CT scanners have some type of scout image tion angiographic procedures, therefore,
capability (such as the GE Scoutview), are clearly impossible. The extension to a
which is in fact slit radiography. GE calls larger image matrix would make the x-ray
the technique "scanned projection radi tube load and exposure time drawbacks
ography." The biggest problem is that, be even more significant.
cause of the size of individual detector el
ements, spatial resolution is poor for There are some extensions to the tech
general radiographic work. A typical scan nique that might help to solve some of
ning slit imaging system with a single-line these problems. For instance, the slit might
image receptor currently being applied to be made larger, and several lines of detec
chest radiography digitizes the line into tors might be used to increase the number
1024 separate pixels. There is controversy of lines defined per exposure. Unfortu
over whether 1024 elements in one dimen nately, this tends to increase the complexity
sion is adequate for chest radiography, and and consequently the cost of the system.
image matrix sizes of greater than 1024 x Slit radiography was originally developed
1024 may be necessary. on a film-screen system, which is a two
dimensional image receptor. There may be
The slit radiography approach that de little net advantage for digital radiography
pends on a single-line image receptor does in using a receptor system that is inherently
have some significant drawbacks. Each in one-dimensional versus using one that is
dividual line of the image requires that inherently two-dimensional.
enough x-rays be detected to define that
line. It is true that fewer x rays (and less Fixed Two-Dimensional Image Recep
patient exposure) are required to arrive at tors. For fixed systems there are alterna
the same contrast detectability in the ab tives to lis and TV cameras. An old idea
sence of scatter, and it is also true that the for replacement of conventional x-ray lis
detector system might be more efficient in was to use optical coupling of the light
stopping x rays. The slit radiography sys image formed on an x-ray screen, followed
tem, however, still requires that a certain by light amplification. Each absorbed x ray
minimum number of x rays be delivered to produces so much light than an efficient
each line of the system. For a 1024-line lens system can guarantee that each x ray
image, this essentially amounts to making will be detected in the light amplifier. It is
1024 separate exposures. Each exposure easy to amplify the light enough so that the
will be considerably less than required for presence of the x ray is detected in the final
a single film-screen radiograph, but the image. Compared to a small x-ray II, the
sum of all individual exposures will still be solution is both bulky and expensive. For
quite large. larger field sizes, however, the approach
does have some merit. The input x-ray
The net result is that the x-ray tube must screen can be flat if that is desirable. Good
deliver about 100 times the radiation for optical systems with low veiling glare char
the single-line slit radiography system as acteristics can be designed.
would be required for a film-screen ex
posure with similar photon statistical con Alternatives to conventional TV cameras
trast detectability characteristics. These ex are also under development. One of the
posure requirements can be met in a most promising, which has a light-sensitive
dedicated chest imaging system. The prob region about the size of the input phosphor
lem becomes more acute when higher ex on a conventional TV camera tube, is sim
posures are needed, as in abdominal imag- ilar in appearance to a large semiconductor
electronic chip. A two-dimensional array of
430 DIGITAL RADIOGRAPHY
light detectors is embedded in this light play of recently acquired radiographs, and
sensitive area. Each element of the array a somewhat slower method for transfer
defines a single pixel of the image, and is ring images from archival storage.
essentially independent of all other pixels.
The advantages, in addition to size, are that The digital archive storage problem ap
the system is more light-sensitive than most pears to be intractable with currently avail
types of conventional TV tubes, and has
much lower electronic noise. able technology. Given 2048 x 2048
Film-Screen Cassette Replacement. The images, each image would require the stor
benefits of having an image receptor that age of about 4,000,000 pieces of data. Dig
can be carried to remote locations and used ital discs capable of storing 250 such images
with virtually any existing radiographic
x-ray machine are obvious. An image re are becoming more economical (larger and
ceptor similar to a film-screen cassette in more expensive discs are also available),
portability, resolution, and x-ray detection
efficiency will eventually be developed for but storage of even 1 week's radiographs
use in digital radiography. There are many
possibilities. For instance, xeroradio for a sizable radiology department would
graphic plates initially accumulate an be prohibitively expensive. Other digital
image in the form of a charge distribution disc technology (such as the much publi
that has been altered by the absorption of cized optical or laser discs) is under devel
x rays. Several methods have been pro opment. Archiving large numbers of
posed and tried for scanning this charge images in digital form presents a formi
distribution to convert the charge image dable challenge.
into an electronic video image directly. Cas
settes similar to xeroradiographic cassettes Fortunately, medical imaging is not the
could be used at any convenient location only area with the need for better digital
and then brought to a central facility for displays and storage retrieval methods. Ap
"processing" and storage as digital images. plications as diverse as robotics, earth re
sources satellites, and computer games are
Archiving and Display of Large Image adding impetus to development of the nec
Matrices essary technology. There no longer seems
to be a question about whether an all-digital
At present, almost all DF display ma radiology department will be possible. The
question now is how long it will be before
trices are 512 x 512 pixels. Archiving is such a department actually comes into be
mg.
usually accomplished by recording the
video display of the DF images onto film. SUMMARY
The development of a digital radiogra The most common type of digital radi
phy apparatus that uses larger image ma ography system is digital fluoroscopy (DF).
trices will require better display systems A DF system requires an image intensifier
than those presently in use. Some expen
sive display systems are available with res (II) with a high contrast ratio and a TV
olution of 2048 x 2048 pixels or better, chain with low lag and low electronic noise.
The TV system may be operated in an in
but currently these are expensive and not terlaced, progressive, or slow scan mode.
very reliable. Presumably a radiology de
partment that handles all images in digital The digital image processor performs
format will require a large number of such four basic functions: forming the image,
display consoles, each with a moderate storing the image, displaying the image,
amount of image postprocessing and en and manipulating the image.
hancement capability. Each console will
probably need some rapid method of trans An analog-to-digital converter converts
ferring images from a central area for dis- the analog video image into digital form.
The computer handles numbers in binary
form. Digital information is any informa
tion represented by discrete units. Analog
information is any information repre-
DIGITAL RADIOGRAPHY 431
sented in continuous, rather than discrete, 1. Image correction and preprocessing
fashion . 2. Formation of viewable images appro-
Manipulating the window width of the priate to the application
digitized image changes image contrast in 3. Image enhancement
a manner analogous to changing film 4. Image information extraction
gamma in routine radiography. Changing
the digital window level is analogous to Exciting new types of hardware are be-
changing film-screen speed. Logarithmic ing developed. Many technical problems
tr-ansformation of the digitized image en
sures that equal absorber thickness changes must be overcome before all medical
will result in approximately equal bright
ness changes, whether in thin or thick body images are routinely acquired and manip
regions. Film-screen radiographs inher ulated by digital computers.
ently contain an analogous transformation.
REFERENCES
The major sources of noise in a digital
fluoroscopic system are electronic noise 1. Brody, W.R., and Macovski, A.: Dual-energy dig
and quantum noise. Higher subject con ital radiography. Diagnost. Imag., 18: 1981.
trast, increased patient exposure, large ob
ject size, and frame averaging all reduce 2. Foley, W.D., Lawson, T.L., Scanlon, G.T.,
the prominence of noise. Heeschen, R.C., and Bianca, F.: Digital radiog
raphy using a computed tomography instrument.
X-ray scatter rejection increases contrast Radiology, 133:83, 1979.
and dose efficiency by reducing x-ray
quantum requirements, and provides a 3. Frost, M.M., Fischer, H.P., Nudelman, S., and
final image that reflects true attenuation in Rohrig, H.: Digital video acquisition system for
thin or thick body regions more accurately. extraction of subvisual information in diagnostic
Veiling glare reduces contrast. medical imaging. SPIE 127:208, 1977.
We have described four techniques for 4. Kruger, R.A., Mistretta, C.A., Crummy, A.B.,
digital subtraction angiography: Sackett, J.F., Riederer, S.J., Houk, T.L., Goodsit,
M.M., Shaw, C.G., and Flemming, D.: Digital K
1. Mask subtraction (most common) edge subtraction radiology. Radiology, 125:243,
2. Dual energy subtraction 1977.
3. Time interval differencing
4. Temporal filtering 5. Mistretta, C.A., and Crummy, A.B.: Digital flu
oroscopy. In The Physical Basis of Medical Imag
Digital image processing is intended to ing. Edited by G.M. Coulam, J.J. Erickson, F.D.
accomplish one or more of four basic func Rollo, and A.E. james. New York, Appleton-Cen
tions: tury-Crofts, 1981, p. 107.
6. Mistretta, C.A., Crummy, A.B., Strother, C.M.,
and Sackett, J.F.: Digital Subtraction Arteriog
raphy: An Application of Computerized Fluo
roscopy. Chicago, Year Book Medical Publishers,
1982.
7. Ovitt, T.: Noninvasive contrast angiography. Pro
ceedings of a Conference on Noninvasive Car
diovascular Measurements. Palo Alto, CA, Stan
ford University Press, 1978.
CHAPTER Nuclear Magnetic
Resonance
23
Nuclear magnetic resonance (NMR) is a Perspective
powerful technique for the investigation of
chemical and physical properties at the mo We are going to look in detail at the phys
lecular level. Since its inception in the mid- ics (without the mathematics) of NMR.
1940s, it has been used extensively as an Note that the physics of NMR is completely
analytical tool for biologic studies as well as different from anything that has been in
for physical and chemical investigations. troduced and used in the radiological sci
The first imaging technique is attributable ences. This very fact is going to make NMR
to Lauterbur.2 In 1972, at Stony Brook, more difficult to understand than was, for
New York, he was able to generate the first example, CT. For CT scanning we already
two-dimensional NMR image of proton understood the principles of x rays, detec
density and spin lattice relaxation time. tors, and attenuation; all we needed to
Lauterbur coined the term "zeugmatog learn were image reconstruction, computer
raphy" (from the Greek zeugma, meaning capabilities, and how to read the cross-sec
that which joins together) for his tech tional images. For NMR we need to start
nique. Joined together are a radio fre with the very basic concepts of the nucleus
quency magnetic field and spatially defin and proceed from there.
ing magnetic field gradients that produce
the NMR image. (If you try to pronounce So the road is clear, if somewhat rocky.
the word, or even spell it, it is easy to see We must describe nuclear structure and
why "NMR imaging" is used more exten nuclear angular momentum, and then dis
sively.) We will use the term Nuclear Mag cuss gyroscopic behavior (beautifully illus
netic Resonance (NMR) to indicate the trated by the toy top). The combination of
physics of nuclear magnetic resonance angular momentum and gyroscopic effects
phenomena (there is also an electron spin will lead us to the resonance (R) part of
resonance that has not yet appeared in NMR. Resonance here refers merely to the
medicine). In the next chapter, we will use change in energy states of the nuclei caused
the term Magnetic Resonance Imaging by absorption of a specific radio frequency
(MRI) to indicate the way that NMR is used (RF) radiation (but not of RF radiation at
to produce a medically useful image. MRI any other frequency). The resonance con
will be introduced in this chapter and ex cept is one that we have already seen in
panded in the next chapter. We do not feel characteristic x-ray production. Finally, we
strongly about these terms, but note that will find that resonance can occur in an
most physics texts discuss NMR while med external magnetic field, which of course i:;
ical texts discuss MRI. The physics is the the magnetic (M) part of NMR.
same; it's difficult and beautiful.
We are going to try to convince you in
the next few pages that a proton in a mag-
432
NUCLEAR MAGNETIC RESONANCE 433
netic field will precess about the magnetic electromagnetic theory, and even a bit of
field because it has spin angular momen classical mechanics. (Normally six graduate
tum and a magnetic dipole moment. physics courses cover this material.) One of
There are three terms in the last sentence the biggest problems we will find as we go
that we have not introduced before in the along is to represent three-dimensional en
field of radiology. Before we discuss them tities with two-dimensional drawings; some
in relation to the hydrogen nucleus, or the of the drawings are more successful than
proton if you prefer, we would like to ex others, but we have tried our best.
plain these three terms by using the earth
as an example. ANGULAR MOMENTUM
We are all familiar with the day-night The description of NMR must be made
rotation of the earth, or at least we ought in terms of the angular momentum of the
to be. We are aware that the earth rotates nucleus, so let us introduce the concept of
ab,out an axis which we call the north-south angular momentum now. Angular momen
axis (the two ends being the north pole and tum is one of the sacred cows of physics
south pole). In discussing rotation, it is nec because, like energy, it is a constant of mo
essary to discuss that rotation relative to tion. Angular momentum describes the
some axis. The day-night rotation of the rotational motion of a body. Unlike en
earth is analogous to the "spin rotation" of ergy, angular momentum has direction (it
the nucleus (proton). The earth also has a is a vector) as well as magnitude.
magnetic field, with the north pole of that
magnetic field fairly close to the spin axis The angular momentum of a body may
of the earth. We call the north pole of the be changed by applying a torque on the
earth the magnetic north pole. Because the body. Torque is a force that tends to rotate
earth has two magnetic poles (north and the body, rather than moving it in a straight
south) it is a magnetic dipole. The earth is line. Sometimes the change in angular mo
a spinning magnetic dipole. As the earth mentum increases or decreases the rota
spins on its axis it also precesses. Precession tional motion of the body. Sometimes the
is change in the direction of the axis of change in angular momentum merely
rotation. The earth's precession will cause changes the direction of the axis about
the axis of the earth's rotation to move so which the body is moving. Later we will see
that Polaris will no longer be the North these statements illustrated by the spinning
Star. In 12,000 years, the North Star will top.
be Vega.
There are two types of rotational motion,
The proton precesses a bit faster than orbital and spinning. As you might guess,
the earth, but it is still the precession of there is an angular momentum associated
the proton that allows magnetic resonance with each of these motions. The earth and
imaging. And for this reason, it is necessary sun are good examples. The earth is or
that we investigate these strange things that biting the sun in a stable (unchanging) orbit
we call "spin angular momentum" and and completes an orbit in I year. The an
"magnetic dipole moment." With the earth gular momentum caused by orbiting, the
we do not see resonance because we cannot orbital angular momentum, depends on
make the earth flip on its axis. So our anal the earth's mass and velocity and on the
ogy falls down on the resonance part. For radius of the orbit. In addition, the earth
continued well being of the human race, is rotating (spinning) about its own axis.
we do not want to see resonance of the This rotation, or spin, produces the day
earth. night period; there is one complete rota
tion about its axis in 1 day. We wish to em
We will present a brief discussion of nu phasize the difference between rotational
clear physics, quantum mechanics, some angular velocity and angular momentum.
434 NUCLEAR MAGNETIC RESONANCE
Angular velocity is simply a measure of the Chapter 1, h was introduced in its relation
rate of rotation. Rotational angular mo to the energy of a photon. In this chapter,
mentum is the angular velocity times the h is introduced as the fundamental unit of
moment of inertia. The moment of inertia angular momentum. It is the same constant
is just a description of the mass and how in both of these applications. (Isn't it
the mass is distributed over the body (a disc astounding that the same constant can be
and a wheel, though they have the same used to express both the energy of a pho
mass, will have a different moment of in ton and the angular momentum of a par
ertia). In nuclear physics we call the day ticle?)
night rotation "spin;' which has a spin an
gular momentum associated with it. The Two interacting electrons always exist in
spin motion is an intrinsic property of the the lowest possible energy state unless they
earth and does not depend on its interac are disturbed from the outside world. The
tion with the sun. If the sun were to dis lowest energy state for the interaction is
appear, the earth's orbital motion would when the spin angular momenta are in an
cease; it would move off in a straight line tiparallel directions. The direction of the
but would continue to rotate on its axis. Of spin is along the axis of rotation. Imagine
course, that would matter little to us since a ball with a sharpened pencil through it
we would all be frozen very quickly. (Fig. 23-1A). Now rotate the ball about the
pencil so that the fingers of your right hand
Electron Angular Momentum curl in the same direction the ball is rotat
ing and your thumb points to the sharp
We will briefly discuss electron angular end of the pencil. In this simple model, the
momentum even though electrons are not pencil represents the spin angular momen
involved in NMR. The electrons in atoms tum of the electron (represented by the
have both orbital and spin rotation. The ball. Physicists really don't like to think of
electron's orbital angular momentum de electrons as spherical particles, but for this
pends on its relative motion to the nucleus text the picture is acceptable). The point of
(i.e., which shell it is in), but the electron's the pencil is aimed in the direction of the
spin angular momentum is an intrinsic spin angular momentum of the electron.
property that it has by existing. The total With two balls representing two electrons
electron angular momentum is some com (Fig. 23-1B), the lowest energy state exists
bination of the spin and orbital angular when the pencils are parallel but pointing
momenta. The value of the spin angular in opposite directions (i.e., the spin angular
momentum of every electron in the cosmos momenta are in antiparallel directions).
is the same. The detectable spin angular This configuration of the lowest energy
momentum of an electron equals the spin state between electrons is usually called
quantum number multiplied by a constant. spin-pairing, a term we will use frequently
The spin quantum number (usually more in this chapter. In the helium atom, there
simply called "electron spin") is given the are two K-electrons. These two electrons
are spinning in opposite directions, called
symbol s, and s always equals I,-;;. The con by physicists "spin-up" and "spin-down."
We suspect that if there were two earths in
stant is given the symbol hand equals h/27T the earth's orbit, the sun would rise in the
west and set in the east on the other earth.
(h = Planck's constant = 6.6 X 10-34 joule This certainly represents the concept of
spin-up and spin-down. In atomic struc
·seconds). The symbol his pronounced "h ture, electrons will nearly always pair up
cross." with one spin-up and one spin-down. The
In Chapter 1, the value of h was given
as 4.13 x 10-18 keV · sec. Both keV and
joules are energy units, so that the differ
ence in the value of h is just a matter of
the size of the energy unit we are using. In
NUCLEAR MAGNETIC RESONANCE 435
I
I
I
I
I
AB
Figure 23-1 Spin angular momentum direction (A) and spin pairing (B)
net spin angular momentum for a spin-up that holds the nucleus together. (The origin
and spin-down pair is zero. of the nuclear force will not be discussed
here.) The concept of the protons and neu
There are a few exceptions in which the trons maintaining their identity while in
lowest energy state of a group of electrons the nucleus is acceptable although not en
is not produced by spin pairing. Nonspin tirely correct. This concept most readily al
pairing results in ferromagnetic materials, lows discussion of nuclear magnetism, and
of which iron is the best-known example. is the picture that we will use. Therefore,
The very strong magnetic properties of we have the nucleus with protons and neu
iron are caused by nonpairing electrons. trons being contained in a small volume by
large nuclear forces.
Nuclear Angular Momentum
One further step is required. The nucle
The nucleus is composed of neutrons ons (both protons and neutrons) do, in
and protons. Recall from Chapter 2 that some fashion, orbit about the center of the
protons have one unit of positive charge nucleus and have orbital angular momen
(equal to the unit of negative charge on the tum. The orbital motion of the nucleons is
electron) while the neutron has none. actually caused by the spinning motion of
Their mass is about the same, about 1836 the entire nucleus rather than by inde
times larger than the electron's mass. The pendent orbital motion of the individual
collection of protons and neutrons, called particles within the nucleus. An analogy is
collectively nucleons, is confined to a very Mount Everest orbiting about the earth's
small volume called the nucleus. axis of rotation. In addition, both protons
and neutrons have the same spin and
It should be obvious that the nucleus is therefore the same spin angular momen
not held together by an electrostatic force tum as does the electron.
(i.e., Coulomb force, which is the force be
tween charged particles), because the like Furthermore, there are energy levels for
charges of the protons would be expected the nucleons very similar to the electronic
to repel each other. There is a nuclear levels (shells) in atomic structure. By now
force, much larger in magnitude but it comes as no surprise that the protons will
shorter in range than the Coulomb force,
436 NUCLEAR MAGNETIC RESONANCE
fill these energy states by pairing them momentum). Why is angular momentum
selves with spin-up and spin-down, or that of the nucleus important to NMR? Without
the neutrons do the same. A proton will angular momentum, a nucleus would not
not pair with a neutron. This pairing of precess when placed in a magnetic field.
protons or neutrons produces cancellation Without precession there would be no res
of their spin angular momentum. The nu onance, and the R part of NMR would not
cleus, however, does have angular momen exist. We hope this introduction to angular
tum. The angular momentum of the nu momentum will help you develop a better
cleus is determined by the spin of the understanding of nuclear resonance.
unpaired neutrons and protons and by the
orbital angular momentum of the neu Up to this point we have discussed the
trons and protons. Something very inter fact that the charged nucleus is spinning
esting happens here. The combination of and has angular momentum. Now we must
all these functions produces a very simple investigate the magnetic effects caused by
number for the value of the nuclear spin, this spin. We will introduce the subject by
designated by the letter I. The maximum using illustrations involving electrons flow
detectable nuclear angular momentum is ing in a wire.
Ih. The letter I is called the nuclear spin
(analogous to s, the electron spin). MAGNETISM AND THE MAGNETIC
DIPOLE MOMENT
Maximum detectable nuclear angular momentum = IIi Magnetic Field Due To Electron Flow
I = nuclear spin To see how magnetism occurs in the nu
cleus, and also in the orbiting electrons, we
h = h/27T (h is Planck's constant) need to retreat from the world of tiny par
ticles to the more conventional world. Con
The nuclear spin, I, is always either zero, sider electrons flowing through a wire. The
electron flow will produce a magnetic field
multiples of ':t];, or whole numbers. (Note (H) surrounding the wire. The direction of
the magnetic field can be determined by a
that this is a bit more complicated than with
electrons, for which s is always V:;.) Thus left-hand rule (Fig. 23-2A). With the
there are only three kinds of nuclei as far
as the spin is concerned: thumb of the left hand pointing in the di
rection of electron flow, the fingers will curl
1. If the mass number A (protons plus in the direction of the magnetic field. (Note
neutrons) is odd, the nuclear spin, I, that most physics tests define current in
terms of positive charge motion. For such
is a multiple of ':t]; (':t];, %, %, %) a definition, all the left-hand rules become
2. If the mass number A and the atomic right-hand rules.) When the wire is formed
into a circle, the same electron flow will
number Z (protons) are both even, I produce a magnetic field upward inside the
is 0 circle and a field downward outside the cir
3. If the mass number A is even but the
atomic number Z is odd, I is a whole cle (Fig. 23-2B). The magnetic field about
number (I, 2, 3, 4, or 5)
the loop of wire looks very much like the
There are no other possibilities. Al field surrounding the short bar magnet of
though the concepts concerning the nu
clear angular momentum are difficult, the Figure 23-3A. Note that Figure 23-3B is
nuclear spin I that gives the value of the the same as Figure 23-2B.
nuclear angular momentum is rather an
uncomplicated number. Of more immediate interest is what hap
pens if both the bar magnet and the wire
Why do we include angular momentum? loop with electrons flowing through it are
Angular momentum is a physical quantity placed in another (or external) uniform
that describes the rotational motion of a
body (i.e., a spinning nucleus has angular
NUCLEAR MAGNETIC RESONANCE 437
A. B.
Figure 23-2 Magnetic field (H) caused by electron flow
Figure 23-3 Magnetic field (H) comparison between bar magnet (A) and loop of electron flow
(B)
magnetic field. In Figure 23-4A, the bar The rotation will be such that the arrow
magnet will have equal but opposite forces from the S pole to the N pole will align
on the ends (actually, nearly the ends with the arrows representing the magnetic
where the magnetic poles are located), and field. We say that the magnet aligns itself
therefore will have no net force (a net force along the field. As the magnet moves to
would cause the bar to move up or down). align along the field, the torque decreases
Each pole has a torque, however, that will to zero when the bar is parallel to the field.
cause a rotation about the center of the bar. We have just described a magnetic com
pass.
A. B.
The loop with electrons flowing in it will
Figure 23-4 Effect of external field on bar also have a net torque and will rotate to
magnet (A) and wire loop (B) align the loop itself perpendicular to the
field. The axis line is defined as a line that
is perpendicular to the plane of the loop
and that passes through the center of the
loop (Fig. 23-4B). This axis is analogous
to the axle of the wheel. When the loop is
aligned perpendicular to the magnetic
field, the axis line is along the field, just like
the bar magnet in Figure 23-4A. The loop
alignment in a field is the principle on
which voltmeters and ammeters operate.
438 NUCLEAR MAGNETIC RESONANCE
Magnetic Dipole Moment Magnetic Dipole Moments for Rotating
The magnetic dipole moment (MOM) is Charges. Please note that a single electvon
a property of a magnet or of a loop of wire orbiting about the nucleus constitutes an
with electrons flowing through it. The rea electron flowing in a circle (loop); it has a
MDM. If the electron orbit is the smallest
son for introducing the MOM is that the possible orbit (K shell), the MDM is called
nuclei we use in NMR also have a mag a Bohr magneton. For an electron in a
higher shell (e.g., L, M), the MDM is the
netic dipole moment. If we understand the orbit number (L = 2, M = 3, etc.) multi
effects of the MDM for these large bar plied by the Bohr magneton.
magnets, we can more easily understand
the effects for the smaller, invisible nuclei. In addition to its orbital rotation, the
electron has intrinsic spin. This spin rota
Perhaps the best way to describe the tion also represents a rotating charge. The
MDM is to say that it is that property or
electron has a MOM of one Bohr magne
characteristic of a magnet (or wire loop) ton associated with the spin (this is in ad
that indicates how quickly the magnet will dition to the Bohr magneton associated
align itself along a magnetic field. For a with orbital motion). We will give the value
bar magnet, the stronger the magnet, the of the Bohr magneton (1-LB) in two systems
more quickly it will align with the field. In of units:
addition, the length of the magnet is sig
nificant: long magnets will align faster than 1-L• = 9.27 x 1 D-24 J/tesla (SI units)
short ones, all else being equal. For the loop 1-L• = 9.27 x 1 D-21 erg/gauss (cgs units)
of wire, the larger the electron flow, the
more quickly the loop will align itself. In We include cgs units becauseNMR mag
addition, larger area loops will align faster nets are sometimes described in terms of
than smaller loops for a given electron flow. gauss rather than tesla. Remember that a
joule or an erg is a unit of energy, and tesla
If we were clever, we would define the and gauss are units of magnetic field
MDM so that the direction or orientation strength (really units of magnetic induc
of the MDM would give us the orientation tion; see "Addendum" for a discussion of
of the object possessing the MDM. It seems H and B at the end of this chapter.) One
obvious that the MDM for a bar magnet tesla = 104 gauss, and 1 J = 107 erg. Refer
would give the orientation of the bar mag to Chapter 1 for a brief description of SI
net if the MDM were along the length of units.
the magnet . For the loop, however, we can
not draw a single line along the entire loop, If spinning electrons represent a rotat
but we can draw a line through the center ing charge, a nucleus must also be a rotat
of the loop. If that line were perpendicular ing charge. The differences between a pro
to the loop, that line would give the ori ton and electron are the sign of their
entation of the loop. In Figure 23-4A the charge and their mass. In deriving the
MDM for the bar is a line going through Bohr magneton, the electron mass shows
the SandN poles and pointing out theN up in the equation (not shown here) . If we
end. For the loop the axis line becomes the merely replace that electron mass by the
line of the MDM. The MDM, however, can proton mass, we have the nuclear magne
be along the axis in one of two directions. ton. The nuclear magneton is designated
The proper direction is obtained by an by the symbol 1-LN·
other left-hand rule: curl the fingers of
your left hand in the directions of electron Let us consider the meaning of this term
flow, and your thumb will give the direction "magneton." A magneton is a unit used to
of the MDM. Test yourself on Figure
23-3A. express the value of the magnetic dipole
moment. There are two units (these units
The words you are searching are inside this book. To get more targeted content, please make full-text search by clicking here.
Christensen’s Physics of Diagnostic Radiology
Discover the best professional documents and content resources in AnyFlip Document Base.
Search
Christensen’s Physics of Diagnostic Radiology
- 1 - 50
- 51 - 100
- 101 - 150
- 151 - 200
- 201 - 250
- 251 - 300
- 301 - 350
- 351 - 400
- 401 - 450
- 451 - 500
- 501 - 535
Pages: