THE IDENTIFICATION OF IrNHOIMOGENEITIES FOR TUMO10R DOSE
CALCULATIONS DURING TREATMENT PLANNING
Francis Joseph B3ova
A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF
THE UNIVERSITY OF FLORIDA
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE
DEGREE OF DOCTOR OF PHILOSOPHY
To my parents without whose support and many
sacrifices my education would not
have been possible.
I would like to express my sincere appreciation to my advisory
committee for their help and guidance throughout this work.
like to give special thanks to my committee chairman, Dr. Walter iMauderli,
help and guidance with thi
project and to Dr. Rodney Million
support, both financial and moral, and for providing an
atmosphere without which this research would never have been
I would also like to thank Drs. Genevieve Roessler
Roessler and Hugh Campbell for their guidance throughout my graduate
career at the University of Florida.
I feel as though I can never adequate
give thanks to Dr. Lawrence
Fitzgerald who not only made himself available at all hours for advice
and guidance over the last three years, and who has spent many laborious
hours wading through the early drafts of this manuscript, but because
of whom this research effort has been an enjoyable
I sincerely feel that without his
friendship and guidance
work would never have been possible
I would like to give special thanks
to Barbara Smith whose
support and companionship throughout the last two years of this work
has so greatly influenced my life.
Sincere thanks go to Amy Tanner for her assistance in typing the
final manuscript and my sincerest appreciation goes to Deni
I would like to express my sincere thanks
of the Mechanical
Engineering Department and his stude
nts for their
work on the original
I would d
ike to thank the family of Kathryn McCluney Baldwin for
their gift of $10,000 and the American Cancer Society for their grants
totalling $9,000 in
the support of this work.
TABLE OF CONTENTS
S. . S . S S S . S t .. t . S .S S S Vli
Methods of Internal Dose Corrections
Automation of Plann ng .. ......... . .... .. .
Inhomogeneity Corrections ......... ............
Computerized Axial Tomography ...... ...........
Reconstruction from Projections
.......9.S e. .....
..S..... *.. *t
Numerical Reconstructive Tomography Methods
*.. 5....*........ 5
S Q S wS S S S S S S
* a S S S S S **
* S S S S S S S S S
Iterative Least Squares Technique ............
Simultaneous Iterative Reconstruction Technique
Algebraic Reconstructive Technique ...........
Analytical Reconstructive Tomography Methods
The Fourier Transform Method
The Convolution Method ..
St***S** S *SStt*atSS S S S S S 5555555**C#ts~ S
Patient Support System ...
Radiation Source ............
Radiation Detection .........
Radiation Beam Collimation
Collimator Shield ...........
ELECTRONIC LOGIC DESIGN
The Sequence Controlling Logic
Ramping Logic ....... .. ..
AX Circuit .......
AR Circuit .......
R Counter .....
* 4 S S
* S C S *
* S C S C
* S S S
* C P P
* C p 5 P~o~ P C P C p *
* C S S Pt S S 5 o 5 3 5 S C S S
* .. ..C. .S. .S S P S S C .
S.. .. .S S *.S. S .S P.- S C ..S .. S
viortenmator amnlifier Controllin Circuitr
DISCUSSION OF RESULT
System Performance ................
n Grid .. .............................
ng Algori thm . . . .
TS . . ... .
tronics . . .... .......
and Recording . . .... ....
L VIII~ ~L 1 llllr
Abstract of Dissertation Presented to the Graduate
Council of the University of Florida in Partial Fulfillment
of the Requirements for the Degree of Doctor of Philosophy
THE IDENTIFICATION OF INHOMOGENEITIES FOR TUMOR DOSE
CALCULATION DURING TREATMENT PLANNING
Francis Joseph Bova
Walter Mauderli, D.
nce T. Fitzaerald, Ph. D.
Nuclear Engineering Sciences
The purpose of this work was to develop an apparatus which de-
ineated the linear attenuation coefficient and position of anatomical
for routine clinical use in radiotherapy
body cobalt-60 axial tomographic scanner has been designed and built
to fulfill this objective.
The criteria of overall low cost
, simplicity of operation, and
the ability to interface easil
with the department's
has been used.
The scanner has therefore been designed around a low
cost dedicated digital computer.
Cobalt-60 was chosen as the
source of the scanning beam in an
effort to minimize the scaling of data to the regions of interaction
used in routine radiotherapy.
Because of the heavy, bulky shielding usually
cobalt-60 sources, a special collimator
shield was designed.
fabricated from depleted uranium.
The design incorporates a fixed
1.98 millimeter, straight-bore collimator with a source which
I~' I *II -1.. -:- uL~A ~ -
collimator hole and is considered "on. "
The detector, mounted opposite
is a 4
long sodium iodide crystal
able straight-bore collimators.
Both the collimator shield and detector are moved across the
region of interest by stepping motors, gear reduction units, and
arrangement is used to assure accurate
transverse motion with a minimum of computer control
After a trans-
scan has been completed,
the apparatus is rotated on a
inch diameter wheel.
This rotation will
again be control
stepping motors and gear reduction units
The width of the transverse
variable, as is the number of degrees per angular rotation.
The transmission data are collected on a
reconstruction is performed on a one-quarter inch grid.
The grid size
can readily be altered and is only dependent upon the number of trans-
mission measurements taken.
The data are recorded on a computer-
the tape can be transferred to the departments time-sharing computer.
The raw data are then reconstructed by an algorithm using filtered
A treatment planning algorithm will
these data to correct internal dose distributions.
The path which radiation treatment planning has followed is not
unlike that of many other branches of
a physical phenomenon prompted a scientific
The need to understand
tigation with the
object of a delineation of parameters which affect its
end goal of thi
s investigation has
been the formulation of these para-
nto mathematical expressions with which the phenomenon can be
The early days of treatment planning saw crude and inexact tech-
such as calibrations of radiation fields by means of
. Today these calibrations are performed with sophis-
ticated equipment which allows higher degrees of precision and accuracy.
The state of the art for obtaining radiation dose distributions within
a patient involves several steps, the first of which is the measuring
of radiation field profiles
are commonly known as
isodose curves and are obtained with the use of tissue-equivalent
These phantoms are usually rectangular Lucite tanks filled
Since the skin surfaces of patients who must be irradi-
are normally not flat
a two-dimensional contour, of the surface
upon which the radiation field will be imposed, is taken.
Most planning procedures stop at this
although with use of only the aforementioned procedure, known
exist in the dosimetric pro
X and gamma rays used in radi-
action therapy are absorbed primarily through Compton
dependent upon electron density.
ption of hydro-
elements have essentially
the same number of
ectrons per mol
or per gram/centimeter2
the water tank phantom would be accurate; however
structures within the body do vary in density
x and gamma ray
to be absorbed nonuniformly through-
It is therefore essential
to have detail
distribution within the contour in order to proceed with the
correction process so that the next
can be achieved.
It has become increasingly more common to find dosimetry systems
which allow the introduction of inhomogeneities within a contour.
input of these inhomogeneity data tends
to be system dependent, most
stems requiring the area to be
sketched out on a visual
entered on a digitizing surface.
density values for these regions
ou to enter the
require you to
identify them as
lung or bone and then use preset density values for
When this procedure i
it can be
seen that small errors in size and position of inhomogeneti
estimating their densiti
lead to errors
ch would have been encountered if no
correction at all
had been used.
It can safel
tated that without the aid of inhomo-
Many methods for positioning inhonlmogeneities have been used;
orthogonal x-rays, transaxial tomography, computerized axial tomography,
and ultrasound are among those most widely used.
Of these, onl
puterized axial tomography can give the information required on position
as density throughout all regions of the body
. At first glance,
the new generation of diagnostic scanners seems very well suited for
the requirements of treatment planning, but a closer
ook shows that
several disadvantages exist.
The first questions which must be asked are
what is the quantity
being reconstructed by these scanners, and how can these data
from a polychromatic beam operating in a photoelectric region be extra-
polated with accuracy to attenuation
coefficients for the
therapy, which is operating primarily in the Compton region
concerns the actual treatment planning
If a local therapy
department manages to obtain time to
scan their patients on a local
whole-body scanner, how will the remainder of the treatment planning
procedure then be carried out?
Either the raw data or reconstructed data
would have to be transferred to a treatment-planning computer, or el
the scanner's computer would have to be used for the treatment planning
Finally, there is the question of cost.
scans costs approximately
Currently, a series of
0 when performed in a diagnostic setting.
If a therapy department were to obtain its own scanner
one which would
see much 1
use than the one in a diagnostic setting
, the cost per
scan would then increase above these pri
the department's existing systems have been used.
Assuming that a
therapy department capable
of utilizing inhomogeneity data
to have either a dedicated treatment-planning computer of
use of a macro-computer via
the scanner will
quire the intelligence of a central
therefore been designed around the hard-wired digital
and low-cost computer
, costing between $100 and $250,
ability to control
with variable scan widths
and variable angular shifts.
also has the
start and stop all
scanning motion through precise digital
and to control
To eliminate the problem of
of interaction from the photoele
to the Compton region
region, cobalt-60 is evaluated as
the source of the
reconstruct to the
canning beam. Since the reconstruction algorithms
linear attenuation coefficient of the energy being
, the output of the reconstruction algorithm i
value of the
inear attenuation coefficient for
cobalt-60 for each of
Because of the heavy, bulky shie
associated with cobalt-60 sources, a special collimator
Both the collimator shield and detector are moved across the region
of interest by stepping motors, gear reduction units, and precision ba
The width of the transverse scan and the number of degrees
per angular rotation are variable from scan to scan.
data are collected on a 3.3 millimeter grid, and the reconstruction
The raw data are then reconstructed by an algorithm using filtered
The proposed treatment planning algorithm utilizes
these data to correct internal dose distributions.
In an effort to eliminate artifacts which would result from a
standard treatment couch, a
ongitudinal as well as vertica
special two-section couch, which has
movement has been developed.
This paper documents the original design
assembly, and verifi-
cation of an apparatus which, for the first time, makes accurate
and reliable inhomogeneity data available to the radiotherapist.
isodose summation was done manually.
the overlapping of isodose
and adding up all
Because of the time involved in
uch a metho(
d, a specific set of
composite curves was not always compiled for each individual
was therefore a need for improved dosimetry techniques and tool
(1954) stated that
for therapy put forth by Bloor and Quick
, the aim of radiotherapy,
in treatment of any
the uniform irradiation of a minimum but adequate
volume of tissue to a dose that i
s likely to cause complete destruction
of the growth.
In order to achieve these goal
criteria must be met. These criteria are complete
the depth dose distribution throughout the entire
e demonstration of
rradiated volume of
the patient so that, in
the tumor may be judged
the inhomogeneity of dose within
and that unnecessary radiation i
tumor bearing volume
Although these authors proposed new methods
for tabulating isodose data,
their methods still
Methods of Internal
I Dose Corrections
Automation of Planning
It was a year later when Tsien (1955) stated that for system-
atic and reproducible therapy it would be essential to make up isodose
distributions for each particular treatment in planning a patient's
He was able to devi
a coordinate scheme for
doses within the radiation field with the criterion of limiting expo-
sures to all non-tumor tissue.
Unfortunately, Tsien was limited by
the computational methods of the mid-fifties and thus employed punched
cards, a card sorter, and a tabulating machine.
Once the data for each
patient had been transferred to punched cards, the automated method
took 10-15 minutes to sort and tabulate the isodose values.
, the method was very cumbersome and time-consuming; however
it was the first large stride forward toward the automation of treat-
It was not until the 1960s that the next
step was taken.
1961) stated that one of the obstacle
that had prevented
widespread application of automation was the difficulty of translating
the usual isodose graphs into numbers capable of being used by computing
At this time, they proposed a method of digitizing the curves
manually into systematic grids.
These grids were then fed into a
computer which summed the doses at various field combination points.
Because the state of "readily available" computers in 1961 was not
much more sophisticated than in
955, computing by machine was still
minimum number of fields needed for routine work can easily explain
at this point in time,
not everyone was willing to automate.
of storing field data on punched cards
was realized by
Siler and Laughlin (196
library necessary to achieve a reasonable
,000,000 punched cards.
estimated that a minimum
They decided to abando
of accuracy was
n storing data on
and go to an alternate
stem of equations which would,
, specify the radiation field.
Their method used tissue-to-
(TAR), off-center ratios
and an inverse
correction as field parameters.
They felt that inhomogeneities should
be considered in the field corrections
they expressed the TAR as a
electron density and t
Although the authors were correct in attempting to take
into account inhomogeneities
, they posed no method for
years of development
, many methods
computing radiation fields within the body
Bentley and Inst
(1963) and Hallden, Ragnhult and Roos
3) were but a
few of the
more prominent researchers of thi
It was not
, however, until
1965 that a completely automated method of treatment planning with auto-
mated output plotting of isodose curves
within the body cross
therapy was developed by Mauderli
and Fitzgerald (1965).
Although the method reported employed manually digiti
zed isodose curves,
a method of acquiring the isodose field data
form by the
direct measurement of the radiation field had been proposed and de-
At this time, the accuracy of treatment calculations were limited
by the lack of one important set of patient parameters
positioning the actual inhomogeneities within the body
addressed this problem and developed a method of internal organ
localization based upon views in two orthogonal x-rays
of inhomogeneities were transferred to a "contour equivalent" of the
patient and the data then hand digitized for computer use.
encountered with slight movements of the patients between
contour mapping lead to inaccuracies which limited the use of the
The first attempt to accurately compensate for inhomogeneities
was by Eichorn (1967)
Eichorn built a phantom of the thorax in which
nhomogeneities that simulated bones and lungs.
actual position of the internal structures and their x-ray attenuation
properties, calculations were made.
The phantom was equipped with
measuring sites and thermoluminescent dosimeters, TLDs were used
to measure the dose for a
The good agreement
between the calculated and measured values demonstrated the ability to
calculate actual isodose values given the necessary information on
internal structure and attenuation coefficient.
The increase in knowledge of isodose fields
and isodose contour displays since 1967 have all added to the
speed and accuracy with which the routine treatment plan can be executed.
Unfortunately, the accuracy and speed are still limited to two factors:
in solving the problem of inhomogeneity defi-
nation has been in the development of axial
first developed into a useful
by Hounsfield (19
1969, yields the positioning of anatomical
via a map
of relative radiation attenuation numbers.
first unit was dedicated
to examination of the head.
However, by the time a marketable
was announced in
, the development of a
similar unit capable of
rendering tomographs of any
section of the body was announced by
nearly 40 companies
production of axial
The availability of axial
tomographic devices which scan with
x-ray beams of energy
ranging from approximately 80 to
significant scientific interest.
140 Kv have
The numbers which these
units obtain, as solutions to their reconstructive algorithms, show
promise in their ability to correlate with
ectron densities of the
The work by Phelps
the relationship between the computerized tomography,
, numbers, and
the electron density of materials such as
The fact that one
at a time was scanned
is of interest.
disputes the ability of CT
to achieve a resolution of 1
in the "quantity"
He alludes to a resolution in
This error would
only be the first error in the calculation for the attenuation coef-
ficient needed for therapy
large number of therapeutic
The type of procedure currently in practice is similar to that
explained by Jelden, et al.
and usually involves
The CT scan must be taken and the image must be transferred from the
scanner into the treatment planning computer.
Some companies, real
izing the applicability of this data to radiation therapy
computer systems which will
support a computerized axial tomographi
CAT scanner and also support a therapy's department treatment planning
plot is calculated.
i the data transfer has been accomplished, a density
is done by the bracketing of CT numbers
into several discrete levels.
, a simple algorithm
areas as tissue or muscle equivalent,
and dense bone equivalent might be use
soft bone or cartilage equivalent
The scale which might typical
be available on a CT scanner may range, depending upon the unit, from
-500, the value for air, to +500
, the value for reconstructed dense bone,
with water being at 0.
scale can lend itself to many density ranges
but usually three to five are sufficient.
The data are then used by
a treatment planning program which is sensitive to density data.
An alternative to the normal x-ray CT scanner is a cobalt-60 CT
This type of scanner has several advantages over presently
One of the main advantages i
that the mono-
chromatic beam enables the reconstructive algorithm to reconstruct each
element to the linear attenuation coefficient for cobalt-60.
second advantage is that
since very fast scan times are not necessary,
constant intensity isotope has replaced the x-ray source, the
overall design of the apparatus can be simplified.
Thirdly, since most
Cobalt-60 scanning systems have been proposed by Thieme, et al
(1975) and Hendee
et al., (1976).
However, a clinically useable
system has yet to be announced.
A functional design for a high energy scanner is not
as is its need.
The problems associated with the shielding of a high
energy isotope complicates the design of both the mechanical and the
The final design presented, is the result of many
trial and error design procedures and fulfills the requirements of
reliability, precision and low cost.
The basic principle on which axial tomographic scanners are based
the taking of multiple transmission measurements through an
object and then reconstructing these measurements into an image free of
interference from overlapping material.
The method of imaging internal structure without the interference
of overlapping material has been a long standing problem in many
sciplines of science.
, the interdisciplinary communi-
cation of the scientific community
often very poor.
Only after an
advance significant enough to receive wide publicity was the fundamental
applicability of many independent works realized and classified under
the common heading of reconstruction of images from their projections.
One of the first attempts to solve the internal imaging problems
was known as tomography
The early tomograms were performed by the
relative movement of an x-ray source, and recording film wa
so that only one sagittal plane within the body remained fixed relative
focused plane superimposed on a background of blurred planes.
of tomography was known originally as
tomography remained the
only type of tomography availabi
to the medi
community for over
From 1956 to
1972 the advances
day tomography units were taken in the fields of radioastronomy and
for the most part
and only after the
large interest generated by
were the iso
lated works categorized under
heading of Reconstruction from Projections.
Reconstruction from Projections
The first step towards a reconstruct
taken in radio-
astronomy by Bracewell
microwave image of the
He faced the problem of obtaining a
of the sun with a radiotelescope which
could only focus on strips across the entire
surface of the star.
signal would therefore be the
emitted in a two dimensional
ummation of all
proposed that these
"reconstructed" into an image of the entire surface by
utilizing Fourier transforms, but in
the state of the art in
science made the computation of an inverse two dimensional
Fourier transform an insurmountable task.
He was therefore forced to
Twelve years after Bracewell's publication the problem was being
solved again in the field of
lectronmicroscopy (Morgan, 1968; DeRosier
and Klug, 1968)
The problem was to obtain a
section of an object
which could only be viewed by a transmission electron beam.
was analagous to Bracewell
could be obtained
in that onl
In the twelv
y the integral value of the strip
years that lapsed since Bracewell
reconstructive attempts, the field of computer science had advanced to
the point where the implementation of inverse two dimension
transforms was now applicable.
Aside from these two advances
there were literal
dozens of arti-
cles published on the topic in both fields with variation in reconstruc-
tive methods as well as data acquisition being reported.
article of Brooks and DiChiro
1976) details the history and put the
various reconstructive approaches in perspective.
The applicability of reconstructive
tomography was not introduced
to the medical community until EMI Limited introduced their axial tomo-
graphic scanner in 1973, (Hounsfield, 197
The EMI scanner collected transmission data of a patient's head.
These transmission measurements were again a summation of the partial
transmission of many single elements
similar to the data obtained in
In this original unit
the reconstructive approach
was known a
the Arithmetic Reconstruction Technique.
The valuable information which the EMI scanner made available to the
medical community generated an interest in not only the apparatus used,
but the mathematical techniques employed
It was at thi
Before various methods of reconstructing cross
projections are explained,
the nomenclature and methodology of the
projections should be discussed.
Let the object 0 in Figure 3.1
object to be scanned and reconstructed.
Sitting on opposite sides
of the object 0 are the Detector D and
The source emits a beam;
of the cobalt-60
the beam i
composed of the gamma radiation of
a ten Ci
The detector measures
the transmitted portion of the radiation
this portion will
be denoted as P.
The gamma-ray beam
at a distance r from the origin and makes an angl
0 with the
If the path
length of the
s, then P,
mission of the beam
, is given as P
(r,0) and is equal
to the transmission
of the ray through path
the function which describes the attenuation of beam.
monoenergetic beam of radiation
unattenuated beam intensity at the detector
s the intensity of the beam after it has traversed path
( I it
can be rewritten as
P'(r,oc) = In ioy)-
During the scanning procedure the object being scanned is
confined to a space of diameter d.
is collected and the
reconstruction performed at
pacing of the ray width a.
number of points in any scan pass at an angal
be N=d/a and
number of reconstructed points will
Each of these
henceforth be referred to as pi
After N measurements are made at angle 0
the source and detector
rotate A0 about the origin and another
set of N values
This procedure i
K sets have been measured, where
= ( /A0)
The scanning is stopped at this point because
= P'(r,0 + i
further data collection would therefore be redundant.
After the P'(r,0) array has been determined,
the data collection
In the following discussion on reconstructive techniques,
be assumed that the measurement and recording of transmission data
performed without distortion or alteration of the data
. It will
fore be assumed that any distortions or artifacts in the final
are due to either the scanning procedure or the reconstructive technique.
hows that the scanned data, or transmission data,
dependent upon only one quantity
therefore attempt to
field a quantity which can be
correlated to the
Reconstructive Tomogra phy Methods
This method was used by Oldendorf
for the first experiments
in reconstructive tomography
each angular orientation,
0, are proj
ected back to a common
transmission value at a particular angle, P(r,0
, is projected back on
or added to, each pixel
along the ray path
The magnitude of each pixel is their
through which it was
before the summation of all
transmission rays which pass
. Although the
estimation of the original
have merit as a qualitative
The advantage of thi
that it can b
mented without the aid of a computer, although the quality of the re-
construction generally is poor.
The effect of projecting the ray value to each pixel which con-
This produces a star pattern around the
of points on the star being equal to th
inhomogeneity with the number
e number of views,
The object of the iterative techniques
unlike that of the
is to ascertain the correct value
The technique obta
, for each of the N pi
, through various procedures, a matri
linear attenuation coefficients.
ion data are
values and then they are compared to the measured data.
of the attenuation coeffi
clients are altered to obtain a better agreement
between the measured and calculated data sets.
This procedure i
have been adjusted.
fit of the
to the measured transtmi
within a preset tol
the procedure is
culated and measured transmit
Iterative Least Squares
The Iterative Least Squares
technique performs the above procedure
by calculating the entire transmission matrix and then calculating the
corrections for each element of the attenuation matrix.
The correction of
are made after which another calculated
procedure is repeated until
the error between cal
ulated and measured
within a preset
corrected from all K views before it is re-evaluated.
To impede the
size of the correction the best-least-square fit to the measured data is
used to decide upon the degree of dampening required
criteria, this technique has been termed the Iterative
Because of this
Simultaneous Iterative Reconstruction Technique
An alternative method of adjusting the linear attenuation coef-
ficient is to alter the values point by point.
In this method
the transmission rays
which pass through a single pi
1 are calculated.
adjusted and the
next pixel i
After all N pixels have been adjusted
closeness of calcu-
lated to measured data is examined.
If the two differ by too large an
amount, the process is reiterated.
method corrects the
simultaneously with the
calculation of all transmission rays through
, it has been termed the
Algebraic Reconstructive Technique
The third technique calculates the transmission data for a parti-
cular angular orientation.
It then corrects the attenuation
and goes on to another orientation.
If the calculated values do not
agree to within a specified tolerance with the measured data
, the pro-
cedure is reiterated. This procedure has been termed the Algebraic Re-
construction technique (ART).
an optimum iterative procedure may be one that uses ART
for the first one or two iterations and switches to ILST.
These authors chose the ILST over the SIRT because of the shorter
computational time per iteration.
Analytical Reconstructive Tomography Methods
The Fourier Transform Method
A second approach to reconstructing the raw data is to use analy-
One such method involve
of Fourier Transforms.
This method is explained by Gordon and Herman (1970, pg.
The Fourier method depends on transforming the projec-
tions into Fourier space, where they define part of the
Fourier transform of the whole object.
may be shown to yield values on a central section of
Fourier space, which is a line or plane (corresponding
to the two or three dimensional problem) through the
origin at an angle corresponding to the direction of the
projection in real space.
An attempt is then made to
interpolation a reverse Fourier transform provides an
estimate of the object's structure.
In this method, the raw transmission data are obtained in the scan-
interpolate the unknown values of the full Fourier trans-
form from the values of the central sections.
ning sequence previously explained.
If we represent the
data of a particular view by a continuous function P with a period d,
where d represents the scan width, then the function P(0) is a one dimen-
sional projection of the data at a particular angle 0
If we allow F IP to be the Fourier Transform of this projection
then for any R
This now represents the line projection of the central section of
The Fourier Transform of a two variable function, for
the two-dimensional surface of the image, is defined
where in thi
case f(x,y) represents the two-dimensional linear attenu-
The inverse two-dimensional transform is defined
3.8 demonstrates that if [F~,f] (x,y) is known, the f(x,y)
can be ascertained.
be the operator that maps a two-dimensional function onto a
one variable function by restricting it to a line through the origin
Then for R
, which measures the distance along the central section of the
= [F P ](R),
and, by substituting Eq. 3.10 into Eq. 3.9,
= [F1P (R)
This demonstrates that the two dimensional Fourier Transform F(x,y)
can be obtained by the use of the original transmission data, P(r, ).
Because the reconstruction matri
is a rectangular coordinate
tem and the scanning procedure employs a polar coordinate system, the
data at a specific point (x,y) may not be available.
This means an
n two dimensional Fourier space must be performed. If
ng scheme, more complex then a simple linear fit, is used,
interpolation time dominates the overall computation time of the
The Convolution Method
In order to eliminate the two dimensional Fourier
and to decrease the total computational time, an alternate method was
The following developments follow closely that of Ramachandran
and Lakshminarayanan (1971).
Their method employs
the well known convolution theroem.
two functions f(x) and g
x) and their Fourier transforms F(t) and G(t)
\rl .1.. 7 1
the German term for folding, of function f(x) and g(x).
The Fourier inverse of a product of Fourier transforms is the convolution
of the original function
rewritten in polar form:
where 0 is the angular orientation of the reconstruction grid, and
the orientation of the data acquisition system.
This can be rewritten
If P' (p,
then by substitution
changing Eq. 3.17 into polar form
P(z,e) = F(R,e)exp[-2nRR]dR.
It can now be shown that the Fourier transform of P'(z,e) equals the
Fourier transform of P( ,e9) times the Fourier transform of g(z) where
using the definition of the convolution
)(z,e)q(t- l )d91
,e) is the transmission data, which are known, if g(9) can be
obtained then using Eq. 3.1
one can obtain the attenuation coefficient
Fourier inversion of Eq. 3.20 yields
It can be seen that this equation can not be evaluated because of the
divergence of the integral.
If the limits
-a to +- are replaced by -A/2
and +A/2 where A i
a very large finite number, Eq.
can be written
is replaced by na where a is the ray width from Eq.
n is an integer, the solution to Eq.
can be shown to reduce to:
= l/(ln) a
= 0 for n=even
can now be rewritten using
is a positive or negative integer.
.24 yields a set of filtered or weighted transmission values.
can now be used to backproject these values to the common
Because the sampling of the data occurs at a regular spacing
and the angular
hifts also are performed along regular angular
Eq. 3.17 in discrete form is:
and k are integers and ro
are the spacings of r and
As can be readily seen
The transmission of ray P(r,0)
of Equation 3.1
denotes the trans-
ssion of a photon beam through a group of pixels.
in the reconstructive
theoretically ideal movement of
both transverse and rotational
ion required during
data acquisition can be brought into perspective by examining a
size and comparing it to the total
distance traversed during the
entire distance traversed during the scanning
of a 40 centimeter by 40 centimeter grid with 36 angular shifts is
14 meters, neglecting rotational movement
. When one considers
that each pixel
than one-thousandth of that distance,
strict requirements placed upon the mechanical
system can be appreciated.
Most first generation
, those with moving source and
fixed the source and detector to a hollow yoke whi
is traversed and rotated around the patient.
ration scanners were being designed
, the basic design for the
presented in thi
work,was taking place.
It was decided to
loss of accuracy when the screw is reversed
misalignment of detector and source due to variation in the
c inaccuracy due to a nonuniform surface of the
rotating drum, and
(4) maintaining rigidity of the unit to withstand the changing
forces as the detector and collimator traverse.
Some of these problems are more difficult when dealing with a cobalt-60
scanner than with a conventional x-ray
due to the
several hundred pounds of special materials which are required for
shielding and collimation of the radiation beam.
In order to determine the consequence of these potential problems,
a detailed examination of the system must be made.
The equation for the nth transmission ray at ang
Y = (-x)tan(0+Ac1 )+(n-n,
where the error due to drum misalignment and rotational inaccuracy is
AE1 and the error due to inaccuraci
in the traverse mecha-
nism is given by
2. Since the scanner utilizes rotation as well as
the traverse motion, these errors can be either positive or negative
For example, if the scanner is in the orientation
shown in Figure 4.1,
the load on the drum will cause an error resulting from the flexing or
looseness in the rotational mechanism, in the counterclockwi
while when in the orientation of Figure 4
just one traverse later,
_ __ _ =
have a negative or positive error, the backlash of the ball nut will
give an error
in the direction of the prior traverse when the screw is
horizontal, or in the direction of gravitational forces when the screw
has a force component opposing gravitational forces.
The final scanner design has resolved thes
reduced the errors to acceptable limits. The i
national center were minimized by machining the
and other problems and
naccuracies in the ro-
surface of the rotational
drum to within 0.005 inches of round over its 54 inch diameter.
was also decided to use a metal drum supported by bare metal bearings
to eliminate any problems due to a padded
surface flexing under load.
In the original design, the
drum was to be
driven through the use of a
chain, but when the small play in each
ink was totaled over the seven
feet of chain required to
span the drum and driv
error would allow the drum to rotate
situations of Figures 4.1 and 4
1 degrees during th
solved by the
use of a nylon core rubber belt which could be loaded so that undesirable
shifts were eliminated.
The drive system for the drum
consists of the above mentioned drive belt, a
unit, and a DC stepping motor, SLOSYN Model No
0:1 gear reduction
steps in 1
The design of the motor is such that the
error per step is noncumulative and has a maximum error of plus or minus
3% of one step.
shafts have been used to support the
To el imi-
the backlash double ball
nuts were used with preloading to an
The stepping motors used,
WARMER Motor No.
024-0140-FB, which step in
plus or minus
of one step and
with the SLOSYN motor, the error
screws are driven by a
near reduction unit
which is driven by one or more DC
In the original
stepping motor wa
used to control
source and one to con-
The calculated and measured torque are within
rated range of the stepping motors
when stepping at a speed of about
gear reduction was to be
which would move the
source and detector at a
speed of four centimeters
the stepping motors could not be made to
step at thi
under the required load.
solution employed ramping sequences
to bring the motors up to
speed i n
considerable effort it was
step rate of 720
second would have to be temporarily
In an effort to increase the available torque,
n series to drive the source.
dampers on both source
and detector were used to avoid resonance
, a problem whi
motors can experience while
The maximum speed which could be
reliably obtained was
There was still
the problem of being sure that the motors followed the pulse sequence
sent to them,
especially a problem at the beginning and end of
This final design has several advantages over those normally used
in axial tomographic units.
Since no signal is required to be sent
back from the mechanics,the driving electronics could be simplified.
A constant traverse speed allows the measurement of transmission data
by the method of repetitive interval
requires that the integration over a specified time interval be equal
to the integration of the
signal over a specified distance.
DC or AC motors are used in such a changing
situation and the
relies on positional pulses from the mechanical
initiate or terminate integration intervals, a
large variation in inte-
gration time could be experienced.
Patient Support System
In order to
support the object to be
scanned, a couch was required.
The couch should fulfil
the criteria of minimal perturbation of the
scanning beam while allowing the patient to
ie in a position
to that used during treatment.
and joined by a two-inch thick
fabricated in two
eight foot long,
styrofoam, allowed the object to be scanned with onl
the plane of the scanning beam.
the styrofoam in
In order to eliminate any beam perturb-
action due to the styrofoam, the couch was placed in the scanning position
during collection of data used to formulate the correction matrix, a
procedure which will be discussed later.
The algorithm which corrects
for system misalignments would then simultaneously correct for any
artifacts produced by the couch.
The cobalt-60 beam ha
several criteria involving collimation and
intensity which in turn dictate design restrictions for both the source
and its collimator shield housing as well as the collimator for the
When looking at the intensity
first criteria which should be inves
required for the source the
the statistical fluctu-
nations per counting interval
It is desirable for each interval to have
a measured pulse rate accurate to within plus or minus 1
guarantee this accuracy, a pulse rate of 10,000 pul
be set as the lowest pulse rate obtainable. During
it was decided to collect data at 0.5 centimeter interval
traversing at a speed of four centimeters per second.
In order to
per interval must
I the initial design,
into a minimum pul
rate of 80,000 pulses per second
under which the minimum count exists should be that of maximum patient
Assuming that the worst case i
that of 45 centimeters of
tissue attenuating the beam, only
available for counting. The full
the worst case, would need to be 1
per second minimum.
of the initial beam would be
intensity of the unattenuated beam
.5 times more intense than the
Thus 106 is the number of pulses
which must be detected when the beam passes through an area which lacks
any attenuating material other than air.
The actual intensity of the
beam would be such that when multiplied by the efficiency of the detector
106 counts per second are detected.
best suited for this particular application.
time of NaI(T1
Although the response
is not exceedingly fast, when compared to other detec-
high detection efficiency makes a large enough difference in
source strength, and therefore source shielding, to outweigh this slow
A NaI(TI) crystal 1.9 centimeters in diameter and 10.16
centimeters long was fabricated by Harshaw Chemical .Company, and coupled
to a 0.75 inch photomultiplier tube.
The crystal and photomultiplier
assembly was hermetically sealed inside a stainless steel cylinder in
such a way that the photomultiplier wa
insulated from the
that is could be used with either positive or negative high voltage
rates above approximately 0.8
x 106 pulses per second rlal(T1
cannot be used in the pulse mode, but instead must be used in the cur-
This is advantageous because the detection efficiency for
NaI(T1) in the current mode is much larger than in the pulse mode.
above detector has an efficiency of over
Therefore, the total
number of photons per second reaching the detector must be approximately
x 106 for an effective detection rate of 106
Radiation Beam Collimation
The fact that pulse counting will not actually take place does not
alter the fact that the minimum pulse rate mentioned will be required
to assure that there be 1
than 1% fluctuation of detectabi
It is not possible to perform pulse height and analysis when NaI(T1) is
used in a current mode, therefore scattered radiation cannot be distin-
Photon Flux= in
the radiation beam and detector during scanning.
at which the radiation
s the diameter of
the source collimator is
the collimator over its
diameter of source collimation
length of source collimation
the source collimator wa
designed with a
in diameter and 10
The angle 0
a viewing angle 0D whose
tangent is simi-
larly defined and with a detec
and 150 mil
The value of OD can therefore be calculated
= 1.9 degrees.
The maximum angle within which
the detector can accept scatter is
sum total of t
shown that the
hese angles, which equals
scattered radiation detec
ted is small
It must now be
for a cobalt-60 beam with
these collimation restrictions.
the photon flux which would enter the detector if no scat-
tering medium were present,
x the distance traver
the detector ha
must be traversed after the scattering event,
then the number of scat-
tered photons reaching the detector per steradian will
Since some photons wil
1 be scattered but not absorbed in the distance
these photons will
be available for further scatter.
therefore used for the
Once a photon is
scattered into the detector'
angle of acceptance, any further inter-
likely remove it from the path of acceptance.
the term u
sed to describe th
second region of interaction
linear attenuation coefficient.
be assumed that all
simplify Equation 4
of the scatter for an entire thickness D will
occur in a one centimeter strip in the center of th
the previous assumptions,
yields a worse than actual
can now be reduced to
In view of the assumptions the integration of
is simply Ns,
number of scattered photons, and dNe is the sum of electrons in
If it is assumed that all of the
largest scatter coefficient,
is through the angle with the
electron per unit solid angel
ally scattered into a unit
since the radiation will be isotropic-
olid angle, the number of scattered photons
Ns must be multiplied by the fraction of a steradian which the detector
The detector with a diameter of 0.5 centimeters will always
be at least 20 centimeters from the scattering medium.
The portion of
teradian it occupies is
= 0.001 steradian.
Table 4.1 was obtained from Equation 4.5 for tissue thicknesses ranging
from one centimeter to 40 centimeters.
Column II of Tabl
4.1 was ob-
trained by dividing both sides of Equation 4.5 by No, the total photon
column III was obtained by dividing Equation 4.5 by the
number of photons, Ntot, reaching the detector
= Noexp(-att D)
It can be seen that the maximum scatter fraction of the total beam is
4% per steradian for 40 centimeters of tissue.
Examining Columns II and III of Table 4.1
it can be seen that the
amount of scatter radiation reaching the detector, for varying patient
o fl0N N-) IC) Cfl ~ r
0Cl N-O N- On CO Co
0d 0 0- O0C
F- CO N-- C 0C
Cte a 0 Or t- CO N- CO IC) On O
C') 01 0 10r N-3 CO N. CM N. Nl 10 0
Li 4-fl tf Cdv Ct to 03 (0 CO Cci N- Ct
cc C) 00 QO
> o .a C
F- Cd CO1 Ct FS O
On the other hand the ratio of scattered radiation to the
amount of total beam penetrating the patient continually increases
with increasing thickness.
The use of an isotope
n place of an x-ray tube
requires that the
source be shielded whether the beam is effectively "on" or "off."
shield must also have the ability to automatically return the isotope to
the "off" position in the event of a 1
With these requirements in mind,
of system power.
it was decided to combine the
shield and primary collimation into one solid unit.
millimeter by one millimeter by two millimeter coba
The source, a one
ilt-60 pellet, is
encapsulated onto a rod and i
held in the center of a
shield when in
its "off" position.
To produce the transmission beam, the rod is drawn
back, bo a solenoid
approximately one centimeter,
so that the
aligned with a straight bore collimator.
In moving the rod to this
tracted position a spring which will return the source to the "off"
position is compressed whenever th
solenoid is deenergized.
having only one moving part, maximizes reliability and safety
The next step in the design was the
which to build the shield collimator. I
selection of a material from
regardless of the material
chosen, the amount of attenuation required from the shield must be the
x is the fractional decrease in beam intensity required, it
is defined as
, is the linear attenuation coefficient of the shielding
material being used and r
is the linear thickness of attenuating
Solving for the linear thickness of attenuating material
This defines the length of material which must be traversed
function of beam reduction and linear attenuation coefficient.
spherical shield-collimator is to be built, the volume required would
substituting the attenuating thickness for the radius
if then all constants are combined and set equal to C1
= C1(10/ )
The weight of this sphere would simply be the volume times the material
= C1(1/u P)
here m is the mass attenuation coefficient.
The weight can be expressed
as a function of u and
Dropping the constant C1 and evaluating this expression for lead, tung
sten, and depleted uranium, it can be seen in table
that the weight
can be minimized through the use of depleted uranium.
There exists, however, a problem with the machining of special
materials such as depleted uranium and a compromise had to be
made between the shield shape, weight, and ability to securely mount
it on the scanner.
Because of the problems associated with sliding
depleted uranium against itself, the source wa
encapsulated onto a
The final collimator shield and the two-section couch
can be seen in Figure 4.4
The resultant design utilizing depleted
uranium weighed approximately 260 lb., which is in contrast to the
600 1bs. of lead
which would have been required for the equivalent
EVALUATION OF SHIELDING MATERIALS*
these numbers reflect only primary attenuation and do not reflect
the effect of build-up factors.
ELECTRONIC LOGIC DESIGN
At the beginning of a scan the detector and source,
rotational system, must be positioned.
as well as
This is conveniently achieved
through the use of specially positioned mricroswitches
The source and
detector are brought up to a constant speed of 4 centimeters per second
by a digital ramping
sequence over a 6.6 millimeter distance.
peed is achieved, the measuring of transmission data begins.
These transmission measurements continue until the source and detector
are 6.6 millimeters from the end of the traverse.
At this point, the
transversing system is ramped down to a stop.
The rotational drive
is then pulsed and a rotational shift i
After rotation has been
the second traverse i
initiated and proceeds identically to
the first but in the opposite direction.
process, of alternating
traverse scans and rotations, continues until the scanner i
orientation 1800 from its original position.
A digital computer was designed and fabricated to control the
traverse and rotational sequences and the data acquisition system.
proved adequate for all switching requirements.
tronics can be subdivided into five categories; the clock, the sequence
, the ramping logic, the data acquisition
the motor driving logic.
sequence control logic initiates each traverse and at the tra-
verse completion, initiates and terminates the required rotational shift.
This circuitry also terminates the scanning
paratus to its reset orientation. The ramp
the controlling logi
sequence and resets the ap-
ing logic, upon a signal from
fabricates a positive accelerating eight step
ramp at the initiation of each traverse.
The data acquisition system
electrometer amplifier and provides the signals to properly
sequence the recording
The motor driving logic provides the
various motors with the proper sequence of pulses for either clockwise or
The entire scanning procedure is dependent upon the signals from the
The choice of a 4047, used as an stable multivibrator, was
made based upon its stability, less than 0.5% deviation at 40 kilohertz,
and the availability of easily adjusting its output for experimentation.
During initial setup, the
clock pulses were observed on the ten volt
igh it seemed unlikely that the
was the cause of the
, it was decided to isolate it from the power supply as
5.1 (the 4050 gates shown in the figure are actually six
Seouence Control ing
Output To Digital
Dianran of the clock circuit.
The Sequence Controlling Logic
The main logic control was fashioned after a similar design used by
It allows the alternating of traverse and rotation
and a means for resetting the scanning apparatus.
shows the basic
originate at the main clock
AB, and are divided by a
seven-stage binary counter, AA.
arrangement is used to provide the
nominal 24 kilohertz signal required by the ramping
and also makes av
'ailable a 50 kilohertz
signal required by the digital
When the equipment originally i
switched on, the
SCR conducts and gate V sends a reset pul
to all counters, in-
cluding the ramping electronics.
In this reset condition, the
electronics divides the incoming pulse by 100.
The clock pulses do not progress further than NAND gate
has one input held low by the anode of the SCR.
Pulses are, however,
supplied to relays R1 through R4 which allow manual control of the
various motors for initial position.
When any one of the four manual
relays are switched from their scan mode to a manual mode
, the gate W
sends the SCR into conduction and therefore all counters are sent into
This arrangement i
used so that once manual control of the unit
is assumed, a deliberate effort must be made to restart the scanning
The initiation of a scan
S1 to low.
involves the setting of the start switch
This inhibits the bilateral switch X from conducting, thus
the output of gate V goes low taking all appropriate counters out of
Simultaneously, the inhibiting output of gate
is brought high
allowing clock pulses to be transmitted and the scanning procedure to be
The pulses being passed by gate
are inverted by inverter
R which delays them one half pulse, and then go to the transverse and
The ramping logic Y
reset when a rotation is made.
are being divided by 100, resu
arranged so that it is in
Therefore, the pul
lilting in a
from counter AA
.4 kilohertz signal availabi
for control of rotational motors which requires a 40 hertz pul
In order to reduce the frequency of this pul
Q is used.
Since this counter also inverts the signal, inverter D is
used to resynchronize the pulse train.
Throughout the entire scanning
and rotation are being sent to gates A and
which run to the Ax and Ar
and to gates C and J.
all counter outputs
are low after a reset pul
the Exclusive-OR gate E has a low output,
prohibiting passage of rotational pulses through gate G.
put of the
The low out-
r counter also inhibits gate 0 from passing pulses to the
rotational drive system.
When the three inputs to NAND gate J are high,
the pulses for translation are passed to relay R2 and the driver buffer
B2. The function of the buffers B1 through B4 is to provide enough cur-
rent to drive the TTL loads of the motor drivers and also to drop the
voltage of the logical high from positive ten volts to positive five
x counter has received a preset number of pulses
The pulses for rotation are passed through inverter L to
gate K, and to relay R3 and buffer B3 which enabi
a c ounter-clockwise
Once the predetermined number of motor pul
accumulated, the Ar
counter goes high, sending gate E low which inhibits
conduction through gate G and enabi
the conduction through gate
The level changes of the Ar counter also places an inhibit on gate J
and removes the inhibit from gate C.
sends the motor driving
through relay R1 and buffer B1 which drive the translational
system in the direction opposite to the previous traverse.
translation is completed, the
Ax counter goes low sending gate E high.
The termination of this translation once again initiates a rotation.
The rotation, again, sends pul
through gate K and once the preset
number of rotational counts have been reached, the next traverse is
After every other traverse
AX counters are in their
initial state; therefore
mulation of pul
, the only change in the circuit is the accu-
being sent to the rotational system by the r counter.
When the scanner has reached an orientation 1800 from its initial tra-
verse, the r counter goes high.
This switches inverter n output to a
low inhibiting conduction through gates A, C, G, and K while enabling
pulses to pass through gate 0.
The rotational drive signal
gate 0 and to relay R4 and the r return counter
The sending of pulses
through relay R4 causes rotation in a clockwise direction until counter
T goes high.
The signal from the counter places a ten volt high, via
a 104 ohm resistor, on the gate of the SCR causing it to conduct
In order to achieve a transverse speed of four centimeters per
second, the stepping motors must operate at a pulsed rate of 720 pulses
or one pulse every 1
It was determined
experimentation that the motors would not respond, under load, to
an initial pul
of 120 pulses per second
or one pulse
In order to accelerate the motors to and from
the required speed a digital ramping sequence was employed.
sequence can be broken into two sections.
determines when in the traverse a ramping sequence i
employed and when a constant traverse speed i
to be maintained
second circuit, Figure 5.4
incoming clock pulses and
sequence, either increasing in period
or decreasing in
period, depending upon whether a negative or positive acceleration is
initiation of the acceleration is controlled by gate G of
while the sign of the acceleration i
determined by NAND
gate C of Figure 5.5. The
use of counter T of Figure
frequency reduction is achieved through the
, a programmable divide-by-"N" counter,
circuit has the ability to divide an input pul
train by any integer between three and 15,999 inclusive.
is a positive pulse one clock pulse wide occurring at a rate equal
to the input frequency divided by N
the divide-by number.
oT ;C o4-,
X S 8 "" "'2
g 8 :
allnl? 8 a g d '
al I S
As can be seen by the fourth column of Table 5.1, there exists
no obvious pattern to the ramp
It was determined by
mentation and the only comment that can be made i
it works properly.
The unusual step pattern dictates that the final integer used
not be the lowest integer
ible, i.e. three.
simply because the
next higher divide-by integer, four, would
dictate the last step in the ramp to be an increa
in speed of
It was therefore determined that during the full-speed traverse the
would be the result of a divide-by-32, allowing the
of the previous step to be a divide-by-34, an increase in speed of only
selection of the programmed divide-by integer is accomplished
through the use of a set of AND gates, actually one NAND gate is employed
but its output i
input of th
inverted to make it equivalent to an AND gate.
AND gate is one of a pair of Decade Counter/Dividers, counters
K and L of Figure 5.4
Since it is desirable to use the same set of gates for the positive
accelerating ramps,an up-down decade
counter is re-
At the time this circuit was designed
, this specific piece of
logic was not available as a single integrated
ircuit so the
of an up-down counter was fabricated
and 16 bilateral switches
It uses two 4017 Decade Counters
, which tie the output of the two counters
together,(see Figure 5.4)
such that during the
positive accelerating ramp the input to inverter D i
high, thus putting
the 4066s whose inputs are tied to counter K in a conducting mode and
acceleration, at which time the input of gate D is low, counter K
controls the jam inputs of the 4059 while counter L
circuit also holds the decade counter not being used in reset so it
does not accumulate pul
during the opposite ramp.
The two counters K and L of Figure 5.4 are arranged so that the
"eight" output of counter K is exchanged, during the transition from
negative to positive ramping, with the "O" output of counter L
"seven" output of counter K is exchanged with the "one" output of counter
L, and so on.
Since counter L is in reset when counter K has reached its
"eight" output, the transition from positive to negative does not occur
until counter L accepts its first pulse and its "one" output goes high.
The pulses which control the ramping sequence are identical to the
which trigger the motor controllers.
Since it was necessary to
have each ramp step exist for more than one pul
by counter H, Figure 5.4, which is set for a divide-b
Since eight ramping steps are required the entire sequence takes 64 motor
however, full speed is not achieved until the 65th motor pul
has been received.
This is due to the internal design of the 4059,
counter T, which only transfers the jam input to buffers after each
Since the divide-by-32 is programmed after the 64th pulse
the counter must go through one more cycle of the previous divide-by mode,
, before the transfer of the jam input occurs.
Since the beginning of the first traverse, latch K of Figure 5.3
OR gate B of Figure
low, allowing clock pulses to pass through gate
D to counter G.
For the remainder of thi
discussion, it will be
sumed that the logic is set for a scan width of 31 centimeters, i.e. a
divide-by-six mode for Figure 5
, Figure 5.4, and Figure
counter G of Figure
ts output Q6 goes
high placing a reset pulse on latch K.
atch has been
in reset, the pulse has no effect on the
Q7 of counter G
goes high, NAND gate H goes low and latch K changes levels to a low.
level change puts a low on the input of gate C of Figure
to counters K and L
At this time, 64 motor pul
and counter K of Figure 5.4 has its output "eight"
, pin nine, high
setting the jam input of counter T for a divide-by
for full speed
pulse also puts a low on one of the inputs of gate B of
to counter G.
This state exists until counter B of Figure
5.5 reaches a count of
depending if the divide-by-four
mode has been
this will be 128
from the end of the traverse).
This allows NAND gate C of Figure
go low which in turn allows gate B of Figure 5.3 to go low and permitting
clock pulses to pass to counter G.
nverter Q of Figure
high to set latch K it also reset counter G
Counter G now accumulates
until it reaches a count of
latch K to a high.
Since the pul
and Q6 goes high.
were allowed to pas
to counter G
92 pulses were left in the traverse, there exists 1
the end of the traverse.
21 centimeter scan width was in use,
through counter G of Figure
to initiate the negative ramping sequence.
se, if a 40 centimeter ramp were used,
the divide-by-eight mode,
eight times 16 or 128 pulses would be left in the ramp and latch K would
not change state until 1
pulses had passed.
Upon completion of the last 1
T of Figure 5.4 i
motor pulses of the traverse, counter
brought to the divide-by-100 mode in eight steps
identical to those which were used for the positive acceleration.
completion of the traverse, gate C of Figure
5.5 would once again go high
and the next pulses sent to the traversing motors would
next ramping sequence.
The traverse i
controlled by the
The circuit con-
sists of a presetable divide-by-"N" counter
, a 14 stage
ripple-carry binary counter/divider
4020, and an
eight input NAND
CMOS 4068,(see Figure 5.5)
The clock pul
identical to those sent to the motor driver boards.
Switch S1 allows
the incoming pulses to be divided by either four, six, or eight nominally
for the 20, 30, or 40 centimeter scan widths respectively. The pulses
required to traverse the various widths are 4096 for
30 centimeters, and 8192 for 40 centimet
higher divide-by numbers results in more total
quired to send the Q 1 output of the 4020 high
scan width is desired
clock pulses being re-
Depending upon which
, the output of the Q11 will go high after the
appropriate number of pulses have been accumulated
- a a a -
by the ramping circuit to initiate a countdown procedure which will
first inhibit the electrometer amplifier circuit and secondly ramp the
traversing motion to a stop.
, the number of pulses required for completion
of rotational shifts was not a convenient power of two.
It was found
that a total of 6228 pulses were required for 1800 of rotation.
to have 36 views, one view every five degrees
required per rotational shift.
motor pulses are
For other rotational shifts, i.e. ten
degrees, 346 pul
are required and 20 degrees, 692 pul
The pulse signifying the termination of rotation
use of the circuit in Figure 5.6
The clock pul
was achieved by the
the Ar circuit.
going to counters A and B are identical to those
being sent to the rotational stepping motor controller.
are wired into an eight input H1AND gate
one gate in such a manner
to trigger a low on the accumulation of 1
NAND gate C going
low increments counter D by one and reset
counters A and B enabling
the next count of 173 to again send gate C low.
counter D can be
selected through the use of switch S1.
The Ar counter
output will then go high on either 173, 346, or 692 pul
respond to 5
0 degree rotational
The r ci
rcuit, Figure 5.7, receives its input from the r circuit,
3 Q4 Q5 Q6 Q7
Q1 02 Q3
- e% S )
This signifies the end of a scan and the initiation of the
Hlotor Control 1 ing Logic
In order to properly sequence a stepping motor, either clockwise or
counter-clockwise, the various windings must be energized in a sequence
particular to each motor and set by the motor's physical design.
stepping motor manufacturer makes
to their specific motor's require
available control circuitry tailored
ents. It was decided to utilize such
circuitry for all stepping motors used on the cobalt-60 scanner.
The control boards for the Warner motors provide pul
to two sets
simultaneously in an attempt to obtain more torque.
of these pu
is composed of two voltage levels.
the pulse a 50 volt pul
high starting torque.
initially applied to the motor to obtain
The motors, however, can not dissipate enough
heat if 50 volts were used for the entire puls
Therefore, at the
preset time, the controller switches from the 50 volt pul
to a 1
The input requirement for the controller is a negative going five
volt pulse not shorter than ten microseconds duration.
The Slo-Syn motor used for rotation performed adequately with a
single voltage pulse.
The manufactured motor controller was used to
correctly sequence the energizing of the windings for clockwi
counter clockwise operation.
In order to obtain the data required for reconstruction, P(ma,0)
the current signal
being produced by the photomultiplier
tube must be recorded
It was decided to use a method of repetitive
, to obtain these measurements.
been proven to be
an effective method to measure small
shift of the data, due to a resistor-capacitor time con-
this method u
integrating amplifier with a
The voltage output of the
ed near the beginning of the
again near the
assumed to be
the accumulated current value for that interval
The amplifier i
reset and i
ready for the next integrating cycle
over the interval
taken as the
instantaneous current at the center
of that interval.
the mean current i
The smaller the
to the actual
if the mea
were infinitely small
the measured transmission profile
the true profile
it has been shown
nm 1 1 4mc+ a olc 1ian ilrI ho r cii ffiriant
In its original application, the repetitive integral method was
used to measure currents a
s low as a few picoamperes.
available from the photomultiplier tube
application) is orders of magnitude above
tube voltage versus current curve can be
seen in table 6.1
currents enabled the circuit, used by Fitzgerald
that of Figure 6.1.
to be simplified to
One problem was encountered however, due to these
higher currents and that was being able to reset the amplifier within the
restraints of the amplifier cycle time.
The resetting of the circuit is ach
eved by discharging capacitator
Since the currents involved in Cobalt-60 scanning are much larger
than those of Fitzgerald'
original application, the capacitor
and the charge which must be dealt with during reset are al
The transistor used to reset the capacitor must also have a high enough off
resistance to impede leakage currents, which would in turn cause amplifier
Of the transistors availabi
at the time of fabrication,
none met these dual
One solution was found in the use of series bilateral switches,
low off-leakage c
switch has low on-resistance, typically 80 ohms, and
current, less than ten picoamperes at ten volts.
The problem of leakage effecting the amplifiers linearity was
amined by placing a constant current source on the input of the amplifier
and recording output voltage versus time.
The response of the amplifier,
CURRENT VERSES VOLTAGE FOR THE
NaI(T1) DETECTOR SYSTEM
(Negative High Voltage)
Diagram of the Electrometer Amplifier Circuit.
Electrometer Amplifier Controlling Circuitry
As previously mentioned, at the beginning of a
e, a ramping
sequence accelerates the transverse mechanism then maintain
speed and at the end of the traverse dece
rates the mechanism to a
repetetive integral method integrates
a period of time;
the data required by the
rithm are the
transmission data versus
of distance versus
only period during
which time and di
ed are proportional
is during the constant
section of the traverse
therefore important to accumulate
data only in the time interval
and the beginning of the
between the end of the acceleration
The data recording
tem chosen was an
IBM compatible nine track
ectronics is a complete system
except for the electrometer amplifier.
t requires only four signals
to process data placed on its
These pulses are a
a pulse to trigger the first reading sequence
a pulse to
second reading sequence
and a pu
to trigger the
registers, which in turn transfer the data
electrometer amplifier circuit
, Figure 6.4, control
data from being taken during accelerations, and sends
to the recording
on a 64 pul
to those sent to the motor driver boards and operates
From Ramp Elect
Simulate Pulses I
Motor Pueses I
01 02 03 04 Q
The pulses to the circuit enter via switch S1, which for
in the position shown.
The alternate function of the switch
to allow the amplifier to be cycled during the scanner setup,
allow adjustment of the amplifier gain
is being brought up to speed, gate A
While the traverse
inhibited by the in
put from the
allowing gate A to pass
to counter B and in
turn counter C
the trailing edge of the first motor pulse,
bringing gate F low
of counter C goes high
thus bringing the electrometer amplifier out of
The current from the photomultiplier tube
the third motor pulse the first read
is accumulated and after
is triggered by gate E going
The amplifier is then allowed to accumulate current until
59th pulse at which time gate 0 goes
high and triggers the second read.
within the recording system subtracts
and stores the
pulse also initiates
to the recording equipment where
is recorded on a
nine track magnetic tape.
The 63rd motor pulse brings counter C outputs
zero and the 65th pulse begins the second measurement cycle.
number of cycles in a traverse 1
dependent upon the
can width chosen.
The 40 centimeter
the 30 centimeter width has 92, and the
20 centimeter width has 64
Although the number of interval
the distance traversed during each measuring interval
being determined by the mechanical
design of the traverse system.
require 24 pulses
the gear reduction units
ten to one ratios, and the
lead of the ball
screw is one-half
The accuracy of the axia
tomographic scans made by this system is
each traverse being
executed with source and detector
correctly responding to each
the alignment of the source and detector in all planes,
the accurate detection and recording of the radiation
by the data acquisition
The tests required to verify if either the source or detector
have mistepped during a traverse was straightforward.
In using two
stepping motors to drive the source, a situation is created whereby
both motors must perform flawlessly
since a missed step in either or
both motors will result in the loss of driving torque.
starting point of the source'
By marking the
s first traverse, a check can be made con-
firming that at the end of every second traverse the
to the same position
procedure was followed with the source
and detector traversing in the vertical direction, the condition of
orientation and in every second traverse the source and detector
returned to the same initial reference point indicating accurate
mechanical movement by the stepping motors. The number of pulses sent
to the motors for each traverse were also identical. It was felt
that,in order to verify the alignment of the
source and detector
planes, the output of the detector
and reliable test possible. The r
ten would be the most sensitive
otational system was held fixed with
the source and detector traversing horizontally and the
several traverses was recorded.
beam intensity were found. Upo
Significant variations in the detected
in further investigations using an optical
system showed a misalignment in a plane perpendicular to the face of
the main rotational drum.
An attempt to correct this situation was made
by shimming the support shafts, but further scans involving rotation
as well as translation surfaced two other system
which caused inconsistency in data collection.
The first was an abrupt
change in beam intensity occurring several times per scan at angular
orientations between plus or minus 45 to the horizontal traverse.
These changes occurred only during rotation and not translation and
were attributed to a shift of the source inside its seated capsule
The second system characteristic
was a variation in transverse align-
ment of source and detector at different angular orientations.
The above inaccuracies were too large to simply ignore, therefore,
a mathematical correction was investigated
Since the objects to be
scanned should never completely fill the transversing distance
there should always be unattenuated transmit
ssion values at the edge of
The algorithm first requires a scan with no object
in the beam to
It then creates
a set of normalization
factors which when applied to the raw transmit
scan corrected free from misalignment errors.
ssion data yields a
is not made
for the abrupt change in
The reconstruction algorithm requires
that the unattenuated value
the beam be known at each transmission measurement position.
transmission data has
, any unattenuated value
be used as the value for
the first and last
few transmission measurements
s free of attenuating material
therefore can be used to cal
transmission for their
By calculating the transmit
in this manner,
intensity during rotation can be ignored.
Data Acquisition System Performance
After the mechanical
scanning system was aligned the reproducibility
and linearity of the data acqui
first examined by viewing multiple
ition system were determined.
electrometer amplifier output voltage versus time.
voltage versus time
relationship for a number of integrating cycle
with the source and detector stationary and a negative
Both reproducibility and linearity of the
ments can be seen.
test was repeated after increasing the photo-
multiplier tube voltage to 600 volts, Figure
The only noticeabi
- -...nu m
-- -- ~-m
- -- ----r ar all me
I I -. : II
I_ _~__ __ _
-- e6-tj. LOA
I C )--
I __________ -o
* ___ a.
* _____ (,1111 r 3r~
* ___ ______ ___
-- -_ Ic,
* m_ _____ 4-'
* ____ _I
U _ ____ U')
*Z m -- -- -
I~ er1----- ---
*1 ______ --i C)
*r --- m-- -
U __ ___a
- ae _____
*I _____ C
___ __ ,' U-__ --
to cause this effect and to quantify perturbation
it would have on
, further experimentation was required.
The effect was
examined by quickly moving the radiation source to
with a negative 500 volt across
the photomultiplier tube.
The first four
of Figure 7
were the result of the source
During the fifth cycle,
the source was quickly moved to
the off position.
If there was not an afterglow
voltage should stay at the value it had obtained when the
was not the case and the voltage con-
The afterglow current can continue to be observed
in the integration of the next few
was at all
dependent upon photomultiplier tube voltage,
if this effect
was repeated with a negative 980 volts
applied to the photomultiplier
These results can be
seen in Figure 7.4 and are
of Figure 7.
, demonstrating the
is actually a
Although the afterglow effect could be demonstrated by complete
of radiation signal,
the effect that it would have on the transmission data
canning procedure had to be determined
effect of three millimeters of lead being placed in the
beam between the
sixth integrating cycle
A slight afterglow effect may be
present on the seventh cycle, but from the
signal can be attributed to the
ead not being held steadily
in the beam.
This amount of lead inserted into the
beam represents a
reduction of beam intensity of approximately
a step response of the
magnitude that could typically be encountered during scanning.
The next step was to determine the effect during transverse scanning
with the rotational system locked at one angular orientation.
first transverse scan was performed to test the response of the system
to a large step change of beam intensity.
In order to obtain this
beam profile, a four inch by four inch lead brick was placed in the
The results can be seen in Figure 7.6.
The abscissa is
incremented in intervals of integration and the ordinate incremented
in the logarithm of transmission.
The asterisks indicate the values
scanning right to left while
x marks the points for the
eft to right
During a left to right
scan, the edge of the lead brick i
encountered during the
integration interval and by the eighth
interval the detector system has equilibrated to the decreased radiation
, results predicted by Fitzgerald (1974)
On the thirty-seventh
interval, the beam emerges from the brick and the increase in beam
intensity is encountered.
When scanning from the opposite direction
the difference in the transmission values between the asterisks and
xs can be seen.
At the abscissa point marked as the sixth integration
xs are measuring a decrease in radiation signal while the
asterisks are measuring an increase.
The afterglow phenomenon causes
xs not to equilibrate to the decreasing beam condition as quickly
as the asterisks show the response to an increasing beam.
side of the brick, at the abscissa value of
On the opposite
xs are measuring the
increasing field while the asterisks are measuring the decreasing field,
the same effect i
It is significant to notice that the correct
values were always obtained by the first full cycle after the step
SCAN DIST (MMI
simulate the effect which could be expected during a routine scan
six inch diameter Lucite cylinder was scanned in the same manner as the
with the xs
again the shift in data can be seen in Figure
leading and lagging each other during the
same corresponding beam
shift can more easily be seen
in which th
xs have been replaced by a solid line and
the asterisks by diamond shaped symbols.
The symbol which i
the decreasing field always lags the symbol measuring the increasing
A third experiment performed with a smaller Lucite cylinder, is
shown in Figure 7.9.
This cylinder being of a smaller diameter caused
the radiation intensity gradients to be steeper
but after examining the
, it was found that the deviations due to the afterglow effect were
similar in magnitude to those of the larger cylinder.
the two sets of data
, the smaller cylinder may appear to have much larger
deviations, but this is a result of the change in ordinate scaling.
, the question of whether the afterglow effect would mask
small changes in beam intensity was examined.
Five Lucite rods, with
diameters of 6.5 centimeters,
, 1.7 centimeters,
, and 0.67 centimeters were placed in the scan path.
results of two scan passes, from the same direction
are shown in Figure
The measuring system, taking data on the
3.3 millimeter grid,
adequately detected and measured the transmission through even the
The data also demonstrates the reproducibility of the
recorded transmission values for each rod.
V 1 S
'p) llrr)~ )t
011 h. t a V h l I
-- 4t -b.. ~- f~~.~~~~~~-~-~.. -. ----+~~~. --...
SCAN DIS fMM.
Data System Response to a Cylinder in
2 r n
bC~ '4' .,
a. A *
_______~--- I-- ~---~- --~-4-- _____-I I --- +---- -
SCrN OlIST IMI
-I- -- -
SCPN; Ijti !N1 i~
-f--- -t --
Q? 0' it 0r
t: x '.-
SCaN DI$T iM'"I
---j- -------r--------t -
than 1% during normal
It is also of inter-
est to note that if a curve is fit to the transmission data, these
inaccuracies are reduced.
It was therefore decided to continue this
subject alternate detection systems to
testing at a later time.
The first test of the
as a whole was the scan and recon-
struction of a solid Lucite cylinder.
This demonstrated the system's
ability to reconstruct a homogeneous volume with an attenuation coef-
ficient close to that of normal tissue.
For this first scan, as in all subsequent scans, the photomultiplier
tube voltage of negative
600 volts was used.
ssion data were
collected on a
millimeter, 92 by
92 member, grid with 36 even
spaced angular views taken.
When these data were reconstructed, it is obvious from the poor
results that 36 views is too few to specify a unique solution for a
92 by 92 member matrix.
If the total number of data points do not
equal the number of reconstruction point
the data will not have the
independence required for a unique solution.
Many of the reconstruction methods can, however
even if the proper number of data points are not taken.
of such reconstruction generally shows
produce a matrix,
arce statistical fluctuations
through homogeneous areas and overall inaccuracies throughout the entire