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The identification of inhomogeneities for tumor dose calculations during treatment planning

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Title:
The identification of inhomogeneities for tumor dose calculations during treatment planning
Creator:
Bova, Francis Joseph, 1950-
Publication Date:
Language:
English
Physical Description:
ix, 115 leaves : ill. ; 28 cm.

Subjects

Subjects / Keywords:
Algorithms ( jstor )
Amplifiers ( jstor )
Attenuation coefficients ( jstor )
Cylinders ( jstor )
Dosage ( jstor )
Fourier transformations ( jstor )
Inhomogeneity ( jstor )
Pixels ( jstor )
Signals ( jstor )
Stepping motors ( jstor )
Cobalt -- Isotopes -- Therapeutic use ( lcsh )
Radiology, Medical -- Instruments ( lcsh )
Radiotherapy ( lcsh )
Tumors ( lcsh )

Notes

Thesis:
Thesis--University of Florida.
Bibliography:
Includes bibliographical references (leaves 112-114).
General Note:
Typescript.
General Note:
Vita.
Statement of Responsibility:
by Francis Joseph Bova.

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University of Florida
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University of Florida
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Copyright [name of dissertation author]. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
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AAX4787 ( NOTIS )
04083101 ( OCLC )

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THE IDENTIFICATION OF IrNHOIMOGENEITIES FOR TUMO10R DOSE
CALCULATIONS DURING TREATMENT PLANNING















BY

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.











ACKNOWLEDGEMENTS



I would like to express my sincere appreciation to my advisory


committee for their help and guidance throughout this work.


I would


like to give special thanks to my committee chairman, Dr. Walter iMauderli,


for hi

for hi


help and guidance with thi


project and to Dr. Rodney Million


support, both financial and moral, and for providing an


edu-


cationa


atmosphere without which this research would never have been


possible.


I would also like to thank Drs. Genevieve Roessler


Charles


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


and personally


rewarding educational


experience.


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


Keefer






I would like to express my sincere thanks


of the Mechanical


to Dr


Engineering Department and his stude


George Piotrowski

nts for their


work on the original


I would d


design.


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


Page


ACKNOWLEDGEMENTS


ABSTRACT


S. S S S S S t .. t S .S S S Vli


CHAPTER


INTRODUCTION


HISTORICAL DEVELOPMENTS

Objectives .........


Methods of Internal Dose Corrections


Automation of Plann ng .. ......... .... .. .
Inhomogeneity Corrections ......... ............
Computerized Axial Tomography ...... ...........


RECONSTRUCTIVE METHODS

Tomography ........


Reconstruction from Projections


History ....
Nomenclature


.......9.S e. .....
..S..... *.. *t


Numerical Reconstructive Tomography Methods


Back Projection
Iterative Techniques


*.. 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 ..


MECHANICAL DESIGN


St***S** S *SStt*atSS S S S S S 5555555**C#ts~ S






CHAPTER


Page


Patient Support System ...

Radiation Source ............

Radiation Detection .........

Radiation Beam Collimation

Collimator Shield ...........


ELECTRONIC LOGIC DESIGN


Overview

The Clock


The Sequence Controlling Logic

Ramping Logic ....... .. ..


Transverse Motion
Ramping Sequence
AX Circuit .......
AR Circuit .......
R Counter .....
Motor Controlling


* 4 S S
* S C S *
* S C S C
* S S S
* C P P
Logic


* 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


DATA ACQUISITION


Electrometer Amplifier


viortenmator amnlifier Controllin Circuitr


SYSTEM PERFORMANCE


Data Acquisition


Reconstructi or

Treatment Plannii


DISCUSSION OF RESULT


mechanical Syster

Controlling Elec'

Data Acquisition


System Performance ................

n Grid .. .............................

ng Algori thm .

TS ... .




tronics .... .......

and Recording .... ....


L VIII~ ~L 1 llllr





Page


CHAPTER

BIBLIOGRAPHY


BIOGRAPHICAL SKETCH





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

by

Francis Joseph Bova


December, 1977


Chairman:
Co-Chairman


Walter Mauderli, D.


Lawre


Major Department:


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


nhomogeneiti


for routine clinical use in radiotherapy


A whole-


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


existing


s tem


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


asso


ciated with


shield was designed.


It was


fabricated from depleted uranium.


The design incorporates a fixed


1.98 millimeter, straight-bore collimator with a source which


doubly


I~' I *II -1.. -:- uL~A ~ -


" ''


_ I


--





collimator hole and is considered "on. "


The detector, mounted opposite


the source,


is a 4


inch


long sodium iodide crystal


with interchange-


able straight-bore collimators.

Both the collimator shield and detector are moved across the

region of interest by stepping motors, gear reduction units, and


precision ball


screws


. Thi


arrangement is used to assure accurate


transverse motion with a minimum of computer control


After a trans-


verse


scan has been completed,


the apparatus is rotated on a


large


inch diameter wheel.


This rotation will


again be control


ed by


stepping motors and gear reduction units


scan


The width of the transverse


variable, as is the number of degrees per angular rotation.


The transmission data are collected on a


millimeter grid


and the


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-


compatible, write-only,


tape recorder.


Once the


data are


complete,


the tape can be transferred to the departments time-sharing computer.

The raw data are then reconstructed by an algorithm using filtered


back projections.


A treatment planning algorithm will


then utilize


these data to correct internal dose distributions.











CHAPTER 1



INTRODUCTION



The path which radiation treatment planning has followed is not


unlike that of many other branches of


science.


a physical phenomenon prompted a scientific


The need to understand


inves


tigation with the


object of a delineation of parameters which affect its


interaction.


end goal of thi


s investigation has


been the formulation of these para-


meters


nto mathematical expressions with which the phenomenon can be


predicted.

The early days of treatment planning saw crude and inexact tech-


niques employed


such as calibrations of radiation fields by means of


erythemal


evels


. 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


These profile


are commonly known as


isodose curves and are obtained with the use of tissue-equivalent


phantoms

with water.


These phantoms are usually rectangular Lucite tanks filled

Since the skin surfaces of patients who must be irradi-


ated


are normally not flat


a two-dimensional contour, of the surface


upon which the radiation field will be imposed, is taken.


The original







Most planning procedures stop at this


level


of sophistication,


although with use of only the aforementioned procedure, known


inaccu-


raci


exist in the dosimetric pro


cess


X and gamma rays used in radi-


action therapy are absorbed primarily through Compton


s interaction,


which i


dependent upon electron density.


With the


exce


ption of hydro-


gen, all


elements have essentially


the same number of


ectrons per mol


or per gram/centimeter2


If all


anatomical


structures


had identical


densiti


the water tank phantom would be accurate; however


various


structures within the body do vary in density


These


anatomical


nhomo-


genetics cause


x and gamma ray


to be absorbed nonuniformly through-


out the


contour


It is therefore essential


to have detail


ed density


distribution within the contour in order to proceed with the


isodose


correction process so that the next


level


of accuracy


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


display or


entered on a digitizing surface.


density values for these regions


Some


stems allow


while others


ou to enter the

require you to


identify them as


lung or bone and then use preset density values for


attenuation


coefficients.


When this procedure i


examined,


it can be


seen that small errors in size and position of inhomogeneti


or in


estimating their densiti


can


lead to errors


large


or larger


than


those


ch would have been encountered if no


correction at all


had been used.


It can safel


tated that without the aid of inhomo-




3


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


com-


puterized axial tomography can give the information required on position


as well


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


which i


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


supervol tage


therapy, which is operating primarily in the Compton region


The second


question


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

procedure.


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


ess


use than the one in a diagnostic setting


, the cost per


scan would then increase above these pri


ces.







the department's existing systems have been used.


Assuming that a


therapy department capable


of utilizing inhomogeneity data


likely


to have either a dedicated treatment-planning computer of


use of a macro-computer via


time-sharing,


the scanner will


not re-


quire the intelligence of a central


processing unit.


therefore been designed around the hard-wired digital


tem ha


computer.


This


simpi


and low-cost computer


, costing between $100 and $250,


has th


ability to control


scanning sequences


with variable scan widths


and variable angular shifts.


The device


also has the


capability to


start and stop all


scanning motion through precise digital


ramping


sequences


and to control


data


collection.


To eliminate the problem of

of interaction from the photoele


calling data


ctri


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


used to


scan


, the output of the reconstruction algorithm i


then the


value of the


inear attenuation coefficient for


cobalt-60 for each of


our region


of interest.


Because of the heavy, bulky shie


Hiding usually


associated with cobalt-60 sources, a special collimator


shield was


required.

Both the collimator shield and detector are moved across the region


of interest by stepping motors, gear reduction units, and precision ba


screws.


The width of the transverse scan and the number of degrees


per angular rotation are variable from scan to scan.


The transmission


data are collected on a 3.3 millimeter grid, and the reconstruction


own




5


The raw data are then reconstructed by an algorithm using filtered


back projections.


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.













CHAPTER


HISTORICAL DEVELOPMENT



Objectives


Unti l


1965, all


isodose summation was done manually.


This involved


the overlapping of isodose


lines.


charts


and adding up all


Because of the time involved in


uch a metho(


intersecting isodose

d, a specific set of


composite curves was not always compiled for each individual


case.


There


was therefore a need for improved dosimetry techniques and tool


The practical

(1954) stated that


goals


for therapy put forth by Bloor and Quick


, the aim of radiotherapy,


in treatment of any


malignant growth


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


certain minimum


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


particular,


the inhomogeneity of dose within


and that unnecessary radiation i


avoided outside


tumor bearing volume


Although these authors proposed new methods


for tabulating isodose data,


their methods still


involved manual


sum-







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


therapy.


He was able to devi


a coordinate scheme for


calculating


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.


standards


still


By today


, the method was very cumbersome and time-consuming; however


it was the first large stride forward toward the automation of treat-

ment planning.


It was not until the 1960s that the next


step was taken.


Sterling


and Perry


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


machines


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




8


minimum number of fields needed for routine work can easily explain


at this point in time,


The impracticality


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


level


They decided to abando


of accuracy was

n storing data on


cards


and go to an alternate


stem of equations which would,


in place


of cards


, specify the radiation field.


Their method used tissue-to-


air ratio


(TAR), off-center ratios


(OCR)


and an inverse


square


correction as field parameters.


They felt that inhomogeneities should


be considered in the field corrections


To achi


eve


this correction,


they expressed the TAR as a


function of


electron density and t


thickness.


Although the authors were correct in attempting to take


into account inhomogeneities


, they posed no method for


locating them.


Through


next


several


years of development


, many methods


computing radiation fields within the body


were developed.


Skaggs


and Savic


(1962)


Sterling, Perry


and Katz


(1963)


Bentley and Inst


(1963) and Hallden, Ragnhult and Roos


3) were but a


few of the


more prominent researchers of thi


era.)


It was not


, however, until


1965 that a completely automated method of treatment planning with auto-


mated output plotting of isodose curves


for rotational


within the body cross


therapy was developed by Mauderli


section


and Fitzgerald (1965).


Although the method reported employed manually digiti


zed isodose curves,


a method of acquiring the isodose field data


in digital


form by the


direct measurement of the radiation field had been proposed and de-







Inhomogeneity Corrections


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


(1965


the coordinates

Setala


addressed this problem and developed a method of internal organ


localization based upon views in two orthogonal x-rays


The positions


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


The problems


x-rays


contour mapping lead to inaccuracies which limited the use of the

method.

The first attempt to accurately compensate for inhomogeneities


was by Eichorn (1967)


Eichorn built a phantom of the thorax in which


he placed


nhomogeneities that simulated bones and lungs.


Knowing the


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


simulated treatment.


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


planning


computer treatment


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:







Computerized Axial


Tomography


largest


trides


in solving the problem of inhomogeneity defi-


nation has been in the development of axial


tomography


Thi


technique,


first developed into a useful


clinical


by Hounsfield (19


1969, yields the positioning of anatomical


inhomogeneiti


via a map


of relative radiation attenuation numbers.


first unit was dedicated


to examination of the head.


However, by the time a marketable


machine


was announced in


1972


, the development of a


similar unit capable of


rendering tomographs of any


section of the body was announced by


Ledley


et al.


(1974)


Since


nearly 40 companies


have proposed


production of axial


tomographi


scanners


The availability of axial


tomographic devices which scan with


x-ray beams of energy


attracted


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


material


being


scanned.


The work by Phelps


et al


(1975) demonstrates


the relationship between the computerized tomography,


, numbers, and


the electron density of materials such as


Teflon, Bake


lete, Plexiglas,


nylon


and water.


The fact that one


material


at a time was scanned


is of interest.


McCullough


, (1976)


disputes the ability of CT


scanners


to achieve a resolution of 1


structed.


in the "quantity"


He alludes to a resolution in


excess


that i


being recon-


This error would


only be the first error in the calculation for the attenuation coef-


ficient needed for therapy


Since a


large number of therapeutic




11


The type of procedure currently in practice is similar to that


explained by Jelden, et al.


(1976


and usually involves


several steps.


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


are designing


support a computerized axial tomographi


CAT scanner and also support a therapy's department treatment planning


requirements. Once

plot is calculated.


i the data transfer has been accomplished, a density


is done by the bracketing of CT numbers


into several discrete levels.


For example


, a simple algorithm


assigning


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.


This


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


scanner.


This type of scanner has several advantages over presently


available x-ray


scanners.


One of the main advantages i


that the mono-


chromatic beam enables the reconstructive algorithm to reconstruct each


image


element to the linear attenuation coefficient for cobalt-60.


second advantage is that


and a


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.


as obvious


The problems associated with the shielding of a high


energy isotope complicates the design of both the mechanical and the


electronic systems.


The final design presented, is the result of many


trial and error design procedures and fulfills the requirements of

reliability, precision and low cost.












CHAPTER 3



RECONSTRUCTIVE METHODS



The basic principle on which axial tomographic scanners are based


invol


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.


Unfortunately


, 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.



Tomography



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


synchronized


so that only one sagittal plane within the body remained fixed relative







focused plane superimposed on a background of blurred planes.


This


type


of tomography was known originally as


planigraphy


(Andrews,


1935) and


later


focal


plane tomography


Focal


plane


tomography remained the


only type of tomography availabi


to the medi


community for over


forty years


From 1956 to


1972 the advances


which eventually


lead to


the present-


day tomography units were taken in the fields of radioastronomy and


electronmicroscopy.


These


efforts were,


for the most part


, independent


and only after the


large interest generated by


diagnostic tomographic


scanners


introduced in


were the iso


lated works categorized under


the general


heading of Reconstruction from Projections.


Reconstruction from Projections


History


The first step towards a reconstruct


image was


taken in radio-


astronomy by Bracewell

microwave image of the


1956)


surface


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.


microwave


signal would therefore be the


emitted in a two dimensional


rectangle.


ummation of all


Bracewell


the signals


proposed that these


strips b


"reconstructed" into an image of the entire surface by


utilizing Fourier transforms, but in


1956


a method


the state of the art in


computer


science made the computation of an inverse two dimensional


Fourier transform an insurmountable task.


He was therefore forced to




15


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


cross


section of an object


which could only be viewed by a transmission electron beam.


problem


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.


Fourier


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


The review


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


electronmi croscopy


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


time that







Nomenclature


Before various methods of reconstructing cross


sections


from their


projections are explained,


the nomenclature and methodology of the


projections should be discussed.


Let the object 0 in Figure 3.1


be the


object to be scanned and reconstructed.


Sitting on opposite sides


of the object 0 are the Detector D and


the source


The source emits a beam;


in the


case


of the cobalt-60


scanner


the beam i


composed of the gamma radiation of


a ten Ci


cobalt-


60 pellet.


The detector measures


the transmitted portion of the radiation


beam;


this portion will


be denoted as P.


The gamma-ray beam


in Figure


at a distance r from the origin and makes an angl


0 with the


ordinate.


If the path


length of the


ray is


s, then P,


the partial


trans-


mission of the beam


, is given as P


(r,0) and is equal


to the transmission


of the ray through path


s or


P(r,0


x,y)ds


where r


= (y)


sine


and f(x,y)


the function which describes the attenuation of beam.


the ca


of the


monoenergetic beam of radiation


= Ioexp[


-v(x,y)ds]


where:


the initial


unattenuated beam intensity at the detector


s the intensity of the beam after it has traversed path


r,





















































-,_. SOURCE


Figure


( I it


flPVIFCT m


[WIFCTflP-'DO'


X axis


Scanning Geometry.




18




= ln(I/I


then Ez.


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.


The data


is collected and the


reconstruction performed at


pacing of the ray width a.


number of points in any scan pass at an angal


0 will


be N=d/a and


the total


number of reconstructed points will


be N.


Each of these


points will


henceforth be referred to as pi


cture


elements


pixel


After N measurements are made at angle 0


the source and detector


rotate A0 about the origin and another


set of N values


is obtained.


This procedure i


continued until


K sets have been measured, where


= ( /A0)


The scanning is stopped at this point because


P'(r,0)


thus all


= 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,


it will


be assumed that the measurement and recording of transmission data


performed without distortion or alteration of the data


. It will


there-


fore be assumed that any distortions or artifacts in the final


image


are due to either the scanning procedure or the reconstructive technique.


Equation


hows that the scanned data, or transmission data,


dependent upon only one quantity


namely iu(


Most reconstructive


techniques will


therefore attempt to


field a quantity which can be


correlated to the


linear attenuation


coeffi


lent.


Humeri cal


Reconstructive Tomogra phy Methods


Back- Projection


This method was used by Oldendorf


(1961


for the first experiments


in reconstructive tomography


In this


technique


the data


taken at


each angular orientation,


0, are proj


ected back to a common


space.


Each


transmission value at a particular angle, P(r,0


, is projected back on


or added to, each pixel


measured.


along the ray path


The magnitude of each pixel is their


through which it was

before the summation of all


transmission rays which pass


through it


. Although the


image i


an over-


estimation of the original


object


it will


have merit as a qualitative


representation.


The advantage of thi


method i


that it can b


irnpl


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


Iterative


inhomogeneity with the number


e number of views,


Technique


The object of the iterative techniques


unlike that of the


Back


Projections


is to ascertain the correct value


x,y)


near


attenuation coefficient

The technique obta


, for each of the N pi


xels.


, through various procedures, a matri


of N


linear attenuation coefficients.


Transmiss


ion data are


calculated using


these


values and then they are compared to the measured data.


The values


of the attenuation coeffi


clients are altered to obtain a better agreement


between the measured and calculated data sets.


This procedure i


con-


tinued until


N pi


have been adjusted.


If the


overall


fit of the


calculated transmit


ssion rays


to the measured transtmi


ion rays


within a preset tol


erance,


the procedure is


reiterated until


the error


between the


culated and measured transmit


ssion data


is within


acceptable


limits.


Iterative Least Squares


Technique


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


pixel


are made after which another calculated


scan i


performed.


procedure is repeated until


the error between cal


ulated and measured


data


within a preset


limit.






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


Least Square


technique (ILST).



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


all of


the transmission rays


which pass through a single pi


1 are calculated.


That pixel'


value i


adjusted and the


next pixel i


then considered.


After all N pixels have been adjusted


the overall


closeness of calcu-


lated to measured data is examined.


If the two differ by too large an


amount, the process is reiterated.


Because thi


method corrects the


pixel


simultaneously with the


calculation of all transmission rays through


, it has been termed the


simultaneous Iterative


Reconstructive


technique (SIRT).



Algebraic Reconstructive Technique


The third technique calculates the transmission data for a parti-


cular angular orientation.


It then corrects the attenuation


coefficient


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-


tical methods.


One such method involve


the us


of Fourier Transforms.


This method is explained by Gordon and Herman (1970, pg.


113):


The Fourier method depends on transforming the projec-
tions into Fourier space, where they define part of the


Fourier transform of the whole object.


Each projection


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.


After


ning sequence previously explained.


If we represent the


transmission


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


The following




23


If we allow F IP to be the Fourier Transform of this projection

then for any R


[F P]j(R)


+0
= exp[-2rjRP]


This now represents the line projection of the central section of


the object.


ample


The Fourier Transform of a two variable function, for


the two-dimensional surface of the image, is defined


[F.f](X,Y


f(x,y)exp[2nj(


,Y)]dxdy


where in thi


action coefficient.


f(x,y


Equation


case f(x,y) represents the two-dimensional linear attenu-


The inverse two-dimensional transform is defined


[F2f](x,y)exp[-2rj(X,Y)]dXdY
CO2


3.8 demonstrates that if [F~,f] (x,y) is known, the f(x,y)
C-


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


projected object


[SF2f]
02


= [F2f](Rcos0,Rsin0).


SPC]ud







[S0F2f]


= [F P ](R),
1 0


and, by substituting Eq. 3.10 into Eq. 3.9,


[F2f](Rcos0,Rsin0)


= [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


sys-


tem and the scanning procedure employs a polar coordinate system, the


data at a specific point (x,y) may not be available.


interpolation


any interpolati


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


method.



The Convolution Method


In order to eliminate the two dimensional Fourier


space interpolation


and to decrease the total computational time, an alternate method was


developed.


The following developments follow closely that of Ramachandran


and Lakshminarayanan (1971).


Their method employs


the well known convolution theroem.


Given


two functions f(x) and g


x) and their Fourier transforms F(t) and G(t)


respectfully, then:


rt (I


\rl .1.. 7 1


FL







the German term for folding, of function f(x) and g(x).


shown by


Arfken (1966


F(t)G(t)exp(-itx)dt
r-Co


+of)
= f(x-y)g(y)dy.
-cc


3.13


The Fourier inverse of a product of Fourier transforms is the convolution


of the original function


If Eq.


rewritten in polar form:


f(r,0)


2n

0


F(R,o)exp[-2niRrcos(0-e)]RdRde


3.14


where 0 is the angular orientation of the reconstruction grid, and


the orientation of the data acquisition system.


This can be rewritten


f(r, )


=T
0


IR F(R,o)exp[-2niRrcos(0-e)]dRdn.


3.15


If P' (p,


is defined


P'(a,e)


RIF(R,e)exp[-2riR,]dR,


--Co


then by substitution


f(r,0)


'IT

0


P' (rcos(0-e),o)de;


3.17


changing Eq. 3.17 into polar form










P +0R
P(z,e) = F(R,e)exp[-2nRR]dR.
A-CO


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


3.19


+t


q(z)exp[27TiR9.]d!


3.20


using the definition of the convolution


+P
P'(,e) =


)(z,e)q(t- l )d91


3.21


Since P(


,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


matrix


Fourier inversion of Eq. 3.20 yields


q(Z>


+ 0


Rlexp(-2rRz)dR.


3.22


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.


3.22


can be written


- In







is replaced by na where a is the ray width from Eq.


3.22


n is an integer, the solution to Eq.


3.23


can be shown to reduce to:


q(na


q(na)


= 1/4a


= l/(ln) a


for n=O


for n=odd


q(na


= 0 for n=even


can now be rewritten using


= ma:


P' (na,e)


P(ma,R)q((m-n)a


3.24


m= c


where


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


f( e)


space


Because the sampling of the data occurs at a regular spacing


and the angular


hifts also are performed along regular angular


nter-


Eq. 3.17 in discrete form is:
k


f(jro,0o)


P' ((jroCos(k00-teo),te


3.25


where:


t, j


and k are integers and ro


are the spacings of r and
o


As can be readily seen



jrocos(k00-too)


Bo













CHAPTER 4



MECHANICAL DESIGN



Design Criteria


The transmission of ray P(r,0)


of Equation 3.1


denotes the trans-


ssion of a photon beam through a group of pixels.


The equations


used


in the reconstructive


process


assume


theoretically ideal movement of


both transverse and rotational


stems.


The preci


ion required during


data acquisition can be brought into perspective by examining a


size and comparing it to the total


scanning process.


single


distance traversed during the


entire distance traversed during the scanning


of a 40 centimeter by 40 centimeter grid with 36 angular shifts is


over


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


scanners


, those with moving source and


moving detectors,


fixed the source and detector to a hollow yoke whi


is traversed and rotated around the patient.


While


these


first gene-


ration scanners were being designed


, the basic design for the


cobalt-60


stern


presented in thi


work,was taking place.


It was decided to




29

loss of accuracy when the screw is reversed

misalignment of detector and source due to variation in the

screw lead


isocentri


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


scanner


due to the


addition of


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,


0 is:


)tan(0+Ar-),


where the error due to drum misalignment and rotational inaccuracy is


given by


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


direction,


just one traverse later,


a+~F1;2

























* i


3U













U


'no


Gi L
SLw





a)0

r3
cmr







r-
Cs-r

(\.

01
S..
__ =
C-) v
~I1II~ *














=1L





*
(0
w-L
0(0




4-u
I
015






-Jcr
in


Lr-O


rJ


CL)

A I..-.


Ir
C3 L
r




31

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.



Mechanical System


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


load


situations of Figures 4.1 and 4


several


the pull


1 degrees during th


problem was


the overall

e shifting


solved by the


use of a nylon core rubber belt which could be loaded so that undesirable


rotational


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

SS1800-1007, which


steps in 1


degree increments.


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.







steel


shafts have been used to support the


load transaxially.


To el imi-


nate


the backlash double ball


nuts were used with preloading to an


excess


300 pounds.


The stepping motors used,


WARMER Motor No.


024-0140-FB, which step in


15 degree


ncrements,are accurate


to within


plus or minus


of one step and


with the SLOSYN motor, the error


noncumul ativ


The ball


screws are driven by a


10:1


near reduction unit


which is driven by one or more DC


stepping motors.


In the original


design one


stepping motor wa


used to control


source and one to con-


the detector.


The calculated and measured torque are within


rated range of the stepping motors


when stepping at a speed of about


0 steps


per second.


The original


gear reduction was to be


which would move the


per second


source and detector at a


Unfortunately,


speed of four centimeters


the stepping motors could not be made to


step at thi


speed while


under the required load.


first attempted


solution employed ramping sequences


to bring the motors up to


speed i n


several


steps,


but after


considerable effort it was


finally decided


that th


step rate of 720


steps per


second would have to be temporarily


abandoned.


In an effort to increase the available torque,


two motors


were placed


n series to drive the source.


scus


dampers on both source


and detector were used to avoid resonance


, a problem whi


ch stepping


motors can experience while


lewing.


The maximum speed which could be


reliably obtained was


steps


per second.


There was still


, however,


the problem of being sure that the motors followed the pulse sequence


sent to them,


this was


especially a problem at the beginning and end of




33

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


s (Fitzgerald


- 1974).


This method


requires that the integration over a specified time interval be equal


to the integration of the


signal over a specified distance.


either


DC or AC motors are used in such a changing


situation and the


electronic


relies on positional pulses from the mechanical


stem to


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


similar


to that used during treatment.


dent section


system


and joined by a two-inch thick


fabricated in two


eight foot long,


ndepen-

lab of


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.




34


Radiation Source


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


detector.


When looking at the intensity


first criteria which should be inves


required for the source the


tigated i


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,


while


translates


into a minimum pul


rate of 80,000 pulses per second


The conditions


under which the minimum count exists should be that of maximum patient


thickness.


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


80,000 pul


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


tors, it


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


response.


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


walls so


that is could be used with either positive or negative high voltage


For pul


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-


rent mode.


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


85%.


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


radiation.


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


SOURCE


DTr CToP


TOTAL
TFICVIrIESS







the radiation beam and detector during scanning.


tangent of


e, 0


defined a


at which the radiation


s the diameter of


eaves


the source collimator is


the collimator over its


length:


= tan


diameter of source collimation
length of source collimation


In the


cobalt-60 scanner


the source collimator wa


designed with a


portal


that i


.98 millimeters


in diameter and 10


mill meters


long.


The angle 0


therefore


= tan


= tan


1. 99mm
--I
1O1m I2"


degrees.


a viewing angle 0D whose


tangent is simi-


larly defined and with a detec


tor porta


five millimeters


in diameter


and 150 mil


meters


long.


The value of OD can therefore be calculated


= tan


0.5cm
-cm
15cm


= 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


three degrees

ted is small


It must now be


compared to


primary


signal


for a cobalt-60 beam with


these collimation restrictions.


If No


the photon flux which would enter the detector if no scat-


tering medium were present,


x the distance traver


sed within


the medium


Similar


the detector ha







must be traversed after the scattering event,


then the number of scat-


tered photons reaching the detector per steradian will


= Notexp(-uabs


*dNe'exp(att


*(D-X))


Combining terms


= Nocr


Since some photons wil


*dNe.exp(-x.(uabs -att>)-attD)



1 be scattered but not absorbed in the distance


these photons will


be available for further scatter.


The absorption


coefficient is


therefore used for the


x interval.


Once a photon is


scattered into the detector'


angle of acceptance, any further inter-


action wi


likely remove it from the path of acceptance.


Therefore


the term u


sed to describe th


second region of interaction


D-x, util


zed the


will


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,


volume.


yields a worse than actual


As in


case situ-


ation.


Equation 4


can now be reduced to


= Noa


*dNe.exp(ua *(.5-D)-.5uabs


In view of the assumptions the integration of


total


is simply Ns,


number of scattered photons, and dNe is the sum of electrons in







= No*o


If it is assumed that all of the


largest scatter coefficient,


scatter


will be


is through the angle with the


centimeters
centimeters per


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


occupies.


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


angle


6.5
4


1
(20)2


= 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


flux, while


column III was obtained by dividing Equation 4.5 by the


number of photons, Ntot, reaching the detector


Ntot


where


= Noexp(-att D)
att


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


Ne.exp(~,tt(5-D)-. 5rlbs)


-26
x 10






40


























4-' EC
pte. rd)

o fl0N N-) IC) Cfl ~ r
0Cl N-O N- On CO Co

0d 0 0- O0C

0lr 014-
wrawaI t







F-



0 rLD-

rddJ0
o r1L



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
a-,-

C')



C)(r

~ (A


3 U

F- Cd CO1 Ct FS O
F-
01



I-.







meters.


On the other hand the ratio of scattered radiation to the


amount of total beam penetrating the patient continually increases

with increasing thickness.



Collimation Shield


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


source is


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.


This design,


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


same.


x is the fractional decrease in beam intensity required, it


is defined as







Where


, is the linear attenuation coefficient of the shielding


material being used and r


material


is the linear thickness of attenuating


Solving for the linear thickness of attenuating material


ln(1


This defines the length of material which must be traversed

function of beam reduction and linear attenuation coefficient.


as a

If a


spherical shield-collimator is to be built, the volume required would

be


volume


4
=r


substituting the attenuating thickness for the radius


volume


-= (In(l
3


Cl/vt )
9.


if then all constants are combined and set equal to C1


volume


= C1(10/ )


The weight of this sphere would simply be the volume times the material

density


weight


= C1(1/u P)




43


= (H(


here m is the mass attenuation coefficient.


The weight can be expressed


as a function of u and


weight


= C1(1/p


(1/ )


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


atomi


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


tungsten rod.


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


shielding.




44









TABLE 4.2

EVALUATION OF SHIELDING MATERIALS*


Density


Mass attenuation


Relative


coefficient


Lead


weight


0.698


Tungsten


18.00


Depleted Uranium


.05755


18.35


16.19


.0669


9.92


these numbers reflect only primary attenuation and do not reflect
the effect of build-up factors.





































































































lv












CHAPTER 5



ELECTRONIC LOGIC DESIGN



Overview


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.


Once


full


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


motor


is then pulsed and a rotational shift i


begun.


After rotation has been


completed


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


in an


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.


Tile controlling


elec-


tronics can be subdivided into five categories; the clock, the sequence


controlling logic


, 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.


controls the


The data acquisition system


electrometer amplifier and provides the signals to properly


sequence the recording


stem.


The motor driving logic provides the


various motors with the proper sequence of pulses for either clockwise or

counter-clockwise operation.



The Clock



The entire scanning procedure is dependent upon the signals from the


system


lock.


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


supply.

problem

Figure I


Althou


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


shown in

gates


...



































scillator
Output


'Q' Output


Output To
Seouence Control ing
Lonic


Output To Digital
Pecordinn System


Figure 5.1


Dianran of the clock circuit.




49

The Sequence Controlling Logic



The main logic control was fashioned after a similar design used by


Fitzgerald (1974).


It allows the alternating of traverse and rotation


movement

Figure 5


The pul


and a means for resetting the scanning apparatus.


shows the basic


The logic


stem design.


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


r, and


r circuits


and also makes av

recording system.


'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


ramping


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.


which


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


reset


This arrangement i


used so that once manual control of the unit


is assumed, a deliberate effort must be made to restart the scanning

procedure.


The initiation of a scan


S1 to low.


involves the setting of the start switch


This inhibits the bilateral switch X from conducting, thus


















->
S- Cl-




51


the output of gate V goes low taking all appropriate counters out of


reset.


Simultaneously, the inhibiting output of gate


is brought high


allowing clock pulses to be transmitted and the scanning procedure to be


initiated.


The pulses being passed by gate


are inverted by inverter


R which delays them one half pulse, and then go to the transverse and


rotational sections.


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.


train.


train, counter/divider


Since this counter also inverts the signal, inverter D is


used to resynchronize the pulse train.


Throughout the entire scanning


sequence


for translation


and rotation are being sent to gates A and


which run to the Ax and Ar


counters respectively


and to gates C and J.


Since


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

volts.


Once the


x counter has received a preset number of pulses







rotation.


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


rotation.


Once the predetermined number of motor pul


have been


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


Once thi


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

begun.


After every other traverse


, the


r and


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


pass through


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


Thi s




53


Ramping Logic


Transverse [lotion


In order to achieve a transverse speed of four centimeters per

second, the stepping motors must operate at a pulsed rate of 720 pulses


per second


or one pulse every 1


milliseconds.


It was determined


through


experimentation that the motors would not respond, under load, to


an initial pul


rate in


excess


of 120 pulses per second


or one pulse


every


milliseconds


In order to accelerate the motors to and from


the required speed a digital ramping sequence was employed.


The logic


for thi


sequence can be broken into two sections.


The first


section


Figure 5.3


determines when in the traverse a ramping sequence i


to be


employed and when a constant traverse speed i


to be maintained


second circuit, Figure 5.4


actually


takes the


incoming clock pulses and


produces


a pul


sequence, either increasing in period


or decreasing in


period, depending upon whether a negative or positive acceleration is

required.


initiation of the acceleration is controlled by gate G of


Figure 5


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,


4059.


This


integrated


circuit has the ability to divide an input pul


train by any integer between three and 15,999 inclusive.


The output


signal


is a positive pulse one clock pulse wide occurring at a rate equal


to the input frequency divided by N


the divide-by number.


The divide-





















































Figure


Diagram of


Ranpi nm


Controlling


Logic.




155














ci t






o0110





-th t




oT ;C o4-,












-i.









C,
C


a

0L




4-J
0

X S 8 "" "'2
g 8 :
allnl? 8 a g d '
'Cr




ao -4



--
al I S
LI







tOt

*1 -









AX


Motor
Pulses


Data


-COUNTER


4068


Ranpi ng
Circui t


OUTPUT


4920


Ql0 Q11





























cua
Wa

ara




58


As can be seen by the fourth column of Table 5.1, there exists


no obvious pattern to the ramp


sequence.


It was determined by


experi-


mentation and the only comment that can be made i


that


it works properly.


The unusual step pattern dictates that the final integer used


divide-by number


not be the lowest integer


poss


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


33o/.


It was therefore determined that during the full-speed traverse the


would be the result of a divide-by-32, allowing the


section


of the previous step to be a divide-by-34, an increase in speed of only

6%.


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


as well


as negative


accelerating ramps,an up-down decade


counter is re-


quired.


At the time this circuit was designed


, this specific piece of


logic was not available as a single integrated


ircuit so the


equivalent


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)


Thi


circuit i


arranged


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




59


acceleration, at which time the input of gate D is low, counter K


controls the jam inputs of the 4059 while counter L


is isolated.


This


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


while the


"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


the pul


are divided


by counter H, Figure 5.4, which is set for a divide-b


ight mode


Since eight ramping steps are required the entire sequence takes 64 motor


ses,


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


output pulse.


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,


i.e. 34


, before the transfer of the jam input occurs.


Ramping Sequence

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


accumulates pulses


ts output Q6 goes


high placing a reset pulse on latch K.


Since


this


atch has been


in reset, the pulse has no effect on the


circuit.


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


This


inhibiting


to counters K and L


At this time, 64 motor pul


have


passed


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


-32,


for full speed


ramping


. Thi


pulse also puts a low on one of the inputs of gate B of


Figure


inhibiting pulse


to counter G.


This state exists until counter B of Figure


5.5 reaches a count of


1008


depending if the divide-by-four


divide-by-si


or divide-by-eight


mode has been


selected


this will be 128


or 2


56 pul


respectively


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.


When


nverter Q of Figure


went


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


This resets


to counter G


when


92 pulses were left in the traverse, there exists 1


the end of the traverse.


If the


21 centimeter scan width was in use,


-






through counter G of Figure


to initiate the negative ramping sequence.


Likewi


se, if a 40 centimeter ramp were used,


i.e.


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


Upon


5.5 would once again go high


and the next pulses sent to the traversing motors would


nitiate the


next ramping sequence.



AX Circuit


The traverse i


controlled by the


AX circuit


The circuit con-


sists of a presetable divide-by-"N" counter


CMOS


4018


, a 14 stage


ripple-carry binary counter/divider


4020, and an


eight input NAND


gate


CMOS 4068,(see Figure 5.5)


The clock pul


received b


counter A


are i


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


20 centimeters,


6144 for


30 centimeters, and 8192 for 40 centimet


ers.


choosing of


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


signifying


- a a a -




62


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.


Circuit


Unlike the


circuit


, 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.


In order


motor pulses are


For other rotational shifts, i.e. ten


degrees, 346 pul


are required and 20 degrees, 692 pul


are required.


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


These counters


one gate in such a manner


to trigger a low on the accumulation of 1


pulses.


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


specific


selected through the use of switch S1.


output of


The Ar counter


output will then go high on either 173, 346, or 692 pul


which cor-


respond to 5


0 degree rotational


shifts.


R Counter


The r ci


rcuit, Figure 5.7, receives its input from the r circuit,









AR-COUNTER


4024


Rotational
Pulses


3 Q4 Q5 Q6 Q7


4068


Reset


4071


To R-Counter


-S


4020


4024


Q1 02 Q3















R-COUNTER


From R-
Counter


4068


OUTPUT


- e% S )


4024







goes high.


This signifies the end of a scan and the initiation of the


reset procedure.



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


Each


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


of windings


simultaneously in an attempt to obtain more torque.


Each


of these pu


is composed of two voltage levels.


At the


beginning of


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


volt pulse.

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.












CHAPTER 6



DATA ACQUISITION



In order to obtain the data required for reconstruction, P(ma,0)


of Eq.


3.24,


the current signal


being produced by the photomultiplier


tube must be recorded


It was decided to use a method of repetitive


integral, Fitzgerald


(1974)


, to obtain these measurements.


been proven to be


an effective method to measure small


currents


without


experiencing a


shift of the data, due to a resistor-capacitor time con-


stant.


In short,


this method u


integrating amplifier with a


long time


constant,


typi


call


100 seconds.


The voltage output of the


amplifier i


sampi


ed near the beginning of the


integrating


le and


again near the


end.


The difference


in these


readings


assumed to be


the accumulated current value for that interval


The amplifier i


then


reset and i


ready for the next integrating cycle


The average


signal


over the interval


taken as the


instantaneous current at the center


of that interval.

the mean current i


The smaller the


to the actual


sampling interval


current.


become,


Theoretically


closer


if the mea


during interval


were infinitely small


the measured transmission profile


would equal


the true profile


However,


it has been shown


(Fitzgerald,


1074n\


nm 1 1 4mc+ a olc 1ian ilrI ho r cii ffiriant


th~t ;nfnrrl3]


nC 1




67


Electrometer Amplifier



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


for the


The signal


cobalt-60 scanning


that level.


The photomultiplier


tube voltage versus current curve can be


seen in table 6.1


These


arger


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


s size


and the charge which must be dealt with during reset are al


larger.


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


nonlinearity.


Of the transistors availabi


at the time of fabrication,


none met these dual


specifications.


One solution was found in the use of series bilateral switches,


CMOS 4066


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,




68






TABLE 6.1

CURRENT VERSES VOLTAGE FOR THE
NaI(T1) DETECTOR SYSTEM


Tube Voltage
(Negative High Voltage)
volts


Tube Current
(Source on)
108 amps


0.0011


0.0021


0.00


0.0084


0.0289


0.1040


.3280


0.9050


.240


1000


4.390


1100


9.080


1200


7.65


1300


32.3





























ANODE OF


TUBE


Figure 6.1.


RESET PULSE


OUTPUT


ICH8500A


Diagram of the Electrometer Amplifier Circuit.


4066
RESET





















































































































































































































































MI E*


r*




71


Electrometer Amplifier Controlling Circuitry


As previously mentioned, at the beginning of a


travers


e, a ramping


sequence accelerates the transverse mechanism then maintain


speed and at the end of the traverse dece


a constant


rates the mechanism to a


stop.


repetetive integral method integrates


the detector


signal over


a period of time;


however,


the data required by the


reconstruction algo-


rithm are the


transmission data versus


transverse di


stance.


graph


of distance versus


time,


Figure 6.3,


s hows


that the


only period during


which time and di


tance travel


ed are proportional


is during the constant


speed


section of the traverse


It


therefore important to accumulate


data only in the time interval


and the beginning of the


between the end of the acceleration


deceleration.


The data recording


tem chosen was an


IBM compatible nine track


tape recorder.


The recording


tem el


ectronics is a complete system


except for the electrometer amplifier.


t requires only four signals


to process data placed on its


input


1 ines.


These pulses are a


clock


a pulse to trigger the first reading sequence


a pulse to


trigger the


second reading sequence


and a pu


to trigger the


shift


registers, which in turn transfer the data


to magnetic


tape,


Fitzgerald


1974)


electrometer amplifier circuit


, Figure 6.4, control


the ampli-


fier cycle,


prevents


data from being taken during accelerations, and sends


appropriate


signal


to the recording


tem.


circuit receives


identical


on a 64 pul


to those sent to the motor driver boards and operates


cycle
















From Ramp Elect
Simulate Pulses I
I
Motor Pueses I


4011


4068


ABCD


4078


To Reset
Electrometer
Amplifier


To Enable
2nd Read


To Enable


st Read


To A/D


onvert


4024


4024
01 02 03 04 Q


4047







5.2.

ning i


The pulses to the circuit enter via switch S1, which for


s


in the position shown.


scan-


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


mechanism


put from the


ramping electronic


Once full


speed i


reached,


input goes


high


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


reset.


The current from the photomultiplier tube


the third motor pulse the first read


sequence


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.


The electronics


within the recording system subtracts


these


two values


and stores the


difference.


pulse also initiates


a sequence


which


shifts


the data


to the recording equipment where


is recorded on a


nine track magnetic tape.


to all


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


scan ha


128,


the 30 centimeter width has 92, and the


20 centimeter width has 64


Although the number of interval


change,


the distance traversed during each measuring interval


being determined by the mechanical


remains constant,


design of the traverse system.


motors


require 24 pulses


per rotation,


the gear reduction units


ten to one ratios, and the


lead of the ball


screw is one-half


inch per


At












CHAPTER 7



SYSTEM PERFORMANCE


The accuracy of the axia


tomographic scans made by this system is


dependent upon:


each traverse being


executed with source and detector


correctly responding to each


stepping motor


command,


the alignment of the source and detector in all planes,

and,

the accurate detection and recording of the radiation


transmission profile


by the data acquisition


system.


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


source returns


procedure was followed with the source


and detector traversing in the vertical direction, the condition of




76


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


in all


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


signal over


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.


characteristics

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


accumulate the


alignment data.


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


Compen station


transverse


is not made


for the abrupt change in


intensity.


The reconstruction algorithm requires


that the unattenuated value


the beam be known at each transmission measurement position.


Since the


actual


transmission data has


been corrected


, any unattenuated value


could


be used as the value for


As previously


stated


the first and last


few transmission measurements


are alway


s free of attenuating material


therefore can be used to cal


culate


the fractional


transmission for their


particular traverse.


By calculating the transmit


ssion


in this manner,


changes


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.


integrating cycle


electrometer amplifier output voltage versus time.


These were


examining the


Figure 7.1


shows the


voltage versus time


relationship for a number of integrating cycle


with the source and detector stationary and a negative


photomultiplier tube.


500 volt


Both reproducibility and linearity of the


across the

measure-


ments can be seen.


test was repeated after increasing the photo-


multiplier tube voltage to 600 volts, Figure


The only noticeabi

































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I_ _~__ __ _


6 o
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79













* -
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I __________ -o
I_ z-

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- S

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to cause this effect and to quantify perturbation


it would have on


the data


, further experimentation was required.


The effect was


first


examined by quickly moving the radiation source to


off position,


with a negative 500 volt across


the photomultiplier tube.


The first four


integrating cycle


of Figure 7


were the result of the source


in the


on position


During the fifth cycle,


the source was quickly moved to


the off position.


If there was not an afterglow


effect the


amplifi


voltage should stay at the value it had obtained when the


radiation beam


was interrupted.


, however


was not the case and the voltage con-


tinued to


increase.


The afterglow current can continue to be observed


in the integration of the next few


was at all


To determine


dependent upon photomultiplier tube voltage,


if this effect


experiment


was repeated with a negative 980 volts


applied to the photomultiplier


tube.


These results can be


seen in Figure 7.4 and are


identi


to those


of Figure 7.


, demonstrating the


effect


is actually a


crystal


phenomenon.


Although the afterglow effect could be demonstrated by complete


of radiation signal,


loss


the effect that it would have on the transmission data


during the


canning procedure had to be determined


Figure 7.6


hows the


effect of three millimeters of lead being placed in the


beam between the


fifth and


sixth integrating cycle


A slight afterglow effect may be


present on the seventh cycle, but from the


ighth cycle


the small


variation in


signal can be attributed to the


ead not being held steadily


in the beam.


This amount of lead inserted into the


beam represents a


step


reduction of beam intensity of approximately


a step response of the


magnitude that could typically be encountered during scanning.


From these









82






















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84


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


scan path.


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


scan.


During a left to right


scan, the edge of the lead brick i


first


encountered during the


sixth


integration interval and by the eighth


interval the detector system has equilibrated to the decreased radiation


evel


, 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.


cycle the


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


seen.


It is significant to notice that the correct


values were always obtained by the first full cycle after the step
































































41.00 9.00O
SCAN DIST (MMI


Figure


Data


ystemrn


Response


a Lead


Brick


Traverse


Path.


q rn


I[ 00


2',00


3.00


S7l00


65.00


1;
~~lllrlrrWWY(Wl~lllr~YlrYl(lulr~Vrl)rlr IXr(ltlllll







simulate the effect which could be expected during a routine scan


six inch diameter Lucite cylinder was scanned in the same manner as the


lead brick.

with the xs


Once


again the shift in data can be seen in Figure


and asterisks


leading and lagging each other during the


same corresponding beam


situations.


shift can more easily be seen


in Figure


in which th


xs have been replaced by a solid line and


the asterisks by diamond shaped symbols.


The symbol which i


s following


the decreasing field always lags the symbol measuring the increasing

field.

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


data


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


In examining


, the smaller cylinder may appear to have much larger


deviations, but this is a result of the change in ordinate scaling.


Finally


, 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,


centimeters


, 1.7 centimeters,


centimeters


, and 0.67 centimeters were placed in the scan path.


results of two scan passes, from the same direction


are shown in Figure


7.10.


The measuring system, taking data on the


3.3 millimeter grid,


adequately detected and measured the transmission through even the


smallest cylinder.


The data also demonstrates the reproducibility of the


recorded transmission values for each rod.




































































It
V 1 S


'p) llrr)~ )t


011 h. t a V h l I


-- 4t -b.. ~- f~~.~~~~~~-~-~.. -. ----+~~~. --...


SCAN DIS fMM.


&t 1


1 ln


-4- -
Q'i


Figure


Data System Response to a Cylinder in


Traverse Path.


-- 1--


2 r n


SuO


: .rg













































bC~ '4' .,


a. A *


_______~--- I-- ~---~- --~-4-- _____-I I --- +---- -


I J.00


2S. 00


SCrN OlIST IMI


r,0nf


1 nn


c, no


Figure


Data


System


Response


a Cylinder


in the


Traverse


Path.






























































'4I;


-I- -- -
SCPN; Ijti !N1 i~


-f--- -t --
Q? 0' it 0r


Figure


Data


Sys ten


Response


a 6.5


centimeter


lender.


t: x '.-


-t en---


'I Ilr
YI



















































/


I


,i nO


U4 30


SCaN DI$T iM'"I


S '


--- t-F--


Pr


Figure


Data


Sys tern


Response


to Cylinders


Varying


Diameters.


q nr


H OP


-f
,,1


---j- -------r--------t -







than 1% during normal


scanning situations.


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


detector


tem and


subject alternate detection systems to


similar


testing at a later time.



Reconstruction Grid


The first test of the


stem


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.


The transmit


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,


The results


arce statistical fluctuations


through homogeneous areas and overall inaccuracies throughout the entire

reconstruction.




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