Note : Les descriptions sont présentées dans la langue officielle dans laquelle elles ont été soumises.
10~1773
BACK:GROVND OF THE IN~7ENTION
Field o'f the Invention
The general field of this invention is tomography, that
field which relates to obtaining by radiographic means an image
of internal body parts in a plane through the body. Specifically,
the field of this ;nvention, called transverse axial tomography,
relates to the method and apparatus for applying a plurality
of X- or gamma ray beams through a plane of a body, measuring
the absorption of each beam as it passes through one segment
of the body and using the multiple measurement information
obtained to reconstruct individual absorption coefficients for
each element of a defined element matrix in the body plane.
Descrip'tion of'th'e P'ri'o'r Art
A prior art method and apparatus for transverse axial
tomography is described in United States Patent 3,778,614 of
G.N. Hounsfield issued December 1, 1973. That patent describes
a technique to reconstruct a cross-sectional view of a body
from a series of transmission measurements obtained by translating
a radiation source and detector across the body section and
repeating this translation motion at a number of angular
oxientations in the plane of the section.
The obj~ecti~e of these measurements is to obtain, after
computer analysis of thousands of pieces of raw information about
beam attenuation through the body plane, the attenuation
coefficient associated with each element of a matrix defined
in the body plane. The method is useful for internal description
of any body, but is primarily useful for identification of
internal human body abnormalities. The attenuation coefficients
-~ are different for normal body tissue, tumors, fat, etc. and
consequently provide identifying information about soft tissues
,~,
2-
";
1071773
in a human body. Especially useful for identification of brain
disease and abnormalities, tomography by computer reconstruction
eliminates obvious disadvantages of patient discomfort and
morbidity normally associated with brain investigations using
pneumography, angiography and radio-active isotope scanning.
In the prior art method an X-ray tube and detector, fixed
in positions opposite from one another, are linearly translated
so that the X-ray beam traverses a body. A narrow beam is
defined by means of collimators at the output of the X-ray tube
X and at the detector so that the readings of the X-ray detector
at each translational and rotational position is a measure of
the total attenuation along the particular beam path. Each
detector measurement is stored for subsequent computer process-
ing. After each linear scan, the X-ray tube/detector combination
is rotated about an axis perpendicular to the body plane.
In the prior art method, the scan signals are processed
to yieId visual information and local values of the beam
attenuation coefficients over the body section. Detector
scan signals are applied to an analog/digital converter to
con~ert the analog scan signals which are proportional to each
beam attenuation to digital form and subsequently are recorded
in a storage un~t. Computer analysis of the entire matrix
of scan signals, typically about 28,000 points, yields
attenuation coefficients associated with an element matrix defined r
for the body. These attenuation coefficients are related to
the local physical properties in the body plane. After they are
~'
.~. ~, .
~'
~ -3-
;:
,,, . ~ . .
1071773
computed, by a computer, the attenuation coefficients are
recorded in a storage unit, and subsequently converted to
analog signals by means of a digital/analog converter. These
signals drive a viewing unit, typically a CRT, with the
information content to pictorially display the attenuation
coefficient for each matrix element. A permanent record of the
display is achieved by means of a camera.
A disadvantage of the prior art method and apparatus
is that the entire body section must be scanned before the local
value of the attenuation coefficients can be extracted. This
is due to the fact that the readings at each position of the
X-ray beam affect the computation of the attenuation coefficient
at every point in the section. Thus the body section must be
scanned in its entirety; the scanning cannot be confined to
some particular region of interest. Furthermore, severe
restriction is placed on the stability of the X-ray tube and
detector systems and upon the mechanical precision of the devices
since consistent data must be obtained over the entire scan time
in order to compute the local attenuation coefficient values.
2Q Problems of reconstruction may similarly arise in regions of
the body subject to motion. A scanning motion consisting of
~ translation followed by rotation is clumsy and subject to
L mechanical vibration and wear. Because of the mechanical
problems involved, it is also difficult to speed the sequence
of translation and rotation movement to reduce the scanning time.
i Further problems are related to the complexity of the computer
~ ,
~'
f~
, .
.'. ~
- 1071773 10- i 1 -1 976
.
program necessary for restoration and thesophistication
of the programs that are required.
- I~ o~ercoming the disadvantages of the
prior art, the invention described hereinafter has a
valuable advantage in that it provides a novel fast scan-
ning process which climinates the acceleration of large
masses associated with X-ray sources and detectors required
in the prior art step of linear translational scanning.
Another important advantage of the invention
is that it alLowed a reconstructlon of areas of the body
plane with a limited number of transmission data obtained
in a localized region containing that area.
- Another advantage of the invention is that
it provides quasi-instantaneous measurement of the local
attenuation constants as the scanning process proceeds.
- Another advantage of the invention is that
it provides inherently higher precision control of the
scanning mechanism.
;` SUMMARY OF THE INVENTION
These advantages are embodied in a novel
method and apparatus for examining a thln cross-section
or plane through a body by passing X- or gamma ray beams
~ through the body plane. The body plane is depicted for
,`' ' .
;~ examination purposes as a two-dimensional matrix of ele-
. ~ .
,~l 5 ments defined by a plurality of concentric circles which
create concentric rings. The outermost ring is denoted
~' as the R ring, the next inner ring to the outermost ring
; ` described as the R-1 ring, and so on. Elements in the
,~ ; . O
~; rings are created by dividing each of the rings into Nr
f~`
`~ 30 elements. In this manner, the notation NR represents any
number equal to two or greater equally angularly spaced
elements of the outermost R ring, the R-1 ring being
-5
¦ PHA.20751
10~ 1976
1071773
divided into NR_1 elements, and so on.
The method of determining individual ab-
sorption or transmission coefficients for each element
in the defined element matrix begins by rotating X- or
gamma ray beams 360 degrees around the outside of the
body, where one beam is provided for each concentric
ring and is so directed in the plane under investigation
as to be continuously tangent to its associated ring.
From each beam emerging from the body, at
Nr discrete angular intervals during the beams' 360 de-
gree rotation, a discrete output signal is recorded re-
presenting the sum of the attenuation of the elements in
each respective concentric ring intersected by the res-
pective beam.
For the outermost R ring, the NR discrete
output signals from the beam tangent to the R ring are
used in deriving signals proportional to the individual
; absorption or transmission elements associated with each
of the NR elements in the R ring.
In response to the NR 1 discrete output
signals from the beam tangent to the R-1 ring and the
signals proportional tothe individual attenuation co-
efficients associated with the elements in the R ring
,;~
through which the beam tangent to the R-1 ring passes
: 25 at each of the NR 1 discrete angular intervals, signals
are derived proportional to the individual attenuation
i coefficients associated with each of the NR 1 elements in
; the R-1 ring.
This method is repeated for each succeeding
ring in turn for ring R-~ toward the center of the con-
:,
centric circles. For each concentric ring, signals pro-
portional to the individual attenuation coefficients
-6-
:: ~
1071773
associated with each of the Nr elements in the ring are derived
in response to the Nr discrete output signals from the beam
tangent to that ring and the previously derived signals
proportional to the indi~idual absorption or transmission
coefficients associated with the elements in all other rings
through which the beam passes at each of the Nr discrete angular
inter~als. `;~
In the ~ethod according to the invention, certain beam
measurements about concentric rings are first translated to an
alternate concentric ring coordinate system about a point in
the body plane POr and th~n used to derive a signal proportional
to the attenuation coefficient at a point PO~ thereby providing
a method of reconstruction in any selected area of the body
plane.
Novel apparatus is disclosed for performing the method.
A rotating frame is provided supported with respect to a fixed
frame by means of a ball bearing and rotated by means of a
motor. A source of X- or gamma rays is mounted on a first arm
rigidly attached to the rotating frame. The source generates
one or more beams in a plane perpendicular to the axis of
rotation. The beams are intercepted by a system of detectors
mounted on a second arm rigidly attached to the rotatary frame.
The beams are defined by collimators associated with both the
-. ~
~; X- or gamma ray source and the detection system and directed
so as to be tangent to concentric rings defined about the axis of
rotation of the rotating frame in a plane of a body placed in
or near the axis of rotation between the source and detector
system.
In a preferred embodiment of the detector system a
reference crystal detector and a plurality of measurement crystal
detectors are provided in groups,
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`t~
~ PHA.20751
1~1773 10 11-1976
which may be moved in position on a track so as to inter-
cept different beams passing through the body on diffe-
rent rotations of the rotating frame. Photomultiplier
tubes are provided, one for each measurement crystal de-
tector~ to ~enerate electrical signals proportional to
the corresponding beam intensity. Means are provided to
- magnetically store the beam attenuation signals in digital
form. A stored program digital computer is provided for
deriving signals proportional to attenuation or trans-
mission coefficients for the defined element matrix in
the body plane. These signals are stored, and are then
useful to provide a representation of the absorption
characteristics of the body plane.
BRIEF DESCRIPTION OF THE DRAWING
This invention, as well as its objects and
features, will be better understood by reference to the
following detailed description of the preferred embodiment
of this invention taken in conjunction with the accompa-
nying drawings in which:
Figs. 1(a) and 1(b) show a prior art method
and apparatus for performing transverse axial beam measure-
ments;
Fig. 2 shows a prior art system for calculat-
:ing absorption or transmission coefficients of a prior
art defined element matrix from a set of transverse axial
:
beam measurements;
.
~
Fig. 3 shows an X- or gamma ray source de-
tector orientation, constructed in accordance with this
~; O
invention, for rotation of a beam pattern about a body in
which an element matrix is defined by concentric circles
and equally spaced radii;
Fig. 4 shows in more detail the defined
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1(~71773
element matrix, constxucted in accordance with this invention,
for measurement of absorption coefficients in a body plane;
Fig. 5 shows a defined element matrix, constructed in
accordance with this invention, for determining the absorption
coefficient at a particular point;
Fig. 6 shows a perspective of physical apparatus,
constructed in accordance with this invention, for rotating a ~ -
beam pattern through a plane of a body and the measurement of
beam attenuations after the beams pass through it;
Fig. 7 shows an X-ray tube beam spread, constructed in
accordance ~ith this invention, as it rotates about the body
under investigation; ;
, Fig. 8 shows a schematic diagram of beam generation
- and detection in accordance with this invention;
Fig. 9 shows a schematic diagram of an alternative
,~ embodiment of beam generation and detection in accordance with
this invention; and
Fig. 10 shows a schematic diagram of measurement data
collection, recording and processing in accordance with this
invention.
Fig. 11 shows a flow chart for the construction of a
computer program for the method of localized reconstruction in
accordance with this invention.
In the prior art method an X-ray tube X and detector D,
fixed in positions opposite from one another, are linearly
"
translated so that the X-ray beam traverses a body B. A narrow
beam is deined ~y means of collimators at the output of the
X-ray tube X and at the detector D so that the readings of the
X-ray detector D at each translational and rotational position
3Q is a measure of the total attenuation along the particular beam
~ _g_ ' .
1~71773
path. Each detector measurement is stored for subsequent
computer processing. After each linear scan, the X-ray tube/-
detector combination is rotated about an axis perpendicular to
the body plane. This is more or less shown in Figures la and lb.
In the prior art method, the scan signals are processed
to yield visual information and local values of the beam
attenuation coefficients over the body section. Detector scan
signals are applied to an analog/digital converter AD to convert
the analog scan signals which are proportional to each beam
attenuation to digital form and subsequently are recorded in
a storage unit S. Computer analysis of the entire matrix of
scan signals, typically about 28,000 points, yields attenuation
coefficients associated with an element matrix defined for the
body B. These attenuation coefficients are related to the local
physical properties in the body plane. After they are computed,
by a computer K, the attenuation coefficients are recorded in
a storage unit S, and subsequently converted to analog signals
by means of a digital~analog converter DA. These signals drive
" 't
~' a viewing unit V, typically a CRT, with the information content
to pictorially display the attenuation coefficient for each
'~ matrix eIement. A permanent record of the display is achieved
by means of a camera C. Foregoing is more or less shown in
'1 Fig. 2.
, 'DESCRIPTI'ON OF THE INVENTION
Concentric Ring Scanning
a~ Un'i'f'orm body 's'cannin~
F;g. 3 shows a sketch of a body plane 101 to be examined
by transverse axial tomography according to thi,s invention.
The body 111 is assumed to be placed between a source 300 of X-
or gamma rays and a detector
C -9a-
1071773 7 o-; 1 1976
301, which may be a scintillator and a photomultiplier
and which preferably also includes a collimator. For
illustrative purposes, detector 301 is assumed to be
` movable on a track 302 such that beams 310, 311, 312,
313 may be detected which pass at various angles from the
source through body 111. Multiple detectors, each with
an associated collimator can of course be provided as
detectors 301, 301', 301", etc., or multiple detectors
may be movable on track 302~ The X-ray source 300 and
detectors 301, are attached to a rotating ring 303 which
s rotatable about an axis 0 perpendicular to the body
plane 101. Body 111 is shown in Fig. 3 coexistent with
axis 0, but it may be placed anywhere within the beam
' range of source 300 and detector 301.
As shown in Fig. 3 a series of concentric
circles is defined about axis of rotation 0 As C ring
303 rotates about the axis of rotation 0, the X-ray
beam or beams is continuously directed (as shown at one
- orientation angle of rotation) perpendicular to subse-
quent radii from axis 0 at point P at all times as C
ring 303 rotates about axis 0. As a result a beam such
as 310 is at all times tangent to the outer ring about
center 0 as the source-detector system rotates.
Fig. 4 shows in more detail the concentric
system defined about axis of rotation 0. Beam 310 is
shown at a particular orientation during its rotation
about body 111 and is perpendicular to a particular
radius vector r at point P. By appropriate collimation,
the beam width W can be made to approximate the concen-
¦ 30 tric ring width ~ r. The example depicted in Fig. 4
¦ shows beam 310 passing through the outermost concentric
ring i. Perpendicular to radius vector r, beam 310 is
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PHA.20751
~ 071773 ~o~ 976
depicted as passing through elements labeled j = ni ~ l,
,. ni, 1, 2 and 3. These elements are amon~" those elements
¦ in the ring i~ totaling ni elements.
In order to describe the interior of body
1 5 111 according to the matrix of elements throughout the
', concentric ring-radius vector system shown in Fig. 4,
each small element is assigned an unknown value of atte-
' nuation coefficient. For example, the attenuation coeffi-
cient for element j = 1 in the ring i is designated
, ~ .
/ui 1 for example j = 2, /Ui 2; for the j th element~
` /Ui j. The measured beam attenuation for beam 310 shown
,~ will be given by the sum of the average value of the
, ,i
,~ linear attenuation constants tu for each element through
which the beam passes.
, 15 During rotation about axis 0, the beam
attenuation between source 300 and detector 301 is ob-
tained at ni different positions, only one of which is
j shown in Fig. 4. Beam attenuation for each measurement
,l designated ~ i k is simply the sum of the linear atte-
nuation constants for each element through which the
¦ beam passes multiplied by an individual geometrical fac-
tor determined by the interceptlon of the beams with
each cell. The rotation-measurements steps of the beam
310 as source 300 and detector 301 rotate about 0 are
identified by an index k. This index k runs from 1 in
, steps of ~ until k = ni, equal to the number of elements
in ring i. Thus3~ the measurement of the beam at-tenuation
at each position of the first intercepting ring leads
to the equations
ni
30 ~ ~k)(/Ui j) = ~ i k (1)
j=1
, . ..
107177a lo~ 976
where
k = 1, 2~ ni-
The term ~ k represents the geometrical
factor determined by the interception of the beam 3101
j 5 with each element j as it rotates in k steps about ring i.
¦ Since j is taken equal to k, that is, the
number of elements in ring i is j, and the number of
measurements around ring i is equal to k, equation (1)
represents a system of equations k = ni in number, having
j = ni unknown parameters /Ui j. The solution of the
system of equations (1) yields the values of /u asso
ciated with each element on the ring i.
In the nest scanning ring, the ring i-1, the
measurement of the beam attenuation leads to the new
;- 15 system of equations
. ni- 1 ni
~ (~i-., j-k)(/Ui-l j) ~ , k ~ ( 1,j-k)(/ui,j)
j=1 j=1 (23
for,
k = 1, 2, ... ni_1,
wherein ~ 1 j k is the geometrical factor determined by
the interception of the beam (e.g. beam 311, ~ig. 3) in
the new ring, i-1 with the elements of the outer ring i.
The values /ui j have been determined by the
solution of equations (1~; the solution of the system of
equations (2) provides the values of /Ui 1 j in thc ring
i-1. The measurement in each scanning ring with decreasing
radii provides a system of equations similar to (2) with
terms on the right hand side containing known values of
/u in the elements pertaining to the outer rings. It is
apparent that the number of elements of each outer ring
which contributes to the attenuation along an inner ring
..
-12-
1071773
decreases rapidly as the scanning radius approaches zero, i.e.
as the scanning beam approaches the center of rotation.
Thus, the local properties are fully determ~ned upon
complet;on of each scanning ring without having to wait for the
^ total scanning of the body section.
The number of equations in each set, similar to equation
~, (2~, is relativeIy small and can be arranged to decrease as
.; .
the interior rings with smaller radii are measured. Assuming
for example a scann;ng radius of the outer ring of the order of
150 mm and an element width of the order of 3 mm, each independent
equation set for the outer rings consists of only several hundred
~.i,,: i - .
equations. The solution for the unknown ~'s for each ring
sequent~ally~ from the outside ring toward the inside rings,
requ;res far less computational time than prior art X-ray
tomographic systems. As the inner rings are measured, it is
possible to decrease the number of measurements taken around
the ring (i.e. define ni to be less for the inner rings than
for the outer rings, thereby keeping the element size approxi-
mateIy constant~ with the result that the equation set size is
reduced. Computational time is correspondingly reduced for
solution of inner ring ~'s.
b) Local;zed reconstruction
The method of determining the absorption coefficients
for the elements defined as elements in concentric rings about
the axis of rotation (Fig. 4~ requires that all of the beam
attenuation data be used i~ the successive ring equation
solutions especially for a particular element near the axis 0.
It is often the case, however, that a diagnostician is primarily
interested ;n investigating a particular point of the body plane
; 30 101. In the method according to the invention is is possible
to use the beam attenuation data as des-
-13-
PHA.20751
~071773 lo~ 976
cribed above to reconstruct an absorption coefficient
. matrix about a point P0 in the body section not centered
at the axis 0.
Fig. 5 shows body 111 which has been scanned
. 5 by rotating beams, one of which, beam 310 is shown. ~bout
. a particular point P0 are sketched a sequence of concen-
., tric circles having uniform spaced radii. These circles
: define a plurality of rings equally spaced by a radius
distance r1. Thus the radius for each circle from center
: 10 Po is
. ^ ~ = Jrl (3)
where j = 0, 1, 2, ....
~ven if beam attenuation data is collected
for a concentric ring system defined about center 0,
15 these data may by coordinate transformation, be trans-
lated to the concentric ring system defined by center
P0 and having radii de*ined by equation (3). The value
of the attenuation of a beam tangent to a ring of radius
~ and center P0 coincides with the value of the attenu-
20 ation measured with a beam tangent to the ring at center
0, having a radius r according to the equation
r = ~ ~rp cOs(e - ep) (4)
where e is the angular coordinate of the point of tangency
and rp, ~p are the polar coordinates of P . By means of
25 equation (4), the measured beam attenuation values ~ in
the concentric ring system about center 0 may be compu-
tationally translated to achieve a. set of beam attenu-
ation values tangent to the concentric rings about P0.
These values, ~ j indexed with the subscript j, repre-
¦ 30 sent beam attenuation values measured completely around
concentric circles ~ = irl, about P .
These beam attenuation values about ring j,
-14-
iO~17~3
are equal to the sum of the inter~sections over all rings outside of ring j.
This relationship is Written
2 ~ O~
J ~ jd~ = 4 ~f jrl ~ ~j,h~ (5)
~, o h=j
where j h j+l is a geometrical parameter given by
~j,h-j~l j [ ~ ~h+l)2 j2 ~ ] (6)
The parameter O measures the length of the path between the circle of radius h
: and the circle of radius h~l.
From equation (5), an expression /uO~ the desired attenuation
coefficient at PO is written as:
2 ~r 0~
/Uo = 4~ rl ~ ( ~ o ~ ~ ~ j)d~ (7)
o j=l
where ~ O is the attenuation value of a beam passing through PO and the
coefficients kj are given by
k~
1,1 (8)
k2 ~z I [ 1 ~1,2 kl ]
kj ~ 2,j-1 k2 ~ ~~j 1 2kj 1 ]
For large j,
lim k. = - -
~ lr j (~)
The coefficients kj/j of ~ j in equation (7) decrease asymptotically as j
20 As a consequence, in a quasi-uniform distribution of values of j over the body
section under scrutiny, the contribution of the computation of /uO of the
values of Pj in areas surrounding PO decreases
- 15 -
~;
lQ7~773 1 10-;1-1976
: ..
essentially as j 1, which means that the scanning of an
area located at a distance ~ from PO affects the com-
putation of /u as ~ 1. This slow rate of decay of the
effect of surroundlng areas on the computation of /u at
each point would make it necessary to use uniform scan-
ning of the entire body section in order to proceeed to
I the image reconstruction. Thus, the solution for /uO at
; point PO presented in equation (7) indicates that the
confinement of the scanning to a limited area of the
body section would lead to an error in the image recon-
struction unless the area boundary partially coincides
with the body section boundary.
On the other hand, if the difference of
values of /u between two points is computed, the scanning
in the surrounding areas affects the difference as
r1 r2
where rl and r2 are the distances between an area of the
body section and the two points. Thus for large values
of rl and r2, the effect of the scanning in the surroun-
ding areas decreases essentially as rl 2 . This rapid
rate of decay makes it possible to use a differential-
like approach in the image reconstruction of a portion
of the body section under scrutiny without the need of a
complete uniform scanning of the body section. To proceed
with this approach the average value /u within a circle
of radius ~ r' is first calculated by the equation:
,Q -1
/ ~ 2 ~ ~ (h~l) - h2 ~ /u (10)
By virtue of Eq. (5), Eq.(10) transforms to
_ 1 1 ~ [ ~ e,J ~ j d~
-16-
. ,.
:
1~71773
, ;
where
ki j = ~l [ 2j ~ i j.ki l ~ 9j-l 2 . Ki j l ~ (12)
ki,l l 1 (13)
k ~ j'ke 1- ''' ~ ~j-1,2 ke,j-l ~ (14)
~ 1,j'ki,1~-' +~ +l.k~ 1 (15)
The coefficients kj in Eq.(7) and ke j in Eq.~ll) satisfy the asymptotic
condition.
lim ~ j ke~ l m [ jkj] (16)
Thus from Eqs.(7) and (11) one ob~ains
21r 1 ~-1 cy~
/uo~/u= 4 ~r r ~ (1 e2) ~o ~ i,j j ~e~e,j ~ j dO
where
i,j ~ [~2 ki j + kj ~
~ 2 e,j j ] (18)
Asymptotically the coefficient ~e j decreases as j 3 and this rapid
rate of decay makes it possible to limit the number of terms in the second
sum on the right hand side of Eq.(17~ for the computation of /uO - /u . This
means that it is possible to confine the scanning procedure to an area of the
body section surrounding the region where the reconstruction of /uO - /u has
to be performed. Table I here below shows numerical values for kj as a
function of j = 1 to j = 95; ki j as a function j from j = l to j = lO (~ = 10)
and ke j as a function of j from j = ll to j = 95; and ~ i j as a function of
j from j = l to j = lO (~ = 10) and ~ e j as a function of j from j = 11 to
j = 95.
:
1071773 . 0--i 1 -1976
TABLE I
C _ K j Ki j and ~ and
1 57735E+oo .11547E+01 .5868gE+oo
2 .32826E+oo .244s4E+o1 ~17424E+OO
3 .221s3E+00 37332E+01 .84126E-ol
4 .16542E+00 .50167E+01 .5l720E-ol
.13153E+0O .62g74E+01 k. . 36715E-Ol ~ i
6 .10gO3E+00 .75764E+o1 lJJ . 28608E-o 1 ~ J
7 .73064E-ol .88542E+ol .23748E-o
1o 8 .81161E-01 .10131E+02 .20611E-O
9 o71gs3E~01 .1l407E+02 .18470E-Ol
lo .64621E-01 .12683E+02 .16g44E-Ol .
11 .5864sE-ol .3879sE+o2l -.23816E-O
~2 .53681E-01 .20222E+02¦ --94539E-ol
13 4943E-ol .13gl4E+02--50385E-02 ~e -
14 .45g12E-01 .1077gE+02e ~ J - 30383E-ol J
.42814E-01 .88g58E+01 -.20470E-02
16 .401 O9E-0 1 762s8E+ol ~ -.14342E-02
17 .37735E-01 .76142E+02 -.1044gE-02
18 .35610E-01 .60172E+01 _.78441E-03
l9 .3371gE-01 .54664E+ol -.6030sE-03
.3201gE-01 .50184E+01 _.47279E-03
21 .30482E-ol .4645gE+ol _-37682E-03
22 .2gO87E-01 43303E+ol -.30460E-03
23 .27813E-01 .40sglE+ol -.24g4sE-o3
24 .26647E-ol .38230E+ol -.20616E-03
.25575E-01 .361s3E+01 -.17216E-03
26 .2~s8sE-01 .34310E+0~ 4sooE-03
27 .23670E-ol .32661E+01 _.12307E-03
3o 28 .22820E-01 .31176E+01 -.10s1sE-03
29 .2202gE-01 .2g830E+01 -.go485E-o4
.212glE-01 .28604E+ol -.782~Ejo4
-18-
10~773 PHA . 20751
10-11-1976
3l .20601E-01 .274s2E+ol -.6s1o5E-o4
32 1ggssE-01 .Z6451E+01 -.59s41E-04
33 . 1 9348E-o 1 . 25499E+o 1 - 52293E-o4
34 ~187~6E-01 .2461 7E+0 1 - . 46126E-04
.1s23sE-o1 .2379sE+o1 -.4os49E-o4
36 .1772gE-01 .23034E+ol -.36311E-04
37 .17248E-01 .22321E+01 -.323s1E-04
38 ~167g3E-01 ~2l6s2E+ol -.28ggoE-o4
39 .16361E-01 .2102sE+01 -.26027E-04
.15951E-01 .20~34E+o1 -.23435E-o4
4l ~lss60E-01 ~19878E+01 -~21160E-04
42 . 1518gE-01 lg3s2E+01 -.1glssE-04
43 .14834E-01 .188s4E+01 -.17384E-04
.44 .144g6E-01 .18383E+01 -~15s14E-o4
.1~11g3E-01 .17g3sE+01 -.14419E-04
46 ~13864E-01 .1750gE+01 -.13174E-04
47 ~13s6gE-01 .17104E+01 -.12062E-04
48 .l32s5E-ol .16718E+ol -~11065E-04
49 ~13014E-01 ~1634gE+01 -.10169E-04
.127s3E-01 .159g7E+ol _-93627E-05
51 .12502E-01` .15660E+ol -.s63soE-o5
52 .12261E-01 ~15338E+01 --7s768E-o5
53 .1202gE-01 .15029E+01 _-73804E-05
54 ~11806E-01 .14732E+01 -.6s389E-os
.115g1E-01 .14447E~01 _.63463E-Os
56 .11384E-o1 .14174E+01 _.58975E-05
57 ~11183E-01 .13911 E+0 1 - . 54877E-o5
58 .10ggOE-01 .13657E+01 -.51130E-05
59 .10804E-01 .13413E+01 -.47699E-o5
3o 60 .10623E-01 .13178E+01 -.44551E-Os
61 .10449E-01 .1295l E+0 1 - . 41660E-05
62 .10280E-01 .12731E+01 _.39000E-05
- l9 -
1, , ~ .
P~A . 20751
` ~717'73 lo-1 1-1976
63 .10117E~01 .12520E+01-.36549E o5
64 99583E-02 .1231sE+01-~34288E-o5
¦ 65 .g8048E-o2 .121 1 7EIO1 _.32200E-05
66. .96560E-02 .11926E+01-.30269E-05
67 .s5ll7E-o2 11740E+ol-.2s4slE-o5
68 93716E-02 .11s60E+01-.26823E-05
¦ 69 .923s6E-02 .11386E+01.25284E-os
¦ 70 .glO35E-02 .11217E+01.23sssE-05
¦ 71 .s975lE-o2 .11053E+01-.2252sE-05
1o 72 .88502E-02 .10g84E~01-. 21 286E-Os
73 .87288E-02 .10740E+01-.20132E-05
74 .s6lo7E-o2 .10590E+01-.1905sE-Os
7~5 .84g53E-o2 .lo444E+ol-.lso5oE-o5
76 .83838E-02 .10302E+01_.17110E-05
77 .82748E-02 .10164E+01-.16230E-05
78 .8l6s6E-o2 .1002gE+01-.15406E-05
79 .so65lE-o2 .989s6E+oo-.l4634E-os
79641E-02 97713E+00-.13glOE-05
81 .786s7E-o2 .g6472E+oo_.13230E-05
82 .776s7E-o2 .95262E+oo_.12591E-Os
83 .76760E-02 .94083E+oo-.1199lE-05
84 .75845E-o2 92933E+00-.11426E-05
.74952E-o2 .g1812E+00_.lo893E-o5
86 .7407gE-02 90717E+00-.10392E-05
87 .73227E-02 .s964sE+oo-~g9189E-06
88 72394E-02 .s86o5E+oo-.94736E-o6
89 .7157gE_02 .87s86E~oo-.gO511E-06
9o .7o7s3E-o2 .s659oE+oo-.s6528E-o6
.70005E-02 .s56l7E~oo-.s2762E-o6
3o 92 .69243E-o2 ~84666E+oo-.79200E-06
93 .68498E-o2 83736E~oo-.75827E-06
, 94 .67768E-o2 .82826E+oo-.72631E-06
¦ 95 .67054E-02 .81936E+00-.69603E-o6
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1~71773 PHA.20751
10~ 1976
An important property of both Eqs.(7) and
(17) is the uniform averaging of the attenuationmeasure-
ments over each circle of the image reconstruction se-
quence, as a result of the integration over 21t. Thus
the effect of the statistical fluctuations of the in-
dividual measurements of ~ is minimized uniformly over
the entire reconstruction area.
Eqs.(7) and (17) provide the solution of
the reconstruction problem and in particular Eq.(17)
defines the approach for a localized measurement and
reconstruction of /u. Obviously in Eq.(17) an independent
measurement of /u is required. However the measurement
of /u requires only a coarse scanning of the body section
under scrutinu with less stringent requirements on the
1 15 statistics of the corresponding attenuation measurements.
¦ Concentric ~in~ Scanner
Illustrated in Fig. 6 is a perspective
drawing of a concentric ring scanning apparatus. A
fixed frame 600 supports a rotating fram 601 which is
free to revolve about an axis of rotation 602. A motor
drive 624 is provided in fixed frame 600 to propel
~ rotating frame 601. Attached to rotating frame 601 are¦ two arms 603, 604 spaced approximately 180 degrees from
¦l one another. Arm 603 supports an X-ray tube 605 and anassociated X-ray tube collimator control 606. Arm 604
carried a detector assembly 607 and associated detector
collimators.
O A couch 608 is provided to allow a part of
a human body 111 to be positioned in the aperture 701
between X-ray tube 605/-X-ray tube collimator control
606 and detector assembly 607. Couch 608 is supported by
¦ couch support 609. A couch control system 610 is provided
-2~-
1 ~071773 PHA.20751
, 10-11-1976
which translates the couch 608 parallel to the axis of
1 rotation 602, thereby positioning body 111 to a point
'I where beams from X-ray tube 605 may int~rsect a desired
plane 101 through the body 111. In addition, the couch
control system 610 translates the couch 608 in any direc-
tion in a pla~e perpendicular to the axis of rotation,
thereby positioning the axis of rotation close to the
desired area of the body 111.
Since the X-ray tube 605 is rotatable about
the axis of rotation 602, means are provided to cool it
and provide it with high voltage electrical power while
it is rotating. These means, shown in modular form, are
a water cooling rotating assembly 611 and a high voltage
slip ring assembly 612. Means must also be provided to
send command and control signals to X-ray tube 605 and
its associated collimator assembly and collimators associ- ,-ated with detectors 607 while they are rotating. Command
and control slip ring assembly 614 is provided for that
purpose. Likewise data transmission slip ring assembly
¦ 20 613 is provided to provide a means for t,ransmission of
data signals from detectors 607 while they are rotating.
Fig. 7 shows a preferred orientation of
X-ray tube 656 and its associated collimator control 606
with respect to detector and detector collimator appa-
ratus 607.
;~ As indicated in Fig. 6, X-ray tube 605 and
detector assembly 607 are rigidly connected to each other
by arms 603, 601~ to rotating frame 601. Rotation of the
frame 601 about center line 602 (point 0 of Fig. 7)
causes the X-ray beam pattern 700 to sweep out a fan-
shaped pattern, which substantially covers any body to be
scanned placed within aperture 701. In a preferred em-
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: . :
1071773 10; ~ 1976
bodiment, the fan shaped beam subtends approximately a
30 degree arc as the X-ray tube-detector assemblies are
rotated at speeds of up to one complete rotation per
` second for at least 10 revolutions. The aperture 701 is
~ 5 approximately 65 cm in diameter. The arms 603, 604
- attaching the X-ray housing 605 and detector system 607¦ are approximately 75 cm long. The rotating frame 601
is supported with respect to fixed frame 600 by a single
90 cm diameter precision ball bearing.
Fig. 8 illustrates the multiple beam scan-
ning aspects of this invention. The X-ray tube 605 emits
a continuous fan-shaped array of X-rays~ but this continu-
ous array must be collimated into beams in order for the
methods described previously in this specification to be
applicable. Collimators 806 and 800 are provided to cre-
ate a plurality of beams passing through a cross section
of a body 111 placed within aperture 701. For illustra-
tive purposes three detector system pairs consisting of
crystal scintillators and photomultipliers (811, 820;
812, 821; 813,827) are shown in position 1. A reference
scintillator 810 and its associated photomultiplier 823
are stationary. The detector pairs remain in position I
for the first rotation of rotating frame 601 (Fig. 6).
At the start of the second rotation, the detector sys-
tem pairs are shifted along track 302 to position I~ for
absorption coefficient detection of beams intersecting
that position. The detectors are shifted to position III
at the start of the third revolution, and so on. This
shifting of detectors at the end of one rotation and the
¦ 30 beginning of another rotation assures that the entire body
! . " placed within aperture 701 may be scanned.
A preferred embodiment of the scanning
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. . : : :
1 0 PH~.20751
71773 10-11-1976
system of Fig. 8 consists of an arrangement capable of
Scanning a test object contained within a 50 cm diameter
circle about axis of rotation 0. Thirteen detector units
are provided one of which is the reference pair 810~
823, the other twelve of which are movable to ten posi-
tions along detector track 302. Each detector system is
used to scan a 2~ degree sector of the total scanning
area, ten revolutions of the X-ray tube/detector system
604 being used to scan the entire body 111.
Crystal detector 810/photomultiplier 823
is used to generate a reference beam attenuation signal
for all the other detectors to account for any variations
with time in beam strength eminating from X-ray rube 605.
As shown in Fig. 8 a particular beam 855 is collimated by
tube collimator 806 and passes through an attenuator 850
located outside the location of the body being examined.
The absorption characteristics of attenuator 850 are
preferably selected to be similar to that of the body
being examined. Tissue equivalent plastic is an example
of an attenuator material suitable for this purpose. De-
tector pair 810, 823 generates a signal, the intensity
of which is proportional to the strength of the X-ray
beam by attenuator 850 and collimated by collimator 800.
Each detector pair for the beams passing
through the body under investigation generates a signal
proportional to a particular beam's intensity after it
passes through the body 111. The crystal scintillators
produce a high-frequency signal (visible light spectrum)
proportional to the number of photons in the X- or
gamma ray beams impinging on them. The photomultiplier
tubes associated with each crystal scintillator, reacting
to the light energy from their respective scintillators
,.
~, -24_
~,
~7~773
PIIA.20751
10~ 1976
generate an electrical signal proportional to beam strength
impinging on the scintillators. For example, an electrical
! signal proportional to the beam strength of beam 856 is
! generated at the output of photomultiplier tube 820. Si-
milarly, crystal scintillator/photomultiplier pairs gene-
rate output signals proportional to the strength of
~ other beams at position I, position II, etc. for the
¦ entire beam pattern after successive rotations of system
604.
In a preferred embodiment of this invention,
the X-rays generated by X-ray tubes 605 are collimated
by means of a 15 cm long collimator 806 at the X-ray tube
source~ and a 20 cm long collimator 800 at the detector
system 604. This collimation at the X-ray source and de-
tector de~ines radiation beams having a rectangular profile
of 1 mm by 5 mm width as measured by scanning a lead edge
at the mid-point of the beam path.
The range of values for which the photomul-
tiplier must respond can be reduced by covering the body
being examined with a material, the absorption of which
is known, so that beam intensities received by the detec-
tors are kept as constant as possible as they pass through
the body.
Fig. 9 shows an alternate embodiment of
detector orientation. Detectors 910 and 911 are located
on track 901, and detectors 920 and 921 are located on
track 902. As shown, detectors 910 and 911 measure beam
attenuation through circular rings defined about ro-tation
axis 0 different from those measured by detectors 920 and
921. Multiple positions on each track can be established
and the detectors shifted in position with each rotation
until a defined ring matrix is entirely scanned and
~25-
s
~, .
1071773 ~o; 1-1976
¦ detected. Collimators 906 are provided at the X-ray source
¦ and collimators 930 at the detectors are also provided.
! The X-ray tube appropriate for the parti-
i cular embodiment discussed above is a modified version of
a Philips 160 kV Beryllium Window Tube Model MCN 160.
Appropriate detectors include scintillation
detectors such as NaI, Ca F2, BG0 and proporbional coun-
ters such as high pressure xenon detectors and solid state
¦ detectors.
Fig. 10 indicates how the beam attenuation
¦ data measured by the detectors systems including the
photomultipliers 10001, 10002, ... 10003, are processed
during the rotational scanning of a body. An information
signal is generated in each photomultiplier at each de-
fined increment for each rotation of the X-ray source/
detector system. These signals are individually amplified
by amplifiers 10101, 10102, ... 10103, are each taken
up in turn by serializer 1020, converted to digital form
by analog to digital converter 1030, and stored in a
data storage medium 1040 such as magnetic tape, disk, or
drum or solid state memory. This data collecti~n process
continues for each detector position for each defined
increment step for the complete rotation. During or after
the data collection process, a computer 1050 under direc-
tion of a stored program, processes the collected data
according to the methods discussed previously in this
specification. The output of the computer 1050 is a se-
quence of` digital signals proportional to the absorption
coefficients of each element in the defined circular ring
matrix. These signals are stored in a data storage unit
lo60 which may be the identlcal unit 1040 or similar to
it. The output digital signals can then be printed and/or
-26-
s
1~71773
converted to an~log ~orm and used to drive a display on a
cathode-ray tube thereby pictorially indicating the absorption
coefficients for the defined matrix in the cross section of the
body~being investl:gated.
Fig. 11 discloses a flow chart which serves as an outline
for the construction of a computer program for localized
reconstruction according to the invention as described in this
specification .
Details of the flowchart -in Fig. 11
- After START 500 follows reading of the measured attenuation
values and necessary constants at 501 and 502, respectively.
- At 503 reading of parameters for the image reconstruction, such
as number of rings, elements.
- At 504 and 505, respectively, initiating the program variables
L and 3, respectively.
- At 506 the coordinates r, ~ of a reconstruction point are
determined, as well as the value ~j from the attenuation values.
- At 507 the coordinates (r,~) are calculated and ~j by means of
the compensation formula.
- At 508 and 509, respectively, the indicated calculations are
carried out.
- At 510 ~ and ~ is computed, after which at 511 follows a
print of numbers or draw-ings.
The calculations terminate at STOP 512.
- The parts 520 and 530, respectively, denote feedback loops
AA, BB which are followed if the conditions imposed in 521 and
531, respectively, are not (N) satisfied.
Various changes and modifications may be made in the
details of performing, constructing and designing the above
specifically described embodiments of this invention without
departing from the spirit thereof, such changes and modifications
being restricted only by the scope of the following claims.
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