Ct1

Iil the x-ray tube. electrons are ernltted by a hot filc-i;~?ent cathode and are focused onto ~~stiicf:?d area of t h e anode that is typically rrlade of tungsten or a tungsten alloy X-ray p17~lfunsare et111lted i4rst7zrl the electrons perletrate the anode surface, rungsten is used as the arlode nlateriai because of ~ t high s rnett~rtgpoint and high atornic ncrmber. Accelet-ding electrons t h i o ~ y l hryh i v o i t a g ~ar-tcf allciv ir~g thern to strike a tungsten target produce X-rays. Whet? the high-speed elt3r;tron approaches a tnetal atarn, it is strongly repelled and decelerated by the electron clotrd of tile atorn, thereby ioosiitg kinetic energy Most of this energy goes into raising the temperature of the nlctai target, but J ~ J V L : ~ 4 % of it is given off ~n the form of x-rays. Because different electrons may bc decelerated at ~ f i i f ? i r . : l ~ t rates, x-ray can b e produced w ~ t ha high spread of wavelength. I:

l,,'P,>-.;!9,l

ltll"n+;ty !ol rn,irnt:cn :*R $<:rig iSvit'%,l) F71 cl 1% ppnrtri!.;", I; elt!n:i.q!o t y !:tn;c f;%blrr?i>( t.;[>p~r

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rlfil4rir~rr!ir'ig ! ! : c ! rn.fintinnhnra!a:r2;t -. - .,I]!~: . .................. -

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energy

of

Ilistribtition spectrutn.

in

coniini.iuus

x-ray

X-ray spectra for two cfifferertl voltages I.>, aild

-

c

[I..;. .

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1 tie eieciron kine'tic eneigy

elei:tron kinetic energy is ch;?ngcd to crlergy of X-i;?\~ ,,, , , ,,,,

13 e i ~ i . ; ~ !

o+-Fnrrncd

@-<-,

,,

2.n aln-f-ip f j , - i 4 oi,,~+:-", . ..,CL~+ .L. bsc.::t2 ...... : , . $ I ,:I <..,

8

L ~ t w e e ncaii-orje and anode (metal target) of an X - m y t!-he:E k = eII l h i ! ~ -

-

!"~>,,h efp: Z -- cr;to~:.?ickl~jfnbcr e/ - DC voltage i?, - ariodc c11r:cnt inir$i;si$

C - iarnp constant

.\-myproduction. Y,

P T O ~ I - J C Ffjj/ ~ ~ accelerat~ng electrons thrcugPa high DC vortage (20,060to 200,000 volts) and aflow~ngit-rern to strike a nleral target.

>(-r.ay ar'e

!I-

such that U2>UI

Tile stlorlest wave is produced t v h e r ~all of the p f l ~ f o r lE :

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'Tkle ertergy of elcctrcrrr~n(jr~c?fi<: r.;~iiriltiunahsort:6:!f i r t t.~or~es, fat tissi.ie, :~\[~:..clrtissrle znrJ LVZI~F;.~c j ~ ? p ~ : r ~ cjri d serwrCqy of i r ~ ~ i c l e ph~lto:~=;. rlt A5 (ntie car1 ri!stir:c, substnr~lial~fir:t:r@nces in absork~tiori[m;c:t.rr f r l r sr.:!;-rll ;:t{li,l ff:>i t'cxry t - 4 ~ erlery iss of pt~otni~s.

-.

rlist tomography machine: 1972 - €MI Limited in Mrddliesex - G.N.i-lounsfield

Basic prillciples Tftc bas~cprincple of CT is that the internal structure 0%an object can be recoristructccf frt~rnmultiple ~ t ~ , ' ~ ~ l i ~ / i of the ahject. The proleclions can be obtained by passing an x-ray thro~ighthe object at different direct~orlsand differentli<>sltions and measuring the transmitted rad~at~on (i.e. inters~tyor number of photons) - Fig.? Numbers at the sides of the rectangles *epresentsattenuated radiation by the rsi~rnherof bii:cks in each row. The ,rcrizcntal sums called ,,ray prajections" are si:o\?,,n on ike 5 right; the vertical ray suins are shown below the objzct 4

2 4

5 5

4

2

4

5

Fig. l Square shaped object with a cross-shaped hole inside 1-eprec.entsan analyzed object.

5

4

2

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5

5

4

2

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1

5

Numetical representation of the object. Atl the horizontal and vertical ray surris are added, iik.e the; ttvo shown in Fig 2.3 to produce the rlurnerical represer~tat~on of the object 2b. Fry 2

The ray projections are formed by scanning a thin )cross seciio!~of ti!.. body with a nzrrow X-ray ilearn and meastlr.ir?g$hz trzsr1s;;iiited raciiatior.1 with a sensitive radiation detector (Fig.4).

'The detector iiself does not form the image. It n~erelyacicjs kip tiw errergy of aH the iransrnitted photons that pass througia the irrg?riia!etj sain-ple (e.g. element of a pattent body) (Fig.5).

- ,

Fig.4 Examined slice

ff

Fig 5 X-ray beam of ~ntenstty1,; ] I ~ S S " J S through a sampli; of thickness d B e a n of intensity f , lower than lob is detected by ths detector.

The intensity of eleceromagnetic X-ray radiation that passes through a sample of a material sf thicftrless d rs attenuated and the attentration is described by t h e Lamkert-Beer law (3) (2) where stands for the ~ntensityof radiation that passed ti-rough the sample of thickness d. fo stands icr in*?17:;itj of ir-rcidenf beam, k t is finear attenuation coefficientand e is the base of natural logart'tltm Synibals i, and f car1 :e replaced fsry IPJ, and N,which stand for number of incids-it and passing through photons respectively.

lI=l,e7

DATAACCUMh5MBION Four generations of data-gathering techniques have becil distinguished. The division cr different+at~cn is based upon the X-ray tube and detector configrrration. 1. First generation -translafe-rotate,carre detector, Kay projections are colfected by translation rnotion and rota:ional motion. A rigid scanner gantry maintai~stile relative position of x-ray tube and detector and ensures their proper alignment (Fig. 6). The X-ray beam is eraclly collin-tatedto the exact size of the detector. The gantry moves through two different types of rnotinrr, one linear and one the other rotary. The linear mol'or; is repeated over and over 160 tirnes. Between each of these 160 \inear rnovernen:~, t h e gsnfry ro"lates 1". T i - .~ i ~ q the total rotatory motion encompasses a 100" semicircle. The axis of roiaticn passes throt~ghthe cer?8cr of t h e p:::ii.lcnt's body. In Fig.6 the linear m ~ t i u rare l called "scans". Three of the 180 sosriible lirlear n?otions are shcv~ij;?: 4 5 , 90- and 135-scan.

-

F i g 3 The first generation scanner. The possible total number of tracsrn~ssionmeasurements (that is the detector raadicgs) by this Pjpe of C i f r a chine is equal to. linear inovenler~tsfe7.s x rota~ystep:; = f60k480 = 28,800

.Ir..-

Zr

A rnajor objective of all later configurations was to shcprtes; the scanninr ime 7 lie rr-rc-easedspecri rvat; xc:in7 plished by abandoning the single detector and pendt-l ke bearn by a shaped brrirn and rnif!tipk Ce;e~t~?i5 The physical makeup and rnoverner-ttsof a bj'dpical ~econd-generatjonscanner is sl'man in Fig 7 The movement of the x-ray tube and detector array is both linear and rotary, j ~ ~like s t a first gznesatiarl :;canc:kxr but :he rotary steps ars larger (Fig 7 )

Fig:? The second generation - translate --rotate, rnultip!e detectors.

Fig.8 Third generation - rotate-rotate, fzn--beam $3ornetry. In this type of C f rnacfiine (Fig.3) t h e tr~n~iatioil ::wtion is completely eliminated. Only rotziicn r-rmtion is required, with both the x-ray tube a:?d ar-rr;y i;f c!c_.t~f.- .' tors rotating around tile patier.lt. Muitiple detect.oi,s are aligned along the arc of a cir~fefloss center is t h e x-ray tube focal spot Both the x-ray :!)be an3 ri'e-fectors rota* ;abi;~Hti;epG:ient in , - s ~ r . > r*r r ~!'.t,r :r-,- : r <~,*:72. r.Lr whose centers approximately coirlcide with tFre c~:-I.ter of the patient. The fan beam ccwl;p!etel\j :loYi>r3 the object to be imaged. The nntnber of scan ii::?; i:i one projection was equal to t h e iun7L:;lr G:' d:i3;.t:i~r~?. A single image is ccrnptjted from many ;:rojei:?icr;s often more than 'I 000. u ~ ,>,.., ,

,%>

FoeriPiit~generation - RatateFixad The detectors form a ring that cornpiete!y sttrrol;i-ds t i 2 2 patient The detectors do not move. The x-ray tube rotates in a circle inside the detector r:ng 2nd ti-rz x-ray beam is collimated to form a fc?nbean1 (Fig.9). Number of detectors it? a ring car1 be as high as 2000 \;?j93r.r; the X-I-ay tube is at a given pcsitior:.at a pfes~:/i=edangle, ti~c detectzlrs are read. For exampie, zn arqatar san?pliny rate ecf one projection each 1/3" will ~rocJuce1080 prc>ject:~~?s

lO8O in one full revcrlutiam?.Thus, o w C'T scan jlrrmgi!

af a one slice) will be made up of marly projecti~ns,each projection taken at a sfightfy different m s ! ~The . tisrie necessar:: ia colfect,the data from one fi~lf360" rctatinn is about 7 secon.;l:

Fig.9

Fourth garterstion scanner

I~BBAGE RECONSTRUCTION In cornputeci tomography a cross.-sectional layer of the body is divided into nlanjr tin?; blocks {&ig.i0).The i!~d!vidual blocks are calfed vexe!s (volume elements). Then, each block is assigned a number proportior~aito the degree that it attenuate x-ray bearn. To quanlliate the attenuation the tinear attenuation coefficient , ~ is r used. Value of jr depends on: a) composition of the voxet (bone, bone marrow, soft tissue fatty tissue), and

the quality of X-ray beam that is on energy of incident photons (E=hr.) bccausz t h e valtue of the iincar attenuation coefficient depends on cfiergy of' p!?otons.

b!

Evaluation of ;i of a vu.we1 The mathematics that leads to evalt:alion ni L I is rek3tively sintple. vosel

Fig 10 The tissue section represerlted in the computer rnztnx

The Lambert-Beer law can be re\.jisiFer>in :be fc;l/g~v~:~~~~

form:

IN-N,eq

,

\ + ?,

4 1 .'

where No,is a umber of incident photons, P3 number of transmitted photons and x - thickness of absor-l:>l!-iij layer. All they can be measured. The li:~earattenuation cosfficier~ijr is the only u r i k r ~ o ~ quantrv ~n i? thtn i;'i::.12::.'/i? (4) That describes the process of atterl~iation(- eq.3j. if two blocks of tissue with different linear altenc~arioncozfficlenls ,fml and p~ are piaced in t-i-tepath of the beam (fig.?I) the p;ob[t.tgl> i;nrr~ediate!i;hefsnjes n-!i=j:e cc:-;:pkx. Now the equation has Wc, unknotvns and has the faa'lowing form: 'C: i, L,? ,'

The values of both variables cannot be found without i?ddiil~i?:?!!TI-, formation. At least one additiar-ial equation is rer;i.iii..?il.,id.;;ir!:x~ai equatian can be obtained by exa:nini~~g t h e biocks f,;:yrlim diEer@nt;:lj-

h -.l --"? 3

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rection. j (Fig.12).

tiere wi3 have rtow four unknown caeffictents of attenzation jrr, ,ii;!, ji3 and jr4. To find out values of four unkr:ovvn one need.; fotr: Indel.i;ini<et~t equations with this four unknown cocf4icieiats as inbependeiil variabin:;. These equatio;ls have the foiloi*iing farm: 1,

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@rq

i f,)

+ii2)~

N, = ~ , e - ( ~ ' N2 = NO8(/"+tllr)x

N3 = Aloe- ( p ,

N4

+i13!.x

-(112+)")~ = $t,$e

and represent four independent readings of a detector. Each 1reaJir.y (N,, N2,N3,bJ4i of the detector represenis t f ; ~ cornposrk of hvo b:~:;i?s

Exactly the same principle applies to eo~nptiksdturnography , bii; f.rc :lurnber of unknowns is much larger. For instance in Ike first EM! scanner (firstgeneration scanr-ier)tire i~iztrixirl the! computer contained of 80x80=6400 separate pict~reelements. Each transrnisslan measuremerit rtcocded the coinposite of 80 separate linear coeficicnls, In this case the equation is lnr~gerarrd looks incredibly c;lti%g~!i-, cated but it has exactty the same format: -..--:r

i r-2

;orret'tions necessaq in image reconstr~~ction: I. Linear arten~aiioncoefficient depends on photon's energy. X-ray beam is usually heterornrornatk i.2. contains photnns of different energies determined by th:: working made of the X-ray sotlrce. Low energy photons are attenuaie.2 more effectively than high-energy photorts. Because of this the etectromayr-ietic X-ray radiation is !'fiIteredwlT5is r e a n s that more distant parts of the jrradiated body (looking along the direction of the X-ray travtil from the sclurce to the detector) are "examined" by radiation carrying photons 05: higher energy than the parts of the bcdy cioser to the X-ray source. In the result of this ,,filtrationua bvo different positioned pads jvoseis) of the exasiced object of identical composition can attenuate the X-ray beam in different degree becaijse p is dcpe-dent on the energy of incident photons. Thus, t h e C:T computer program rnr~stbe written to coinper;safe this

~ffest.

2. Far diffcront directions of X - r a y tic-lr different projections) the length of g);i+h that X-ray beam traveis cuiting ihr~::cjl-~ the body elemeni is different T'his ef-fect is cornpensatcd by introdi~ctisn5ri called welc_rhtiugfac:furtVfz jF!g.l3':

ALGQR~THMS FOR lMAGE RECBNSTWIJGTIOPJ ;'ha objective of all t h e rnetklods is to produce an ncc,~rate cross-section disp!ay of the lit-issr attcsnuaticrt3 cf:cfficients nf each element in the image matrix Back projection (summa fian ss~ethod) Ttie block shuwn in Fig.14 is scanned from bottm the top and the left size by a rnovlng X-ray beam to D T G ~ L I C fh-l ? so-called Image profiles. The image profile looks like steps The height of the steps is proportional io the amount (interisrfpiof ract~aficr? that passed through the block. At the center passed :he most rad!ation, so this is the highest step In the i:na~je profrle The steps are next assigrted to a gray scale density, which is proportronal to tt-ic /!right of ?he sizpC; These densrttes are arranged in rows and are G E I ~ ! F ~rays. When the rays from kzfo projec:ioqs are si~perlr?;posed or ,.back-projected'they produce an approximate not very exact reprodi:ct~onof orrginai object l~ pi-ac,:.~ many rnore projections arc added to improve the image quality*

X-rays

CT NUMBERS Pi conlputer program that processes data collected during scanning procedure cowver?s watcies cf 1lr:ear .i:it fion coefficrents ,LI of each matrix e!ernent to a new numbers called "CT" n~imbers(CTi\ff Tlic talculaiior: !;. 2,:s the computer to present the rnformat~onas a picture with a large gray scale

-IIC--

f%owis the CT number determined?

T h e computer program calculates a relattonship between the actual vafuc of pVof a voxef and the ! I , . of ,i.r~:cr the fatlow~ngway'

CTN == M A - ,Ll,rYrY Pw "!J

where: K

-

rnagnificatrori constant,

linear attenuation coefficient cf a woxel, linear attenuation caeficieni; ~ 1water. " For 9xarnple CTN for air is equal to - K: Pv

i"w

-

For water CTN = 0:

$1

Fig.75. Values of lirlear attenuation coefficients expressed in Hounsiield units f~ C ~ O S Gtis~ sale..;srtd f i x X-ray photons of energies used in CT rnachinss (i.c. appruximateiy 300 keil). ~UAGED~SPLAY

Typically display unit is a monitor of resolution 512x512 picture elerner~ts(pixels). Typically 256 s'r-lades:;l i7!-ii; .,.., are available. g

: c .,:

t - ! ~ wto represent 2000 14 (from -4000 H to +?000 OJ) wjfh 256 shades cf gray? 2000 . Q: i:i.. One Could simply assigned 8 CT numbers to the same shade of gray --- % 8 and <$;splay er3fji.e3;:i: 2 56 fornra!iem in a compressed scale. This is hoviever rarel!i done. Usually an a%.ieraGeCT number char:~cfr.iis;:,: :oi ;;: tissue l?eir!g ~xaminedis chosen. Such s 6-h nltmber might be -200 for lungs, Tile compi;ter 1-1:2:; i.i^:i:n i-:~? it-\.sYiu~t& to assign one shade of gray to each of the 528 CB nuambers below arrd eacl-t af the 12'3 C'i- 1;; .:iX'-:,rc ,?,.. above the k~aselineequal to -200. In this case CT nurr;t:erstake values from -328 tpo -72 H The c ; : t e : -CT :t:.;;;; ber is c;afled the "~b~ir?EdO~v lever and the range of CT nura~bersabove and below the windotv level is sailed ':r:;;r:'o$tj wi~ffh".Of course, it is possible to set the window level at any desired CT number and sat the W~~~?:~IJPZI' +~iibil? ro any width desired by the operator (Fig.$6). .,

,.a

?+

Values of ~vindowlevel and wind m t$didt!'i may vary widely depending on the type of examinabur1 and pathology. in practice

multipie window levels and multipi.? window widths may be ex-

arniried in an effort to extract m ~ x ~ r n atnfannation m from each oaminaiion.

1 Fig16 Bone rA&sy& Gone structure in higi~erden:sity ranijc? sii~~.,:~:; ::: i scarlned a" {f?ig';:zlfan# broader ~>~jindo:>, ic;~~;;! fee;?' .. IL wi:.1-.30, L ~ \ ~ * / : ~ O ( I C )i ! ~ ) -.: ..... r7:~;.

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