An investigation of computed tomography (CT)

An investigation investigation of of computed computed tomography tomography (CT) (CT) Linearity Linearity R.J. Kriz* Kriz* and and Keith Keith J. J, Strauss Strauss** R.J. ** ^Department Illinois at at Chicago, Chicago, Chicago, Chicago, Illinois Illinois *Department of of Radiology, Radiology, University of Illinois **Department * *Department ofofRadiology, Radiology, The The Children's Children's Hospital, Hospital, Boston, Boston, Massachusetts

60612

02115

Abstract

The linear linear dependence of Computed Tomography Tomography (CT) (CT) numbers numbers on on linear linear attenuation attenuation The coefficients investigated. CT numbers were fit fit to to linear linear attenuation attenuation coefficients coefficients coefficients was investigated. using for energies energies from from 55 55 to to 80 80 keV. keV. The variance was was recorded. recorded. using the the least least squares squares method for The lowest variance was assumed assumed to to be be the the effective effective energy energy of of the the The energy energy representing representing the lowest scanner. Six insufficient to to unambiguously unambiguously define define the the effective effective energy. energy. Nine Six points points were insufficient materials were used in in all all subsequent subsequent studies; studies; unambiguous unambiguous values values were were obtained. obtained. materials Linearity was as aa function function of of field field of of view, view, phantom phantom size size from from 10 10 cm cm to to 30 30 Linearity was determined as cm energy. Two plastics (polysulfone cm diameter, diameter, and energy. (polysulfone and and acetal) acetal) are are described described which which extend extend Two plastics the 215 and and 360 Houndsfield numbers respectively respectively (scale (scale is is 1000). the linearity linearity curve curve to to 215 Practical investigated. Practical applications applications were investigated. Introduction

CT linearity linearity measures the the mathematical relationship relationship between between the the linear linear attenuation attenuation coefficients in an an object object and and the the corresponding corresponding Houndsfield Houndsfield numbers numbers assigned assigned by by coefficients present present in the CT in the image of that that object. object. This This relationship relationship is is given given by: by: the CT scanner scanner in the reconstructed image number == CC Houndsfield number

U P

--

Uuww

(1) (1)

uw

where yV = linear linear attenuation attenuation coefficient coefficient of of the the object, object, uy w = linear linear attenuation attenuation coefficient of water, water, CC == constant constant (C (C == 1000 1000 by by definition definition Wfor for Houndsfield numbers). numbers). coefficient of normalizes number of water water to normalizes the the Houndsfield number to zero'. zero^-.

This

From this this relationship it it is is easy easy to to show show that that the the theoretical theoretical slope slope and and intercept intercept of of From the linearity equation are: are: the linearity slope =« CC/uw /uw

(2) (2)

intercept = -C intercept -C

(3) (3)

The linear attenuation coefficient for for water water as as aa function function of of effective effective scan The linear scan energy energy and and the allow one to to calculate calculate the the the constant constant C, C, chosen chosen by by the scanner's manufacturer, manufacturer, allow theoretical theoretical slope and and intercept intercept for for the the scanner. scanner. Thus, a measurement of of effective effective energy energy Thus, a and linearity allows check of accuracy and and uniformity uniformity of of the the contrast contrast scale and linearity allows a check of both the accuracy scale in in a scanner's images. images. a McCullough and others others discussed the the importance importance of of linearity linearity and and described described measurement measurement McCullough and techniques cylinders with with different linear linear attenuation techniques using using plastic plastic cylinders attenuation coefficients coefficients as as early early as 1974.2-4 xIn as 1974.L-4 n 1977 developed a phantom using five five different different plastic plastic cylinders 1977 the the AAPM AAPM developed cylinders in an standardize linearity linearity measurements. measurements.5 Millner and others in in an effort effort to standardize in 1978 1978 reported reported aa method energy of aa CT scan scan from from linearity linearity data data collected collected method to to determine determine the effective energy using the the AAPM standard phantom. using phantom." White and Speller Speller developed developed a method to measure method to measure effective in 1980 1980 using using various various mixtures of effective energy energy and and linearity in of organic organic liquids. liquids.' With this found independently independently of of the this method, method, the the effective energy was found the slope slope and and intercept. intercept. While the the above above methods are are relatively relatively straight straight forward, forward, practical practical problems problems exist exist with each. each. Since plastics exist,° exist,° the the density, density, chemical chemical composition Since wide variations of plastics composition and the actual actual material used used must must accurately accurately be and hence, hence. linear linear attenuation coefficient of the be determined. The AAPM phantom construction construction does does not not allow allow this this nor nor the the movement movement of of the the pins to different radii within within the the phantom. phantom. The organic pins to organic liquids liquids required required in in the the second second purity, carefully carefully dispensed. method must be high purity, dispensed, and and temperature temperature controlled controlled during during scanning. and special special storage storage containers containers are are required required to to scanning. Care Care to to protect protect eyes and skin and these liquids. liquids.' handle these This paper presents presents aa method of of using using carefully carefully chosen This paper chosen plastic plastic cylinders cylinders which which optimizes optimizes SPIE SPIEVol. Vol.555 555Medical MedicalImaging Imagingand andInstrumentation Instrumentation'85 '85(1985) (1985)/ / 195 195

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the precision and subsequent subsequent linearity linearity of of any any clinical clinical CT CT the precision of of the the measured measured effective energy and After discussion of method and typical experimental scanner. After of the the method and its its accuracy, accuracy, typical experimental results results of energy and and linearity measurements are are given given as as aa function function of of kVp. kVp. phantom phantom of effective effective energy linearity measurements size, field of for images images from from aa GE 9800 9800 scanner. scanner. These results are are compared compared size. and and scan scan field of view for with 2 and and 3. 3. Finally, Finally, data on reproducibility reproducibility of of aa CT CT with the the expected expected values values from equations 2 8800 scanner scanner is 8800 is presented. Methods Phantoms

water filled 20.3 ") diameter diameter phantom phantom was was constructed constructed of plexiglass. A water 20.3 cm cm (8 (8") plexiglass. See Figure is referred referred to as as the the "head" phantom. phantom. The The phantom has eight eight 3.7 3.7 Figure 1. 1. This This phantom phantom is cm ports equally equally spaced spaced at at aa radius radius of of 7.0 7.0 cm. cm. This This allows allows all all pins pins to to cm diameter diameter access access ports be at Thus. the xx-rays -rays will will undergo undergo approximately the at the same same depth within within the the phantom. phantom. Thus, the same same effective effective energy energy at at each each pin pin location. location. An same filtration filtration and and have have approximately the same additional port port is located in the center of the The phantom has aa usable additional is located the phantom. phantom. The usable depth depth of cm. The cap for for each each access access port port has has of 4.9 cm. 2.5 cm cm diameter diameter well well drilled aa 2.5 drilled into the the This allows surface. This allows the the cap to to inside surface. support 2.5 cm diameter diameter test test support and and align align the the 2.5 well is is also also set set into into the the pins. A shallow well inside back of of the inside back the phantom phantom to to aid aid in in keeping pins aligned aligned properly. properly. A 5.0 5.0 mm thick thick pins teflon available that that slides slides over over the the teflon ring ring is is available phantom for beam hardening. hardening. phantom to to simulate simulate bone bone for

A "body" "body" version of of the the phantom phantom is is also also It is is similar similar to used. See Figure Figure 2. 2. It to the previously except that that previously described described head head version except its its diameter is is 30.5 30.5 cm cm (12 (12"). 11 ). A second set is available with with their their set of of 88 ports ports is centers set at at a radius of of 11.1 11.1 cm. cm. centers set An 8" diameter solid pelxiglass pelxiglass phantom phantom An 8" diameter solid was constructed constructed that that is is capable capable of of holding holding 12 12 samples at the same same radius. radius. See Figure 3. 3. samples at Two Two additional additional water filled filled plexiglass plexiglass phantoms of 4 and and 66 inches inches phantoms having having diameters diameters of also constructed. constructed. Eight pins at at radii radii were also Eight pins of 3.5 3.5 and and 5.7 5.7 cm cm respectively were fitted of fitted into into these two two phantoms. phantoms.

The 25 Figure 1: 1: The 25 cm diameter "head" "head" phantom is is shown. shown. The plexiglass plexiglass phantom phantom is filled filled with an access access is with water water through an port been port after after various various test pins have been inserted.

Figure 2: 2: The 30.5 cm cm diameter diameter "body" "body" phantom is is shown. shown. The inner inner ring ring of of access access ports is is at at the the same same radius (7.0 (7.0 cm) cm) as as those those ports of of the "head" phantom. phantom. The outer ring ring access access is at at a is a radius of 11.1 11.1 cm. cm. This allows allows simultaneous determination of linearity linearity and and simultaneous effective energy at at two two depths within within the the effective phantom.

The 25 Figure 3: 3: The 25 cm diameter plexiglass plexiglass 12 is shown shown with with 12 12 sample sample 12 sample sample phantom is pins in place. place. The is used used to to The phantom is pins in investigate the investigate the effects of of sample sample selecselection of samples on on linearity linearity tion and and number number of and energy determinations. determinations. and effective energy

196 // SPIE SPIE Vol. '85 (1985) (1985) 196 Vol.555 555 Medical Medical Imaging Imaging and Instrumentation Instrumentation '85


inserts Plastic inserts Eight plastic materials selected with with nominal nominal Houndsfield Houndsfield numbers numbers ranging ranging from Eight plastic materials were selected from -125 -125 to +365. These materials, with their their chemical chemical formulas, formulas, measured measured densities, densities, nominal materials, with nominal Houndsfield values values and and linear linear attenuation attenuation coefficients coefficients at at 66 66 keV keV are are shown Houndsfield shown in in Table Table I. I. Additional materials used used in in the the twelve twelve sample sample study study are are shown shown in in Table Additional Table II. II. TABLE II NINE STANDARD STANDARD MATERIALS MATERIALS NINE PIN

MATERIAL NAME

CHEMICAL FORMULA

NO.

MEASURED DENSITY

TYPICAL HOUNDSFIELD NUMBER

LINEAR ATTENUATION COEFFICIENT (66 keV) keV) (66

cm"l 0. 2645 cm-1 0.2645 cm-1 2357 cm-1 0. 0.2357

12 12

Acetal

CH20 CH2O

1. 426 g/cc 1.426

358

11

Polysulfone

H 2 2C270 3 S H22C2703S

1. 234 g/cc 1.234

208

99

Polymethyl Polymethyl Methacrylate

CC5H802 5H80 2

1. 187 g/cc 1.187

119

77

Nylon 6/6

C 12 H 22°2 N 2 C12H2202N2

1. 154 g/cc 1.154

95

-

Water

H20 H20

1. 00 g/cc 1.00

6

6

Polystyrene

C 8H8 C8H8

049 g/cc 1. 1.049

-36 -36

cm"l 0. 1963 cm-1 0.1963 cm"l 0. 1899 cm-1 0.1899

5

5

High High Density Density Polyethylene (HOPE) (HDPE)

CH 2 CH2

9495 g/cc 0. 0.9495

-79 -79

cm"l 0. 1820 cm-1 0.1820

44

Ultra High Ultra High Molecular Weight Polyethylene (UHMWPE) (UHMWPE)

CH2

0. 9310 g/cc 0.9310

-98 -98

0. 1778 cm-1 0.1778

22

Polypropylene (PP) (PP)

C 3H6 C3H6

9044 g/cc 0.9044 0.

-131 -131

cm"l 0. 1727 cm-1 0.1727

00

cm-1 0. 2297 cm-1 0.2297 cm"! 0. 2150 cm-1 0.2150

cm-1

TABLE II II FOUR ADDITIONAL MATERIALS PIN NO.

MATERIAL NAME

FORMULA CHEMICAL FORMULA

MEASURED DENSITY

Low Low Density Density Polyethylene (LDPE) (LDPE)

CH 2 CH2

0.9216 0.9216 g/cc

8

Polycarbonate (PC) (PC)

CC16H1403 16 H 14 0 3

1.195 1.195 g/cc

11

Polymethylpentene (PMP) Polymethylpentene (PMP)

CC6H12 6 H 12 (Ch2) (Ch 2 )

Polyetherimide

C 37 H24N 2 0 6 C37H24N206

3

10

TYPICAL HOUNDSFIELD NUMBER

LINEAR ATTENUATION COEFFICIENT (66 keV) keV) (66

-114

0.1751 cm-1 cm-1

100

0.2149 cm-1 0.2149 cm-1

0.8308 0.8308 g/cc

-200

0.1587 cm-1 cm-1 0.1587

1.278 g/cc 1.278

163

0.2268 cm-1 cm-1

The each material was determined by by using using aa calibrated The density density of of each calibrated Mettler Mettler balance balance to to determine cylinder precisely machined to determine the the mass mass of of a cylinder to aa volume of of 40.00 40.00 cm3. cm^. Hounds Hounds-field numbers using the head head mode, mode, 10 10 mm slice slice thickness, thickness, 600 600 mA, mA, 120 120 kVp kVp field numbers were were determined determined using and G.E. CT CT/T and 576 576 views views on a G.E. /T 8800, 8800, using using the the 8" 8" diameter diameter phantom phantom without the the "bone" "bone" ring. To optimize selection of plastic plastic materials, materials, three three separate separate problems problems must must be be considered. considered. To optimize First, points should be evenly spaced spaced over the the clinical clinical range range of First, the the measured measured data data points of Hounds Hounds-field (and linear linear attenuation attenuation coefficients). coefficients). This field numbers numbers (and is required required to to verify verify that that the the This is linearity is in in fact fact aa straight straight line. linearity curve curve is line. Choices artifacts in in the the scan scan Choices must must avoid artifacts (note absence of teflon in in Tables Tables II and and II). II). (note absence of SPIE Vol. SPIE Vol.555 555Medical MedicalImaging Imagingand andInstrumentation Instrumentation'85 '85(1985) (1985)/ / 197 197


The that the the materials selected selected must must allow allow the The second second problem is that the determination determination of of effective energy of of the the scan. scan. If If the effective the selected selected the linear linear attenuation coefficients of the materials as a function of energy energy differ from from one one another another only only by by aa constant, constant, the materials as the effective effective energy of energy of the the scan scan can can not not be be determined determined by by selecting selecting the the linear linear fit fit with with the the maximum maximum correlation coefficient. for the the correlation correlation of of coefficient coefficient is6: The equation for NEpi(E)Yi - Epi(E)EYi R _

(4) (4)

.)2]l/2 [NEpi(E)2 - (Epi(E))2]1 /2[NEY? -- (zY (EY02]1 /2 where pi(E) y^CE) is is the the linear linear attenuation attenuation coefficient coefficient of of the the ith i tn material material at at energy energy E. E. Yj is is the Houndsfield number number of of the the ith i tn material material and and NN is is the the total Yi total number number of of materials. materials, It that: It is is assumed that: y t (E) =- Cif(E) pi(E) C

(5) (5)

is a constant for for the the ith i^ material and and f(E) f(E) is is aa function where C^ Ci is function dependent dependent on on energy. (Note, the mass (Note, f(E) f(E) represents represents the mass attenuation coefficieint coefficieint and and Ci C^ represents represents the the density i tn material.) density of of the ith Substituting:

NECif(E)Yi - ECif(E)EYi

R =R

(6) (6)

[N2C?f2(E) i f(E))2]l/2[ NzY 2 .- (EY02]1 /2 [NEC ?f2(E) - - (ZC (ECif(E))2]ij2[NEY? At energy, f(E) f (E) is is the the same same for for all all materials; materials; it At a given energy, it can can be be moved moved outside outside the the summasummasign. f(E) f(E) cancels; is independent independent of tion sign. of energy energy for for this this case. case. Therefore: cancels; R is NECiYi - ECiEYi

R=

(7) (7) [NEC? - (ECi)2]1 /2[NEY?

-- (EY i )2]l/2 (EY02]1 /2

Under 5 is is approximately approximately true, Under conditions conditions where where equation 5 true, there there will will be be only only small small changes changes in the the correlation coefficient coefficient as as aa function function of of energy. energy. It in It may difficult to to may then be difficult the effective effective energy. energy. determine the Finally, purity considered when Finally, purity of of the materials must be considered when choosing choosing materials. materials. Many standard plastics include include fire fire retardants, retardants, elastomers, elastomers, coloring standard formulations formulations of of plastics coloring additives additives (such (such as as titanium dioxide), etc. etc. Also some plastics plastics are made of of mixtures whose whose ratios ratios may Also some vary as urethane.8 urethane.° vary such such as coefficients Attenuation coefficients The linear linear attenuation coefficients were wer obtained obtained from from the the Library Library on on Photon The Photon Interaction Interaction Coefficients and Electron Stopping Stopping Powers.9 Powers. Coefficients This library not not only provides provides mass "attendThis library attenuation for all all the elements, elements, but but includ includess methods for for determining determining the the mass ation coefficients coefficients for mass attenuation coefficients compounds and and mixtures.10 attenuation coefficients of of compounds mixtures . ^ The the photon photon The library contains the interaction coefficients the Lawrance Livermore Laboratory.1 interaction coefficients from the Laboratory.il Data Data collection collection and and statistics statistics Various pins were placed Various pins placed in in the the phantoms. phantoms. The scanned normally. normally. The The phantoms were scanned average for each each pin was calculated using the average Houndsfield Houndsfield number number for the scanner's scanner's region region of of interest software. software. A computer program was written interest written to to calculate calculate the the variance variance (fitted (fitted sum sum of squares), linear coefficieint, slope, slope, error in in slope, slope, intercept, of squares), linear correlation coefficieint, intercept, and and error error in intercept. The program in program uses aa least least squares squares technique technique to to fit fit the the Houndsfield Houndsfield numbers numbers to the the respective linear linear attenuation attenuation coefficients. to coefficients. This is repeated for for energies energies from from 50 50 This is keV to to 85 keV 85 keV in in 11 keV keV increments. increments. The energy energy corresponding to to the the minimum variance variance or or linear correlation coefficient coefficient is is taken taken as as the the effective effective energy maximum linear energy of of the the scan. scan. One may error matrix^2 estimate the the standard standard deviation deviation in may use the error matrix12 to estimate in the the least least square fitted slope, slope, m, m, and and intercept, intercept, b: b: square fitted a

= No2 /[N(Ep?) - (EPj)2]

SPIE Vol. Vol. 555 Medical Medical Imaging and Instrumentation '85 (1985) (1985) 198 //SPIE Instrumentation '85


(8)

(9) (9)

ag = a2EP2 /[N(Ep ?) - (EPi)2]

both in both exists in a2 the uncertainty which exists is the a2 is fitted. materials fitted. of materials the number of is the where N is by!2 : estimated by12: is estimated It is numbers. It Houndsfield numbers. the Houndsfield and the linear attenuation coefficients and the linear the 02 = (AH)2 ++ m2(Au)2 a2 = (AH)2 m2011)2

(10)

AU in the where AH AH is is the the estimated estimated error error in the Houndsfield Houndsfield number, number, mm is is the the fitted fitted slope, slope, and and AP where that assumes that 10 assumes coefficient. Equation 10 attenuation coefficient. the linear attenuation in the is is the the estimated estimated error error in not do not coefficients do attenuation coefficients linear attenuation the uncertainties uncertainties in the Houndsfield numbers or linear in the the scan. vary from from one one material material to to another within aa given scan. vary Results intercept and intercept slope and fitted slope in fitted Errors Errors in field of a scan and a Data collected collected using using 120 120 kVp kVp and scan field of view view large large enough enough to to encompass encompass the the Data coefficients attenuation coefficients linear attenuation the linear in the error in The error III. The in Table III. shown in entire entire phantom phantom are are shown each for each numbers for in the Houndsfield numbers The error error in water). The for water). (3% for cm~l (3% was was assumed assumed to to be be 0.006 0.006 cm-1 scan AH, was was calculated calculated using using the the scanner's scanner's region region of of interest interest standard standard deviation deviation scan AH, software. TABLE

III I I I

ERRORS INTERCEPT ERRORS SLOPE AND INTERCEPT TYPICAL SLOPE ERROR

INTERCEPT

(cm)

ERROR IN SLOPE (am ) (am)

2

4890

320

-979 -979

70 70

64

2

4990

330

-984 -984

70 70

25

66 66

3

4930

350

-984 -984

70 70

20* 20*

25 25

68 68

3

5020

360

-967 -967

70 70

30

35 35

70 70

4

4930

360

-940 -940

70 70

PHANTOM DIAMETER (cm) (cm)

SCAN FIELD OF (cm) VIEW (cm)

EFFECTIVE ENERGY

10

25 25

62

15 15

25 25

20 20

AH

(keV)

ring *Phantom plus plus Teflon "bone" ring *Phantom

SLOPE

IN IN INTERCEPT (%) (ab)

0.006 cm-1 to 0.006 assumed equal to Ay assumed Ap

is intercept is and intercept fitted slope the fitted in the uncertainty in the uncertainty that the Table slope and illustrates that III illustrates Table III the This occurs because the This in AH). (change in noise (change DH). scan noise the scan relatively independent independent of the relatively 10. Therefore, equation 10. in equation dominates in coefficient dominates attenuation coefficient uncertainty the linear attenuation in the uncertainty in constant assume constant can assume one can sizes, one patient sizes, and patient techniques and for routine routine clinical clinical ranges ranges in in scan techniques for the in the uncertainty in the uncertainty intercept. These are double the and intercept. slope and uncertainties fitted slope in the fitted uncertainties in calibration. linearity calibration. the linearity for the used for the material used of the linear linear attenuation coefficients of study Twelve sample study (pin numbers The phantom phantom containing containing 12 12 materials materials (pin numbers 11 through through 12) 12) was was scanned scanned using using the the The CT the CT on the views on 576 views and 576 slice width and 10 mm slice kVp, 10 120 kVp, infant body body (25 cm) mode, mode, 600 mA, mA, 120 (25 cm) infant (from lowest the range The range range refers refers to range of of Houndsfield Houndsfield numbers numbers (from lowest to to highest) highest) to the 8800. The study. included included in the study. first the first is shown The best best least least squares squares fit of aa straight straight line line to to the the 12 12 values values is shown on on the fit of The to used to scan were also used same scan the same each of groups of of nine materials each of the nine materials row of Table IV. Seven groups Table IV. same the same of the samples of 10 samples one group of 10 addition one In addition G). In to G). (groups AA to fit (groups calculate the best fit calculate the indicate the pin the group The numbers group letters letters indicate after the parentheses after in parentheses numbers in data were run. run. The attenuahighest attenuato highest lowest to in order of lowest The pin pin numbers numbers are in studies. The the studies. in the numbers numbers used in II. and II. tion coefficient. See Tables II and scanner. the scanner. of the energy of effective energy the effective determine the accurately determine to accurately fail to F, and HH fail B, F. A, B. Groups A, the results This results results in in aa relatively relatively large large error error in in the the slope slope calculation calculation compared compared to to the results This calcuto calcuused to be used can be accurately can However, these groups accurately 7). However, (column 7). from 12 materials (column from all 12 in case, in In this case, 9). In (column 9). known (column is known scan is the scan of the late the slope if energy of if the effective energy the slope late numbers, Houndsfield numbers, the Houndsfield of the range of the range on the dependent on is dependent slope is general, the slope of the accuracy of general, the accuracy 6. column 6. column SPIE SPIE Vol. Vol.555 555Medical Medical Imaging Imaging and andInstrumentation Instrumentation '85 715(1985) (1985)// 199


TABLE TABLE IV COMPARISON OF 12 12 SCANNED MATERIALS VS. VS. GROUPS GROUPS OF OF 9, 9, 10, AND 55 GROUP

SLOPE (cm)

INTERINTERCEPT

VARIANCE

EFFECTIVE ENERGY

RANGE

(keV)

% DIFFER IN SLOPE IN AT MIN. VARIANCE

SLOPE @

66 keV 66 (cm)

% DIFFER DIFFER SLOPE IN SLOPE 66 AT 66 keV

12 All 12 Materials

5297

-1041

71.0

66

557

N.A.

5297

N.A.

(1-9) A (1-9)

5322

-1042

51.4

67 67

319

0.46

5287

-0.19 -0.19

BB (2-10) (2-10)

5754

-1081

44.5

78

294

8.62

5333

0.68

C (3-11) (3-11) C

5307

-1043

40.7

66 66

322

0.19

5307

0.19

(4-12) D (4-12)

5284 5284

-1038

45.2

66 66

455

-0.25

5284

-0.25 -0.25

(1-3,5,6, E (1-3,5,6, 8,10-12)

5310

-1044

51.9

66

557

0.24

5310

0.25

F (2,4-9, (2,4-9, 11,12)

5241

-1036

53.2

65 65

489

-1.10

5302

0.10

G (1-4,6, (1-4,6, 9-12)

5294

-1041

50.0

66 66

557

-0.07

5294

-0.06 -0.06

(1-10) H (1-10)

5345

-1046

59.9

67 67

363

0.92

5312

0.28

I

I (1,6,10-12)

5279

-1037

12.1

66 66

557

0.34

5297

N.A.

(AAPM) J (AAPM)

5415

-1052

23.9

69 69

198

2.23

5292

-0.02 -0.02

study Five sample study To inability of To determine determine the the inability of some some groups groups of of materials materials to to determine determine the the effective effective energy of scan, five five materials were were selected selected whose whose linear linear attenuation attenuation coefficients energy of the scan, coefficients are are multiples same mass attenuation attenuation coefficient. coefficient. This multiples of of the same This occurred occurred because the the chosen chosen compounds were composed of only Hydrogen and and Carbon Carbon in in the the ratio ratio of compounds of 2:1. 2:1. Thus, Thus, the the equation 55 was was satisfied. satisfied. The materials were polymethylpentene, polymethylpentene, polypropylene, polypropylene, condition of equation low high molecular weight polyethylene polyethylene and low density density polyethylene, polyethylene, ultra high and high high density density polypolyethylene, pins 11-5, I and II. II. The resultant ethylene, pins -5, Tables Tables I resultant variances and and correlation correlation coefficients coefficients did not not vary for for all all energies energies from from 50 50 keV keV to to 85 85 keV, keV, as as predicted predicted by by equation equation 7. 7. did In selected to have aa wide range range in in Houndsfield Houndsfield In comparison, comparison, five five more more materials materials were were selected values and and also different mass attenuation attenuation coefficients. coefficients. The values polymethylThe materials materials were polymethylpentene, and acetal, acetal, pins pins 1, 1, 6, 6, 10, 10, 11, pentene, polystyrene, polystyrene, polyetherimid, polyetherimid, polysulfone and 11, and and 12, 12, and II. II. The variance was plotted plotted as as aa function function of of energy energy in Tables II and in Figure Figure 4. 4. This 5 materials accurately reproduced reproduced the the slope slope and and intercept intercept of of the the curve curve drawn group of of 5 materials accurately drawn from from all and indicated indicated the same energy. energy. See all twelve twelve materials materials and See Group I, I, Table Table IV. IV. The five materials used in in the the AAPM phantom (polymethyl The five materials used (polymethyl methacrylate, methacrylate, polycarbonate, polycarbonate, nylon, polystyrene and polyethylene, polyethylene, pins nylon, pins 9, 9, 8, 8, 7, 7, 6, 6, and and 5, 5, Tables II and and II) II) were were also also used to to determine linearity and effective effective energy. energy. The variance as as aa function function of used of energy energy was plotted plotted in in Figure Figure 5. 5. Note that that the the variance variance had values was values only only from from aa high high of of 55 55 to to aa low of 23.6. 23.6. Note also also that that there there are are multiple multiple local local minimums minimums on on the the curve. curve. While the the lowest about 69 keV (close (close to to the the 66 66 determined determined from lowest minimum minimum is is centered centered about from 12 12 materials), materials), this choice of 55 materials does not not allow allow precise precise or or accurate accurate determination determination of this choice of of the the effective energy. energy. See Group J, J, Table Table IV. IV. Nine sample sample study: study;

kVp, field field of view, view, phantom size size kVp,

The listed in in Table II were used used for for this this study. study. Linearity calculations The nine nine materials materials listed were completed completed as as a function function of of kVp, kVp, field field of of view, view, or or phantom phantom size. size. These scans scans were were from aa GE GE 9800 CT unit. from unit. The placed on the the table table and and centered centered in in the the gantry. gantry. The phantom was was placed A 3600 360° scan rotation, rotation, standard resolution resolution algorithm, algorithm, and and 256 256 matrix matrix size size were were selected. selected. A nominal 10 10 mm mm slice slice thickness thickness and and 1200 1200-680 mAs at at 80 80-140 to minimize minimize the the -680 mAs -140 kVp kVp were used to random noise. noise. (When (When the used, the mAs was reduced reduced in in some some cases cases the 4" 4" and and 6" 6" phantoms phantoms were used, to to eliminate "overscan" "overscan" error). error). Approximately 140 pixels averaged to to measure the Approximately 140 pixels were were averaged measure the 200 / /SPIE SPIEVol. Vol. 555 555Medical MedicalImaging Imaging and and Instrumentation '8511985) '85 (1985) 200


MATERIALS SELECTED MATERIALS FIVE FIVE SELECTED

MATERIALS AAPM MATERIALS FIVE AAPM FIVE

10000 8000 6000 4000

10000

8000 6000 4000

1

2000

•

1000 800 600 0) 600

•

•

2000 • 4

.•

v0

= 400 400

*

1000 800 CD 600 cp 600 o 400 c400

.t

-9————

^^

•

.2 0CO 200 > 200

l_

CO 200 > 200

• • •

100 100 on ou 80 60 40

• •

•

100 80 60 40