che p

Medt of

of California, Davis, Rm. 2303, GBSF, 451 E. Health Science Dr., Davis, California 95616Dale Gelskey

Diagnostic Imaging Specialists Corporation (DISC), 163 St. Malo Street, St. Malo,Manitoba R0A 1T0, Canada

Kai YangDepartment of Radiology, University of California, Davis Medical Center, Rm. 0505, ACC Ellison Bldg.,4860 Y St., Sacramento, California 95817Shin-ying Huang, Lin Chen, and John M. BooneaDepartment of Radiology, University of California, Davis Medical Center, Rm. 0505, ACC Ellison Bldg.,4860 Y St., Sacramento, California 95817 and Department of Biomedical Engineering, Universityof California, Davis, Rm. 2303, GBSF, 451 E. Health Science Dr., Davis, California 95616Received 23 June 2010; revised 12 January 2011; accepted for publication 13 January 2011;published 18 February 2011

Purpose: Beam-shaping or bow tie BT filters are used to spatially modulate the x-ray beam ina CT scanner, but the conventional method of step-and-shoot measurement to characterize a beamsprofile is tedious and time-consuming. The theory for characterization of bow tie relative attenua-tion COBRA method, which relies on a real-time dosimeter to address the issues of conventionalmeasurement techniques, was previously demonstrated using computer simulations. In this study,the feasibility of the COBRA theory is further validated experimentally through the employment ofa prototype real-time radiation meter and a known BT filter.Methods: The COBRA method consisted of four basic steps: 1 The probe was placed at the edgeof a scanners field of view; 2 a real-time signal train was collected as the scanners gantry rotatedwith the x-ray beam on; 3 the signal train, without a BT filter, was modeled using peak valuesmeasured in the signal train of step 2; and 4 the relative attenuation of the BT filter was estimatedfrom filtered and unfiltered data sets. The prototype probe was first verified to have an isotropic andlinear response to incident x-rays. The COBRA method was then tested on a dedicated breast CTscanner with a custom-designed BT filter and compared to the conventional step-and-shoot char-acterization of the BT filter. Using basis decomposition of dual energy signal data, the thickness ofthe filter was estimated and compared to the BT filters manufacturing specifications. The COBRAmethod was also demonstrated with a clinical whole body CT scanner using the body BT filter. Therelative attenuation was calculated at four discrete x-ray tube potentials and used to estimate thethickness of the BT filter.Results: The prototype probe was found to have a linear and isotropic response to x-rays. Therelative attenuation produced from the COBRA method fell within the error of the relative attenu-ation measured with the step-and-shoot method. The BT filter thickness estimates resulting from thedual energy scans on the breast CT system were equivalent to the manufacturing specifications. Theclinical CT evaluation produced data conceptually similar to previous computer simulations andplausible relative attenuation profiles were observed.Conclusions: The COBRA method is a fast and accurate method for BT filter characterization,which requires a simple experimental setup in a clinical environment. Because of the ease of dataacquisition, multienergy scans can be acquired which allow characterization of the BT filterthickness. 2011 American Association of Physicists in Medicine. DOI: 10.1118/1.3551990

Key words: bow tie filter, real-time dosimetry, CT

I. INTRODUCTIONCT dosimetry relies increasingly on Monte Carlo simula-tions. Within the past decade, the high computational de-mands of Monte Carlo dosimetry techniques are being metwith affordable and easily accessible computer hardware.

Despite an increase in processing power, the accuracy of adosimetry simulation primarily relies on the researchersability to characterize the physical parameters of a CT scan-ners geometry and x-ray beam properties.1

In commercial whole body scanners, a beam-shaping filterExperimental validation of a methodin CT scanners using a real-time dos

Sarah E. McKenney and Anita NosratiehDepartment of Radiology, University of California, Davis4860 Y St., Sacramento, California 95817 and Departmen1406 Med. Phys. 38 3, March 2011 0094-2405/2011/383aracterizing bow tie filtersrobe

ical Center, Rm. 0505, ACC Ellison Bldg.,Biomedical Engineering, University1406/1406/10/$30.00 2011 Am. Assoc. Phys. Med.

probe

1407 McKenney et al.: Validation of bow tie filter attenuation characterization method 1407or bow tie BT filter is placed in the x-ray beam to equal-ize the fluence incident on the detector and to reduce theradiation dose to a patient.2 The BT-filtered beam reduces thedynamic range demands of a detector and improves the re-sulting images,3 specifically in terms of contrast-to-noise ra-tio, scatter-to-primary ratio, CT number accuracy, and uni-formity. The added benefit of dose reduction4 is particularlynoticeable at the periphery of a patient.5 While there arebeam-shaping filters that intentionally shape the x-ray beamin the z-direction,6 all clinical whole body scanners use BTfilters with a constant profile in the z-direction, with someminor beam divergence. This is not to say that the x-rayprofile is flat along the z-dimension; indeed, most CT beamprofiles along the z-axis of the beam show evidence of theheel effect. It is possible to apply filtration to the scanner thatreshapes the beam profile along z to compensate for the heeleffect; however, the filtration employed for z-dimensionbeam correction is constant as a function of the fan angle.Therefore, these elements of beam filtration are considered tobe part of the x-ray tube inherent filtration; that is, it is con-stant in the fan angle direction.

The geometry and composition of a BT filter is typicallyproprietary information. Unless this information isprovided,7 medical physicists are unable to accurately modelthe x-ray beam incident on the patient in commercial CTscanners.

8 Recognizing this, a method to characterize a CTscanners BT filter using a real-time exposure meter was pre-viously proposed and demonstrated using computersimulation.9 The characterization of bow tie relative attenu-ation COBRA method outlines a protocol to quickly andaccurately describe F, the relative attenuation of a BTfilter across the fan angle of the scanner.

Accurate Monte Carlo studies in CT rely on knowledge ofthe x-ray energy-dependent modulation of the x-ray beamalong the fan angle. Therefore, knowledge of the overall at-tenuation of the x-ray beam F as a function of fan angle for a polyenergetic x-ray spectrum is not sufficient. Conse-quently, the COBRA method involves a final step, wherebythe BT filter characterization of angle-dependent attenuationat different x-ray beam energies e.g., 80140 kVp is usedwith basis material decomposition techniques to estimate thephysical thickness of the bow tie filter. Knowing the esti-mated thickness of the bow tie filter for one or two basismaterials as a function of fan angle then allows the investi-gator to take the energy dependence of the bow tie filter intoaccount. Even if the selection of basis materials such asaluminum and polymethyl methacrylate PMMA is not acorrect physical depiction of a given vendors bow tie filtercomposition, the derived thickness information will providethe same energy-dependent attenuation properties as thecharacterized BT filter, as this is the basic tenant of basismaterial decomposition techniques.10

In this paper, experimental measurements are describedusing the COBRA technique with a prototypical dose probein both a custom-designed CT system and a commercialwhole body CT system.Medical Physics, Vol. 38, No. 3, March 2011II. THEORY REVIEWThe following is a brief overview of the COBRA method

for determining the relative attenuation properties of a beam-shaping filter in CT; for a more detailed review, refer toBoone.9 In order for the method to work properly, the entireactive area of the x-ray probe must be completely envelopedwithin the collimated x-ray beam and no other objects, suchas a patient table, can be in the beams path during the ac-quisition. The geometry of the CT scanner is shown in Fig. 1,where the frame of reference has been centered on the x-raysource such that the source appears to be stationary at posi-tion xt ,yt and the real-time dose probe appears to rotate adistance r around isocenter with a position of xp ,yp as de-termined by the gantry angle at. It is assumed that thesource-to-isocenter distance s is known and is fixed and thatthe anode-cathode direction is parallel to the z-direction.

The x-ray fluence detected by the probe at time t is de-pendent on the distance of the probe from the x-ray tube,denoted by gt. When no BT filter is present, it is assumedthat the x-ray probes output M0 is independent of theangular incidence of the x-rays. When a bow tie filter isadded to the system, the probes output with filtration M1is equal to M0 at t=0 and t=. At these two posi-tions, the relative attenuation of the probes signal due to thebow tie filter at a fan angle of , F, is unity i.e., F=1. Note that

F =M1M0

. 1

Given M10 and M1 and assuming that the effects offocal spot size, off-focal radiation, and detective volume arenegligible, it is possible to use the inverse square law todeduce the output in the absence of a BT filter over all tsuch that

M0 = I0 sg2, 2

where I0 is the probes output at isocenter. Consequently, it ispossible to measure the relative attenuation of a BT filter

bow tie filter

g(t)r

(t)

xp(t)

yp(t)

x-ray

tube

(xt,yt)

isocenter(t)

s

probe path

FIG. 1. Geometry of the CT scanner in a rotating frame of reference suchthat the gantry and x-ray tube appear to be stationary while the probe ap-pears to rotate around isocenter. As the fan angle t varies, the x-ray beamincident on the probe is modulated by the varied thicknesses of the BT filter.As the x-ray source rotates, the probes filtered signal train M1 has amaximum signal at t=0; a local maxima also occurs at t=, since thebeam is minimally reduced by the BT filter.

1408 McKenney et al.: Validation of bow tie filter attenuation characterization method 1408through the analysis of the real-time dosimetric output of aCT scanner as it executes a minimum of one complete rota-tion.

Assuming that the same BT filter is used when x-rays aregenerated at different peak voltages, a least-squares algo-rithm can be used to estimate the filters thickness. Usingdual energy basis decomposition,11 the filter is assumed toconsist of one or two basis materials, typically a metal and aplastic,10 where the linear attenuation coefficient materialEis known.12 The theoretical relative attenuation ofx-rays generated at a single peak energy V is described as

V =E=0

EMaxkEVEeaEabEbdEE=0

EMaxkEVEdE, 3

where a and b are the thicknesses of the material, Eis the x-ray energy fluence, and kE is a factor that convertsphoton fluence into the probes measurement units, such asmGy/s.

The thicknesses of the filter material can be estimatedwith the least-squares method from an overdetermined sys-tem, consisting of measurements made at multiple x-ray tubepeak voltages, such that

2 = V=V1V=Vn FV V2 4

is minimized by iterating over possible values of a andb. The end result is an estimation of the bow tie filtersthickness as a function of fan angle. The extent of the utilityof the relative attenuation measurements for Monte Carlosimulation depends greatly on the accuracy of the scannersspectral characterization at isocenter =0. Note that thismethod assumes that a0=b0=0; consequently, the inher-ent filtration of the system, including contributions from thebow tie filter at =0, is included in M0.

III. MATERIALS AND METHODSIII.A. System setup: Breast CT bCT scanner

Probe validation and preliminary relative attenuation datasets were acquired on a prototype dedicated bCT scanner.13This scanner allowed for continuous rotation of the x-raytube model MXR-160HP/20, Comet, Flamatt, Switzerlandup to an angular position of =415; the x-ray tube couldalso be held fixed at any angular position for a stationaryexposure. The beam was filtered with 0.2 mm copper; thex-ray generator model CP 160/1, Gulmay, Chertsey, UnitedKingdom produced a ripple 0.5%.

While standard operation of the bCT scanner did not in-clude a BT filter; a removable Teflon filter was custom-designed and machined for the purposes of reducing radia-tion dose to the periphery of a breast see Fig. 2.14,15 The BTfilter was designed for breasts with a diameter of 14 cmusing an in-house simulation. There was no beam modula-tion in the z-direction and the filter was symmetric about thesource beams central ray. The filter was positioned153.05.5 mm from the x-ray focal spot, as determinedfrom three individual measurements N=3.Medical Physics, Vol. 38, No. 3, March 2011III.B. System setup: Clinical CT scanner

The COBRA technique was also used to characterize theBT filter of a commercial clinical CT scanner model AS+,Siemens Medical Systems, Florsheim, Germany. This CTsystem had s=590 mm and its BT filters shape and compo-sition were proprietary. The beams ripple was assumed to be5%.

III.C. Probe characterization

Real-time measurements were obtained using a prototypedose probe from Diagnostic Imaging Specialists Corp.DISC. DISC also provided a preamplifier, allowing forvariable gains of 1, 10, 50, 100, and 1000. Ananalog to digital converter ADC Data Translation modelDT9804, Waltham, MA converted the probes output into adigital signal and allowed for additional gain levels of 1,

2, 4, and 8. The digital signal was acquired usingcustom-written data acquisition software. The probes activearea was a small cylindrical solid-state scintillator with aheight of 7 mm and a diameter of 5 mm see Fig. 3; themanufacturers reported sampling rate was under 1 kHz.

On the bCT scanner, the probes position was determinedrelative to the scanners rotational isocenter see Fig. 4. Pre-

FIG. 2. Photograph of the Teflon bow tie filter mounted in the breast CTscanner. The filter has a thickness ranging from 0.2 mm at its center to 62.8mm along its edge. The filter is bilaterally symmetric and has a uniformthickness along the z-direction.

FIG. 3. Projection image of the active volume of the prototype x-ray probeat isocenter.

1409 McKenney et al.: Validation of bow tie filter attenuation characterization method 1409viously, a geometric calibration method that estimates thescanners isocenter and source-to-isocenter distance s wasdeveloped for the bCT system.16 This was used for the initialplacement of the probe. A series of 360 scans were madewith a 120 kVp/7 mA x-ray source and the probe was manu-ally translated until its output was relatively constant; thisposition was defined as isocenter. Note that this method fordetermination of the systems isocenter was not necessary forthe COBRA method if the isocenter was previously defined.On the whole body clinical CT scanner, the laser alignmentlights were assumed to correctly demark isocenter and thex-ray tubes plane of rotation.

III.C.1. Probe isotropyTo quantify the prototype probes dependence on the an-

gular position of the x-ray source, the probe was positionedat the scanners isocenter and then it was manually rotated360 about its longitudinal axis in 90 intervals. At eachposition, the probe was exposed for 5 s to a stationary x-raysource generated by a 120 kVp/7 mA tube voltage and cur-rent. The probe was rotated a total of four times such thatthere were four measurements collected at each angle.

III.C.2. Probe linearityAssessment of the linearity of the prototype probes re-

sponse to an incident x-ray beam was performed. The x-raysource was held stationary and the probe was positioned atisocenter. For each x-ray tube voltage 80 and 120 kVp, thetube current was increased from 0 mA, in 1 mA intervals, tothe maximum current allowed. At each tube current, theprobe was exposed for 5 s to the resulting x-ray beam. Theprobes output was cropped to exclude the probes responselag; an observation point was the average of a cropped trace.This method was repeated for permutations of the probespreamplifiers gain 50 and 100 and the ADCs gain1, 4, and 8.

x-ray tube

x-ray detector

source path

bow tie filter

dose probe

isocenter

FIG. 4. General experimental scheme of the real-time dose probe with a CTscanner. The bCT x-ray tube and detector were either held stationary orrotated up to 415. The dose probe had a fixed position at the edge of theimaging field of view for COBRA acquisitions. The probe could also bemanually shifted for conventional profile measurements.Medical Physics, Vol. 38, No. 3, March 2011To convert the raw output signal into accurate values ofair kerma, a RadCal 9010 general-purpose ion chamber wasfixed at isocenter and the x-ray tube voltage and the currentwas varied as for the assessment of the probes linearity. Theion chamber was exposed for approximately 30 s and anexposure rate in R/min was measured. Assuming that thechambers response was linear, a simple transformation con-stant, nominally W=8.76 mGy /R,17 allowed the probesoutput voltage signal to be converted into air kerma inGy /s.

III.D. Bow tie filter characterizationIII.D.1. Profile estimation from a stationary source

To validate the COBRA method, dose profiles of the bCTscanners x-ray beam were measured manually with andwithout the BT filter see Fig. 5. The probe was translated12 cm along an axis perpendicular to the beams centralray and passing through the systems isocenter. To reduce theeffects of systematic drift, the probe was first translated inone direction and measurements were taken at x=2n dis-tances from isocenter, with 0n12. Once the final posi-tion was reached, the probe was translated back to its startingposition with measurements made at x=2n1 distances fromisocenter. For each observation, the probe was irradiated 5 sby an x-ray beam generated at 120 kVp, 7 mA. As with thelinearity measurements, the probes output signal trace wascropped and averaged to a single observation point. The rela-tive attenuation at a given fan angle was calculated as theratio of the probes output with the BT filter present M1 towithout the BT filter present M0 as described in Eq. 1,where =tan1x /s.

III.D.2. Profile estimation from a rotating sourceThe COBRA method detailed by Boone9 was performed

on the prototype bCT scanner, described previously Sec.III A. The DISC probe was positioned 8 cm from isocenter,at the edge of the field of view FOV of the bCT scanner, as

FIG. 5. Experimental setup for step-and-shoot measurements of a fan beamsrelative attenuation. The probes position was incremented from isocenterx=1 cm with steps in the fan angle of 1. Measurements wereacquired at each position with and without the bow tie filter in place.

1410 McKenney et al.: Validation of bow tie filter attenuation characterization method 1410depicted in Fig. 4. To estimate the bow tie thickness, dualenergy scans were conducted at 120 kVp/7 mA and 80kVp/11 mA. To assess the accuracy of the unfiltered beammeasurements, two more identical scans were made withoutthe BT filter. The maximum allowable source rotation wasused 415 and the probe was irradiated approximately 17.5s as a scan was executed. Because the probe was highlysensitive to repositioning, the probes position was held fixedthroughout all four runs. The data was collected at 100samples per second.

While the effect of the inverse square law was measureddirectly when the BT filter was removed from the setup, theeffect was also modeled using only the BT-filtered data, asoutlined in Sec. II. The maxima of the scans were estimatedusing a simple peak-finding algorithm that stepped along theobservation points of the probe. Essentially, peak intervalswere identified and the maximal value was the average of thedata points that were one standard deviation above the aver-age of the interval; this diminished the noise contributions tothe maxima while avoiding its underestimation. The positionof the maxima was the average position of the data pointscontributing to the maximal value. The period of rotation was computed from the difference of the two maxima. Thegantry angle was calculated for each observation pointfrom the period and observation time of the first maximum such that

=2t

, 5

where t is an observations timestamp and the caret notationdistinguishes an estimated value from a direct measurement.

The distance between the probe and isocenter was esti-mated r using source-to-isocenter distance s and the mea-sured signal M1 at t=0 and t= from

M1M10

=

s r2

s + r2

such that

r = s 1 M1M10

1 +M1M10

. 6Using the probes position, the flux at isocenter I0 was esti-mated as

I0 = M1 s rs or, equivalently, I0 = M10 s + r

s .7

The probes position was also used to estimate distance fromthe source g byMedical Physics, Vol. 38, No. 3, March 2011g = s2 + r2 2sr cos . 8Finally, using these estimated values, the unfiltered measure-ment M 0 was modeled at all gantry angles as described inEq. 2.

The estimated values of M 0 and the BT-filtered measure-ments M1 were used to calculate F as in Eq. 1, using thesystems geometry Fig. 1, to transform gantry angle intofan angle. The bow tie filter was assumed to be symmetric,such that F=F. Finally, the estimates of relative at-tenuation were binned and averaged in quarter-degree inter-vals of fan angle; a smoothing spline was then fit to theresults to better capture the smooth geometry of the BT filter.

After confirming that the model of the unfiltered sourcewas acceptable, the relative attenuation function was used toestimate the thickness of the bCT bow tie filter. TheTASMIP18 spectral model was used to calculate the relativeattenuation at each fan angle. The TASMIP-generated spectrawere calibrated from half value layer HVL measurementsmade on the bCT scanner at isocenter with a RadCal 9010ion chamber. A single basis material least-squares algorithmEq. 4 was used to estimate the thickness of a Teflon CF2bow tie filter. The mass attenuation coefficients for Teflonwere estimated using tabulated attenuation coefficients12 andthe photon fluence output was converted into kerma unitsGy. For each independent fan angle, a custom-writtenprogram varied the thickness of Teflon in 0.01 mm steps andthe thickness that minimized the 2 value was selected.

III.D.3. Clinical CT applicationsThe COBRA method was evaluated using the body BT

filter in a commercially available whole body scanner modelAS+, Siemens Medical Systems, Florsheim, Germany. Theprobe was positioned on a stand on the opposite side of thegantry from the patient table see Fig. 6. The active area ofthe probe was placed at the edge of the FOV of the system.Scans at several kVps were conducted. The scanning proto-cols for the abdominal scans, used to characterize the bodyfilter, were 80 kVp/100 mAs, 100 kVp/100 mAs, 120 kVp/50mAs, and 140 kVp/50 mAs. The slip ring construction of thescanner allowed for unlimited rotations of the source; conse-quently, a 10 s acquisition reflects approximately ten full

FIG. 6. Photograph of the experimental setup of the prototype x-ray probe inthe clinical CT scanner.

1411 McKenney et al.: Validation of bow tie filter attenuation characterization method 1411rotations of the gantry about the systems isocenter. Measure-ments were collected at 1000 samples per second.

The method of data analysis of the clinical CT scan wasthe same as for the bCT data, except that it was necessary toaccount for the much larger data set. The average period ofthe gantry rotation was computed from the difference be-tween the absolute maxima of the signal train. The measuredsignal M1, used for estimations of r and I0, was averagedwith M1+2n such that

M 1 =1N n=0

n=N

M1 + 2n , 9

where = 0, and N is the number of gantry rotation pe-riods. Estimates of F and BT filter thickness were deter-mined as in Sec. III D 2. Following the work of Lehmann,11PMMA and aluminum were chosen as two basis materials.BT filter thickness was determined under the assumption thatthe filter was composed entirely of one material, eitherPMMA or Al.

IV. RESULTSIV.A. Probe isotropy

In Fig. 7, the angular response of the prototype probe over2 is shown to be quite uniform. The average percent erroris 0.80% with a maximum of 0.92%, which is acceptable forthe purposes of this study. It should be noted that if the probeis held at a fixed angle, the relative error over a single signaltrain reduces to 0.2%. The variation in probe response atdifferent angular positions is most likely a result of both thepositioning method used to obtain the measurements as wellas the intrinsic properties of the probe.

IV.B. Probe linearity

The probes response, as a function of tube current, islinear Fig. 8, with r2=0.999 at both 80 and 120 kVp. Thelinear relationship between the prototype probes raw outputsignal, S in V, and the ion chambers air kerma rate, K in

0.96

0.97

0.98

0.99

1.00

1.0190

0

270

180

FIG. 7. Relative signal of the DISC probe as a function of the probes anglefor a stationary x-ray beam produced at 120 kVp/7 mA, N=4.Medical Physics, Vol. 38, No. 3, March 2011Gy /s, was determined to be KS=3993.1S3.6 r2=0.999 at 80 kVp and KS=3512.2S+4.6 r2=0.999 at120 kVp.

IV.C. Bow tie filter characterizationIV.C.1. Profile estimation from a stationary source

The fan beam profiles of the bCT scanner are depicted inFig. 9. The dose rate precision is relatively good with anaverage standard deviation of 5.1 Gy /s across all observa-tion points. There was a translational positioning error of 1mm, resulting in a fan angle error of 0.1. The asymmetryof the beam profile, at angles greater than 12, is the result ofasymmetric collimation of the cone beam; this was verifiedby measuring the profile of the uncollimated beam. Relativeattenuation analysis was limited to the imaging FOV, extend-ing 8.5. The relative attenuation of the bow tie filter wasused as the gold standard for the evaluation of the COBRAmethod.

IV.C.2. Profile estimation from a rotating sourceFigure 10 plots the registered measured air kerma rates

for the four runs as a function of gantry angle. As expected,there are only two angular positions of the source where thefiltered beam is unattenuated and matches the unfiltered

0.0

0.5

1.0

0 5 10 15

ProbeOutputSignal(V)

Tube Current (mA)

80 kVp

120 kVp

FIG. 8. Linearity of probe in the bCT scanner at varied values of tubecurrent r2=0.999; observation points have a standard deviation of 1 mV.

0

1

2

3

4

-15 -5 5 15

AirKermaRate(m

Gy/s)

Fan Angle (degrees)

M1M 0

8.5-8.5

FIG. 9. Profile traces of the bCT scanner using the conventional methoddepicted in Fig. 5, corrected for inverse square law effect. M1 traces theprofile of the bow tie filter, while M0 traces the unfiltered beam. Note thatthe interval of interest is 8.5, the imaging field of view.

2.50

1412 McKenney et al.: Validation of bow tie filter attenuation characterization method 1412beam, when t=0 and . As the source rotates through therest of the gantry positions, the bow tie filter dramaticallyattenuates the x-ray beam.

Using the method described in Sec. III D 2, the probesestimated position r from the two scans was 80.30.5 mmfrom isocenter; this is in very good agreement with themanually measured position of 80.01 mm from isocenter.Figure 11 is a plot of the correlation between the measuredM0 and estimated M 0 air kerma rates at 80 and 120 kVp;additional BlandAltman plots are inset. While the estimatedair kerma rates seem to be systematically higher than themeasured rates, the average relative difference between theestimated and measured data is 1.25% at 80 kVp and 1.26%at 120 kVp. The estimates exhibit adequate correlation withthe measured data; at 80 kVp, the r2=0.997 and at 120 kVp,the r2=0.995.

It is observed in Fig. 12 that the relative attenuation esti-mated using the COBRA method falls within the uncertaintyof the measurements made using the more traditional methodsummarized in Sec. III D 1. Figure 13 is a comparison ofthe estimated thicknesses to the known thickness as a func-tion of fan angle. The COBRA estimates of BT filter thick-ness compare well to thicknesses estimated from 1 thecomputer-aided design CAD drawings of the filter or 2

0.0

1.0

2.0

-45 0 45 90 135 180 225 270 315 360

AirKermaRate(mGy/s)

Gantry Angle (degrees)

(a)

0.0

1.0

2.0

3.0

4.0

-45 0 45 90 135 180 225 270 315 360

AirKermaRate(mGy/s)

Gantry Angle (degrees)

Unfiltered beam Filtered beam

(b)

FIG. 10. Raw output of the probes signal train at a 80 and b 120 kVp onthe bCT scanner with the Teflon bow tie filter black and without the bowtie filter gray. The unfiltered signal train was also estimated not depictedin the figure from the peaks of the measured signal with the bow tie filter.The estimated unfiltered signal was compared to the measured signal train inFig. 11.Medical Physics, Vol. 38, No. 3, March 2011from the simulation used as a basis for the CAD drawings.14The thickness estimates from the COBRA method had anaverage error of 1 mm. Because Teflon is highly scattering,the scatter-to-primary ratio dramatically increases with thethickness of the filter; consequently, the difference betweenthe COBRA estimate and CAD thickness climbs to 12 mm atfan angles larger than 8. Again, it should be noted that thisphenomena occurred near the edge of the FOV 8.5 of thedetector.

1.00

1.50

2.00

1.00 1.50 2.00 2.50

Estimatedsignal(mGy/s)

Measured signal (mGy/s)

-0.05

0.00

0.05

0.10

1.0 1.5 2.0 2.5

(a)

2.00

3.00

4.00

2.00 3.00 4.00

Estimatedsignal(mGy/s)

Measured signal (mGy/s)

-0.05

0.00

0.05

0.10

0.15

2.0 3.0 4.0

(b)

FIG. 11. Plot of the correlation between the measured and estimated airkerma rates for unfiltered beams at both a 80 and b 120 kVp. The linesignifies y=x, the ideal relationship between the model and measurement ofthe unfiltered beam. BlandAltman plots of the residuals are displayed asinsets.

0.0

0.2

0.4

0.6

0.8

1.0

0 2 4 6 8 10

F()

Fan Angle (degrees)

Conventional Method

COBRAMethod

FIG. 12. Comparison of the relative attenuation F of the two BT filtercharacterization methods for the bCT scanner at a tube voltage of 120 kVp.

1413 McKenney et al.: Validation of bow tie filter attenuation characterization method 1413IV.D. Bow tie filter characterization: Clinical CTapplications

An example of the raw signal train of the probe as theclinical CT gantry makes multiple revolutions is plotted inFig. 14; the modeled signal without a BT filter M 0 is alsoshown. The periodicity of the signal train reflects the rotationof the x-ray gantry; the consistency of peak maxima is in-dicative of the probes stationary positioning. The probe po-sition during the body scan was computed as r=240.52.5 mm. Figure 15 depicts the bow tie attenuationproperties derived for the body BT filter and the data areshown for 80, 100, 120, and 140 kVp. The continuous gantryrotation provides a multitude of samples, all within a single10 s acquisition; an average of 10 ,400 data points are plottedat each tube voltage. Figure 16 is a plot of the thickness ofthe body BT filter as estimated from the attenuation data.

V. LIMITATIONSWhile relative attenuation measurements from the CO-

BRA method match those made with the conventional step-and-shoot method, there are some limitations of the method.First, the algorithm that models M0 could be more robust.Currently, M 0 may differ significantly from the M0 measure-ments, particularly for scans with a limited number of gantryrotations. A linear regression plot of the model vs measure-

0

20

40

60

0 5 10

Thickn

ess(m

m)

Fan Angle (degrees)

ComputedThickness from CADCOBRA Method

FIG. 13. Comparison of BT filter thickness from the COBRA method to thecomputed thickness used for the filters design as well as its final CADdrawing.

0

2

4

6

8

10

12

14

0 2 4 6 8 10

AirKermaRate(mGy/s)

Time (s)

Unfiltered beam Filtered beam

FIG. 14. Raw output from the prototype probe in the clinical CT scanner forthe body filter at 120 kVp gray. The model unfiltered signal train is alsoincluded black; samples were acquired at 1000 Hz.Medical Physics, Vol. 38, No. 3, March 2011ment data from the breast CT signal train Fig. 11 revealsthat the slope m differs significantly from m=1 at 120 kVpand that the intercept differs significantly from zero at bothtube voltages when using a students t-test. Ideally, the modeland measurements should match at each data point. The mostobservable evidence of an imperfect model is a trend in theresiduals of nonlinearity and non-normality in the BlandAltman plots. These differences indicate errors in the esti-mates of both I0 and g; these errors primarily result fromslight errors in identifying the peak of the measured wave-forms. Fortunately, the residual differences using the CO-BRA method are small enough to have only a minor impacton the estimate of F. To achieve more robust results, thesignal train can be measured over a larger number of gantryrotations. Alternately, an iterative model-based solution tothe entire waveform may be sought, equivalent to one-dimensional iterative reconstruction techniques.

While estimations of the BT filters thickness were accu-rate, these estimates are dependent on a well-characterizedx-ray spectrum at F=0. One limitation of the experimen-tal setup was an inability to directly assess the HVL of thewhole body scanner. Optimized characterization of BT filterthickness across multiple CT scanners would be more robustif accurate kVp and HVL measurements were available.19,20While basis decomposition allows any material to be de-

FIG. 15. Estimated relative attenuation of the body filter on the clinical CTscanner before data have been binned and averaged.

0

20

40

60

80

100

0 5 10 15 20 25

FilterThickness(mm)

Fan Angle (degrees)

PMMA filter

Al Filter

FIG. 16. Estimated thickness of the bow tie filter for a body scan on theclinical CT scanner. Thicknesses were estimated for a filter made entirely ofeither PMMA black circles or Al white circles.

1414 McKenney et al.: Validation of bow tie filter attenuation characterization method 1414scribed as a function of basis materials, the thickness estima-tion will likely be more accurate when the composition ofthe BT filter is known. Moreover, care must be given toavoid inaccurate solutions, from describing materials with ahigh atomic number, or unrealistic solutions, such as nega-tive material thicknesses, when choosing basis materials.10

The COBRA method computes the BT filter thicknessesalong the fan angle, but assumes that the scanners filtrationin the z-dimension is constant as a function of fan angle.Most CT scanners have a measurable heel effect in thez-dimension, but the shape of this along z is the same at allfan beam angles . Filters to compensate for the heel effectcan be used and these would not compromise the accuracy ofthe COBRA method, as they would be invariant as a functionof fan angle. In general, a consistent beam profile along z, asa function of fan angle, is a necessary requirement for arti-fact free CT imaging.

VI. DISCUSSIONThis study describes the experimental validation of the

COBRA method, where the theory was developed previouslyand was illustrated used computer simulation.9 The results inthe current study demonstrate that a practical characteriza-tion of the BT filter attenuation and of the angle-dependentthickness can be made in the clinical environment.

It is anticipated that the primary utility of the COBRAmethod will be to characterize the angle-dependent thicknessof one or two component BT filters for the purposes ofMonte Carlo simulation studies. Another key advantage ofthis measurement technique is that since no proprietaryknowledge is used in the characterization, the beam-shapingcharacteristics of bow tie filters across scanner models andmanufacturers can be measured, discussed, and compared inthe open literature.

The COBRA technique requires that a real-time probe beused with temporal resolution on the order of approximately200 Hz2 kHz. There are a number of high bandwidth do-simeter systems that are currently available commercially; ingeneral, these systems are capable of importing the measuredwaveform directly into spreadsheet software. Currentlyavailable real-time dosimeters include both air ionization andsolid-state systems. All dosimeters have energy dependenciesand techniques for correcting for their energy dependence arenecessary to achieve similar results across dosimeters. His-torically, dose measurement has been performed using airionization chambers; nevertheless, it is noted that the energydependence of solid-state scintillator based dosimeters bet-ter represents the energy dependence of the detectors in theCT scanners. Thus, for solid-state detector systems, the com-puted attenuation curve F will be a good match to theactual response of CT detectors to the BT filter. The fact thatthe measured data are normalized with respect to each otherin the COBRA method means that only relative values, notabsolute x-ray beam intensity values, are used. This reducesbut does not eliminate the energy dependence of the com-puted F functions.Medical Physics, Vol. 38, No. 3, March 2011The COBRA method, as described here, requires the sen-sitive region of the dosimeter to be fully contained within thewidth of the CT beam along the z-dimension. Given the in-creasing beam width of modern CT scanners, this should notbe a problem. We are also interested in characterizing thex-ray beam profile along the z-dimension of the scanner and,combined with the F measurements determined from theCOBRA method, achieving a comprehensive understandingof the beam properties emitted from the x-ray tube assemblyin CT systems.

VII. CONCLUSIONSThe COBRA method of characterizing the angle-

dependent attenuation properties of a bow tie filter was com-pared against time-consuming step-and-shoot measurementtechniques and excellent agreement was demonstrated. With-out revealing proprietary information, the attenuation fea-tures of a CT beam-shaping filter are described from a seriesof 10 s scans performed at four different tube voltages. Ad-ditionally, the thickness of a bow tie filter can be estimated towithin 10% of the manufacturing specifications. While thistechnique can noninvasively and rapidly characterize the BTproperties of any commercial whole body CT scanner, it re-lies on a dependable definition of the scanners distance fromsource to isocenter or probe to isocenter as well as state ofthe art, real-time dosimetric hardware. In particular, thismethod requires a linear-response dose probe with high tem-poral frequency, real-time output, and an isotropic detectionvolume that fits well within the collimated width of the scan-ners x-ray beam. Further experimental work is necessary toextend characterization in the z-direction.

ACKNOWLEDGMENTSThis research was funded from the National Institutes of

Health Grant No. R01 EB002138 and also by a grant fromthe UC Davis Health system. The authors would like tothank Dr. J. Anthony Seibert, Ph.D. University of Califor-nia, Davis for his advice and assistance with the use of theclinical CT scanner.

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