Page 1

Attenuation-emission alignment in cardiac PET/CT based

on consistency conditions

Adam M. Alessio,a?Paul E. Kinahan, and Kyle M. Champley

Department of Radiology, University of Washington Medical Center, 4000 15th Avenue NE, Box 357987,

Seattle, Washington 98195-7987

James H. Caldwell

Division of Cardiology, University of Washington Medical Center, 1959 NE Pacific Street, Box 356113,

Seattle, Washington 98195-6113

?Received 2 September 2009; revised 21 January 2010; accepted for publication 21 January 2010;

published 19 February 2010?

Purpose: In cardiac PET and PET/CT imaging, misaligned transmission and emission images are a

common problem due to respiratory and cardiac motion. This misalignment leads to erroneous

attenuation correction and can cause errors in perfusion mapping and quantification. This study

develops and tests a method for automated alignment of attenuation and emission data.

Methods: The CT-based attenuation map is iteratively transformed until the attenuation corrected

emission data minimize an objective function based on the Radon consistency conditions. The

alignment process is derived from previous work by Welch et al. ?“Attenuation correction in PET

using consistency information,” IEEE Trans. Nucl. Sci. 45, 3134–3141 ?1998?? for stand-alone PET

imaging. The process was evaluated with the simulated data and measured patient data from

multiple cardiac ammonia PET/CT exams. The alignment procedure was applied to simulations of

five different noise levels with three different initial attenuation maps. For the measured patient

data, the alignment procedure was applied to eight attenuation-emission combinations with initially

acceptable alignment and eight combinations with unacceptable alignment. The initially acceptable

alignment studies were forced out of alignment a known amount and quantitatively evaluated for

alignment and perfusion accuracy. The initially unacceptable studies were compared to the pro-

posed aligned images in a blinded side-by-side review.

Results: The proposed automatic alignment procedure reduced errors in the simulated data and

iteratively approaches global minimum solutions with the patient data. In simulations, the alignment

procedure reduced the root mean square error to less than 5 mm and reduces the axial translation

error to less than 1 mm. In patient studies, the procedure reduced the translation error by ?50% and

resolved perfusion artifacts after a known misalignment for the eight initially acceptable patient

combinations. The side-by-side review of the proposed aligned attenuation-emission maps and

initially misaligned attenuation-emission maps revealed that reviewers preferred the proposed

aligned maps in all cases, except one inconclusive case.

Conclusions: The proposed alignment procedure offers an automatic method to reduce attenuation

correction artifacts in cardiac PET/CT and provides a viable supplement to subjective manual

realignment tools. © 2010 American Association of Physicists in Medicine.

?DOI: 10.1118/1.3315368?

Key words: cardiac PET/CT, Radon consistency, attenuation correction, attenuation artifact

I. INTRODUCTION

The goal of this work is to improve the attenuation-emission

alignment in cardiac PET/CT imaging. Misaligned attenua-

tion correction can result in artifacts and quantitative errors

incardiac PETimages.

attenuation-emission scans are common with conventional

PET imaging in which attenuation maps are formed over

multiple respirations with a transmission rod source ?21% of

conventional cardiacPET

attenuation1?. The potential for misalignment/artifacts is fur-

ther increased in dual modality PET/CT systems since the

CT scan provides the attenuation map. This CT scan is often

performed as a rapid helical acquisition imaging a snapshot

of the respiratory cycle, whereas the PET image is acquired

Artifactsfrom misaligned

caseshaveartifacts from

over multiple respirations. Misalignment of these temporally

different scans is common and often occurs in the diagnostic

region of interest ?along the anterior and lateral free walls of

myocardium adjacent to the left lung?, leading to moderate to

severe perfusion artifacts in 40% of cardiac PET-helical CT

acquisitions.2These misalignment artifacts are well appreci-

ated in cardiac PET/CT3,4and have been shown to cause

myocardial uptake errors of up to ?35% over conventional

cardiac PET imaging in which attenuation maps are formed

over multiple respirations with a transmission rod source.5

Several approaches have been proposed to minimize these

artifacts. Groups have explored the option of performing the

CT scan at an optimal time during respiration, such as at

midexpiration, to minimize potential mismatches.5,7Our

1191 1191Med. Phys. 37 „3…, March 20100094-2405/2010/37„3…/1191/10/$30.00© 2010 Am. Assoc. Phys. Med.

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clinical experience has found that asking a patient to hold his

or her breath at a certain point in the respiratory cycle causes

highly variable results. Another approach is to acquire mul-

tiple helical CT scans for each PET acquisition with the ex-

pectation that at least one of the CT scans will be aligned

with the PET data.8Athird solution is to form the attenuation

map with a cine CT acquisition, which acquires multiple

low-dose CT scans over a period of time at each slice in the

patient. The average or intensity maximum of these cine im-

ages can be used to reduce the potential of artifact-forming

mismatches.9,10

If a mismatch is evident, some vendors offer realignment

tools to fix major errors. These realignment tools provide a

user interface to manually shift the attenuation map until the

user perceives that the attenuation and emission images are

aligned. These tools are nonoptimal for two key reasons.

First, it is a subjective process to visually align three-

dimensional volumes with different intensity values. Some

efforts have attempted to perform image-based registration

of the CT and PET image based on alignment metrics such as

mutual information11or based on dedicated segmentation

and registration schemes.12These image-based registration

methods remove the subjectivity of user intervention. Both

the manual and automatic image-based registration methods

are nonoptimal because the attenuation image is aligned with

the attenuation corrected emission image formed from poten-

tially flawed attenuation correction. The flaws manifest

themselves as artifactual boundary regions that are the pri-

mary regions of interest for determining alignment. Artifac-

tual regions will confound manual and automatic methods.

The main motivation for the effort in this paper is to improve

upon the image-based realignment tools with an objective

data-driven method, leading to reproducible attenuation cor-

rection alignment.

The quality assurance of the attenuation and emission

alignment by a trained user is an important step in cardiac

PET/CT imaging. The proposed method could provide an

initial improved alignment and more accurate attenuation

corrected PET image for the user, who could then ensure

acceptable alignment and make minor shift adjustments as

necessary. In this “just-enough-information” ?JEI? approach,

a user interacts with the quality assurance of the alignment as

little as possible while still ensuring clinically acceptable re-

sults. It has been shown that minimizing user input with JEI

approaches reduces processing time and intra- and interop-

erator variability.13

In this work, we developed and tested a method for auto-

mated alignment of attenuation and emission data. The align-

ment process is driven by the Radon consistency conditions

on the emission data and derives from previous work by

Welch et al.14For this process, the optimal rigid-body trans-

formation of the attenuation image volume is found, which

results in the most consistent attenuation corrected emission

data and improved attenuation-emission alignment. In a

follow-up to their original work, Bromiley et al.15proposed

the alignment approach for stand-alone PET systems with

attenuation maps from a rotating rod source and presented

results with simulation and phantom studies. Our current

work extends their efforts by applying the approach to

PET/CT systems and demonstrating efficacy with patient car-

diac exams. We test the process with the simulated data and

measured patient data from ammonia cardiac PET/CT ex-

ams.

II. ALIGNMENT METRIC

The attenuation image, formed from scaling the CT image

volume to attenuation coefficients at PET energy,16is aligned

with the PET emission image by applying rigid-body trans-

formations until the attenuation corrected PET data minimize

an alignment metric based on the two-dimensional ?2D? Ra-

don consistency conditions. In this work, we enforce the first

three moments of the Helgason–Ludwig consistency condi-

tions on 2D Radon transforms in a method originally pro-

posed by Welch et al.14Their method uses Natter’s formula-

tion of the consistency conditions

?m,k=?

0

−?

2??

?

smeik?eA?s,??E?s,??dsd?,

?1?

where E?s,?? are the measured data, A?s,?? are the projec-

tions of the attenuation image, m?0 is the moment being

computed, and k is Fourier component.17The radial distance

from the center of rotation s and the azimuthal angle of ro-

tation ? index the Radon transform space.

If the attenuation corrected projection data are consistent,

?m,k=0 when k?m or when k+m is odd. This relationship is

a result of the fact that the moments of projections through

an object are periodic in azimuthal angle. We present a proof

of Eq. ?1? in the Appendix; to the best of our knowledge, this

is a new proof of this well-accepted relationship. Figure 1

plots the projection moments ?inner integral over s in Eq.

?1?? for noise-free data versus azimuthal angle. The zero-

order moment of the consistency conditions states the well

FIG. 1. Moments of noise-free projection data versus azimuthal angle bin

reveal the periodicity of higher order moments and conceptually support the

proposed formulation of the Radon consistency conditions. Curves are pre-

sented in normalized units.

1192 Alessio et al.: Attenuation-emission alignment in cardiac PET/CT1192

Medical Physics, Vol. 37, No. 3, March 2010

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known property that the sum of the projection data for each

view of a set of parallel-beam projections is a constant, in-

dependent of the projection angle. The zeroth moment in Fig.

1 shows that the sum of projections is the same at all angles.

The first order moment shows that the projections of the

center of mass in the object ?a single point? form a sine wave

with period one in the sinogram. The second moment plot

reveals a sine wave with period 2; the third contains sine

waves with periods 1 and 3. Likewise, higher order moments

result in combinations of sine waves with greater periodicity.

If projections are inconsistent, the moments will contain

higher frequency information. The outer integral of Eq. ?1?

performs the Fourier transform of these moments; if the Fou-

rier coefficients greater than the moment ?k?m? have val-

ues, then the projections are inconsistent.

Bromiley et al.,15in a follow-up to their original work,

used these conditions to perform attenuation-emission align-

ment in conventional PET imaging through transformations

of a flawed ?misaligned? attenuation image. In this work, we

modify their method for use with cardiac PET/CT imaging.

We find the CT derived attenuation image which minimizes

the objective function defined as

?ˆ=?

z?

m=0

2

?

k=?Cm?

?m,k?z?,

?2?

where ?m,k?z? is calculated for each transaxial slice z. The

set of coefficients Cm varies for each moment as C0

=?1,...,9?, C1=?0,2,...,9?, C2=?1,3,...,9?. The sum-

mation range of m and k is a potentially adjustable parameter

in this objective function. After application to several patient

PET data sets, we determined that the optimal alignment

parameters essentially do not change with the incorporation

of larger ranges for moments or Fourier coefficients.

III. OPTIMIZATION ALGORITHM

The search for the optimally aligned attenuation map is

performed with a simplex algorithm.18In our method, the

algorithm is optimized over six rigid-body transformation

variables: Volume translations in x,y,z and rotations around

the x,y,z axes. A single PET field of view ?FOV? spans

approximately 15 cm in the z direction. In this work, we

enforce the consistency conditions over the central 12 cm

?central slices? to apply alignment in the problematic regions

for cardiac imaging ?mediastinum and right diaphragm? and

to allow for errors at the edge of the axial FOV as the at-

tenuation image is translated and rotated out of the FOV.

Furthermore, most mismatch of attenuation/emission images

in PET/CT occurs because of respiratory motion, which is

primarily a z axis translation. We modified the simplex opti-

mization to preferentially search the z translation space and

allow for greater variation in the z translation than the other

variables. As the attenuation map is shifted out of axial

slices, we replace voxels with replicates of the nearest slice

to ensure that there is an attenuation map for all slices.

IV. METHODS

IV.A. NCAT simulations

In order to evaluate the performance of the alignment al-

gorithm at different noise levels and different initial mis-

aligned attenuation maps, we performed PET simulations

basedon the NURBS-based

phantom.19We generated emission and attenuation maps.

Voxelized realizations of the activity and attenuation were

forward projected into 2D PET data with a geometry and

sampling similar to clinical PET scanners. Photon attenua-

tion was added to the emission data and 20% scattered and

random coincidences were modeled as a uniform additive

term. The resulting emission distribution was scaled to five

different levels before adding Poisson noise to model acqui-

sitions with 1?108, 5?107, 2.5?107, 1?107, and 1?106

total events. The maximum event number roughly matches

the number of events in a typical clinical cardiac PET am-

monia acquisition with 10 mCi injected and imaged 5 min

postinjection for 15 min. As a result, these event levels rep-

resent typical clinical levels down to 1/100 the typical num-

ber of events. To evaluate reproducibility of alignments, we

simulate five independent and identically distributed noise

realizations of each noise level.

We attempted to align three variations in the attenuation

map with the simulated emission data. First, we start with a

matched attenuation map to ensure that the alignment proce-

dure does not estimate an erroneous transformation. We also

applied rigid transformations to the map consisting of an

x translation=10 mm and z translation of +15 mm ?mist-

match 1? and an x translation=−10 mm and z translation of

?15 mm ?mistmatch 2?.

The attenuation maps were automatically aligned with the

simulated emission data with the proposed method. In total,

the three different attenuation maps were aligned with the

five noise realizations of five different event levels for a total

of 75 different scenarios. The root mean square error

?RMSE? of the three translation dimensions and the error in

the z axis translation in the resulting aligned attenuation map

are reported.

cardiactorso

?NCAT?

IV.B. Single patient studies

To explore the basic behavior of the proposed method, we

applied the method to a few single patient studies. We first

tested the alignment process with two sets of patient data

from N13-ammonia cardiac perfusion PET/CT studies. These

studies were performed on a General Electric Healthcare

?Waukesha, WI? DSTE PET/CT scanner in 2D mode. The

attenuation map and emission projection data were extracted

for offline processing. The emission data were corrected for

all physical effects ?random, normalization, dead time, and

scatter? except attenuation using the product estimates. The

scatter estimate was derived from the initial attenuation map.

Considering that scatter is very smoothly varying, we assume

that the initial estimate will not change significantly for the

up to 2 cm transformations that will be applied, so we use the

initial estimate for the entire alignment process. All image

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Medical Physics, Vol. 37, No. 3, March 2010

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transformations and reconstructions were performed with

custom software ?not with the product reconstruction en-

gine?.

Patient A is a study with “correct” attenuation-emission

alignment, as deemed by visual inspection of attenuation and

emission images. With this realistic noise study, we first

evaluated the behavior of the objective function with mul-

tiple transformations. There are six transformation dimen-

sions to explore; we performed exhaustive searches of the

value of the objective function for z translations ?our expe-

rience shows that this is the dimension with greatest fre-

quency of misalignment?, x translations, and rotation around

the z axis. To assess the values of different orders of mo-

ments, we forced a 16 mm inferior translation on the attenu-

ation map and evaluated the objective function to determine

the presence of local minimum. Second, we forced an arbi-

trary ?x,y,z? translation=?−16.4,−10.9,19.6? mm and rota-

tion around ?x,y,z? axis=?3°,0°,1°? for the attenuation

map. This misaligned map was the starting map for the sim-

plex search for the optimal transformation.

Patient B is a study with initially misaligned attenuation

and emission images, as determined by visual inspection. We

performed the simplex search for 70 iterations to find an

“aligned” attenuation map.

IV.C. Multiple patient studies

To evaluate reproducibility, we tested the proposed

method with the patient data from six N13-ammonia cardiac

PET/CT exams. In this study approved by the University of

Washington Institutional Review Board, we enrolled patients

?98?28 kg? referred for cardiac PET perfusion exams for

routine clinical evaluation. Five patients received both a rest

and stress PET exam and one patient received only a rest

exam ?total of 11 exams?. Each rest/stress exam had two

separate cine CT scans ?one exam had only one cine CT

scan? ?total of 21 CT acquisitions?. The average and intensity

maximum10of these cine acquisitions lead to n=42 separate

emission-attenuation combinations. All exams were per-

formed with quiet tidal breathing. These combinations were

evaluated by three independent reviewers, who scored the

alignment as unacceptable ?visible emission artifacts due to

attenuation mismatch?, borderline ?possible artifacts?, or ac-

ceptable ?no artifacts?. Through this scoring procedure, eight

combinations from five different patients were scored accept-

able and eight combinations from four different patients were

scored as unacceptable by all reviewers.

Similar to patient A above, the eight acceptable combina-

tions were tested by forcing a known transformation on the

attenuation map, evaluating the ability of the automatic algo-

rithm to return the map back to the acceptable alignment. We

applied a ?x,y,z? translation=?10.9,−10.9,13.1? mm and

rotation around ?x,y,z? axis=?0°,0°,−3°? on the attenua-

tion maps. We compared the sum of the RMSE of each trans-

formation dimension after the proposed realignment. There-

fore, each case started with a known RMSE error of 11.7 mm

and 3°. Using custom reorientation and segmentation soft-

ware based on prior work,6we generated polar maps of the

reoriented PET images attenuation corrected with the origi-

nal acceptable map, the forced misaligned map, and the au-

tomatically aligned map. The polar maps were divided into

17 segments.20In each segment, we computed the ratio of

the misaligned AC PET polar map with the original AC PET

polar map and the ratio of the automatically aligned AC PET

polar map with the original AC PET polar map. Since

nuclear perfusion images are evaluated clinically based on

the relative perfusion of each segment, this ratio comparison

provides a clinically relevant evaluation of the quantitative

impact of misaligned attenuation.

Similar to patient B above, the eight unacceptable combi-

nations were aligned with the proposed algorithm. We recon-

structed images with the original unacceptable attenuation

map and with the attenuation map after the proposed algo-

rithm. Two independent observers reviewed the originally

unacceptable emission/attenuation images and the automati-

cally aligned emission/attenuation imaged. In a custom re-

view software, both the original and autoaligned emission

and attenuation images were presented simultaneously in a

blinded fashion. The observer selected the preferred align-

ment combination.

V. RESULTS

V.A. NCAT simulations

Figure 2 presents attenuation maps and attenuation cor-

rected reconstructions ?filtered backprojection with 12 mm

Hanning filter? of one simulation study with 2.5?107events.

The proposed method improved the alignment of the emis-

a) Truthb) Mismatch 1 c) Aligned

FIG. 2. Coronal views of simulations of cardiac PET/CT study. The attenuation images ?row 1? provided attenuation correction for the PET images ?row 2?

simulated with 2.5?107events ?roughly 1/4 typical number of events?. Column ?a? contains true attenuation correction. Column ?b? contains mismatched

attenuation correction that was aligned with the proposed method to generate results in column ?c? containing reduced artifacts. The attenuation maps have

matched colormaps and the PET images have matched colormaps.

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sion and attenuation images and removed the artifacts due to

attenuation errors, particularly in the mediastinum.

Table I summarizes the mean alignment errors along with

the standard deviation of the error across the five noise real-

izations for each scenario. The patient studies evaluated in

this work had a mean of 2?108events, as discussed in Sec.

V C below. As a result, 2.5?107–1?108events can be con-

sidered a conservative range for clinically relevant count lev-

els. In this range, the alignment procedure reduced the

RMSE to ?4.3 mm and the z-axis error to ?1.4 mm. When

the events levels are an order of magnitude less than clinical,

the z-axis error was greater ??2.6 mm? and the standard

deviation of the error increased demonstrating that the align-

ment is less reproducible at higher noise levels. In the case of

extreme noise ?1?106events?, the RMSE is not improved,

although the z-axis error is reduced to ?4.4 mm on average.

For all cases, the error in the rotation variables was less than

1°, which can be considered negligible.

V.B. Single patient studies

For patient A with a 16 mm forced z translation, the value

of ?ˆas a function of z translation of the attenuation image is

presented in Fig. 3. The value of the objective function

across two transformation parameters, with the other param-

eters fixed, appears in Fig. 4. This offers some insight into

the behavior of the objective function for a single patient but

does not take into account the effect of the other transforma-

tion dimensions. For this example, the objective function is

well behaved with no local minimum in the range of interest.

The variation in slope as the minimum is approached from

different directions suggests that the choice of initial values

for the transformation will affect the rate of convergence for

this application.

We also performed the full alignment optimization for

patient A when the attenuation map was given a known mis-

alignment. After 150 iterations, the simplex algorithm had

fully converged to the estimated alignment transformation of

?x,y,z?translation=?21.8,7.1,−25.7? mm androtation

FIG. 3. Objective function values for patient A as a function of translation in

axial location with the other transformation dimensions fixed. Plots the val-

ues of Eq. ?2? for different moments and for the sum of moments m

=0,1,2. These curve shows that the objective function is well-behaved for

this patient and for this dimension. The minimum should occur at approxi-

mately ?1.6 cm since we forced a translation of 1.6 cm on the original

aligned data.

TABLE I. Error in alignment parameter estimates for NCAT simulations of multiple initial misalignments and noise levels. Mean ?std? across five noise

realizations.

Initial AC map

Initial RMSE

?mm?

RMSE ?mm? of aligned AC map—Different count levels

1?108events5?107events 2.5?107events1?107events1?106events

Matched

Mismatch 1

Mismatch 2

0

10

10

0.4?0.3?

0.9?0.4?

3.8?0.9?

0.4?0.1?

1.0?0.3?

4.2?0.0?

0.8?0.2?

0.9?0.0?

4.3?0.1?

2.8?1.1?

5.1?1.3?

4.9?0.7?

6.4?3.5?

11.2?2.0?

9.3?6.9?

Initial Z error

?mm?

0

15

?15

Z ?mm? error of aligned AC map

0.3?0.3?

1.4?0.3?

0.8?0.3?

Matched

Mismatch 1

Mismatch 2

0.2?0.3?

0.7?0.8?

0.3?0.7?

0.3?0.1?

1.1?0.4?

0.5?0.2?

1.8?0.9?

1.2?0.6?

2.6?0.6?

3.7?3.8?

4.4?1.0?

3.7?0.1?

−3.8

−3.8

−2.9

−2.9

−2

−2

−2

−1.1

x translation (cm)

rotation around z axis (degrees)

−6−4−20246

−8

−6

−4

−2

0

2

4

6

minimum value

FIG. 4. Contours of objective function values for patient A as a function of

rotation around z and translation in x with the other transformation dimen-

sions fixed. This case started with the original aligned data and the minimum

should occur at approximately ?0,0?.

1195Alessio et al.: Attenuation-emission alignment in cardiac PET/CT 1195

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around ?x,y,z? axis=?−1.1°,1.5°,−0.5°?. These values

haveadifference of

?x,y,z? translation=?5.3,−3.8,

−6.1? mm and rotation ?x,y,z?=?1.9°,1.5°,0.5°? with the

forced misalignment, representing an improved alignment.

Furthermore, assessment of the images in Fig. 5 show that

the automatically aligned attenuation map reduces artifacts in

the attenuation corrected PET image, particularly along the

lateral wall.

In patient B, the proposed method successfully aligned

the attenuation image as presented in Fig. 6. Note the major

artifacts in the emission image when using a mismatched

attenuation image and the lack of these errors in the aligned

image.

V.C. Multiple patient studies

In all patient combinations representing a range of patient

sizes and noise levels, the proposed method reproducibly

converged to single solutions of aligned attenuation maps.

The patient cohort enrolled in this study had a weight of

96?28 kg, a BMI of 32?7 kg/m2, and included 5 males

and 1 female. For the originally acceptable attenuation/

emission studies with a known forced transformation, the

proposed algorithm was able to reduce the error of the forced

transformation. When the known translation was applied, the

RMSE of the translation parameters was 11.7 mm for all

patients ?all patients received same transformation?. The av-

erage of the RMSE of the translation parameters across pa-

tients after proposed alignment was 6.6 mm. Table II sum-

marizes the alignment errors. In one case ?combination 3?,

the proposed algorithm estimated a rotation in the wrong

direction ?4.3° error?, but reduced the error in the translations

and resulting PET image as discussed below.

The polar maps for two representative patients are shown

in Figs. 7 and 8. The PET image formed with the original

acceptable aligned AC appears in the top row, followed by

the map after a forced misalignment and the map after the

automatic alignment. Assuming that the PET image formed

with the original AC is truth, the ratio of the PET image

formed with alternate AC to the original quantifies the rela-

tive error. The ratio images show that the forced misalign-

ment caused an inferior wall artifact, with a 30% reduction in

the apparent uptake. The automatic alignment resolved this

artifact. Figure 8 presents polar maps for the patient with the

most realignment error. Despite the realignment error and the

introduction of a mild basal inferior error, there is no clini-

cally relevant difference between the autoaligned AC image

and the original AC image. The average across the eight

studies for each segment is shown in Fig. 9 along with the

complete segmental values plotted in Fig. 10. The misaligned

AC PET image had, on average, a 30% reduction in the

inferior wall, which would be considered an artifactual mild

perfusion defect. All of the alignment methods removed this

artifact. The average and standard deviation of the ratio im-

ages are presented in Table II, confirming that the error and

variation in error is reduced for all patients with the auto-

matic method.

For the side-by-side blinded comparison of the eight

originally unacceptable attenuation/emission combinations,

the two reviewers preferred the combination after the pro-

posed algorithm in all cases, except one in which a single

observer was unable to see a significant difference between

the original and proposed. This evidence supports the argu-

ment that the proposed algorithm provides improved align-

ment.

V.D. Algorithm computation performance

The current implementation of the proposed alignment al-

gorithm has not been optimized for computational complex-

(b)(a)

FIG. 6. Coronal views of reconstructed images from patient B ammonia

PET/CT study. Column ?a? presents the original attenuation map ?row 1?,

attenuation corrected PET image ?row 2?, and fused PET/CT image. Column

?b? presents the images after alignment with the proposed method. The

alignment process reduced the incorrect attenuation correction values along

the lateral free wall, removing the artifactual perfusion defect in the PET

image. The cross hairs are triangulated to the same location in all images

highlighting the lateral free wall of the myocardium.

(a)“Correct” Attenuation (b) Mismatched Attenuation (c) Aligned Attenuation

FIG. 5. Coronal views of a cardiac ammonia PET/CT study from patient A. The PET images ?row 2? were attenuation corrected with the corresponding

attenuation images from row 1. The original CT scan provided reasonable attenuation correction, as deemed by visual inspection and is labeled correct ?a?. We

shifted the attenuation image to force a mismatch ?column b?. The alignment process successfully aligned the attenuation image ?column c? with the emission

data. Note that in column ?b? the PET myocardium appears in the CT lung space and chest wall, leading to artifacts throughout the lateral wall in the PET

image.

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ity. The steps for each evaluation of the objective function

include ?1? rigid-body transform the attenuation volume, ?2?

forward project, ?3? apply attenuation correction to emission

data, ?4? compute moments of AC emission data, ?5? FFT the

moments in ?, and ?6? compute the objective function value.

In the clinical patient studies presented here using 8?105

image voxels and a projection space with 4?106entries,

each function evaluation took 3 s on a 2.3 GHz PowerPC G5.

A total optimization with 150 simplex iterations required 8

min.

TABLE II. Error in alignment parameter estimates and AC PET polar map values for patient combinations with initially acceptable attenuation maps that were

transformed a known amount and then automatically aligned.

Patient combination

Error transformation Ratio AC PET to initial AC PET

Number events

z rotation

?deg?

Translation

?mm?

Mean ?std? of 17 segments

xyz

RMSE Autoalign ACMisaligned AC

1

2

3

4

5

6

7

8

4.8?108

7.0?107

2.0?108

6.7?107

8.6?107

2.0?108

1.4?108

3.2?108

2.0?108

?2.3

?2.4

?4.3

0.5

?3.0

?2.9

?2.8

?0.4

?2.2

?3.0

?3.8

2.2

?0.3

?5.5

0.5

?3.7

15.1

?3.9

0.1

10.9

?3.9

?4.6

?14.0

11.7

?7.7

?10.1

4.5

8.6

8.0

4.1

5.8

9.3

7.5

5.4

6.8

10.8

2.9

6.6

11.7

1.01?0.02?

0.96?0.04?

1.00?0.04?

1.00?0.03?

1.01?0.06?

1.01?0.04?

1.06?0.07?

0.98?0.05?

1.00?0.03?

0.84?0.09?

0.92?0.15?

0.92?0.11?

0.97?0.05?

0.86?0.21?

0.92?0.11?

0.95?0.11?

0.89?0.11?

0.91?0.04?

?0.9

5.4

4.7

10.1

1.5

5.3

13.1

4.2

2.6

Mean

?2.7

?10.9 Applied transformation

FIG. 7. Polar maps for a patient combination 1 showing the AC PET data

with originally aligned map, after forced misalignment ?row 2?, and after

proposed alignment ?row 3?. Ratio maps in the second column show that

forced misalignment causes a clear AC artifact. After proposed alignment,

there are no AC artifacts. In the first column, each polar map has its color

range scaled to its maximum value to correspond to clinical qualitative

presentation of a polar map.

FIG. 8. Polar maps for a patient combination 7, showing the AC PET data

with originally aligned map, after forced misalignment ?row 2?, and after

proposed alignment ?row 3?. Ratio maps in the second column show that

forced misalignment causes a clear AC artifact. This study had the most

realignment error ?RMSE of 10.8 mm? with the known transformation. The

alignment resolved the apical and basal anteroseptal errors, but reversed the

basal inferior error.

1197Alessio et al.: Attenuation-emission alignment in cardiac PET/CT1197

Medical Physics, Vol. 37, No. 3, March 2010

Page 8

VI. DISCUSSION

Simulation and patient data demonstrate the efficacy of

the proposed alignment scheme. A reasonable concern with

the proposed method is whether the consistency criterion of-

fers a sufficiently strong metric to drive an optimization of

transformation parameters in the presence of the noise levels

in cardiac PET exams. In simulation studies with a clinical

range of count levels ??2.5–10??107events?, the proposed

algorithm reduced the misalignment to less than 5 mm

RMSE. Likewise, in all patient studies, the proposed algo-

rithm converged to improved alignment parameters, showing

that the method works across a range of data noise levels and

patient sizes. We choose to simulate very low count studies,

such as 1/100 the clinical level ?1?106events?, to demon-

strate that the algorithm will eventually fail to improve align-

ment in the presence of extreme noise.

In multiple patients with originally acceptable alignment,

we showed that the proposed method can recover known

rigid-body translations and attenuation correction artifacts in

the emission images. The automatic alignment procedure re-

duced the RMSE in the translation parameters by, on aver-

age, 40%. These results are not the true reduction in mis-

alignment because we are using a potentially flawed truth

based on the visual perception. As a result, the quantitative

reduction in translation errors should not be accepted as ab-

solute.

The simulation and patient evaluation does not test the

ability to recover from potentially more realistic nonrigid

misalignments. In practice, we assume that the attenuation

image is relatively well-aligned with the emission data and

simple rigid-body changes account for most of the mismatch

errors. This assumption is not accurate in some extreme

cases, such as this full inspiration to full expiration align-

ment. At present, the clinically accepted solution for mis-

alignment is manual rigid-body translations. The proposed

method could complement this manual procedure.

For patient cases with unacceptable alignment, the pro-

posed method can automatically improve alignment between

0.97

0.88

0.80

0.71

0.84

0.97

1.02

0.98

0.92

0.81

0.91

1.02

1.03

0.92

0.80

0.950.91

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.00

1.02

1.00

1.04

0.99

0.97

0.99

1.02

1.04

1.04

1.00

0.98

0.99

1.02

1.02

0.981.00

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

(b)(a)(c)

FIG. 9. ?a? Seventeen segment nomenclature. ?b? Ratio polar plots of the misaligned to truth and ?c? automatic alignment to truth values. The plots present the

average ratio in each segment across the eight combinations. On average, the alignment method returned all segments to the original true value.

246810121416

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

segment number

forced misalignment/truth

246810121416

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

segment number

automatic alignment/truth

FIG. 10. Plot of the ratio of misaligned to truth ?left? and automatic aligned to truth ?right? for 17 segments for all eight patient combinations. The left plot

reveals artifact causing defects particularly in mid- and basal inferior segments. Alignment method removes defects as shown in the right plot.

1198Alessio et al.: Attenuation-emission alignment in cardiac PET/CT1198

Medical Physics, Vol. 37, No. 3, March 2010

Page 9

attenuation and emission data according to human observers.

These results suggest that the proposed method could supple-

ment the current standard of practice which is a manual

alignment tool requiring subjective user intervention. We

were unable to rigorously prove that the proposed method is

superior to the manual tool because our initial subjective

evaluation of attenuation-emission alignment with multiple

observers led to highly variable results. For example, in the

initial read of the acceptability of attenuation-emission com-

binations by three independent viewers, the interobserver

variability in the scores was ?40%. These observations con-

firm visually rating alignment is highly subjective and that a

subjective manual alignment tool can lead to highly variable

attenuation-emission alignments. This variability supports

the need for an automatic approach such as the one proposed

here that could at least provide an initial improved alignment

to reduce the variability inherent with user interaction. Fur-

thermore, the proposed method leads to an attenuation cor-

rected PET image with reduced attenuation misalignment ar-

tifacts that could serve as a better image for attenuation-

emission quality control.

The consistency conditions for the Radon transform are

only accurate for continuous data with zero-width lines of

response with uniform sensitivity. Herraiz et al.21showed

that small animal PET systems with their finite width, asym-

metric responses are not “ideal” and that the consistency

conditions are only approximately valid. We assert that our

proposed use of the consistency conditions is still valid be-

cause we are ranking the consistency of projection data with

different attenuation corrections. The consistency metric,

with its slight flaws from being calculated on nonideal data,

will still lead to the correct ranking of attenuation correc-

tions. Furthermore, PET data from whole-body PET scanners

have less asymmetry and are more “ideal” than data from

small animal systems since intercrystal penetration and scat-

ter is less of a concern with the larger detectors.22

VII. CONCLUSION

We developed an automated attenuation correction align-

ment method for use with cardiac PET/CT imaging. We dem-

onstrated the proof of principle of the proposed method with

simulation studies and measured patient data. Evaluation of

the optimization shows that it converges to transformation

parameters at a global minimum, leading to improved attenu-

ation correction for cardiac PET imaging. We demonstrated

improved alignment with the method across multiple patient

studies with known mismatches and with initially unaccept-

able alignments. The proposed method provides an auto-

matic, objective approach to align attenuation and emission

images to provide an improved initial alignment. The images

from the initial alignment could be used with manual quality

assurance to potentially reduce user interaction.

ACKNOWLEDGMENTS

This work was supported by the NIH under Grant Nos.

HL086713 and CA115870. The authors thank Dr. Kelley

Branch for helping review initial attenuation-emission align-

ments.

APPENDIX: CONDITIONS FOR ?=0

Proof that consistent attenuation corrected projection data

have certain zero-valued ?m,kfrom Eq. ?1?. Let ?=?cos ?

??=?−sin ?

h:R2→R is given by

Rh?s,?? =?

R

sin ??,

cos ??, and x=?x1

x2?. The Radon transform of a function

h?s? + t???dt.

Let f:R2→R be the activity concentration and ?:R2→R be

the attenuation map. Then, the emission and attenuation data

are given by

E?s,?? = e−R??s,??Rf?s,??,

A?s,?? = R??s,??,

respectively. Now we set out to show that

?m,k??

0

2??

R

smeik?eA?s,??E?s,??dsd? = 0

for k?m or k+m odd. Then,

?

R

smeA?s,??E?s,??ds =?

R

R?

smRf?s,??ds

=?

=?

R

smf?s? + t???dtds

R2?x · ??mf?x?dx,

where we let x=s?+t??. Now we have that

?m,k=?

0

R2f?x??

2??

R2eik??x · ??mf?x?dxd?

=?

0

2?

?x · ??meik?d?dx.

We will now show that the inner integral is zero for k?m

and k+m odd, which will conclude our proof. Now with the

help of the binomial theorem we have

1199 Alessio et al.: Attenuation-emission alignment in cardiac PET/CT1199

Medical Physics, Vol. 37, No. 3, March 2010

Page 10

?

0

2?

?x · ??meik?d? =?

0

2?

?x1cos ? + x2sin ??meik?d? =?

m?m

m?m

m?m

0

2???x1

2+x2

2i?ei?+?x1

2−x2

2i?e−i??

m

eik?d?

=?

0

2??

l=0

l??x1

l??x1

l??x1

2+x2

2i?

2i?

2i?

l?x1

l

eil??x1

2i?

l?x1

2−x2

m−l?

2i?

2i?

m−l

e−i?m−l??eik?d?

=?

l=0

2+x2

2−x2

0

2?

ei?2l+k−m??d?

= 2??

l=0

2+x2

2−x2

m−l

?2l+k−m.

Since ?2l+k−m=0 for l=0,...,m and k?m or k+m odd, the proof follows.

a?Author to whom correspondence should be addressed. Electronic mail:

aalessio@u.washington.edu; Telephone: 206-543-2419; Fax: 206-543-

8356.

1C. Loghin, S. Sdringola, and K. Gould, “Common artifacts in PET myo-

cardial perfusion images due to attenuation-emission misregistration:

Clinical significance, causes, and solutions,” J. Nucl. Med. 45, 1029–1039

?2004?.

2K. Gould, T. Pan, C. Loghin, N. Johnson, A. Guha, and S. Sdringola,

“Frequent diagnostic errors in cardiac PET/CT due to misregistration of

CT attenuation and emission PET images: A definitive analysis of causes,

consequences, and corrections,” J. Nucl. Med. 48, 1112–1121 ?2007?.

3L. Le Meunier, R. Maass-Moreno, J. A. Carrasquillo, W. Dieckmann, and

S. L. Bacharach, “PET/CT imaging: Effect of respiratory motion on ap-

parent myocardial uptake,” J. Nucl. Cardiol. 13, 821–830 ?2006?.

4R. Lautamäki, T. Brown, J. Merrill, and F. Bengel, “CT-based attenuation

correction in 82Rb-myocardial perfusion PET/CT: Incidence of misalign-

ment and effect on regional tracer distribution,” Eur. J. Nucl. Med. 35,

305–310 ?2008?.

5G. Goerres, C. Burger, E. Kamel, B. Seifert, A. Kaim, A. Buck, T. Bue-

hler, and G. von Schulthess, “Respiration-induced attenuation artifact at

PET/CT: Technical considerations,” Radiology 226, 906–910 ?2003?.

6G. Germano, H. Kiat, P. B. Kavanagh, M. Moriel, M. Mazzanti, H. T. Su,

K. F. Van Train, and D. S. Berman, “Automatic quantification of ejection

fraction from gated myocardial perfusion SPECT,” J. Nucl. Med. 36,

2138–2147 ?1995?.

7Y. Nakamoto, M. Osman, C. Cohade, L. T. Marshall, J. M. Links, S.

Kohlmyer, and R. L. Wahl, “PET/CT: Comparison of quantitative tracer

uptake between germanium and CT transmission attenuation-corrected

images,” J. Nucl. Med. 43, 1137–1143 ?2002?.

8R. L. Eisner and R. E. Patterson, “Attenuation correction for stress and

rest PET 82Rb myocardial perfusion images,” J. Nucl. Med. 48, 1912–

1913 ?2007?.

9T. Pan et al., “Attenuation correction of PET images with respiration-

averaged CT images in PET/CT,” J. Nucl. Med. 46, 1481–1487 ?2005?.

10A. Alessio, S. Kohlmyer, K. Branch, G. Chen, J. Caldwell, and P. Kina-

han, “Cine CT for attenuation correction in cardiac PET/CT,” J. Nucl.

Med. 48, 794–801 ?2007?.

11A. Martinez-Moller, M. Souvatzoglou, N. Navab, M. Schwaiger, and S.

G. Nekolla, “Artifacts from misaligned CT in cardiac perfusion PET/CT

studies: Frequency, effects, and potential solutions,” J. Nucl. Med. 48,

188–193 ?2007?.

12K. Khurshid, R. J. McGough, and K. Berger, “Automated cardiac motion

compensation in PET/CT for accurate reconstruction of PET myocardial

perfusion images,” Phys. Med. Biol. 53, 5705–5718 ?2008?.

13S. Pathak, V. Chalana, D. Haynor, and Y. Kim, “Edge-guided boundary

delineation in prostate ultrasound images,” IEEE Trans. Med. Imaging 19,

1211–1219 ?2000?.

14A. Welch et al., “Attenuation correction in PET using consistency infor-

mation,” IEEE Trans. Nucl. Sci. 45, 3134–3141 ?1998?.

15A. Bromiley et al., “Attenuation correction in PET using consistency

conditions and a three-dimensional template,” IEEE Trans. Nucl. Sci. 48,

1371–1377 ?2001?.

16P. E. Kinahan, B. H. Hasegawa, and T. Beyer, “X-ray-based attenuation

correction for positron emission tomography/computed tomography scan-

ners,” Semin Nucl. Med. 33, 166–179 ?2003?.

17F. Natterer, The Mathematics of Computerized Tomography ?Wiley, New

York, 1986?.

18J. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, “Convergence

properties of the Nelder-Mead simplex method in low dimensions,”

SIAM J. Optim. 9, 112–147 ?1998?.

19W. Segars and B. Tsui, “Study of the efficacy of respiratory gating in

myocardial SPECT using the new 4-D NCAT phantom,” IEEE Trans.

Nucl. Sci. 49, 675–679 ?2002?.

20M. D. Cerqueira et al., “Standardized myocardial segmentation and no-

menclature for tomographic imaging of the heart,” Circulation 105, 539–

542 ?2002?.

21J. Herraiz, S. Espana, E. Vicente, E. Herranz, J. Vaquero, M. Desco, and

J. Udias, “Revised consistency conditions for PET data,” IEEE Nuclear

Science Symposium Conference Record, 2007, Vol. 5, pp. 3865–3870

?unpublished?.

22A. M. Alessio and P. E. Kinahan, “Improved quantitation for PET/CT

image reconstruction with system modeling and anatomical priors,” Med.

Phys. 33, 4095–4103 ?2006?.

1200 Alessio et al.: Attenuation-emission alignment in cardiac PET/CT1200

Medical Physics, Vol. 37, No. 3, March 2010