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A Simpliﬁed Pipeline for Motion Correction in

Dual Gated Cardiac PET

Lars Ruthotto1, Fabian Gigengack2,3, Martin Burger4, Carsten H. Wolters5,

Xiaoyi Jiang3, Klaus P. Sch¨

afers2and Jan Modersitzki1

1Institute of Mathematics and Image Computing, University of L¨

ubeck

2European Insitute for Molecular Imaging, University of M¨

unster

3Department of Mathematics and Computer Science, University of M¨

unster

4Institute for Computational and Applied Mathematics, University of M¨

unster

5Institute of Biomagnetism and Biosignalanalysis, University of M¨

unster

lars.ruthotto@mic.uni-luebeck.de

Abstract. Positron Emission Tomography (PET) is a nuclear imaging

technique of increasing importance e.g. in cardiovascular investigations.

However, cardiac and respiratory motion of the patient degrade the image

quality due to acquisition times in the order of minutes. Reconstructions

without motion compensation are prone to spatial blurring and aﬀected

attenuation correction. These eﬀects can be reduced by gating, motion

correction and ﬁnally summation of the transformed images.

This paper describes a new and systematic approach for the correction

of both cardiac and respiratory motion. Key contribution is the splitting

of the motion into respiratory and cardiac components, which are then

corrected individually. For the considered gating scheme the number of

registration problems is reduced by a factor of 3, which considerably sim-

pliﬁes the motion correction pipeline compared to previous approaches.

The subproblems are stabilized by averaging cardiac gates for respiratory

motion estimation and vice versa. The potential of the novel pipeline is

evaluated in a group study on data of 21 human patients.

1 Introduction

Positron Emission Tomography (PET) is a nuclear imaging technique that pro-

vides insight into functional processes in the body. Its ﬁelds of applications range

from oncology via neuroimaging to cardiology. Due to acquisition times in the

order of minutes, motion is a well-known problem in PET. In thoracic PET two

diﬀerent types of motion degrade the image quality: respiratory and cardiac mo-

tion. Neglecting the resulting spatial mislocalization of emission events during

the reconstruction leads to blurred images and aﬀects attenuation correction.

Gating, i.e. grouping the entire list of emission events by breathing and/or

cardiac phases reduces the extent of motion contained in each single gate [1,2]. A

downside is the higher noise level in each gate since only a small fraction of the

available events is considered. This is a severe problem in dual gating schemes,

which demand a very ﬁne division into both respiratory and cardiac gates.

2 Ruthotto et al.

Diﬀerent strategies for motion correction were proposed in the literature and

for a detailed overview see [3]. This paper follows the idea of ﬁrst eliminating

the motion in the dual gated data by image registration and ﬁnally summation

of the gated images to consider all measured emission events and thereby lower

the noise level. This strategy has proven successful for respiratory motion cor-

rection [4,5] and cardiac motion correction [6]. Recently, both types of motion

were eliminated after dual gating using nonlinear mass-preserving registration

[7]. Mass-preservation is a key idea in order to cope with intensity modulations

owing to partial volume eﬀects. Another key contribution is the discretization of

a hyperelastic regularization energy [8]. This sophisticated regularizer is manda-

tory as it achieves meaningful motion estimates and guarantees diﬀeomorphic

transformations even for data with high noise level and large deformations. The

algorithm was embedded into the registration toolbox FAIR that is freely avail-

able at http://www.siam.org/books/fa06/ and documented in [9].

However, the scheme in [7] is computationally very expensive since all gated

images are treated individually. This yields a total number of m·n−1 challenging

registration problems for a gating into mcardiac and nrespiratory gates.

In this paper the nature of the gating scheme is exploited to provide a system-

atic approach to motion correction and to simplify the registration pipeline. The

motion between a template gate and the reference gate is modeled as a simple

concatenation of a respiratory and a cardiac transformation under the assump-

tion that cardiac and respiratory motion are approximately independent. This

scheme reduces the number of registration tasks to m+n−2 and thus saves com-

putation times which allows ﬁner gating schemes. In the considered 5 ×5 gating

this yields a reduction from 24 to 8 registration subproblems. Furthermore each

sub-problem is stabilized by averaging over cardiac phases in the respiratory

motion estimation and vice versa. Results for a group of 21 patients indicate the

eﬀectiveness of the simpliﬁed approach and its positive impact on image quality.

2 Materials and Methods

2.1 Data acquisition

Data of 21 patients (19 male, 2 female; 37-76 years old) with known coronary

artery disease was acquired in a 20 minute list mode scan on a Siemens Biograph

Sensation 16 PET/CT scanner. The data was cropped to the ﬁrst three minutes

to resemble a clinically feasible protocol and dual gating into 5 respiratory and 5

cardiac gates was performed, [2]. The 3D EM software EMrecon was used for

reconstruction of all data see [10]. The images are sampled with 128 ×100 ×44.

2.2 Mass-preserving hyperelastic registration

A key contribution in [7] is the incorporation of the mass-preserving property of

PET into motion correction. The idea is that the total amount of intensity of the

template image Tshould remain unchanged after registration to the reference R,

Motion correction of dual gated PET 3

which is not guaranteed for standard registration approaches. This is realized by

an intensity modulation accounting for volumetric changes given by the Jacobian

determinant of the transformation [7]. The natural distance term for density

images is the sum of squared diﬀerences yielding the image registration functional

J[y] := 1

2k(T ◦ y)·det(∇y)− Rk2+Shyper(y)

where Shyper is the hyperelastic energy [8], which was recently integrated into

FAIR: Shyper(y) = αlSlength(y) + αaSarea (y) + αvSvolume(y). It controls the

changes in length, area and volume induced by the transformation y. Since in-

ﬁnite energy is required to annihilate or enlarge a volume Shyper guarantees

the invertibility of the transformation even for large displacements and noisy

data. While this regularizer is a desirable feature in many registration tasks, it

is mandatory in this application to guarantee the preservation of mass.

2.3 Simpliﬁed registration pipeline

The used gating protocol provides 25 images denoted by Ir

cwhich are related to

5 respiratory phases r= 1, ..., 5 and 5 cardiac phases c= 1, ..., 5. The assump-

tion is that for each ﬁxed respiratory phase rgeometric diﬀerences in Ir

1, ..., Ir

5

are only due to cardiac motion. Hence, all these cardiac phases are displaced by

the same respiratory motion yr. Respiratory motion is eliminated ﬁrst from the

gated dataset as this motion shows less nonlinearities. To this end, cardiac av-

erages I1,...,I5are computed, where Ir= (P5

c=1 Ir

c)/5, and used to estimate

the respiratory displacements y1, . . . , y5based on the above mass-preserving hy-

perelastic registration. Next, respiratory motion is compensated in all 25 images.

Subsequently, I1,...,I5are computed, where Icis the average of the trans-

formed respiratory gates. These images are then used to estimate the cardiac

displacements y1, ..., y5. Note that even after removing the respiratory motion

each such gate relates to diﬀerent realization of (stochastic) radioactive decay.

Hence averaging reduces the noise level even for perfect spatial alignment.

After these 4 respiratory and 4 cardiac motion estimations both types of

motion are eliminated from all 25 images. To this end yrand ycare concatenated

and the mass-preserving transformation model is applied. Finally, the motion

compensated image is obtained by summation over all gates.

3 Results

The proposed motion correction scheme is applied to the image data of 21

human patients. To minimize the geometric mismatch the mid-expiration dias-

tole gate is chosen as reference image denoted by IRef. The images are cropped

to a rectangular region of 128 ×100 ×44 voxels around the torso. Regularization

parameters are set to αl= 5, αa= 1 for length and area term as in [7]. Control

of volumetric change is tightened for respiratory by choosing αv= 100 and kept

4 Ruthotto et al.

4 Ruthotto et al.

IRef ITem and yinitial di↵erence ﬁnal di↵erence

Fig. 1. Results of the 3D registration for an arbitrary chosen patient out of the 21 pa-

tients. Three orthogonal cross-sections sharing the point marked by a white crosshair

are shown. A visualization of the mid-expiration diastolic gate IRef (ﬁrst col.) is com-

pared to the furthest apart end-expiratory systolic gate ITem that is visualized with

superimposed deformation y(second col.) in a small region around the heart. The

decline in absolute di↵erence (third and fourth col.) images and the increase of normal-

ized cross correlation from 0.522 to 0.681 before and after nonlinear mass-preserving

registration show the positive impact of the proposed method on image similarity.

performed on a coarse-to-ﬁne hierarchy of levels and stopped at the second ﬁnest

discretization level (64 ⇥50 ⇥22) to improve stability against noise and speed

the correction up. The total computation time is about 8 minutes per patient

on a Linux PC with a 6 core Intel Xeon X5670@2,93 GHz using Matlab 2010b.

The volumetric change induced by the transformations serves as an indicator

to validate the injectivity of the transformation. The minimum and maximum

of the Jacobian determinant over all patients and all transformations is between

0.81 and 1.19 for respiratory and 0.55 and 1.31 for cardiac motions. Thus all

transformations including their concatenations are di↵eomorphic.

Exemplarily, the registration result is illustrated for an arbitrary chosen pa-

tient in Fig.1 using three orthogonal slice views. Presentation is restricted to the

most challenging sub-problem of registration between the end-expiration systolic

single gate no motion correction proposed motion correction

Fig. 2. Reconstruction results for an arbitrary chosen patient out of the group of 21

patients. Coronal views of the mid-expiration diastolic gate IRef (left, minimal mo-

tion blur, high noise level), reconstruction without motion correction (center, motion

blurred, acceptable noise level) and the result using the novel motion correction scheme

(right, considerably reduced motion, acceptable noise level) are visualized.

Fig. 1. Results of the 3D registration for an arbitrary chosen patient out of the 21 pa-

tients. Three orthogonal cross-sections sharing the point marked by a white crosshair

are shown. A visualization of the mid-expiration diastolic gate IRef (ﬁrst col.) is com-

pared to the furthest apart end-expiratory systolic gate ITem that is visualized with

superimposed deformation y(second col.) in a small region around the heart. The

decline in absolute diﬀerence (third and fourth col.) images and the increase of normal-

ized cross correlation from 0.522 to 0.681 before and after nonlinear mass-preserving

registration show the positive impact of the proposed method on image similarity.

at the same level, αv= 10, for cardiac motion correction. Registration is per-

formed on a coarse-to-ﬁne hierarchy of levels and stopped at the second ﬁnest

discretization level (64 ×50 ×22) to improve stability against noise and speed

the correction up. The total computation time is about 8 minutes per patient

on a Linux PC with a 6 core Intel Xeon X5670@2,93 GHz using Matlab 2010b.

The volumetric change induced by the transformations serves as an indicator

to validate the injectivity of the transformation. The minimum and maximum

of the Jacobian determinant over all patients and all transformations is between

0.81 and 1.19 for respiratory and 0.55 and 1.31 for cardiac motions. Thus all

transformations including their concatenations are diﬀeomorphic.

Exemplarily, the registration result is illustrated for an arbitrary chosen pa-

tient in Fig.1 using three orthogonal slice views. Presentation is restricted to the

4 Ruthotto et al.

IRef ITem and yinitial di↵erence ﬁnal di↵erence

Fig. 1. Results of the 3D registration for an arbitrary chosen patient out of the 21 pa-

tients. Three orthogonal cross-sections sharing the point marked by a white crosshair

are shown. A visualization of the mid-expiration diastolic gate IRef (ﬁrst col.) is com-

pared to the furthest apart end-expiratory systolic gate ITem that is visualized with

superimposed deformation y(second col.) in a small region around the heart. The

decline in absolute di↵erence (third and fourth col.) images and the increase of normal-

ized cross correlation from 0.522 to 0.681 before and after nonlinear mass-preserving

registration show the positive impact of the proposed method on image similarity.

performed on a coarse-to-ﬁne hierarchy of levels and stopped at the second ﬁnest

discretization level (64 ⇥50 ⇥22) to improve stability against noise and speed

the correction up. The total computation time is about 8 minutes per patient

on a Linux PC with a 6 core Intel Xeon X5670@2,93 GHz using Matlab 2010b.

The volumetric change induced by the transformations serves as an indicator

to validate the injectivity of the transformation. The minimum and maximum

of the Jacobian determinant over all patients and all transformations is between

0.81 and 1.19 for respiratory and 0.55 and 1.31 for cardiac motions. Thus all

transformations including their concatenations are di↵eomorphic.

Exemplarily, the registration result is illustrated for an arbitrary chosen pa-

tient in Fig.1 using three orthogonal slice views. Presentation is restricted to the

most challenging sub-problem of registration between the end-expiration systolic

single gate no motion correction proposed motion correction

Fig. 2. Reconstruction results for an arbitrary chosen patient out of the group of 21

patients. Coronal views of the mid-expiration diastolic gate IRef (left, minimal mo-

tion blur, high noise level), reconstruction without motion correction (center, motion

blurred, acceptable noise level) and the result using the novel motion correction scheme

(right, considerably reduced motion, acceptable noise level) are visualized.

Fig. 2. Reconstruction results for an arbitrary chosen patient out of the group of 21

patients. Coronal views of the mid-expiration diastolic gate IRef (left, minimal mo-

tion blur, high noise level), reconstruction without motion correction (center, motion

blurred, acceptable noise level) and the result using the novel motion correction scheme

(right, considerably reduced motion, acceptable noise level) are visualized.

Motion correction of dual gated PET 5

Motion correction of dual gated PET 5

cardiac 1 cardiac 2 cardiac 3 cardiac 4 cardiac 5

0.5

0.6

0.7

0.8

0.9

1

Normalized Cross Correlation

Fig. 3. Motion correction results for our group study of 21 patients. Normalized cross-

correlations between the 24 template gates and the reference gate are shown before

(gray) and after (black) motion correction in a box plot. The considerable increase of

NCC shows the e↵ectiveness and robustness of the new method.

0.81 and 1.19 for respiratory and 0.55 and 1.31 for cardiac motions. Thus all

transformations including their concatenations are di↵eomorphic.

Exemplarily, the registration result is illustrated for an arbitrary chosen pa-

tient in Fig.1 using three orthogonal slice views. Presentation is restricted to the

most challenging sub-problem of registration between the end-expiration systolic

gate and the mid-expiration diastolic reference gate. The di↵erence images before

and after registration clearly show the considerably improved image similarity.

Furthermore the transformation y5

2- obtained by concatenating the respiratory

motion y5and the cardiac component y2is smooth and regular.

The positive impact of the new strategy on image quality is illustrated for

the same dataset in Fig. 2 in a coronal view. The e↵ect of gating - minimal

motion blur, but high noise level - is visible in the reference gate (left). The not

motion-corrected reconstruction (center) shows acceptable noise level, but the

hearts contour is motion-blurred. Both advantages - minimal motion blur and

acceptable noise level - are combined by the resulting image of the new method.

The improvement of image similarity after motion correction is presented in

Fig. 3 for the whole group of 21 patients. Normalized cross-correlations (NCC)

between MathcalIRef and the 24 template gates computed in a rectangular re-

gion around the heart for all patients are illustrated in a box plot. A considerable

increase of NCC can be seen by comparing the gray (before registration) and

black (after registration) boxes and whiskers.

4 Discussion

This paper presents an systematic approach to cardiac and respiratory motion

correction in dual gated thoracic PET. The main contribution is the simpliﬁca-

tion of the processing pipeline achieved by a splitting of the displacement into a

respiration and cardiology component and individually correction of both e↵ects

in the dual gated dataset. A considerably lower number of registration problems

Fig. 3. Motion correction results for our group study of 21 patients. Normalized cross-

correlations between the 24 template gates and the reference gate are shown before

(gray) and after (black) motion correction in a box plot. The considerable increase of

NCC shows the eﬀectiveness and robustness of the new method.

most challenging sub-problem of registration between the end-expiration systolic

gate and the mid-expiration diastolic reference gate. The diﬀerence images before

and after registration clearly show the considerably improved image similarity.

Furthermore the transformation y5

2- obtained by concatenating the respiratory

motion y5and the cardiac component y2is smooth and regular.

The positive impact of the new strategy on image quality is illustrated for

the same dataset in Fig. 2 in a coronal view. The eﬀect of gating - minimal

motion blur, but high noise level - is visible in the reference gate (left). The not

motion-corrected reconstruction (center) shows acceptable noise level, but the

hearts contour is motion-blurred. Both advantages - minimal motion blur and

acceptable noise level - are combined by the resulting image of the new method.

The improvement of image similarity after motion correction is presented in

Fig. 3 for the whole group of 21 patients. Normalized cross-correlations (NCC)

between IRef and the 24 template gates computed in a rectangular region around

the heart for all patients are illustrated in a box plot. A considerable increase of

NCC can be seen by comparing the gray (before registration) and black (after

registration) boxes and whiskers.

4 Discussion

This paper presents an systematic approach to cardiac and respiratory motion

correction in dual gated thoracic PET. The main contribution is the simpliﬁca-

tion of the processing pipeline achieved by a splitting of the displacement into a

respiration and cardiology component and individually correction of both eﬀects

in the dual gated dataset. A considerably lower number of registration problems

need to be solved, which are stabilized by averaging cardiac gates for respira-

tory correction and vice versa. The correction results for a group of 21 patients

suggest that the underlying assumption that cardiac and respiratory motion are

independent is approximately fulﬁlled for our data.

6 Ruthotto et al.

The presented pipeline is in principle compatible with existing approaches to

cardiac and respiratory motion correction techniques [6,4,5,7]. Here, a nonlinear

mass-preserving approach is chosen as it is well-suited for the registration of

density images such as PET, [7]. The preservation of mass can be ensured under

certain assumptions including the invertibility of the transformation. Therefore

an implementation of a hyperelastic regularizer [8], which is integrated in the

freely available toolbox FAIR [9], is used. This regularizer guarantees diﬀeomor-

phic solutions of the problem, but still allows large and ﬂexible transformations.

Individual treatment of respiratory and cardiac motion seems reasonable as

both types of motion are very diﬀerent in nature. While the further is almost

locally rigid, the hearts contraction tends to be more ﬂexible. In the proposed

pipeline this can be addressed by e.g. the choice of diﬀerent regularization pa-

rameters for both types as done in this work. This enforces a smaller range of

the volumetric changes due to respiratory motion for our data.

Despite the considerably reduced distance, the heart structure is still visible

in the ﬁnal diﬀerence images, see Fig.1. The registration could be improved

by performing a number of outer loops over respiratory and cardiac motion

correction to be investigated in future work.

The very promising results presented in this paper mark a next step towards

clinical applicability of motion correction methods in thoracic PET. With the

simpliﬁed registration pipeline the quality of motion correction can be further

improved as ﬁner subdivision schemes become feasible.

5 Acknowledgements

The authors thank Otmar Schober from the Department of Nuclear Medicine at

the University of M¨

unster for providing the interesting data.

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