Rigid-body transformation of list-mode projection data ...

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Rigid-Body Transformation of List-Mode Projection Data For Respiratory Motion Correction In Cardiac PET L. Livieratos, L. Stegger, P.M. Bloomfield, K. Schafers, D.L. Bailey, P.G. Camici

Abstract—Respiratory motion is a source of artefacts and quantification errors in cardiac imaging. Preliminary studies with retrospective respiratory gating in PET support the observation of other imaging modalities of a rigid-body motion of the heart during respiration. However, the use of gating techniques to eliminate motion may result in poor count statistics per reconstructed image. We have implemented a motion correction technique which applies rigid-body transformations on list-mode data event-by-event on the basis of a geometric model of intersection of the lines-of-response with the scanner. Pre-correction for detector efficiencies and photon attenuation before transformation are included in the process. Projection data are acquired together with physiological signal (every ms) from an inductive respiration monitor with an elasticised belt at chest level. Data are retrospectively sorted into separate respiratory gates on an off-line workstation. Transformation parameters relating the gated images, estimated by means of image registration, can be applied on the original list-mode data to obtain a single motion-corrected dataset. The accuracy of the technique was assessed with point source data and a good correlation between applied and measured transformations, estimated from the centroid of the source, was observed. The technique was applied on phantom data with simulated respiratory motion and on patient data with C15O and 18FDG. Quantitative assessment of preliminary C15O patient datasets showed at least 4.5% improvement in the recovery coefficient at the centre of the left ventricle. Index Terms— Positron emission tomography, Motion compensation, Cardiovascular system, Respiratory system.

I. INTRODUCTION

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ardiac and respiratory motion in cardiac imaging and head movement in neuro-imaging are sources of artefacts and quantification errors in PET. In cardiac imaging the effects of respiratory motion have been recognised since the very early

Manuscript received October 16, 2003. L. Livieratos was with the MRC Clinical Sciences Centre, Hammersmith Hospital, London, UK. He is now with the Nuclear Medicine Department, Guy’s & St Thomas’ Hospitals, London, UK (phone: +44-207-9554855; fax: +44-207-9552802; e-mail: Lefteris.Livieratos@ kcl.ac.uk). L. Stegger and K. Schafers are with the Department of Nuclear Medicine, Muenster University Hospital, Muenster, Germany P. Bloomfield is with the Centre for Addiction and Mental Health, Toronto, Canada D. Bailey is with the Department of Nuclear Medicine, Royal North Shore Hospital, Sydney, Australia P.G. Camici is the head of PET Cardiology, MRC Clinical Sciences Centre, Imperial College, Hammersmith Hospital, London, UK

development of PET [1]-[3]. However, due to the practical limitations, such as long scan duration and limited signal-tonoise conditions, the issue received little further attention. Recently, respiratory gating schemes were implemented in real-time [4] and list-mode [5] systems. Preliminary patient studies with respiratory gating [6] support the observation of other imaging modalities of a rigid-body motion of the heart during respiration. The extend of motion during respiration, in the range of several millimeters [7],[8], will affect effective spatial resolution and quantification in the latest generation of PET scanners with increased intrinsic resolution. Gated acquisition may be used to eliminate these effects by collecting data in separate phases of respiration. However, even with the increased sensitivity of the current generation of PET scanners, acquisition of data in separate gates may result in reconstructed images of poor statistical properties if scan duration is not adequately prolonged. Furthermore, the nonrigid component of the motion of the heart throughout the cardiac cycle would require additional electrocardiographic (ECG) gating, resulting in further reduction of counting statistics per reconstructed image. We have implemented a motion correction technique which applies rigid-body transformations on list-mode data event-byevent on the basis of a geometric model of intersection of the lines-of-response with the scanner. ECG gating can be maintained after correction for respiration-related rigid-body motion. Correction for detector efficiencies and photon attenuation are included in the process before transformation is applied.

II. MATERIALS AND METHODS A. Data Acquisition Acquisition of list-mode projection data was performed on the ECAT EXACT3D scanner. The EXACT3D [9] has an axial field-of-view of 23.4 cm and an absolute sensitivity of 5.8%. Acquisition of list-mode data is enabled by a 32 Mbyte RAM memory and a 34 Gbyte RAID hard-disk [10]. Real-time sorting in the VSB Sorter of the ACS II is by-passed during list-mode acquisition. Double buffering of the data from the List-Mode RAM to the RAID disk is supported by the Read/Write Controller. Data are written into the RAID disk from where they are available through the local network. The

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reported access rate to the RAID disk is approximately 18Mbytes/sec. The above hardware configuration can achieve transfer rates of ~4.5Mevents/sec (18Mbytes/sec¸ 4bytes/event) which is above the count rate limit of the EXACT3D. List-mode data consist of 32-byte words representing either a detected coincidence event (random or prompt) or elapsed time from the beginning of the acquisition. Four bits in the timing words are reserved for gating information. Projection data were acquired together with physiological signal from an inductive respiration monitor (RespiTrace R250, Studley Data Systems) with an elasticised belt around the patient’s chest. Measurements are based on the changes of inductance of the coil formed by the fine flexible wire incorporated into the elasticised belt. Changes of the inductance are translated into an analogue output at the range of 0-5 V. A purpose built electronic circuit was used as interface between the monitoring devices and the gating input board of the scanner. Respiration signal was sampled into the gating byte of the timing list-mode words, represented by bits 0 to 15. Signal from an ECG monitor was simultaneously acquired and recorded in the most significant bit of the gating byte. However, for this application the ECG signal was ignored. Physiological signals are recorded every millisecond. Data are retrospectively sorted into separate respiratory gates on an off-line SUN Ultra10 workstation. Transformation parameters relating the gated images, estimated by means of image registration, can be applied on the original list-mode data to obtain a single motion-corrected dataset. B. Spatial Transformation List-mode events were spatially transformed on the basis of a geometrical model of intersection of lines-of-response (LOR) with the scanner cylinder [11]. Individual events from the stream of list-mode data were assigned to LORs defined by a pair of points in the Cartesian space. A geometrical model of the scanner was used to assign each detector element pair to a LOR (x1,y1,z1,x2,y2,z2). Each point r defining a LOR was then spatially transformed by the rotation matrix M and translation matrix b:

r ' = Mr + b (1) where M and b are defined by the ϕx , ϕy , ϕz rotations and bx, by and bz translations along the x-, y- and z-axis as:  s x cos ϕ z cos ϕ y s x sin ϕ z cos ϕ x − s x cos ϕ z sin ϕ y sin ϕ x s x sin ϕ z sin ϕ x + s x cos ϕ z sin ϕ y cos ϕ x  (2)   M =  − s y sin ϕ z cos ϕ y  − s sin ϕ z y 

s y cos ϕ z cos ϕ x + s y sin ϕ z sin ϕ y sin ϕ x − s z sin ϕ x cos ϕ y

b x 

and b =  b y 

s y cos ϕ z sin ϕ x − s y sin ϕ z sin ϕ y cos ϕ x   s z cos ϕ y cos ϕ x 

(3)

 bz 

All spatially transformed lines (x'1,y'1,z'1,x'2,y'2,z'2) were then projected onto the scanner cylinder and were re-assigned to detector pairs to form a new LOR by the intersection of the transformed line with the scanner cylinder. The solution lp =

− b ± b 2 − 4ac 2a

(4)

of the binomial equation

al 2 + bl + c = 0 where:

a = ( x ′2 − x1′ ) 2 + ( y ′2 − y1′ ) 2 b = 2x1′ ( x ′2 − x1′ ) + 2 y1′ ( y ′2 − y1′ ) c = x1′ 2 + y1′ 2 − R 2

provides the points of intersection of the LOR with the detector cylinder. Lines that did not intersect with the scanner cylinder after transformation were rejected. During the transformation process projections may be assigned to a new positions of different detector or geometric efficiency to the initial position. Similarly, spatially transformed LORs may fall outside the group of detector elements associated with an entry of single photon count rates and therefore result to wrongly assigned dead-time correction factors. In order to maintain quantitative accuracy and avoid potential artifacts, detection normalisation was implemented at the level of histogramming of the list-mode data. Normalisation factors ni,j,k,l were calculated for each projection pi,j,k,l before spatial transformations were applied. Each projection element pi’,j’,k’,l’ of the transformed data set will be the sum of each LOR that falls into (i',j',k',l') after transformation, weighted by the normalisation factor at the original position (i,j,k,l): pi' j' k' l' = n(i, j, k, l) p(i' , j' , k ' , l' ) (5)

∑

The set of normalisation factors ni,j,k,l was calculated for each time frame of the data as, although detector efficiency and geometric factors remain unchanged, dead-time correction is dependent on the single photon count-rates during the acquisition interval. Similarly, pre-correction for photon attenuation was included in order to avoid potential artifacts from misalignment of the emission and transmission data. Each projection element pi’,j’,k’,l’ of the transformed data set will be the sum of each LOR that falls into (i',j',k',l') by transformation, after being multiplied by the attenuation correction factor (ACF) at (i,j,k,l) : pi' j' k'l' =

∑ACF(i, j, k,l)p(i' , j' , k', l' )

(6)

In cardiac imaging and for limited spatial transformations precorrection for attenuation might not be necessary as the cardiac ventricles, myocardium and surrounding tissue have practically indistinguishable attenuation coefficients at the energy of 511 keV. In this case, the pre-correction scheme may be omitted by the algorithm. After histogramming of listmode data with spatial transformations the resulting sinograms were reconstructed with the 3D re-projection algorithm. Corrections applied during histogramming/spatial transformation were excluded at the level of reconstruction. The accuracy of the technique was assessed with point source data upon which a set of spatial transformation parameters was applied. A ceramic ball (∅ = 1 mm) soaked in 18 F solution was placed 10 cm off the transaxial centre and at the axial centre of the FOV of the scanner. Over 20 million true counts were acquired in list-mode and the data were transferred to an off-line workstation for processing. A set of transformation parameters was applied to the raw data and the resulting sinograms were reconstructed with the ramp filter at

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the Nyquist frequency. The centroid of the point source was calculated for every set of transformation parameters. A data set with no transformations was used to obtain the initial position of the source. The resulting transformations were estimated from the centroid co-ordinates. C. Phantom Study The technique was applied on phantom data with simulated respiratory motion. The left ventricular wall was simulated by a fill-able part created between two flexible balloon-type compartments. A ‘defect’ was created in the ventricular wall by a lightweight insert. The heart compartment was placed in 45° orientation in a perspex phantom simulating the thorax. Respiratory motion was simulated on the phantom arrangement in the axial? direction of the scanner with an extent of 2 cm. Post-acquisition, the list-mode data were sorted into sinograms with and without motion correction and were reconstructed with the same parameters for comparison. D. Patient Studies The method was applied on 18FDG and C15O patient data. Data were acquired in list-mode with respiratory gating information and were retrospectively sorted into 6 respiratory gates. For the C15O data venous blood samples were taken every minute during the scan, and the C15O concentration in whole blood was measured using a NaI well counter crosscalibrated with the scanner. Spatial transformation parameters relating the gated images were derived using a mutual information registration algorithm. The six sets of transformation parameters (one set of three rotations and three translations per respiratory phase) were applied to the original list-mode data as described above and the resulting sinograms were reconstructed. Quantitative assessment of the C15O patient data was performed by applying a small circular ROI over the centre of the left ventricle on six consecutive transaxial slices on the gated and summed images with and without motion correction.

III. RESULTS The results for the different spatial transformation parameters applied on the point source data are shown in fig. 1. A good correlation for all applied transformations, with negligible residual values for the other transformation parameters, was observed. A good agreement between the applied and measured transformation parameter was found, with a slight underestimation especially for transaxial translations. This may be related to the discrete geometry of the scanner cylinder and the need of rounding of the LOR position to the nearest physical detector element. Images from the phantom data with and without motion correction are shown in fig. 2. A good definition of the edges of the ventricular wall was observed on the motion corrected images. A successful recovery of the myocardial wall borders was observed on the motion corrected images. Recovery of tracer distribution and contrast was clearly evident, especially for the defect area and the more apical and basal areas of the left

ventricle. Short-axis images from the cardiac 18FDG study without correction for motion and with motion correction are shown in fig. 3. Both un-corrected and motion-corrected images were reconstructed and resliced to short-axis orientation with the same parameters. Uncorrected images appear spatially smoothed compared to the corrected images; this might be due to motion averaging during respiration. Differences in tracer distribution can be attributed to the averaging of the data at different positions of the heart during respiration in the uncorrected images and the effect of misaligned transmission data with the emission data. Results from ROI applied onto C15O patient data are shown in fig. 4. A large variation of the ROI mean counts was observed between gates of end-phases of respiration. An improvement of at least 4.5% in the recovery coefficient at the centre of the left ventricle was observed on the summed gated images after motion correction. IV. DISCUSSION AND CONCLUSSIONS A method for applying rigid-body spatial transformations on single-event list-mode projection data was reported in this paper. On the basis of the observation that respiration-related motion of the heart is approximated by rigid-body parameters, the technique can be used for reducing the dimensions of dual (respiratory and ECG) gated data, while compensating for motion at no loss of total counts and ECG gating. Validation results with point source data showed a generally good accuracy. A linear response to the input spatial transformation was measured in the reconstructed images with negligible residual errors. A slight underestimation of the applied parameter was found for certain types of transformations such as transaxial translations. Generally this may be related to the discrete geometry of the scanner where the position of the LORs after transformation is rounded to the nearest physical detector element. In the case of transaxial translations, the additional effect of increased size of the projection elements towards the centre of the scanner, which is not accounted for in the current model, may result in a further underestimation of the transformation parameters. Additional correction for this effect can easily be implemented if the variation of the projection bin size, as a function of distance from the centre of the FOV, is known for the particular scanner from experimental measurements. On the same point-source data it was observed that the number of counts is preserved for transformations that do not result in LORs being placed outside the acceptance limits of the scanner. For many transformations, such as rotations about the X- and Y-axis and translations along the axial direction, a number of LORs will be rejected as they will fall outside the acceptance limits of the scanner. This holds for LORs of either direct or oblique projections. For example, in the case of translations along the axial direction, although the vast majority of direct projections will be within the range of displacement of the point source, a number of oblique projections will be rejected. A solution to this would be the completion of the rejected LORs by forward-projection of the original data. This feature was not included in the present work, however, its implementation and

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testing in the future would improve motion correction for a wider range of values of the transformation parameter. Images from the phantom data clearly demonstrate the effect of motion correction with obvious recovery of uptake contrast especially in the defect and apical and basal myocardial areas. Results from the application of the motion correction technique on patient 18FDG data show differences in myocardial uptake between motion corrected and noncorrected images, which may be the result of averaging of data at different positions during respiration and the effect of misaligned transmission data. However, it is difficult to draw conclusions with regard to the accuracy of the two images in the absence of a known reference value to be used as golden standard. A more objective test is available with the C15O data where the actual tracer’s concentration could be measured by well counting of the blood-samples taken during the scan. Quantitative assessment of C15O patient data on the basis of a small circular ROI at the centre of the left ventricle showed an improvement of at least 4.5% in the recovery coefficient. A larger improvement should be expected for more peripheral ROIs in the heart, in areas which are subject to stronger influence from respiratory motion. It is also expected that this methodology would improve recovery of tracer uptake values in imaging of small tumor nodules in or near the lung.

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E. J. Hoffman, M. E. Phelps, G. Wisenberg, H. R. Schelbert, D. E. Kuhl, “Electrocardiographic gating in positron emission computed tomography.” 1979, J Comput Assist Tomogr 3(6): 733-9. M.M. Ter-Pogossian, S.R. Bergmann, B.E. Sobel, “Influence of cardiac and respiratory motion on tomographic reconstructions of the heart: implications for quantitative nuclear cardiology.” 1982, J Comput Assist Tomogr 6(6): 1148-55 H. Susskind, P.O. Alderson, N.N. Dzebolo, G.W. Bennett, P. Richards, J.M. Rosen, A.B. Brill, “Effect of respiratory motion on pulmonary activity determinations by positron tomography in dogs.” 1985, Invest Radiol 20(9): 950-5. G. J. Klein, B.W. Reutter, M.H. Ho, J.H. Reed, R.H. Huesman, “Realtime system for respiratory-cardiac gating in positron tomography.” 1998, IEEE Trans Nucl Sci 45(4): 2139-43. L. Livieratos, P.M. Bloomfield, D.L. Bailey, O. Rimoldi, C. Rhodes, T. Jones, P. Camici, “Cardiac and respiratory gating of list-mode data on a high sensitivity PET scanner, the ECAT EXACT3D.” 1999, J Nucl Cardiol 6(1(2)): S16. L. Livieratos, K. Rajappan, D.L. Bailey, O. Rimoldi, P. Camici, “Respiratory Gating of Cardiac PET Data”, European Association of Nuclear Medicine Annual Meeting, 2003, Eur J Nucl Med, 30(2):S174.

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REFERENCES

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The authors would like to thank A. Westrip and M. Renton for the design and construction of the interface electronic circuit used for gating.

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ACKNOWLEDGMENT

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Fig. 1. Spatial transformations of the point source in the reconstructed images against input parameters in the transformation process. Translation of the point source in the x-, y- and z- direction (bx, by, and bz) and rotation about the x-, y- and z-axis (fx, fy and fz respectively) were calculated from the position of the source in the reconstructed images after spatial transformation of the list-mode projection data. The horizontal axis of the graphs shows the input parameter in the transformation process.

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Fig. 2. Short-axis images of the cardiac phantom data set with no motion correction (top rows) and with motion correction (bottom rows). Both un-corrected and motion-corrected images were reconstructed and resliced to short-axis orientation with same parameters.

Fig. 3. Short-axis images of the cardiac 18FDG study (from left to right: base to apex) with no motion correction (top row) and with motion correction (bottom row). Both un-corrected and motion-corrected images were reconstructed and resliced to short-axis orientation with same parameters. Spatial transformation parameters were derived from the reconstructed respiration-gated images using an image registration algorithm based on mutual information. [7]

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Summed Gates-Motion Corrected Mean Blood Counts

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Fig. 4. Mean ROI values across respiratory-gated images of a C O study. Mean value of the ROI applied to the summed image with and without motion correction is indicated together with the mean counts in the blood samples.

A.M. Taylor, P. Jhooti, F. Wiesmann, J. Keegan, D.N. Firmin, D.J. Pennell, “MR navigator-echo monitoring of temporal changes in diaphragm position: implications for MR coronary angiography.” 1997, J Magn Reson Imaging 7(4): 629-36. [8] H. W. Korin, R. L. Ehman, S. J. Riederer, J. P. Felmlee, R. C. Grimm, “Respiratory kinematics of the upper abdominal organs: a quantitative study.” 1992, Magn Reson Med 23(1): 172-8. [9] T.J. Spinks, T. Jones, P.M. Bloomfield, D.L. Bailey, M. Miller, D. Hogg, W.F. Jones, K. Vaigneur, J. Reed, J. Young, D. Newport, C. Moyers, M.E. Casey, R. Nutt, “Physical characteristics of the ECAT EXACT3D positron tomograph.” 2000, Phys Med Biol 45(9): 2601-18. [10] P.M. Bloomfield, T.J. Spinks, J Reed, L Schnorr, A.M. Westrip, L. Livieratos, R. Fulton, T Jones, “The design and implementation of a motion correction scheme for neurological PET.” 2003, Phys. Med. Biol. 48(8): 959-978. [11] M. Menke, M.S. Atkins, K.R. Buckley, “Compensation methods for head motion detected during PET imaging.” 1996, IEEE Trans Nucl Sci 43(1): 310-17.