Rigid-body transformation of list-mode projection data for respiratory motion correction in cardiac PET

Transcription

1 INSTITUTE OF PHYSICS PUBLISHING Phys. Med. Biol. 50 (2005) PHYSICS IN MEDICINE AND BIOLOGY doi: / /50/14/008 Rigid-body transformation of list-mode projection data for respiratory motion correction in cardiac PET L Livieratos 1,2, L Stegger 1,3, P M Bloomfield 4, K Schafers 3, D L Bailey 5 and P G Camici 1 1 PET Cardiology, MRC Clinical Sciences Centre, Imperial College, Hammersmith Hospital, London, UK 2 Nuclear Medicine Department, Guy s & St Thomas Hospitals, St Thomas Street, SE1 9RT, London, UK 3 Department of Nuclear Medicine, Muenster University Hospital, Muenster, Germany 4 Centre for Addiction and Mental Health, Toronto, Canada 5 Department of Nuclear Medicine, Royal North Shore Hospital, Sydney, Australia Lefteris.Livieratos@gstt.sthames.nhs.uk Received 18 November 2004, in final form 7 April 2005 Published 6 July 2005 Online at stacks.iop.org/pmb/50/3313 Abstract High-resolution cardiac PET imaging with emphasis on quantification would benefit from eliminating the problem of respiratory movement during data acquisition. Respiratory gating on the basis of list-mode data has been employed previously as one approach to reduce motion effects. However, it results in poor count statistics with degradation of image quality. This work reports on the implementation of a technique to correct for respiratory motion in the area of the heart at no extra cost for count statistics and with the potential to maintain ECG gating, based on rigid-body transformations on list-mode data event-by-event. A motion-corrected data set is obtained by assigning, after pre-correction for detector efficiency and photon attenuation, individual linesof-response to new detector pairs with consideration of respiratory motion. Parameters of respiratory motion are obtained from a series of gated image sets by means of image registration. Respiration is recorded simultaneously with the list-mode data using an inductive respiration monitor with an elasticized belt at chest level. The accuracy of the technique was assessed with point-source data showing a good correlation between measured and true transformations. The technique was applied on phantom data with simulated respiratory motion, showing successful recovery of tracer distribution and contrast on the motioncorrected images, and on patient data with C 15 O and 18 FDG. Quantitative assessment of preliminary C 15 O patient data showed improvement in the recovery coefficient at the centre of the left ventricle. (Some figures in this article are in colour only in the electronic version) /05/ $ IOP Publishing Ltd Printed in the UK 3313

2 3314 L Livieratos et al 1. Introduction Cardiac 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 recognized since the very early development of PET (Hoffman et al 1979, Ter-Pogossian et al 1982, Susskind et al 1985). However, due to the practical limitations, such as long scan duration and limited signal-to-noise conditions, the issue received little further attention. Recently, with the introduction of combined PET/CT systems, discussion on the problem of respiratory motion has resumed mainly due to artefacts produced by acquisition of the two modalities during different breathing conditions and the need for accurate localization of small nodules and quantification with PET (Goerres et al 2002, Nehmeh et al 2002). In cardiac PET imaging, respiratory gating schemes were implemented in real-time (Klein et al 1998) and list-mode (Livieratos et al 1999) systems. Our preliminary patient studies with respiratory gating in PET (Livieratos et al 2003) as well as studies with other imaging modalities (Korin et al 1992, Taylor et al 1997) support the validity of modelling respiratory motion of the heart as a rigid-body motion. The extent of motion during respiration, which is in the range of several millimetres, will adversely affect achievable spatial resolution and quantification in PET scanners with high intrinsic resolution. Gated acquisition may be used to eliminate these effects by collecting data in separate phases of the respiratory cycle. However, even with the increased sensitivity of the current generation of PET scanners, acquisition of data in separate gates results in reconstructed images of poor statistical properties if scan duration is not adequately prolonged or injected dose increased. Furthermore, the non-rigid 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-by-event on the basis of a geometric model of intersection of the lines-of-response (LOR) with the scanner. ECG gating can be maintained after correction for respiration-related rigid-body motion in the area of the heart. Corrections for detector efficiencies and photon attenuation are included in the process before transformations are applied. Although corrections for motion can equally be performed in the image space, application in list-mode offers certain advantages such as the option to retain ECG gating thus avoiding summation of cardiac phases and an excellent time resolution which could potentially be utilized for interpolation of motion parameters within respiratory phases. 2. Materials and methods 2.1. Data acquisition Acquisition of list-mode projection data was performed on the ECAT EXACT3D scanner (Spinks et al 2000). The EXACT3D is a full ring BGO-based scanner operating only in 3D mode with an axial field-of-view of 23.4 cm and an absolute sensitivity of 5.8%. Intrinsic spatial resolution is 4.8 mm FWHM (mean transaxial at 1 cm off-centre) and 5.6 mm FWHM (mean axial, on-axis). Acquisition of list-mode emission data is enabled by a 32 MB RAM memory and a 34 GB RAID hard disk (Bloomfield et al 2003). Real-time sorting in the acquisition computer system 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 reported access rate to the RAID disk is approximately 18 MB s 1.

3 Respiratory motion correction of PET list-mode projection data 3315 The above hardware configuration can achieve transfer rates of 4.5 Mevents s 1 (18 MB s 1, 4 bytes/event) which is above the count rate limit of the EXACT3D (approximately 2.9 Mevents s 1, prompts + randoms). List-mode data consist of 32-bit 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 elasticized 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 elasticized belt. Changes of the inductance are translated into an analogue output. 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 bits of the timing list-mode words, represented by gating states As the signal from the respiration monitor is proportional to the expansion of the chest belt, gating was based on signal amplitude thus not relaying on periodicity of the respiration motion. The relative amount of time spent in every respiratory gate was available by the list-mode data. Signal from an ECG monitor was simultaneously acquired and the presence of the R-wave trigger was encoded as the maximum gating state (all bits set to 1). However, for this application the ECG signal was ignored. Physiological signals are recorded every millisecond. Single-photon transmission data are acquired in histogram mode with a 137 Cs (E γ = 662 kev, t 1/2 = 30.2 years, 150 MBq) point source and attenuation maps are initially segmented (Xu et al 1994) prior to be forward-projected to form attenuation correction factors (Bailey et al 1998). List-mode acquisition and gating were not supported by the single-photon transmission system. Emission data were 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 data set 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 (Menke et al 1996) which we developed and initially applied for correction of head movement in brain imaging (Bloomfield et al 2003). 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 (x 1, y 1, z 1, x 2, y 2, z 2 ). Each point r defining a LOR was then spatially transformed by the rotation matrix M and translation vector b: r = Mr + b (1) where M applies rotations ϕ x, ϕ y and ϕ z about the x-, y- and z-axes, respectively, in this order and b is defined by the b x, b y and b z translations along the x-, y- and z-axes, as [ ] sx 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 M = and s y sin ϕ z cos ϕ y s y cos ϕ z cos ϕ x + s y sin ϕ z sin ϕ y sin ϕ x s y cos ϕ z sin ϕ x s y sin ϕ z sin ϕ y cos ϕ x s z sin ϕ y s z sin ϕ x cos ϕ y s z cos ϕ y cos ϕ x b x b = b y. (3) b z (2)

4 3316 L Livieratos et al Although transformation parameters are time dependent, the above equation refers to transformations averaged over a particular respiratory phase. The scaling factors s x, s y and s z for the x-, y- and z-axes, respectively, were kept to 1. 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 of radius R. The solution l p = b ± b 2 4ac (4) 2a of the binomial equation al 2 + bl + c = 0 where a = (x 2 x 1 )2 + (y 2 y 1 )2 b = 2x 1 (x 2 x 1 ) +2y 1 (y 2 y 1 ) c = x y 2 1 R2 provides the points of intersection of the LOR with the detector cylinder. Due to the discrete geometry of the scanner the position of the new LOR after transformation was assigned to a detector pair using nearest neighbour interpolation. Lines that did not intersect with the scanner cylinder after transformation were rejected. During the transformation process projections may be assigned to a new position 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 artefacts, detection normalization was implemented at the level of histogramming of the list-mode data. Normalization factors n i,j,k,l were calculated for each projection p i,j,k,l before spatial transformations were applied. Each projection element p i,j,k,l of the transformed data set was the sum of each LOR that falls into (i,j,k,l ) after transformation, weighted by the normalization factor at the original position (i,j,k,l): p i j k l = n(i, j, k, l)p(i,j,k,l ). (5) The set of normalization factors n i,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 artefacts from misalignment of the emission and transmission data. Each projection element p i,j,k,l of the transformed data set was 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): p i j k l = ACF(i,j,k,l)p(i,j,k,l ). (6) After histogramming of list-mode 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 Point-source data The accuracy of the technique was assessed with point source data upon which a set of spatial transformation parameters was applied. A ceramic ball ( = 1mm) 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

5 Respiratory motion correction of PET list-mode projection data 3317 measured transformation (mm) 60 bx y = x by R 2 = bz measured transformation (mm) 60 bx y = x R 2 = by bz measured transformation (mm) bx 60 by y = x R 2 = 1 bz x-axis translation (mm) y-axis translation (mm) z-axis translation (mm) measured transformation ( ) ϕ fx x y = x fy ϕ y R 2 = ϕ fz z measured transformation ( ) ϕ fx x y = x fy ϕ y R 2 = ϕ fz z measured transformation ( ) ϕ fx x y = x fy ϕ y R 2 = ϕ fz z x-axis rotation ( ) y-axis rotation ( ) z-axis rotation ( ) Figure 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-directions (b x, b y and b z ) and rotation about the x-, y-andz-axes (ϕ x, ϕ y and ϕ z, 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. 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 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 vector between the origin and the centroid of the point source in the original and the transformed data 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 ventricular 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. The parameters for motion correction were obtained from a series of respiration-only gated images via edge-tracking of the left ventricle (Biedenstein et al 1999, Stegger et al 2001) Patient studies The method was applied on fluorine-18 labelled fluorodeoxyglucose ( 18 FDG) and oxygen-15 labelled carbon monoxide (C 15 O) patient data sets. Data were acquired in list mode with

6 3318 L Livieratos et al Figure 2. Short-axis images of the cardiac phantom data set with no motion correction (top rows) and with motion correction (bottom rows). Both uncorrected and motion-corrected images were reconstructed and re-sliced to short-axis orientation with the same parameters. respiratory gating information and were retrospectively sorted into six respiratory gates. For the C 15 O data venous blood samples were taken every minute during the scan, and the C 15 O concentration in whole blood was measured using a NaI(Tl) well counter cross-calibrated with the scanner. Spatial transformation parameters relating the respiration-only gated images were derived using an automated image registration algorithm that minimizes mutual information between the two images (Studholme et al 1999). The registration algorithm was applied between the end expiration gate and each of the other respiratory phases. The six sets of transformation parameters (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 C 15 O 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. 3. Results The results for the different spatial transformation parameters applied on the point-source data are shown in figure 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

7 Respiratory motion correction of PET list-mode projection data 3319 Figure 3. Short-axis images of the cardiac 18 FDG study (from left to right: base to apex) with no motion correction (top row) and with motion correction (bottom row). Both uncorrected and motion-corrected images were reconstructed and re-sliced to short-axis orientation with same parameters. Spatial transformation parameters were derived from the reconstructed respirationgated images using an image registration algorithm based on mutual information. 45 mean counts in ROI (kbq/ml) Respiratory Gated Summed Gates-Uncorrected Summed Gates-Motion Corrected Mean Blood Counts gate number Figure 4. Mean ROI values across respiratory-gated images of a C 15 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. 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 figure 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 18 FDG study without correction for motion and with motion correction are shown in figure 3. Both uncorrected and motion-corrected images were reconstructed and re-sliced 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 the ROI applied onto C 15 O patient data are shown in figure 4. A large

8 3320 L Livieratos et al variation of the ROI mean counts was observed between gates of end-phases of respiration. An improvement of 4.5% in the recovery coefficient at the centre of the left ventricle was observed on the summed gated images after motion correction compared to the uncorrected images. This was measured on the C 15 O images for a small ROI at the centre of the left ventricular blood pool in order to avoid the influence of additional (non-respiration related) partial volume effects. The recovery coefficient was calculated against the activity concentration of the blood samples. A larger improvement should be expected for more peripheral ROIs in the heart, in areas which are subject to stronger influence from respiratory motion. 4. Discussion and conclusions A method for applying rigid-body spatial transformations on single-event list-mode projection data is 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. This may be further improved by employing a weighted interpolation scheme. In the case of transaxial translations, the additional effect of increased size of the projection elements towards the centre of the scanner, which is partly accounted for by the normalization process on the basis of adjusting counts per projection bin but with no geometric considerations, 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, thus confirming that the pre-transformation normalization process maintains quantitative accuracy. For many transformations, such as rotations about the x- and y-axes 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 through the object 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 testing in the future would improve motion correction for a wider range of values of the transformation parameter. Although the effect of rejected LORs after transformation is likely not acute in imaging of the heart, centrally located in the FOV and with restricted range of motion transformations, the issue has received further attention in motion correction for brain imaging (Rahmim et al 2004). 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. Phantom motion was restricted to translations to simulate respiratory motion. The inclusion of rotation and motion caused by heart contraction would have been nearer to reality.

9 Respiratory motion correction of PET list-mode projection data 3321 However, in this work the emphasis was on the feasibility of the method and adequacy of the technical implementation, so a simple simulation was employed. Motion parameters were estimated on a set of respiration-only gated images. A total of six respiratory gates were used as a compromise for adequate count statistics. The accuracy of motion correction could probably be further improved by interpolation of transformation parameters based on a model of motion. However, this was outside the scope of the present feasibility study and it may be included in a future implementation. Results from the application of the motion correction technique on patient 18 FDG data show differences in myocardial uptake between motion-corrected and non-corrected 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 C 15 O data where the actual tracer concentration could be measured by well counting of the blood samples taken during the scan. This allows for a quantitative assessment of the improvement of the recovery of blood activity within the left ventricle. An improvement of 4.5% was observed in the recovery coefficient for a small ROI over the centre of the left ventricle. It should be noted that this is a conservative estimate with an ROI centrally defined over the blood pool of the left ventricle. It should be expected that larger improvements from respiration motion correction are measured in areas close to the boundaries of the myocardium. This was not possible to quantitatively assess on the basis of C 15 O blood pool data as a more peripheral ROI would be subject to additional (non-respiration related) partial volume effects. Motion correction in list-mode on an event-by-event basis offers advantages such as the option to retain ECG gating thus avoiding summation of cardiac phases and the potential to utilize the time resolution of list mode for interpolating motion parameters. The later should improve accuracy of motion correction in future implementations of the methodology by honouring the time dependence of the transformation parameters within each respiratory phase. Although the described methodology is currently applied as a two-pass method (i.e. requires intermediate image reconstruction for the estimation of motion) and is therefore computationally more intensive, it may be possible in future to implement as a one-pass method if models of motion based on external markers are established. Further work is required in this area in order to establish models of motion of internal organs in relation to external markers, perhaps with contribution from similar studies with other imaging modalities (McLeish et al 2002, Ablitt et al 2004). Outside the main application in cardiac imaging, it is also expected that this methodology might be useful for PET imaging of other structures subject to motion such as intrapulmonary nodules, liver and kidney lesions and abdominal lymph nodes. Accurate tracer recovery is often vital to identify malignant tumours. Recently, with the introduction of dual PET/CT systems, artefacts related to respiratory motion and data acquisition of the two modalities at different breathing modes (breath-hold versus free breathing) became more evident (Goerres et al 2002, Nehmeh et al 2002). Although the assumption of a rigid-body mode of organ movement during respiration cannot be generalized and needs assessment specific to the clinical application and targeted organ, it might be possible to utilize the presented methodology in certain areas to eliminate motion artefacts at no further expense in counting statistics. References Ablitt N A, Gao J, Keegan J, Stegger L, Firmin D N and Yang G Z 2004 Predictive cardiac motion modeling and correction with partial least squares regression IEEE Trans. Med. Imaging

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