MOTION is one source of degradation in positron emission

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1 476 IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL 25, NO 4, APRIL 2006 Lung Motion Correction on Respiratory Gated 3-D PET/CT Images Mohammad Dawood*, Norbert Lang, Xiaoyi Jiang, and Klaus P Schäfers Abstract Motion is a source of degradation in positron emission tomography (PET)/computed tomography (CT) images As the PET images represent the sum of information over the whole respiratory cycle, attenuation correction with the help of CT images may lead to false staging or quantification of the radioactive uptake especially in the case of small tumors We present an approach avoiding these difficulties by respiratory-gating the PET data and correcting it for motion with optical flow algorithms The resulting dataset contains all the PET information and minimal motion and, thus, allows more accurate attenuation correction and quantification Index Terms Gating, lung, motion, motion correction, optical flow, PET, PET/CT I INTRODUCTION MOTION is one source of degradation in positron emission tomography (PET)/computed tomography (CT) images The PET images are acquired over an elongated period of time (typically 5 min/bed position for studies) and, thus, represent the sum of information gained over the whole period of acquisition As the patients are continuously breathing during the procedure, there is unavoidable lung movement Breathing results in displacement of organs in the thorax such as lungs, heart, ribs etc The extent of this motion depends upon different factors such as organ location, patient height, anatomical and physiological circumstances, etc, and, thus, is variable In one study of 20 patients with lung tumors in magnetic resonance tomography (MRT), it was found that the diaphragm moved about mm due to respiration [1] Due to this prime motion displacements of up to 5 mm were present in 70% of the tumors In 30% of the tumors this motion was even larger, in the range of 6 23 mm depending upon the location of the tumor Similarly the diaphragm movement along with that of the heart was found to be approximately 15 mm in supine position in [2] In patients this movement was shown to be about 20 mm [3] The range of the diaphragm motion is given in [5] from as little as 4 mm to as much as 38 mm Manuscript received September 28, 2005; revised December 16, 2005 This work was supported in part by the Deutsche Forschungsgemeinschaft (DFG) through the Sonderforschungsbereich (SFB) Project 656 MoBil and in part by the University Hospital Münster, Munster, Germany, under Grant SC Asterisk indicates corresponding author *M Dawood is with Department of Nuclear Medicine, University of Münster, D Münster, Germany ( dawood@uni-muensterde) N Lang and K P Schäfers are with Department of Nuclear Medicine, University of Münster, D Münster, Germany X Jiang is with the Department of Mathematics and Computer Science, University of Münster, D Münster, Germany Digital Object Identifier /TMI Fig 1 The problem of respiratory motion in PET images demonstrated with the help of software phantom data Left: data without motion, right: data with motion (Both images without noise) A Problem The large motion leads to two sources of possible artifacts Wrong attenuation correction and image blurring, see Fig 1 Attenuation correction is the method for correcting the PET data for the effects of different types of tissues the photons pass through on their way to the detectors Dense tissue, like bones, will absorb a larger part of the photons whereas soft tissue, like lungs, will absorb much less The images without attenuation correction will, thus, show apparently greater activity in areas of soft tissue as compared with dense tissue This effect is corrected by scaling the number of photons registered in the detectors in accordance with the density of tissues In PET/CT the CT scan, which gives information about the densities of tissue, is used for this purpose [4] As the CT images are acquired much faster than PET images (on the order of seconds) and moreover in breath hold technique, they represent an instantaneous snapshot during the breathing cycle in contrast to the PET which is acquired over several minutes per bed position Therefore, a part of the PET data will be wrongly attenuated (eg, activity from heart may be attenuated with lung density, etc) and only that part of the PET data which corresponds to the CT position in the breathing cycle will be correctly attenuated The second disadvantage of motion is image blur As the source of radioactive emission is in constant motion, the information on the ungated PET images will be dispersed over an area proportional to the magnitude of the motion This leads to loss of contrast in presence of high noise This effect has been examined by Erdi et al [6] Their results show that the motion of lungs during the PET acquisition may lead to wrong staging of tumors Another study of 42 patients showed that in 98% of the cases, artefacts due to respiratory motion were present on the images /$ IEEE

2 DAWOOD et al: LUNG MOTION CORRECTION ON RESPIRATORY GATED 3-D PET/CT IMAGES 477 [7] Again, studies showed that the lesions near the lung base, which has the most pronounced motion due to breathing, might constitute a significant problem [8] Another study showed that 84% of patients had respiratory motion induced artefacts in the right lung, including 2% classified as severe and 84% had the same in the left lung including 10% classified as severe respiratory motion artefacts [9] Motion of tumors situated in the lower lobes was found to be about 12 mm in one study [10] Thus the attenuation correction of PET images with CT may lead to clinically significant inaccurate localization of lesions [11], wrong attenuation correction, misstaging of tumors and wrong calculation of standard uptake value (SUVs) (defined as tissue concentration of activity in a region of interest divided by activity injected per gram body weight) [12] The aim of this study was to find a solution to this problem B Previous Attempts Previous attempts to solve the problem of motion correction in pulmonary PET imaging largely followed the strategy of externally monitoring the motion of the patient with the help of external markers and video cameras The images are then sorted in accordance with the motion of these external markers Nehmeh et al [13] used an external block which is fastened to the patient s abdomen The movement of this block monitored with video cameras and the position of the block is used for sorting the data into different gates Only the first gate is used for reconstruction Such a procedure reduces the motion on the images in each gate by some extent, however, most of the information is lost in the unused gates To get the same statistics as in the ungated images, a proportionally larger amount of the radio-tracer must be administered to the patient which is not an option under normal clinical circumstances Nehmeh et al recognized this problem and proposed another method in [14] This method is based upon the use of a radioactive point source which is present at the end of a low density plastic rod This rod is fastened to a block of Styrofoam which is again attached to the abdomen of the patient The whole apparatus is placed in a way so that the radioactive point source extends into the plane of the lung lesion The data is acquired into 200 frames of 1 s each A ROI is placed over the point source in any one frame by the user Now all other frames in which the point source falls within the same ROI are selected The corresponding sinograms of the selected frames are then summed up and the image is again reconstructed with this new sinogram This method utilizes more information then the first one However, information on all frames in which the marker lies outside the ROI window is lost Moreover, there is no motion correction, it is rather a selection of frames which are good Finally, the position of the lesion has to be known a priori Both of these methods are, thus, not a real solution to our problem Attempts were made at motion correction in PET images of other organs too, such as brain [15] or heart studies [18], but they represent a different case from ours Head motion is not a periodic motionanditcanbedetectedeasilywiththehelpoftheskullalso the motion inside the skull is uniform and only rotational or translational in nature Even then, Picard et al [15] and following them Fulton et al [16] used video cameras to monitor the skull position externally Even more recent attempts at motion correction in brain studies are based on external monitoring [17] Klein [18] achieved motion correction in heart studies by using deformable elastic membranes as a model But his method is applied to heart only as it attempts to simulate the elasticity of the heart muscle Moreover it requires segmentation of the heart prior to motion correction, as the underlying equations change for each organ and fluid in accordance with the tissue type and its physiological properties Finally, it can neither motion correct different organs at the same time, if they are not already segmented and underlying elastic properties defined, nor can it motion correct organs which do not behave as elastic membranes Lungs are an example in case, as they behave more like a filled and expanding balloon rather then a deforming membrane Another method, similar to the above one, was proposed by Zhang et al [19] The main drawback of their method is again the use of elasticity properties of the tissue For this the authors propose to use either tensile tests or to use special anchor testing images, made under laboratory conditions with no noise, with landmark correspondence to find out these physical properties The accuracy of the method will critically depend upon the accuracy of this landmark correspondence The method is two-dimensional and no data on its qualitative goodness is provided, nor is it compared with any other method Another drawback is that a global registration is a prerequisite to perform this method An elastic deformable registration method was proposed by He et al [20] This method is essentially similar to a global optical flow method The method uses four conditions to perform the deformable registration All four conditions, intensity similarity, incremental transformation, smoothness, and error minimization are all used in global optical flow methods Thus, the method suffers from the same disadvantages in presence of heavy noise as do other similar optic flow methods See the references given in the next section for further details of these disadvantages There have also been some attempts at correcting the motion in PET studies in the pre-image forming stage also, ie, directly in the sinograms [21] or by rebinning the listmode data [17] The first method corrects the motion by detecting high intensity nodes (if they are present in the images) in the sinogram and can correct only the inplane motion via scaling, whereas the second method needs video monitoring with external markers to find the position of the chest and resort the bins accordingly C Our Idea Our idea is to use respiratory gating for obtaining relatively motion free images of the lungs and then minimize the motion with software methods The disadvantage of gating the PET data is the loss of statistics Thus, the signal-to-noise ratio (SNR) in each of the gates is much lower then the SNR of the ungated PET image set Second, the reduced SNR leads to the same disadvantage of loosing the significant information in noise as is the disadvantage of the large motion in the ungated PET images Thus, gating alone is not sufficient for our purposes To retain all information and yet to reduce the motion is necessary To achieve this we transform the PET image data from the individual gates to one position in the breathing cycle and then add them up to achieve an image set with minimum motion and containing all information

3 478 IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL 25, NO 4, APRIL 2006 with the phase of respiratory signal resulting in eight image sets with reduced motion Each of these gates contains another phase of the total motion and, thus, simple addition of the gates will reproduce the data as if acquired without gating Details of the gating procedure can be seen in Lang et al [29] A schematic diagram of gating is given in Fig 2 The eight listmode respiratory gates are then reconstructed individually with an OSEM reconstruction algorithm [30] without attenuation correction Respiratory gating reduces the motion but the images now have a worse signal to noise ratio due to the reduction in statistical power Fig 2 Gating scheme The respiratory cycle is divided into eight parts Y-axis show the change in lung volume against time For this we can only use the raw, nonattenuation corrected, images This is due to the fact that we have only one phase of the respiratory motion in CT-images, which is used for attenuation correction Therefore, using this single phase of motion in CT images for attenuation correction will lead to artifacts Thus, motion correction must be done before attenuation correction Rigid or affine transformations [22], [23] between two image frames are not sufficient for our data where different organs inside the human thorax undergo different motions with varying directions and amplitudes Only elastic transformations come into question As even elastic registration methods show disadvantages in case of very localized deformations [24], we opted for optical flow methods for motion correcting the individual gates Optical flow methods [25] try to find the motion between two time frames at each pixel position A large number of optical flow methods have been developed for specific applications by now Evaluations and comparisons by Galvin [26], Barron [25], and Bruhn [27] have shown that the Lucas-Kanade algorithm is one of the best methods for calculating optical flow fields under different aspects, especially in presence of noise As the PET data is inherently very noisy, we have chosen the Lucas-Kanade algorithm as the basis for our application We use the three-dimensional (3-D) extension of this algorithm with a weighting function and a matched set of smoothing and derivative filters, which will be described in more detail below II METHODS We essentially use three steps for solving the problem of motion in PET/CT images These are: 1 Respiratory gating, 2 Optical flow calculation, 3 Projection to target position These methods are now described in detail in the following sections A Respiratory Gating To correct the lung motion on the images, we need images with as less motion as possible The obvious method for that is to divide the PET data into smaller parts, with each part representing only a fraction of the total respiratory motion This is called respiratory gating We divide the normal breathing cycle into eight parts by using the respiratory signal The PET listmode data is then sorted into these eight gates in accordance B Optical Flow Optical flow methods try to calculate the motion between two image frames which are taken at times and at every pixel position As a pixel at location with intensity will have moved by,,, and between the two frames, following image constraint equation can be given: Assuming the movement to be small enough, we can develop the image constraint from (1) at with Taylor series to get where higher order terms (HOT) are small enough to be ignored From these equations, we achieve or which results in where,, and are the,, and components of the velocity or optical flow of and,,, and are the derivatives of the image at in the corresponding directions We will write,,, and for the derivatives in the following: Thus or This is an equation in three unknowns and cannot be solved as such This is known as the aperture problem of the optical flow algorithms To find the optical flow we need another set of equations which is given by some additional constraint The method used by us is given by Lucas and Kanade [31] (1) (2)

4 DAWOOD et al: LUNG MOTION CORRECTION ON RESPIRATORY GATED 3-D PET/CT IMAGES 479 Lucas and Kanade use a noniterative method which assumes a locally constant flow The extension of the Lucas-Kanade method to three dimensions is now described Assuming that the flow is constant in a small window of size with, which is centered at voxel,, and numbering the pixels as we get a set of equations and outliers Median filters for smoothing are usually preferred for this purpose We have used the matched smoothing and derivative filters presented by Simoncelli [32] with kernels of up to five pixels length His matched kernels reported better results then filters based upon difference building, such as Prewitt or Roberts filters and smoothing filters like median filter [33] We smoothed our data in, and directions over five pixels each and smoothed over the dimension over two consecutive frames The Simoncelli matched filters for one dimensional convolution of length 5 are given as: With this, we get more then three equations for the three unknowns and, thus, an over-determined system We get where designates the smoothing filter and the derivative filter of length For the temporal dimension we used the filters of length 2 or To solve the over-determined system of equations, we use the least squares method C Projection The last step in our method deals with projection of the data to the required position One, user specified gate,, is taken as the target gate in the breathing cycle to which all other gates are to be projected, ie, or or (3) where are the gates to be transformed to the target position The transformation matrices used for this purpose are given by the optical flow algorithm which gives us the displacement for each pixel in the data, ie, it supplies us with all,, and in This means that the optical flow can be found by calculating the derivatives of the image in all four dimensions A weighting function, with should be added to give more prominence to the center pixel of the window Gaussian functions are preferred for this purpose We have used a quasi gaussian weighting scheme by using the square of the euclidian distance from the center pixel as a measure of weighting Other functions or weighting schemes are possible The next step is now to calculate the derivatives of the image in all spatio-temporal directions Different methods are possible for accomplishing this task One simple method is to use the following equation for the derivative in direction: It is clear that this method will be prone to noise, which constitutes a big problem in PET emission images To suppress the effects of noisy pixels it is usually preferable to build the derivatives over many pixels Some sort of smoothing helps in derivative calculation additionally by suppressing the effects of noise Inverting the displacement vectors would correct the data for motion However, the displacements are not necessarily discrete Thus, interpolations have to be used for nondiscrete displacement values The whole process can be, thus, described as where is the optical flow algorithm, is the transformation matrix given by the optical flow algorithm for transforming the data of gate to the target gate and is the deformed data which is acquired by interpolating gate with the transformation matrix Different interpolation methods have been proposed [34] We have experimented with nearest neighbor, tri-linear, cubic, and spline interpolations All of them, except nearest neighbor, give similar results This similarity in results of different interpolation methods is probably due to the high ratio of noise present on our data and the poor resolution of PET images The results shown here were achieved with the splines based interpolation method

5 480 IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL 25, NO 4, APRIL 2006 Fig 4 Coronal view of the NCAT software phantom simulating PET data without noise (See Fig 5 for four gates with noise) Fig 3 The process flow The flow can be visualized as shown in Fig 3 The motion between the gates is calculated with the help of optical flow algorithm Please note that the maximum motion is reached at gate four and not gate seven! This is due to the cyclic motion during the respiration After gate four the lungs begin to contract again and reach the original position after gate eight The flow information, which is fraction at some places, eg,, is used to interpolate the original gates to the motion corrected form The gates can now be added to give a complete, motion corrected, and high SNR data set Another method of projection is based upon the fact that the optical flow algorithms can calculate the transformation matrices with smaller motion much more precisely This fact is founded in the basic equations of optical flow, see Section II-B above, which require small motion between two frames for the Taylor expansion Thus, it is better to calculate the optical flow between the adjacent gates rather then to calculate it for every gate directly The individual gates are then projected to the target gate successively The results of experiments with both methods of projection are given and discussed in Section IV III TEST DATA We have used two types of data to evaluate our methods Phantom Data and Patient data A NCAT Phantom The four-dimensional nonuniform rational B-splines (NURBS)-based cardiac-torso (NCAT) phantom was developed to provide a realistic and flexible model of the human anatomy and physiology to be used in nuclear medicine imaging research [28]) The organ models are based on NURBS It contains all organs inside the torso like lungs, heart, liver, spleen, ribs, kidneys etc and simulates PET emission and CT scans All of the organ and skeletal models with the exception of the heart are based on CT scans from the visible human male data set The heart model is based on gated magnetic resonance imaging cardiac scans of a normal patient A cross section of the frontal view of the phantom is given in Fig 4 The phantom software also provides the option of saving the data in different respiratory or cardiac gates This option was utilized to obtain eight respiratory gates for each simulated patient study The phantom software allows a large degree of flexibility by giving the option to manually set the degree of motion of different organs (eg, diaphragm motion, lung motion, etc) and body size (eg, lung size, chest width, etc) The motion of an organ is described by a physiologically based mathematical model in the program The extent of this motion is controlled by the parameters given by the user and the position and volume of the organ is then calculated at different positions in the respiratory or cardiac cycle by interpolation The parameters can also be used to simulate the data for different patients The original data is noise free, therefore, we added gaussian white noise with mean 0, and less then 0001 variance in different experiments to the phantom images to make them more analogue to the real data B Patient Data The real patient datasets were acquired in our clinic We requested routine patients and volunteers to remain on the PET scanner for some extra time during which the listmode PET data was acquired along with the respiratory signal We used a PET/CT (Siemens Biograph Sensation 16) camera for the patient studies A special research package allowed us to store the PET data in listmode The respiratory signal of the patient was recorded with the help of the Biovet -system For this a pneumatic sensor is attached to the abdomen of the patient with simple adhesive tape and the breathing motion of the chest wall is recorded Three patient data sets have been acquired with this technique so far

6 DAWOOD et al: LUNG MOTION CORRECTION ON RESPIRATORY GATED 3-D PET/CT IMAGES 481 Fig 5 Coronal slices from the first four gates of the respiratory cycle from the NCAT phantom data The movement of lungs is clearly seen at the base of lungs, which is moving downwards in this series Fig 6 Comparison of the projection methods Top row: motion correction with direct projection Lower row: motion correction with successive projection Column 1: G1, the target gate Column 2 to 4 show the results of motion correction of Gates 2,3,4 IV RESULTS AND DISCUSSION TABLE I COMPARISON OF DIRECT AND SUCCESSIVE METHODS A Criteria for Measuring Improvement The question of evaluation of any method is of prime importance to quantify the results As we are dealing with motion correction, some criteria, which provides us with an objective measure of correspondence between two data sets is required Many such evaluation methods are possible [35] We have chosen correlation coefficient (CC) due to its linear properties The CC is defined as (4) where, are the values from two datasets and mean values from the same, are the B Projection Method We first apply the direct and the successive projection schemes for motion correction to the software phantom data and then use the best of these two for the other experiments The images resulting from direct and successive projection scheme are shown in Fig 6 The images show how the motion correction fails progressively as the distance between the target gate and the current gate increases, if direct projection method is applied On the other hand, the successive projection scheme is successful in minimizing the distorting effects of large motion This improvement, however, is achieved at the cost of small image smearing which is produced due to repeated interpolations during the successive projection method It should be remembered that the number of optical flow calculations remains the same in both methods Only the number of interpolations increases with successive projections The smearing effect on the images does not distort the edges Thus, successive projection method is superior than the direct projection method in correcting the motion artefacts on PET images This result is substantiated by comparing the CC obtained from the postcorrected data as shown in Table I We can see, how the CC decreases when the direct method is applied, eg, the correlation decreases for the fourth gate from in successive method to in direct method This shows that the successive method is to be preferred to the direct projection method Therefore, in the following we will use the successive projection method

7 482 IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL 25, NO 4, APRIL 2006 Fig 7 Result with the noisy phantom data (coronal slice) Left: gate 1, the target gate; middle: sum of first four gates; right: all four gates after motion correction with successive projection method Fig 8 Result with the noisy phantom data, successive projection method (transversal slice) Left: gate 1; middle: sum of four gates; right: all four gates after motion correction The results of motion correction are visible around the tip of lungs at the top of the images C Motion Correction Our experiments with both the NCAT software phantom of human thorax as well as with real patient data showed significant improvement in the motion correction of the gated data The effects of motion correction are readily seen in the areas of greatest movement, ie, lung base and the outer boundary of the lungs Moreover, the motion of heart due to respiration was also corrected to a large extent Results of one such experiment on the phantom data are shown in Figs 7 and 8 The lung base on the uncorrected, total image has become blurred due to motion Similarly the heart walls show large motion artefacts This motion of heart is solely due to respiratory motion of the lungs In the corrected images the improvement due to motion correction is evident The improvement before and after motion correction can be quantified with the help of the CC For our data the CCs between the gates 1 to 4 with the target gate (G1) were as given in Table II The percentage of motion correction as given in the Table II is calculated as the ratio of maximum possible correlation, which is 100%, to the improvement in CC, thus As can be readily seen, we have been able to motion correct the data, measured in terms of CC, by at least 75% We also see that, as expected, the performance of the algorithm is greater in gates nearer to the target gate In addition to the phantom data, we also applied our methods to real respiratory gated human PET/CT data The results of the first such experiment with are shown in Fig 9 TABLE II IMPROVEMENT IN CORRESPONDENCE TO THE TARGET GATE (CC) To quantify the improvements of the motion correction, we present a comparison of the precorrection and postcorrection data in the form of intensity profiles along a single column through the lungs in Fig 10 The profile was taken from the lung visible on the right side of the image (ie, left lung) The intensity plots show that after motion correction the large dispersion in the uncorrected data in the horizontal direction has been improved significantly Our results show that the motion of the lung base, which is seen on the plots as the large drop in intensity around columns 25 35, is greatly reduced, we measured a reduction in motion of around 70% at the diaphragm in pixels This is also shown by the improvement in the CC with reference to the uncorrected data Reduction in data dispersion in the vertical direction on the plots is due to motion correction in the y and z directions Pixels actually belonging to another plane or slice of the 3-D data with different uptake properties were placed on the same slice in the uncorrected images due to the movement of lungs After motion correction they are projected back to their correct position and this resulted in improvement in the dispersion of intensity values in the vertical direction on the plots Another experiment with the second human dataset gave similar results The intensity profile plots from this dataset are given in Fig 11 This data was acquired by administering to a volunteer The corresponding CCs are given in Table III

8 DAWOOD et al: LUNG MOTION CORRECTION ON RESPIRATORY GATED 3-D PET/CT IMAGES 483 Fig 9 Result with real patient data Patient 1 dataset, coronal slice Left: gate 1; middle: sum of first four gates; right: all four gates after motion correction The dotted line in the left image shows the location of the profile in Fig 10 Fig 10 Result with real patient data Profile from the slice shown in Fig 9 Left: profiles of first four gates before motion correction Right: same profiles after motion correction The effects of motion correction can be readily seen in the diaphragm movement correction The diaphragm is represented by the sudden drop in intensity values around columns (X-axis: slice no, Y-axis: gray value) Fig 11 Result with real patient data Profile from a vertical slice from Patient 2 dataset Left: profiles of first four gates before motion correction Right: same profiles after motion correction TABLE III CORRELATION COEFFICIENTS WITH PATIENT DATA The CCs show that the motion has been reduced after correction for motion in all four gates Moreover, after motion correction the images are all in the same phase of organ motion as the correlation with the target gate of all four gates is ca 96%

9 484 IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL 25, NO 4, APRIL 2006 Fig 12 Comparison of the gating scheme Left: sum of all four gates, middle: all gates after motion correction with G as target; right: all gates after motion correction with G as target Compare with Fig 7 D Effect of Weighting As described above in Section II-B, the optical flow algorithm can also be used with a weighting function which gives more weight to the central pixel of the window and less weight to the pixels away from it We measured the effect of this weighting scheme on the results of the optical flow algorithms for our data For this purpose, we experimented with two weighting functions where,, and are the position of the central pixel of the window and,, and is the position of the neighboring pixel The second function is given by The results we obtained with both functions show that the unweighted implementations give better results This seems to be due to the presence of noise of very high magnitude in our data The noise effects are, thus, also weighted and amplified with the window weighting functions On the other hand, the large number of equations used by us (window of size ) reduces the effects of noise, which is gaussian noise with mean zero, more effectively then the weighting scheme E Gating Order Another parameter for optimization is the gating scheme To keep the motion at minimum for the optical flow algorithm, it is advisable not to choose the gate with the minimum or maximum magnitude of motion Selecting the gate with average magnitude of motion has two advantages It reduces the discrepancy between the data and the algorithm, which requires minimal motion (see Section II-B) Second, it reduces the number of interpolations needed to project the gates to the target position successively Both of these advantages are worth implementation The results of one such experiment with as the target gate are shown in Fig 12 A comparison with the results from Fig 7 shows immediately that the new gating scheme gives significantly better results The thickness of the heart membrane has been projected more accurately with the new gating scheme Note: The change in the position of the lung and heart is due to the use of as target gate, which represents another phase of the respiratory cycle V CONCLUSION AND FUTURE WORK We have presented a method of correcting PET images of the human torso for respiratory motion with the help of respiratory gating and optical flow algorithms The methods were tested on software based phantom data as well as real patient data The results show significant improvements in motion reduction on both datasets We plan to improve the results further by optimizing the gating scheme As the lungs complete their expansion, then contract back to the original position to restart the respiratory cycle once again, it will be possible to add up gates representing the same phase of displacement, even though the direction of motion will be opposite in the gates Similarly the width of the gates should be adopted to the motion Gates with smaller width are needed during the phase with rapid movement whereas a larger gate width is possible during the more flat phase of breathing Another improvement can be achieved by choosing the target gate intelligently Taking the middle gate as the target gate ensures that the motion between the target gate and any of the other gates is minimal This reduces the motion between the target and reference gates and, thus, increases the accuracy of the optical flow calculations REFERENCES [1] A J Schwarz and M O Leach, Implications of respiratory motion for the quantification of 2D MR spectroscopic imaging data in the abdomen, Phys Med Biol, vol 45, pp , Aug 2000 [2] R H Huesman, G J Klein, B W Reutter, and T F Budinger, Preliminary Studies of Cardiac Motion in Positron Emission Tomography, Lawrence Berkeley National Laboratory, Berkeley, CA, Tech Rep, 2001 [3] B M W Tsui, W P Segars, and D S Lalush, Effects of upward creep and respiratory motion in myocardial spect, IEEE Trans Nucl Sci, vol 47, no 3, pp , Mar 2000 [4] P E Kinahan, D W Townsend, T Beyer, and D Sashin, Attenuation correction for a combined 3D PET/CT scanner, Med Phys, vol 25, no 10, pp , 1998 [5] S S Vedam, V R Kini, P J Keall, V Ramakrishnan, H Mostafavi, and R Mohan, Quantifying the predictability of diaphragm motion during respiration with a noninvasive external marker, Med Phys, vol 30, no 4, pp , Apr 2003 [6] Y E Erdi, S A Nehmeh, T Pan, A Pevsner, K E Rosenzweig, G Mageras, E D Yorke, H Schoder, W Hsiao, O D Squire, P Vernon, J B Ashman, H Mustafavi, S M Larson, and J L Humm, The CT motion quatitation of lung leasions and its impact on PET-measured SUVs, J Nucl Med, vol 45, no 8, pp , Aug 2004

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