Abstract:
A method and system for normalization of a positron emission tomography system is provided. The method includes acquiring three-dimensional normalization scan data from a positron emission tomography system with at least one septum and determining a down-sampling factor based in part on the configuration of the at least one septum. The method further includes modifying the three-dimensional normalization scan data using the down-sampling factor.

Description:
BACKGROUND OF THE INVENTION 
   The present invention relates generally to image reconstruction in positron emission tomography (PET) systems. More particularly, the present invention relates to the determination of normalization factors utilized in image reconstruction. 
   Various techniques or modalities may be used for medical imaging of, for example, portions of a patient&#39;s body. PET imaging is a non-invasive nuclear imaging technique that allows the study of the internal organs of a human body. PET imaging allows the physician to view the patient&#39;s entire body at the same time. PET imaging produces images of many functions of the human body that are otherwise unobtainable. 
   In PET imaging, positron emitting isotopes are injected into the patient&#39;s body. These isotopes are referred to as radiopharmaceuticals, which are short-lived unstable isotopes. Once injected into the body, these isotopes decay and discharge positively charged particles called positrons. Upon being discharged, when these positrons encounter an electron, they are annihilated and converted into a pair of photons. The two photons are emitted in nearly opposite directions. A PET scanner typically includes several coaxial rings of detectors around the patient&#39;s body for detecting such annihilation events. 
   The detectors include crystals or scintillators to sense the scintillation of photons or gamma rays colliding with them. Coincidence detection circuits connected to the detectors record only those photons that are detected simultaneously by two detectors on opposite sides of the patient. During a typical scan, hundreds of millions of events are detected and recorded to indicate the number of annihilation events along lines joining pairs of detectors in the ring. The collected data is then used to reconstruct an image. 
   The existing PET scanners are based on either two-dimensional (2D) or three-dimensional (3D) data acquisition. In the case of 2D acquisition PET scanners, data is collected only along planes perpendicular to the central axis of the scanner. In order to collect data only from a single plane, the detector rings of the 2D PET scanners are separated by short septa or detector shields. 
   In the case of 3D PET scanners, the septa between the detector rings are removed. Data is collected throughout the sample volume and then reconstructed based on its actual trajectory through image space. These trajectories may or may not exist in one particular plane. 
   The data collected during a scan may contain inconsistencies. These inconsistencies may arise due to different factors, or the operating characteristics of the imaging systems, one of them being the presence of shields or septa between the detector rings of the PET scanner. The collected data is therefore normalized prior to using such data for reconstruction of the image. In accordance with the known methods for the normalization of scan data, correction factor is a product of (i) the single-crystal efficiencies of the two detectors forming the coincidence, and (ii) a geometric factor. 
   Several normalization methods are used to account for the differences in detection efficiency among the lines of response (LORs) in the system. Existing normalization methods account for the LOR radius and transaxial angle, but generally do not take the axial angle of the detector line or response into account. In at least one known method, the geometric factor is assumed to be a function of an LOR radius and an LOR angle in a single plane parallel to the detector rings. In 2D scanning, all the data is in the plane and the axial angle is zero. In 3D PET scanners, the absence of septa generally makes the response of the system independent of the axial angle. When septa are added to the 3D system, however, this is no longer true. Therefore, there exist significant axial angle effects. 
   These known methods for the normalization of scan data have several disadvantages. For example, in the case of 2D scanning, minor errors in the positioning of the septa of one millimeter (mm) or less can cause significant inaccuracies in the scan data. In many applications, such positioning errors are likely to occur. Further, in the case of 3D acquisition with the septa removed, the system records a larger number of false coincidence events and scattered photons. This increases noise in the image and therefore reduces image quality. When the septa are introduced between the detector rings of a 3D PET scanner there is a substantial geometric factor in the axial direction. There is no compensation for this substantial geometric factor in the known methods of image reconstruction. 
   Therefore, known image reconstruction methods fail to take into account the presence of septa for the purpose of the normalization in case of 3D PET scanners. Further, the known normalization methods do not compensate for the geometric factor that arises in the axial direction. 
   BRIEF DESCRIPTION OF THE INVENTION 
   In one exemplary embodiment, a method for the normalization of a positron emission tomography system having at least one septum is provided. The method includes acquiring three-dimensional normalization scan data from a positron emission tomography system having at least one septum and determining a down-sampling factor based in part on the configuration of the at least one septum. The method further includes modifying the three-dimensional normalization scan data using the down-sampling factor. 
   In another exemplary embodiment, a positron emission tomography system is provided. The system includes a positron emission tomography scanner for performing three-dimensional scans, with the positron emission tomography scanner having at least one septum. The system further includes a controller for controlling the normalization of the positron emission tomography scanner, with the controller configured to down-sample three-dimensional scan data received from the positron emission tomography scanner based in part on the configuration of the at least one septum. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  is a schematic diagram showing multiple detector rings of a PET system in, accordance with one exemplary embodiment of the invention; 
       FIG. 2  is a block diagram of a PET system in accordance with one exemplary, embodiment of the invention; 
       FIG. 3  is a flowchart illustrating a method for determining a normalization factor for image reconstruction, in accordance with one exemplary embodiment of the invention; and 
       FIG. 4  and  FIG. 5  are exemplary images illustrating the effect of a 3D normalization scheme on the reconstruction of a PET image. 
   

   DETAILED DESCRIPTION OF THE INVENTION 
     FIG. 1  is a schematic diagram showing an exemplary embodiment of multiple detector rings  50  of a PET system  100  (shown in  FIG. 2 ). PET system  100  may include several detector rings  50 , with each detector ring  50  being formed of a plurality of detectors. In one embodiment of the invention, the PET system includes 24 co-axial detector rings. Detectors  102  and  104  are positioned on a detector ring  50  on opposite sides of detector ring  50 . Detectors  106  and  108  are positioned on different detector rings  50 . In one embodiment of the invention, each detector ring is separated by a septum  110 . Septa  110  are annular disks shaped in the form of a ring or toroid. In another embodiment, septa  110  are present after every alternate detector ring  50 . Septa  110  may be spaced after any number of detector rings  50 . Septa  110  allow photons or gamma rays to travel only in the plane of a particular detector ring  50 , and partially shield cross-plane photons. In one exemplary embodiment each of the septa  110  are 0.8 mm thick and 20 mm high. A 3D PET system  100  operating with such septa  110  will be referred to herein as operating in a 2.5-dimensional (2.5D) mode of operation. It should be noted that the various embodiments of the present invention may be implemented in connection with PET systems having septa  110  with different dimensions or different types of septa, such as, for example, sparse septa or focused septa (e.g., septa of varying length defined by distance from an axial center). Further, the various embodiments of the present invention may be implemented in connection with PET systems operating in different modes. 
   The lines along which the photons or gamma rays travel may or may not fall in the plane of a single detector ring  50 . For example, a photon may encounter an electron and gets annihilated at point  112 . The resulting pair of photons may travel in the plane of a single detector ring  50  along line of response (LOR)  114 , or in a cross-plane along LOR  116 . Photons moving in cross-plane LOR  116  are not shielded by septa  110  because of the height of septa  110  (e.g., their shorter height). In operation, LOR  114  is detected by a single ring of detectors  50 , whereas LOR  116  is detected by two different detector rings  50 . 
     FIG. 2  is a block diagram of an exemplary embodiment of a PET system  100 . PET system  100  includes a PET scanner  202  and a controller  203  for controlling normalization and image reconstruction. Controller  203  for controlling normalization and image reconstruction, further includes an operator workstation  204 , a data acquisition processor  206  and an image reconstruction processor  208 . PET scanner  202 , operator workstation  204 , data acquisition processor  206  and image reconstruction processor  208  are interconnected via a communication link  210  (e.g., serial communication or wireless link). PET scanner  202  also referred to as a gantry, acquires scan data and transmits the scan data to data acquisition processor  206 . The operation of the PET scanner  202  is controlled from operator workstation  204 . The data acquired by data acquisition processor  206  is reconstructed into an image by image reconstruction processor  208 . 
   PET scanner  202  supports a plurality of detector rings. One such detector ring, detector ring  212 , is illustrated in the  FIG. 2 . Detector ring  212  includes a central opening, in which a patient  214  may be positioned using, for example, a motorized table, that is aligned with the central axis of detector ring  212 . The motorized table moves patient  214  into the central opening of detector ring  212  in response to one or more commands received from operator workstation  204 . A PET scanner controller  216 , also referred to as gantry controller, is provided (e.g., mounted) within PET scanner  202 . PET scanner controller  216  responds to the commands received from operator workstation  204  through communication link  210 . Thus, the operation of PET scanner  202  is controlled from operator workstation  204  through PET scanner controller  216 . 
   Detector ring  212  includes a plurality of detector units. In one exemplary embodiment, each detector ring comprises 70 detectors. For example, detector ring  212  includes detector  102  (shown in  FIG. 1 ), detector  104  (shown in  FIG. 1 ), and several other detectors. Detector  102 , like the other detectors, includes a set of scintillator crystals arranged in a matrix that is disposed in front of a plurality of photomultiplier tubes (e.g., four tubes). In an exemplary embodiment, each detector comprises 6 crystals. When a photon collides with a crystal on a detector, it produces a scintilla on the crystal. Each photomultiplier tube produces an analog signal on line  218  when a scintillation event occurs. A set of acquisition circuits  220  is provided within PET scanner  202  to receive these analog signals. Acquisition circuits  220  produce digital signals indicating the 3D location of the event and the total energy of the event. Acquisition circuits  220  also produce an event detection pulse, which indicates the time or moment that the scintillation event occurred. These digital signals are transmitted through a communication link, such as, for example, a cable to an event locator circuit  222  in data acquisition processor  206 . Data acquisition processor  206  includes event locator  222 , an acquisition CPU  224 , and a coincidence detector  226 . Data acquisition processor  206  periodically samples the signals produced by acquisition circuits  220 . Acquisition CPU  224  controls communications on a back-plane bus  228  and on communication link  210 . Event locator circuit  222  processes the information regarding each valid event and provides a set of digital numbers indicative of the detected event. Specifically, this information indicates when the event took place and the position of the scintillation crystal that detected the event. An event data packet is communicated to coincidence detector  226  through back-plane bus  228 . Coincidence detector  226  receives the event data packets from event locator circuit  222  and determines if any two of the detected events are in coincidence. Coincidence is determined by a number of factors. First, the time markers in each event data packet must be within a predetermined time period (e.g., 6.25 nanoseconds) of each other. Second, the LOR formed by a straight line joining the two detectors that detect the coincidence event, should pass through the field of view in the PET scanner  202 . Events that cannot be paired are discarded. Coincidence event pairs are located and recorded as a coincidence data packet that is conveyed through a communication link to a sorter  230  in image reconstruction processor  208 . 
   Image reconstruction processor  208  includes sorter  230 , a memory module  232 , an image CPU  234 , an image processor  236 , and a back-plane bus  238 . Sorter  230  counts all events occurring along each projection ray and organizes the events into 3D data. This 3D data or sinograms are organized in one exemplary embodiment as a data array  240 . Data array  240  is stored in memory module  232 . Back-plane bus  238  is linked to communication link  210  through Image CPU  234 . Image CPU  234  controls communication through back-plane bus  238 . Array processor  236  is also connected to back-plane bus  238 . Array processor  236  receives data array  240  as an input and reconstructs images in the form of image arrays  242 . Resulting image arrays  242  are stored in memory module  232 . 
   The images stored in image array  242  are communicated by image CPU  234  to operator workstation  204 . Operator workstation  204  includes a CPU  244 , a display device  246  and an input device  248 . CPU  244  connects to communication link  210  and receives inputs (e.g., user commands) from input device  248 . Input device  248  may be, for example, a keyboard, mouse or a touch-screen panel. Through input device  248  and associated control panel switches, the operator can control the calibration and configuration of the PET scanner  202 , and the positioning of the patient  214  for a scan. Similarly, the operator can control the display of the resulting image on display device  246  and perform image enhancement functions using programs executed by workstation CPU  244 . 
     FIG. 3  is a flowchart illustrating a method for determining normalization factors for image reconstruction in accordance with one exemplary embodiment of the present invention. The method may be performed, for example, by processor  236  on data arrays  240  as a part of the image reconstruction process. Specifically, at  302 , 3D normalization scans data S(r,θ,φ,z) is obtained, where ‘r’, ‘θ’, ‘φ’ and ‘z’ are dimensions as shown in  FIG. 1  and  FIG. 2 . ‘r’ is the perpendicular distance of an LOR from the central axis of detector ring  50 ; ‘θ’ is the angle that an LOR makes with a vertical passing through the central axis of the PET scanner, on a plane defined by the vertical and the central axis; ‘φ’ is angle that an LOR makes with the vertical; ‘z’ is the distance between the two detectors detecting an event in the direction of the axis of detector ring  50 . This data may be obtained by performing a normalization scan using a rod source. The rod source is rotated along an orbit co-axial to the scanner and readings from different detectors are measured. This data also may be obtained by direct calculation using an analytic model. Further, this data may be predicted through Monte Carlo simulation of a scan, or through a combination of an analytic model and simulations. 
   At  304 , the normalization scan data is down-sampled and a geometric factor g(r,θ,φ,z) is calculated. Normalization scan data is down-sampled to a {r,θ,φ,z} data set, wherein ‘r’ is the radial dimension of the data sinogram. For example, r is equal to 249 for a GE Discovery ST™ scanner manufactured by GE Medical Systems, which is a 3D image acquisition PET scanner. The total number of angles that are acquired by the scanner is 210. Down-sampling of normalization scan data is performed to take advantage of the symmetry in the detector geometry. In an exemplary embodiment of the invention, there are 420 crystals per ring, formed into 70 blocks of 6 crystals each. The crystals are arranged in the ring such that there exists a 70-fold symmetry around the detector ring. The geometric factors are expected to behave in a similar manner over this symmetry. Therefore, the value of the angular dimension of the down-sampled sinograms would be 6. 
   The down-sampled geometric scan data may also be represented in a {r,M,φ} data set. ‘M’ is the total number of sinograms. For example, if a particular scanner includes 24 detector rings, the total number of combinations of detector ring pairs would be 576 (24×24). In one embodiment, ‘M’ excludes combinations accounted for twice in the case of the neighboring or adjacent rings, in which case, the value of parameter M in this case is equal to 553 (576−23). Parameter ‘M’ therefore accounts for the parameter ‘z’ and parameter ‘θ’ in the {r,θ,φ,z} data set. ‘φ’. is a down-sample integral factor of a total number of acquired views. Therefore, a down-sampled set of {249,553,6} is obtained in this example. 
   This data set is then used to calculate a geometric factor g(r,θ,φ,z). In one embodiment of the invention, the average of normalization scan data S(r,θ,φ,z) over every six values of φ is calculated to obtain the geometric factor g(r,θ,φ,z). Other methods may also be used to calculate the values of geometric factor g(r,θ,φ,z) from the normalization scan data S(r,θ,φ,z). 
   At  306 , a 3D normalization data array is determined using the geometric factor g(r,θ,φ,z) and a crystal efficiency factor. A 3D phantom acquisition scan data is acquired to calculate the crystal efficiency factor. In accordance with one embodiment of the present invention, a phantom scan is performed, by limiting the range of the projection plane width, to cover the phantom only. Phantom scan data S(u,v,φ,θ) is obtained from the phantom scan. Here, ‘φ’ and ‘θ’ define a projection plane for a particular LOR; ‘u’ and ‘v’ define Cartesian Coordinates in the projection plane. The ‘u’ and ‘v’ coordinates of the phantom scan data are related to the ‘r’ and ‘z’ coordinates, respectively, of the geometric factor according to the geometry of the particular PET scanner. The phantom scan S(u,v,φ,θ) data is then divided by the geometric factor g(r,θ,φ,z) to produce a sinogram S′(u,v,φ,θ). A mean sinogram row S′(u) is determined from the arithmetic or geometric mean of the rows of sinogram S′(u,v,φ,θ). Further, sinogram S′(u,v,φ,θ) is divided by the mean sinogram S′(u) to produce a sinogram S″(u,v,φ,θ). A crystal-averaging scheme can then be performed on S″(u,v,φ,θ) to produce a crystal efficiency array e(X,Z), which represents the number of events each crystal (X,Z) participated in. The efficiency array e(X,Z) is scaled such that its average value over all e(X,Z) is 1.0. Crystal-averaging schemes are well known and described, for example, by Chesler and Stearns, IEEE Trans. Nucl. Sci., Vol. 37(2), pgs. 768–772. Thereafter, a 3D normalization data array is created. The normalization data array N(u,v,θ,φ) is defined as 1[g(r,θ,φ,z)e(X 1 Z 1 )e(X 2 Z 2 )]. 
   The normalized data array N(u,v,θ,φ) is used, for example, after performing a patient scan to normalize the data obtained in the scan. In particular, the measured scan data is multiplied by the normalization data array N(u,v,θ,φ) to normalize the measured scan data. Other correction methods may also be performed as a part of the 3D image reconstruction process. These correction methods include methods for the correction of the dead time factor that arises because a single detector cannot process two simultaneous coincidences. Also, methods for artifact correction are performed, which account for scattered and random coincidences and attenuation of photons within a patient&#39;s body. 
   The various embodiments of the normalization data array methods described herein for use in creating the normalization array take into account that the septa and crystals may not be exactly located in their desired positions. Also the various embodiments disclosed compensate for sensitivity variations within a single detector ring as well as for relative cross-planar sensitivities across different detector rings. The various embodiments also take into account effects such as fishnet artifacts and variations in module-to-module spacing. As a result, the created normalization data array N(u,v,θ,φ), facilitates the reconstruction of an improved image. 
   Moreover, the geometric factor arising in the axial or ‘z’ dimension may be significant in PET scanners containing septa between the detector rings. The various embodiments of the present invention compensate for this geometric factor, which also facilitates reconstruction of improved images. 
     FIG. 4  and  FIG. 5  show the effect of performing the 3D normalization in accordance with an embodiment of the invention on reconstruction of a PET image. Image  402  is an exemplary phantom image, reconstructed without using the 3D normalization. Image  502 , on the other hand, is reconstructed using the 3D normalization in accordance with the disclosed method. Images  402  and  502  were obtained using a twenty centimeter (cm) diameter, twenty cm long uniform phantom flood in a PET scanner. 
   It should be noted that because the geometric factors do not change significantly over time, the 2D normalization scan to determine the geometric factors can be performed relatively infrequently. For example, the normalization scan may be performed once in every three months, or only once for a particular scanner or even for a particular scanner design. The 3D phantom acquisition scan and creation of an updated 3D normalization data array N(u,v,θ,φ) based on the phantom acquisition scan is typically performed more often to estimate faster-changing single crystal efficiencies. 
   While the invention has been described in terms of various specific embodiments, those skilled in the art will recognize that the invention can be practiced with modification within the spirit and scope of the claims.