Patent Publication Number: US-11648422-B2

Title: Apparatus and methods of generating 4-dimensional computer tomography images

Description:
TECHNICAL FIELD 
     The present invention relates generally to single photon emission computed tomography (SPECT)/computed tomography (CT) or positron emission tomography (PET)/CT scan to measure an absorbed dose of ionising radiation. 
     BACKGROUND 
     SPECT and PET scan have been proven to be accurate for activity quantification, making 3-dimensional (3D) dosimetry feasible for targeted radionuclide therapy (TRT). However, SPECT and PET images have relatively poor resolution, high noise levels, and insufficient anatomical information, leading to large uncertainties for image registration and segmentation. 
     SPECT and PET scan can be improved by using sequential CT images. However, CT-aided dosimetry requires good alignment between SPECT and CT images or PET and CT images at each time instance. A 1-voxel (&lt;4.42 mm) mis-registration between CT and SPECT images could result in quantitation errors as large as 6% for bone marrow. 
     Sequential CT images require multiple CT to be performed on a subject, which raises radiation concerns. For example, in serial (4-5) SPECT/CT scanning sessions of  111 In-octreotide with 6 mCi injected doses for treatment planning, the effective dose from SPECT scan is 12.0 mSv 5 , while the effective dose from a low dose CT scan (e.g., having voltage: 120 kV, current: 100-300 mA, pitch: 0.984, slice thickness: 0.625 mm, rotation time: 0.5 s) is 7 mSv 6 . The total effective dose of both SPECT and CT scans can be up to 47 mSv. Thus, in some cases, only a single CT scan is performed along with the serial SPECT scans for TRT dosimetry, with an effective dose of about 19 mSv. 
     There is a need to improve the SPECT/CT and PET/CT protocols for TRT. 
     SUMMARY 
     It is an object of the present invention to substantially overcome, or at least ameliorate, one or more disadvantages of existing arrangements. 
     Disclosed are arrangements to improve SPECT/CT or PET/CT scan for a dosimetric analysis. The present disclosure uses multiple SPECT/PET scans and one CT scan to generate multiple virtual CT images (i.e., 4-dimensional CT images). The virtual CT images can then be used to improve the SPECT/PET scan. 
     Aspects of the present disclosure provide that the generation of the 4-dimensional virtual CT images (i.e., a series of virtual CT images over time) is performed by determining motion vectors for registration between the single CT image and the SPECT/PET images and using the determined motion vectors to generate the virtual CT images. 
     Other aspects of the present disclosure provide that the generation of the virtual CT images is performed by determining motion vectors for registration between a SPECT/PET image corresponding to the single CT image and the remaining SPECT/PET images and using the determined motion vectors to generate the virtual CT images. 
     According to a first aspect of the present disclosure, there is provided a system comprising: a SPECT or PET device; a CT device; and a computer comprising memory and a processor in communication with the memory, the memory comprising a computer application program for a method of performing dosimetric analysis of an organ, wherein the computer application program is executable by the processor to perform the method, the method comprising: receiving single photon emission computed tomography (SPECT) or positron emission tomography (PET) images at time instances, the SPECT or PET images relating to the organ; receiving a computed tomography (CT) image at one of the time instances, the CT image relating to the organ; generate virtual CT images at the other time instances based on the received SPECT or PET images and the CT image; and measure an absorbed dose of ionising radiation on the organ based on the received SPECT or PET images, the received CT image, and the generated virtual CT images. 
     According to a second aspect of the present disclosure, there is provided a non-transitory computer readable medium comprising a computer application program for a method of performing dosimetric analysis of an organ, the method comprising: receiving single photon emission computed tomography (SPECT) or positron emission tomography (PET) images at time instances, the SPECT or PET images relating to the organ; receiving a computed tomography (CT) image at one of the time instances, the CT image relating to the organ; generate virtual CT images at the other time instances based on the received SPECT or PET images and the CT image; and measure an absorbed dose of ionising radiation on the organ based on the received SPECT or PET images, the received CT image, and the generated virtual CT images. 
     According to a third aspect of the present disclosure, there is provided a computer-implemented method of performing dosimetric analysis, the method comprising: receiving single photon emission computed tomography (SPECT) or positron emission tomography (PET) images at time instances, the SPECT or PET images relating to an organ; receiving a computed tomography (CT) image at one of the time instances, the CT image relating to the organ; generate virtual CT images at the other time instances based on the received SPECT or PET images and the CT image; and measure an absorbed dose of ionising radiation on the organ based on the received SPECT or PET images, the received CT image, and the generated virtual CT images. 
     Other aspects are also disclosed. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       At least one embodiment of the present invention will now be described with reference to the drawings and appendices, in which: 
         FIG.  1    shows a system for performing SPECT/CT scan in accordance with aspects of the present disclosure; 
         FIGS.  2 A and  2 B  form a schematic block diagram of a general purpose computer system upon which arrangements described can be practiced; 
         FIG.  3    is a flow chart of a method of measuring an absorbed dose of ionising radiation in accordance with aspects of the present disclosure; 
         FIG.  4 A  is a flow chart of a sub-process of generating virtual CT images for the method of  FIG.  3   ; 
         FIG.  4 B  illustrates the sub-process of  FIG.  4 A ; 
         FIG.  5 A  is a flow chart of an alternative sub-process of generating virtual CT images for the method of  FIG.  3   ; 
         FIG.  5 B  illustrates the sub-process of  FIG.  5 A ; 
         FIG.  6 A  is a flow chart of another alternative sub-process of generating virtual CT images for the method of  FIG.  3   ; 
         FIG.  6 B  illustrates the sub-process of  FIG.  6 A ; 
         FIG.  7 A  shows SPECT images generated by a model for registration (without attenuation and scatter correction); 
         FIG.  7 B  shows the SPECT images of  FIG.  7 A  after attenuation and scatter correction using the generated virtual CT images; 
         FIG.  8 A  shows simulated real CT images at different time instances; 
         FIG.  8 B  shows virtual CT images generated using the sub-process of  FIG.  4 A ; 
         FIG.  9    shows the difference images generated when comparing simulated virtual CT images against simulated real CT images at the same time instance; 
         FIG.  10    shows the average normalized mean square errors (NMSE) for the virtual CT images generated by the respective sub-processes of  FIGS.  4 A,  5 A, and  6 A ; and 
         FIGS.  11 A and  11 B  show the dosimetric results in assessing the performance of using the virtual CT images. 
     
    
    
     DETAILED DESCRIPTION INCLUDING BEST MODE 
     Where reference is made in any one or more of the accompanying drawings to steps and/or features, which have the same reference numerals, those steps and/or features have for the purposes of this description the same function(s) or operation(s), unless the contrary intention appears. 
       FIG.  1    shows a system  100  for performing the SPECT/CT scan. The system  100  includes a SPECT device  110 , a CT device  120 , and a computer system  130 . The system  100  is used to acquire SPECT images (using the SPECT device  110 ) and CT images (using the CT device  120 ) of an organ of a subject  190 . 
     In an alternative arrangement, a PET device is used instead of a SPECT device to perform PET/CT protocol. Hereinafter, for convenience sake, the present disclosure will only describe the use of the SPECT device  110  to acquire SPECT images and use the acquired SPECT images to generate the 4-dimensional CT images. However, it should be understood that the SPECT device  110  can be replaced by a PET device to acquire PET images. The acquired PET images can then be used rather than the SPECT images described below. 
     The SPECT device  110  includes a gamma camera (not shown) to capture a gamma-emitting radioisotope (a radionuclide) that is inserted into the subject  190 . The SPECT device  110  then captures SPECT images of an organ of the subject  190 . The SPECT images are then forwarded to the computer system  130 . 
     The CT device  120  includes an X-ray generator (not shown) and an X-ray detector (not shown) to perform X-ray measurements of an organ of the subject  190 . The X-ray measurements are then transmitted to the computer system  130 , which processes the X-ray measurements to produce CT images. 
     In one arrangement, the SPECT device  110  and the CT device  120  may be integrated into one device. 
     The subject  190  can be a person or an animal. The SPECT device  110  and the CT device  120  can take images of an organ (e.g., brain, lungs, heart, etc.) of the subject  190 . 
     Computer System  130   
       FIGS.  2 A and  2 B  depict a general-purpose computer system  130 , upon which the various arrangements described can be practiced. 
     As seen in  FIG.  2 A , the computer system  130  includes: a computer module  1301 ; input devices such as a keyboard  1302  and a mouse pointer device  1303 ; and output devices including a display device  1314  and loudspeakers  1317 . An external Modulator-Demodulator (Modem) transceiver device  1316  may be used by the computer module  1301  for communicating to and from a communications network  1320  via a connection  1321 . The communications network  1320  may be a wide-area network (WAN), such as the Internet, a cellular telecommunications network, or a private WAN. Where the connection  1321  is a telephone line, the modem  1316  may be a traditional “dial-up” modem. Alternatively, where the connection  1321  is a high capacity (e.g., cable) connection, the modem  1316  may be a broadband modem. A wireless modem may also be used for wireless connection to the communications network  1320 . 
     The computer module  1301  typically includes at least one processor unit  1305 , and a memory unit  1306 . For example, the memory unit  1306  may have semiconductor random access memory (RAM) and semiconductor read only memory (ROM). The computer module  1301  also includes an number of input/output (I/O) interfaces including: an audio-video interface  1307  that couples to the video display  1314  and loudspeakers  1317 ; an I/O interface  1313  that couples to the keyboard  1302 , mouse  1303 , and optionally a joystick or other human interface device (not illustrated); and an interface  1308  for the external modem  1316 . In some implementations, the modem  1316  may be incorporated within the computer module  1301 , for example within the interface  1308 . The computer module  1301  also has a local network interface  1311 , which permits coupling of the computer system  130  via a connection  1323  to a local-area communications network  1322 , known as a Local Area Network (LAN). As illustrated in  FIG.  2 A , the local communications network  1322  may also couple to the wide network  1320  via a connection  1324 , which would typically include a so-called “firewall” device or device of similar functionality. The local network interface  1311  may comprise an Ethernet circuit card, a Bluetooth® wireless arrangement or an IEEE 802.11 wireless arrangement; however, numerous other types of interfaces may be practiced for the interface  1311 . 
     The I/O interfaces  1308  and  1313  may afford either or both of serial and parallel connectivity, the former typically being implemented according to the Universal Serial Bus (USB) standards and having corresponding USB connectors (not illustrated). Storage devices  1309  are provided and typically include a hard disk drive (HDD)  1310 . Other storage devices such as a floppy disk drive and a magnetic tape drive (not illustrated) may also be used. An optical disk drive  1312  is typically provided to act as a non-volatile source of data. Portable memory devices, such optical disks (e.g., CD-ROM, DVD, Blu-ray Disc™), USB-RAM, portable, external hard drives, and floppy disks, for example, may be used as appropriate sources of data to the system  130 . 
     As shown in  FIG.  2 A , the SPECT device  110  and the CT device  120  are connected to the WAN  1320 . In an alternative arrangement, the SPECT device  110  and the CT device  120  can be connected to the LAN  1322  or the I/O Interfaces  1308  to communicate with the computer system  130 . 
     The components  1305  to  1313  of the computer module  1301  typically communicate via an interconnected bus  1304  and in a manner that results in a conventional mode of operation of the computer system  130  known to those in the relevant art. For example, the processor  1305  is coupled to the system bus  1304  using a connection  1318 . Likewise, the memory  1306  and optical disk drive  1312  are coupled to the system bus  1304  by connections  1319 . Examples of computers on which the described arrangements can be practised include IBM-PC&#39;s and compatibles, Sun Sparcstations, Apple Mac™ or like computer systems. 
     The method and sub-processes for dosimetric analysis and generating virtual CT images may be implemented using the computer system  130  wherein the processes of Figs.  FIG.  3    and sub-processes of  FIGS.  4 A to  6 B  to be described, may be implemented as one or more software application programs  1333  executable within the computer system  130 . In particular, the steps of the method of  FIG.  3    and sub-processes of  FIGS.  4 A to  6 B  are effected by instructions  1331  (see  FIG.  2 B ) in the software  1333  that are carried out within the computer system  130 . The software instructions  1331  may be formed as one or more code modules, each for performing one or more particular tasks. The software may also be divided into two separate parts, in which a first part and the corresponding code modules performs the dosimetric analysis and virtual CT image generation methods and a second part and the corresponding code modules manage a user interface between the first part and the user. 
     The software may be stored in a computer readable medium, including the storage devices described below, for example. The software is loaded into the computer system  130  from the computer readable medium, and then executed by the computer system  130 . A computer readable medium having such software or computer program recorded on the computer readable medium is a computer program product. The use of the computer program product in the computer system  130  preferably effects an advantageous apparatus for performing dosimetric analysis and generating virtual CT images. 
     The software  1333  is typically stored in the HDD  1310  or the memory  1306 . The software is loaded into the computer system  130  from a computer readable medium, and executed by the computer system  130 . Thus, for example, the software  1333  may be stored on an optically readable disk storage medium (e.g., CD-ROM)  1325  that is read by the optical disk drive  1312 . A computer readable medium having such software or computer program recorded on it is a computer program product. The use of the computer program product in the computer system  130  preferably effects an apparatus for performing dosimetric analysis and generating virtual CT images. 
     In some instances, the application programs  1333  may be supplied to the user encoded on one or more CD-ROMs  1325  and read via the corresponding drive  1312 , or alternatively may be read by the user from the networks  1320  or  1322 . Still further, the software can also be loaded into the computer system  130  from other computer readable media. Computer readable storage media refers to any non-transitory tangible storage medium that provides recorded instructions and/or data to the computer system  130  for execution and/or processing. Examples of such storage media include floppy disks, magnetic tape, CD-ROM, DVD, Blu-ray™ Disc, a hard disk drive, a ROM or integrated circuit, USB memory, a magneto-optical disk, or a computer readable card such as a PCMCIA card and the like, whether or not such devices are internal or external of the computer module  1301 . Examples of transitory or non-tangible computer readable transmission media that may also participate in the provision of software, application programs, instructions and/or data to the computer module  1301  include radio or infra-red transmission channels as well as a network connection to another computer or networked device, and the Internet or Intranets including e-mail transmissions and information recorded on Websites and the like. 
     The second part of the application programs  1333  and the corresponding code modules mentioned above may be executed to implement one or more graphical user interfaces (GUIs) to be rendered or otherwise represented upon the display  1314 . Through manipulation of typically the keyboard  1302  and the mouse  1303 , a user of the computer system  130  and the application may manipulate the interface in a functionally adaptable manner to provide controlling commands and/or input to the applications associated with the GUI(s). Other forms of functionally adaptable user interfaces may also be implemented, such as an audio interface utilizing speech prompts output via the loudspeakers  1317  and user voice commands input via a microphone. 
       FIG.  2 B  is a detailed schematic block diagram of the processor  1305  and a “memory”  1334 . The memory  1334  represents a logical aggregation of all the memory modules (including the HDD  1309  and semiconductor memory  1306 ) that can be accessed by the computer module  1301  in  FIG.  2 A . 
     When the computer module  1301  is initially powered up, a power-on self-test (POST) program  1350  executes. The POST program  1350  is typically stored in a ROM  1349  of the semiconductor memory  1306  of  FIG.  2 A . A hardware device such as the ROM  1349  storing software is sometimes referred to as firmware. The POST program  1350  examines hardware within the computer module  1301  to ensure proper functioning and typically checks the processor  1305 , the memory  1334  ( 1309 ,  1306 ), and a basic input-output systems software (BIOS) module  1351 , also typically stored in the ROM  1349 , for correct operation. Once the POST program  1350  has run successfully, the BIOS  1351  activates the hard disk drive  1310  of  FIG.  2 A . Activation of the hard disk drive  1310  causes a bootstrap loader program  1352  that is resident on the hard disk drive  1310  to execute via the processor  1305 . This loads an operating system  1353  into the RAM memory  1306 , upon which the operating system  1353  commences operation. The operating system  1353  is a system level application, executable by the processor  1305 , to fulfil various high level functions, including processor management, memory management, device management, storage management, software application interface, and generic user interface. 
     The operating system  1353  manages the memory  1334  ( 1309 ,  1306 ) to ensure that each process or application running on the computer module  1301  has sufficient memory in which to execute without colliding with memory allocated to another process. Furthermore, the different types of memory available in the system  130  of  FIG.  2 A  must be used properly so that each process can run effectively. Accordingly, the aggregated memory  1334  is not intended to illustrate how particular segments of memory are allocated (unless otherwise stated), but rather to provide a general view of the memory accessible by the computer system  130  and how such is used. 
     As shown in  FIG.  2 B , the processor  1305  includes a number of functional modules including a control unit  1339 , an arithmetic logic unit (ALU)  1340 , and a local or internal memory  1348 , sometimes called a cache memory. The cache memory  1348  typically includes a number of storage registers  1344 - 1346  in a register section. One or more internal busses  1341  functionally interconnect these functional modules. The processor  1305  typically also has one or more interfaces  1342  for communicating with external devices via the system bus  1304 , using a connection  1318 . The memory  1334  is coupled to the bus  1304  using a connection  1319 . 
     The application program  1333  includes a sequence of instructions  1331  that may include conditional branch and loop instructions. The program  1333  may also include data  1332  which is used in execution of the program  1333 . The instructions  1331  and the data  1332  are stored in memory locations  1328 ,  1329 ,  1330  and  1335 ,  1336 ,  1337 , respectively. Depending upon the relative size of the instructions  1331  and the memory locations  1328 - 1330 , a particular instruction may be stored in a single memory location as depicted by the instruction shown in the memory location  1330 . Alternately, an instruction may be segmented into a number of parts each of which is stored in a separate memory location, as depicted by the instruction segments shown in the memory locations  1328  and  1329 . 
     In general, the processor  1305  is given a set of instructions which are executed therein. The processor  1305  waits for a subsequent input, to which the processor  1305  reacts to by executing another set of instructions. Each input may be provided from one or more of a number of sources, including data generated by one or more of the input devices  1302 ,  1303 , data received from an external source across one of the networks  1320 ,  1302 , data retrieved from one of the storage devices  1306 ,  1309  or data retrieved from a storage medium  1325  inserted into the corresponding reader  1312 , all depicted in  FIG.  2 A . The execution of a set of the instructions may in some cases result in output of data. Execution may also involve storing data or variables to the memory  1334 . 
     The disclosed dosimetric analysis and virtual CT image generation arrangements use input variables  1354 , which are stored in the memory  1334  in corresponding memory locations  1355 ,  1356 ,  1357 . The dosimetric analysis and virtual CT image generation arrangements produce output variables  1361 , which are stored in the memory  1334  in corresponding memory locations  1362 ,  1363 ,  1364 . Intermediate variables  1358  may be stored in memory locations  1359 ,  1360 ,  1366  and  1367 . 
     Referring to the processor  1305  of  FIG.  2 B , the registers  1344 ,  1345 ,  1346 , the arithmetic logic unit (ALU)  1340 , and the control unit  1339  work together to perform sequences of micro-operations needed to perform “fetch, decode, and execute” cycles for every instruction in the instruction set making up the program  1333 . Each fetch, decode, and execute cycle comprises: 
     a fetch operation, which fetches or reads an instruction  1331  from a memory location  1328 ,  1329 ,  1330 ; 
     a decode operation in which the control unit  1339  determines which instruction has been fetched; and 
     an execute operation in which the control unit  1339  and/or the ALU  1340  execute the instruction. 
     Thereafter, a further fetch, decode, and execute cycle for the next instruction may be executed. Similarly, a store cycle may be performed by which the control unit  1339  stores or writes a value to a memory location  1332 . 
     Each step or sub-process in the processes of  FIGS.  3  to  6 B  is associated with one or more segments of the program  1333  and is performed by the register section  1344 ,  1345 ,  1347 , the ALU  1340 , and the control unit  1339  in the processor  1305  working together to perform the fetch, decode, and execute cycles for every instruction in the instruction set for the noted segments of the program  1333 . 
     The method of performing dosimetric analysis and virtual CT image generation may alternatively be implemented in dedicated hardware such as one or more integrated circuits performing the functions or sub functions of the method and sub-processes of  FIGS.  3  to  6 B . Such dedicated hardware may include graphic processors, digital signal processors, or one or more microprocessors and associated memories. 
     Dosimetric Analysis Method  300   
       FIG.  3    shows a method  300  for performing a dosimetric analysis. The method  300  can be implemented as one or more software application programs  1333  executable within the computer system  130 . 
     The method  300  commences with step  310  by receiving SPECT images from the SPECT device  110 . The SPECT device  110  acquires the SPECT images of an organ of the subject  190  at different time instances. The method  300  proceeds from step  310  to step  320 . 
     In step  320 , the CT device  120  and the computer system  130  operate to produce a CT image of the organ (which is the same organ of step  310 ). The CT image is captured at one of the time instances at which the SPECT images are captured. The method  300  proceeds from step  320  to sub-process  330 . 
     Sub-process  330  generates virtual CT images based on the acquired SPECT images (step  310 ) and the acquired CT image (step  320 ). The generated virtual CT images are at the time instances at which the SPECT images are captured. Three implementations of the sub-process  330  are described respectively in  FIGS.  4 A,  5 A, and  6 A , which will be described hereinafter. The method  300  proceeds from sub-process  330  to step  340 . 
     In step  340 , the method  300  measures an absorbed dose of ionising radiation on the organ based on the acquired SPECT images, the acquired CT image, and the virtual CT images. The acquired CT image and the virtual CT images are first used for attenuation and scatter correction for the corresponding SPECT images. The organ is segmented out on the CT image and the virtual CT images and then used to map out the corresponding organ on SPECT images (acquired at step  310 ). The segmented images are then used to determine the activity of the target organ at different time instances. In particular, the segmented images are curve fitted to estimate the time activity curve and the cumulative activity, which is then convolved to a dose kernel to calculate the absorbed dose of the organs. The method  300  concludes at the conclusion of step  340 . 
     Sub-Process  330 A 
       FIGS.  4 A and  4 B  show the first implementation of the sub-process  330 . Hereinafter, the first implementation of sub-process  330  will be referred to as sub-process  330 A for convenience sake.  FIG.  4 A  shows a flow chart of sub-process  330 A, while  FIG.  4 B  shows an illustration of the sub-process  330 A. 
       FIG.  4 B  shows a CT image  460  (acquired at step  320 ), SPECT images  445 A to  445 N and  440  (acquired at step  310 ) captured at N+1 time instances, and virtual CT images  465 A to  465 N at N time instances. The number of time instances used is for ease of explanation only. 
     Sub-process  330 A commences at step  410  by determining which one of the SPECT images (captured at step  310 ) correspond with the acquired CT image (step  320 ). The determination is performed by comparing the time instances at which the SPECT images  445 A to  445 N and  440  and the CT image  460  are captured. The SPECT image  440  having the same time instance as the CT image  460  is the SPECT image determined to correspond with the acquired CT image  460 . 
       FIG.  4 B  shows the SPECT image  440  as the SPECT image corresponding with the acquired CT image  460  (i.e., the SPECT image  440  is captured at the same time instance as the CT image  460 ). The remaining SPECT images  445 A to  445 N are the SPECT images captured at the remaining N time instances. The SPECT images  445 A to  445 N and  440  are compensated with geometric collimator-detector response (GCDR) without attenuation correction (AC) and scatter correction (SC). 
     Sub-process  330 A proceeds from step  410  to step  420 . 
     In step  420 , sub-process  330  determines a set of motion vectors (e.g.,  450 A) for registering the determined SPECT image  440  to each of the remaining, acquired SPECT images  445 A to  445 N. Therefore, the SPECT image  440  is the moving image and the SPECT images  445 A to  445 N are the fixed images. Each of the motion vectors  450 A to  450 N is a vector describing the transformation of each pixel of the SPECT image  440  in order to register the SPECT image  440  to the other SPECT images  445 A to  445 N. The transformation may include linear transformations (including rotation, scaling, translation, and other affine transforms) and non-rigid transformations (including radial basis functions, physical continuum models, and large deformation models). Therefore, the set of motion vectors  450 A provides the transformation required to register the SPECT image  440  to the SPECT image  445 A at a first time instance. Similarly, the set of motion vectors  450 B provides the transformation required to register the SPECT image  440  to the SPECT image  445 B at a second time instance. 
     Sub-process  330 A proceeds from step  420  to step  430 . 
     In step  430 , virtual CT images  465 A to  465 N are generated based on the determined sets of motion vectors  450 A to  450 N. To generate a virtual CT image  465 A at a first time instance (which is the same time instance as SPECT image  445 A), the CT image  460  is transformed using the set of motion vectors  450 A. Accordingly, the respective virtual CT images  465 A to  465 N are generated at N time instances corresponding with the N time instances at which the SPECT images  445 A to  445 N are captured. 
     In one arrangement, the motion vectors  450 A to  450 N relate to affine plus B-spline non-rigid image registration method. To perform the non-rigid registration, mutual information is normalised for 20000 pixels which are randomly selected for each resolution, and a three-level, multi-resolution approach with different grid sizes (8×8×8, 4×4×4, 1×1×1) is used to speed up both affine and B-spline registrations. For B-spline registrations, a bending energy term regularizes the deformation field to keep the rigidity and avoid the folding of local features. A stochastic gradient descent algorithm with 1000 iterations is used to iteratively solve the registration problem with adaptive step size prediction. 
     Therefore, by applying each set of motion vectors  450 A to  450 N, virtual CT images  465 A to  465 N are generated at N time instances. 
     Sub-process  330 A concludes at the conclusion of step  430 . 
     Sub-Process  330 B 
       FIGS.  5 A and  5 B  show the second implementation of the sub-process  330 . Hereinafter, the second implementation of sub-process  330  will be referred to as sub-process  330 B for convenience sake.  FIG.  5 A  shows a flow chart of sub-process  330 B, while  FIG.  5 B  shows an illustration of the sub-process  330 B. 
       FIG.  5 B  shows a CT image  560  (acquired at step  320 ), SPECT images  545 A to  545 N (acquired at step  310 ) captured at N time instances, and virtual CT images  565 A to  565 N. The number of time instances used is for ease of explanation only. 
     Sub-process  330 B commences at step  510  by determining a set of motion vectors (e.g.,  550 A) for registering the acquired CT image  560  (at step  320 ) to each of the acquired SPECT images  545 A to  545 N. The registration between the CT image  560  and a SPECT image at the same time instance is not required. Therefore, the SPECT images  545 A to  545 N do not include the SPECT image captured at the same time instance as the CT image  560 . The SPECT images  545 A to  545 N are compensated with geometric collimator-detector response (GCDR) without AC and SC. 
     Therefore, in sub-process  330 B, the CT image  560  is the moving image and the SPECT images  545 A to  545 N are the fixed images. Each of the motion vectors  550 A to  550 N is a vector describing the transformation of each pixel of the CT image  560  in order to register the CT image  560  to the SPECT images  545 A to  545 N. The transformation may include linear transformations (including rotation, scaling, translation, and other affine transforms) and non-rigid transformations (including radial basis functions, physical continuum models, and large deformation models). Therefore, the set of motion vectors  550 A provides the transformation required to register the CT image  560  to the SPECT image  545 A at a first time instance. Similarly, the set of motion vectors  550 B provides the transformation required to register the CT image  560  to the SPECT image  545 B at a second time instance. 
     Sub-process  330 B proceeds from step  510  to step  520 . 
     In step  520 , virtual CT images  565 A to  565 N are generated based on the determined sets of motion vectors  550 A to  550 N. To generate a virtual CT image  565 A at a first time instance (which is the same time instance as SPECT image  545 A), the CT image  560  is transformed using the set of motion vectors  550 A. Accordingly, the respective virtual CT images  565 A to  565 N are generated at N time instances corresponding with the N time instances at which the SPECT images  545 A to  545 N are captured. 
     In one arrangement, the motion vectors  550 A to  550 N relate to affine plus B-spline non-rigid image registration method. To perform the non-rigid registration, mutual information is normalised for 20000 pixels which are randomly selected for each resolution, and a three-level, multi-resolution approach with different grid sizes (8×8×8, 4×4×4, 1×1×1) is used to speed up both affine and B-spline registrations. For B-spline registrations, a bending energy term regularizes the deformation field to keep the rigidity and avoid the folding of local features. A stochastic gradient descent algorithm with 1000 iterations is used to iteratively solve the registration problem with adaptive step size prediction. 
     Therefore, by applying each set of motion vectors  550 A to  550 N, virtual CT images  565 A to  565 N are generated. Each of the virtual CT images  565 A to  565 N corresponds to the time instance at which the respective SPECT images  545 A to  545 N are captured. 
     Sub-process  330 B concludes at the conclusion of step  520 . 
     Sub-Process  330 C 
       FIGS.  6 A and  6 B  show the third implementation of the sub-process  330 . Hereinafter, the third implementation of sub-process  330  will be referred to as sub-process  330 C for convenience sake.  FIG.  6 A  shows a flow chart of sub-process  330 C, while  FIG.  6 B  shows an illustration of the sub-process  330 C. 
       FIG.  6 B  shows a CT image  660  (acquired at step  320 ), SPECT images  645 A to  645 N (acquired at step  310 ) captured at N time instances, and virtual CT images  565 A to  565 N. The number of time instances used is for ease of explanation only. 
     Sub-process  330 C commences at step  610  by determining a set of motion vectors (e.g.,  650 A) for registering each of the acquired SPECT images  645 A to  645 N to the acquired CT image  660  (at step  320 ). The registration between the CT image  660  and a SPECT image at the same time instance is not required. Therefore, the SPECT images  645 A to  645 N do not include the SPECT image captured at the same time instance as the CT image  660 . The SPECT images  645 A to  645 N are compensated with geometric collimator-detector response (GCDR) without AC and SC. 
     Therefore, in sub-process  330 C, the SPECT images  645 A to  645 N are the moving images and the CT image  660  is the fixed image. Each of the motion vectors  650 A to  650 N is a vector describing the transformation of each pixel of a SPECT image (e.g.,  650 A to  650 N) in order to register the SPECT image (e.g.,  650 A to  650 N) to the CT image  660 . The transformation may include linear transformations (including rotation, scaling, translation, and other affine transforms) and non-rigid transformations (including radial basis functions, physical continuum models, and large deformation models). Therefore, the set of motion vectors  650 A provides the transformation required to register the SPECT image  645 A to the CT image  660  at a first time instance. Similarly, the set of motion vectors  650 B provides the transformation required to register the SPECT image  645 B to the CT image  660  at a second time instance. 
     Sub-process  330 C proceeds from step  610  to step  620 . 
     In step  620 , the determined sets of motion vectors  650 A to  650 N are inversely transformed to acquire sets of inverse motion vectors  650 A′ to  650 N′. Sub-process  330 C proceeds from step  620  to step  630 . 
     In step  630 , virtual CT images  665 A to  665 N are generated based on the determined sets of inverse motion vectors  650 A′ to  650 N′. To generate a virtual CT image  665 A at a first time instance (which is the same time instance as SPECT image  645 A), the CT image  660  is transformed using the set of inverse motion vectors  650 A′. Accordingly, the respective virtual CT images  665 A to  665 N are generated at N time instances corresponding with the N time instances at which the SPECT images  645 A to  645 N are captured. 
     In one arrangement, the inverse motion vectors  650 A′ to  650 N′ relate to affine plus B-spline non-rigid image registration method. To perform the non-rigid registration, mutual information is normalised for 20000 pixels which are randomly selected for each resolution, and a three-level, multi-resolution approach with different grid sizes (8×8×8, 4×4×4, 1×1×1) is used to speed up both affine and B-spline registrations. For B-spline registrations, a bending energy term regularizes the deformation field to keep the rigidity and avoid the folding of local features. A stochastic gradient descent algorithm with 1000 iterations is used to iteratively solve the registration problem with adaptive step size prediction. 
     Therefore, by applying each set of inverse motion vectors  650 A′ to  650 N′, virtual CT images  665 A to  665 N are generated. Each of the virtual CT images  665 A to  665 N corresponds to the time instance at which the respective SPECT images  645 A to  645 N are captured. 
     Sub-process  330 C concludes at the conclusion of step  630 . 
     Assessing the Performance of SPECT/CT or PET/CT Protocol Using Virtual CT Images 
     The SPECT/CT scans using the virtual CT images is tested using a simulation model having a population of nine, four-dimensional (4D) digital Extended Cardiac Torso (XCAT) phantoms composed of three various anatomies, i.e., body and organ sizes, and three  111 In-Zevalin distributions for each anatomy. The simulation model includes respiratory and cardiac motions. Uniform distribution of activity is simulated in main organs (such as kidneys, liver, and spleen) as well as other background organs (such as muscle and other unspecified organs). Non-uniform distribution of activity is simulated in the lungs with airway activity set to zero, differing from that in lung parenchyma. The time-varying  111 In distribution of each target organ is used to simulate SPECT scans acquired at 1, 12, 24, 72, and 144 hours post-injection of the radioisotope. 
     To simulate non-rigid organ deformations, rotations and translations for each individual organ are randomly simulated within five pixels or degrees while the volume changes are kept within 5%. The rigid body translations and rotations between each session of capturing SPECT images are randomly simulated within five pixels or degrees as well. The attenuation maps of the corresponding XCAT phantoms at different time points are generated at average energy of 192.6 keV for attenuation modelling and serve as the “real” CT (rCT) images. The virtual CT images are generated based on one rCT image at a selected time instance as described above in relation to any one of the sub-processes of  FIGS.  4 A to  6 B . 
     The system  100  is simulated with a medium energy parallel-hole collimator mounted for  111 In acquisition with two 14% energy windows centered at 171 and 245 keV respectively. An analytical projector modelling attenuation, scattering, and GCDR is used to generate 128 noise-free projections over 360°. In order to model the continuous nature of the activity distribution, projections are generated using XCAT phantoms with a voxel size of 0.221 cm 3  and then collapsed to a bin size of 0.442 cm 3  for reconstruction. A system calibration factor of 1.43×10 4  counts·s −1 ·Bq −1  is used to scale the noise-free projections to a clinical count level. 30-minute SPECT scans are simulated for different activities, administration and imaging time instances respectively and then modelled with Poisson noise to obtain realistic noisy projections. 
     Three protocols are used to assess the performance of the virtual CT images. The protocols are as follows:
         a. rCT protocol: for every time instance, both SPECT and CT images are acquired and used.   b. 1CT protocol: only 1 CT image is acquired at the first time instance, while   SPECT images are acquired for every time instance.       

     c. vCT protocol: only 1 CT image is acquired at the first time instance, while SPECT images are acquired for every time instance. Virtual CT images are then generated at the other time instances to correspond to the generated SPECT images. 
     For the rCT protocol, noisy projections are reconstructed iteratively with full (AC, SC and GCDR) compensation and an ordered-subset expectation-maximization (OS-EM) algorithm of eight iterations and 16 subsets i.e., 128 updates using rCT for AC and SC. For the 1CT protocol, AC and SC are performed for SPECT images at all time instances using the acquired single CT image. For the vCT protocol, preliminary reconstruction is first performed only with GCDR correction (see  FIG.  7 A ) to generate SPECT images for registration. A second reconstruction with full compensation is later performed after the virtual CT images are generated (see  FIG.  7 B ). 
     Sub-Process  330  Optimization 
     For three sub-processes  330 A,  330 B, and  330 C, the optimal time instance at which to capture the CT image of step  320  is determined. To determine the optimal time instance, a CT image is acquired at 1, 12, 24, 72 and 144 hours separately using the simulation. Virtual CT images are then generated using the respective sub-processes  330 A,  330 B, and  330 C for each of the acquired CT image. In other words, for the CT image acquired at 1 hour using the simulation, virtual CT images are generated for the time instances of 12, 24, 72 and 144 hours. A similar operation is performed for each acquired CT image so that, for each time instance, there is a CT image and 3 virtual CT images (generated by each of the sub-processes  330 A,  330 B, and  330 C). 
     At each time instance, the CT image is compared with each of the generated virtual CT images to obtain difference images and average normalized mean square errors (NMSE). The difference images and the NMSE are used to evaluate the difference between different virtual CT images and the corresponding CT image for the nine phantoms. The NMSE is determined using the equation: 
                 average   ⁢         NMSE   ⁢     (     x   ,   y     )       =         ∑     i   =   1     4             ∑     j   =   1     9         ∑     k   =   1     N         (       x   k     -     y   k       )     2             36   ⁢       ∑     k   =   1     N       x     k   2               ,         
where x k  and y k  represent the image intensity in virtual CT and rCT images, N is the number of voxels in the whole CT, j is the index for the phantoms and i is the time-point index.
 
     As described in step  340 , dosimetric analysis is performed. Organ absorbed dose error (% ODE) and normalized absolute error (% NAE) of the differential dose volume histogram (DDVH) are compared to reference OD and DVH. The % ODE and % NAE are calculated to assess the 3D dosimetric accuracy for each target organ. The results using the rCT protocol with AC and SC with no segmentation and misalignment errors served as the reference. % ODE is calculated using the equation: 
             %   ⁢         ODE   ⁢     =           D     vCT   ,   rCT   ,     1   ⁢   CT         -     D     r   ⁢   e   ⁢   f           D     r   ⁢   e   ⁢   f         ×   1   ⁢   0   ⁢   0   ⁢   %             
where D vCT,rCT,1CT  refers to the organ absorbed doses calculated based on vCT, rCT or 1CT protocols, while D ref  refers to the reference as described above. % NAE is calculated using the equation:
 
     
       
         
           
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     For each target organ, the DDVH is calculated by computing the volume (V) in each of the 20 dose intervals (indexed by i), which are defined by the dose range divided by 20. 
       FIG.  8 A  shows simulated real CT images at different time instances, while  FIG.  8 B  shows the virtual CT images generated using sub-process  330 A with a single CT image (acquired at step  320 ) at a first time instance.  FIG.  9    shows the difference images between the generated virtual CT image (generated by the respective sub-processes  330 A,  330 B,  330 C) and the corresponding CT image for the same time instance. Errors are mostly found in bone regions such as ribs, pelvis and spine. Based on the errors, sub-process  330 A shows the best result, followed by sub-process  330 C and finally sub-process  330 B. 
       FIG.  10    shows the average NMSE results for each of the sub-processes  330 A,  330 B, and  330 C for the nine phantoms. The error bar in  FIG.  10    shows the one-side standard deviation.  FIG.  10    also shows the average NMSE between the generated virtual CT images and the corresponding rCTs for all time instances, where the virtual CT images are generated using the single CT acquired at the different time instances. Similar to the result in  FIG.  9   , the NMSE shows that sub-process  330 A provides the best result, and using the 1 st  time instance as the moving image shows the best results. 
     Dosimetric Results Evaluation 
     As described above, sub-process  330 A provides the best result for the vCT protocol. The dosimetric results of vCT protocol (generated using sub-process  330 A) are compared against the rCT and 1CT protocols. For vCT and rCT protocols, the target organs (i.e., liver, spleen, kidneys and lungs) are semi-automatically segmented at all time instances on respective virtual CT and real CT images. Organ-by-organ non-rigid registration are then applied. 
     For the 1CT protocol, as some organ-of-interest regions cannot be delineated from SPECT images at later time instances, whole body SPECT registration is performed while the single CT image is used for organ segmentation. Voxel-by-voxel trapezoidal integration is performed on aligned images over five time points and up to 1000 hours post-injection, assuming only physical decay after the last time point to obtain the cumulative activity, followed by Y-90 voxel S-value kernel (VSK) 22  convolution to generate the 3D dose distribution. 
     Sub-process  330 A with a single CT image at the first time instance is further evaluated.  FIGS.  11 A and  11 B  show the dosimetric results of vCT, rCT and 1CT protocols for liver, spleen, kidneys and lungs. For the vCT protocol, both % ODE and % NAE are smaller compared to 1CT protocol for all organs and approached those of rCT protocol. For example, the % ODEs for the liver are −0.24±1.56% vs. −0.49±1.76% vs. −6.37±5.63% for vCT, rCT and 1CT protocols respectively, while the % ODEs are −1.05±2.89% vs. −0.69±2.74% vs. −4.87±4.35% for kidneys. The % ODE decreases in magnitude from about 28% to about −1% using vCT protocol in comparison with 1CT protocol for lungs i.e., −0.73±5.15% vs. 28.46±6.99%. For all organs, the vCT protocol&#39;s DDVH also approach those of rCT protocol and show improvement when compared against 1CT protocol i.e., 17.79±6.82% vs. 15.60±2.96% vs. 53.54±18.99% for the liver, and 23.33±3.56% vs. 20.48±4.03% vs. 29.56±7.04% for the spleen respectively. 
     Comparing  FIG.  7 A  and  FIG.  7 B , it can be observed that the lung and bone regions are more prominent in the preliminary reconstructed images without AC and SC, due to the fact that bone has higher attenuation coefficients and the lungs have lower attenuation coefficients than soft tissues. The non-attenuation corrected images are beneficial for registration, especially for sub-process  330 A where the edges of both moving and fixed images are enhanced. Further, image registration for a single modality is generally less challenging than dual-modality, thereby resulting in sub-process  330 A being preferred. The common use of gradient descent based optimization algorithms in image registration to compute the derivative of the moving image also favours choosing the image with lower noise, i.e., the first time instance image as the moving image for non-rigid registration. 
     For dual-modality image registration, if there is more structural information in the moving images than in the fixed image, the registration process tends to maximize the similarity by “shrinking” the additional structures in the moving images (the bottom images of  FIG.  9   ). Thus, in order to avoid erroneous registration, it is suggested that images with more structural details be used as the fixed images i.e., sub-process  330 C instead of sub-process  330 B for virtual CT image generation. Additionally, cubic B-spline interpolation is applied in all registrations, which provides a realistic, continuous nature of the distribution. It does however, tend to reduce high frequency components and is limited on organ edge performance as shown in  FIGS.  8 A and  8 B . 
     The virtual CT images could be used for AC and SC to provide more accurate quantitative reconstruction and furthermore, it could be used to aid image registration and organ segmentation especially for organs with low uptake on SPECT images. Furthermore, the virtual CT images enhance the dosimetric accuracy as compared to the conventional 1CT protocol without increasing the patient radiation dose i.e., still about 19 mSv. It should be recognized that the radiation dose from the CT scan used for treatment planning is much lower than that of the diagnostic CTs, let alone the subsequent TRT. 
     Therefore, the method  300  and sub-processes  330 A,  330 B,  330 C lower the radiation dose from the CT scan, to the benefit of the patient. 
     INDUSTRIAL APPLICABILITY 
     The arrangements described are applicable to the computer and data processing industries and particularly for dosimetric analysis of organs. 
     The foregoing describes only some embodiments of the present invention, and modifications and/or changes can be made thereto without departing from the scope and spirit of the invention, the embodiments being illustrative and not restrictive.