# US 8,787,644 B2 · Method and device for calculating voxels defining a tube-of-response using a central-ray-filling algorithm > Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt - Number: US 8,787,644 B2 - Document ID: US8787644B2 - Status: Granted - Kind: B2 - Application number: 13/160,145 - Filed: 2011-06-14 - Published: 2012-12-20 - Granted: 2014-07-22 - Earliest claimed: 2011-06-14 - Assignees: Kabushiki Kaisha Toshiba; Toshiba Medical Systems Corporation - Applicants: Hongwei Ye; Wenli Wang - Inventors: Hongwei Ye; Wenli Wang - Web page: https://patentgrep.com/patent/US8787644B2 ## CPC - G01T 1/2985: {In depth localisation, e.g. using positron emitters; Tomographic imaging (longitudinal and transverse section imaging; apparatus for radiation diagnosis sequentially in different planes, steroscopic radiation diagnosis); (using external radiation sources A61B6/02)} - G01T: MEASUREMENT OF NUCLEAR OR X-RADIATION (radiation analysis of materials, mass spectrometry G01N23/00; tubes for determining the presence, intensity, density or energy of radiation or particles H01J47/00) ## Abstract A method and device for calculating voxels defining a tube-of-response (TOR) within a reconstruction space of a Positron Emission Tomography (PET) apparatus having a plurality of crystals, the voxels within the reconstruction space having a predetermined size. The method includes selecting a center on each of two crystals defining a line of response, determining intersected voxels within the reconstruction space that intersect a straight line connecting the centers of the two crystals, calculating neighboring voxels of the intersected voxels, based on an expansion direction and an expansion distance, merging the intersected voxels and the neighboring voxels to form a merged set of voxels, and deleting duplicate voxels in the merged set of voxels to generate the voxels defining the TOR. ## Claims ### Claim 1 A method for calculating voxels defining a tube-of-response (TOR) within a reconstruction space of a Positron Emission Tomography (PET) apparatus having a plurality of crystals, the voxels within the reconstruction space having a predetermined size, the method comprising: selecting a center on each of two crystals defining a line of response; determining intersected voxels within the reconstruction space that intersect a straight line connecting the centers of the two crystals; calculating neighboring voxels for each intersected voxel of the intersected voxels, based on an expansion direction and an expansion distance, the expansion distance being determined for each intersected voxel based on a position of the intersected voxel along the straight line, when lines connecting endpoints of the two crystals are not parallel to each other; merging the intersected voxels and the neighboring voxels to form a merged set of voxels; and deleting duplicate voxels in the merged set of voxels to generate the voxels defining the TOR. ### Claim 2 (depends on 1) The method of claim 1, further comprising: determining the expansion direction based on a location of the two crystals and geometric properties of the PET apparatus. ### Claim 3 (depends on 1) The method of claim 1, further comprising: determining the expansion distance based on a size of the two crystals, the predetermined size of the voxels within the reconstruction space, and a tilted angle of the lines connecting the endpoints of the two crystals. ### Claim 4 (depends on 1) The method of claim 1, wherein the step of calculating the neighboring voxels further comprises: calculating the expansion distance, the expansion distance being equal to half a size of a length of the two crystals projected onto a coordinate axis of the PET apparatus, when the lines connecting the endpoints of the two crystals are parallel to each other. ### Claim 5 (depends on 1) The method of claim 1, wherein the step of calculating the neighboring voxels further comprises: calculating a left expansion distance and a right expansion distance, the left expansion distance corresponding to a left side of the two crystals projected onto an X-axis of the PET apparatus and being different from the right expansion distance corresponding to a right side of the two crystals projected onto the X-axis, when the lines connecting the endpoints of the two crystals are not parallel to each other. ### Claim 6 (depends on 1) The method of claim 1, wherein the step of calculating the neighboring voxels further comprises: calculating an upper expansion distance and a lower expansion distance, the upper expansion distance corresponding to an upper side of the two crystals projected onto a Y-axis of the PET apparatus and being different from the lower expansion distance corresponding to a lower side of the two crystals projected onto the Y-axis, when the lines connecting the endpoints of the two crystals are not parallel to each other. ### Claim 7 (depends on 1) The method of claim 1, wherein the step of calculating the neighboring voxels further comprises: calculating a first Z expansion distance in a negative Z direction along a Z-axis and a second Z expansion distance in a positive Z direction along the Z-axis, based on a distance between a first line connecting two endpoints of a first side of the two crystals projected onto the Z-axis of the PET apparatus, and a second line connecting two endpoints of a second side of the two crystals projected onto the Z-axis, the first line and the second line being located farthest from each other. ### Claim 8 (depends on 1) The method of claim 1, wherein the step of calculating the neighboring voxels is performed in an X-Y plane and in a Y-Z or X-Z plane of the PET apparatus. ### Claim 9 (depends on 1) The method of claim 1, wherein the determining step includes skipping intersections of the intersected voxels based on boundaries of the intersected voxels in an X-Y plane and in a Y-Z or X-Z plane of the PET apparatus. ### Claim 10 A reconstruction device for calculating voxels defining a tube-of-response (TOR) within a reconstruction space of a Positron Emission Tomography (PET) apparatus having a plurality of crystals, the voxels within the reconstruction space having a predetermined size, the reconstruction device comprising: a processing circuit configured to select a center on each of two crystals defining a line of response; determine intersected voxels within the reconstruction space that intersect a straight line connecting the centers of the two crystals; calculate neighboring voxels for each intersected voxel of the intersected voxels, based on an expansion direction and an expansion distance, the expansion distance being determined for each intersected voxel based on a position of the intersected voxel along the straight line, when lines connecting endpoints of the two crystals are not parallel to each other; merge the intersected voxels and the neighboring voxels to form a merged set of voxels; and delete duplicate voxels in the merged set of voxels to generate the voxels defining the TOR. ### Claim 11 (depends on 10) The reconstruction device of claim 10, wherein the processing circuit is further configured to determine the expansion direction based on a location of the two crystals and geometric properties of the PET apparatus. ### Claim 12 (depends on 10) The reconstruction device of claim 10, wherein the processing circuit is further configured to determine the expansion distance based on a size of the two crystals, the predetermined size of the voxels within the reconstruction space, and a tilted angle of the lines connecting the endpoints of the two crystals. ### Claim 13 (depends on 10) The reconstruction device of claim 10, wherein the processing circuit is further configured to calculate the expansion distance, the expansion distance being equal to half a size of a length of the two crystals projected onto a coordinate axis of the PET apparatus, when the lines connecting the endpoints of the two crystals are parallel to each other. ### Claim 14 (depends on 10) The reconstruction device of claim 10, wherein the processing circuit is further configured to calculate a left expansion distance and a right expansion distance, the left expansion distance corresponding to a left side of the two crystals projected onto an X-axis of the PET apparatus and being different from the right expansion distance corresponding to a right side of the two crystals projected onto the X-axis, when the lines connecting the endpoints of the two crystals are not parallel to each other. ### Claim 15 (depends on 10) The reconstruction device of claim 10, wherein the processing circuit is further configured to calculate an upper expansion distance and a lower expansion distance, the upper expansion distance corresponding to an upper side of the two crystals projected onto an Y-axis of the PET apparatus and being different from the lower expansion distance corresponding to a lower side of the two crystals projected onto the Y-axis, when the lines connecting the endpoints of the two crystals are not parallel to each other. ### Claim 16 (depends on 10) The reconstruction device of claim 10, wherein the processing circuit is further configured to calculate a first Z expansion distance in a negative Z direction along a Z-axis and a second Z expansion distance in a positive Z direction along the Z-axis, based on a distance between a first line connecting two endpoints of a first side of the two crystals projected onto the Z-axis of the PET apparatus, and a second line connecting two endpoints of a second side of the two crystals projected onto the Z-axis, the first line and the second line being located farthest from each other. ### Claim 17 (depends on 10) The reconstruction device of claim 10, wherein the processing circuit is configured to calculate the neighboring voxels in an X-Y plane and in a Y-Z or X-Z plane of the PET apparatus. ### Claim 18 (depends on 10) The reconstruction device of claim 10, wherein the processing circuit is further configured to skip intersections of the intersected voxels based on boundaries of the intersected voxels in an X-Y plane and in a Y-Z or X-Z plane of the PET apparatus. ### Claim 19 (depends on 1) The method of claim 1, wherein the step of calculating the neighboring voxels further comprises: judging, based on tilted angles of the lines connecting the endpoints of the two crystals, whether the lines are parallel to each other. ### Claim 20 (depends on 10) The reconstruction device of claim 10, wherein the processing circuit is further configured to, based on tilted angles of the lines connecting the endpoints of the two crystals, judge whether the lines are parallel to each other.