Mathematical model and a method and apparatus for utilizing the model

• US 6,793,496 B2
• Filed: 02/28/2002
• Issued: 09/21/2004
• Est. Priority Date: 04/15/1999
• Status: Expired due to Fees

• Current Assignee: General Electric Company
• Original Assignee: General Electric Company
• Inventors: Yavuz, Mehmet, Cline, Harvey Ellis, Ishaque, Ahmad Nadeem, Edic, Peter Michael
• Primary Examiner(s): FERNSTROM, KURT
• Application Number:
  US10/085,726
• Publication Number:
  US 20020127523A1
• Time in Patent Office: 936 Days
• Field of Search: 434/262, 434/267, 434/272, 434/188, 703/2, 703/11
• US Class Current: 434/262
• CPC Class Codes: G06T 11/006 Inverse problem, transformation from projection-space into object-space, e.g. transform methods, back-projection, algebraic methods
• CPC Class Codes: G06T 13/20 3D [Three Dimensional] animation
• CPC Class Codes: G06T 19/20 Editing of 3D images, e.g. changing shapes or colours, aligning objects or positioning parts
• CPC Class Codes: G06T 2210/41 Medical
• CPC Class Codes: G06T 2211/412 Dynamic
• CPC Class Codes: G06T 2219/2016 Rotation, translation, scaling
• CPC Class Codes: G06T 2219/2021 Shape modification
• CPC Class Codes: G09B 23/28 for medicine

Abstract

The present invention provides a model and a method and apparatus for utilizing the model to simulate an imaging scenario. The model is mathematically defined by analytical basis objects and/or polygonal basis objects. Preferably, the model is a model of the human heart and thorax. Polygonal basis objects are only used to define structures in the model that experience torsion, such as certain structures in the heart that experience torsion during the cardiac cycle. The manner in which the basis objects comprising the model are transformed by scaling, translation and rotation is defined for each basis object. In the case where a basis object experiences torsion, the rotation of the basis object will change as a function of the length along the axis of the basis object about which rotation is occurring. During an imaging system simulation, the model is utilized by a forward projection routine, which integrates the linear attenuation coefficients associated with the rays emitted by a simulated x-ray source and collected by a simulated detector array to obtain line integrals corresponding to forward projection data. The forward projection data is then processed to take into account the physics of the imaging technology, the x-ray source and the detector array. The processed projection data is then processed and back-projected by a reconstruction modeling routine to produce a reconstructed representation of the model of the heart as a function of time.

Claims

1. A computer readable medium storing computer instructions for instructing computer to generate an image, the computer instruction comprising processing a mathematical model to generate an image, wherein the mathematical model comprises basis objects, each basis object being defined by a mathematical function, each basis object having a spatial relationship to all of the other basis objects, the basis objects and the spatial relationships between the basis objects defining a three-dimensional (3-D) geometry of the model, wherein the model is capable of being transformed by one or more transformation operators, each transformation operator being associated with a predetermined transformation operation, wherein when one of the transformation operators operates on one of the basis objects, the spatial relationship between the basis object that is operated on and at least one other basis object is varied, thereby causing the geometry of the model to be varied.

2. The computer readable medium of claim 1, wherein the basis objects are analytical basis objects, and wherein the mathematical function defining each basis object is a quadratic equation.

3. The computer readable medium of claim 1, wherein the basis objects are polygonal basis objects, each polygonal basis object corresponding to at least one polygon, each polygon having at least three vertices, the mathematical function defining each polygonal basis object describing a plane that is defined by line segments that connect the vertices of each polygon comprising the polygonal basis function.

4. The computer readable medium of claim 1, wherein at least one of the basis objects is an analytical basis object and wherein at least one of the basis objects is a polygonal basis object, the mathematical function defining each analytical basis object being a quadratic equation, and wherein each polygonal basis object is comprised of at least one polygon, each polygon having at least three vertices, the mathematical function defining each polygonal basis object describing a plane that is defined by line segments that connect vertices of each polygon comprising the polygonal basis object.

5. The computer readable medium of claim 1, wherein the transformation operations include scaling, translation, rotation and torsion, and wherein one or more of the transformation operations can be performed on the basis objects as a function of time to thereby cause the geometry of the model to be varied as a function of time.

6. The computer readable medium of claim 4, wherein the transformation operations include scaling, translation, rotation and torsion, and wherein one or more of the transformation operations can be performed on the basis objects as a function of time to thereby cause the geometry of the model to be varied as a function of time, and wherein the model includes information that describes the transformation operations that are to be performed on particular basis objects at particular instants in time, the transformation operations to be performed on particular basis objects occurring at particular instants in time such that the 3-D geometry of the model varies as a function of the time.

7. The computer readable medium of claim 4, wherein the model is a model of the human heart and thorax, and wherein the transformation operations include scaling, translation, rotation and torsion, and wherein one or more of the transformation operations can be performed on the basis objects as a function of time to thereby cause the geometry of the model to be varied as a function of time, and wherein the model includes information that describes the transformation operations that are to be performed on particular basis objects at particular instants in time in the cardiac cycle, the transformation operations to be performed on particular basis objects occurring at particular instants in time in the cardiac cycle such that the 3-D geometry of the model varies as a function of the timing of the cardiac cycle.

8. The computer readable medium of claim 1, wherein the transformation operations include scaling, translation, rotation, and torsion, and wherein one or more of the transformation operations can be performed on the basis objects as a function of time to thereby cause the geometry of the model to be varied as a function of time, and wherein the model includes information that describes the transformation operations that are to be performed on particular basis objects at particular instants in time, the transformation operations to be performed on particular basis objects occurring at particular instants in time such that the 3-D geometry of the model varies as a function of time, each basis object having a priority value associated therewith, each basis object having a linear attenuation coefficient associated therewith, the model including information identifying the priority value and the linear attenuation coefficient associated with each basis object.

9. The computer readable medium of claim 1, wherein the model is a model of the human heart and thorax, wherein the transformation operations include scaling, translation, rotation, and torsion, and wherein one or more of the transformation operations can be performed on the basis objects as a function of time to thereby cause the geometry of the model to be varied as a function of time, and wherein the model includes information that describes the transformation operations that are to be performed on particular basis objects at particular instants in time in the cardiac cycle, the transformation operations to be performed on particular basis objects occurring at particular instants in time in the cardiac cycle such that the 3-D geometry of the model varies as a function of the timing of the cardiac cycle, each basis object having a priority value associated therewith, each basis object having a linear attenuation coefficient associated therewith, the model including information identifying the priority value and the linear attenuation coefficient associated with each basis object.

10. A computer readable medium storing computer instructions for instructing computer to generate an image, the computer instruction comprising processing a mathematical model to generate an image of the human heart and thorax, wherein the mathematical model comprises basis objects, each basis object being defined by a mathematical function, each basis object having a spatial relationship to all of the other basis objects, the basis objects and the spatial relationships between the basis objects defining a three-dimensional (3-D) geometry of the model, wherein the model is capable of being transformed by one or more transformation operators, each transformation operator being associated with a predetermined transformation operation, wherein when one of the transformation operators operates on one of the basis objects, the spatial relationship between the basis object that is operated on and at least one other basis object is varied, thereby causing the geometry of the model to be varied.

11. The computer readable medium of claim 10, wherein the basis objects are analytical basis objects, and wherein the mathematical function defining each basis object is a quadratic equation.

12. The computer readable medium of claim 10, wherein the basis objects are polygonal basis objects, each polygonal basis object corresponding to at least one polygon, each polygon having at least three vertices, the mathematical function defining each polygonal basis object describing a plane that is defined by line segments that connect the vertices of each polygon comprising the polygonal basis function.

13. The medal computer readable medium of claim 10, wherein at least one of the basis objects is an analytical basis object and wherein at least one of the basis objects is a polygonal basis object, the mathematical function defining each analytical basis object being a quadratic equation, and wherein each polygonal basis object is comprised of at least one polygon, each polygon having at least three vertices, the mathematical function defining each polygonal basis object describing a plane that is defined by line segments that connect vertices of each polygon comprising the polygonal basis object.

14. The computer readable medium of claim 10, wherein the transformation operations include scaling, translation, rotation and torsion, and wherein one or more of the transformation operations can be performed on the basis objects as a function of time to thereby cause the geometry of the model to be varied as a function of time.

15. The computer readable medium of claim 13, wherein the transformation operations include scaling, translation, rotation and torsion, and wherein one or more of the transformation operations can be performed on the basis objects as a function of time to thereby cause the geometry of the model to be varied as a function of time, and wherein the model includes information that describes the transformation operations that are to be performed on particular basis objects at particular instants in time, the transformation operations to be performed on particular basis objects occurring at particular instants in time such that the 3-D geometry of the model varies as a function of the time.

16. The model computer readable medium of claim 13, wherein the transformation operations include scaling, translation, rotation and torsion, and wherein one or more of the transformation operations can be performed on the basis objects as a function of time to thereby cause the geometry of the model to be varied as a function of time, and wherein the model includes information that describes the transformation operations that are to be performed on particular basis objects at particular instants in time in the cardiac cycle, the transformation operations to be performed on particular basis objects occurring at particular instants in time in the cardiac cycle such that the 3-D geometry of the model varies as a function of the timing of the cardiac cycle.

17. The computer readable medium of claim 10, wherein the transformation operations include scaling, translation, rotation, and torsion, and wherein one or more of the transformation operations can be performed on the basis objects as a function of time to thereby cause the geometry of the model to be varied as a function of time, and wherein the model includes information that describes the transformation operations that are to be performed on particular basis objects at particular instants in time in the cardiac cycle, the transformation operations to be performed on particular basis objects occurring at particular instants in time in the cardiac cycle such that the 3-D geometry of the model varies as a function of the timing of the cardiac cycle, each basis object having a priority value associated therewith, each basis object having a linear attenuation coefficient associated therewith, the model including information identifying the priority value and the linear attenuation coefficient associated with each basis object.