System and method of anatomical modeling

• US 20050018885A1
• Filed: 05/31/2001
• Published: 01/27/2005
• Est. Priority Date: 05/31/2001
• Status: Abandoned Application

• Current Assignee: Agency For Science Technology and Research (Government of Singapore)
• Original Assignee: Agency For Science Technology and Research (Government of Singapore)
• Inventors: Nowinski, Wieslaw T., Chen, Xuesong, Chui, Chee Kong
• Application Number:
  US10/479,402
• Publication Number:
  US 20050018885A1
• Time in Patent Office: Days
• US Class Current: 382/128
• CPC Class Codes: G06T 17/00 Three dimensional [3D] modelling, e.g. data description of 3D objects

Abstract

Methods of modeling anatomical structures, along with pathology including the vasculature, spine and internal organs, for visualization and manipulation in simulation systems. A representation of on the human vascular network is built up from medical images and a geometrical model produced therefrom by extracting topological and geometrical information. The model is constructed using topological and geometrical information. The model is constructed using segments containing topology structure information, flow domain information contour domain information and skeletal domain information. A realistic surface is then applied to the geometric model, by generating a trajectory along a central axis of the geometric model, conducting moving trihedron modeling along the generated trajectory and then creating a sweeping surface along the trajectory. A novel joint reconstruction approach is also proposed whereby a part surface sweeping operation is performed across branches of the joint and then a surface created over the resultatn holes therebetween. A 3-D mesh may also be generated, based upon this model, for finite element analysis and pathology creation.

Claims

1. In a biomedical simulation environment, a method of forming a visually continuous surface across a joint of a plurality of anatomical branches, the method including the steps of:

generating surfaces for the anatomical branches using a part-surface sweeping operation; and

constructing surfaces across any holes in the surface across the joint using a patch filling method to complete the joint surface.

2. Method of claim 1 wherein the surfaces are generated by:

determining an appropriate cross-section for each branch;

dividing the cross-sections into portions, such that each portion is associated with a corresponding portion of a neighboring branch;

performing the part-surface sweeping operation along a trajectory relating to each of the associated portions.

3. Method of claim 2 wherein the trajectories are generated using a cubic Bezier curve, and include the steps of:

generating branch trajectories through vertices of each branch;

determining at least one control point on each branch trajectory;

forming a cubic Bezier curve between each set of neighbouring branches using the at least one control point relating to each branch.

4. Method of claim 2 wherein the part-surface sweeping operation is performed using moving trihedron modelling.

5. Method of claim 4 wherein the moving trihedron modeling includes the following steps:

initiating a trihedron (T_i⁰, N_i⁰, B_i⁰) at an end of the trajectory with parameter t=0, such that T, N and B are unit tangent, normal and binormal vectors of the trajectory at a given point, respectively;

projecting a vector B_i⁰ onto the plane defined by tangent vector T_i¹ with parameter t=⅓

, in order to obtain a new vector B_i¹=B_i⁰−

(B_i⁰•

T_i¹)T_i¹;

calculating vector N_i¹ as the cross-product of B_i¹ and T_i¹;

projecting the vector B_i¹ onto the plane defined by tangent vector T_i² with parameter t=⅔

in order to obtain a new vector B_i²=B_i¹−

(B_i¹•

T_i²)T_i²;

calculating vector N_i² as the cross-product of B_i² and T_i²;

projecting the vector B_i² onto the plane defined by tangent vector T_i³ with parameter t=1 in order to obtain a new vector B_i³=B_i²−

(B_i²•

T_i³) T_i³;

calculating vector Ni³ as the cross-product of B_i³ and T_i³.

6. Method of claim 5 wherein (T_i³, N_i³, B_i³) is used as the new start trihedron for trihedron (T_i+1⁰, N_i+1⁰, B_i+1⁰).

7. Method of claim 2 wherein the construction of surfaces across any holes includes the steps of:

dividing each Bezier curve of each branch surface in two on the boundary with the hole at a particular point;

determining a center vertex of the hole;

dividing the hole into a plurality of subpatches, using the particular points and the center vertex, the number of depending upon the number of branches; and

constructing a surface across each subpatch.

8. In a biomedical simulation environment, a method of constructing a surface of a 3D object using a segmented geometrical model, including the steps of undertaking segment reconstruction and joint reconstruction using the segmented geometric model such that the joint reconstruction is in accordance with claim 2.

9. Method of claim 8 wherein the segment reconstruction includes the steps of:

generating a trajectory along a central axis of the geometric model;

conducting moving trihedron modeling along the generated trajectory; and

creating a sweeping surface along the trajectory.

10. Method of claim 9 wherein the trajectory is generated using a piecewise Bezier curve, and further includes the steps of:

creating a tangent node vector for each node of the central axis;

generating at least one control point between each pair of neighbouring nodes using the tangent node vectors of the applicable pair of neighbouring nodes;

forming a cubic Bezier curve using the at least one control point.

11. Computer program product including a computer usable medium having computer readable program code and computer readable system code embodied on said medium for constructing a surface on a virtual geometric anatomical model, said computer program product further including computer readable code within said computer usable medium for:

undertaking the method according to claim 1.

26. In a biomedical simulation environment, a method of constructing a surface of a 3D object using a segmented geometrical model, including the steps of undertaking segment reconstruction and joint reconstruction using the segmented geometric model such that the joint reconstruction is in accordance with claim 1.

27. Computer program product including a computer usable medium having computer readable program code and computer readable system code embodied on said medium for constructing a surface on a virtual geometric anatomical model, said computer program product further including computer readable code within said computer usable medium for:

undertaking the method according to claim 2.

12. In a biomedical simulation environment, a method of pathological modeling for use in the simulation of the growth of a pathology, the method including:

creating a 3D surface model of the pathology;

applying outward force at one or more surface points of the model; and

calculating the degree of each force and the degree of deformation of the model at the one or more surface points as a result of each force.

13. In a biomedical simulation environment, a method of pathological modeling for use in the simulation of the growth of a pathology, the method including:

creating a 3D surface model of the pathology;

applying an appropriate weight function to the model, the weight function relating to the shape of the pathology being modeled.

14. Method of claim 13 wherein the pathology is a tumor or aneurysm and the weight function applied is a Gaussian filter.

15. Method of claim 14 wherein the Gaussian filter is

$G$

( r , θ

) = R 0 ⁢

ⅇ

- r 2 2 ⁢

 

⁢

σ

2

such that R₀ is a maximum deformable position of a point on the model and a relates to the shape of the deformable surface.

16. In a biomedical simulation environment, a method of interactive pathological modeling, the method including:

obtaining angiographic observations relating to a pathology;

extracting geometric parameter bounds relating to the pathology from the angiographic observations;

incorporating the pathological parameters into a geometric anatomical model;

constructing a 3D anatomical model including the pathology from the geometric model such that the shape of the pathology is capable of modification by a user within the geometric parameter bounds.

17. In a biomedical simulation environment, a method of automatically generating FEM mesh on a virtual anatomical object model for use in simulating deformation of at least a portion of the object, the model being formed from a plurality of cross-sections each having a plurality of points on the edges of the cross-sections with edge lengths between adjacent points on each cross-section, the method including the steps of:

undertaking 2D mesh generation at each cross-section; and

undertaking 3D mesh generation between two adjacent cross sections by subdividing edge lengths of each cross-section to form one or more additional points and connecting corresponding points between adjacent cross-sections; and

undertaking mesh refinement and/or optimization of the resultant 3D mesh.

18. Method of claim 17 wherein the 2D mesh generation is undertaken with a flexible resolution.

19. Computer program product including a computer usable medium having computer readable program code and computer readable system code embodied on said medium for generating a mesh on a virtual geometric model for FEM analysis, the model formed from a plurality of cross-sections each having a plurality of points on the edges of the cross-sections with edge lengths between adjacent points on each cross-section, said computer program product further including computer readable code within said computer usable medium for:

undertaking 2D mesh generation at each cross-section; and

undertaking 3D mesh generation between two adjacent cross sections by subdividing edge lengths of each cross-section to form one or more additional points and connecting corresponding points between adjacent cross-sections; and

undertaking mesh refinement and/or optimization of the resultant 3D mesh.

20. Method of automatically generating a surface mesh on a object model for use in FEM analysis, the model being formed from a plurality of cross-sections each having a plurality of points on the edges of the cross-sections with edge lengths between adjacent points on each cross-section, the method including the steps of:

undertaking 3D mesh generation between two adjacent cross sections by subdividing edge lengths of each cross-section to form one or more additional points and connecting corresponding points between adjacent cross-sections.

21. Method of validating the accuracy of a geometric model, including the steps of:

generating a first binary volume image relating to the geometric model;

generating a second binary volume image relating to a validation threshold;

comparing the first binary volume image with the second binary volume image in order to obtain an indication relating to the degree of accuracy of the geometric model.

22. Method of claim 21 wherein the step of comparing the first and second volume images further includes determining the number of voxels in the first volume image that have values different from equivalent voxels in the second volume image.

23. Method of claim 22 wherein the indication is a factor achieved by dividing the number of voxels with different values by the total number of voxels, whereby the factor approaches zero for an accurate model.

24. Method of claim 21 wherein the geometric model is constructed from one or more volume images, and the steps of generating the first and second binary volume images utilize a volume model derived from parameters of the one or more volume images.

25. Method of claim 24 wherein the parameters include volume size, length, width and height.