Method and system for measuring tooth displacements on a virtual three-dimensional model
It is a common practice with orthodontists in planning treatment for a patient to prescribe dental changes to cure the malocclusion condition of the patient in terms of mesial or distal, buccal or lingual, and occlusal (coronal) or gingival translational displacements; and facial or lingual torque; mesial or distal angulation and mesial or distal rotation displacements. A method and workstation for measuring the dental displacements, or conversely placing the dental elements in desired positions as per the prescriptions for their displacements in a consistent, reproducible and accurate manner is disclosed. A novel orthogonal curvilinear coordinate system is disclosed that enables the measurement of the tooth displacements in conjunction with the individual tooth axes system.
1. A method of measuring displacement of a virtual three-dimensional tooth for treatment planning using a workstation, comprising the steps of:
(a) obtaining a virtual three-dimensional model of each tooth in a jaw of a patient in an initial state;
(b) selecting a tooth origin for said each tooth; wherein said tooth origin for said each tooth is selected based upon anatomical structure of said each tooth; wherein said tooth origin for said each tooth remains fixed on said each tooth;
(c) finding a reference virtual arch based upon location of said tooth origin for said each tooth;
wherein said reference virtual arch is contained in an arbitrary plane;
wherein said arbitrary plane is located based upon location of said tooth origin for said each tooth;
wherein said reference virtual arch is shaped in a monotonous curve;
(d) finding a tooth axes system for said each tooth; wherein said tooth axes system comprises said tooth origin for said tooth, a tooth x-axis in mesial and distal directions of said tooth, a tooth y-axis in buccal and lingual directions of said tooth and a tooth z-axis in occlusal and gingival directions of said tooth; wherein said tooth axes system for said each tooth is connected to said each tooth via said tooth origin for said each tooth;
(e) finding a reference orthogonal curvilinear coordinate system for said each tooth; wherein said reference orthogonal curvilinear coordinate system comprises a reference origin for said tooth, a reference x-axis for said tooth, a reference y-axis for said tooth, and a reference z-axis for said tooth; wherein said reference origin for said tooth resides at a point on said reference virtual arch where an orthogonal projection from an orthogonal projection point meets said reference virtual arch; wherein said orthogonal projection point is located on said arbitrary plane where an orthogonal projection from said tooth origin of said tooth meets said arbitrary plane; wherein said reference x-axis for said tooth coincides with a tangent to said reference virtual arch at said reference origin; wherein said reference y-axis for said tooth is normal to said reference x-axis and passes through said reference origin; wherein said reference z-axis for said tooth is orthogonal to a plane formed by said reference x-axis for said tooth and said reference y-axis for said tooth and passes through said reference origin;
(f) moving a tooth from said initial position to a desired position; and
(g) measuring displacement for said tooth from said initial position to said desired position using said reference virtual arch, said reference orthogonal curvilinear coordinate system for said tooth, and said tooth axes system for said tooth.
2. The method of claim 1 , wherein in step (c) said arbitrary plane is located such that sum of square of orthogonal distance of said each tooth origin from said arbitrary plane is minimized; and
said reference virtual arch is shaped in said monotonous curve such that sum of square of orthogonal distance from said each orthogonal projection point to said reference virtual arch is also minimized.
3. The method of claim 1 , wherein in step (c) said arbitrary plane is located such that sum of orthogonal distance of said each tooth origin from said arbitrary plane is minimized; and
said reference virtual arch is shaped in said monotonous curve such that sum of orthogonal distance from said each orthogonal projection point to said reference virtual arch is also minimized.
4. The method of claim 1 , wherein said displacement of said tooth is mesiodistal displacement of said tooth; wherein said mesiodistal displacement is measured as length of bow segment along said reference virtual arch between said reference origin for said tooth and position of said tooth.
5. The method of claim 1 , wherein said displacement of said tooth is buccolingual displacement of said tooth; wherein said buccolingual displacement is measured as orthogonal distance between a z-plane containing said reference z-axis for said tooth and a plane containing said tooth origin for said tooth and placed parallel to said z-plane.
6. The method of claim 1 , wherein said displacement of said tooth is coronal-gingival displacement of said tooth; wherein said coronal-gingival displacement is measured as orthogonal distance between a y-plane containing said reference y-axis for said tooth and a plane containing said tooth origin for said tooth and placed parallel to said y-plane.
7. The method of claim 1 , wherein said displacement of said tooth is a torque displacement of said tooth; wherein said torque displacement is measured as an angle α between said tooth z-axis and a tooth line; wherein said tooth line passes through said tooth origin; and wherein said tooth line is drawn parallel to said reference z-axis, when viewed from the perspective of the direction of said reference x-axis.
8. The method of claim 1 , wherein said displacement of said tooth is an angulation displacement of said tooth; wherein said angulation displacement is measured as an angle β between said tooth z-axis and a tooth line; wherein said tooth line passes through said tooth origin; and wherein said tooth line is drawn parallel to said reference z-axis, when viewed from the perspective of the direction of said reference y-axis.
9. The method of claim 1 , further comprising the steps of:
(h) moving said tooth to another position;
(i) measuring displacement of said tooth while in said another position; and
(j) determining relative displacement of said tooth from said displacement of said tooth and said displacement of said tooth while in said another position.
10. The method of claim 1 , wherein said displacement of said tooth is a rotation displacement of said tooth; wherein said rotation displacement is measured as an angle θ between said reference y-axis and said tooth y-axis when viewed from the perspective of the direction of said reference z-axis.
11. The method of claim 1 , further comprising the steps of:
(h) moving said tooth to another position;
(i) measuring displacement of said tooth while in said another position;
(j) determining relative displacement of said tooth from said displacement of said tooth and said displacement of said tooth while in said another position; and
(k) repeating steps (h)-(j) until said relative displacement achieves a desired value.
12. The method of claim 1 , wherein said jaw is lower jaw of said patient.
13. The method of claim 1 , wherein said jaw is upper jaw of said patient.