Response surfaces for orthodontic treatment planning

An orthodontic treatment planning method, comprising:

• determining first positions of a patient's teeth;
• determining desired second positions of the patient's teeth;
• selecting one or more response surfaces based on the determined first and second positions of the patient's teeth;
• and
• prescribing one or more orthodontic appliances based on the one or more response surfaces, the one or more response surfaces indicating that the prescription is acceptable.

A computer-readable medium having computer-executable instructions for executing a numerical method for determining tooth movement, the computer-executable instructions performing steps comprising:

• determining an initial position of an orthodontic structure;
• determining an altered position of the orthodontic structure;
• defining a mathematical relationship between the initial position and the altered position, the mathematical relationship defined by a number of parameters useful for determining one or more of the stress, strain, force, and moment associated with movement of the orthodontic structure from the initial position to the altered position;
• and
• generating response surface data using the mathematical relationship.

A system for determining tooth movement, comprising:

• means for determining an initial position of a tooth;
• means for determining an altered position of the tooth;
• and
• means for generating response surface data using a mathematical relationship between the initial position and the altered position.