Method for generating design of orthodontic appliance

A device for generating a design of an orthodontic appliance, the device comprising:

• one or more processors;
• and
• one or more memories coupled to the one or more processors and storing instructions that, when executed by the one or more processors, cause the device to:
• receive a digital three-dimensional (3D) representation of at least one tooth;
• generate a Reduced Order Model (ROM) representing a biomechanical response of a periodontal ligament (PDL) of the at least one tooth based on the digital 3D representation, wherein generating the ROM comprises:
• determining, for the at least one tooth, a plurality of tooth movement parameters resulting from application of a plurality of orthodontic force parameters at a reference point of the at least one tooth;
• determining a calibrated compliance matrix of a baseline PDL of the at least one tooth based at least on the plurality of tooth movement parameters and the plurality of orthodontic force parameters;
• determining a plurality of center of resistance parameters of the baseline PDL based on the calibrated compliance matrix;
• determining a reference mapping matrix based on the plurality of center of resistance parameters of the baseline PDL;
• and
• determining a characteristic compliance matrix of the baseline PDL based on the calibrated compliance matrix and the reference mapping matrix;
• and
• generate the design of the orthodontic appliance based at least partially on the ROM of the PDL of the at least one tooth.

An apparatus for generating a design of an orthodontic appliance, comprising:

• means for receiving a digital three-dimensional (3D) representation of at least one tooth;
• means for determining, for the at least one tooth, a plurality of tooth movement parameters resulting from application of a plurality of orthodontic force parameters at a reference point of the at least one tooth;
• means for determining a calibrated compliance matrix of a baseline periodontal ligament (PDL) of the at least one tooth based at least on the plurality of tooth movement parameters and the plurality of orthodontic force parameters;
• means for determining a plurality of center of resistance parameters of the baseline PDL based on the calibrated compliance matrix;
• means for determining a reference mapping matrix based on the plurality of center of resistance parameters of the baseline PDL;
• means for determining a characteristic compliance matrix of the baseline PDL based on the calibrated compliance matrix and the reference mapping matrix;
• means for generating a Reduced Order Model (ROM) representing a biomechanical response of the PDL of the at least one tooth based on the digital 3D representation and the characteristic compliance matrix;
• means for generating a design of the orthodontic appliance based at least partially on the ROM of the PDL of the at least one tooth;
• means for representing the ROM as a simplified mathematical representation comprising a plurality of numerical values representing compliance or stiffness of the PDL of the at least one tooth;
• and
• means for determining a scale factor of the PDL of the at least one tooth in the digital 3D representation, and wherein a combination of the scale factor and the characteristic compliance matrix of the baseline PDL associates a corrected characteristic matrix of the PDL with the height and the thickness of the PDL.