A system for determining a tooth trajectory for a given tooth of a subject, the tooth trajectory defining movements of the given tooth during an orthodontic treatment, the system comprising a processor of an electronic device configured to execute a method, the method comprising:
- acquiring a 3D model of an arch form associated with the subject from an intraoral scanner, the 3D model of the arch form including 3D models of a plurality of subject's teeth including a 3D model of the given tooth;
- identifying an initial position of the given tooth;
- acquiring an indication of a target position of the given tooth;
- acquiring a stress values range for stress applicable to the given tooth for causing the given tooth to move from the initial position to the target position, the stress values range including:
- a minimum stress value being indicative of a minimum amount of stress for causing the given tooth to move;
- a maximum stress value being indicative of a minimum amount of stress causing permanent damage to the given tooth;
- generating, based on the 3D model of the given tooth, a plurality of segments defining the tooth trajectory of the given tooth from the initial position to the target position, a given segment of the plurality of segments being associated with a start position and with an end position, the given segment of the plurality of segments having been generated by executing an optimization algorithm, the executing comprising:
- identifying the start position associated with the given segment;
- applying an initial force to the 3D model of the given tooth, the initial force causing a first maximum displacement, in a predetermined interval, of the 3D model of the given tooth from the start position associated with the given segment towards the target position associated with the given tooth;
- determining, from the first maximum displacement, if there is an occurrence of a collision between the 3D model of the given tooth and a 3D model of at least one adjacent tooth, the collision being caused by applying the initial force;
- in response to determining that there is the occurrence of the collision, iteratively optimizing, based on the stress values range, the initial force, until:
- a second maximum displacement of the 3D model of the given tooth is caused, by an optimized initial force, in the predetermined interval, from the start position associated with the given segment towards the target position associated with the given tooth provided that an extent of the collision between the 3D model of the given tooth and the 3D model of the at least one adjacent tooth is minimized;
- determining the optimized initial force as being a valid force to be applied to the given tooth, thereby identifying the end position associated with the given segment;
- storing data indicative of the given segment;
- and
- using the tooth trajectory for the given tooth for planning the orthodontic treatment of the subject,
- wherein the applying the initial force causes respective collisions among at least some other of the 3D models of the plurality of subject's teeth including the 3D model of the given tooth, and the processor is further configured to:
- in response to determining an occurrence of at least one of the respective collisions, iteratively optimizing the initial force until a third maximum displacement of the 3D model of the given tooth is caused, by an optimized initial force, in the predetermined interval, from the start position associated with the given segment towards the target position associated with the given tooth provided that an extent of the at least one of the respective collisions is minimized;
- and
- determining the optimized initial force as being the valid force to be applied to the given tooth.