Use of finite element analysis for orthodontic mechanics and appliance selection

Abstract

An effective orthodontic treatment is determined by storing an original position model of a patient's teeth. The patient's teeth are then displayed according to the original position model, and appliances are selected according to a proposed orthodontic treatment. A final position model of the patient's teeth is also stored, and the selected appliances are displayed based upon the final position model. A finite element analysis is performed based on the proposed orthodontic treatment and on a movement of the patient's teeth from the final position to the original position in order to determine stresses, strains, forces, and/or moments on the appliances and on the patient's teeth and bone. If the stresses, strains, forces, and/or moments are not optimized, a new orthodontic treatment is proposed and the process is repeated.

We claim:  
     
         1 . A method of analyzing an orthodontic treatment comprising: 
 modeling first positions of a patient's teeth;    modeling desired second positions of the patient's teeth; and,    performing a finite element analysis based on the orthodontic treatment and a movement of the patient's teeth between the first and second positions.    
     
     
         2 . The method of  claim 1  wherein the performing of the finite element analysis comprises performing the finite element analysis based on a movement of the patient's teeth from the second positions to the first positions.  
     
     
         3 . The method of  claim 1  wherein the orthodontic treatment is based upon a set of orthodontic appliances to be applied to the patient's teeth, and wherein the performing of the finite element analysis comprises performing the finite element analysis based upon the set of orthodontic appliances and the movement of the patient's teeth between the first and second positions.  
     
     
         4 . The method of  claim 3  wherein the performing of the finite element analysis comprises performing the finite element analysis based on a movement of the patient's teeth from the second positions to the first positions.  
     
     
         5 . The method of  claim 1  wherein the performing of the finite element analysis comprises: 
 determining position vectors for each of the patient's teeth between the first and second positions; and,  
 performing the finite element analysis based on the orthodontic treatment and a movement of the patient's teeth along the position vectors.  
 
     
     
         6 . The method of  claim 5  wherein the performing of the finite element analysis comprises performing the finite element analysis based on a movement of the patient's teeth from the second positions to the first positions.  
     
     
         7 . The method of  claim 5  wherein the orthodontic treatment is based upon a set of orthodontic appliances to be applied to the patient's teeth, and wherein the performing of the finite element analysis comprises performing the finite element analysis based upon the set of orthodontic appliances and the movement of the patient's teeth between the first and second positions.  
     
     
         8 . The method of  claim 7  wherein the performing of the finite element analysis comprises performing the finite element analysis based on a movement of the patient's teeth from the second positions to the first positions.  
     
     
         9 . The method of  claim 1  wherein the first positions of the patient's teeth are original positions, and wherein the second positions of the patient's teeth are final positions.  
     
     
         10 . The method of  claim 1  wherein the first positions of the patient's teeth are original positions, and wherein the second positions of the patient's teeth are intermediate positions.  
     
     
         11 . A method of determining an effective orthodontic treatment comprising: 
 a) creating a first model based upon first positions of a patient's teeth;    b) creating a second model based upon second positions of the patient's teeth, wherein the second positions represent desired positions of the patient's teeth;    c) selecting a proposed set of orthodontic appliances according to a proposed orthodontic treatment;    d) performing a finite element analysis based on the proposed orthodontic treatment and a movement of the patient's teeth between the first and second positions;    e) selecting a new set of orthodontic appliances if the finite element analysis indicates that the proposed orthodontic treatment produces undesired effects; and,    f) repeating d) and e) as necessary until the effective orthodontic treatment is achieved.    
     
     
         12 . The method of  claim 11  wherein the undesired effects include stresses and/or strains outside of a desired range.  
     
     
         13 . The method of  claim 11  wherein the undesired effects include stresses and/or strains above or below an acceptable limit.  
     
     
         14 . The method of  claim 11  wherein the performing of the finite element analysis comprises performing the finite element analysis based on the first and second models.  
     
     
         15 . The method of  claim 11  wherein the performing of the finite element analysis comprises performing the finite element analysis based on a movement of the patient's teeth from the second positions to the first positions.  
     
     
         16 . The method of  claim 11  wherein the performing of the finite element analysis comprises performing the finite element analysis in two stages, wherein the first stage determines wire deformation of archwires, and wherein the second stage determines stresses, strains, forces, and/or moments as a result of the wire deformation.  
     
     
         17 . The method of  claim 11  wherein the performing of the finite element analysis comprises: 
 determining position vectors for each of the patient's teeth between the first and second positions; and,  
 performing the finite element analysis based on the orthodontic treatment and a movement of the patient's teeth along the position vectors.  
 
     
     
         18 . The method of  claim 11  wherein the creating of the first model includes displaying the first model.  
     
     
         19 . The method of  claim 18  wherein the selecting of a proposed set of orthodontic appliances comprises selecting the proposed set of orthodontic appliances based on the displayed first model.  
     
     
         20 . The method of  claim 11  wherein the selecting of a proposed set of orthodontic appliances comprises installing the proposed set of orthodontic appliances on the second model.  
     
     
         21 . The method of  claim 20  wherein the selecting of a proposed set of orthodontic appliances comprises displaying the installed set of orthodontic appliances on the second model.  
     
     
         22 . The method of  claim 20  wherein the creating of the first model includes displaying the first model.  
     
     
         23 . The method of  claim 22  wherein the selecting of a proposed set of orthodontic appliances comprises selecting the proposed set of orthodontic appliances based on the displayed first model.  
     
     
         24 . The method of  claim 20  wherein the performing of the finite element analysis comprises performing the finite element analysis in two stages, wherein the first stage determines wire deformation of archwires, and wherein the second stage determines stresses, strains, forces, and/or moments on the proposed set of orthodontic appliances as a result of the wire deformation.  
     
     
         25 . The method of  claim 11  wherein the first positions of the patient's teeth are original positions, and wherein the second positions of the patient's teeth are final positions.  
     
     
         26 . The method of  claim 11  wherein the first positions of the patient's teeth are original positions, and wherein the second positions of the patient's teeth are intermediate positions.  
     
     
         27 . A computer readable storage medium having program code stored thereon which, when executed by a computer, performs the following tasks: 
 a) storing a first position model of a patient's teeth;    b) storing a second position model of the patient's teeth, wherein the second position model represents desired positions of the patient's teeth;    c) storing a set of orthodontic appliances;    d) applying the set of orthodontic appliances to the patient's teeth according to one of the first and second position models; and,    e) performing a finite element analysis based on the first position model, the second position model, and the applied set of orthodontic appliances.    
     
     
         28 . The computer readable storage medium of  claim 27  wherein the performing of the finite element analysis comprises displaying stresses, strains, forces, and/or moments resulting from the applied set of orthodontic appliances.  
     
     
         29 . The computer readable storage medium of  claim 27  wherein the storing of an original position model comprises displaying upper and lower arches of the patient.  
     
     
         30 . The computer readable storage medium of  claim 27  wherein the applying of the set of orthodontic appliances comprises displaying the applied set of orthodontic appliances on the patient's teeth.  
     
     
         31 . The computer readable storage medium of  claim 27  wherein the performing of the finite element analysis comprises performing the finite element analysis based on a movement of the patient's teeth between original and final positions as represented by the original and final position models.  
     
     
         32 . The computer readable storage medium of  claim 27  wherein the performing of the finite element analysis comprises performing the finite element analysis based on a movement of the patient's teeth from a final position to an original position as represented by the original and final position models.  
     
     
         33 . The computer readable storage medium of  claim 27  wherein the applying of the set of orthodontic appliances comprises applying the set of orthodontic appliances to the patient's teeth according to the final position model.  
     
     
         34 . The computer readable storage medium of  claim 27  wherein the performing of the finite element analysis comprises: 
 determining position vectors for each of the patient's teeth between original and final positions as represented by the original and final position models; and,  
 performing the finite element analysis based on the applied set of orthodontic appliances and a movement of the patient's teeth along the position vectors.  
 
     
     
         35 . The computer readable storage medium of  claim 27  wherein the first position model represents original positions of the patient's teeth, and wherein the second positions of the patient's teeth are final positions.  
     
     
         36 . The computer readable storage medium of  claim 27  wherein the first position model represents original positions of the patient's teeth, and wherein the second positions of the patient's teeth are intermediate positions.  
     
     
         37 . A method, implemented with the assistance of a computer, of determining an effective orthodontic treatment comprising: 
 a) storing first positions of a patient's teeth;    b) displaying the patient's teeth according to the first positions;    c) selecting orthodontic appliances according to a proposed orthodontic treatment of the patient's teeth;    d) storing second positions of the patient's teeth, wherein the second positions are desired positions;    e) installing the selected orthodontic appliances on the patient's teeth in the second positions; and,    f) performing a finite element analysis to assess effects on the orthodontic appliances and on the patient's teeth based on the first and second positions and on the proposed orthodontic treatment.    
     
     
         38 . The method of  claim 37  wherein the performing of the finite element analysis comprises performing the finite element analysis based on a movement of the patient's teeth from the second positions to the first positions.  
     
     
         39 . The method of  claim 37  wherein the performing of the finite element analysis comprises performing the finite element analysis based upon the set of orthodontic appliances and the movement of the patient's teeth between the first and second positions.  
     
     
         40 . The method of  claim 37  wherein the performing of the finite element analysis comprises: 
 determining position vectors for each of the patient's teeth based on the first and second positions; and,  
 performing the finite element analysis based on the proposed orthodontic treatment and a movement of the patient's teeth along the position vectors.  
 
     
     
         41 . The method of  claim 40  wherein the performing of the finite element analysis comprises performing the finite element analysis based on a movement of the patient's teeth from the second positions to the first positions along the position vectors.  
     
     
         42 . The method of  claim 37  wherein the performing of the finite element analysis comprises: 
 determining position vectors for each of the patient's teeth between the first and second positions as represented by the first and second models;  
 assigning material properties to the patient's teeth, PDL, and bone and to the proposed orthodontic treatment; and,  
 performing the finite element analysis based on the proposed orthodontic treatment, the assigned material properties, and a movement of the patient's teeth between the first and second positions.  
 
     
     
         43 . The method of  claim 42  wherein the performing of the finite element analysis comprises performing the finite element analysis based on a movement of the patient's teeth from the second positions to the first positions.  
     
     
         44 . The method of  claim 42  wherein the performing of the finite element analysis comprises performing the finite element analysis based on forces on the teeth exerted from deformed wire on the orthodontic appliances and based on the material properties of the teeth, PDL, and bone so as to predict a tooth movement path from original positions of the teeth.  
     
     
         45 . The method of  claim 42  wherein the performing of the finite element analysis comprises displaying stresses, strains, forces, and/or moments on both the patient's teeth and the selected orthodontic appliances used in the proposed orthodontic treatment.  
     
     
         46 . The method of  claim 37  wherein the performing of the finite element analysis comprises displaying stresses, strains, forces, and/or moments on both the patient's teeth and the selected orthodontic appliances used in the proposed orthodontic treatment.  
     
     
         47 . The method of  claim 37  wherein the performing of the finite element analysis comprises performing the finite element analysis in two stages, wherein the first stage determines deformation of archwires, and wherein the second stage determines stresses, strains, forces, and/or moments on the proposed set of orthodontic appliances and on the patient's teeth as a result of the deformation.  
     
     
         48 . The method of  claim 37  wherein the first positions of the patient's teeth are original positions, and wherein the second positions of the patient's teeth are final positions.  
     
     
         49 . The method of  claim 37  wherein the first positions of the patient's teeth are original positions, and wherein the second positions of the patient's teeth are intermediate positions.