Investigating the Ability of the Tooth and Surrounding Support Tissues to Absorb and Dissipate Orthodontic Loads during Periodontal Breakdown—Finite Elements Analysis

Abstract

Herein, the finite elements analysis (FEA) numerical study investigated the absorption–dissipation ability of dental tissues under orthodontic forces, during orthodontic movements and the periodontal breakdown process. Additionally, we investigated the correctness of FEA boundary assumptions up to 2.4 N of loads. Eighty-one models of the second lower premolar were subjected to 810 FEA numerical simulations using Tresca failure criterion under 0.6 N, 1.2 N, and 2.4 N and five movements: intrusion, extrusion, rotation, tipping, and translation. The results showed that both coronal dentine and enamel components had comparable high absorption–dissipation abilities, allowing for only a limited fraction of stresses to reach the circulatory sensitive tissues. Isotropy, linear elasticity, and homogeneity are correct when Tresca is employed up to 2.4 N. Forces of 0.6 N, 1.2 N, and 2.4 N displayed similar qualitative results for all movements and bone levels, while quantitative results doubled for 1.2 N and quadrupled for 2.4 N when compared with 0.6 N. FEA simulations showed 0.6–1.2 N to be safe for application in intact periodontium, while for reduced periodontium more than 0.6 N are prone to resorptive and ischemic risks. For reducing these risks, after 4 mm of bone loss, 0.2–0.6 N are recommended. Rotation and translation were the most stressful followed by tipping.

The Importance of Boundary Conditions and Failure Criterion in Finite Element Analysis Accuracy—A Comparative Assessment of Periodontal Ligament Biomechanical Behavior

“…However, for more than 1 N, there are no available data regarding the linear elasticity and isotropy assumptions. Regarding the non-homogeneity/homogeneity issue of dental tissues, the Tresca criterion is suited for ductile non-homogenous cases, while VM is suited for ductile homogenous cases, as correctly reported in the earlier analysis [1,[21][22][23][24][25]. There are reports of a quantitative difference between these two criteria, with T being 15-30% higher than VM.…”

“…Finite element analysis (FEA) is the only available method allowing the individual study (both qualitatively and quantitatively) of each dental tissue's component, and it has been introduced in dentistry over the last decade [1]. Being a mathematical algorithmbased method that subdivides a larger structure into smaller and simpler parts called finite elements, it is widely used in the engineering field due to its high accuracy [2].…”

“…Being a mathematical algorithmbased method that subdivides a larger structure into smaller and simpler parts called finite elements, it is widely used in the engineering field due to its high accuracy [2]. Nevertheless, its accuracy depends on the accuracy of the input data (i.e., complex geometry, dissimilar material properties, local effects), all acknowledged and known in the engineering field [1].…”

“…FEA dental studies [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19], despite their considerable number, supply various results that differ from one study to another and sometimes contradict clinical data [6][7][8]20]. If the engineering field benefits from long-established knowledge of materials' physical properties and behavioral types, the dental field does not [1].…”

“…Ductile materials have a variable ability to deform and recover when subjected to a load, while brittle materials deform little, usually do not recover from deformations, and suffer from cracks and destruction. Dental tissues are considered to be ductile resemblance materials (with a certain brittle flow mode) [1,[21][22][23][24][25]. The ductile materials' failure criteria are Tresca (T, maximum shear stress) and Von Mises (VM, maximum overall stress); the brittle criteria are S1 (maximum principal stress) and S3 (minimum principal stress); for liquids, hydrostatic pressure is mandatory [21,22].…”