Finite Element Study on Bone Quality and Boundary Conditions

Background: Dental implant stability is critical to long-term implant success and is influenced by bone quality, implant geometry, and boundary conditions. Modal analysis provides a non-invasive method to assess implant stability through evaluation of the system's natural frequencies. Objective: This study investigates how boundary constraints, mandible size, bone quality, and bone-substitutive layers affect the natural frequency of dental implants. Materials and Methods: A three-dimensional finite element model of a biphasic healing titanium dental implant—defined here as an implant initially engaging both cortical and cancellous (trabecular) bone—was developed using micro-CT data. Two mandibular geometries (“long” and “short”) were modeled. Three boundary conditions were applied by fixing the mandible at (1) mesial/distal sides, (2) the inferior surface, and (3) all three sides. Bone quality was categorized using the Lekholm and Zarb classification: •Type I: dense cortical bone only •Type II: thick cortical and dense trabecular bone •Type III: thin cortical and dense trabecular bone •Type IV: thin cortical and sparse trabecular bone Additionally, bone-substitutive layers (magnesium phosphate, hydroxyapatite, PMMA) at two thicknesses (<tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathbf{3 0 0} \boldsymbol{\mu}$</tex> m and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathbf{8 0 0} \mu \mathrm{m})$</tex> were included. Results: Natural frequencies were significantly higher in the short mandible model (e.g., <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$13,959 ~\text{Hz}$</tex> vs. <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$3,826 ~\text{Hz}$</tex> for bone type IV). Increased boundary constraint raised the first mode frequency from <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$1,786 ~\text{Hz}$</tex> (one side fixed) to <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$5,650 ~\text{Hz}$</tex> (three sides fixed). The highest frequencies occurred in Type I bone (up to <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$83,958 ~\text{Hz}$</tex>). Bone-substitutive layers caused frequency changes of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$&lt;1 \%$</tex>, indicating minimal impact. Conclusions: Bone quality is a dominant factor in implant stability, with denser bone yielding higher frequencies. Boundary condition modeling significantly affects frequency results. Thin bone-substitute layers do not notably influence vibrational response, although they remain important for osseointegration.