Related Experiment Video
Updated: Jan 21, 2026
Bioelectric Analyses of an Osseointegrated Intelligent Implant Design System for Amputees
Published on: July 15, 2009
Mathematical equations for dental implant stability patterns during the osseointegration period, based on previous
Attakorn Charatchaiwanna1, Thaned Rojsiraphisa2, Weerapan Aunmeungtong1
1Center of Excellence for Dental Implantology, Faculty of Dentistry, Chiang Mai University, Chiang Mai, Thailand.
Background:
Total stability of dental implant can be obtained from resonance frequency analysis (RFA) device, but without primary and secondary stability values.
Purpose:
To formulate mathematical equations for dental implant stability patterns during the osseointegration period.
Materials And Methods:
An online systematically search of the literature between January 1996 and December 2017 was performed for all prospective clinical trials that measured implant stability using RFA device during the osseointegration period. Initial mathematical function with adjustable parameters were created. Then curve-fitting was performed using a computerized program to formulate mathematical equations stability patterns.
Results:
Nine publications (24 study groups) were included in the mathematical analysis. Curve fitting with low sum of squared errors could be applied in all studies, except one. The stability has been divided into high, medium, and low stability. The curve fitting showed stability dip areas and intersection point which predict the returning of the stability to reach the primary stability. The study groups with low primary stability showed the poorest results, the high and medium stability group showed the stability pattern following the assumed primary stability pattern according to the mathematic equations.
Conclusions:
The model of primary and secondary stability could be predicted from the proposed equations.
Related Concept Videos
01:20Relation between Mathematical Equations and Block Diagrams
02:52Resonance
03:10Chemical Equations
02:59The Nernst Equation
The interconnection between standard cell potentials and various thermodynamic parameters such as the standard free energy change ΔG° and equilibrium constant K has been previously explored. For example, a redox reaction involving zinc(II) and tin(II) ions at 1 M concentration with Eºcell = +0.291 V and ΔG° = −56.2 kJ is spontaneous.
02:48Henderson-Hasselbalch Equation
03:18Radioactivity and Nuclear Equations
A nuclide of an element has a specific number of protons and...