Evaluation Algorithm of Root Canal Shape Based on Steklov Spectrum Analysis.

Dongqing Wu,Jian Gao,Zhengtao Xiao,Xin Chen,Lanyu Zhang,Yunbo He,Xiaoli Hu,Zhuwei Huang

doi:10.1155/2019/4830914

Abstract

In recent years, we have seen more and more interest in the field of medical images and shape comparison motivated by the latest advances in microcomputed tomography (μCT) acquisition, modelling, and visualization technologies. Usually, biologists need to evaluate the effect of different root canal preparation systems. Current root canal preparation evaluation methods are based on the volume difference, area difference, and transportation of two root canals before and after treatment. The purpose of root canal preparation is to minimize the volume difference and ensure the complete removal of the smear layer. Previous methods can reflect some general geometric differences, but they are not enough to evaluate the quality of root canal shape. To solve this problem, we proposed a novel root canal evaluation method based on spectrum and eigenfunctions of Steklov operators, which can be served as a better alternative to current methods in root canal preparation evaluation. Firstly, the ideal root canal model was simulated according to the root canal model before and after preparation. Secondly, the Steklov spectrum of the two models was calculated. Thirdly, based on the spectrum and the histogram of the Gaussian curvature on the surface, the weight of each eigenvalue was computed. Therefore, the Steklov spectrum distance (SSD), which measures shape difference between the root canals, was defined. Finally, the calculation method that quantifies the root canal preparation effect of root canals was obtained. Through experiments, our method manifested high robustness and accuracy compared with existing state-of-the-art approaches. It also demonstrates the significance of our algorithm's advantages on a variety of challenging root canals through result comparison with counterpart methods.

Highlights

In recent years, imaging technology represented by 3D digital geometry technology has widely been used in the medical field. e 3D model can display critical information such as the three-dimensional topological structure, geometric information, and anatomical structure of the lesion more intuitively
A series of thresholds or carefully adjusted penalty functions were often needed to intervene manually. e 3D topology and geometry of root canals are relatively fixed, gradually thinning from top to bottom. erefore, it is possible to avoid the shortcomings of the general algorithm and improve the automaticity and accuracy of the algorithm by thoroughly combining this priori knowledge. us, the design of a particular shape difference evaluation algorithm based on relatively fixed root canal topology will be based on the conicity, permeability, and smoothness of the whole root canal shape. e shortcomings of the previous local and single geometric evaluation method were broken through to provide a more scientific and comprehensive assessment method for root canal preparation effect. e calculation method is deduced as follows
Programming. is paper mainly deals with the numerical solution of the integral equation. e most crucial problem is to find the eigenvalues of a matrix, i.e., to solve large-scale sparse linear system. erefore, we choose the popular eigen algorithm library to calculate

Summary

Introduction

In recent years, imaging technology represented by 3D digital geometry technology has widely been used in the medical field. e 3D model can display critical information such as the three-dimensional topological structure, geometric information, and anatomical structure of the lesion more intuitively. E 3D model can display critical information such as the three-dimensional topological structure, geometric information, and anatomical structure of the lesion more intuitively. With the popularity of measurement tools represented by μCT, the evaluation of anatomical structure before and after root canal preparation has become a hot topic in medical imaging [2,3,4,5,6,7,8,9]. In [10], Vertucci investigated 2,400 permanent teeth and categorized them into eight types He studied the morphology and root canal of adult and established the evaluation criteria of treatment difficulty. Infected dentin should be removed and sterilized by root canal instruments to facilitate root canal obturation. e prepared root canals should contain the original root canal shape, retain the narrow part of the apex, and form the taper from the coronal to apical [3]

Results

Discussion

Conclusion