The paper investigates the risk factors for the severity of orthodontic root resorption. The multidimensional scaling (MDS) visualization method is used to investigate the experimental data from patients who received orthodontic treatment at the Department of Orthodontics and Dentofacial Orthopedics, Faculty of Dentistry, “Carol Davila” University of Medicine and Pharmacy, during a period of 4 years. The clusters emerging in the MDS plots reveal features and properties not easily captured by classical statistical tools. The results support the adoption of MDS for tackling the dentistry information and overcoming noise embedded into the data. The method introduced in this paper is rapid, efficient, and very useful for treating the risk factors for the severity of orthodontic root resorption.
Root resorption is defined as the biological process characterized by destruction of hard structure of the tooth root. Damaging may involve cementum, dentin, or both structures. Orthodontic treatment is associated with a higher frequency and severity of the pathological process of external root resorption. Frequency of orthodontic root resorption is about 100% when diagnostic techniques based on microscopy are used and around 70% when periapical or panoramic radiographs are used [
Etiopathogeny of orthodontic root resorption presents several uncertainties. It seems that higher incidence and severity of orthodontic root resorption are related mainly to patients' characteristics (individual susceptibility has the main role in root resorption appearance) and particularities of the orthodontic treatment applied [
The aim of this study is to investigate the impact of several risk factors (sex of patients, orthodontic extractions, and duration of treatment) on the severity of orthodontic root resorption. The analysis is based on the formation of clusters for experimental data analysis that may indicate similar behavior in some particular clinical situations.
Given the characteristics of the biomedical data, with a plethora of different influential factors, the numerical extraction of characteristics poses difficulties to classical statistical and computer tools. In this line of thought, the adoption of advanced computational tools capable of handling the incertitude implicit in the application is imperative. Therefore, the multidimensional scaling (MDS) method which is an algorithm that does not require initial assumptions about the data is tested. MDS is a computational visualization tool that constructs maps based on comparison criteria [
Bearing these ideas in mind, the paper is organized as follows. In Section
In order to achieve the proposed objectives, we designed and implemented a retrospective observational clinical study.
The sample was composed of patients receiving orthodontic treatment at the Department of Orthodontics and Dentofacial Orthopedics, Faculty of Dentistry, “Carol Davila” University of Medicine and Pharmacy, during October 2005–October 2009. In this study, patients with fixed metallic orthodontic appliances, standard edgewise, or straight-wire technique, applied in both jaws for a period of at least 6 months were included. From this study, patients with radiological signs of root resorption before the treatment start of were excluded. According to the protocol established in the Department of Orthodontics and Dentofacial Orthopedics, all patients sign an informed consent for the use of their medical documents for teaching and scientific purposes.
External root resorption was assessed in terms of root shortening, with the changes of root length being recorded, compared to the situation before applying the orthodontic device. Measurements of upper and lower incisors were made on serial panoramic radiographs, and changes in root length were being assessed using a mathematical formula based on the one proposed by L. Linge and B. O. Linge [
Calculation of the amount of root shortening (root resorption) on serial panoramic radiographs.
In this section, the experimental cases and the mathematical tools to be adopted are briefly described.
In the experiments, two cases were considered, namely, 1 (orthodontic treatment with tooth extraction) and 2 (orthodontic treatment without tooth extraction), denoted as cases 1 and 2 in the sequel, involving
Multidimensional scaling (MDS) has its origins in psychometrics and psychophysics, where it is used as a tool for perceptual and cognitive modeling. From the beginning, MDS has been applied in many fields, such as psychology, sociology, anthropology, economy, and educational research. In the last decades, this technique has been applied also in other areas such as music, finance, and biology.
MDS is a statistical technique used for visualization of information in the perspective of exploring similarities in data. MDS assigns a point to each item in an
An MDS algorithm starts by defining a measure of similarity for constructing a
The most common measure used to evaluate how well a particular configuration reproduces the observed distance matrix is the raw stress defined by
There are several measures that are commonly used, but most of them amount to the computation of the sum of squared deviations of observed values from the reproduced distances. Thus, the smaller the stress value
We can plot
We can also plot the reproduced distances, for a particular number of dimensions, against the observed input data (distances). This scatter plot, referred to as a Shepard diagram, shows the distances between points versus the original dissimilarities. In the Shepard plot, a narrow scatter that is around a 45-degree line indicates a good fit of the distances to the dissimilarities, while a large scatter indicates a lack of fit.
Since MDS is fed with relative distances, the maps are insensitive to rotation and translation. This means that the user can view and zoom the plots interactively in order to interpret the clusters of points that emerge in the map. Furthermore, distinct indices, capturing different characteristics, produce MDS charts, better or worse, merely in the viewpoint of easiness of interpretation in conjunction with the user own experience.
For the comparison of objects
In the sequel will be adopted GGobi [
In the experiments other metrics that lead to inferior results were tested and, therefore, are not analyzed here.
In this section, the sample of patients is described and the MDS results are analysed.
The sample included 55 patients, of which 74.5%
Associated with the orthodontic treatment, there was a mean reduction of 1.32 mm of tooth length. Most of the patients (67.27%,
Figures
Projections of the 3-dimensional MDS map for case 1 (with tooth extraction) involving
Projections of the 3-dimensional MDS map for case 2 (without teeth extraction) involving
In case 1 (with orthodontic extractions) mean root resorption was 1.59 mm. We cannot say anything about the implications of sex on root resorption severity due to the insignificant number of women
In case 2 (without orthodontic extractions) 37 patients were included with mean root resorption being 1.18 mm, indicating a lower severity of this pathological process. In this group, the number of males and females are comparable (13 males and 24 females). Patients presented ages between 10–30 years (mean = 16 years). Treatment time was between 6–48 months (mean = 20.21 months). We report the appearance of the clusters which shows some similarities (Figure
Figure
Stress versus the number of dimensions of the MDS representations for cases 1 and 2.
Orthodontic root resorption is one of the complications of the orthodontic treatment, knowing its etiology being an important factor in prevention of those forms with moderate and severe root shortening.
According to our results, the orthodontic extraction may be a risk for apical root resorption. More frequently it is associated with a more severe root resorption and also a more unpredictable behavior. This aspect is concordant with several clinical studies conducted on this topic [
Nowadays, preventive methods are seen as ensuring the best medical outcome. In this context, it is extremely important to accurately identify diseases risk factors. Interdisciplinary approach of these aspects, interpreting medical data using advanced statistical tools can offer extra knowledge. The paper studied the risk factors for the severity of orthodontic root resorption. The MDS visualization technique was adopted for exploring the data from patients receiving orthodontic treatment at the Department of Orthodontics and Dentofacial Orthopedics, Faculty of Dentistry, Carol Davila University of Medicine and Pharmacy, during a period of 4 years. The clusters in the MDS charts reveal features not easily captured by classical statistical tools and overcome noise effects embedded into the data.
The method introduced in this paper is rapid, efficient, and very useful for identifying the risk factors for the severity of orthodontic root resorption.