ADDITION TO THE METHODOLOGY OF RESEARCH INTO PERMANENT TEETH HARDNESS

This paper examines permanent teeth hardness (microhardness) using the Vickers method. An original methodology was developed and adopted for preparing the experimental material, i.e. the cross sections into four characteristic locations on the tooth: corona dentis, cervix dentis, pars medialis radicis dentis and apex radicis dentis. A new “hardness profile” was introduced, which connects hardness and location along the cross section of the tooth. Hardness was measured 664 times on experimental cross sections with total a average hardness of 73.17 HV according to Vickers and a standard deviation of 55.68 HV. The derived descriptive statistical indicators of tooth hardness were calculated for equivalent cross sections, individual teeth, teeth groups and tooth localizations. Two algorithms were developed for determining the rank of tooth hardness – one for estimating the rank of arithmetic mean of the hardness of the cross sections of the teeth, and the other for estimating the rank of hardness for individual teeth.


INTRODUCTION
Hardness is a property denoting the capability of a material to resist the penetration of other objects into its surface layers.Hardness is a surface characteristic.The extent of surface distortion depends on the material itself, but also on the way the surface is distorted.In this sense, it may prove useful to determine the amount of resistance to scraping, abrasion, dents from impact and indents.According to the type of surface distortion, corresponding hardness measurement methods were created.Even though other techniques are not insignificant, the most common hardness testing technique is indentation.There are several methods of indentation hardness testing: Rockwell's, Vickers' , Brinell's and Knoop's.The principle of measurement in indentation-based methods is that the surface of the material being tested is put into contact with an indentor of specified shape and dimensions, which during a specified time interval applies pressure of a specified intensity of force, after which the hardness is calculated based on the dimensions of the indentor.

Tooth hardness -previous research
In the second half of the twentieth century, there were few papers that could have been used as reference in researching permanent teeth hardness.The papers that were available can be divided into three groups.The first is the group dealing directly with testing tooth hardness with measurement methods.The second is the group of papers that establish a connection between tooth hardness and tooth microstructure, and the papers in the third group try to connect tooth decay -caries -with tooth hardness.
All available papers from the aforementioned period either state that tooth hardness is not explored in a systematic or that it is their main goal.Most papers mention or explore tooth hardness either as a benchmark for the effect being explored (cause -tooth exposure, consequence -tooth decay), or as a bio-physical characteristic which bio-materials in prosthetics and implantology must be compatible with.Exceptions are the first paper on this subject by Saunsbury and Atkinson (1953) and one of the relatively newer papers by Hata and Hata (2000) which makes the connection and calculates the regression curve between the frequency of the tactile sensor and microhardness index by Vickers.However, this paper is limited to surface measurements of the hardness of the enamel and dentin.

Research aim and hypotheses
The aim of the research was to examine permanent teeth hardness, both for individual teeth and teeth groups, on cross-sections (crown, neck and root), covering all tooth structures (enamel, dentin, cement).The significance of researching teeth hardness is in determining the difference in hardness between structures of various histological, morphological and chemical properties, which is directly correlated with the exposure of teeth to external (physical, chemical and biochemical) influences.
The practical significance of researching tooth hardness can be seen in all branches of stomatology, especially in prosthetics, conservative stomatology, oral surgery and others.The biophysical characteristics of teeth, especially teeth hardness, require that the material has appropriate physical and chemical properties, which means that the adequate therapy in tooth treatment is determined by tooth hardness, degree of damage, tooth class etc.
Tooth hardness, from the cross-section, declines from the exterior to the interior structures, i.e. from the enamel towards the cement, and from the crown to the tip of the root.It is assumed that hardness varies between different teeth groups, which is connected to their respective functional requirements.

MATERIALS AND METHODS
The material was gathered over several years in dentists' offices.The selection of the sample was made from a pool of 100 teeth, none of which had been recently extracted.The time range from the extraction to the selection was one to five years.From the available teeth, 52 human teeth were selected.The first selection criterion for the sample was tooth quality.Only teeth with no visible defects were selected, not taking into account any damage at the microstructural level.The second selection criterion was that the teeth belonged to permanent dentition.The third selection criterion for the sample was teeth diversity (belonging to various classes).The aim was to find approximately the same number of teeth from each class.However, considering the available number of teeth and the number of teeth in the sample, it was impossible to fully achieve this aim.But still, the sample contained at least one tooth from each class, so the sample can without a doubt be considered valid and the number of units in the sample, as well as its structure, is in no way a limiting factor for the research.

Preparation of the sample
Each tooth from the sample was cut transversely at the appropriate point.In order to minimize the influence of heat on the crystalline structure of the teeth, and consequently on the hardness of the teeth, during the cutting process the material and the tools were cooled with water.This produced 52 experimental dental plates.The reference for cutting was from the perpendicular to the longitudinal axis of the tooth.The longitudinal axis of the tooth is defined as an imaginary line connecting the two furthest points of the tooth.The experimental plates, the 2-3 mm thick cross sections, were highly polished.This produced the experimental material, 52 experimental tooth plates from 15 characteristic tooth points.The further analysis shows data only for four equivalent cross-sections.

The Vickers hardness test
The Vickers hardness testing method consists of indenting a small diamond square-based pyramid into the material.Because of the brittleness of the diamonds, the indentation must be performed very carefully.The point of the pyramid is cut under a 136 o angle.The indentation force is arbitrary, from 1 to 120 daN, depending on the material being tested.The indentation is then enlarged on a blurred plate, the diagonal is measured by fine measuring tools with 1/1000 mm accuracy, and then the surface of the imprint in mm 2 and the Vickers hardness degree are calculated following the following formula: During this research, tooth hardness was measured with the "LL Tukon" microhardness tester (see image below).This device provides high automatization of the measurement process thanks to a computer and screen which are used to automatically set and display both the size of the indentation and directly the Vickers hardness degree.

Statistical methods of determining tooth hardness
The statistical methodology applied in research can be provisionally presented in four stages: Presentation of the research sample -picture of the sample: This section describes the sample.First the original measurements are processed, which will be given in statistical tables to give a more concise presentation.The analysis primarily assumes determining derived statistical hardness indicators for equivalent cross-sections, individual teeth, teeth groups and tooth location (up -down).The analysis also includes the so-called measurement homogenization.All results of the analysis are shown in the appropriate statistical tables.
The comparative statistical analysis of the derived statistical tooth hardness indicators.This consists of two parts: comparative analysis and testing implicit research hypotheses.
Determining tooth hardness rank: The final part of the methodological procedure for determining tooth hardness is ranking relevant hardness indicators, i.e. equivalent cross-sections, individual teeth, tooth groups and tooth location.For this purpose, ranking algorithms were developed.One is the algorithm for evaluating the rank of arithmetic means of equivalent cross-sections, and the other one is for evaluating the hardness rank for individual teeth, based on testing significant differences between the arithmetic means of individual teeth hardness.I Algorithm hardness rank for equivalent crosssections: , where U RANG denotes the total rank of the average hardness for equivalent tooth cross-sections, and ) (I Rang denotes the individual rank of the average hardness for equivalent tooth cross-sections.The criterion for selecting the hardness rank for equivalent tooth cross-sections is

Descriptive statistical indicators for original tooth hardness measurements
Each series of measurements is followed by data in tables on the tooth hardness profile and the corresponding charts of the hardness profile for the tooth cross-sections depending on the location of the measurement.Tables are then given showing descriptive statistical parameters for individual measurement series.The descriptive parameters were average value, standard deviation, fifth and ninety-fifth percentile and variation coefficient.
Example: Dens incisivus primus superior, pars medialis radicis dentis Table 1 shows that the average hardness value for the middle of the root dens incisivus primus superior is 76.06 HV with the standard deviation of 11.12 HV.It turns out that the series is homogeneous with the variation coefficient of CV=14.62%.The fact that the 5 th and 95 th percentiles are included in the interval encompassed by X sr ± 2SD, indicates that the influence of extreme measurement values to descriptive statistical parameters is negligible.Based on the results of descriptive statistics and conclusions on the ranks of average hardness values   Tooth hardness analysis -derived descriptive statistical indicators for tooth hardness measurement: in equivalent cross-sections of certain tooth types, applying criteria for rank selection produces the rank of average hardness in equivalent tooth crosssections such as: 1. Corona dentis, 2. Pars medialis radicis dentis, 3. Apex radicis dentis, 4. Cervix dentis.

Comparative statistical analysis of tooth hardness:
Comparative analysis of average hardness values in equivalent tooth cross-sections includes unreduced and unhomogenized measurements, but also reduced and homogenized measurements.
Table 2 shows that the total rank of tooth hardness for certain tooth types in homogenized measurements is no different than the total rank of hardness for certain tooth types in unhomogenized measurements, except for dens incisivus primus and dens molaris secundus which have switched places.It also shows that there is no difference in the rank of total hardness for tooth groups and tooth location between unhomogenized and homogenized measurements.

Testing the relevance of difference between arithmetic means of tooth hardness values (individually and among tooth groups)
In order for valid conclusions to be made on testing the relevance of the difference between arithmetic means of tooth hardness it is necessary to determine the rank of hardness based on the conducted tests.
To evaluate the total rank of average hardness value for individual teeth we use the developed algorithms for rank evaluation based on results of mutual individual tests: value is calculated based on the evaluation of the test result among certain teeth in the following way: if the result is of a) high statistically relevant difference, b) some statistically relevant difference or c) no statistically relevant difference, then the numbers 2, 1 or 0, respectively, The rank of average hardness values in equivalent cross-sections according to tooth type are assigned to the result.The criterion for selecting the hardness rank for equivalent tooth crosssections is ) max( U RANG .Using the Spearman rank correlation shows that ρ emp =0,29<ρ gr =0,738 (for p=0,05) which indicates that there is no congruence in the ranks of original and homogenized measurements (p>0,05).

DISCUSSION
A total of 664 hardness measurements were performed on experimental cross-sections with total average hardness of 73.17 HV and standard deviation of 55.68 HV.The variation coefficient of 76.09% indicates that it is a highly inhomogeneous set.The so-called homogenization process was carried out, thus excluding measurement values lower than the th and higher than the 95 th percentile.This process excluded extreme values and produced a homogeneous set with total average hardness of 63.76 HV and standard deviation of 14.66 HV.The homogenization process, removing 5% of the highest and 5% of the lowest hardness values, practically reduced the measurement to testing hardness of the dentin.
With individual teeth, the highest hardness of 73.90 HV belongs to the dens incisivus primus, followed by the dens molaris primus with 69.49HV, dens molaris secundus with 66.11 HV, dens molaris tercius with 63.57HV, dens caninus with 62.05 HV, dens premolaris secundus with 60.83 HV, dens premolaris primus with 59.25 HV and finally dens incisivus secundus with 53.02 HV.When it comes to tooth groups, the highest hardness value is in the molaris dentis with 63.73 HV, followed by the incisivus dentis with 63.33 HV and finally the premolaris dentis with 60.17 HV.Regarding tooth location, the highest hardness is that of the superior dentis with 63.48 HV and then the inferior dentis with 61.63 HV.
The hardness rank and tooth hardness value distribution by individual teeth, tooth groups and tooth location corresponds to the expected hardness model made on the basis of the physiological characteristics of permanent teeth.

CONCLUSIONS
Original methodology was developed for the preparation of the experimental material -experimental plates (cross-sections) in four characteristic tooth locations, i.e. the corona dentis, cervix dentis, pars medialis radicis dentis and apex radicis dentis.Hardness was measured along the larger axis of each cross-section.This methodology implicitly determined the focal point of the hardness testing.
Tooth hardness was measured in different crosssections and different layers.
Based on the hardness measurements the socalled hardness profile was introduced and shown in a table and diagram, linking tooth hardness and location along the tooth cross-section.Along with the hardness profile, we have tables of the descriptive statistical parameters.
The derived descriptive statistical indicators of tooth hardness were calculated for equivalent crosssections, individual teeth, tooth groups and tooth location.
An algorithm was developed for determining the tooth hardness rank for each of the observed categories, i.e. equivalent cross-sections, individual teeth, tooth groups and tooth location, and an algo-rithm was developed for determining hardness rank for certain tooth categories based on test results of implicit research hypotheses on the existence of a statistically relevant difference between arithmetic means of tooth hardness values.The results of the research show that the hardness rank for individual teeth derived from the original measurements and the hardness rank from the homogenized measurements differ.The Spearman rank correlation shows that there is no congruence between ranks in the original and the homogenized measurements (p>0,05).
denotes the Vickers hardness degree, F -denotes the indentation force [daN], and ddenotes the pyramid diagonal [mm 2 ].

Fig. 1 .
Fig. 1.Graphic chart of tooth hardness profile (dens incisivus primus superior, pars medialis radicis dentis) Table of original measurements: The first column shows the number of the measurement.The second column has the depth of the indentation from the hardness test.The third column gives the hardness value by Vickers (HV), and the fourth column is for the location of the indentation in micrometers.The chart (see image), represents the so-called hardness profile.The presentation of the research sample ends with a text additionally explaining the displayed variable and/or table and chart.

Table 2 .
Comparative rank of certain tooth types and groups for unhomogenized and homogenized measurements