1

Introduction

The measurement of wear using contacting or non-contacting profilometers has been reported by a number of authors both for in vitro and in vivo measurements . Most research groups report wear data as two-dimensional (2D) step height measurements recorded from individual profiles from the teeth subjected to wear . A potential problem with 2D measurements is that measuring exactly the same profile before and after the wear episodes is prone to variation as areas have to be visually identified and this relies on the operator’s judgement. For very small dimensional changes the ability of the operator to choose exactly the same location may reduce the repeatability of the measurements. Added to this, measuring wear from single profiles does not give an indication of the total activity of the wear over the whole surface area which may shed more light on the complex interactions of abrasive three-body wear and erosive wear. To counteract this, researchers may obtain various single step height measurements which are then averaged to obtain a mean step height over the number of profiles evaluated.

Increased availability of surface metrology software has made three-dimensional tooth wear measurement methods possible; either reported as volumetric loss or mean step height loss over the whole surface area exposed to the wear , also called three-dimensional (3D) step height. Another way of measuring tooth wear is to ‘normalize’ measurements by dividing the 3D step height by the surface area of the sample subjected to the wear. This method was described by Vieira et al. but the authors did not compare normalized to non-normalized data. It is believed three-dimensional measurements provide a more accurate representation of the activity of the wear over the whole surface area but the differences between 2D and 3D tooth wear measurements have not been reported in the literature.

The aim of this research was to compare two-dimensional (step height from single profiles) and three-dimensional (mean step height over the surface area exposed to the wear and volumetric data) tooth wear measurements on human enamel subjected to an in vitro erosion–abrasion regime. The null hypothesis was that there were no differences in two-dimensional and three-dimensional tooth wear measurements.

2

Materials and methods

Twenty intact human third molars were randomly chosen from a pool of extracted teeth of unknown origin stored in saturated aqueous thymol solution. Ethical approval was obtained from Guy’s Research Ethics Committee (REC reference number: 04/Q0704/57). Mid-coronal enamel sections from the buccal, lingual, mesial and distal surfaces were obtained using a diamond blade (Diamond wafering blade XL-12205, Extec. UK) on a low speed sectioning machine (Isomet 11-1180 Low Speed Saw, Buehler Ltd., USA) and individual sections imbedded in a brass block using cold cure acrylic resin (Forestacryl ^® – Forestadent. UK, Lot No.: 202405 – Exp March/2010). Samples were mounted with a 300 μm ring of aluminum on top. After 24 h and after the acrylic resin had set, the aluminum ring was removed and the samples were polished sequentially and carefully with silicone carbide paper of 800, 1200, 2400 and 4000 grit (Silicon Carbide paper, Struers A/S, Denmark) on a rotating polishing machine (Struers Labopol-1, Denmark) under constant water irrigation until the sample was flush with the mark left by the aluminum ring, indicating that 300 μm had been removed. After this, three dimples were made into the acrylic resin in a triangular pattern surrounding the sample with a fast hand-piece and a small round diamond bur. The dimples served as reference areas to aid the superimpositional procedure to measure wear three-dimensionally. The samples were examined for defects under an optical microscope (EMZ TR, Meiji, Japan) and were randomly allocated to one of the four experimental groups or to the control group. Each group contained 16 enamel samples.

Table 1 shows the contents of the experimental drinks. The pH of the experimental drinks and the control were measured with a previously calibrated pH meter (Hydrus 100, Fisherbrand, UK) and the titratable acidity, the volume of 0.1 mol solution of sodium hydroxide required to raise 20 ml of the experimental drink to pH 7, was measured after agitation and equilibrium (2 min) at 20 °C. These measurements were repeated on three occasions.

The enamel sections were subjected 10 wear cycles in an abrasion–erosion model using methods similar to those described in . Each cycle consisted of initial immersion of the enamel sample in artificial saliva in an agitating machine (Titertek, Flow Laboratories, Germany) and after 2 h they were removed, washed under tap water and gently dried using paper towels. Samples were then immersed in the experimental drinks or control for 10 min under gentle agitation at room temperature (20 ± 3 °C) and then washed under tap water and gently dried using paper towels. Following this, samples were subjected to 200 strokes on a toothbrushing machine (Abrasion testing machine No. 8. The Pepsodent Co. USA). The machine consisted of four reciprocating arms each holding a standard Oral-B ^® Plus Size 40 soft-bristled head from a toothbrush (Oral B, UK) under a load of 200 g using a slurry of fluoride free toothpaste (Kingfisher natural toothpaste, Kingfisher, UK, Lot BN 023) and artificial saliva (1:3 ratio by weight). The enamel samples were firmly secured in acrylic wells. The toothbrush heads were changed for new ones every 2000 cycles.

The artificial saliva was prepared according to a protocol described in and contained the following chemicals in 1 l of distilled water: calcium chloride: 0.7 mmol/l; magnesium chloride: 0.2 mmol/l; potassium hydrogen phosphate: 4.0 mmol/l; HEPES buffer (acid form) 20.0 mmol/l and potassium chloride 30.0 mmol/l. The pH was adjusted to 7 by titration using 0.1 mol sodium hydroxide. Artificial saliva was prepared freshly every day.

Before the first wear episode and after the final wear episode the samples were washed with tap water and gently dried with compressed air and an impression taken using Extrude™ light bodied addition silicone impression material (Kerr Corporation, Romulus, MI, USA). Impressions were taken under a Perspex table weighted with 1 kg to ensure even thickness of individual impressions. The impressions were left to rest for 24 h and scanned on the non-contacting laser profilometer (Taicaan™ Technologies, Southampton UK) at medium precision and using a step-over distance of 15 μm. Digital scans from each paired set of impressions (before and after wear cycle) were superimposed using surface matching software with a superimpositional feature (Boddies ^® v1.92. Taicaan™. Technologies, Southampton, UK). The superimpositional feature of this software required the user to relocate three unchanged reference points, in our case the dimples created with the fast hand-piece, which allowed the software to bring the two scans into the same coordinate in space. Following this, differences in the ‘ Z ’ axis between the before and after impressions can be measured.

Scans from the enamel samples were superimposed using the dimples on the acrylic resin as reference areas. After superimposition, the wear scar was digitally isolated and the volume and surface area measured. From this, four maximum step height measurements were recorded from the reference area to the depth of the scar giving a two-dimensional step height (2D step height).

The resulting superimposition (wear scar) from each enamel sample was irregular so to measure tooth wear three-dimensionally, the surface area of the wear scar was transformed into a circle of the same surface area as the irregular scar. The radius of the circle was found using the formula:

where R = radius, A = surface area of the circle and π = 3.1415. Subsequently, and observing that the wear scar was a three-dimensional, the circle was converted onto a cylinder and its height was found using the formula:

where H = height of the cylinder, V = volume of the solid, r = radius of the circle and π = 3.1415. This measurement was termed the three-dimensional step height (3D step height).

Finally, in order to compensate for the varying surface area of each wear scar the data from each group were normalized by dividing the results from the 3D step height measurements by the surface area. This was termed three-dimensional step height measurements per square millimeter (3D/SA) and is expressed in μm/mm ² . These variables allowed us to compare two-dimensional and three-dimensional measurements of wear and wear by volume. We also compared step height measurements per square millimeter of exposed tooth surface per group, by normalizing the data.

The accuracy of step height and volumetric measurements after superimposition was measured using a section of a 50 μm slip gauge or a frustum made of commercially pure titanium whose volume was 3.9 mm ³ . A flat dental stone base was scanned three times. Once with the 50 μm slip gauge resting on top, then with the frustum resting on top and finally, the dental stone base was scanned without any solid on top. Then using the superimpositional feature of the software, the scan of the base with the 50 μm slip gauge was superimposed against the scan of the stone base without any solid on top. The same procedure was repeated by superimposing the scan of the stone base with the frustum on top with the scan of the base with no solid on top. Step height and volume were measured before and after superimposition and therefore the accuracy of these measurements could be assessed. The results showed accuracy of 0.9 μm for step height and 0.001 mm ³ for volume after superimposition using Boddies ^® v1.92 (Taicaan™ Technologies, Southampton, UK).

Based on power calculations (assuming effect size = 0.55 m; type I error probability, α = 0.05; power, 1 − β = 0.80), 16 enamel samples were included in each group. Outcome data for 2D step height, volume, 3D step height and 3D/SA were not normally distributed so required logarithmic transformations prior to analysis using analysis of variance (ANOVA). Where statistical significance was indicated, differences between individual groups were tested using post-ANOVA Bonferroni tests. Statistical significance was inferred where p < 0.05. Correlation between 2D and 3D step height measurements were tested using Spearman’s rho. Statistical significance was inferred where p < 0.05. The statistical analyses were performed using STATA ^® 11 (StataCorp. Texas, USA).