## Abstract

## Objectives

Esthetic restorations require that dental restorative materials have similar optical properties to teeth. To improve the color perception, the inhomogeneous morphology of the native tooth can be imitated by layering two optically different restorative materials. However until now the benefit of this method has not been satisfactorily demonstrated.

## Methods

The optical parameters, absorption coefficient *μ *_{a }, scattering coefficient *μ *_{s }, anisotropy factor g and effective scattering coefficient <SPAN role=presentation tabIndex=0 id=MathJax-Element-1-Frame class=MathJax style="POSITION: relative" data-mathml='μ′s’>μ′sμ′s

μ ′ s

, were determined for the enamel and dentin material of the restorative material systems Artemis ^{® }and Herculite XRV ^{® }. This was carried out for each material system in the wavelength range between 400 and 700 nm using integrating sphere measurements followed by inverse Monte Carlo simulations.

## Results

Using the optical parameters and a forward Monte Carlo simulation, the color perception of layered samples could be predicted with a sufficient degree of accuracy. The total color impression was shown to be dependent on the sample thickness and the transparency/translucency of the single layers of enamel and dentin materials.

## Conclusion

The study demonstrated that the use of two materials is well-suited for the restoration of front teeth with their relatively high proportion of enamel. This study will continue further with the compilation of a data pool of optical parameters which will enable the application of calculation models to optimize the optical approximation of the natural tooth.

## 1

## Introduction

In an ideal world, esthetic restorations would have the same reflection spectra *R *( *λ *) as the tooth, resulting in no visible difference between the restoration material and the treated tooth under all normal types of illumination. Equal reflection spectra *R *( *λ *) exist when the optical properties absorption coefficient *μ *_{a }( *λ *), scattering coefficient *μ *_{s }( *λ *) and the anisotropy factor *g *( *λ *) of the material are equal to those of the tooth. To get as close as possible to the ideal situation, the optical properties of both the restorative materials and native teeth should be known and matched . Since the natural tooth with enamel and dentin comprises a layered material made up of layers with different optical properties, it is preferable to imitate this layered structure using two optically different restorative materials in order to obtain optimal color perception .

For this purpose, commercial filling materials have been developed which enable the dentist to reconstruct the natural structure of the tooth by modeling layers of different optical behavior. However, there are no guidelines for the expected visual outcome with the materials provided by the industry and the dentist is completely free to choose and combine the appropriate materials as he sees fit. It is still a question of debate as to whether the use of two-layered systems has a clinically relevant effect on the perception of color. There is to our knowledge no detailed information available about the dependence of the observer’s color perception on the layer thickness or optical properties of the combined composites. The hypothesis that esthetic layer preparation technique leads to a significantly improved color perception will be critically examined.

Optically the color perception of layered composite restorations is made up of the diffuse reflectance of the inner dentin composite and the outer translucent enamel composite, and is dependent on the thickness of each layer due to translucency of the materials.

In a previous study the possibility of predicting the color perception of a defined one-layered composite material according to the CIELAB color system (Commission Internationale de l’Eclairage) from simulated diffuse reflectance data <SPAN role=presentation tabIndex=0 id=MathJax-Element-2-Frame class=MathJax style="POSITION: relative" data-mathml='Rds(λ)’>Rsd(λ)Rds(λ)

R d s ( λ )

was described and tested against measurements of the diffuse reflectance <SPAN role=presentation tabIndex=0 id=MathJax-Element-3-Frame class=MathJax style="POSITION: relative" data-mathml='Rdm(λ)’>Rmd(λ)Rdm(λ)

R d m ( λ )

. The forward Monte Carlo simulation (fMCS) used, was based on the optical properties *μ *_{a }, *μ *_{s }and *g *, which were determined by integrating sphere measurements using an inverse Monte Carlo simulation (iMCS).

According to the radiation transport theory the ‘optical behavior’ of turbid media can be described by the optical parameters absorption coefficient *μ *_{a }( *λ *), scattering coefficient *μ *_{s }( *λ *), and the anisotropy factor *g *( *λ *) together with an appropriate phase function. These optical parameters are intrinsic and do not depend on sample geometry and the arrangement of light source and detector. Intrinsic optical parameters cannot be measured directly but can be calculated from the measurable reflectance and transmission spectra by means of iMCS, as this is the most precise theoretical model to solve the light transport equation where complex boundary conditions make analytical solutions impossible .

It was the aim of this study to examine the above mentioned hypothesis by applying this procedure to materials composed of two different layers with different optical properties in the visible wavelength range. The materials selected were two restorative multilayer-composite-systems, Artemis ^{® }and Herculite XRV ^{® }. The diffuse reflectance <SPAN role=presentation tabIndex=0 id=MathJax-Element-4-Frame class=MathJax style="POSITION: relative" data-mathml='Rds(λ)’>Rsd(λ)Rds(λ)

R d s ( λ )

of samples, made up of single layers of the dentin and enamel materials with identical thickness (1 mm), was simulated from the determined optical parameters. The results were compared to measurements of <SPAN role=presentation tabIndex=0 id=MathJax-Element-5-Frame class=MathJax style="POSITION: relative" data-mathml='Rdm(λ)’>Rmd(λ)Rdm(λ)

R d m ( λ )

using the CIELAB system. This was performed for the colors A2, A3, A3.5 and A4.

In the next step the diffuse reflectance of samples with different layer thickness composed of dentin and enamel composites within one color shade range (VITAPAN ^{® }A colors) were simulated and the resulting color perceptions calculated using the CIELAB system. These were compared with the color perception of a reference sample modeled to reflect the layer structure of natural teeth with a 1.1 mm dentin and a 0.4 mm enamel layer thickness. Color differences of <2 are defined to be clinically indistinguishable . Additional samples with extreme thickness relations were also investigated to gain a better understanding of the influence of the layer thicknesses.

Based on the results of the present study and previous experiments , a data pool of the optical parameters is being compiled in order to extend the physical understanding of the optical properties of dental composites. This will enable the application of calculation models as a basis for the optimization of the composition of new materials and their optical appearance. As an example, a calculation method is presented for determination and prediction of the color perception according to the CIELAB color system for a given composite layer.

## 2

## Materials and methods

## 2.1

## Dental materials and preparation technique

Dentin and enamel samples from Artemis ^{® }(Ivoclar Vivadent AG, Schaan, Lichtenstein) and Herculite XRV ^{® }(KerrHawe, Rastadt, Germany) were investigated, each in the commonly available VITA A color shades for enamel, indicated in this study by EA2, EA3, EA35, EA4, and dentin, indicated as DA2, DA3, DA35, DA4. Circular specimen discs, each with a diameter of 22 mm, were prepared using ultrasound and flat glass slides to achieve homogenous samples without air bubbles and with specular surfaces. This method is identical to the preparation method described earlier .

For the main spectrometric measurements, samples composed of dentin and the corresponding enamel layers with a total thickness of 1.5 mm were produced for each of the 4 VITA shades. This included samples of 1.1 mm dentin and 0.4 mm enamel which acted as a reference, as the layer thickness was chosen according to the natural tooth structure. In addition, samples were prepared with 1.4 mm dentin and 0.1 mm enamel, and vice versa. Pure samples of dentin and enamel material with a thickness of 1.5 mm were also prepared. Each sample was prepared in triplicate and subsequently investigated, resulting in a total of 60 samples.

## 2.2

## Spectrometric measurements

In order to determine the optical parameters, the diffuse reflectance <SPAN role=presentation tabIndex=0 id=MathJax-Element-6-Frame class=MathJax style="POSITION: relative" data-mathml='Rdm’>RmdRdm

R d m

, the total transmission *T *_{t }and the diffuse transmission *T *_{d }(= *T *_{t }− transmission within an aperture of 5.3°) of the prepared samples from Artemis ^{® }and Herculite XRV ^{® }were measured in the wavelength range from 400 nm to 700 nm in steps of 5 nm by the integrating sphere technique using an UV/VIS/NIR-spectrometer (Lambda 900, Perkin-Elmer Corporation, Norwalk, USA). The measurement of *T *_{d }instead of the usually used collimated transmission, allows measurements with one integrating sphere. The experimental set-up, described elsewhere , allowed the measurement of light transmission and reflectance with an error of less than 0.1% ( Fig. 1 , top).

## 2.3

## Monte Carlo simulation

A specially developed inverse Monte Carlo simulation program was used which takes into account the geometry of the optical set-up and all radiation losses. Simulations with more than 10 ^{6 }photons for one wavelength were verified leading to statistical errors of less than 0.15%. Typical standard deviations of three determinations of *μ *_{a }, *μ *_{s }, and 1 − *g *(iMCS simulations) were in the range 3–5%. The iMCS procedure is the same as the method used by Friebel et al. . Pre-simulations showed that the Henyey-Greenstein phase function was best suited for iMCS of the dentin and enamel composites . To increase the precision of the simulation, the absorption coefficients *μ *_{a }( *λ *), determined on samples with a thickness of 1 mm, were corrected by measurements of composite samples with 5 mm thickness and a modified iMCS determination of *μ *_{a }( *λ *), keeping *μ *_{s }( *λ *) and *g *( *λ *) at predetermined values for the 1 mm thick sample. This correction step was described in detail in a previous paper .

The wavelength dependent refractive index of the material of each composite, as an important input parameter for the simulation , was determined from 400 nm to 700 nm using an Abbe refractometer. All the samples were prepared by molding on an optical glass surface to minimize any errors which might occur due to surface roughness.

## 2.4

## Determination of the color perception following the CIELAB system

Based on the determined values of *μ *_{a }, *μ *_{s }and *g *, the diffuse reflectance values <SPAN role=presentation tabIndex=0 id=MathJax-Element-8-Frame class=MathJax style="POSITION: relative" data-mathml='Rds’>RsdRds

R d s

for a sample of Artemis ^{® }and Herculite XRV ^{® }with a thickness of 1 mm and color EA2, EA3, EA35, EA4, DA2, DA3, DA3,5 and DA4 were calculated using a forward Monte Carlo simulation (fMCS) program. Based on the material-dependent simulation determined optical parameters, the *X *, *Y *, *Z *standard color values were calculated according to the German DIN-standard 5033 in 10 nm steps in the range 400–700 nm, with respect to the standard light source D65 and the 2° standard observer, and transformed to the *L **, *a **, *b **-values according the CIELAB system. To compare the simulated CIELAB values with the measured ones, color differences <SPAN role=presentation tabIndex=0 id=MathJax-Element-9-Frame class=MathJax style="POSITION: relative" data-mathml='ΔEab’>ΔEabΔEab

Δ E ab

were determined between measured and calculated values in accordance with Eq. (1) (DIN standard 6174 )

Δ E ab = ( ( Δ L ) ) 2 + ( ( Δ a ) ) 2 + ( ( Δ b ) 2 ) 1 / 2

(with Δ *L ** as the difference between <SPAN role=presentation tabIndex=0 id=MathJax-Element-11-Frame class=MathJax style="POSITION: relative" data-mathml='Lsample’>LsampleLsample

L sample

and <SPAN role=presentation tabIndex=0 id=MathJax-Element-12-Frame class=MathJax style="POSITION: relative" data-mathml='Lreference’>LreferenceLreference

L reference

, Δ *a **,Δ *b ** analogous).

The transformation of the measured reflectance and transmission to the CIELAB-values is as follows:

R d m , T d , T d → iMCS → μ a , μ s , g → fMCS → R d s → DIN – standard 6174 → CIELAB-values