Abstract
Objectives
To use the Kubelka–Munk theory to evaluate the scattering ( S ), absorption ( K ) and transmittance ( T ) of noncolored and colored dental zirconia systems and human (HD) and bovine (BD) dentins.
Methods
Two zirconia systems were used: ZC ZirCAD (Ivoclar Vivadent) and LVLAVA (3M ESPE). Specimens from each ceramic system were divided into 3 groups ( n = 5): ZC1 and LV1 (noncolored); ZC2 and LV2 colored to shade A1, and ZC3 and LV3 colored to shade A3. Five human and bovine anterior teeth were flattened and polished through 1200 grit SiC paper to expose the superficial buccal dentin. All samples were prepared to a final thickness of 0.5 mm. Diffuse reflectance was measured against white and black backgrounds, using a spectroradiometer in a viewing booth with D65 illuminant and d/0° geometry. S and K coefficients and T were calculated using Kubelka–Munk’s equations. Data was statistically analyzed using Kruskal–Wallis, Mann–Whitney tests, and VAF coefficient.
Results
Spectral distributions of S , K and T were wavelength dependent. The spectral behavior of S and T was similar to HD (VAF ≥ 96.80), even though they were statistically different ( p ≤ 0.05). The spectral behavior of K was also similar to HD, except for LV1 (VAF = 38.62), yet all ceramics were statistically different from HD ( p ≤ 0.05). HD and BD showed similar values of S and T ( p > 0.05).
Significance
The dental professional should consider the optical behavior differences between the zirconia systems evaluated and the human dentin to achieve optimal esthetics in restorative dentistry.
1
Introduction
The fabrication of a dental restoration with natural appearance requires not only the matching of color (value, hue and chroma), but also the blending of specific optical characteristics of the adjacent dental structures . When light strikes a tooth surface, four phenomena can be described: (a) specular transmission of the light flux through dental structures, (b) specular light reflection at the tooth surface, (c) diffuse light reflection at the tooth surface, and (d) absorption and scattering of light within the dental tissues . Thus, for optimal esthetic results, a favorable shade and appearance of the restoration is of extreme importance.
A large variety of all ceramic systems were recently introduced due to the increased esthetic requirements and demands of both patients and dental professionals . The tetragonal polycrystalline zirconia doped with 3 mol% yttria (3YTZP) has generated considerable interest in the dental community due to its peculiar mechanical properties and optimal biocompatibility .
Initially, 3YTZP ceramic systems were considered as completely opaque materials, due to their high refractive index ( n = 2.1–2.2), low absorption coefficient and high opacity in the visible and infrared regions of the spectrum. The opacity of the zirconium oxide is often attributed to some of its structural characteristics, such as the particle size, which is slightly greater than the wavelength of the incident light, the density (residual porosity < 0.05%) and the homogeneity . Different grades of zirconia have different levels of translucency; the higher the grade, the more translucent the material. Pressing methods, different additives (stabilizing oxides) and sintering conditions may affect its translucency .
Zirconiabased dental restorations are obtained by porcelain veneering a zirconia core. Yet, it has been reported that using a shaded zirconia core results in better esthetics and greater natural appearance, similar to the chromatic dentin overlaid by translucent enamel . Various zirconia core shades have been introduced with few reports on the effect of shaded zirconia on the translucency of the ceramic restorations. One of these studies showed similar translucency parameter (TP) values for 3YTZP systems compared to 0.5mm thick human dentin .
It is well known that the translucency of a material depends on its scattering ( μ _{s }) and absorption ( μ _{a }) coefficients as well as on the thickness of the sample. The scattering and absorption coefficients of dentin are greater than for enamel. In contrast to enamel, the dentin coefficients of scattering and absorption do not change significantly with wavelength . Yet, few reports are available on the scattering and absorption behavior of dental zirconia. One of these studies reported that zirconia (sintered LAVA™ Zirconia) showed a scattering angular behavior more similar to the human dentin than to dental materials and that a thicker (0.5 mm) sample yielded less directed scattering profile than a thinner (0.3 mm) sample .
Kubelka–Munk (K–M) reflectance theory is a mathematical model describing the reflectance resulting from twoflux radiation transfer in a homogenous and uniform medium placed over an opaque backing . The main advantage of this theory is that the absorption and scattering coefficients ( K and S , respectively) can be easily expressed as a function of the reflectance and transmittance of the sample. Yet, the K–M scattering ( S ) and absorption ( K ) coefficients are not directly related to μ _{s }and μ _{a }(physical scattering and physical absorption coefficients, respectively). Nevertheless, several authors have reported on the relationship between Kubelka–Munk S and K coefficients and the μ _{s }and μ _{a }coefficients. Yet, previous studies used the reflectance measurements based on the K–M reflectance theory to calculate the optical properties of dental tissues and materials, such as: human enamel and dentin , porcelain materials , and direct restorative materials . A study showed that corrected K–M reflectance theory may be used to accurately quantify the optical K–M absorption and scattering coefficients of dental resinbased composites .
The objective of this study was to use the Kubelka–Munk theory to evaluate the scattering, absorption and transmittance of noncolored and colored dental zirconia systems and human and bovine dentins, testing the null hypothesis that scattering, absorption and transmittance of dental zirconia systems are not significantly different from the human and bovine dentins.
2
Material and methods
2.1
Sample preparation
2.1.1
Zirconia systems
Two commercially available 3YTZP ceramic systems with similar composition were evaluated ( Table 1 ):

ZC: IPS e.max ^{® }ZirCAD (Ivoclar Vivadent, Schaan, Liechtenstein); and

LV: LAVA™ Zirconia (3M ESPE, St. Paul, MN, USA) .
Features  IPS e.max® ZirCAD (Ivoclar Vivadent) ^{a }  LAVA™ Zirconia (3M ESPE) ^{a } 

Components  ZrO _{2 }, Y _{2 }O _{3 }, HfO _{2 }, Al _{2 }O _{3 }  ZrO _{2 }, Y _{2 }O _{3 }, HfO _{2 }, Al _{2 }O _{3 } 
Yttria content  3 mol%  3 mol% 
Density  6.045–6.065 g/cm ^{3 }  6.08 g/cm ^{3 } 
Sintering temperature  1500 °C  1500 °C 
Grain size  0.52 ± 0.05 μm  0.5 μm 
Batch #  16861  318814 
Specimens were cut from presintered blocks using a low speed (100 rpm), watercooled diamond saw (Accutom 50, Struers, Ballerup, Denmark) and subsequently polished with 500, 800 and 1200 grit SiC abrasive papers (Struers, Ballerup, Denmark) under constant water irrigation. Handling, preparation and sintering of each ceramic system was performed by the same operator in accordance with manufacturerś instructions. The final thickness (after sintering) of all ceramic specimens was 0.5 ± 0.01 mm. Specimens from each ceramic system (ZC and LV) were divided into 3 groups ( n = 5), as follows:

ZC1: regular (no color) samples;

ZC2: samples from preshaded blocks MO1, corresponding to shades A1/A2;

ZC3: colored samples, using coloring liquid CL2 (Ivoclar Vivadent, Schaan, Liechtenstein) corresponding to shades A3/A3.5.

LV1: regular (no color) samples;

LV2: colored samples, using coloring liquid FS1 (3M ESPE, St. Paul, MN, USA), corresponding to shades A1/B1;

LV3: colored samples, using coloring liquid FS3 (3M ESPE, St. Paul, MN, USA), corresponding to shades A2/A3.
Coloring and sintering procedures were performed according to the manufacturers’ indications.
2.1.2
Preparation of human dentin (HD) and bovine dentin (BD)
This study was approved by the local Ethics Committee. Anterior maxillary teeth ( n = 5), free of caries and restorations, extracted because of periodontal disease, were obtained from voluntary patients that signed the informed consent to participate in the study. All teeth were cleaned from any debris and selected to visually match the A3 shade (VITA ^{® }Classical shade guide, VITA Zahnfabrik, Bad Säckingen, Germany). Additionally, 5 bovine incisors were also used in the study. All human and bovine teeth were carefully visual inspected. Teeth with any coronal crack or fracture were excluded from the study. Selected teeth were stored in 1% thymol solution under refrigeration (4 °C) until sample preparation and testing.
Human and bovine teeth were sectioned at the cementumenamel junction using a diamond saw (Accutom 50, Struers, Ballerup, Denmark) under water cooling. The crowns were further cut following their long axis, dividing the buccal and lingual sides of the crowns. The roots and the lingual half of the crowns were discarded in a special container for biological waste following the Biomedical Waste Management Rules. The flattened lingual surface of the specimens was polished with 500grit silicon carbide paper discs on a polisher (EXAKT Apparatebau D2000, Norderstedt, Germany). In order to achieve regular thickness and parallel buccallingual surfaces, the buccal surface of all dental specimens was flattened to remove the enamel, exposing the superficial dentin. Specimens were additionally polished with silicon paper discs (800, 1000 and 1200 grit) to obtain 0.5mm thick specimens, measured in the middle third of the crown slices. The specimens were further polished from 1 to 0.05μm alumina slurry (Alumina Slurry, Electron Microscopy Sciences, Fort Washington, PA, USA). The smear layer was removed in a sonic bath of 0.27 M EDTA (pH 7.4) solution for 5 min and 0.34 M sodium hypochlorite (pH 12.3) solution for 3 min, followed by running water wash for 5 min .
The final thickness of the central area of all specimens was measured three times using a digital caliper (DIGC6, Thorlabs, Inc., NJ, USA) and averaging the value.
2.2
Reflectance measurements
The relative spectral radiance (W/sr m ^{2 }) of the zirconia, bovine and human dentin samples were measured against white ( L * = 94.2, a * = 1.3 and b * = 1.7) and black ( L * = 3.1, a * = 0.7 and b * = 2.4) backgrounds (50 mm × 50 mm ceramic tile, Ceram, Staffordshire, United Kingdom), using a spectroradiometer (SpectraScan® PR704, Photo Research Inc., Chatsworth, CA, USA) with 4% measurement accuracy. A saturated sucrose solution (refractive index n = 1.5, approximately) was used as contact between the samples and the background .
Specimens were measured inside of a colorassessment cabinet (CAC 60, Verivide Limited, Leicester, United Kingdom) under constant illumination (light source simulating the spectral relative irradiance of D65 CIE standard illuminant). Illuminating/measuring configuration corresponded to CIE d/0° .
Shortterm repeated measurements without replacement were performed where each specimen was measured three times. A triangular stand was built to support the specimens and avoid specular reflection from the glossy surface. Since the field of measurement of the spectroradiometer was 1°, the spectroradiometer was placed 25 cm from the specimen, allowing for the measurement of the whole specimen .
Finally, the relative spectral radiance measured for all specimens at each wavelength was converted into absolute reflectance, based on measurements of a white reflectance standard (OPST3C, Optopolymer, Germany).
2.3
Kubelka–Munk coefficients
The Kubelka–Munk scattering ( S ) and absorption ( K ) coefficients were calculated algebraically from the spectral reflectance data of each sample using the Kubelka–Munk equations as described below.
Secondary optical constants ( a and b ) were calculated from the experimentally obtained spectral reflectance values using the black and white backgrounds, as follows:
a = 1 2 R + R 0 − R + R g R 0 R g
b = ( a 2 − 1 ) 1 / 2
where R is the reflectance of the specimen over the white background, R _{0 }the reflectance of the specimen over the black background and R _{g }is the reflectance of the white background.
The scattering coefficient ( S ) for a unit of thickness of a specific material is defined by the following equation:
S ( mm − 1 ) = 1 b X a r c t g h [ ( 1 − a R 0 ) / b R 0 ]
where X is the actual thickness of the specimen, and arctgh is an inverse hyperbolic cotangent. In practical formulas, S always occurs together with the thickness X of the specimen, that is, as the product SX, known as “scattering power” of the specimen.
The absorption coefficient ( K ) and the transmittance ( T ) are then calculated as follows:
K ( mm − 1 ) = S ( a − 1 )
T ( x ) = b a sinh ( b S X ) + b cosh ( b S X )
Finally, the ratio K/S , proportional to the ratio of the scattering and absorption coefficients μ _{a }and μ _{s }, was also calculated.
2.4
Statistical analysis
To study the variations in scattering, absorption, and transmittance, two statistical tests were used: the Kruskal–Wallis, which is a nonparametric method for testing average equality of measures among groups, and the Mann–Whitney U test ( α = 0.05) (SPSS 16.0, Chicago, SPSS Inc.), which is a nonparametric test that enables the pairwise comparison of two distributions.
Also, to determine the level of similarity of two different distributions, the VAF (variance accounting for) coefficient with Cauchy–Schwarz inequality was used as follows:
VAF = ∑ k = 400 700 a k b k 2 ∑ k = 400 700 a k 2 ∑ k = 400 700 b k 2