## Abstract

## Objectives

To optimize a microtomographic (micro-CT) technique to quantitatively evaluate the effectiveness of contemporary caries-excavation techniques.

## Methods

A beam-hardening curve was obtained from an initial reconstruction of a wedge-shaped hydroxyapatite (HAp) block and fitted with a 5th order polynomial function, after which each micro-CT tooth slice was corrected accordingly. Calibration of the 8-bit gray values into mineral-density values was obtained by scanning, reconstructing and processing volume of interests (VOIs) of HAp phantoms with different mineral densities (0.25, 0.75, 3.14 g/cm ^{3 }). One carious tooth was scanned before and after caries removal with an experimental enzyme-based gel. After reconstruction, a 3D-median filter was applied to each micro-CT slice, and a connected threshold grower algorithm was used to blank-out undesired structures in each slice. Volume rendering with a look-up-table (LUT), based on mineral densities, was accomplished for the tooth before and after caries removal. Finally, the actual volume of excavated tissue was quantified.

## Results

Correction for beam hardening produced tooth slices with relatively homogeneous gray values along the whole area of enamel and dentin. Accurate mineral-density values were obtained for enamel, dentin and carious regions (2.89, 1.74 and 0.27 g/cm ^{3 }, respectively). After pre-processing (3D-median filtering and connected threshold grower algorithm), acceptable segmentation of carious dentin based on gray values was accomplished (Otsu method, gray value = 75 or mineral density = 1.12 g/cm ^{3 }), from which quantitative volumetric parameters were calculated.

## Significance

Accurate calibration, standardization of scanning and reconstruction steps and adequate pre-processing of micro-CT slices allowed detailed volumetric calculation of caries-excavation techniques.

## 1

## Introduction

In light of the concept of ‘minimal-invasive’ dentistry , operative treatment of carious teeth is nowadays fairly conservative. Current caries-excavation guidelines preclude as much as possible preservation of sound or potentially remineralizable tooth tissue without compromising the long-term success of the restoration . As the ultimate goal after caries removal is to undermine the tooth as little as possible, enhancing thus its lifetime survival, new conservative caries-excavation approaches that more selectively remove caries-infected dentin have lately been introduced .

Recent literature has shown that the effectiveness of caries-removal techniques can be evaluated non-destructively using X-ray computed microtomography (micro-CT), by comparing the internal tooth structure before and after caries removal . Its working principle is based on a mathematical reconstruction of the linear attenuation coefficient of each spot into a cross-section slice through an object (which is function of its elemental composition and density/concentration), measured from a series of X-ray projections .

Monochromatic (synchrotron) radiation has successfully been used as X-ray source in micro-CT studies to volumetrically determine mineral concentration in sound and carious enamel/dentin . However, the high cost and low availability associated with the use of such synchrotron sources still impairs its widespread use. Today, commercially available desktop micro-CT systems make use of polychromatic X-ray sources, which unfortunately introduce scanning artifacts such as beam hardening and loss of information due to energy averaging . For instance, beam-hardening artifacts arise with polychromatic sources because the attenuation of the incident X-ray beam is not exponentially related to the thickness of the object, as predicted by Beer’s law . The lower X-ray energies of the polychromatic spectrum are thus easily absorbed, while the higher energies are less attenuated. This result in a higher brightness rim around the edge of the cross-section image of the object, possibly combined with scattering of the background in the projection area (‘cupping’ artifacts) . Therefore, the resulting intensities produced in the X-ray projection images are not necessarily proportional to the object thickness if this artifact is not corrected. When studying caries it might impair quantitative analysis of mineral concentration and compromise segmentation of structures with different gray-value peaks in the histogram.

Once the scanning procedures are standardized and inherent artifacts are corrected or at least minimized, micro-CT enables tri-dimensional imaging of the internal structure and quantitative analysis of caries-excavation techniques. Qualitative volume rendering based on micro-CT slices of a primary carious tooth has been previously described . Later, the volume of carious and sound dentin removed by a conventional carbide bur was quantitatively determined , confirming the applicability of micro-CT to measure caries-excavation volumetrically. Such studies however still involved time-consuming scanning and reconstruction procedures, and some methodological aspects were not totally clearly described.

The aim of this study was to present a methodology intended to optimize micro-CT for full-quantitative volumetric and mineral-density measurements of dentin caries with a polychromatic X-ray desktop micro-CT system. A linearization method based on a physical model (hydroxyapatite) to correct beam-hardening artifacts in teeth, as well as pre-processing steps undertaken to accurately segment different regions/volumes of interest in carious teeth was also purposed.

## 2

## Materials and methods

## 2.1

## Beam-hardening curve for hydroxyapatite (HAp) and correction scheme for tooth slices

A square block of sintered HAp (3.14 g/cm ^{3 }) with dimensions of 1 cm × 1 cm × 0.2 cm (Pentax Life Care Division, Tokyo, Japan) was divided diagonally in two equal sections using a 0.15-mm thick diamond cutting saw (Accutom-50, Struers, Kesselsdorf, Germany). The obtained HAp wedge was then scanned at 100 kV, 100 μA, and 18.85 μm pixel size using a 0.5-mm Al/Cu filter to eliminate low-energy X-rays in a Skyscan 1172 high-resolution desktop micro-CT scanner (Skyscan, Kontich, Belgium). Rotation step was set to 0.83°, resulting in 435 two-dimensional projections over a 180° rotation of the specimen ( Fig. 1 A).

An initial reconstruction of the HAp wedge projections was performed using the NRecon software provided by the scanner manufacturer (NRecon, version 1.51, Skyscan, Kontich, Belgium) without any correction for beam hardening. A stack of 8-bit grayscale images was obtained and further processed using the ImageJ 1.41 software interface (NIH, Bethesda, USA) . Conversion of the 8-bit gray values to attenuation values was accomplished by applying the following formulas (as described by the scanner manufacturer for 8-bit images):

scale factor = f max − f min 255

attenuation = 2 π [ ( gray × scale factor ) + f min ]

where *f *_{max }and *f *_{min }are the lower and higher contrast limits input selected by the user.

The resulting projection in the *X *-axis was calculated from this first stack of images wherein each pixel stored the average intensity over all images in the stack at the corresponding pixel location ( Fig. 1 B). A line was drawn along the whole extension of the projected image ( Fig. 1 B; dotted lines) and the average attenuation values were recorded at each pixel along this path. The thickness ( *T *) of the wedge-shaped HAp phantom at each pixel along the path was obtained as follows:

T = tan β [ ( a − i ) × pixel size ]

where *i *= 0, 1, 2, … , *N *(pixel position along the path), while *α *and the angle *β *are mentioned in Fig. 1 A. By plotting the attenuation values against the thickness of the HAp wedge, the beam-hardening curve for HAp following the scanning parameters described above was obtained ( Fig. 1 C). A 5th order polynomial function was fitted to the data points as follows:

y = 7.64 E − 6 x 5 − 1.22 E − 4 x 4 + 7.24 E − 4 x 3 − 1.83 E − 3 x 2 + 6.54 E − 3 x 1 + 6.86 E − 3