3D full field strain analysis of polymerization shrinkage in a dental composite

Abstract

Objective

The objective of this research was to study the polymerization shrinkage in a dental composite using 3D digital image correlation (DIC).

Methods

Using 2 coupled cameras, digital images were taken of bar-shaped composite (Premise Universal Composite; Kerr) specimens before light curing and after for 10 min. Three-dimensional DIC was used to assess in-plane and out-of-plane deformations associated with polymerization shrinkage.

Results

The results show the polymerization shrinkage to be highly variable with the peak values occurring 0.6–0.8 mm away from the surface. Volumetric shrinkage began to significantly decrease at 3.2 mm from the specimen surface and reached a minimum at 4 mm within the composite. Approximately 25–30% of the strain registered at 5 min occurred after light-activation. Application of 3D DIC dental applications can be performed without the need for assumptions on the deformation field.

Significance

Understanding the local deformations and strain fields from the initial polymerization shrinkage can lead to a better understanding of the composite material and interaction with surrounding tooth structure, aiding in their further development and clinical prognosis.

Introduction

Digital image correlation (DIC) is a full-field technique increasingly being promoted to measure the surface strains and displacement in composite materials. Using one or multiple high-resolution couple charged device (CCD) cameras, DIC employs tracking and image registration techniques for 2-dimension (2D) or 3-dimension (3D) measurements of changes in images which are subsequently used to measure deformation, displacement, and strain. In this method, the surface of the specimen is covered with a target pattern that is pictured before and after the application of loads. The digital image correlation methodology determines the shift, rotation, or distortion of key markers in the reference image after developing the required calibrations. Correlation methods are then used to identify a number of unique points and their precise locations in the images before and after loading. The speckle pattern has a unique shape and intensity and needs to act as an ideal target. Sutton et al. provided a detailed literature review of DIC systems, theory, and applications. Application of DIC to polymer materials has been shown to be practical even in ranges of small strain and application as a strain witness .

Two-dimensional DIC through the use of one camera has been used to examine various dental biomaterials in a host of applications. Full field deformations have been studied in composite and ceramic restorative materials . Qian et al. used a digital image correlation method to examine the full-field deformation patterns in the periodontium. Chuang et al. studied the influence of cavity geometry in MOD composite restorations by characterizing polymerization shrinkage and cusp deflection. The effects of dehydration on dentin and dehydration have also been examined . Naru and Dykes used a DIC method to investigate removal of subjectivity in bite mark analysis. Li et al. studied the full-field polymerization shrinkage using a 2D digital image correlation method and found that the shrinkage on the surface was highly non-uniform. They also found that the highest shrinkage occurred at a distance of approximately 1 mm from the surface. Li et al. also used DIC to correlate the Knoop microhardness of an experimental composite to the measured volumetric shrinkage. Review of the literature reveals only one study so far has explored 3D DIC. Miletic et al. evaluated polymerization shrinkage in cylindrical samples of two dental composites by examining strains on the surface opposite of the light curing unit. Strain distribution was nonhomogenous with z -axis displacements occurring toward the light source. Strains on the walls of the cylinder were not evaluated.

In 3D digital image correlation, two cameras are used so that the absolute three-dimensional coordinates of any surface point in space may be determined. This is accomplished by using the known positions of the two cameras relative to each other. The use of a single camera in two-dimensional digital image correlation renders predominantly in-plane strains and displacements. This is especially problematic when investigating three dimensional objects and effects such as out of plane strain and stresses as occurs in dental composites. Small amounts of out-of-plane motion will change the magnification and introduce errors in the measurements . Accurate 3-D deformation contours of the surface can be reconstructed by having adequate contrast markers that allow correlation of identical points from both cameras. Successful implementation requires accurate corrections for distortion, perspective, and bipolar lines. Calibration procedures based on photogrammetry principles are used to reduce the errors and improve the quality of the measurements.

Determining the gray value of a single pixel between different images is not always possible, requiring the use of areas around the pixel to be tracked. The measurement of the stress–strain response for many materials requires the need to measure very small deformations. The motion of these small neighborhoods is tracked by matching the motion of these neighborhoods between successive images where deformation of the specimen has taken place. In its basic form, the solution of this problem is given by Sutton et al. , where the motion vector can be solved by using an optimization criteria based on a sum of squares deviation cost function and using the Lucas–Kanade tracker algorithm. If the reference image is taken as F , and G is the image after displacement, the optimal displacement vector, ˉdopt
d ¯ o p t
, can be solved by minimizing the squared difference in gray values,

ˉdopt=argmin(G(x+ˉd)F(x))2
d ¯ o p t = arg min ∑ G ( x + d ¯ ) − F ( x ) 2

The solution requires an iterative algorithm by expanding the cost function into a first order Taylor series:

χ2(ˉdx+Δx,ˉdy+Δy)=argmin(G(x+ˉd)GxΔxGyΔyF(x))2
χ 2 ( d ¯ x + Δ x , d ¯ y + Δ y ) = arg min ∑ G ( x + d ¯ ) − ∂ G ∂ x Δ x − ∂ G ∂ y Δ y − F ( x ) 2
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Nov 25, 2017 | Posted by in Dental Materials | Comments Off on 3D full field strain analysis of polymerization shrinkage in a dental composite
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