Enamel, the outer protective coating of teeth, is an extremely hard mineral-based material. It exhibits distinct characteristics that vary across mammalian species, showcasing unique features in each [1]. It provides protection for the more sensitive underlying dentin and pulp tissues against mechanical damage and tooth decay, and the enamel itself is a wear-resistant surface necessary for mastication [1]. Due to the combined high hardness and exceptional damage tolerance, the microstructure of tooth enamel is a viable source of inspiration for the advanced manufacturing of bioinspired structures with enhanced capabilities [2], [3], [4], [5], [6], [7].

The most prevalent microstructural feature within the enamel is the enamel rod, an approximately 5 µm cylindrical bundle of hydroxyapatite (HA) nanocrystals. These rods are separated by an interrod enamel phase consisting of HA nanocrystals that have a distinct orientation from the rods [8], [9], [10]. Between the rods and interrod enamel there is a thin layer of organic matter made up largely of non-collagenous proteins. The growth direction of each rod varies through the thickness from the dentin-enamel junction (DEJ) to the outer enamel surface (OES) [11], [12], [13], [14], [15]. Bands of rods are observed to have distinct dominant directions, crossing each other in a feature known as Hunter-Schreger bands or decussation [16], [17], [18], [19], [20]. As cracks tend to propagate along the protein-rich rod interfaces (i.e., rod sheaths) rather than through the rods, the decussated microstructure guides cracks to regions of improved resistance to prevent further crack growth [13]. This process causes the advancing crack to bifurcate, deflect, or undergo bridging, as the crack propagates via the path of least resistance along a more tortuous path. More fracture energy is dissipated via the complex enamel microstructure compared to a monolithic brittle material [21,22]. The orientation and arrangement of these bands can vary between species, suggesting that evolution has optimized their arrangement according to the demands imposed by each species [21]. Prior investigations that have focused on transmission or scanning electron microscopy imaging can only provide 2D representations of the enamel structure on selected single planes through the enamel, or a 3D representation over a very limited depth [23], [24], [25], [26], [27], [28]. A quantitative description of enamel rod orientations through the thickness of enamel and across multiple bands has not been reported to the authors’ knowledge.

The crucial knowledge in creating an enamel-inspired structure therefore lies in replicating the parameters of the microstructural evolution within the decussated inner enamel region. Prior investigations that have focused on transmission or scanning electron microscopy imaging can only provide 2D representations of the enamel structure on selected single planes through the enamel [22,29,30]. Previous approaches to characterizing synchrotron images of enamel microstructure have focused on manually tracing enamel prisms through the thickness of the scanned sections [31,32]. Besnard et al. [33,34] performed 3D reconstructions of carious lesions using synchrotron µX-ray computed tomography (CT) focused on rod and interrod structures within prismatic enamel. By tracking a single particle or microstructural feature through certain axes of growth directions, the convoluted growth can be accurately mapped in a three-dimensional space. In mechanics terms, this provides the Lagrangian description of microstructural growth by following the path of a single particle, or rod, in this case. However, due to the complexity of the enamel rod growth paths, single particle tracking can be extremely tedious. For X-ray CT scans where the resolution may not be sufficiently high to resolve the extremely small microstructural features, single particle tracking is nearly impossible to perform. The problem is further compounded for image datasets containing noisy data and reconstruction artifacts.

In this work, we use optical flow imaging algorithms to extract ensemble rod growth information from X-ray CT scans. To this end, PIV is a method of measuring the velocity of particles flowing within a fluid by tracking their movement. Digital image correlation (DIC) is used by the solid mechanics community to measure the deformation within loaded samples by tracking individual painted speckles on a surface. These two techniques are fundamentally equivalent and by cross-correlating image pairs, a vector field of deformation or flow can be mathematically generated. The practical applications of both PIV [35,36] and DIC techniques [37], [38], [39], [40] have been well explored and detailed in existing literature. Some recent works used optical flow analyses to examine large CT data for the analysis of microstructural deformation of foams [41], but the results are still indirectly interpreted as a function of time (via displacement).

Our team has developed a novel fluid mechanics-based approach to characterize and reconstruct the decussation bands in enamel microstructure. In fluid mechanics, the motion and behavior of particles or fluids can be described in either the Eulerian or Lagrangian specifications of the flow field. The Eulerian specification focuses on fixed points in a particular space where the fluid is flowing through, while the Lagrangian specification follows the flow path of individual particles or material elements. The current work first interprets the enamel rods within the reconstructed tomography slices as a “flow field” moving through a fixed window in space, i.e., an Eulerian description of a deforming field. Instead of different snapshots of moving particles in time, the cross-sections of the enamel rods within X-ray tomographic slices are interpreted as particles “moving” within the image plane as a function of the distance from the DEJ. Using an Eulerian framework, it is possible to group the individual rods comprising the bands into “flow paths” that traverse through the enamel and mathematically generate enamel rod growth vector fields from the tomographic slices.

Notably, with the generated vector fields from the tomographic reconstructions, we then use the Lagrangian framework to reproduce and reconstruct the ensemble growth of these complex enamel microstructures via PIV algorithms. The efficiency of this method is demonstrated with high resolution CT images obtained with high-energy synchrotron X-rays at the Advanced Photon Source (APS), a U.S. Department of Energy User Facility located at Argonne National Laboratory. Prior efforts using benchtop X-ray CT systems have succeeded in imaging cracks or hypoplastic defects [42,43] in the enamel microstructure, but the extremely fine resolution needed to resolve some of the lower length scale microstructural features in the enamel require coherent and focused X-ray sources.

One sample of dental enamel from the cervical region of a Panthera leo (African lion) molar was chosen for this study to exemplify the methods presented herein. Microscale X-ray CT was performed to obtain ensemble microstructural evolution of the enamel rods. Although we chose to focus on elucidating the microstructure of mammalian enamel within this work due to the complexities faced during textural analysis, the methods proposed herein can be extended to examining large quantities of fine microstructures that may otherwise be tedious or impractical to track individually. Open-source software and PIV analysis algorithms were used for feature extraction and reconstruction of the rod growth pathlines to increase the accessibility of such a method for the scientific community. The objective of this study is to demonstrate the application of an optical flow imaging technique to understand the decussation band structure in mammalian enamel, with particular focus on the development of the analytical approach. The methods detailed in this study can provide rapid extraction of complex morphologies to supplement efforts in rapid prototyping of bioinspired ceramics for advanced manufacturing.