Cellular porosity in dentin exhibits complex network characteristics with spatio-temporal fluctuations

Abstract

According to the current hydrodynamic theory, teeth sensitivity is mediated by odontoblast cell processes which can be activated by fluid flow in the pericellular space of bulk dentin. To better understand the possible spatial extent of such phenomena, we investigated the topology and connectivity of dentinal porosity of a healthy human tooth. Using confocal fluorescence microscopy, we modeled the porosity as a spatial graph with edges representing dentinal tubules or lateral branches and nodes defining their connections. A large fraction of porosity channels in crown dentin was found to be interconnected, with 47% of nodes linked in a single component over a millimetric distance from the dentin-enamel junction (DEJ). However, significant differences in network topology were also observed. A sharp transition in connectivity from 83% to 43% occurred at 300 µm from the DEJ, which corresponds to an early stage of tooth formation. This was reflected in all graph metrics investigated, in particular the network resilience which dropped by a factor 2. To test the robustness of our observations, an in-depth analysis of potential remaining biases of the graph extraction was conducted. Most graph metrics considered were found to be within a 10% precision range from a manually annotated ground truth. However, path metrics, which characterize transport properties, proved very sensitive to network defects. Residual errors were classified in 4 topological classes related to fluorescence staining and confocal detection efficiency, instrumental resolution and image processing. Their relative importance was estimated using statistical and physical graph attack simulations in a broad experimental range. Our modeling thus provides a practical framework to estimate the interpretability of calculated graph metrics for a given experimental microscopy setup and image processing pipeline. Overall, this study shows that dentin porosity exhibits typical characteristics of a complex network and quantitatively emphasize the importance of the smallest lateral branches. Our results could be used to model fluid flow more accurately in order to better understand mechanosensing by odontoblasts in dentin.

Fig 1. Methods summary.

a) Transmission light microscopy of the sample section imaged with confocal laser scanning microscopy (CLSM) in the area indicated by a red rectangle (width: 200 µm, height: 900 µm). E: Enamel, D: Dentin, P: Pulp cavity. Scale bar: 2 mm. b) 3D rendering of the resulting image stack. c-f) Image processing pipeline of the image stack: c) original image, d) vesselness filtering, e) porosity segmentation with its skeleton (red), f) cleaned graph. Displayed images are a maximum intensity projection (MIP) of 51.2x51.2x20 µm³ volumes. Scale bar: 10 µm.

Fig 2. Graph metrics summary.

a) Graph descriptors. k is the degree of the node highlighted in red. b) Connectivity metrics. Highlighted nodes in green show the largest connected component containing N* nodes. FS is the ratio of edges (in red) which removal would lead to disconnections. c) Distance metrics. All components but the principal one are faded out to indicate that, in this study, the distance metrics are computed only in the principal component. Displayed numbers correspond to edge lengths. The edges highlighted in red represent the shortest path between two highlighted nodes. The shortest path in this example is the longest in the graph, meaning that its length corresponds to the graph diameter D. The detour index of this specific path is 1.21 (ratio between the route length in red and the Euclidean distance in dashed green). The graph detour index (DI) is the average of the detour index of all shortest paths in the principal component.

Fig 3. Acquired image stack visualization.

a) First slice of the image stack. The red and blue boxes show respectively ROIs 1 and 2 used for further analysis. The dotted white line highlights the different regions, marked by the letters D: dentin and E: Enamel. Yellow dashed lines indicate the location of the orthogonal cuts (in the XZ plane) displayed in f) and g). Scale bar: 50µm. b) ROI 1 first slice. c) ROI 1 maximum intensity projection (MIP). d) ROI 2 first slice. e) ROI 2 MIP. b-e) Scale bar: 10µm. f-h) MIP over a limited number of slices (respectively 10, 9 and 17 slices) in sub-regions of ROIs. Scale bar: 5µm. i) XZ orthogonal cut close to the enamel. j) XZ orthogonal cut far from the enamel. i-j) Scale bar: 10µm. All images were contrasted (different values were used for each ROI) to enhance the visual perception of the structures.

Fig 4. Spatial graph fluctuations.

a) Maximum intensity projection of the image stack, shown as a spatial reference. Scale bar 50 µm. b-f) Metric maps of the cleaned graph. b) number of nodes (N), c) total edge length (W), d) Fault sensitivity (FS), e) mean edge length (<w>) and f) mean degree (<k>). Top and bottom squares indicate respectively the ROI 1 and ROI 2, in which values of the manually corrected graph are displayed. Approximate distance from DEJ to transition zone indicated by dashed lines: 300 µm.

Fig 5. Ground truth graph visualization.

a) MIP of ROI 1 region in the original image; scale bar 20 µm. Ground truth graph in ROI 1, shown in b) with spatially localized nodes or in c) with a “Force Atlas” representation (cf II.3.4) highlighting the different components. d), e) f) same representations for ROI 2. Colors indicate the different components, with red associated with the largest one.

Fig 6. Node disconnections error simulations.

a) Schematic representation of the random and physical simulations. b) Simulation results for selected metrics (all results available in S3 Fig.). The red and blue curves correspond respectively to the ROI 1 and 2.

Fig 7. Edge bridges error simulations.

a) Schematic representation of the random and physical simulations. b) Simulation results for selected metrics (all results available in S4 Fig.). The red and blue curves correspond respectively to the ROI 1 and 2.

Fig 8. Missing edges error simulations.

a) Schematic representation of the random and physical simulations. b) Simulation results for selected metrics (all results available in S5 Fig.). The red and blue curves correspond respectively to the ROI 1 and 2.