Deep-Learning-Assisted Synchrotron microCT Analysis of Enamel Rod Architecture

Cameron Renteria, PhD · University of Washington · 2026

Tracks: 2,423 (DL) / 2,645 (Raw)

ROI: 758 × 816 × 101 px

Pixel size: 0.345 μm/px

HSB band width: 56.3 μm

Fabric C: 3.604 (Woodcock)

K-means: k = 5, sil = 0.364

SOM bands: k = 4, λ = 85.0 μm

§ 1

Project Overview

Pixel Size

0.345 μm/px

20/58 μm isotropic

ROI Dimensions

758 × 816 px

101 slices, ~34.5 μm depth

Z Offset from DEJ

10.0 μm

Deepest slice at ~41 μm

DL Tracks (complete)

2,423

All span 101 slices

Raw CT Tracks

2,645

Watershed pipeline

Mean Yaw (DL)

−1.09°

SD 13.35°, range −45° to +39°

Mean Tilt (DL)

14.01°

SD 8.86°

Tortuosity (DL)

1.099

SD 0.046

    Central Question
    How are enamel rods spatially organised in 3-D, and can that organisation be quantified automatically at scale?
    Synchrotron microCT resolves individual ~5 μm rods; U-Net segmentation makes full-stack analysis tractable.
  

Pipeline Overview

Raw μCT Stack

→

Intensity Normalise

→

U-Net Segment

→

Centroid Extraction

→

PIV Tracking

→

Quantitative Analysis

§ 2

Synchrotron microCT Dataset

Representative Slices & Flow Field

§ Data Description

DL-Segmented

Three representative transverse slices (slices 1, 51, 91) with dense PIV flow field overlay. Each slice viewed perpendicular to the rod long axis, from DEJ toward outer enamel surface.

Rods appear as bright blobs; obliquely cut rods show elongated cross-sections indicating decussation banding.

§ Data Description

Yaw spatial map at slice 091 (41.0 μm from DEJ): rods coloured by lateral lean angle.

Dark = left-lean, orange/white = right-lean. Band structure is clearly visible.

Raw CT Reference Views

§ Data Description

Raw CT

Same three slices from the raw watershed pipeline (n = 2,645 tracks).

Compare directly with DL-segmented version above for boundary quality differences.

§ Stack Visualization

DL-Segmented

Single frame (slice 50 of 101) from the yaw-coloured rod stack animation.

Full animation available in the Animations section below.

§ 3

Preprocessing, Rod Detection & PIV Tracking

    Processing Notes
    Green channel selected for highest rod/matrix contrast in RGB PNG stack.
Connected-component labelling extracts centroids, equivalent diameter, and eccentricity per slice.
PIV (Particle Image Velocimetry) uses cross-correlation to track centroids across consecutive slices (window 32 px, stride 16 px).
Dense PIV field interpolated to image edges via RegularGridInterpolator.
Output: Parquet file with complete 3-D tracks — columns include dx, dy, dz, yaw, pitch, tilt, tortuosity, arc/chord length.

  

Dense PIV Quiver Panels (DL-Segmented)

§ PIV Tracking

DL-Segmented

Dense PIV quiver panels across 10 representative slices (n = 2,423 tracks). Arrows show local rod lean direction.

Window = 32 px, stride = 16 px. Field interpolated to image edges.

Dense PIV Quiver Panels (Raw CT)

§ PIV Tracking

Raw CT

Same 10 slices from the raw watershed pipeline (n = 2,645 tracks).

Flow field density and decussation geometry are near-identical to the DL stack.

Yaw-Coloured Stack Frames

§ PIV Tracking

DL-Segmented

Yaw-coloured rod map, frame 50 of 101. Colour encodes lateral lean angle.

§ PIV Tracking

Raw CT

Same frame from the raw CT pipeline.

DL version shows sharper band boundaries and fewer boundary artefacts.

Watershed Segmentation Comparison

§ Segmentation

Raw CT

Watershed runs: Run 2 (2,589 rods, min_d=8, fill, compact=0.01) vs Run 5 (2,204 rods, min_d=10, no fill).

Raw CT requires tighter parameters to suppress over-segmentation.

§ Segmentation

DL-Segmented

DL watershed: Run 2 (2,339 rods, min_d=5, fill, compact=0.01) vs Run 5 (2,468 rods, min_d=9, no fill), slice 50.

DL Run 5 recovers more rods at matched threshold with fewer merged doublets.

§ 4

Spatial Orientation Maps

    What these maps show
    Six-panel spatial maps of yaw, pitch, tilt, tortuosity, rod diameter, and eccentricity for all
    rod centroids across the ROI. The yaw map is the primary decussation signal: alternating
    left/right lean domains reveal the Hunter-Schreger band architecture. Pitch and tilt are
    more uniform, confirming decussation is primarily a lateral (yaw) phenomenon.
  

DL-Segmented (n = 2,423)

§ Results

DL-Segmented

Six-panel spatial orientation maps: yaw, pitch, tilt, tortuosity, diameter, eccentricity (150 DPI, flush colorbars).

Yaw domain boundaries are sharper; tortuosity map shows less edge noise.

Raw CT (n = 2,645)

§ Comparison

Raw CT

Same six spatial maps from the classical watershed pipeline.

Higher track count includes some spurious boundary artefacts, especially visible in the tortuosity panel.

Rod Morphology Summary (DL Pipeline)

Mean Diameter

4.8 μm

SD 1.2 μm

Eccentricity

0.62

SD 0.09

Tortuosity

1.099

SD 0.046

Yaw Range

−45° to +39°

Mean −1.09°, SD 13.35°

§ 5

HSB Band Periodicity (FFT Analysis)

    Method
    Grid-interpolated yaw map (4 px cell, Gaussian smooth σ = 8 cells). Row-mean subtracted
    before row-wise rfft. Power spectrum averaged across rows. Dominant peak located in 10–150 μm
    search range. Band width read from peak frequency converted to physical units.
  

DL-Segmented → 56.3 μm

§ Results

DL-Segmented

HSB band width analysis: smoothed yaw map, row-averaged power spectrum, and mean yaw profiles.

Dominant band width = 56.3 μm (FFT peak).

Raw CT → 58.8 μm

§ Comparison

Raw CT

Same FFT analysis applied to the raw CT yaw spatial map.

Dominant band width = 58.8 μm. Δ = 2.5 μm, within biological variability (30–100 μm range).

§ 6

Orientation Fabric Analysis

    Method
    Orientation tensor T = V′V / N from unit vectors (dx, dy, dz) / |...|. Eigenvalues
    λ1 ≥ λ2 ≥ λ3.
    Woodcock strength C = ln(λ1/λ3).
    Shape parameter K = ln(λ1/λ2) / ln(λ2/λ3).
    Zones: left / centre / right thirds of ROI x-axis.
  

DL — C = 3.604, K = 4.10

§ Results

DL-Segmented

Orientation tensor fabric: eigenvalue bars, spatial zone map, yaw × pitch scatter, tilt rose.

Woodcock C = 3.604 (λ₁ = 0.924, strongly non-random). Shape K = 4.10, cluster fabric.

Raw CT — C = 3.508, K = 5.10

§ Comparison

Raw CT

Same orientation tensor analysis from the classical watershed pipeline.

Woodcock C = 3.508, K = 5.10; λ₁ = 0.923. DL marginally more ordered by eliminating misidentified interprismatic rods.

§ 7

K-means Rod Clustering

    Method
    StandardScaler applied to (yaw_deg, pitch_deg). K-means with n_init = 20, random_state = 42.
    Optimal k = 5 selected by silhouette score (k2 = 0.296, k3 = 0.321, k4 = 0.345, k5 = 0.364).
    Five clusters: 2 left-lean, 1 central/straight, 2 right-lean.
  

DL — silhouette = 0.364

§ Results

DL-Segmented

K-means clustering (k = 5): yaw × pitch scatter, spatial map, tortuosity boxplots.

C0 −17.6°, C1 −12.1°, C2 +0.2°, C3 +13.7°, C4 +16.1°

Raw CT — silhouette = 0.365

§ Comparison

Raw CT

Same k = 5 clustering from the raw CT pipeline.

C0 −16.9°, C1 −15.3°, C2 −0.6°, C3 +12.7°, C4 +15.4°. Identical cluster structure reproduced.

K-means Animation Frame

§ Results

DL-Segmented

K-means 5-cluster yaw categories, frame 50 of 101. Colour encodes cluster membership.

Full GIF animation available in the Animations section.

§ Comparison

Raw CT

Same frame from the raw CT k-means animation. Cluster geometry is faithfully reproduced.

Cluster Summary Table (DL Pipeline)

Cluster	Label	Mean Yaw	Mean Pitch	n (DL)	n (Raw)	Character
C0	Left A	−17.6°	−11.0°	421	~420	Left-lean, down-pitch
C1	Left B	−12.1°	+7.4°	420	~415	Left-lean, up-pitch
C2	Straight	+0.2°	−2.6°	966	~1010	Central / straight
C3	Right A	+13.7°	−15.1°	329	~320	Right-lean, down-pitch
C4	Right B	+16.1°	+8.8°	287	~280	Right-lean, up-pitch

§ 8

SOM Band Segmentation

    Method
    Self-Organizing Map (12×12 grid, 50k iterations) trained on multi-scale pixel features: local rod density (σ = 8, 16, 32), structure tensor (coherence + orientation), Gabor bank (3 freq × 6 orient), and local variance.
K-Means (k = 4) applied to SOM codebook vectors to segment decussation bands.
POC: single slice 50. 5-Slice: pooled features from slices 1, 26, 51, 76, 101 trained on a single SOM for cross-depth consistency.

  

Proof of Concept (Single Slice)

§ SOM POC

SOM

Overview: raw slice, SOM U-matrix topology, and k = 4 cluster band segmentation on slice 50.

§ SOM POC

SOM

Multi-scale feature maps: density, coherence, orientation, Gabor responses, and local variance.

§ SOM POC

SOM

Band cluster overlay on raw micrograph: 4 clusters map to distinct decussation zones.

5-Slice Cross-Depth Consistency

§ SOM 5-Slice

SOM

Overview: pooled SOM trained on 5 slices (1, 26, 51, 76, 101). Cluster labels are consistent across depth.

§ SOM 5-Slice

SOM

U-Matrix: inter-neuron distances reveal natural cluster boundaries on the SOM lattice.

§ SOM 5-Slice

SOM

Extracted multi-scale texture features averaged across the 5 representative slices.

§ SOM 5-Slice

SOM

Cluster distribution across slices: area fractions remain stable through the stack depth.

Per-Slice Detail Maps

Slice 1

SOM

Band segmentation at slice 1 (DEJ-proximal, z = 10.0 μm).

Slice 26

SOM

Band segmentation at slice 26 (z ≈ 18.6 μm).

Slice 51

SOM

Band segmentation at mid-stack slice 51 (z ≈ 27.2 μm).

Slice 76

SOM

Band segmentation at slice 76 (z ≈ 35.8 μm).

Slice 101

SOM

Band segmentation at slice 101 (outer enamel, z = 44.5 μm).

§ 9

SOM Full-Stack with Displacement Features

    Method
    15×15 SOM, 80k iterations, trained on 32 features per pixel: 26 texture features (density, coherence, orientation, Gabor, local variance) averaged across 101 slices + 6 displacement features (accumulated dx/dy, direction, magnitude, local variance) from PIV fields.
Displacement vectors are the primary discriminator: rods in different decussation bands move in different directions through the stack.

  

Full-Stack Overview & Overlay

§ SOM Full-Stack

SOM

Full-stack SOM overview: U-matrix, cluster assignments, and displacement-integrated band map.

§ SOM Full-Stack

SOM

Band cluster overlay on representative slice: 4 clusters with displacement-informed boundaries.

Displacement & Cluster Analysis

§ SOM Full-Stack

SOM

Accumulated displacement per cluster: direction & magnitude distributions reveal band separation.

§ SOM Full-Stack

SOM

Displacement-only vs. combined (texture + displacement) feature space comparison.

§ SOM Full-Stack

SOM

PIV quiver field coloured by SOM cluster: flow directions align with band assignments.

§ 10

SOM Morphometrics & Band Structure

    Quantitative Band Metrics (from morphometrics.json)
    Dominant wavelength: 85.0 ± 11.4 μm (FFT, 8 transects)
Band area fractions: Band 0: 27.5%, Band 1: 21.8%, Band 2: 27.7%, Band 3: 23.0%
Max boundary mismatch: 179.5° (Band 2 vs 3, anti-parallel — classic parazone/diazone interface)
Mean displacement magnitude: 1.6–6.8 μm across clusters

  

Streamlines & Boundaries

§ Morphometrics

SOM

Displacement streamlines coloured by cluster: ameloblast migration path reconstruction.

§ Morphometrics

SOM

Band boundary map with angular mismatch: high-mismatch interfaces indicate parazone/diazone transitions.

Rose Diagrams & Periodicity

§ Morphometrics

SOM

Polar rose diagrams per cluster: displacement orientation distributions reveal distinct band directions.

§ Morphometrics

SOM

Band transect profiles + FFT: dominant wavelength = 85.0 μm (±11.4 μm across 8 transects).

Consistent with biological HSB spacing of 30–100 μm.

Displacement Evolution Through Depth

§ Morphometrics

SOM

Cluster displacement evolution at z-checkpoints (slices 1, 41, 81, 101): bands progressively separate with depth.

§ Morphometrics

SOM

Displacement magnitude vs. stack depth per cluster: linear accumulation confirms consistent band geometry.

Publication Composite

§ Morphometrics

SOM

Publication-ready composite: band segmentation, streamlines, rose diagrams, boundary analysis, and periodicity.

Band Morphometrics Table

Band	Area (%)	Mean Direction (°)	Circ. Variance	\|Disp.\| (μm)	Width (μm)	Character
Band 0	27.5	+2.3°	0.170	1.6	13.3 ± 24.3	Near-axial, low displacement
Band 1	21.8	+122.4°	0.186	3.4	19.1 ± 22.8	Oblique, moderate displacement
Band 2	27.7	+12.6°	0.068	6.4	26.3 ± 43.0	Right-lean, high displacement, most coherent
Band 3	23.0	−167.6°	0.134	6.8	25.8 ± 41.6	Left-lean (anti-parallel to Band 2)

§ 11

Crack Path Simulation

    Physics
    Mode-I crack propagates horizontally; at band boundaries, rod direction changes force crack deflection.
Deflection angle ∝ local displacement direction gradient. Tortuous crack paths = energy dissipation = toughness.
3-D simulation: crack advances through z (slice 1→101) and deflects in (x, y) at each step based on the local PIV field.

  

2-D Crack Deflection Analysis

§ Crack Paths

SOM

Crack deflection potential map: displacement direction gradient highlights band boundaries as crack deflection sites.

§ Crack Paths

SOM

Updated 3-panel crack deflection: potential map, patch-based analysis, and deflection statistics.

2-D Crack Path Simulation & Patch Analysis

§ Crack Paths

SOM

Simulated 2-D crack paths across the ROI: paths deflect at band boundaries, increasing total path length.

§ Crack Paths

SOM

Patch-level crack deflection analysis: local deflection angles and tortuosity by spatial region.

3-D Crack Path Simulation

§ 3-D Crack Paths

SOM

Hero view: 3-D crack paths propagating through 101 slices, coloured by cumulative deflection angle.

Cracks advance through z (enamel depth) and deflect in (x, y) at each slice based on local PIV field.

§ 3-D Crack Paths

SOM

X–Z projection: crack paths viewed from the side, showing depth-dependent lateral deflection.

§ 3-D Crack Paths

SOM

Multi-view 3-D crack path render: isometric, top-down, and side projections with band overlay.

Most Tortuous Paths

§ 3-D Crack Paths

SOM

Single most tortuous crack path in 3-D: maximum deflection through multiple band boundaries.

§ 3-D Crack Paths

SOM

Top 5 most tortuous crack paths: all cross multiple anti-parallel band boundaries.

§ 12

3-D Rod Statistics Dashboard

    Dashboard Contents (5 rows)
    Row 1–2: Depth-evolution of |mean yaw| and |mean pitch| per slice (np.abs to avoid cancellation of opposing signs).
Row 3: Rose diagrams for yaw, pitch (mapped mod 360°), and tilt (mirrored +180°).
Row 4: Tortuosity spatial map across the ROI.
Row 5: Spatial scatter coloured by tilt angle.

  

DL-Segmented

§ Results

DL-Segmented

5-row dark statistics dashboard: angular depth profiles, rose diagrams, tortuosity map, and spatial scatter.

Tortuosity SD = 0.046. Tighter distribution than raw CT.

Raw CT

§ Comparison

Raw CT

Same 5-row dashboard from the raw watershed pipeline.

Angular depth profiles track closely across both pipelines. DL reduces tortuosity SD by 21% (0.058 → 0.046).

§ 13

Raw CT vs DL-Segmented: Side-by-Side

    Key Finding
    Rod orientation metrics (yaw, pitch, tilt) are near-identical between pipelines (<2% difference
    in mean values). The DL pipeline removes fragmented boundary artefacts, yielding a 21% reduction
    in tortuosity SD and slightly sharper yaw domain boundaries. The 5-cluster HSB architecture is
    reproduced identically by both methods.
  

§ 14

Decussation Parameter Comparison

Parameter	Raw CT	DL-Segmented	Delta / Note
Tracks (n)	2,645	2,423	−222 (DL removes artefacts)
\|Yaw\| mean ± SD (°)	10.6 ± 8.2	10.8 ± 8.4	+0.2° (<2%)
\|Pitch\| mean ± SD (°)	7.9 ± 6.7	7.8 ± 6.2	−0.1° (<2%)
Tilt mean ± SD (°)	14.0 ± 8.9	14.1 ± 8.7	+0.1° (<1%)
Tortuosity mean ± SD	1.113 ± 0.058	1.099 ± 0.046	−21% SD (boundary artefacts removed)
HSB band width (μm)	58.8	56.3	Δ = 2.5 μm; both in 30–100 μm range
Fabric C (Woodcock)	3.508	3.604	DL marginally more coherent
Fabric K	5.10	4.10	Both cluster fabric
λ₁	0.923	0.924	Strongly non-random in both
K-means k / silhouette	5 / 0.365	5 / 0.364	Identical cluster geometry
Mean diameter (μm)	—	4.8 ± 1.2	~5 μm expected for enamel rods
Eccentricity	—	0.62 ± 0.09	Oblique cutting increases eccentricity

§ 15

Animation Gallery (GIFs — all 101 slices)

    Note
    All GIFs animate across the full 101-slice stack (~34.5 μm depth). Slices progress from
    the DEJ-proximal end (slice 1, z = 10.0 μm) to the outer enamel side (slice 101, z = 44.5 μm).
  

Yaw & Tracking Animations

§ PIV Tracking

DL-Segmented

Yaw-coloured rod animation: 101 slices, glow rendering with motion trails.

§ K-means

DL-Segmented

K-means 5-cluster categories animated across 101 slices.

§ Overview

DL-Segmented

Full rod stack with segmentation overlay animated across 101 slices.

Per-Metric Animations

§ Orientation

Pitch angle animation (fore-aft lean).

§ Orientation

Total tilt animation (angular deviation from DEJ normal).

§ Morphology

Rod tortuosity animation (arc/chord ratio per slice).

§ Morphology

Equivalent rod diameter animation across the stack.

Composite & Categorical Animations

§ Categorical

Yaw × tortuosity categorical animation. Cat-score = tortuosity × yaw_deg; tercile split.

§ Categorical

Pitch categorical: Group 1 >+20° (red), Group 2 ±20° (orange), Group 3 <−20° (blue).

§ Overview

Combined multi-metric stack animation.

PIV Dense Quiver & Stream Animations

§ PIV Tracking

Dense PIV quiver animation: 32 px window, 16 px stride, interpolated to image edges.

§ PIV Tracking

Rod centroid quiver animation with per-track yaw colouring.

§ PIV Tracking

Streamline visualisation of the PIV velocity field animated across the stack.

Overlay Animation

§ Segmentation

Segmentation overlay animation: raw slice with DL mask superimposed.

§ Results

DL-Segmented

Tortuosity spatial map: rod arc/chord ratio mapped to centroid position in the ROI.

Edge rods have lower tortuosity; central rods show higher variation.

§ 17

Interactive 3-D Viewers

    3-D Rod Track Outputs
    STL and OBJ meshes exported for 3-D printing and FEA import.
    Two variants: biomimetic (r = 2 μm, no smoothing) and smooth (r = 5 μm, σGauss = 3).
    Plotly HTML viewers allow full 3-D rotation and zoom in the browser.
  

🌐

PIV Rods — Interactive 3-D

Plotly HTML — 2,423 tracks, yaw coloured

🌐

Smooth Rods — Interactive 3-D

Plotly HTML — r = 5 μm, Gaussian σ = 3

🌐

Biomimetic Rods — Interactive 3-D

Plotly HTML — r = 2 μm, no smoothing

Mesh Exports

Biomimetic STL

rods_biomimetic.stl

r = 2 μm, true rod geometry

Smooth STL

rods_smooth_5um.stl

r = 5 μm, Gaussian σ = 3

Biomimetic OBJ

rods_biomimetic.obj

For Blender / CAD import

Smooth OBJ

rods_smooth_5um.obj

For Blender / CAD import

    Publication Readiness
    Core quantitative results (band width, fabric strength, cluster geometry) are in publishable form.
    Pending: pixel-size calibration from scale-bar image, DL validation metrics (Dice, centroid accuracy),
    full-stack extension from 101 slices to ~2,000 slices on NERSC Perlmutter.
  

Cameron Renteria, PhD · University of Washington · Code, figures, and data available on request. · Generated 2026-04-09

Deep-Learning-Assisted Synchrotron microCT Analysis of Enamel Rod Architecture

Project Overview

Central Question

Synchrotron microCT Dataset

Preprocessing, Rod Detection & PIV Tracking

Processing Notes

Spatial Orientation Maps

What these maps show

HSB Band Periodicity (FFT Analysis)

Method

Orientation Fabric Analysis

Method

K-means Rod Clustering

Method

SOM Band Segmentation

Method

SOM Full-Stack with Displacement Features

Method

SOM Morphometrics & Band Structure

Quantitative Band Metrics (from morphometrics.json)

Crack Path Simulation

Physics

3-D Rod Statistics Dashboard

Dashboard Contents (5 rows)

Raw CT vs DL-Segmented: Side-by-Side

Key Finding

Decussation Parameter Comparison

Animation Gallery (GIFs — all 101 slices)

Note

Additional Static Figures

Interactive 3-D Viewers

3-D Rod Track Outputs

Publication Readiness