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🔬 Features

CaravelMetrics extracts 15 features organized into four categories:

Morphometric Features

  • Total Vessel Length: Structural integrity of vascular network
  • Volume: Total vascular volume from radius estimates
  • Average Diameter: Mean vessel diameter across the network

Topological Features

  • Bifurcation Count & Density: Branching complexity and organization
  • Number of Loops: Collateral circulation paths
  • Abnormal Degree Nodes: Detection of anomalous branching patterns (nodes with degree > 3)
  • Connected Components: Network integrity and fragmentation analysis

Fractal Features

  • Fractal Dimension: Multi-scale self-similar organization via box-counting
  • Lacunarity: Spatial heterogeneity and distribution patterns

Geometric Features (Tortuosity Metrics)

  • Geodesic Length: Arc-length parameterized path measurements
  • Spline Arc Length & Chord Length: Path length measurements via B-spline fitting
  • Mean Curvature: Average tortuosity weighted by path multiplicity
  • Mean Square Curvature: Curvature variability along vessels
  • RMS Curvature: Root mean square curvature
  • Arc-over-Chord Ratio: Global segment tortuosity metric
  • Fit RMSE: Spline fitting quality metric

📊 Validation Results

Applied to the IXI dataset (570 TOF-MRA volumes, ages 20-86):

Age-Related Changes

  • 20% decline in total vessel length (r = -0.50, p < 0.001, η² = 0.204)
  • Reduced bifurcations (η² = 0.064), indicating network simplification
  • Increased tortuosity (r ≈ +0.10), consistent with arterial stiffening
  • Preserved fractal organization despite structural changes

Demographic Associations

  • Sex differences: Males show higher bifurcation density, loops, and volume
  • BMI effects: Normal-weight individuals demonstrate longer vessels (η² = 0.032)
  • Education gradient: Stepwise increase in vessel length from no qualification to university degree (η² = 0.055)
  • Height correlations: Positive associations with network complexity (η² = 0.026-0.053)

📖 Feature Definitions

Morphometric Features

  • Total Length: Sum of Euclidean distances between all adjacent graph nodes (mm)
  • Volume: Computed from local radius estimates via distance transform (mm³)
  • Average Diameter: Mean vessel diameter across all centerline points (mm)

Topological Features

  • Number of Bifurcations: Count of nodes with degree = 3
  • Bifurcation Density: Bifurcations per unit length (bifurcations/mm)
  • Number of Loops: Count of cycles in the vessel graph (collateral circulation)
  • Number of Abnormal Degree Nodes: Nodes with degree > 3 (potential artifacts)

Fractal Features

  • Fractal Dimension: Slope of log(N(ε)) vs log(1/ε) from box-counting method
    • Quantifies self-similarity across spatial scales
    • Computed using 10 logarithmically-spaced box sizes
  • Lacunarity: (Variance / Mean²) + 1 of occupied boxes
    • Measures spatial heterogeneity and gaps in the vascular pattern

Geometric Features (Tortuosity)

All tortuosity metrics are computed using arc-length parameterized cubic B-splines with weighted curvature accounting for path multiplicity:

  • Geodesic Length: Total path length through the vessel segment (mm)
  • Spline Arc Length: B-spline fitted arc length (mm)
  • Spline Chord Length: Straight-line distance between endpoints (mm)
  • Mean Curvature: ∫[κ(s)/n(s)]ds - weighted average curvature
  • Mean Square Curvature: ∫[κ(s)²/n(s)²]ds - curvature variability
  • RMS Curvature: √(Mean Square Curvature / Arc Length)
  • Arc-over-Chord Ratio: Spline Arc Length / Chord Length (≥1, higher = more tortuous)
  • Fit RMSE: Root mean square error of spline fit to original points (mm)

Note: n(s) represents path multiplicity, accounting for segments traversed multiple times in the graph

🔬 Technical Details

Graph Construction Algorithm

  1. Mesh Generation: Create surface mesh using vedo for geodesic distance computation
  2. Skeletonization: Uses scikit-image skeletonize function with 3D morphological thinning
  3. Node Detection: 26-connectivity neighborhood analysis to identify:
    • Endpoints (degree = 1)
    • Bifurcations (degree = 3)
    • Abnormal nodes (degree > 3)
  4. Edge Weighting: Euclidean distance between adjacent nodes
  5. Orphan Handling: Connect isolated branches within distance threshold using angle validation
  6. Laplacian Smoothing: Iterative smoothing of node positions (alpha=0.8, iterations=2)
  7. Geodesic Distance: Mesh-based geodesic path lengths for accurate tortuosity measurement
  8. Artifact Removal: Selective pruning of triangular loops (3-node cycles) by removing the longest edge

Tortuosity Computation

The tortuosity pipeline implements weighted curvature analysis:

def compute_tortuosity_metrics(points, smoothing=0, n_samples=500, counts=None):
    """
    Compute arc-length parameterized tortuosity with multiplicity weighting.
    
    Parameters:
        points: (N, 3) array of vessel centerline points
        smoothing: B-spline smoothing factor (default: 0)
        n_samples: Number of arc-length samples (default: 500)
        counts: Multiplicity weights n(x) per point (optional)
    
    Returns:
        dict with 7 tortuosity metrics
    """

Key innovations:

  • Arc-length reparameterization ensures uniform sampling along curves
  • Path multiplicity weighting (n(s)) corrects for graph segments traversed multiple times
  • Weighted curvature: κ(s)/n(s) properly accounts for overlapping vessel representations

Fractal Dimension Algorithm

Box-counting method with logarithmic box sizes:

def fractal_dimension(points, box_sizes=None):
    """
    Compute fractal dimension D = -Δlog(N(ε))/Δlog(ε)
    
    Uses 10 logarithmically-spaced box sizes from max_dim/50 to max_dim
    Fits linear regression to log-log plot
    """