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MRI Tissue Classification via Topological Data Analysis

This example demonstrates using Topological Data Analysis (TDA) to classify tissue samples as healthy or pathological based on topological features.

How to Run

cargo run -p medicine_examples --example mri_tissue_classification

Engineering Value

In medical imaging (MRI/CT), distinguishing between healthy tissue and pathological structures is critical:

  • Tumor Detection: Some tumors have similar density to healthy tissue but distinct structure
  • Necrotic Core Identification: Dead tissue forms "holes" inside tumors
  • Robust Classification: Topology is invariant to noise and deformation

Why Topology?

Traditional methods use pixel intensity (density). TDA adds structural analysis:

Feature Intensity-Based Topology-Based
Solid tumor High density χ = 1 (no holes)
Necrotic tumor Similar density χ ≤ 0 (has holes)
Healthy tissue Normal density χ = 1 (contractible)

Key Concept: Euler Characteristic

The Euler Characteristic (χ) counts topological features:

χ = V - E + F = (connected components) - (holes)
Topology χ Value Meaning
Solid disk 1 Healthy tissue (contractible)
Ring/Torus 0 Has a hole (necrotic core)
Two disks 2 Disconnected (fragmented)

Causal Pipeline

[Step 1] Ingest Points     → Load 3D point cloud from simulated MRI
            ↓
[Step 2] Triangulate       → Build Vietoris-Rips complex (radius=0.6)
            ↓
[Step 3] Compute χ         → Calculate Euler Characteristic
            ↓
[Step 4] Diagnose          → Classify based on topology

Each step is composed monadically via PropagatingEffect::bind().

Output Interpretation

Sample A (Healthy):  χ = 1  → HEALTHY (no holes)
Sample B (Tumor):    χ = 0  → PATHOLOGICAL (has hole/void)

Adapting This Example

  1. Real MRI Data: Replace simulated points with actual scan data
  2. Different radii: Tune triangulation radius for your data scale
  3. 3D Visualization: Export simplicial complex for rendering
  4. Persistent Homology: Use Betti numbers for richer topological features
  5. Multi-scale Analysis: Sweep radius to find optimal classification

Key APIs Used

  • PropagatingEffect::bind() - Monadic composition of analysis steps
  • PointCloud::triangulate() - Vietoris-Rips complex construction
  • BaseTopology::num_elements_at_grade() - Count simplices at each dimension
  • CausalTensor - Store point cloud coordinates