Spatial Neighborhood Enrichment Explorer (2D)

Tissue composition

Immune infiltration 35%

T-cell clustering around tumor 0.50

Neighbor radius (µm) 40

Cell-type pair to test

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Spatial statistics

Enrichment z-score

—

Observed edges

Mean neighbors / cell

0.0

Total cells

Tumor T-cell Macrophage Stroma

How it works

This mirrors neighborhood enrichment analysis, the standard spatial-omics method (e.g. Squidpy's nhood_enrichment) for asking whether two cell phenotypes in a tissue section sit closer together than chance would predict.

1. Build a spatial graph: connect two cells with an edge if their distance is below the neighbor radius r.

2. Count observed edges between the chosen pair of cell types, N_obs.

3. Permutation null model: shuffle the cell-type labels across the fixed positions N times (keeping the graph itself unchanged), and recount edges each time to get a distribution of N_perm.

z = (N_obs − mean(N_perm)) / std(N_perm)

z ≫ 0 — the two types are spatially enriched (co-localized), e.g. immune infiltrate hugging the tumor margin.
z ≪ 0 — the two types are spatially avoided/segregated — an "immune-excluded" pattern.
z ≈ 0 — no significant spatial association beyond random mixing.

The bottom strip shows the actual null distribution built during the permutation test — a live histogram of N_perm across all 200 shuffles, with the observed count N_obs marked as a bright line. That is exactly what a z-score means visually: how far into (or short of) the tail of pure-chance mixing the real tissue sits.

Real-world relevance: this exact statistic is used on multiplexed immunofluorescence / CODEX / spatial-transcriptomics slides to decide whether a tumor is "immune-inflamed" or "immune-excluded" — a call that feeds directly into immunotherapy-eligibility discussions at a molecular tumor board.

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Permutation null distribution (N_perm, 200 shuffles) — bright line = observed