Proximity Areas

Proximity Areas converts a distance map into discrete analysis zones.

1. Reference input: Supply either a Seeds image of the reference structures, such as a coded image of tumor cells or a mask of detected vessels, or a Distance map already computed from them. Only one is required; from Seeds, the engine computes the distance map internally.
2. Distance settings: Choose the Unit, µm (the default) or pixel. The Distance Values list holds the distances that bound the zones. Every value must be positive, the list is sorted in ascending order, and Add, Remove and Remove all manage it.
3. Zone definition: For example, distances of 30, 60 and 100 µm give the zones 0-30, 30-60 and 60-100 µm.
4. Zone masking: Each pixel goes to the zone that contains its distance value. The zones run between consecutive distances in the list, starting at the reference contour, so they do not overlap and stop at the largest distance.
5. Per-zone analysis: The Output Type setting chooses how the zones are returned: Gray, a grayscale image (useful for measurements); Coded, a coded image (useful for visualization); or Gray and Coded, both. Cell counts, phenotype distributions and biomarker intensity per zone are then measured from that output.

Dilation as proximity: Morphological dilation by a disk of radius r gives the set of all pixels within distance r of the object (Gonzalez & Woods). A zone from distance r₁ to r₂ is therefore the dilation by r₂ minus the dilation by r₁. Computing it from a distance map is more efficient, because a single distance transform holds every possible zone boundary at once, where dilation needs a separate operation for each distance.

Neighborhood analysis (MIT Statistical Models): In spatial statistics, a process often behaves differently depending on its distance from a boundary or reference point. Proximity Areas makes that measurable by cutting distance into discrete bins in which spatial statistics can be computed. The resulting distance-dependent profiles are the empirical counterpart of the theoretical spatial correlation functions used in geostatistics and spatial point process analysis.

The invasive margin, a proximity zone by definition: In tumor immunology research, the invasive margin is the region within about 500 µm of the tumor border, which makes it a proximity area. The Immunoscore for colorectal cancer quantifies immune cell density separately in the tumor center and at the invasive margin, two zones defined relative to the tumor boundary. In published colorectal cancer cohorts, the densities in the two zones are associated with patient outcome. The Immunoscore is therefore an example of proximity zones that carry biological information.

Suppose you want the immune infiltration gradient around tumor nests.

1. Create a tumor mask from CK+ cells.
2. Define Proximity Areas with distances of 25, 75 and 200 µm: 0-25 µm (immediate border), 25-75 µm (perilesional) and 75-200 µm (stroma).
3. Count CD8+ T cells per zone and normalize by zone area.
4. Read the CD8+ density profile, for example 50 cells/mm² at the border, 120/mm² in the perilesional zone and 80/mm² in the stroma.

The density peaks in the perilesional zone, not at the immediate border, which suggests immune cells accumulate near the tumor but not within it. That pattern is consistent with partial immune exclusion.