# Quantifying Subtle Regions of Order and Disorder in Tumor Architecture by Calculating the Nearest-Neighbor Angular Profile

## TL;DR

This paper introduces a novel method to quantify and visualize subtle regions of order and disorder in tumor architecture by analyzing nuclear alignment angles, potentially improving diagnostic accuracy.

## Contribution

The study presents a new quantitative approach using nearest-neighbor angular profiles to detect subtle patterns in tumor images that are invisible to the human eye.

## Key findings

- Effective detection of subtle ordered regions in tumor images
- Generation of heat maps illustrating spatial nuclear arrangements
- Potential correlation with clinical outcomes and treatment resistance

## Abstract

Pathologists routinely classify breast tumors according to recurring patterns of nuclear grades, cytoplasmic coloration, and large-scale morphological formations (i.e. streams of spindle cells, adenoid islands, etc.). The fact that there are large-scale morphological formations suggest that tumor cells still possess the genetic programming to arrange themselves in orderly patterns. However, small regions of order or subtle patterns of order are invisible to the human eye. The ability to detect subtle regions of order and correlate them with clinical outcome and resistance to treatment can enhance diagnostic efficacy. By measuring the acute angle that results when the line extending from the longest length within a nucleus intersects with the corresponding line of an adjacent nucleus, the degree of alignment between two adjacent nuclei can be measured. Through a series of systematic transformations, subtle regions of order and disorder within a tumor image can be quantified and visualized in the form of a heat map. This numerical transformation of spatial relationships between nuclei within tumors allows for the detection of subtly ordered regions.

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Source: https://tomesphere.com/paper/1704.07567