Tumor pleomorphism index

Nuclear pleomorphism refers to variability in the size and shape of tumor cell nuclei. When tumor cells display a wide range of nuclear sizes — from small, uniform nuclei to large, irregular ones — the tumor is described as pleomorphic. Nuclear pleomorphism is one of the most important histological features assessed by pathologists when grading cancers.

In breast cancer, nuclear pleomorphism is scored on a 1–3 scale as part of the Nottingham histological grade: Score 1 (mild) — nuclei are small and uniform with minimal variation; Score 2 (moderate) — nuclei show moderate size variation with visible nucleoli; Score 3 (marked) — nuclei vary dramatically in size and shape with prominent nucleoli and frequent irregular contours.

Traditional pleomorphism scoring is categorical (1/2/3) and subjective, leading to significant inter-observer variability. HistoAtlas bridges this gap by computing a continuous pleomorphism index — the coefficient of variation (CV) of tumor nuclear area. This captures the same biological signal (nuclear size heterogeneity) as a precise, reproducible number:

$$\text{Pleomorphism Index} = \frac{\operatorname{IQR}(A_{\text{nuc}})}{\operatorname{median}(A_{\text{nuc}}) + \varepsilon}$$

where $A_{\text{nuc}}$ is the nuclear area of each tumor cell. Normalizing by the median reduces correlation with absolute nuclear size, making the metric interpretable as "relative pleomorphism" that is comparable across cancer types.