8. Same rate, different picture — scattered versus clumped · Dr. Seok's Tumour-Infiltrating Lymphocytes, First Steps

So far we have been turning one map into one number. A picture of 136,517 cells became the single line "45.66%". What disappeared along the way?

Where things are disappeared.

Lymphocytes spread evenly through the tumour, and lymphocytes piled into one corner. A pathologist would never call those two pictures the same, and yet they get the same number.

And yet the cluster counts are 235 against 2. Completely different pictures.

Python Runs in your browser

import til

d = til.slides()
# two slides with nearly the same rate but very different clustering
a = d[d.slide.str.startswith("TCGA-EY-A548")].iloc[0]
b = d[d.slide.str.startswith("TCGA-D9-A6EA")].iloc[0]

for r in (a, b):
    print("%s  %s" % (r.participant, r.tumor))
    print("   infiltration     %6.2f%%" % r.til_pct)
    print("   clusters         %6s" % format(int(r.n_clusters), ","))
    print("   biggest cluster  %6s tiles  (%.1f%% of all lymphocyte tiles)"
          % (format(int(r.biggest_cluster), ","), 100*r.biggest_frac))
    print()
print("The rates are 5.8% and 6.2% - practically the same.")

Put the two maps side by side. In the scatter plot below, points stack vertically above the same x.

Loading…

How do you count clusters? With a very simple algorithm called connected-component labelling: group touching red cells into one blob and number them. One line of scipy.ndimage.label().

One stomach cancer slide — its red cells are scattered across hundreds of small clusters.

Python Runs in your browser

import til
import numpy as np
from scipy import ndimage

c = til.tilmap("TCGA-BR-8483")
lab, n = ndimage.label(c == 2, structure=np.ones((3, 3)))   # 8-connected
size = np.bincount(lab.ravel())[1:]                         # index 0 is background

print("%s red cells form %s clusters" % (format(int((c == 2).sum()), ","), format(n, ",")))
print("counting only clusters of 5 tiles or more: %s" % format(int((size >= 5).sum()), ","))
print()
print("the five largest clusters:", np.sort(size)[::-1][:5])
print("the largest holds %.1f%% of all lymphocyte tiles" % (100*size.max()/size.sum()))

Each cancer type has its own character of scattering — texture the infiltration rate alone never showed.

Python Runs in your browser

import til

d = til.slides()
d = d[d.til_patches > 200]
t = d.groupby("tumor").agg(
        slides=("slide", "count"),
        clusters=("n_clusters", "median"),
        biggest_share=("biggest_frac", "median")).round(3)
t["cancer"] = [til.NAMES_EN[x] for x in t.index]
print(t.sort_values("clusters", ascending=False).to_string())
print()
print("Stomach and endometrium scatter finely; prostate and breast have few clusters.")

🤔 Check yourself

Two slides have the same infiltration rate but very different cluster counts. Which is true?

🤔 Check yourself

Why impose a minimum size like '5 tiles or more' when counting clusters?