4. The size of a tile — what 50 µm decided · Dr. Seok's Tumour-Infiltrating Lymphocytes, First Steps

50 × 50 µm. Where did that come from?

It is the size of tile the CNN was trained on. That is all. Cut finer and each tile holds only a few cells, making the call hard. Cut coarser and "is there a lymphocyte in this tile" stops meaning anything. 50 µm is three or four cell diameters — the size at which a few lymphocytes are visible together.

But that decision fixes the meaning of the word "infiltration rate" itself. Change the grid and the same tissue gives a different number. Let us do it.

Three rules over the same tissue — positive if any red / positive if over half / the ratio of tile counts.

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import til
import numpy as np

c = til.tilmap("TCGA-44-2668")

print("%8s%10s%11s%11s%11s" % ("cell", "tissue", "any red", "over half", "tile ratio"))
for f in (1, 2, 4, 8, 16):
    h, w = (np.array(c.shape) // f) * f          # trim to a multiple
    b = c[:h, :w].reshape(h // f, f, w // f, f)   # group f x f
    tis = (b >= 1).sum((1, 3))
    tl  = (b == 2).sum((1, 3))
    live = tis > 0
    print("%6dum%10s%10.2f%%%10.2f%%%10.2f%%"
          % (50*f, format(int(live.sum()), ","),
             100*(tl[live] > 0).mean(),
             100*(tl[live] >= tis[live]/2).mean(),
             100*tl.sum()/tis.sum()))

Read the result.

Positive if any red — 45.66% → 88.81%. It keeps climbing as the grid coarsens, because a bigger cell is bound to contain at least one red tile.
Positive if over half — 45.66% → 30.07%. This one falls. Bigger cells are more mixed inside, so clearing half gets harder.
Ratio of tile counts — 45.66%, unchanged. Grouping does nothing to it.

That the third one holds still is no accident. "red tiles ÷ tissue tiles" is counting the same thing before and after grouping — you are only adding up numerator and denominator together.

Change the cell size and compare what the three rules give.

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It is even clearer by eye. The same slide reddens as you go.

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import til
import matplotlib.pyplot as plt
import numpy as np

c = til.tilmap("TCGA-44-2668")
fig, ax = plt.subplots(1, 3, figsize=(12, 3.4))
for a, f in zip(ax, (1, 4, 16)):
    h, w = (np.array(c.shape) // f) * f
    b = c[:h, :w].reshape(h // f, f, w // f, f)
    tis = (b >= 1).sum((1, 3)); tl = (b == 2).sum((1, 3))
    code = np.where(tl > 0, 2, np.where(tis > 0, 1, 0)).astype(np.uint8)
    til.show(code, a, "%d um cells" % (50*f))
plt.tight_layout()

print("The coarser you look, the more red area there seems to be - with the tissue unchanged.")

🤔 Check yourself

Which definition is unchanged when you group the grid coarser?

🤔 Check yourself

Two papers report different TIL values for the same slide. Which is NOT the first thing to check?