Flow vs anatomy at brain scale

Whole-brain activity simulated with The Virtual Brain on its 76-region connectome, which is directed: it comes from tract tracing, so many connections exist in one direction only. If dPTE recovered anatomy, its strongest flows would run along those one-way tracts.

The simulation needs the optional tvb dependencies and is too heavy to run on every documentation build, so this page reads a cached result made by docs/_ext/make_tvb_flow.py.

How often does a strong flow sit on a real tract?

Rank every ordered pair by dPTE and ask how well that ranking separates one-way tracts from unconnected pairs. An AUC of 0.5 is chance; the same estimator reaches 0.96 to 1.00 on the sparse synthetic networks of the tutorial.

from pathlib import Path

import numpy as np
from scipy.stats import rankdata

from examples.utils import style, teaching

style.use()
cache = np.load(Path("..") / "_data" / "tvb_flow.npz")
weights, dPTE, labels = cache["weights"], cache["dPTE"], list(cache["labels"])

off_diagonal = ~np.eye(weights.shape[0], dtype=bool)
one_way = (weights > 0) & (weights.T == 0)
unconnected = off_diagonal & (weights == 0) & (weights.T == 0)
scores = np.concatenate([dPTE[one_way], dPTE[unconnected]])
ranks = rankdata(scores)
n_pos, n_neg = int(one_way.sum()), int(unconnected.sum())
auc = (ranks[:n_pos].sum() - n_pos * (n_pos + 1) / 2) / (n_pos * n_neg)
density = (weights > 0).sum() / off_diagonal.sum()
print(
    f"{weights.shape[0]} regions, {density:.0%} of pairs connected, "
    f"{n_pos} one-way tracts, AUC {auc:.2f}"
)

76 regions, 27% of pairs connected, 268 one-way tracts, AUC 0.61

The strongest flows, drawn

Regions sit around a circle, each hemisphere on its own side. a shows the 60 strongest one-way tracts, mostly within a hemisphere. b shows the 60 strongest dPTE flows, in red where a one-way tract runs the same way.

With most region pairs connected, nearly every pair is also joined by a short indirect route, and dPTE ranks those as highly as direct ones. Use it to ask which way activity flows, not to infer the wiring.

teaching.chord_pair(weights, dPTE, labels)