5D Library › The Default Mode Network, the Entropic Brain and Neural Oscillations · 中文
Chapter 1 The Default Mode Network and the Cost of a Self
The brain’s dark energy
The adult brain is about 2 % of the body’s mass and uses about 20 % of its energy at rest. For most of the history of brain imaging, researchers studied the small changes in activity that a task produces on top of that baseline, and treated the baseline itself as noise. Raichle and his colleagues argued that this had things the wrong way round: the changes evoked by tasks are small compared with the brain’s ongoing, intrinsic activity, which therefore deserves study in its own right (Raichle et al. 2001).
Calculation
The brain’s energy budget in round figures, and how little a demanding task adds to it.
# The brain's energy budget (round textbook figures, see the text).
body_watts = 100 # resting metabolic rate of an adult, about 100 W
brain_share = 0.20 # the brain uses about 20 % of it ...
brain_mass_share = 0.02 # ... while being about 2 % of body mass
task_extra = 0.05 # task-evoked increases: typically under 5 % of baseline
brain_w = body_watts * brain_share
print(f"brain at rest: {brain_w:.0f} W, {brain_w * 86400 / 4184:.0f} kcal per day")
print(f"energy per kg, brain vs body average: {brain_share / brain_mass_share:.0f} ×")
print(f"a demanding task adds at most about {brain_w * task_extra:.1f} W")
print(f"so ongoing 'default' activity is ≥ {100 * (1 - task_extra / (1 + task_extra)):.0f} % "
"of what the brain spends during a task")
# brain at rest: 20 W, 413 kcal per day
# energy per kg, brain vs body average: 10 ×
# a demanding task adds at most about 1.0 W
# so ongoing 'default' activity is ≥ 95 % of what the brain spends during a taskThe analogy that Raichle later used was cosmological (Raichle 2010): most of the brain’s energy, like most of the universe’s, is “dark”, spent on something we do not directly observe. Part of the answer is housekeeping, maintaining ion gradients and synapses. Part of it is organised activity in large networks that keep running whether or not we are doing anything in particular.
A default network
Evidence
Raichle and colleagues identified a set of regions, including the medial prefrontal cortex, the posterior cingulate cortex and precuneus, and parts of the lateral parietal cortex, whose activity decreased consistently across many different attention-demanding tasks, and proposed that they form a “default mode” of brain function (Raichle et al. 2001). Later work described this default network as active during remembering, imagining the future, thinking about other people’s minds and thinking about oneself, and as anticorrelated with networks that serve external attention (Buckner et al. 2008).
The two best-known hubs are the medial prefrontal cortex (mPFC), associated with evaluating information in relation to oneself, and the posterior cingulate cortex (PCC), which sits at a crossroads of the brain’s connections. Together with the angular gyri and the hippocampal formation they support what psychologists call the narrative self: the continuous story of who I am, where I have been and where I am going. The same machinery supports mental time travel and, when it runs without direction, mind-wandering.
Evidence
In a study that sampled the thoughts of thousands of people through their phones during daily life, people reported that their minds were wandering in 46.9 % of the samples, and they were less happy when their minds wandered than when they did not, whatever they were doing (Killingsworth and Gilbert 2010). Repetitive, negative self-focused thought, rumination, is associated with increased activity and connectivity in the default network in people with depression (Hamilton et al. 2015).
This is the sense in which a self has a cost. The default network is not a fault; it lets us learn from the past, plan and understand others. But when it runs on its own, in loops of self-referential thought, it occupies attention and can sustain low mood.
Hubs in a network
To see why a few regions matter so much, it helps to treat the brain as a graph: regions are nodes and the connections between them are edges. Network neuroscience describes the human connectome in these terms (Bullmore and Sporns 2009). Some nodes have many connections (high degree); some are connected to other well-connected nodes (high eigenvector centrality); and a few highly connected hubs, the posterior cingulate and precuneus among them, are densely linked to each other in what is called a “rich club” (Heuvel and Sporns 2011). A standard measure of how easily information can travel across the whole network is global efficiency, the average of the inverse shortest-path lengths between all pairs of nodes (Latora and Marchiori 2001).
Calculation
A toy network of 16 regions in five modules, joined through a few hubs. It is built by hand to illustrate the idea, not taken from connectome data. The program finds the hubs by eigenvector centrality and measures the loss of global efficiency when a hub, a less central node or a peripheral node is removed.
from collections import deque
# A toy brain network (not real connectome data): five modules joined
# through a few hubs, the posterior cingulate (PCC) among them.
edges = """mPFC-PCC mPFC-AG_L mPFC-AG_R mPFC-HF PCC-AG_L PCC-AG_R PCC-HF AG_L-AG_R
FEF-IPS_L FEF-IPS_R IPS_L-IPS_R dlPFC_L-dlPFC_R dlPFC_L-PPC dlPFC_R-PPC
dACC-AI dACC-dlPFC_L AI-dlPFC_R V1-V2 V2-IPS_R M1-FEF M1-V1
PCC-dlPFC_L PCC-dACC PCC-IPS_L PCC-V2 mPFC-dACC PPC-IPS_L""".split()
G = {}
for e in edges:
a, b = e.split("-")
G.setdefault(a, set()).add(b)
G.setdefault(b, set()).add(a)
def eigen_centrality(G, steps=200):
x = {v: 1.0 for v in G}
for _ in range(steps): # power iteration on (A + I)
y = {v: x[v] + sum(x[u] for u in G[v]) for v in G}
norm = max(y.values())
x = {v: y[v] / norm for v in G}
return x
def efficiency(G):
"""Global efficiency: mean of 1/shortest-path length over all pairs."""
nodes, tot = list(G), 0.0
for s in nodes:
dist, q = {s: 0}, deque([s])
while q:
v = q.popleft()
for u in G[v]:
if u not in dist:
dist[u] = dist[v] + 1
q.append(u)
tot += sum(1 / d for t, d in dist.items() if t != s)
n = len(nodes)
return tot / (n * (n - 1))
def without(G, node):
return {v: G[v] - {node} for v in G if v != node}
ec = eigen_centrality(G)
print("top hubs by eigenvector centrality:")
for v in sorted(G, key=ec.get, reverse=True)[:4]:
print(f" {v:8s} degree {len(G[v])}, centrality {ec[v]:.2f}")
base = efficiency(G)
print(f"global efficiency, whole network: {base:.3f}")
for v in ("PCC", "dACC", "M1"):
e = efficiency(without(G, v))
print(f" without {v:5s}: {e:.3f} ({100 * (e / base - 1):+.1f} %)")
# top hubs by eigenvector centrality:
# PCC degree 8, centrality 1.00
# mPFC degree 5, centrality 0.76
# dACC degree 4, centrality 0.60
# AG_L degree 3, centrality 0.56
# global efficiency, whole network: 0.532
# without PCC : 0.428 (-19.6 %)
# without dACC : 0.517 (-2.8 %)
# without M1 : 0.548 (+3.0 %)Removing the posterior cingulate, the most central node, cuts the network’s efficiency by about a fifth, because many of the shortest routes between modules ran through it. Removing a less central node costs little. Removing a peripheral node such as the motor cortex in this toy model even raises the average efficiency, because it takes away some of the longest paths; global efficiency is an average, and averages behave like that. The lesson is that the role of a region depends on its position in the network, not only on what it does locally.
Note
Real brain networks are estimated from imaging data with many choices about how to define regions and connections, and the results depend on those choices. The toy model shows a principle: a hub is a bottleneck as well as a meeting point. It does not say anything about any particular brain.
Hypothesis · not established
Not established. The subjective sense of being absorbed in a stream of self-related thought corresponds, at the network level, to the posterior cingulate acting as a hub that routes information between the default network and other networks; when its integrating role is reduced, by training of attention or otherwise, self-related thought becomes less “sticky”. The hypothesis predicts that, across people and sessions, the eigenvector centrality of the posterior cingulate in resting-state data correlates with self-reported time spent in self-related thought. It would be refuted if no such correlation appeared in an adequately powered study.
References
Fan, Y. (2026). The Default Mode Network, the Entropic Brain and Neural Oscillations: 5-HT2A Receptor Kinetics, Pineal Calcite Microcrystals and the Computational Neuroscience of Meditative Attention [默认模式网络、熵脑与神经振荡] (Version 1.0.0). 5D Library. https://doi.org/10.5281/zenodo.23697320 · Licensed under Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0).