Hemodynamics and capillaries

Epistemic status: mixed. The physics (Poiseuille) is textbook. The capillary-diameter range is well-established. The "~400 miles" cerebral vessel figure is widely cited but the original measurement is hard to pin down (C2/C3). The "capillaries collapse by ~90% in volume during ischemia" claim is a simplification of a more complicated literature — the modern picture is "~20–40% of capillaries stalled/narrowed," not "all capillaries 90% smaller."

1. Poiseuille's law applied to brain perfusion

Poiseuille's law for laminar, Newtonian, steady pipe flow:

Q = (π · ΔP · r⁴) / (8 · η · L)

where Q is volumetric flow, ΔP the pressure drop, r the radius, η the viscosity, L the length. (CV Physiology; Hagen-Poiseuille eq.)

Implications for ASC-style perfusion:

• Resistance ∝ 1/r⁴. A 2× reduction in diameter → 16× resistance (quote: "a 2-fold increase in diameter decreases resistance by 16-fold" — cvphysiology.com, C1).
• If you set a fixed perfusion pressure (e.g. Alcor's ≤100 mmHg cap, Alcor protocol), nearly all flow goes preferentially to the lowest-resistance paths: big pipes first, then whichever capillaries haven't closed.
• "Pressure" is not "flow." You can push more pressure at a blocked bed and get almost no extra flow, but you get increasing risk of bursting what's still open. This is the heart of Aurelia's "big pipe vs small pipe" framing.

Note the standard caveats: blood is non-Newtonian (shear-thinning; Fåhræus-Lindqvist effect makes effective viscosity drop in small vessels), vessels are elastic, and capillary flow is dominated by RBC-plug flow, not Poiseuille flow strictly. Still, the r⁴ scaling is the right first-order intuition, and it's what cerebral hemodynamics teaching uses.

2. Capillary diameter vs. red blood cell diameter

• Human brain capillary luminal (inside) diameter: 2-5 μm in one review (Chakraborty et al. 2023, PMC10503221), with confocal-measured means of 5.9 or 6.5 μm depending on method. Mean 4.93 ± 0.29 μm hypocapnic vs 5.91 ± 0.10 μm hypercapnic, measured in cats (Villringer et al. 1993, PubMed 8408311). Outer diameter 7-9 μm, depending on wall thickness.
• Wikipedia/physiology texts cite capillary diameter range of 5–10 μm.
• Human RBC diameter: 7–8 μm, biconcave disc, thickness ~2 μm.

Key observation: the RBC is usually larger than the capillary lumen. RBCs must deform into parachute or bullet shapes to pass. The cerebral microcirculation literature quantifies this directly:

"Red blood cells undergo major deformation depending on blood flow dynamics within microvessels, particularly when they pass through capillaries that are smaller than their diameter." (Hudetz 1997)

"Erythrocytes themselves act as oxygen sensors that autonomously regulate their own deformability and thereby flow velocity through capillaries in response to physiological decreases in oxygen tension." (Wei et al., Neuron 2016)

RBC velocities in brain capillaries: 0.3–3.2 mm/s (Cipolla, "The Cerebral Circulation," NBK53086); 2–3 mm/s capillary, 10 mm/s arteriole, 20–30 mm/s pial vessels (Hudetz review).

Implication for perfusion preservation: If capillaries shrink even modestly (a few micrometers), not only blood, but anything of RBC-comparable size — including leukocytes (neutrophils 12-15 μm), platelet aggregates, and cryoprotectant-entrained particulates — gets stuck. A 1–2 μm reduction in lumen is catastrophic, not cosmetic.

3. Total vessel length / density

• "~400 miles" figure: Confirmed via Cipolla's "Anatomy and Ultrastructure" chapter (NBK53086, ref 11). The more common form in the literature is ~400 miles (~640 km) of total cerebral microvasculature in the human brain. This appears to trace back to Pawlik et al. 1981 and is somewhat loose (mouse-scale extrapolations dominate). Confidence C2.
• Surface area of the BBB: ~12 m² per adult brain, with nearly every neuron having its own neighboring capillary (Cipolla).
• Mean intercapillary distance in gray matter: ~40 μm (so diffusion from any capillary reaches most tissue within <40 μm). This is why a few percent unperfused is not "a few percent tissue damage" but rather a fine-grained Swiss-cheese pattern on EM.

Implication: the network's extreme density is its strength (oxygen & CPA reach everywhere) and its failure mode. Blocking many capillaries simultaneously does not present as an obvious large infarct; it presents as spotty ultrastructural degradation visible only at EM scale.

4. The "no-reflow" phenomenon — Ames 1968 and later

Ames et al. 1968

Ames et al., "Cerebral ischemia. II. The no-reflow phenomenon," Am J Pathol (PubMed 5635861). Original protocol: inflated 350 mmHg cervical cuff on rabbits to block both common carotids + basilar; ischemia held 5–15 minutes; then attempted reperfusion with carbon-black-stained Ringer's; quantified unperfused tissue.

Key observations (summarized via Zhang 2024 review and Kloner 2018):

"No reflow could be seen after as early as 5 minutes of ischemia with almost the entire cerebral hemisphere affected after only 15 minutes of ischemia." (Zhang 2024)

"No-reflow is an intra-ischemia rather than post-ischemic process, whose severity is proportional to the duration of ischemia." (ibid.)

Mechanism proposed in the original paper: "extrinsic compression of the capillaries by vasogenic edema and perivascular glial and endothelial cell swelling as a response to ischemia." (C1, via 2024 review)

Reassessment — Little et al. 1977

Little, Kerr, Sundt (PubMed 835156) could not reproduce the extreme perivascular swelling / luminal collapse in their series: "structural changes in ischemic capillary walls in themselves are not sufficient to explain failed cerebral reperfusion, or the no-reflow phenomenon." They did note an excess of small-diameter capillaries in ischemia. (C1)

This is a meaningful counter to a simple "capillaries collapse by 90% in volume" story: the dominant mechanism is not pure geometric collapse — it's multifactorial.

Modern understanding

The contemporary synthesis across 2018–2024 reviews gives four interacting contributions, each quantified separately:

1. Pericyte contraction: Hall et al. 2014 (Nature, PubMed 24670647) showed capillary pericytes constrict in ischemia and die "in rigor" — leaving capillaries irreversibly constricted even after reperfusion. Quantitative: "pericyte death was higher in ischaemia at 40 and 60 min"; capillaries produce ~84% of activity-induced blood-flow change.
2. Endothelial/astrocyte end-foot swelling (cytotoxic edema): measurable as ~37% diameter reduction at pericyte sites in cardiac models; for brain, reviewers say "postischemic swelling ... results in decreased luminal size within an hour after reperfusion" (Kloner 2018).
3. Neutrophil capillary plugging: El Amki et al. 2020 (Cell Reports, PubMed 33053341): in mouse ischemic stroke, ~35% of capillaries in core and ~15% in penumbra remain stalled after thrombolysis; "stalling of approximately 20%-30% of capillaries in the distal vascular network by neutrophils limited tissue reperfusion to only approximately 60% of baseline." (C1)
4. Microthrombi + RBC trapping: the original Ames observation — columns of trapped blood in regions of no-reflow.

Aurelia's "~90% collapse in capillary volume" claim

Not supported as literally stated. What the literature does support:

• Individual capillaries at pericyte sites can show 37% diameter reduction in cardiac models (elifesciences 29280). 37% diameter → ~60% volume reduction at that location.
• 20–40% of capillaries become non-perfusing after ischemia; those that remain open can be somewhat narrowed.
• The language "90% collapse in volume" probably conflates (a) the local volume reduction at pinched points, (b) the total fraction of tissue not reached, and (c) the fact that even small diameter reductions are functionally catastrophic because of r⁴ scaling.

Better-evidenced framing: after ~15 minutes of global cerebral ischemia, most of the brain becomes unreachable by blood-borne agents via the normal arterial tree, due to a combination of pericyte constriction, endothelial/glial swelling, neutrophil plugging, and trapped blood components. The failure is patchy at the scale of individual capillaries but complete at the scale of reaching every neuron uniformly. This is the correct version of the claim and it fully supports Aurelia's operational conclusion: "you can't just wait and preserve later."

5. Timeline of capillary closure post-arrest

Rough integration of the sources:

This is why Nectome's 14-minute window is in the right order of magnitude: the perfusability window should end somewhere between "cytotoxic edema appears" and "most capillaries have closed." 14 min lives inside that interval and is operationally cautious vs. Ames's 15-min-is-already-most-of-the-hemisphere.

Caveat: all these numbers degrade substantially (are longer) under hypothermia; see 06-cooling-physics.md.

6. Upshot

• Poiseuille's r⁴ is not rhetorical. In a perfused brain, tiny changes in lumen size dominate flow distribution.
• Brain capillaries are at the RBC-deformation threshold in health. They have no safety margin.
• The no-reflow phenomenon is the central mechanical obstacle. It is real, is driven by multiple mechanisms (not one), and progresses on the 5-to-15 min time scale after normothermic ischemia.
• The number "90% capillary volume collapse" is not literally correct but points at a real and important thing: a combination of partial collapse, stalling, and plugging that makes the vast majority of the microvascular network unreachable ~15 min post-arrest.
• Aurelia's framing is basically right, compressed for conversational use. The cited literature supports the operational claim "if you wait, you lose" and supports why Nectome's target is ~14 minutes.