= Solution
\b[The <brain> needs continuous, locally matched <perfusion> within a nearly rigid <skull>.] Its arterial connections, venous drainage, fluid compartments and vascular regulation meet different parts of that requirement. No single arrangement guarantees an unchanging intracranial <blood> volume or an uninterrupted supply under every condition.
There are two principal arterial approaches: the paired <internal carotid arteries> and the <vertebral arteries>, the latter joining as the <basilar artery>. At the base of the <brain>, the <cerebral arterial circle> connects the anterior and posterior supplies through communicating <arteries>. Connections between superficial cerebral arterial territories provide additional collateral routes. This permits redistribution if one route becomes inadequate, but individual anatomy varies, and some deep penetrating <arteries> have limited effective collateral supply. The existence of an anatomical circle therefore does not establish that any one <artery> can be obstructed harmlessly.<The Cerebral Circulation by Marilyn J. Cipolla/Anatomy and Ultrastructure>[Arteries; Collaterals: cerebral arterial circle, pial anastomoses and variation in collateral capacity]{ref}
The bends of the entering <arteries> and their branching course accompany a distributed <vascular resistance> and compliance. They should not be described as mechanically abolishing every pulse: cerebral <blood flow> remains pulsatile. Numerous small branches spread the supply over the surface before penetrating the tissue, while dense <capillary> networks bring exchange close to <neurons> and supporting <cells>.
Superficial and deep cerebral <veins> drain into <dural venous sinuses>. These are channels supported by folds and attachments of <dura mater>, rather than freely collapsible thin-walled <veins>. Their connections lead chiefly towards the <internal jugular veins>, with communicating vertebral, diploic and emissary routes providing additional possibilities. The valveless nature of many of these communications allows pressure-dependent changes of direction; it is not an assurance of one-way flow. Head position, neck pressure and the available alternative routes consequently matter to drainage.
The <brain>, <blood> and <cerebrospinal fluid> share the cranial enclosure. A small increase in one component can initially be accommodated by displacement of venous <blood> and <cerebrospinal fluid>, including fluid movement towards the spinal compartment. This reserve is finite. When compensation is exhausted, further volume increase can produce a large rise of <intracranial pressure> and reduce <cerebral perfusion pressure>. The skull does not make cerebral anaemia physically impossible, as an overly literal historical constant-volume argument might suggest.
A simplified pressure relation, useful in the modern account, is
$$
\boxed{\mathrm{CPP}\simeq\mathrm{MAP}-\mathrm{ICP}},
$$
where CPP is <cerebral perfusion pressure>, MAP is <mean arterial pressure> and ICP is <intracranial pressure>. The approximation assumes that the effective downstream pressure is represented adequately by ICP; high venous pressure can complicate it. <Cerebral autoregulation> adjusts arteriolar tone and hence resistance when <perfusion> pressure changes. It has limited capacity and depends on physiological state, so a fixed universal pressure interval should not be inferred.<Physiology, Cerebral Autoregulation (StatPearls)>[Mechanism; Cerebral Blood Flow Regulation and Physiology: perfusion pressure, resistance and regulatory responses]{ref}
Local metabolic regulation and <neurovascular coupling> also match supply to activity. A rise of arterial <carbon dioxide> tends to dilate cerebral vessels; vigorous overbreathing can lower arterial <carbon dioxide> and reduce cerebral <blood flow>. This is distinct from pressure-driven autoregulation. The <blood-brain barrier>, based principally on specialized <capillary> <endothelium> with tight junctions, helps stabilize the chemical environment while permitting regulated exchanges. It is a selective exchange arrangement, not the structure that supports the dural sinuses or generates the arterial pressure. These modern mechanisms refine the anatomical account without attributing all their molecular details to 1865.
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