(Stroke. 2001;32:275-a.)
© 2001 American Heart Association, Inc.
Letters to the Editor |
Stress-Related Intracerebral Hemorrhage and the Water-Hammer Effect
Department of Physiology, University of Turku, Turku, Finland, (retired at Sibbvik, Västanfjärd, Finland)
To the Editor:
Lammie et al1 described thalamic hemorrhage following emotional upset in an elderly man with old lacunar infarcts in other parts of the brain. The case supported Caplan’s hypothesis that acute rises in blood pressure or cerebral blood flow may cause rupture of the small perforating arteries,1 which branch at almost right angles from the middle and posterior cerebral arteries to supply, among others, the thalamus and basal ganglia.
At autopsy of cases of not only infarct but also hemorrhage, I paid attention to the frequent occurrence of potential sources of small arterial emboli in the heart or at carotid artery atheromatous plaques. That emboli might be related to hemorrhage made no sense until, as a retiree, I began to poke into the physiology2 and physics3 4 of flow.
A water-hammer phenomenon was studied in the late 19th
century.3 When flow of fluid in a pipe is stopped by sudden closure of a valve,
the kinetic energy of the upstream fluid is reduced to zero very rapidly, creating a high
pressure at the valve and causing a pressure wave to move upstream from
it. Downstream, momentum reduces pressure. The primary waves are
followed by secondary ("bouncing") ones, until the fluid comes to
rest.4 The theory3 4 is complicated, but the brief upstream rise of pressure
(
p) at rapid closure of valves may be calculated (G.A. Öhman, personal communication,
2000) from the rather simple equation
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I use it to calculate a theoretical rise in pressure in the middle cerebral artery at embolic occlusion at its first major lateral bifurcation, located downstream from the orifices of its perforating arteries.
A blood flow velocity (
) of 0.36 m/s in the middle
cerebral artery during
anesthesia5 is
low. The density (
) of the blood is 
1050
kg/m3. The compressibility
(K) of blood may be close to
that of water, 4.8 10-10/Pa. At autopsy the
internal diameter (d) of one
undistended middle cerebral artery seemed to be 2.2 mm and its
wall thickness (
) 0.25 mm, both possibly underestimated. The
elasticity modulus (E) of the
artery may be unknown, and I use that of a rubber specimen, 5.5
106
Pa.4 If embolic occlusion is
sudden, these figures result in a pressure increase
(p) of 69 mm Hg
transmitted upstream in the middle cerebral artery past the orifices of
its perforating arteries.
To be sudden, the time of valve closure must not exceed
twice the length of the upstream pipe divided by the velocity of the
pressure waves of sound in the fluid in the pipe studied, which can be
calculated from the data
given.4 If a middle cerebral
artery 20 mm long is held as the upstream pipe, the occlusion,
to be sudden, must occur in 1.6 ms. If 80 mm of the carotid artery
is included, 8 ms is sufficient. At high blood and embolus flow
velocity, occlusion of the middle cerebral artery might be sudden in a
physical sense.
During brain activity and emotional upset, brain blood flow
velocity is higher than during anesthesia, and
p is directly proportional
to . The elasticity of the rubber may differ from that of the middle
cerebral artery, the wall stiffness of which increases with age. In a
model of the artery made of steel with a high
E
(2.1x1011 Pa), the other figures result in
a p of 3788 mm Hg.
Fibrinoid changes of the small perforating
arteries1 may increase their
fragility.
The above supports the
hypothesis1 that acute rises
in brain blood flow velocity may trigger intracerebral
hemorrhage: If combined with embolic occlusion of middle and
posterior cerebral arteries downstream from perforating artery
orifices, a high velocity ought to result in a local blood pressure
exceeding that elsewhere in the circulation. Retrospectively, I regret
that I, in cases of hemorrhagic stroke, never looked for downstream
emboli. All factors in the equation can be quantified, and
biophysicists might be able to test this hypothesis in models of the
carotid-vertebral and cerebral arteries. The high frequency of primary
hemorrhage in the brain compared with other sites might be
related to the thicker and more resistant media of extracranial
arteries of perforating artery diameter, but this quality of
extracranial arteries of cerebral artery size may increase
p (equation). This
water-hammer mechanism is not dealt with in my textbooks of physiology.
Medline gave 21 hits on "water hammer" (pulse, etc), but none dealt
with primary intracerebral
hemorrhage.
Göran A. Öhman, PhD (Laboratory of Heat Engineering, Åbo Akademi University), gave generous help but declined authorship, citing lack of insight in blood flow in humans.
References
1.
Lammie GA,
Lindley R, Keir S, Wiggam MI. Stress-related primary
intracerebral hemorrhage: autopsy clues to
underlying mechanism. Stroke. 2000;31:1426–1428.
2. Ahlqvist J. 160 years of laminar flow: what have we learned? J Rheumatol.. 2000;27:2053.[Medline] [Order article via Infotrieve]
3. Streeter VL. Mechanics, fluid. In: The New Encyclopaedia Britannica, Macropaedia. Chicago, Ill: Encyclopaedia Britannica Inc; 1981;11:779–793.
4. Streeter VL. Fluid Mechanics. New York, NY: McGraw-Hill; 1962.
5.
Sakai K, Cho S,
Fukusaki M, Shibasta O, Sumikawa K. The effects of propofol on human
cerebral blood flow velocity and CO2 response.
Anesth Analg. 2000;90:377–382.
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