Stress-Related Intracerebral Hemorrhage and the Water-Hammer Effect
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 (Δp) at rapid closure of valves may be calculated (G.A. Öhman, personal communication, 2000) from the rather simple equation ⇓
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 (ν) of 0.36 m/s in the middle cerebral artery during anesthesia5 is low. The density (ρ) 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 (δ) ≈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 (Δp) 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 Δp is directly proportional to ν. 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 (2.1×1011 Pa), the other figures result in a Δp 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 Δp (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.
- Copyright © 2001 by American Heart Association
Lammie GA, Lindley R, Keir S, Wiggam MI. Stress-related primary intracerebral hemorrhage: autopsy clues to underlying mechanism. Stroke. 2000;31:1426–1428.
Streeter VL. Mechanics, fluid. In: The New Encyclopaedia Britannica, Macropaedia. Chicago, Ill: Encyclopaedia Britannica Inc; 1981;11:779–793.
Streeter VL. Fluid Mechanics. New York, NY: McGraw-Hill; 1962.