Jan Löfgren

The cerebrospinal fluid pressure-volume curve was determined by measuring the pressure response to rapid injection of fluid into the cisterna magna of dogs, by means of a constant flow infusion pump. The shape of the curve is complex, with two plateaus at the levels of the venous and arterial pressures, respectively. The slope dP/dV is referred to as the elastance of the system (mmHg/ml). The elastance has a low value in the normal pressure range and shifts at a fluid pressure of about 15 mmHg to a value approximately 20 times higher, with a relatively minute change in the volume of the system.

BACKGROUND AND PURPOSE: The principle of minimum work is a parametric optimization model for the growth and adaptation of arterial trees. It establishes a balance between energy dissipation due to frictional resistance of laminar flow (shear stress) and the minimum volume of the vascular system, implying that the radius of the vessel is adjusted to the cube root of the volumetric flow. The purpose of this study is to verify whether the internal carotid artery system obeys the principle of minimum work. METHODS: Measurements of the radius of parent and branch segments of the internal carotid, anterior, and middle cerebral arteries were performed on analog angiographs chosen at random from a set classified as normal. The branch angles were measured from lateral projections in bifurcations of the anterior cerebral artery. The relation of the calibers of parent and branch vessels was analyzed. RESULTS: The area ratio of the bifurcations (N = 174) was 1.2 +/- 0.4 (mean +/- SD). The equation (r0)n = (r1)n + (r2)n was solved for n, resulting in n = 2.9 +/- 0.7 (mean +/- SD, N = 157). Optimum proportions between the radii of parent (r0) and branch (r1 and r2) vessels in the internal carotid artery system were verified in normal carotid angiographs up to four branch generations, according to the theoretical equation r0(3) = r1(3) + r2(3) (r = 0.989, N = 174). No clear correlation was found between the measured branch angles, the relative branch cross-sectional area, and the theoretical optimum angles. CONCLUSIONS: This study demonstrates that the process of branching of the internal carotid artery system obeys the principle of minimum work, as the diameter exponent approximates 3. The principle of minimum work establishes strict functional relations between volumetric flow, flow velocity, and vessel radius. This model was extended to parametric optimization of branch angles, which has proved irrelevant in terms of functional optimization. Our results corroborate this finding. Shear stress-induced endothelial mediation seems to be the regulating mechanism for the maintenance of this optimum vessel design. The magnitude of wall shear stress is the same at every point in a vascular network obeying the principle of minimum work, because the flow rate influences the shear stress proportionally to the third power of the vessel radius. This observation has implications for understanding the remodeling of the cerebral vascular network in the presence of arteriovenous malformations and for the pathogenesis of saccular aneurysms.

A quantitative analysis of the contributions of the cranial and spinal compartments to the cerebrospinal fluid pressure-volume curve was made using dogs. The curve was determined by rapid continuous injection of fluid into the cisterna magna with simultaneous measurement of the pressure. Spinal block at the C 1 level was produced by inflation of an epidural rubber balloon allowing the recording of the pressure-volume curve for the isolated cranial system. By subtraction of the two curves obtained, the spinal pressure-volume curve could be calculated. 70 % of the variation in volume within the system was related to the spinal section and 30 % to the cranial section. The intracranial curve represents the effects on the fluid pressure of forced alterations in the volume of the intracranial vascular bed. The spinal compartment has a quantitatively defined and probably mechanically important function as an expansion vessel for the intracranial system.

Abstract Effects of short‐term variations in cerebrospinal fluid pressure on cerebral blood flow in dogs were measured with the radioactive krypton clearance technique of Lassen et al . The cerebrospinal fluid pressure was increased stepwise by infusion of artificial cerohrospinal fluid, the pressure range from ‐15 to +150 mm Hg being investigated. The cerebral blood flow remained virtually stable, when the induced cerebrospinal pressure was lower than about 100 mm Hg. At higher values the cerebral blood flow began to fall. Thus, the existence of flow auto‐regulation was demonstrated also for the situation when perfusion pressure is reduced by a rise of the intracranial pressure. At very high cerebrospinal fluid pressures an additional reaction appeared in the form of a rise in the systemic arterial blood pressure. A discussion of the relative roles of these two regulating mechanisms is given.