Mathematical study of the role of non-linear venous compliance in the cranial volume-pressure test

Abstract

The role of the cerebral venous bed in the cranial volume-pressure test was examined by means of a mathematical model. The cerebral vascular bed was represented by a single arterial compartment and two venous compartments in series. The lumped-parameter formulation for the vascular compartments was derived from a one-dimensional theory of flow in collapsible tubes. It was assumed in the model that the cranial volume is constant. The results show that most of the additional volume of cerebrospinal fluid (deltaV(CSF)) was accommodated by collapse of the cerebral venous bed. This profoundly altered the venous haemodynamics and was reflected in the cranial pressure P(CSF). The cranial volume-pressure curve obtained from the model was consistent with experimental data; the curve was flat for 0 < or = deltaV(CSF) < or = 20 ml and 35 < or = deltaV(CSF) < or = 40 ml, and steep for 20 < or = deltaV(CSF) < or = 35 ml and deltaV(CSF) > or = 40 ml. For deltaV(CSF) > 25 ml and P(CSF) > 5.3 kPa (40 mmHg), cerebral blood flow dropped. When P(CSF) was greater than the mean arterial pressure, all the veins collapsed. The conclusion of the study was that the shape of the cranial volume-pressure curve can be explained by changes in the venous bed caused by various degrees of collapse and/or distension.