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

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 less than or equal to DeltaV(CSF) less than or equal to 20 ml and 35 less than or equal to DeltaV(CSF) less than or equal to 40 ml, and steep for 20 less than or equal to DeltaV(CSF) less than or equal to 35 ml and DeltaV(CSF) greater than or equal to 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.