William D. Fraser

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 (ΔVCSF) was accommodated by collapse of the cerebral venous bed. This profoundly altered the venous haemodynamics and was reflected in the cranial pressure PCSF. The cranial volume-pressure curve obtained from the model was consistent with experimental data; the curve was flat for 0<-ΔVCSF<-20 ml and 35<-ΔVCSF<-40 ml, and steep for 20<-ΔVCSF<-35 ml and ΔVCSF>-40 ml. For ΔVCSF>25 ml and PCSF>5.3 kPa (40 mmHg), cerebral blood flow dropped. When PCSF 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.