A mathematical model of cerebral perfusion subjected to Gz acceleration

When the human body is exposed to a high gravitational load, the blood supply to the brain is reduced and loss of consciousness may occur. Our goal is to identify the principal mechanical causes of reduced blood supply to the brain during high +Gz.

We have developed a mathematical model to investigate the influence of Gz on the cerebral circulation. Blood flow is modeled using a one-dimensional flow approximation, in which the cross-sectional area of elastic vessels is determined as a non-linear function of the transmural (blood minus external) pressure. The intracranial vessels are subjected to cerebrospinal fluid pressure (PCSF) which is determined from the condition that the cranial volume is conserved.

For a constant pressure difference of 100 mm Hg applied to the arterial and venous ends of the model, blood flow is diminished for +Gz. At approximately +5 G, the blood flow predicted by the model is insufficient to maintain normal functioning of the brain. PCSF is approximately equal to the blood pressure in the large intracranial veins for all values of Gz. Extracranial arteries and the intracranial vessels do not collapse, even when Gz is substantially higher than normal. However, the extracranial veins are collapsed even for moderate +Gz.

Even if cardiac output is maintained at normal levels, cerebral perfusion will fall because of the increasing resistance of the cerebral flow circuit. This increase is largely due to the collapse of the extracranial veins, which begins at moderate Gz and becomes dominant at a Gz of approximately 4.5.