Interstitial fluid transport in a multi-compartment model of cerebral blood flow

Whole brain models are a valuable tool to gain a better understanding of cerebral blood flow and metabolism. Recent work has developed multi-compartment models of blood flow and oxygen transport that can be used in a Finite Element framework to simulate whole brain behaviour with low computational expense, helping to move such tools towards clinical application. However, the transport of fluid between the vascular space and the interstitial space has not yet been considered in detail in this context, despite this playing an important role in several cerebrovascular diseases. In this study, an extended framework is proposed to include this transport, coupled with a linear elastic model of tissue displacement to simulate the movement of fluid and the resulting displacement of brain tissue. This framework is compared in detail with previous models. The resulting Eqs. are found to exhibit multiple time scales, and a separation of scales is performed to analyse the behaviour at different time scales. Finally, a simplified model is proposed that can be easily implemented within existing computational frameworks, providing a valuable extension of the pathological conditions that can be simulated.