Interactions of brain, blood, and CSF: a novel mathematical model of cerebral edema

Abstract

Background

Previous models of intracranial pressure (ICP) dynamics have not included flow of cerebral interstitial fluid (ISF) and changes in resistance to its flow when brain swelling occurs. We sought to develop a mathematical model that incorporates resistance to the bulk flow of cerebral ISF to better simulate the physiological changes that occur in pathologies in which brain swelling predominates and to assess the model’s ability to depict changes in cerebral physiology associated with cerebral edema.

Methods

We developed a lumped parameter model which includes a representation of cerebral ISF flow within brain tissue and its interactions with CSF flow and cerebral blood flow (CBF). The model is based on an electrical analog circuit with four intracranial compartments: the (1) subarachnoid space, (2) brain, (3) ventricles, (4) cerebral vasculature and the extracranial spinal thecal sac. We determined changes in pressure and volume within cerebral compartments at steady-state and simulated physiological perturbations including rapid injection of fluid into the intracranial space, hyperventilation, and hypoventilation. We simulated changes in resistance to flow or absorption of CSF and cerebral ISF to model hydrocephalus, cerebral edema, and to simulate disruption of the blood–brain barrier (BBB).

Results

The model accurately replicates well-accepted features of intracranial physiology including the exponential-like pressure–volume curve with rapid fluid injection, increased ICP pulse pressure with rising ICP, hydrocephalus resulting from increased resistance to CSF outflow, and changes associated with hyperventilation and hypoventilation. Importantly, modeling cerebral edema with increased resistance to cerebral ISF flow mimics key features of brain swelling including elevated ICP, increased brain volume, markedly reduced ventricular volume, and a contracted subarachnoid space. Similarly, a decreased resistance to flow of fluid across the BBB leads to an exponential-like rise in ICP and ventricular collapse.

Conclusions

The model accurately depicts the complex interactions that occur between pressure, volume, and resistances to flow in the different intracranial compartments under specific pathophysiological conditions. In modelling resistance to bulk flow of cerebral ISF, it may serve as a platform for improved modelling of cerebral edema and blood–brain barrier disruption that occur following brain injury.