Numerical modeling of the cerebrospinal system to explore the coupling of brain stiffness and heart rate.

Abstract

In adults, the skull forms a rigid closed cavity whose contents are governed by a dynamic interaction among four main compartments: brain tissue, arterial blood, venous blood, and cerebrospinal fluid (CSF). The CSF occupies two intracranial regions: the subarachnoid spaces at the periphery of the brain, and the ventricular system at its center, connected by the narrow cerebral aqueduct. To maintain physiological intracranial pressure, the total intracranial volume must remain constant throughout the cardiac cycle. A third compartment, the spinal canal, acts as a pressure-relief reservoir by accommodating CSF displaced from the intracranial space. The interaction of CSF flows across these compartments remains poorly understood and constitutes a major obstacle to elucidating several cerebral pathophysiologies. We present a simplified macroscopic model accounting for fluid-structure interaction between CSF dynamics and brain tissue displacement. An existing numerical algorithm was selected to ensure strong coupling. The variational formulation is solved using the finite element method within a monolithic semi-implicit framework, assuming small structural displacements and employing Arbitrary Lagrangian-Eulerian coordinates. The global mesh is updated at each time step, ensuring a stable time-advancing scheme. The model enables simulation of the system dynamics and identification of the key governing parameters. A systematic exploration of the parameter space reveals a strong coupled interdependence of CSF dynamics on brain tissue stiffness and heart rate. The heart rate dependence is consistent with experimental observations, and several pathologies are known to involve significant changes in cerebral viscoelasticity, highlighting the clinical relevance of this model.