Pulse pressure in cerebral arteries creates cyclic loading on the walls and surrounding tissue. MRI measurements show that the brain shifts by fractions of a millimeter with every heartbeat, but images alone can't separate the contributions of vessel geometry, wall properties, and tissue characteristics. Most computational studies look at either the blood flow inside the vessel or the mechanics of the whole brain, and a fully coupled model with realistic anatomy had not yet been built. This work fills that gap, using geometry from high-field MRI and a coupled simulation.
From 5-Tesla MRI scans of a healthy woman around 30 years old, four segments were segmented: the middle cerebral artery (M1), its bifurcation, the basilar artery, and the internal carotid artery. For each, a three-dimensional model was built of the lumen, a variable-thickness wall, and surrounding tissue as a cube with three concentric layers around the vessel. Blood was described with the Carreau model for shear thinning, the wall with the Ogden hyperelastic model, and the tissue with the Storakers hyper-viscoelastic model with multiple relaxation times. The blood-wall-tissue interaction was solved with the finite element method in COMSOL using two-way coupling and a moving mesh. Physiological pulsatile flow and pressure profiles were applied at the inlet, and the results were compared with literature MRI data on gray matter volumetric deformation.
The simulations reproduced the time course of volumetric deformation: a rise during systole, a peak around 30% of the cycle, and a decline during diastole. Deformation is highest in the wall and decays rapidly with distance from the vessel, staying within experimentally measured values for gray matter. The internal carotid artery produced the largest deformation due to a combination of high flow velocity and pronounced tortuosity, whereas the basilar artery showed a more symmetric and localized pattern. Wall thickness acts inversely: at minimum thickness, volumetric deformation in the first tissue layer reached 7.75×10⁻³, while at maximum thickness it was 1.68×10⁻³. Wall-level hemodynamic metrics (TAWSS, OSI, RRT) were non-uniform: elevated values appeared at bifurcations, bends, and stenoses, but overall the flow remained unidirectional.
This work is the first to combine realistic cerebral artery geometry, nonlinear blood rheology, hyperelastic walls, and viscoelastic tissue in a single coupled model with validation against MRI data. This makes it possible to separate the contribution of vessel shape from tissue and wall properties, something that neither purely hemodynamic nor purely tissue models can do. The results highlight that deformation and hemodynamic disturbances are governed by geometry in different ways, so assessing vessel condition requires joint analysis of mechanical and wall-level indices.
The model can be extended to realistic anatomy with cerebrospinal fluid, meninges, and perivascular spaces, as well as to patient-specific geometries with aneurysms, stenoses, or age-related stiffness changes. Including transport processes would allow studying how pulsatile deformation modulates drug transport in the intercellular and perivascular spaces.
The results will be useful in neurosurgery and neuroradiology for assessing the risk of aneurysms and stenoses, as well as in pharmacokinetics for predicting drug distribution in the brain.
The next step is validation on a larger number of subjects and comparison with DENSE MRI data in a spatially co-registered form. Then one can move on to modeling pathological changes in geometry and tissue properties.
In brain tissue mechanics, it remains an open question how pulsatile loads are distributed among the vascular network, cerebrospinal fluid, and parenchyma, and how this affects transport and damage in pathologies. This model brings us closer to an answer but does not account for cerebrospinal fluid or tissue anisotropy.
With every heartbeat, the brain shifts by roughly 0.1–0.3 mm, comparable to the thickness of a human hair, yet this deformation is enough to influence substance transport in perivascular spaces.
Not published on arXiv. Here are its page, the PDF and the formalization: you can check it yourself, not only read our account.