Computational modelling of transport phenomena in cerebral aneurysms
Keywords: cerebral aneurysms
computational fluid dynamics
oxygen distribution
mass transport phenomena
mathematical modelling of aneurysm evolution

An estimated 85% of haemorrhagic strokes are secondary to the rupture of an intracranial aneurysm (IA), a localised, blood-filled dilation of the artery wall. The clinically observed rupture of occluded IAs has led to hypothesise that the presence of thrombus may restrict the transport of nutrients, most notably oxygen, to the aneurysmal wall, thus heightening the risk of rupture through the deleterious effects of hypoxia on cellular functionality. The limited research into O2 transport within IAs demonstrate the need for further exploration into the possible detrimental hypoxic conditions as a result of intrasaccular haemodynamics and thrombusformation in untreated, treated and evolving IAs, with the ultimate goal of further understanding disease evolution and developing prognostic decision support models for clinical intervention.
Preliminary computational fluid dynamic simulations conducted on a 2Daxisymmetric model of a thrombosed artery highlighted the relative importance of wall-side versus the fluid-side mass transport of oxygen. A sensitivity analysis demonstrated that variations in thrombus thickness, and arterial wall cellular respiration rates have the greatest influence on the oxygen distribution to the portion of wall in direct contact with the thrombus.
The results of the coupled flow-mass transport computational fluid dynamic simulations within patient-specific IA show that a reduction in intrasaccular flow as a consequence of stent deployment affects the rate at which oxygenated blood reaches the entirety of the dome. Nonetheless, the distribution ofO2 to the aneurysmal wall itself does not differ from the observed oxygen distribution across the wall when the same IA is left untreated. Conversely, the low velocity recirculations observed in an IA presenting with a very high aspect ratio (i.e a narrow neck and high sack height) limited the transport of oxygen to such an extent as to completely deprive the delivery of oxygen to the fundus. The presence of thrombus within the IA dome results in a dramatic reduction in oxygen delivery to the wall, the extent of which is dependent on the local thrombus thickness.
Finally, a novel fluid-solid-growth-mass transport (FSGT) mathematical model is conceived to explore the biochemical role of thrombus on the evolution of an IA. The shear-regulate propagation of a thrombus layer during membrane expansion leads to the gradual decrease in oxygen tension within the wall. Moreover, as a consequence of coupling this oxygen deficiency to fibroblast functionality, the collagen fibre mass density was shown to increase at an insufficient rate to compensate for the transfer in load from the degrading elastinous consitituents to the collagenous constituents, thus resulting in the increased stretch of collagen fibres in order to maintain mechanical equilibrium. Moreover this over-expansion results in the gradual unstable evolution of the IA.
The observed obstruction to oxygen delivery as a result of intrasaccular haemodynamics and thrombosis compounds the need for further development of more comprehensive chemo-mechano-biological models of IAs so as to better ascertain the level of rupture risk posed by a hypoxic environment. Refinement to the models proposed within this work would prove invaluable to creating a fully integrated multi-physics, multi-scale in silico framework in aid to patient diagnostics and individual treatment planning of IAs.