A fully dynamic multi-compartmental poroelastic system: Application to aqueductal stenosis

Abstract

This study proposes the implementation of a fully dynamic four-network poroelastic model which is underpinned by multiple-network poroelastic theory (MPET), in order to account for the effects of varying stages of aqueductal stenosis and atresia during acute hydrocephalus. The innovation of the fully dynamic MPET implementation is that it avoids the commonplace assumption of quasi-steady behaviour; instead, it incorporates all transient terms in the casting of the equations and in the numerical solution of the resulting discrete system. It was observed that the application of mild stenosis allows for a constant value of amalgamated ventricular displacement in under 2.4h, whereas the application of a severe stenosis delays this settlement to approximately 10h. A completely blocked aqueduct does not show a clear sign of reaching a steady ventricular displacement after 24h. The increasing ventricular pressure (complemented with ventriculomegaly) during severe stenosis is causing the trans-parenchymal tissue region to respond, and this coping mechanism is most attenuated at the regions closest to the skull and the ventricles. After 9h, the parenchymal tissue shows to be coping well with the additional pressure burden, since both ventriculomegaly and ventricular CSF (cerebrospinal fluid) pressure show small increases between 9 and 24h. Localised swelling in the periventricular region could also be observed through CSF fluid content, whilst dilation results showed stretch and compression of cortical tissue adjacent to the ventricles and skull.

Fluid–structure interaction for highly complex, statistically defined, biological media: Homogenisation and a 3D multi-compartmental poroelastic model for brain biomechanics

“…In the literature, several works have utilised a poroelastic approach in modelling parenchymal tissue within the realm of hydrocephalus and oedema formation in the brain and small intestine (Tully and Ventikos, 2011;Vardakis et al, 2013b;Guo et al, 2018;Vardakis et al, 2017Vardakis et al, , 2016Chou et al, 2016;Chou, 2016;Vardakis et al, 2013a;Kaczmarek et al, 1997;Levine, 1999Levine, , 2000Smillie et al, 2005;Sobey and Wirth, 2006;Shahim et al, 2012;Aldea et al, 2019;Thompson et al, 2019). The poroelastic modelling of parenchymal tissue for the purpose of investigating AD yields a narrower selection of relevant work (Guo et al, 2018;Thompson et al, 2019).…”

Functional hyperemia drives fluid exchange in the paravascular space

“…Some authors have used poroelastic models to predict that oscillatory ows can enhance metabolite transport in the brain through dispersion 118 . Poroelastic models can also explore the effect of static and dynamic occlusions to ow 119,120 , which our uid-structure model does not simulate. We also ignore the elastic response of the collagen bers in the PVS and only simulate the uid dynamics in this region.…”

Conservative discretizations and parameter‐robust preconditioners for Biot and multiple‐network flux‐based poroelasticity models

“…Here, we consider the simplest case of a system with only one pressure and one flux, namely, Biot's consolidation model. We solve system (8) for…”

“…Then, the boundary conditions are as follows: u = 0 on Γ 4 , ( − p 1 I − p 2 I − p 3 I − p 4 I)n = (0, 0) T on Γ 1 ∪ Γ 2 , ( − p 1 I − p 2 I − p 3 I − p 4 I)n = (0, −1) T on Γ 3 , p 1 = 2 on Γ, p 2 = 20 on Γ, p 3 = 30 on Γ, and p 4 = 40 on Γ. The right-hand sides in (8) are chosen to be f = 0, g 1 = 0, g 2 = 0, g 3 = 0, and g 4 = 0.…”

“…As a consequence, the efficacy of treating such clinical conditions by surgical procedures that focus on relieving the buildup of CSF pressure in the brain's third or fourth ventricles could be explored by means of computer simulations, which could also assist in finding medical indications of oedema formation. 8 Recently, the MPET model has also been used to better understand the influence of biomechanical risk factors associated with the early stages of Alzheimer's disease (AD), the most common form of dementia. 9 Modeling transport of fluid within the brain is essential in order to discover the underlying mechanisms currently being investigated with regard to AD, such as the amyloid hypothesis, according to which the accumulation of neurotoxic amyloid-(A ) into parenchymal senile plaques or within the walls of arteries is a root cause of this disease.…”