Mixed and galerkin finite element approximation of flow in a linear viscoelastic porous medium

This is the post-print version of the Article. The official published version can be accessed from the link below - Copyright @ 2013 ElsevierThis article has been made available through the Brunel Open Access Publishing Fund.We propose two fully discrete mixed and Galerkin finite element approximations to a system of equations describing the slow flow of a slightly compressible single phase fluid in a viscoelastic porous medium. One of our schemes is the natural one for the backward Euler time discretization but, due to the viscoelasticity, seems to be stable only for small enough time steps. The other scheme contains a lagged term in the viscous stress and pressure evolution equations and this is enough to prove unconditional stability. For this lagged scheme we prove an optimal order a priori error estimate under ideal regularity assumptions and demonstrate the convergence rates by using a model problem with a manufactured solution. The model and numerical scheme that we present are a natural extension to ‘poroviscoelasticity’ of the poroelasticity equations and scheme studied by Philips and Wheeler in (for example) [Philip Joseph Philips, Mary F.Wheeler, Comput. Geosci. 11 (2007) 145–158] although — importantly — their algorithms and codes would need only minor modifications in order to include the viscous effects. The equations and algorithms presented here have application to oil reservoir simulations and also to the condition of hydrocephalus — ‘water on the brain’. An illustrative example is given demonstrating that even small viscoelastic effects can produce noticeable differences in long-time response. To the best of our knowledge this is the first time a mixed and Galerkin scheme has been analysed and implemented for viscoelastic porous media

Magnetic resonance elastography (MRE) of the human brain: technique, findings and clinical applications

Neurological disorders are one of the most important public health concerns in developed countries. Established brain imaging techniques such as magnetic resonance imaging (MRI) and x-ray computerised tomography (CT) have been essential in the identification and diagnosis of a wide range of disorders, although usually are insufficient in sensitivity for detecting subtle pathological alterations to the brain prior to the onset of clinical symptoms—at a time when prognosis for treatment is more favourable. The mechanical properties of biological tissue provide information related to the strength and integrity of the cellular microstructure. In recent years, mechanical properties of the brain have been visualised and measured non-invasively with magnetic resonance elastography (MRE), a particularly sensitive medical imaging technique that may increase the potential for early diagnosis. This review begins with an introduction to the various methods used for the acquisition and analysis of MRE data. A systematic literature search is then conducted to identify studies that have specifically utilised MRE to investigate the human brain. Through the conversion of MRE-derived measurements to shear stiffness (kPa) and, where possible, the loss tangent (rad), a summary of results for global brain tissue and grey and white matter across studies is provided for healthy participants, as potential baseline values to be used in future clinical investigations. In addition, the extent to which MRE has revealed significant alterations to the brain in patients with neurological disorders is assessed and discussed in terms of known pathophysiology. The review concludes by predicting the trends for future MRE research and applications in neuroscience

Is the Donnan effect sufficient to explain swelling in brain tissue slices?

Brain tissue swelling is a dangerous consequence of traumatic injury and is associated with raised intracranial pressure and restricted blood flow. We consider the mechanical effects that drive swelling of brain tissue slices in an ionic solution bath, motivated by recent experimental results that showed that the volume change of tissue slices depends on the ionic concentration of the bathing solution. This result was attributed to the presence of large charged molecules that induce ion concentration gradients to ensure electroneutrality (the Donnan effect), leading to osmotic pressures and water accumulation. We use a mathematical triphasic model for soft tissue to characterize the underlying processes that could lead to the volume changes observed experimentally. We suggest that swelling is caused by an osmotic pressure increase driven by both non-permeating solutes released by necrotic cells, in addition to the Donnan effect. Both effects are necessary to explain the dependence of the tissue slice volume on the ionic bath concentration that was observed experimentally

Cerebral magnetic resonance elastography in supranuclear palsy and idiopathic Parkinson's disease

Detection and discrimination of neurodegenerative Parkinson syndromes are challenging clinical tasks and the use of standard T1- and T2-weighted cerebral magnetic resonance (MR) imaging is limited to exclude symptomatic Parkinsonism. We used a quantitative structural MR-based technique, MR-elastography (MRE), to assess viscoelastic properties of the brain, providing insights into altered tissue architecture in neurodegenerative diseases on a macroscopic level. We measured single-slice multifrequency MRE (MMRE) and three-dimensional MRE (3DMRE) in two neurodegenerative disorders with overlapping clinical presentation but different neuropathology — progressive supranuclear palsy (PSP: N = 16) and idiopathic Parkinson's disease (PD: N = 18) as well as in controls (N = 18). In PSP, both MMRE (Δμ = − 28.8%, Δα = − 4.9%) and 3DMRE (Δ|G*|: − 10.6%, Δφ: − 34.6%) were significantly reduced compared to controls, with a pronounced reduction within the lentiform nucleus (Δμ = − 34.6%, Δα = − 8.1%; Δ|G*|: − 7.8%, Δφ: − 44.8%). MRE in PD showed a comparable pattern, but overall reduction in brain elasticity was less severe reaching significance only in the lentiform nucleus (Δμ n.s., Δα = − 7.4%; Δ|G*|: − 6.9%, Δφ: n.s.). Beyond that, patients showed a close negative correlation between MRE constants and clinical severity. Our data indicate that brain viscoelasticity in PSP and PD is differently affected by the underlying neurodegeneration; whereas in PSP all MRE constants are reduced and changes in brain softness (reduced μ and |G*|) predominate those of viscosity (α and φ) in PD

Pathophysiology of normal pressure hydrocephalus

Normal pressure hydrocephalus (NPH), a CSF circulation disorder, is important as a reversible cause of gait and cognitive disturbance in an aging population. The inconsistent response to CSF shunting is usually attributed to difficulties in differential diagnosis or co-morbidity. Improving outcome depends on an increased understanding of the pathophysiology of NPH. Specifically, this thesis examines the contribution of, and inter-relationship between, the brain parenchyma and CSF circulation in the pathophysiology of NPH. Of the four core studies of the thesis, the first quantifies the characteristics of the CSF circulation and parenchyma in NPH using CSF infusion studies to measure the resistance to CSF absorption and brain compliance. The second study assesses cerebral blood flow (CBF) was using O15-labelled positron emission tomography (PET) with MR co-registration. By performing CSF infusion studies in the PET scanner, CBF at baseline CSF pressure and at a higher equilibrium pressure is measured. Regional changes and autoregulatory capacity are assessed. The final study examines the microstructural integrity of the parenchyma using MR diffusion tensor imaging. These studies confirm the importance of the inter-relationship of the brain parenchyma and CSF circulation. NPH symptomatology and its relationship to the observed regional CBF reductions in the basal ganglia and thalamus are discussed. Regional CBF reductions with increased CSF pressure and the implications for autoregulatory capacity in NPH are considered. The reduction in CBF when CSF was increased was most striking in the periventricular regions. In addition, periventricular structures demonstrated increased diffusivity and decreased anisotropy. The relationship between these changes and mechanisms such as transependymal CSF passage are reviewed. The findings of this thesis support a role of both the CSF circulation and the brain parenchyma in the pathophysiology of NPH. The results have implications for the approach to the management of patients with NPH

Arterial Spin-Labeling Perfusion Metrics in Pediatric Posterior Fossa Tumor Surgery

BACKGROUND AND PURPOSE: Pediatric posterior fossa tumors often present with hydrocephalus; postoperatively, up to 25% of patients develop cerebellar mutism syndrome. Arterial spin-labeling is a noninvasive means of quantifying CBF and bolus arrival time. The aim of this study was to investigate how changes in perfusion metrics in children with posterior fossa tumors are modulated by cerebellar mutism syndrome and hydrocephalus requiring pre-resection CSF diversion. MATERIALS AND METHODS: Forty-four patients were prospectively scanned at 3 time points (preoperatively, postoperatively, and at 3-month follow-up) with single- and multi-inflow time arterial spin-labeling sequences. Regional analyses of CBF and bolus arrival time were conducted using coregistered anatomic parcellations. ANOVA and multivariable, linear mixed-effects modeling analysis approaches were used. The study was registered at clinicaltrials.gov (NCT03471026). RESULTS: CBF increased after tumor resection and at follow-up scanning (P = .045). Bolus arrival time decreased after tumor resection and at follow-up scanning (P = .018). Bolus arrival time was prolonged (P = .058) following the midline approach, compared with cerebellar hemispheric surgical approaches to posterior fossa tumors. Multivariable linear mixed-effects modeling showed that regional perfusion changes were more pronounced in the 6 children who presented with symptomatic obstructive hydrocephalus requiring pre-resection CSF diversion, with hydrocephalus lowering the baseline mean CBF by 20.5 (standard error, 6.27) mL/100g/min. Children diagnosed with cerebellar mutism syndrome (8/44, 18.2%) had significantly higher CBF at follow-up imaging than those who were not (P = .040), but no differences in pre- or postoperative perfusion parameters were seen. CONCLUSIONS: Multi-inflow time arterial spin-labeling shows promise as a noninvasive tool to evaluate cerebral perfusion in the setting of pediatric obstructive hydrocephalus and demonstrates increased CBF following resolution of cerebellar mutism syndrome

New Mechanics of Traumatic Brain Injury

The prediction and prevention of traumatic brain injury is a very important aspect of preventive medical science. This paper proposes a new coupled loading-rate hypothesis for the traumatic brain injury (TBI), which states that the main cause of the TBI is an external Euclidean jolt, or SE(3)-jolt, an impulsive loading that strikes the head in several coupled degrees-of-freedom simultaneously. To show this, based on the previously defined covariant force law, we formulate the coupled Newton-Euler dynamics of brain's micro-motions within the cerebrospinal fluid and derive from it the coupled SE(3)-jolt dynamics. The SE(3)-jolt is a cause of the TBI in two forms of brain's rapid discontinuous deformations: translational dislocations and rotational disclinations. Brain's dislocations and disclinations, caused by the SE(3)-jolt, are described using the Cosserat multipolar viscoelastic continuum brain model. Keywords: Traumatic brain injuries, coupled loading-rate hypothesis, Euclidean jolt, coupled Newton-Euler dynamics, brain's dislocations and disclinationsComment: 18 pages, 1 figure, Late

Pathophysiology of normal pressure hydrocephalus

Normal pressure hydrocephalus (NPH), a CSF circulation disorder, is important as a reversible cause of gait and cognitive disturbance in an aging population. The inconsistent response to CSF shunting is usually attributed to difficulties in differential diagnosis or co-morbidity. Improving outcome depends on an increased understanding of the pathophysiology of NPH. Specifically, this thesis examines the contribution of, and inter-relationship between, the brain parenchyma and CSF circulation in the pathophysiology of NPH. Of the four core studies of the thesis, the first quantifies the characteristics of the CSF circulation and parenchyma in NPH using CSF infusion studies to measure the resistance to CSF absorption and brain compliance. The second study assesses cerebral blood flow (CBF) was using O15-labelled positron emission tomography (PET) with MR co-registration. By performing CSF infusion studies in the PET scanner, CBF at baseline CSF pressure and at a higher equilibrium pressure is measured. Regional changes and autoregulatory capacity are assessed. The final study examines the microstructural integrity of the parenchyma using MR diffusion tensor imaging. These studies confirm the importance of the inter-relationship of the brain parenchyma and CSF circulation. NPH symptomatology and its relationship to the observed regional CBF reductions in the basal ganglia and thalamus are discussed. Regional CBF reductions with increased CSF pressure and the implications for autoregulatory capacity in NPH are considered. The reduction in CBF when CSF was increased was most striking in the periventricular regions. In addition, periventricular structures demonstrated increased diffusivity and decreased anisotropy. The relationship between these changes and mechanisms such as transependymal CSF passage are reviewed. The findings of this thesis support a role of both the CSF circulation and the brain parenchyma in the pathophysiology of NPH. The results have implications for the approach to the management of patients with NPH

Cerebrospinal Fluid Pulsations and Aging Effects in Mathematical Models of Hydrocephalus

In this Thesis we develop mathematical models to analyze two proposed causative mechanisms for the ventricular expansion observed in hydrocephalus: cerebrospinal fluid pulsations and small transmantle pressure gradients. To begin, we describe a single compartment model and show that such simple one-dimensional models cannot represent the complex dynamics of the brain. Hence, all subsequent models of this Thesis are spatio-temporal. Next, we develop a poroelastic model to analyze the fluid-solid interactions caused by the pulsations. Periodic boundary conditions are applied and the system is solved analytically for the tissue displacement, pore pressure, and fluid filtration. The model demonstrates that fluid oscillates across the brain boundaries. We develop a pore flow model to determine the shear induced on a cell by this fluid flow, and a comparison with data indicates that these shear forces are negligible. Thus, only the material stresses remain as a possible mechanism for tissue damage and ventricular expansion. In order to analyze the material stresses caused by the pulsations, we develop a fractional order viscoelastic model based on the linear Zener model. Boundary conditions appropriate for infants and adults are applied and the tissue displacement and stresses are solved analytically. A comparison of the tissue stresses to tension data indicates that these stresses are insufficient to cause tissue damage and thus ventricular expansion. Using age-dependent data, we then determine the fractional Zener model parameter values for infant and adult cerebra. The predictions for displacement and stresses are recomputed and the infant displacement is found to be unphysical. We propose a new infant boundary condition which reduces the tissue displacement to a physically reasonable value. The model stresses, however, are unchanged and thus the pulsation-induced stresses remain insufficient to cause tissue damage and ventricular expansion. Lastly, we develop a fractional hyper-viscoelastic model, based on the Kelvin- Voigt model, to obtain large deformation predictions. Using boundary conditions and parameter values for infants, we determine the finite deformation caused by a small pressure gradient by summing the small strain deformation resulting from pressure gradient increments. This iterative technique predicts that pediatric hydrocephalus may be caused by the long-term existence of small transmantle pressure gradients. We conclude the Thesis with a discussion of the results and their implications for hydrocephalus research as well as a discussion of future endeavors

A multiple-network poroelastic model for biological systems and application to subject-specific modelling of cerebral fluid transport

Biological tissue can be viewed as porous, permeable and deformable media infiltrated by fluids, such as blood and interstitial fluid. A finite element model has been developed based on the multiple-network poroelastic theory to investigate transport phenomenon in such biological systems. The governing equations and boundary conditions are adapted for the cerebral environment as an example. The numerical model is verified against analytical solutions of classical consolidation problems and validated using experimental data of infusion tests. It is then applied to three-dimensional subject-specific modelling of brain, including anatomically realistic geometry, personalised permeability map and arterial blood supply to the brain. Numerical results of smoking and non-smoking subjects show hypoperfusion in the brains of smoking subjects, which also demonstrate that the numerical model is capable of capturing spatio-temporal fluid transport in biological systems across different scales