Our new preprint on Uncertainty quantification of parenchymal tracer distribution using random diffusion and convective velocity fields is now out on bioRxiv! My first time submitting to bioRxiv rather than good old arXiv.
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Over the last decade, there has been a significant renewed interest in the waterscape of the brain; that is, the physiological mechanisms governing cerebrospinal fluid (CSF) and interstitial fluid (ISF) flow in (and around) the brain. A number of new theories have emerged, but a great deal of uncertainty relating to the roles of diffusion, convection and clearance within the brain remains. With this study, we aimed to rigorously quantify how the aforementioned uncertainties in the physiological parameters and in ISF flow affect the spread of a tracer into the brain. We assumed movement of tracer in the brain to occur by diffusion and/or convection. To account for uncertainty and variability, we circumvented the lack of precise parameter values by modelling velocity and diffusivity as Matérn stochastic fields. We then set up a PDE model with these stochastic (random) fields as coefficients and quantify the uncertainty in the model prediction via the Monte Carlo (MC) method.
I have finally updated my laptop from the arcane Ubuntu 16.04 to 18.04. First thing to configure: fluxbox :heart: of course. Second, xterm and emacs font, size and color. And third, custom FEniCS installation! Very easy this time around, but recording it here for future reference:
# Install curl
sudo apt install curl
# Download FEniCS project script
curl -s https://get.fenicsproject.org | bash
# fenicsproject script is installed as /foo/.local/bin/fenicsproject
# Add to e.g. .bashrc:
# export PATH=/foo/.local/bin/fenicsproject:$PATH
# Check that you are using the expected version of fenicsproject, by
# examining output of
# Ready to go!
Our paper on Fluid dynamics in syringomyelia cavities: Effects of heart rate, CSF velocity, CSF velocity waveform and craniovertebral decompression was published earlier this fall in The Neuroradiology Journal.
How fluid moves during the cardiac cycle within a syrinx (a fluid-filled cyst in the spinal cord) may affect its development. We measured syrinx fluid velocities before and after craniovertebral decompression in a patient and simulated syrinx fluid velocities for different heart rates, syrinx sizes and cerebrospinal fluid (CSF) flow velocities in a model of syringomyelia. With phase-contrast magnetic resonance we measured CSF and syrinx fluid velocities in a Chiari patient before and after craniovertebral decompression. With an idealized two-dimensional model of the subarachnoid space (SAS), cord and syrinx, we simulated fluid movement in the SAS and syrinx with the Navier-Stokes equations for different heart rates, inlet velocities and syrinx diameters. In the patient, fluid oscillated in the syrinx at 200 to 210 cycles per minute before and after craniovertebral decompression. Velocities peaked at 3.6 and 2.0 cm per second respectively in the SAS and the syrinx before surgery and at 2.7 and 1.5 cm per second after surgery. In the model, syrinx velocity varied between 0.91 and 12.70 cm per second. Increasing CSF inlet velocities from 1.56 to 4.69 cm per second increased peak syrinx fluid velocities in the syrinx by 151% to 299% for the three cycle rates. Increasing cycle rates from 60 to 120 cpm increased peak syrinx velocities by 160% to 312% for the three inlet velocities. Peak velocities changed inconsistently with syrinx size. In conclusion, CSF velocity, heart rate and syrinx diameter affect syrinx fluid velocities, but not the frequency of syrinx fluid oscillation. Craniovertebral decompression decreases both CSF and syrinx fluid velocities.
Our new paper on A mixed finite element method for nearly incompressible multiple-network poroelasticity is now available on arXiv!
In this paper, we present and analyze a new mixed finite element formulation of a general family of quasi-static multiple-network poroelasticity (MPET) equations. The MPET equations describe flow and deformation in an elastic porous medium that is permeated by multiple fluid networks of differing characteristics. As such, the MPET equations represent a generalization of Biot’s equations, and numerical discretizations of the MPET equations face similar challenges. Here, we focus on the nearly incompressible case for which standard mixed finite element discretizations of the MPET equations perform poorly. Instead, we propose a new mixed finite element formulation based on introducing an additional total pressure variable. By presenting energy estimates for the continuous solutions and a priori error estimates for a family of compatible semi-discretizations, we show that this formulation is robust in the limits of incompressibility, vanishing storage coefficients, and vanishing transfer between networks. These theoretical results are corroborated by numerical experiments. Our primary interest in the MPET equations stems from the use of these equations in modelling interactions between biological fluids and tissues in physiological settings. So, we additionally present physiologically realistic numerical results for blood and tissue fluid flow interactions in the human brain.
Congratulations to Cécile Daversin-Catty for winning the Best postdoctoral presentation award at the FEniCS’18 conference at the University of Oxford from March 21-23 2018! Cécile, postdoctoral fellow with the Waterscales project, presented her exciting and versatile work on mixed-dimensional coupled finite elements in FEniCS.
Overall, the Waterscales and Waterscape projects were well represented in the FEniCS’18 program with additional talks from Waterscape post doc Travis Thompson (on Stokes-Biot stable H(div)-based mixed finite element methods for generalized poroelasticity), from SUURPh PhD candidate Eleonora Piersanti (on Parameter-robust discretization and preconditioning of the multiple-network poroelasticity equations), and a poster presentation from Waterscales PhD candidate Ada Ellingsrud (on Numerical modelling of the role of glial cells in cerebral interstitial fluid movement). Well done Waterscapers!
Our new paper on Efficient white noise sampling and coupling for multilevel Monte Carlo with non-nested meshes is now available on arXiv!
When solving stochastic partial differential equations (SPDEs) driven by additive spatial white noise, the efficient sampling of white noise realizations can be challenging. In this paper, we present a new sampling technique that can be used to efficiently compute white noise samples in a finite element method and multilevel Monte Carlo (MLMC) setting. The key idea is to exploit the finite element matrix assembly procedure and factorize each local mass matrix independently, hence avoiding the factorization of a large matrix. Moreover, in a MLMC framework, the white noise samples must be coupled between subsequent levels. We show how our technique can be used to enforce this coupling even in the case of non-nested mesh hierarchies. We demonstrate the efficacy of our method with numerical experiments. We observe optimal convergence rates for the finite element solution of the elliptic SPDEs of interest in 2D and 3D and we show convergence of the sampled field covariances. In a MLMC setting, a good coupling is enforced and the telescoping sum is respected.
This week I’ve been in Odense for a PhD defense (Congratulations to Dr. Christian Valdemar Hansen!), while today I am giving at a talk at Nansensenteret i Bergen for a meeting organized by Norges Tekniske Vitenskapsakademi and Tekna. I will talk about the brain’s waterscape/Hjernens vannveier, of course. This presentation targets a semi-academic, semi-technical audience and the slides are publicly available.
Our new paper on Uncertainty in cardiac myofiber orientation and stiffnesses dominate the variability of left ventricle deformation response is now available on arxiv!
Computational cardiac modelling is currently evolving from a pure research tool to aiding in clinical decision making. Assessing the reliability of computational model predictions is a key factor for clinical use, and uncertainty quantification (UQ) and sensitivity analysis are important parts of such an assessment. In this study, we apply new methods for UQ in computational heart mechanics to study uncertainty both in material parameters characterizing global myocardial stiffness and in the local muscle fiber orientation that governs tissue anisotropy. The uncertainty analysis is performed using the polynomial chaos expansion (PCE) method, which is a non-intrusive meta-modeling technique that surrogates the original computational model with a series of orthonormal polynomials over the random input parameter space. In addition, in order to study variability in the muscle fiber architecture, we model the uncertainty in orientation of the fiber field as an approximated random field using a truncated Karhunen-Loéve expansion. The results from the UQ and sensitivity analysis identify clear differences in the impact of various material parameters on global output quantities. Furthermore, our analysis of random field variations in the fiber architecture demonstrate a substantial impact of fiber angle variations on the selected outputs, highlighting the need for accurate assignment of fiber orientation in computational heart mechanics models.
Congratulations to Ada Ellingsrud for winning the Best Poster Award at last week’s 3rd Human Brain Project School on Future Neuroscience! Ada, PhD candidate with the Waterscales project, presented her exciting research plan on developing computational models of astrocyte water dynamics to explore how osmotic pressure and microscopic fluid flow impact movement of metabolic waste and solutes in the parenchyma. Her poster is available on figshare: Modelling the role of glial cells in cerebral interstitial fluid movement .