Cerebral Fluid Flow

This is one of two conversations which Gudrun Thäter recorded
alongside the conference Women in PDEs which took place at our
faculty in Karlsruhe on 27-28 April 2017. Marie Elisabeth Rognes
was one of the seven invited speakers.


Marie is Chief Research Scientist at the Norwegian research
laboratory Simula near Oslo. She is Head of department for
Biomedical Computing there. Marie got her university education
with a focus on Applied Mathematics, Mechanics and Numerical
Physics as well as her PhD in Applied mathematics at the Centre
for Mathematics for Applications in the Department of Mathematics
at the University of Oslo.


Her work is devoted to providing robust methods to solve Partial
Differential Equations (PDEs) for diverse applications. On the
one hand this means that from the mathematical side she works on
numerical analysis, optimal control, robust Finite Element
software as well as Uncertainty quantification while on the other
hand she is very much interested in the modeling with the help of
PDEs and in particular Mathematical models of physiological
processes. These models are useful to answer What if
type-questions much more easily than with the help of laboratory
experiments.


In our conversation we discussed one of the many applications -
Cerebral fluid flow, i.e. fluid flow in the context of the human
brain.


Medical doctors and biologists know that the soft matter cells of
the human brain are filled with fluid. Also the space between the
cells contains the water-like cerebrospinal fluid. It provides a
bath for human brain. The brain expands and contracts with each
heartbeat and appoximately 1 ml of fluid is interchanged between
brain and spinal area. What the specialists do not know is: Is
there a circulation of fluid? This is especially interesting
since there is no traditional lymphatic system to transport away
the biological waste of the brain (this process is at work
everywhere else in our body). So how does the brain get rid of
its litter? There are several hyotheses:


Diffusion processes,

Fast flow (and transport) along the space near blood vessel,

Convection.



The aim of Marie's work is to numerically test these (and other)
hypotheses. Basic testing starts on very idalised geometries. For
the overall picture one useful simplified geometry is the annulus
i.e. a region bounded by two concentric circles. For the
microlevel-look a small cube can be the chosen geometry.


As material law the flow in a porous medium which is based on
Darcy flow is the starting point - maybe taking into account the
coupling with an elastic behaviour on the boundary.


The difficult non-mathematical questions which have to be
answered are:


How to use clinical data for estabilishing and testing models

How to prescribe the forces



In the near future she hopes to better understand the multiscale
character of the processes. Here especially for embedding 1d-
into 3d-geometry there is almost no theory available.


For the project Marie has been awarded a FRIPRO Young Research
Talents Grant of the Research Council of Norway (3 years -
starting April 2016) and the very prestegious ERC Starting Grant
(5 years starting - 2017).
References

M.E. Rognes: Mathematics that cures us.TEDxOslo 3 May 2017

Young academy of Norway

ERC Starting Grant: Mathematical and computational
foundations for modeling cerebral fluid flow 5 years

P.E. Farrell e.a.: Dolfin adjoint (Open source software
project)

FEniCS computing platform for PDEs (Open source software
project)

Wikipedia on FEniCS

Collection of relevant literature implemented in FEniCS