**
Kent-Andre Mardal, Professor in Mechanics, Department of Mathematics,
University of Oslo
and
Adjunct Research Scientist,
Simula Research Laboratory
E-mail:
kent-and@math.uio.no,
kent-and@simula.no
**

- Biomechanics of the Brain
- Aging Brain, Dementia
- Interstitial fluid flow, glymphatic system
- Stroke caused by aneurysms
- The Chiari malformation and syringomyelia
- Partial Differential Equations
- Finite Element Methods
- Fluid and Solid mechanics
- Scientific Software and Scripting, in particular FEniCS
- Preconditioning, Multigrid and High-Performance Computing

For cerebrospinal fluid flow we have considered Chiari in idealized models in [AJNR 2010], [AJNR 2010], [AJNR 2011], craniovertebral decompression [J Neurosurgery], exercise [AJNR 2013], and patient-specific modelling in [AJNR 2012], [Plos One 2016], transitional/turbulent effects in [J Biomech 2014], [J Numer Method Biomed Eng 2017] and drug dispersion in [Plos One 2017]. The interstitial fluid flow in the poro-elastic cord was studied in [Comput Methods Biomech Biomed Engin 2016].

My research on the glymphatic system concerns the insterstitial fluid flow which appears to be dominated by diffusion, [PNAS 2017] even though on a macroscale the clearance seem to happen faster than diffusion, [JCI Insight 2018]. Furthermore, the traditional view of the 3. circulation where CSF is produced in the Choroid Plexus is challenged by PC-MRI findings in [NeuroImage 2018]. Appropriate numerical methods are proposed in [arXiv 2018] for multiple-network poroelasticity simulations.

I have been working with blood flow in cerebral aneurysms, the flow of cerebrospinal fluid that surrounds the central nervous system and the interstitial fluid flow in the extracellular matrix. Crucial for these applications is the development of personalized computational models. For the cerebral aneurysms we have considered nonlinear rheology in [J Biomech 2013], turbulence/transitional effects in [J Biomech 2011], [J Biomech 2013], with a proper DNS in [Computers&Fluids 2016] , and the sensitivity of numerical resolution wrt common risk indicators in [Plos One 2017], comparison with 4D PC-MR in [Med Phys 2011] and [Med Phys 2016] and inverse modelling based on 4D PC-MR in [arXiv 2016].

Already in my PhD, the concept of

Schemes for multi-physics and multi-scale problems can lead to fractional differential equations. 2D-1D or 3D-2D couplings were considered in [SISC 2016] and corressponding 3D-1D schemes in [NMPDE 2018]. Multilevel schemes are proposed in [arXiv 2018].

My research on software was earlier related to Diffpack, but from 2007 and onwards I have been working with FEniCS". In the early days, I worked with several core components Symbolic computations and code generation, UFC, Trilinos, assembly and the Python interface, see the book. Nowadays, I work more with applications and a main topic is now to interface FEniCS with FreeSurfer, a widely used software framework in neuroscience.

In the book chapter we considered the mathematics of zombies and demonstrated that most zombie movies are not really realistic.

Finally, in the paper we considered methods for assessing the cosmic background radiation.

A full list of publications can be found in my CV.