# Kent-Andre Mardal

## Adjunct Chief Research Scientist

- Department
- Numerical Analysis and Scientific Computing
- Organisation
- Simula Research Laboratory

- kent-and@simula.no

## Publications

### 2023

#### Journal Articles

T. Koch, V. Vinje and K. Mardal

Estimates for the astrocyte endfoot sheath permeability of the extra-cellular pathway

biorxiv

V. Vinje, B. Zapf, G. Ringstad, P. K. Eide, M. E. Rognes and K. Mardal

Human brain solute transport quantified by glymphatic MRI-informed biophysics during sleep and sleep deprivation

bioRxiv

L. Bojarskaite, A. Vallet, D. M. Bjørnstad, K. M. G. Binder, C. Cunen, K. Heuser, M. Kuchta, K. Mardal and R. Enger

Sleep cycle-dependent vascular dynamics in male mice and the predicted effects on perivascular cerebrospinal fluid flow and solute transport

Nature Communications

A. Budisa, X. Hu, M. Kuchta, K. Mardal and L. T. Zikatanov

Algebraic multigrid methods for metric-perturbed coupled problems

SIAM J. Sci. Comput.

K. Mardal

notifi tests

Global conf

B. Gomez-Vargas, K. Mardal, R. Ruiz-Baier and V. Vinje

Twofold saddle-point formulation of Biot poroelasticity with stress-dependent diffusion

SIAM J. of Numerical Analysis

T. Koch, V. Vinje and K. Mardal

Estimates for the astrocyte endfoot sheath permeability of the extra-cellular pathway

Fluids and Barriers of the CNS

V. Vinje, B. Zapf, G. Ringstad, P. K. Eide, M. E. Rognes and K. Mardal

Human brain solute transport quantified by glymphatic MRI-informed biophysics during sleep and sleep deprivation

Fluids and Barriers of the Central Nervous System

J. E. Schreiner, U. Kessler, K. J. Oedegaard, K. Mardal and L. Oltedal

Exploring New Electroencephalogram Parameters in Electroconvulsive Therapy

The Journal of ECT

#### Proceedings, refereed

A. Budisa, X. Hu, M. Kuchta, K. Mardal and L. T. Zikatanov

Rational approximation preconditioners for multiphysics problems

Numerical Methods and Applications (NMA 2022)

### 2022

#### Books

K. Mardal, M. E. Rognes, T. B. Thompson and L. M. Valnes

Mathematical modeling of the human brain: from magnetic resonance images to finite element simulation

Simula SpringerBriefs on Computing

#### Journal Articles

K. Mardal, J. Sogn and S. Takacs

Robust Preconditioning and Error Estimates for Optimal Control of the Convection--Diffusion--Reaction Equation with Limited Observation in Isogeometric Analysis

SIAM Journal on Numerical Analysis

M. Hornkjøl, L. M. Valnes, G. A. Ringstad, M. E. Rognes, P. K. Eide, K. Mardal and V. Vinje

CSF circulation and dispersion yield rapid clearance from intracranial compartments

Frontiers in Bioengineering and Biotechnology

J. Schreiner and K. Mardal

Simulating epileptic seizures using the bidomain model

Scientific Reports

W. M. Boon, M. Hornkjøl, M. Kuchta, K. Mardal and R. Ruiz-Baier

Parameter-robust methods for the Biot–Stokes interfacial coupling without Lagrange multipliers

Journal of Computational Physics

T. Bohr, P. G. Hjorth, S. C. Holst, S. Hrabětová, V. Kiviniemi, T. Lilius, I. Lundgaard, K. Mardal, E. A. Martens, Y. Mori, V. Nägerl, C. Nicholson, A. Tannenbaum, J. H. Thomas, J. Tithof, H. Benveniste, J. J. Iliff, D. H. Kelley and M. Nedergaard

The glymphatic system: Current understanding and modeling

iScience

B. Zapf, J. Haubner, M. Kuchta, G. Ringstad, P. K. Eide and K. Mardal

Investigating molecular transport in the human brain from MRI with physics-informed neural networks

Scientific Reports

W. M. Boon, T. Koch, M. Kuchta and K. Mardal

Robust Monolithic Solvers for the Stokes--Darcy Problem with the Darcy Equation in Primal Form

SIAM Journal on Scientific Computing

A. Budisa, X. Hu, M. Kuchta, K. Mardal and L. T. Zikatanov

HAZniCS – Software Components for Multiphysics Problems

ACM Transactions on Mathematical Software

M. Kuchta, S. G. Wubshet, N. K. Afseth, K. Mardal and K. H. Liland

Encoder–decoder neural networks for predicting future

Journal of Biophotonics

L. Bojarskaite, D. M. Bjørnstad, A. Vallet, K. M. G. Binder, C. Cunen, K. Heuser, M. Kuchta, K. Mardal and R. Enger

Sleep cycle-dependent vascular dynamics enhance perivascular cerebrospinal fluid flow and solute transport

bioRxiv

Q. Hong, J. Kraus, M. Kuchta, M. Lymbery, K. Mardal and M. E. Rognes

Robust approximation of generalized Biot-Brinkman problems

Journal on Scientific Computing

B. Gomez-Vargas, K. Mardal, R. Ruiz-Baier and V. Vinje

Twofold saddle-point formulation of Biot poroelasticity with stress-dependent diffusion

arXiv

#### Talks, contributed

M. Kuchta, W. M. Boon, T. Koch, K. Mardal and R. Ruiz-Baier

Parameter-robust monolithic solvers for coupled Biot/Darcy-Stokes models

27th International Domain Decomposition Conference, DD27

C. Daversin-Catty, V. Vinje, I. Gjerde, K. Mardal and M. E. Rognes

Modeling fluid flow in perivascular networks

ECCOMAS22, Oslo (Norway)

#### Talks, invited

M. Kuchta

Parameter-robust monolithic solvers for Stokes-Darcy/Biot systems

The 8th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS), Oslo, Norway

M. Kuchta, W. M. Boon, K. E. Holter, M. Hornkjøl, T. Koch, K. Mardal and R. Ruiz-Baier

Fractional operators in coupled multiphysics problems with implicit coupling

Numerical Solution of Fractional Differential Equations and Applications NSFDE&A’22

M. Kuchta, W. M. Boon, M. Hornkjøl, T. Koch, K. Mardal and R. Ruiz-Baier

Parameter-robust Methods for Biot-Stokes and Darcy-Stokes Interfacial Coupling without Lagrange Multipliers

15th World Congress on Computation Mechanics

M. Kuchta, A. Budisa, X. Hu, L. T. Zikatanov and K. Mardal

Fractional Laplacians and Hybridized DG

Simula's Workshop on computational mechanics models on domains of heterogeneous dimensionality, Split, Croatia

### 2021

#### Book Chapters

A. J. Ellingsrud, C. Daversin-Catty and M. E. Rognes

A cell-based model for ionic electrodiffusion in excitable tissue

Modeling Excitable Tissue: The EMI Framework

K. H. Jæger, K. G. Hustad, X. Cai and A. Tveito

Operator Splitting and Finite Difference Schemes for Solving the EMI Model

Modeling Excitable Tissue: The EMI Framework

K. H. Jæger and A. Tveito

Derivation of a Cell-Based Mathematical Model of Excitable Cells

Modeling Excitable Tissue: The EMI Framework

Å. Telle, S. Wall and J. Sundnes

Modeling Cardiac Mechanics on a Sub-Cellular Scale

Modeling Excitable Tissue: The EMI Framework

M. Kuchta and K. Mardal

Iterative Solvers for EMI Models

Modeling Excitable Tissue: The EMI Framework

A. P. Buccino, M. Kuchta, J. Schreiner and K. Mardal

Improving Neural Simulations with the EMI Model

Modeling Excitable Tissue: The EMI Framework

M. Kuchta, K. Mardal and M. E. Rognes

Solving the EMI Equations using Finite Element Methods

Modeling Excitable Tissue: The EMI Framework

#### Edited books

Modeling Excitable Tissue: The EMI Framework

#### Journal Articles

M. Kuchta, F. Laurino, K. Mardal and P. Zunino

Analysis and approximation of mixed-dimensional PDEs on 3D-1D domains coupled with Lagrange multipliers

SIAM Journal on Numerical Analysis

W. M. Boon, M. Kuchta, K. Mardal and R. Ruiz-Baier

Robust Preconditioners for Perturbed Saddle-Point Problems and Conservative Discretizations of Biot's Equations Utilizing Total Pressure

SIAM Journal on Scientific Computing

P. K. Eide, L. M. Valnes, E. K. Lindstrøm, K. Mardal and G. Ringstad

Direction and magnitude of cerebrospinal fluid flow vary substantially across central nervous system diseases

Fluids and Barriers of the CNS

B. A. Young, J. Adams, J. M. Beary, K. Mardal, R. Schneider and T. Kondrashova

Variations in the cerebrospinal fluid dynamics of the American alligator (Alligator mississippiensis)

Fluids and Barriers of the CNS

E. Piersanti, J. J. Lee, K. Mardal, M. E. Rognes and T. Thompson

Parameter robust preconditioning by congruence for multiple-network poroelasticity

SIAM Journal of Scientific Computing

K. Mardal, M. E. Rognes and T. Thompson

Accurate discretization of poroelasticity without Darcy stability – Stokes-Biot revisited

BIT Numerical Mathematics

P. K. Eide, V. Vinje, A. H. Pripp, K. Mardal and G. A. Ringstad

Sleep deprivation impairs molecular clearance from the human brain

Brain

#### Proceedings, refereed

E. Piersanti, M. E. Rognes and K. Mardal

Parameter robust preconditioning for multi-compartmental Darcy equations

Numerical Mathematics and Advanced Applications ENUMATH 2019

#### Talks, invited

C. Daversin-Catty, I. Gjerde, K. Mardal, M. E. Rognes and V. Vinje

Modeling fluid flow in perivascular networks

Oslo glymphatics symposium, Oslo (Norway)

### 2020

#### Journal Articles

T. Landet, K. Mardal and M. Mortensen

Slope limiting the velocity field in a discontinuous Galerkin divergence-free two-phase flow solver

Computers & Fluids

K. E. Holter, M. Kuchta and K. Mardal

Robust preconditioning for coupled Stokes–Darcy problems with the Darcy problem in primal form

Computers & Mathematics with Applications

W. M. Boon, M. Kuchta, K. Mardal and R. Ruiz-Baier

Robust preconditioners for perturbed saddle-point problems and conservative discretizations of Biot's equations utilizing total pressure

arXiv preprint arXiv:2011.05236

T. Bærland, M. Kuchta, K. Mardal and T. Thompson

An observation on the uniform preconditioners for the mixed Darcy problem

Numerical Methods for Partial Differential Equations

L. M. Valnes, S. Mitusch, G. Ringstad, P. K. Eide, S. W. Funke and K. Mardal

Apparent diffusion coefficient estimates based on 24 hours tracer movement support glymphatic transport in human cerebral cortex

Scientific Reports

V. Vinje, A. Eklund, K. Mardal, M. E. Rognes and K. Støverud

Intracranial pressure elevation alters CSF clearance pathways

Fluids and Barriers of the CNS

K. E. Holter, M. Kuchta and K. Mardal

Robust preconditioning of monolithically coupled multiphysics problems

arXiv preprint arXiv:2001.05527

A. H. Erhardt, K. Mardal and J. Schreiner

Dynamics of a neuron–glia system: the occurrence of seizures and the influence of electroconvulsive stimuli: A mathematical and numerical study

Journal of computational neuroscience

C. Daversin-Catty, V. Vinje, K. Mardal and M. E. Rognes

The mechanisms behind perivascular fluid flow

PLOS ONE

### 2019

#### Books

H. P. Langtangen and K. Mardal

Introduction to Numerical Methods for Variational Problems

#### Journal Articles

V. Vinje, G. A. Ringstad, E. K. Lindstrøm, L. M. Valnes, M. E. Rognes, P. K. Eide and K. Mardal

Respiratory influence on cerebrospinal fluid flow – a computational study based on long-term intracranial pressure measurements

Scientific Reports

J. Lee, E. Piersanti, K. Mardal and M. E. Rognes

A mixed finite element method for nearly incompressible multiple-network poroelasticity

SIAM Journal on Scientific Computing

T. Bærland, M. Kuchta and K. Mardal

Multigrid Methods for Discrete Fractional Sobolev Spaces

SIAM Journal on Scientific Computing

A. P. Buccino, M. Kuchta, K. H. Jæger, T. V. Ness, P. Berthet, K. Mardal, G. Cauwenberghs and A. Tveito

How does the presence of neural probes affect extracellular potentials?

Journal of Neural Engineering

P. K. Eide, L. M. Valnes, A. H. Pripp, K. Mardal and G. Ringstad

Delayed clearance of cerebrospinal fluid tracer from choroid plexus in idiopathic normal pressure hydrocephalus

Journal of Cerebral Blood Flow & Metabolism

T. Gergelits, K. Mardal, B. F. Nielsen and Z. Strakoš

Laplacian Preconditioning of Elliptic PDEs: Localization of the Eigenvalues of the Discretized Operator

SIAM Journal on Numerical Analysis

E. K. Lindstrøm, G. Ringstad, A. Sorteberg, W. Sorteberg, K. Mardal and P. K. Eide

Magnitude and direction of aqueductal cerebrospinal fluid flow: large variations in patients with intracranial aneurysms with or without a previous subarachnoid hemorrhage

Acta neurochirurgica

D. S. Seljebotn, T. Bærland, H. K. Eriksen, K. Mardal and I. K. Wehus

Multi-resolution Bayesian CMB component separation through Wiener filtering with a pseudo-inverse preconditioner

Astronomy & Astrophysics

M. Kuchta, K. Mardal and M. Mortensen

Preconditioning trace coupled 3D-1D systems using fractional Laplacian

Numerical Methods for Partial Differential Equations

M. Kuchta, K. Mardal and M. Mortensen

On the singular Neumann problem in linear elasticity

Numerical Linear Algebra with Applications

#### Miscellaneous

T. Bærland, M. Kuchta, K. Mardal and T. Thompson

An Observation On The Uniform Preconditioners For The Mixed Darcy Problem

#### Talks, contributed

M. Kuchta and K. Mardal

Robust preconditioners for multiphysics problems involving porous flow in physiology modeling

ICIAM 2019, Valencia, Spain

K. Mardal

Mathematical modeling of the g - lymphatic system – preconditioning of Darcy - Stokes systems

Biomechanics of living systems, Tøyen hovedgård, Norway

#### Proceedings, refereed

K. E. Holter, M. Kuchta and K. Mardal

Sub-voxel Perfusion Modeling in Terms of Coupled 3d-1d Problem

Numerical Mathematics and Advanced Applications ENUMATH 2017

#### Talks, keynote

M. Kuchta and K. Mardal

Robust Preconditioners for Multiscale Systems in Biomechanics

12th International Conference on Large-Scale Scientific Computations, Sozopol, Bulgaria

#### Talks, invited

V. Vinje, K. Støverud, M. E. Rognes, K. Mardal and A. Eklund

Intracranial pressure elevation alters CSF clearance pathways

The 2019 CSF Symposium, Oslo, Norway

K. Mardal

Preconditioning of multi-physics problems with applications to the biomechanics of the brain

MOX, Milan, Italy

K. Mardal

Mathematical modeling of the glymphatic system

ICIAM, Valencia, Spain

K. Mardal

Parameter Identification of Brain Cleaning

ICIAM, Valencia, Spain

K. Mardal

Mathematical modeling of the g-lymphatic system – preconditioning of Darcy - Stokes systems

IMG 2019, Kunming, China

K. Mardal

Preconditioning with some application to brain modeling

Symposium on the occasion of Ragnar Winther's 70th birthday, Oslo, Norway

### 2018

#### Journal Articles

E. K. Lindstrøm, J. Schreiner, G. Ringstad, V. Haughton, P. K. Eide and K. Mardal

Comparison of phase-contrast MR and flow simulations for the study of CSF dynamics in the cervical spine

The Neuroradiology Journal

P. K. Eide, A. Sorteberg, W. Sorteberg, E. K. Lindstrøm, K. Mardal and G. Ringstad

“Bucket” cerebrospinal fluid bulk flow: when the terrain disagrees with the map

Acta Neurochirurgica

E. K. Lindstrøm, G. Ringstad, A. Sorteberg, W. Sorteberg, K. Mardal and P. K. Eide

Magnitude and direction of aqueductal cerebrospinal fluid flow: large variations in patients with intracranial aneurysms with or without a previous subarachnoid hemorrhage

Acta Neurochirurgica

S. W. Funke, M. Nordaas, Ø. Evju, M. S. Alnæs and K. Mardal

Variational data assimilation for transient blood flow simulations

International Journal for Numerical Methods in Biomedical Engineering

V. Vinje

Fluid dynamics in syringomyelia cavities: Effects of heart rate, CSF velocity, CSF velocity waveform and craniovertebral decompression

The Neuroradiology Journal

G. Ringstad, L. M. Valnes, A. M. Dale, A. H. Pripp, S. S. Vatnehol, K. E. Emblem, K. Mardal and P. K. Eide

Brain-wide glymphatic enhancement and clearance in humans assessed with MRI

JCI insight

E. K. Lindstrøm, G. Ringstad, K. Mardal and P. K. Eide

Cerebrospinal fluid volumetric net flow rate and direction in idiopathic normal pressure hydrocephalus

NeuroImage: Clinical

K. Valen-Sendstad, A. Bergersen, Y. Shimogonya, L. Goubergrits, J. Bruening, J. Pallares, S. Cito, S. Piskin, K. Pekkan, A. J. Geers, I. Larrabide, S. Rapaka, V. Mihalef, W. Fu, A. Qiao, K. Jain, S. Roller, K. Mardal, R. Kamakoti, T. Spirka, N. Ashton, A. Revell, N. Aristokleous, G. Houston, M. Tsuji, F. Ishida, P. G. Menon, L. D. Browne, S. Broderick, M. Shojima, S. Koizumi, M. Barbour, A. Aliseda, H. G. Morales, T. Lefèvre, S. Hodis, Y. M. Al-Smadi, J. S. Tran, A. L. Marsden, S. Vaippummadhom, A. Einstein, A. G. Brown, K. Debus, K. Niizuma, S. Rashad, S. Sugiyama, O. M. Khan, A. R. Updegrove, S. C. Shadden, B. M. W. Cornelissen, C. B. L. M. Majoie, P. Ber, S. Saalfield, K. Kono and D. A. Steinmam

Real-World Variability in the Prediction of Intracranial Aneurysm Wall Shear Stress: The 2015 International Aneurysm CFD Challenge

Cardiovascular Engineering and Technology

#### Posters

V. Vinje

Respiratory influence on intracranial pressure gradients and aqueductal flow in normal pressure hydrocephalus

#### Talks, contributed

V. Vinje, J. Brucker, M. E. Rognes, K. Mardal and V. Haughton

Fluid dynamics in syringomyelia cavities

Vancouver, Canada

V. Vinje, G. A. Ringstad, M. E. Rognes, P. K. Eide and K. Mardal

The Influence of Breathing on Cerebrospinal Fluid Movement in the Brain

Glasgow, United Kingdom

T. Thompson and M. E. Rognes

A Stokes-Biot Stable H(div)-based mixed method for generalized poroelasticity

SIAM Life Sciences 2018, Minneapolis, Minnesota, USA

#### Talks, keynote

K. Mardal

Mathematical modeling of the glymphatic system – the physics of Alzheimer’s disease ?

Mathematical models in health sciences, Nantes, France

K. Mardal

Mathematical modeling of the glymphatic system – the physics of Alzheimer’s disease?

INdAM, Rome, Italy

#### Talks, invited

E. Piersanti, J. J. Lee, K. Mardal and M. E. Rognes

Parameter-robust discretization and preconditioning of multiple-network poroelasticity equations

Glasgow, UK

K. Mardal

Preconditioners for PDE constrained optimization problems (coarse observations, boundary control)

SIAM ALA, Hong Kong, China

E. Piersanti, J. J. Lee, K. Mardal and M. E. Rognes

Parameter-robust discretization and preconditioning of multiple-network poroelasticity equations

University of Oxford, UK

### 2017

#### Journal Articles

A. Tveito, K. H. Jæger, M. Kuchta, K. Mardal and M. E. Rognes

A cell-based framework for numerical modelling of electrical conduction in cardiac tissue

Frontiers in Physics, Computational Physics

K. E. Holter, B. Kehlet, A. Devor, T. J. Sejnowski, A. M. Dale, S. W. Omholt, O. P. Ottesen, E. A. Nagelhus, K. Mardal and K. H. Pettersen

Interstitial Solute Transport in 3D Reconstructed Neuropil Occurs by Diffusion Rather than Bulk Flow

Proceedings of the National Academy of Sciences

Ø. Evju, J. M. Pozo, A. Frangi and K. Mardal

Robustness of common hemodynamic indicators with respect to numerical resolution in 38 middle cerebral artery aneurysms.

PLoS ONE

G. Pizzichelli, B. Kehlet, Ø. Evju, B. Martin, M. E. Rognes, K. Mardal and E. Sinibaldi

Numerical study of intrathecal drug delivery to a permeable spinal cord: effect of catheter position and angle

Computer Methods in Biomechanics and Biomedical Engineering

J. Lee, K. Mardal and R. Winther

Parameter-robust discretization and preconditioning of Biot's consolidation model

SIAM Journal of Scientific Computing

P. T. Haga, G. Pizzichelli, M. Mortensen, M. Kuchta, S. H. Pahlavian, E. Sinibaldi, B. A. Martin and K. Mardal

A numerical investigation of intrathecal isobaric drug dispersion within the cervical subarachnoid space

PLoS ONE

G. Ringstad, E. Lindstrøm, S. A. Vatnehol, K. Mardal, K. Emblem and P. K. Eide

Non-invasive Assessment of Pulsatile Intracranial Pressure with Phase-Contrast Magnetic Resonance Imaging

PLoS ONE

#### Talks, contributed

E. Piersanti, J. J. Lee, K. Mardal and M. E. Rognes

Modelling pulsatility in the context of Normal-Pressure Hydrocephalus via multiple-network poroelasticity

5th International Conference on Computational and Mathematical Biomedical Engineering, Pittsburgh, US

#### Talks, keynote

K. Mardal, E. K. Lindstrøm and V. Haughton

Physics of oscillatory CSF Flow

ASSR, San Diego, USA

K. Mardal

Computational modeling of the glymphatic system: how is waste cleared from the brain?

Interpore 2017, Rotterdam, the Netherlands

K. Mardal

Computational modeling of the glymphatic system: how is waste cleared from the brain?

HPCSE 2017, Ostrava, Czech Republic

K. Mardal

The operator preconditioning framework with various applications to interstitial fluid flow and the aging human brain

Enumath, Voss, Norway

#### Talks, invited

K. Mardal, V. Frostlid, A. Jensen and K. Jain

Experimental investigation of transitional effects at low Reynolds number in blood vessels - X-ray, microphones and simulations

CMBE 2017, Pittsburgh, USA

K. Mardal, K. E. Holter and K. H. Pettersen

Simulating the fluid flow of the lymphatic system - extracellular fluid flow

The 4th CSF symposium, Atlanta, USA

V. Vinje

Is Respiration the main driver of CSF Flow?

International Convention Center, Kobe, Japan

V. Vinje, M. E. Rognes, K. Mardal and E. Piersanti

The Brain as a Poroelastic Medium - Simulating pulsatile motion and flow

Hamburg, Germany

K. Mardal

Coupling CSF flow, perfusion and glymphatics (?)

2nd Workshop on computational aspects of perfusion and flow in live tissue, Bergen, Norway

K. Mardal

Biographical note on biomedical applications

International Conference on Computational Science and Engineering, Oslo, Norway

K. Mardal

Blood flow in cerebral aneurysms, water flow clearance in Alzheimer and operator preconditioning

Prague, Czech Republic

### 2016

#### Book Chapters

W. Bradley, V. Haughton and K. Mardal

Cerebrospinal fluid flow in adults.

Handbook of clinical neurology

#### Journal Articles

M. Kuchta, M. Nordaas, J. C. G. Verschaeve, M. Mortensen and K. Mardal

Preconditioners for saddle point systems with trace constraints coupling 2D and 1D domains

SIAM Journal of Scientific Computing

K. Støverud, H. P. Langtangen, G. A. Ringstad, P. K. Eide and K. Mardal

Computational Investigation of Cerebrospinal Fluid Dynamics in the Posterior Cranial Fossa and Cervical Subarachnoid Space in Patients with Chiari I Malformation

PLOS ONE

K. Mardal, B. F. Nielsen and M. Nordaas

Robust preconditioners for PDE-constrained optimization with limited observations

BIT Numerical Mathematics

K. Jain, G. Ringstad, P. Eide and K. Mardal

Direct numerical simulations of transitional hydrodynamics of the cerebrospinal fluid in Chiari I malformation – the role of cranio-vertebral junction

International Journal for Numerical Methods in Biomedical Engineering

K. Jain, J. Jiang, C. Strother and K. Mardal

Transitional hemodynamics in intracranial aneurysms - Comparative velocity investigations with high resolution Lattice Boltzmann simulations, normal resolution ANSYS simulations and MR imaging

Medical Physics

R. Fric, E. K. Lindstrøm, G. Ringstad, K. Mardal and P. K. Eide

Association of pulse pressure gradient across cranio-cervical junction as derived from phase-contrast magnetic resonance imaging and invasively measured pulsatile intracranial pressure in symptomatic patients with Chiari malformation type 1

Acta Neurochirurgica

#### Talks, contributed

J. J. Lee, K. Mardal, E. Piersanti and M. E. Rognes

Modelling and simulation of viscous and poroelastic fluid flow in the brain

FEniCS16, Simula Research Laboratory

J. J. Lee, K. Mardal, E. Piersanti and M. E. Rognes

On accurate and efficient simulations of multiple-network poroelastic modelling with applications to interstitial fluid flow in the human brain

WCCM XII & APCOM VI, Seoul

V. Vinje, K. Mardal, V. Haughton and M. E. Rognes

Simulating Cerebrospinal Fluid Flow and Spinal Cord Movement Associated with Syringomyelia

Chalmers Institute of Technology

M. Kuchta

Solving singular problems. The right way.

FEniCS'16 Workshop, Simula Research Laboratory, Oslo, Norway

#### Talks, invited

K. Mardal

Overview of the modeling of water flow in and surrounding the central nervous system

Istituto Italiano di Tecnologia, Piza, Italy

K. Mardal

Brain & Water:computational modeling of the aging brain

MedViz conference, Bergen

K. Mardal, S. W. Funke, M. Nordaas, Ø. Evju and M. S. Alnæs

Variational data assimilation for blood flow simulations

MS at SIAM UQ, Zurich

K. Mardal, Ø. Evju, J. Soler and A. Frangi

Robustness of common hemodynamics indicators with respect to numerical resolution in 38 middle cerebral artery aneurysms

MS at WCCM16, Seoul

K. Mardal, V. Frostlid and A. Jensen

Experimental investigation of transitional effects at low Reynolds number in blood vessels: X-ray, Microphones and Simulations

EarthFlows Workshop, UiO, Oslo

K. Mardal

Poroelastic modeling of the central nervous system: Chiari and dementia

Workshop on modeling of flow in live tissue: Methodological interaction between geo and life-sciences, CMR, Fantoft, Bergen

### 2015

#### Book Chapters

Ø. Evju and K. Mardal

On the Assumption of Laminar Flow in Physiological Flows: Cerebral Aneurysms As an Illustrative Example

Modeling the Heart and the Circulatory System

#### Journal Articles

M. S. Alnæs, K. Mardal, S. J. Bakke and A. Sorteberg

Computational fluid dynamics evaluation of flow reversal treatment of giant basilar tip aneurysm

Interventional Neuroradiology

K. Støverud, M. S. Alnæs, H. P. Langtangen, V. Haughton and K. Mardal

Poro-elastic modeling of Syringomyelia – a systematic study of the effects of pia mater, central canal, median fissure, white and gray matter on pressure wave propagation and fluid movement within the cervical spinal cord

Computer Methods in Biomechanics and Biomedical Engineering

K. Jain, S. Roller and K. Mardal

Transitional flow in intracranial aneurysms–a space and time refinement study below the Kolmogorov scales using Lattice Boltzmann Method

Computers & Fluids

#### Talks, contributed

N. Kylstad, K. Mardal, V. Haughton and M. E. Rognes

Effect of Spinal Cord Viscoelasticity on Its Response to CSF Pressure Waves: a Computational Study

ASNR 53rd Annual Meeting & The Foundation of the ASNR Symposium 2015, April 25 – 30, Chicago, Illinois

M. Nordaas, K. Mardal and B. F. Nielsen

Robust preconditioners for PDE-constrained optmization with limited data

2015 SIAM CSE, Salt Lake City

K. Mardal

Computational modelling of the biomechanics in the central nervous system – Chiari and syringomyelia

Simula Research Laboratory, Oslo

#### Proceedings, refereed

M. Kuchta, K. Mardal and M. Mortensen

Characterization of the space of rigid motions in arbitrary domains

MekIT'15 8th National Conference on Computational Mechanics

M. Mortensen, M. Kuchta, K. Mardal and J. Verschaeve

BEND|P|Y: Python framework for computing bending of complex plate-beam systems

MekIT'15 8th National Conference on Computational Mechanics

K. Jain and K. Mardal

Exploring The Critical Reynolds Number For Transition In Intracranial Aneurysms–highly Resolved Simulations Below Kolmogorov Scales

4th International Conference on Computational and Mathematical Biomedical Engineering - CMBE2015

#### Talks, invited

K. Mardal

Computational modelling of the biomechanics in the central nervous system – Chiari and syringomyelia

Simpla meeting, Oslo

K. Mardal

Poroelastic modeling of Syringomyelia - the effects of pia mater, central canal, median fissure, white and grey matter on pressure wave propagation and fluid movement within the cervical spinal cord

International Hydrocephalus Imaging Working Group, Chicago

V. Haughton and K. Mardal

Role of CSF flow in the pathogenesis of Syringomyelia

ASNR 53rd Annual Meeting & The Foundation of the ASNR Symposium 2015, April 25 – 30, 2015; Chicago, Illinois

K. Mardal, K. Jain, K. Støverud, G. Ringstad and P. K. Eide

On the complexity of the Cerebrospinal fluid flow in the upper spinal column – is the assumption of laminar flow appropriate?

Cerebrospinal Fluid Dynamics Society Meeting, Amiens

K. Mardal

Computational modelling of the biomechanics in the central nervous system – Chiari and syringomyelia

Complex materials; Mathematical models and numerical methods, Oslo

K. Mardal

Flows in complex geometries such as blood vessels and the central nervous system

EarthFlows kick-off meeting, Oslo

### 2014

#### Journal Articles

V. Haughton and K. Mardal

Spinal Fluid Biomechanics and Imaging: an Update for Neuroradiologists

American Journal of Neuroradiology

S. Linge, K. Mardal, A. Helgeland, J. Heiss and V. Haughton

Effect of Cranio-Vertebral Decompression on CSF Dynamics in Chiari I Malformation Studied With Computational Fluid Dynamics

Journal of Neurosurgery

A. Helgeland, K. Mardal, V. Haughton and B. A. P. Reif

Numerical Simulations of the Pulsating Flow of Cerebrospinal Fluid Flow in the Cervical Spinal Canal of a Chiari Patient

Journal of Biomechanics

D. S. Seljebotn, K. Mardal, J. Jewell, H. K. Eriksen and P. Bull

A Multilevel Solver for Gaussian Constrained CMB Realizations

The Astrophysical Journal Supplement Series

#### Talks, keynote

K. Mardal

On the Modeling of the Central Nervous System in Chiari Patients - Transitional Flow, Poroelasticity and Porous-Viscus Flow Couplings

Gordon Conference on Flow & Transport in Permeable Media

M. Mortensen

Preliminary study of the impact of spinal cord nerve roots and denticulate ligaments on drug movement in the cervical spinal subarachnoid space

21 July, Barcelona, Spain

#### Talks, invited

K. Mardal, T. Seland, H. P. Langtangen and P. Røtnes

Er Zombier En Trussel Mot Menneskeheten?

Upop aften - Det norske student samfund

K. Mardal

On the Assumption of Laminar Flow in the Modeling of Physiological Flow

Anvendt og beregningsorientert matematikk, Bergen

K. Mardal, A. Helgeland, V. Haughton, B. A. P. Reif and K. Støverud

On the Assumption of Laminar Flow of CSF in Chiari Patients

international Chiari Research Group

K. Mardal, K. Støverud, G. Ringstad and P. K. Eide

CSF Flow at Foramen Magnum

International Hydrocephalus Imaging Working Group,Montreal, Canada

K. Mardal, O. M. Khan and K. Valen-Sendstad

On Numerical Methods for Transitional Flow - Application to Blood Flow in Aneurysms

Quality and Validation of Computational Cardio-vascular Biomechanics, WCCM-ECCM-ECCOM

K. Mardal, K. Støverud, M. Mortensen, K. Jain, B. Martin and S. Pahlavian

Cerebrospinal Fluid Flow in Association With the Central Nervous System - Chiari and Drug Delivery

MS on Computational Biomechanics, WCCM-ECCM-ECCOM

### 2013

#### Book Chapters

H. P. Langtangen, K. Mardal and P. Røtnes

Escaping the Zombie Threat by Mathematics

Zombies in the Academy: Living Death in Higher Education

#### Edited books

A. Logg, K. Mardal and A. Massing

Proceedings of the 26th Nordic Seminar on Computational Machanics

#### Journal Articles

K. Mardal, G. Rutkowska, S. Linge and V. Haughton

Estimation of CSF Flow Resistance in the Upper Cervical Spine

The Neuroradiology Journal

K. Støverud, H. P. Langtangen, V. Haughton and K. Mardal

CSF Pressure and Velocity in Obstructions of the Subarachnoid Spaces

The Neuroradiology Journal

S. Linge, K. Mardal, V. Haughton and A. Helgeland

Simulating CSF Flow Dynamics in the Normal and the Chiari I Subarachnoid Space During Rest and Exertion

American Journal of Neuroradiology

B. F. Nielsen and K. Mardal

Analysis of the Minimal Residual Method Applied to Ill-Posed Optimality Systems

SIAM Journal on Scientific Computing

K. Mardal, J. Schoberl and R. Winther

A Uniformly Stable Fortin Operator for the Taylor-Hood Element

Numerische Mathematik

Ø. Evju, K. Valen-Sendstad and K. Mardal

A Study of Wall Shear Stress in 12 Aneurysms With Respect to Different Viscosity Models and Flow Conditions

Journal of Biomechanics

K. Valen-Sendstad, K. Mardal and D. A. Steinman

High-Resolution Computational Fluid Dynamics Detects High-Frequency Velocity Fluctuations in Bifurcation, But Not Sidewall, Aneurysms of the Middle Cerebral Artery

Journal of Biomechanics

I. N. Drøsdal, K. Mardal, K. Støverud and V. Haughton

Effect of the Central Canal in the Spinal Cord on Fluid Movement Within the Cord

The Neuroradiology Journal

#### Manuals

K. Mardal and H. P. Langtangen

Combining FEniCS With Your Favorite Software in C, C++, Fortran, Or MATLAB

#### Talks, contributed

Ø. Evju, K. Mardal, S. J. Bakke and A. G. Sorteberg

Patient-Specific Simulations of Vasospasm in 3 Different Cases

Modelling Physiological Flows

#### Proceedings, refereed

S. Claus, A. Massing and E. Burman

A Stabilized Nitsche Fictitious Domain Formulation for the Three-Field Stokes Problem

The 26th Nordic Seminar on Computational Mechanics

M. Kuchta and M. Mortensen

A Second Order Fast Sweeping Method for the Eikonal Equation Based on Minimization

The Nordic Seminar on Computational Mechanics

K. Støverud, K. Mardal and H. P. Langtangen

Effect of Oscillatory Cerebrospinal Fluid Pressure on Fluid Movement in the Spinal Cord

Seventh National Conference on Computational Mechanics (MekIT'13)

M. Mortensen, K. Mardal, B. Martin and S. Pahlavian

Preliminary Study of the Impact of Spinal Cord Nerve Roots and Denticulate Ligaments on Drug Movement in the Cervical Spinal Subarachnoid Space

The Nordic Seminar on Computational Mechanics

#### Talks, keynote

K. Mardal

Operator Preconditioning for Well-Posed and Ill-Posed Problems

Preconditioning 2013

K. Mardal

On the Assumption of Laminar Flow in the Modeling of Physiological Flow

Modelling of physiological flows (MPF 2013)

#### Talks, invited

K. Mardal and B. F. Nielsen

Efficient Preconditioning of Optimality Systems With Non-Self-Adjoint State Operators

IFIP 2013, minisymposia Preconditioning for PDE-Constrained Optimization, Linz, Austria

#### Technical reports

D. S. Seljebotn, K. Mardal, J. Jewell, H. K. Eriksen and P. Bull

A Multilevel Solver for Gaussian Constrained CMB Realizations

### 2012

#### Book Chapters

R. C. Kirby and K. Mardal

Constructing General Reference Finite Elements

Automated Solution of Differential Equations by the Finite Element Method

R. C. Kirby and A. Logg

FErari: an Optimizing Compiler for Variational Forms

Automated Solution of Differential Equations by the Finite Element Method

I. Wilbers, K. Mardal and M. S. Alnæs

Instant: Just-in-Time Compilation of C/C++ in Python

Automated Solution of Differential Equations by the Finite Element Method

M. S. Alnæs, A. Logg and K. Mardal

UFC: a Finite Element Code Generation Interface

Automated Solution of Differential Equations by the Finite Element Method

S. Støle-Hentschel, S. Linge, A. E. Løvgren and K. Mardal

Cerebrospinal Fluid Flow

Automated Solution of Differential Equations by the Finite Element Method

K. Selim

An Adaptive Finite Element Solver for Fluid-structure Interaction Problems

Automated Solution of Differential Equations by the Finite Element Method

J. E. Hake and K. Mardal

Lessons Learned in Mixed Language Programming

Automated Solution of Differential Equations by the Finite Element Method

L. Vynnytska, S. Clark and M. E. Rognes

Dynamic Simulations of Convection in the Earth's Mantle

Automated Solution of Differential Equations by the Finite Element Method

R. C. Kirby and A. Logg

Finite Element Variational Forms

Automated Solution of Differential Equations by the Finite Element Method

M. S. Alnæs

UFL: a Finite Element Form Language

Automated Solution of Differential Equations by the Finite Element Method

J. E. Hake

A Coupled Stochastic and Deterministic Model of Ca2+ Dynamics in the Dyadic Cleft

Automated Solution of Differential Equations by the Finite Element Method

A. Logg, G. N. Wells and J. E. Hake

DOLFIN: a C++/Python Finite Element Library

Automated Solution of Differential Equations by the Finite Element Method

R. C. Kirby, A. Logg, M. E. Rognes and A. R. Terrel

Common and Unusual Finite Elements

Automated Solution of Differential Equations by the Finite Element Method

A. Logg, K. Mardal and G. N. Wells

Finite Element Assembly

Automated Solution of Differential Equations by the Finite Element Method

R. C. Kirby and A. Logg

Tensor Representation of Finite Element Variational Forms

Automated Solution of Differential Equations by the Finite Element Method

R. C. Kirby, M. G. Knepley, A. Logg, R. Scott and A. R. Terrel

Discrete Optimization of Finite Element Matrix Evaluation

Automated Solution of Differential Equations by the Finite Element Method

M. S. Alnæs and K. Mardal

SyFi and SFC: Symbolic Finite Elements and Form Compilation

Automated Solution of Differential Equations by the Finite Element Method

M. Mortensen, K. Mardal and H. P. Langtangen

Simulation of Transitional Flows

Automated Solution of Differential Equations by the Finite Element Method

M. E. Rognes

Automated Testing of Saddle Point Stability Conditions

Automated Solution of Differential Equations by the Finite Element Method

K. Valen-Sendstad, A. Logg, K. Mardal, H. Narayanan and M. Mortensen

A Comparison of Some Common Finite Element Schemes for the Incompressible Navier-Stokes Equations

Automated Solution of Differential Equations by the Finite Element Method

K. Valen-Sendstad, K. Mardal and A. Logg

Computational Hemodynamics

Automated Solution of Differential Equations by the Finite Element Method

H. P. Langtangen

A FEniCS Tutorial

Automated Solution of Differential Equations by the Finite Element Method

R. C. Kirby and A. Logg

The Finite Element Method

Automated Solution of Differential Equations by the Finite Element Method

A. Logg, K. B. Ølgaard, M. E. Rognes and G. N. Wells

FFC: the FEniCS Form Compiler

Automated Solution of Differential Equations by the Finite Element Method

H. Narayanan

A Computational Framework for Nonlinear Elasticity

Automated Solution of Differential Equations by the Finite Element Method

K. Mardal and J. B. Haga

Block Preconditioning of Systems of PDEs

Automated Solution of Differential Equations by the Finite Element Method

#### Edited books

A. Logg, K. Mardal and G. N. Wells

Automated Solution of Differential Equations by the Finite Element Method

#### Journal Articles

G. Rutkowska, V. Haughton, S. Linge and K. Mardal

Patient-Specific 3D Simulation of Cyclic CSF Flow at the Cranio-Cervical Region

American Journal of Neuroradiology

#### Posters

K. Valen-Sendstad, K. Mardal and D. A. Steinman

Revisiting 'Turbulence' in Cerebral Aneurysms

Ø. Evju, K. Mardal and K. Valen-Sendstad

On Non-Newtonian Effects in Cerebral Aneurysms: a Computational Study on 12 Patient Specific Aneurysms

#### Talks, contributed

K. Mardal and H. P. Langtangen

Will FEniCS Fly?

FEniCS 12 workshop

K. Mardal

The Finite Element Library FEniCS + Blood Flow Simulations in Cerebral Aneurysms

Marsden's lab at UCSD

K. Mardal

The Finite Element Library FEniCS

Steinman's lab, University of Toronto

K. Støverud, V. Haughton, H. P. Langtangen and K. Mardal

CSF Flow Dynamics: Effects of Viscosity and Inertia

ANSR 2012, New York

B. F. Nielsen and K. Mardal

The Minimal Residual Method Applied to Ill-Posed Optimality Systems; Eigenvalues and Convergence Properties

Numerical Methods for Optimal Control and Inverse Problems workshop, Munich, Germany

K. Mardal, H. P. Langtangen and P. Røtnes

Are Zombies a Threat to Mankind?

Invited talk for the opening of RF kjelleren at the University of Oslo

K. Mardal, B. F. Nielsen and M. S. Alnæs

Efficient Preconditioning of Optimality Systems

EMG 2012

K. Mardal

On Well-Posedness and Stability

CBC Seminar series

Ø. Evju, K. Valen-Sendstad and K. Mardal

Non-Newtonian Effects in Cerebral Aneurysms. a Computational Study on 12 Patient Specific Aneurysms

ICS '12

#### Talks, invited

K. Mardal

Blood Flow in Cerebral Aneurysms - Can Turbulence Be a Risk Indicator?

SDU workshop

#### Technical reports

K. Mardal, J. Schoberl and R. Winther

A Uniform Inf-Sup Condition With Applications to Preconditioning

### 2011

#### Book Chapters

K. Mardal and R. Winther

Construction of Preconditioners by Mapping Properties for Systems of Partial Differential Equations

Efficient preconditioning methods for elliptic partial differential equations

#### Journal Articles

K. Valen-Sendstad, K. Mardal, J. Isaksen and M. Mortensen

A Quantitative Characterization of Differences in Flow Patterns in Ruptured Versus Unruptured MCA Aneurysms

journal

S. Linge, V. Haughton, A. E. Løvgren, K. Mardal, A. Helgeland and H. P. Langtangen

Effect of Tonsilar Herniation on Cyclic CSF Flow Studied With Computational Flow Analysis

American Journal of Neuroradiology

K. Valen-Sendstad, K. Mardal, M. Mortensen, B. A. P. Reif and H. P. Langtangen

Direct Numerical Simulation of Transitional Flow in a Patient-Specific Intracranial Aneurysm

Journal of Biomechanics

T. K. Nilssen, G. A. Staff and K. Mardal

Order Optimal Preconditioners for Fully Implicit Runge-Kutta Schemes Applied to the Bidomain Equations

Numerical Methods for Partial Differential Equations

K. Støverud, K. Mardal, V. Haughton and H. P. Langtangen

CSF Flow in Chiari I and Syringomyelia From the Perspective of Computational Fluid Dynamics

The Neuroradiology Journal

K. Mardal and R. Winther

Preconditioning Discretizations of Systems of Partial Differential Equations

Numerical Linear Algebra with Applications

J. Jiang, K. Johnson, K. Valen-Sendstad, K. Mardal, O. Wieben and C. Strother

Flow Characteristics in a Canine Aneurysm Model: A Comparison of 4-D Accelerated Phase-Contrast MR Measurements and Computational Fluid Dynamics Simulations

Medical Physics

#### Talks, contributed

K. Mardal

On the Construction of Preconditioners for Systems of PDEs

SIAM Conference on Computational Science and Engineering, MS2

K. Valen-Sendstad, K. Mardal, M. Mortensen, B. A. P. Reif and H. P. Langtangen

Why Blood Flow in the Vicinity of Aneurysms Is Difficult to Compute

Talk at CBC Workshop on CBC Key Topics

K. Mardal and B. F. Nielsen

Efficient Preconditioning of Optimality Systems

Precond 11

K. Valen-Sendstad, K. Mardal, M. Mortensen, B. A. P. Reif and H. P. Langtangen

Simulation Methodology for Cerebral Blood Flow

Biomedical Simulation Lab, Institute of Biomaterials and Biomedical Engineering at the University of Toronto

K. Valen-Sendstad, K. Mardal, M. Mortensen, B. A. P. Reif and H. P. Langtangen

Computational Cerebral Hemodynamics

The Norwegian Defence Research Establishment

K. Valen-Sendstad, K. Mardal, M. Mortensen, B. A. P. Reif and H. P. Langtangen

Direct Numerical Simulation of Transitional Flow in Patient-Specific Intracranial Aneurysms

ASME 2011 Summer Bioengineering Conference

K. Valen-Sendstad, K. Mardal, M. Mortensen, H. P. Langtangen, B. A. P. Reif and D. A. Steinman

'Turbulence' in Cerebral Aneurysms

CBC Workshop on Biomechanics, 17-18 November

#### Proceedings, refereed

I. N. Drøsdal, V. Haughton, K. Mardal and K. Støverud

Porous and Viscous Flow Modeling on the Study of Cyst Development in the Human Spinal Cord

8th International Conference on CFD in Oil & Gas, Metallurgical and Process Industries

S. Linge, K. Mardal, V. Haughton and A. Helgeland

Cerebrospinal Fluid Flow Characteristics at Double Heart Rate

Neuroradiology, 53 (Suppl. 1), S33, 35th European Soc of Neuroradiology ann. meeting, Antwerpen, Belgium

K. Støverud, K. Mardal, H. P. Langtangen and V. Haughton

The Effect of Varying Cross-Sectional Areas on Cerebrospinal Fluid Flow and Pressure in the Cervical Spine

MekIT'11. Sixth national conference on Computational Mechanics

S. Linge, V. Haughton, A. E. Løvgren, K. Mardal, A. Helgeland, H. P. Langtangen and K. Støverud

Cyclic Cerebrospinal Fluid Flow (I): Towards the Understanding of Cerebrospinal Fluid Flow Dynamics in Chiari I Malformation

ASNR 49th Annual Meeting & the Foundation of the ASNR Symposium, June 4 - 9, 2011.

K. Valen-Sendstad, K. Mardal, M. Mortensen, B. A. P. Reif and H. P. Langtangen

On the Complexity of Stationary Flow in Patient-Specific Aneurysms

MekIT'11 Sixth national conference on Computational Mechanics

K. Valen-Sendstad, M. Mortensen, K. Mardal, B. A. P. Reif and H. P. Langtangen

Investigations of Transistional Flows Using Image Based Hemodynamics

8th International Conference on CFD in Oil & Gas, Metallurgical and Process Industries

#### Talks, invited

K. Mardal, K. Støverud, V. Haughton, S. Linge, H. P. Langtangen, G. Rutkowska and I. N. Drøsdal

Cerebrospinal Fluid Flow in the Upper Cervical Canal in Patients With the Chiari I Malformation

1ST CSF Hydrodynamics Symposium

K. Mardal

FEniCS: an Attempt to Combine Simplicity, Generality, Efficiency and Reliability

Python-based Software for Solving Partial Differential Equations Minisymposium at SIAM Conference on Computational Science and Engineering

K. Mardal, K. Valen-Sendstad and Ø. Evju

Simulating Blood Flow in Cerebral Aneurysm

Minisymposium Numerical Methods for Biomedical Problems on Enumath

K. Mardal, K. Valen-Sendstad, M. S. Alnæs, M. Mortensen, H. P. Langtangen and B. A. P. Reif

The Finite Element Library FEniCS and Simulation of Blood Flow in Cerebral Aneurysms

Talk at CSB Seminar, University of Stuttgart

### 2010

#### Book Chapters

A. Schroll

Automatic Calibration of Depositional Models

Automated Scientific Computing

#### Proceedings, non-refereed

K. Støverud, K. Mardal, V. Haughton and H. P. Langtangen

CSF Flow in Chiari I and Syringomyelia - From the Perspective of Fluid Dynamics

Proceedings of the XIX Symposium Neuroradiologicum, Bologna, Italy

#### Journal Articles

B. F. Nielsen and K. Mardal

Efficient Preconditioners for Optimality Systems Arising in Connection With Inverse Problems

SIAM Journal on Control and Optimization

M. S. Alnæs and K. Mardal

On the Efficiency of Symbolic Computations Combined With Code Generation for Finite Element Methods

ACM Transactions on Mathematical Software

M. Burger, K. Mardal and B. F. Nielsen

Stability Analysis of the Inverse Transmembrane Potential Problem in Electrocardiography

Inverse Problems

H. Lindekleiv, K. Valen-Sendstad, M. K. Morgan, K. Mardal, K. Faulder, J. Magnus, K. Waterloo, B. Romner and T. Ingebrigtsen

Sex Differences in Intracranial Arterial Bifurcations

Gender Medicine

S. Hentschel, K. Mardal, A. E. Løvgren, S. Linge and V. Haughton

Characterization of Cyclical CSF Flow in the Foramen Magnum and Upper Cervical Spinal Canal With MR Flow Imaging and Computational Fluid Dynamics

American Journal of Neuroradiology

#### Talks, contributed

K. Mardal, H. P. Langtangen and P. Røtnes

Is Zombies a Threat to Mankind?

Talk presented at FEniCS 2010

A. Blechingberg, K. Mardal, F. Strisland, J. Sundnes, T. O. Rognum, Å. Vege, M. Weensvangen and A. Stray-Pedersen

The Baby Justicia Project: Biomechanical Investigations of the Shaken Baby Syndrome (SBS)

WCB2010, Seminar session, Head/Brain Injury - Models

K. Mardal

CSF Strømning I Forbindelse Med Chiari Malformasjon Og Syringomyelia

CBC Workshop on Clinical Issues Related to the Cerebrospinal Fluid

K. Støverud, K. Mardal and H. P. Langtangen

From a Physical Problem to Computer Simulations

CBC Workshop on Cerebrospinal Fluid Flow in the Brain and Spinal Canal - Clinical, Experimental and Mathematical Models and Problems, Simula, May 28

K. Støverud, K. Mardal, V. Haughton and H. P. Langtangen

Cerebrospinal Fluid (CSF) - Oscillating Flow and Pressure

CBC Workshop on Aerosols: Dispersion, Transport and Effects, Simula, November 10

K. Støverud, K. Mardal, V. Haughton and H. P. Langtangen

Cerebrospinal Fluid (CSF) - Oscillating Flow and Pressure

Selected Topics Seminar IWS Stuttgart

K. Støverud, K. Mardal, V. Haughton and H. P. Langtangen

CSF Hydrodynamic in Patients With Syringomyelia and Chiari I Malformations

Annual NUPUS meeting in Freudenstadt

K. Mardal and B. F. Nielsen

An Operator Theoretical Approach to Preconditioning Optimality Systems

Talk at European Multi-Grid Conference, EMG, 2010

#### Proceedings, refereed

J. Jiang, K. Johnson, K. Valen-Sendstad, K. Mardal, D. Consigny, O. Wieben and C. Strother

Comparison of Aneurismal Hemodynamics Between 4D Accelerated Phase-Contrast MR Angiography and Computational Fluid Dynamics Simulations: Initial Experience in a Canine Aneurysm Model

Proceedings of the ASME 2010 Summer Bioengineering Conference

### 2009

#### Book Chapters

B. F. Nielsen, O. M. Lysaker, P. Grøttum, K. Mardal, A. Tveito, C. Tarrou, K. Haugaa, A. Abildgaard and J. G. Fjeld

Can ECG Recordings and Mathematics Tell the Condition of Your Heart?

Simula Research Laboratory - by thinking constantly about it

#### Journal Articles

T. K. Karper, K. Mardal and R. Winther

Unified Finite Element Discretizations of Coupled Darcy-Stokes Flow

Numerical Methods for Partial Differential Equations

M. S. Alnæs, A. Logg, K. Mardal, O. Skavhaug and H. P. Langtangen

Unified Framework for Finite Element Assembly

International Journal of Computational Science and Engineering

S. Linge, V. Haughton, A. E. Løvgren, K. Mardal and H. P. Langtangen

CSF Flow Dynamics at the Cranio-Vertebral Junction Studied With an Idealized Model of the Subarachnoid Space and Computational Flow Analysis

American Journal of Neuroradiology

#### Talks, contributed

K. Mardal, S. Hentschel, A. Logg and K. Valen-Sendstad

Cerebral Blood Flow

Invited talk at Telemark College, Engineering Faculty, Porsgrunn, Norway, 2009

K. Mardal, S. Hentschel, A. Helgeland, H. P. Langtangen, S. Linge, A. E. Løvgren, A. Logg and K. Valen-Sendstad

Patient-Specific Simulations of Stroke and Syringomyelia

Talk : Advisory commitee meeting FFI project P1112 Aerosols: Dispersion, Transport and Consequences, Nov 03

K. Mardal, V. Haughton, S. Hentschel, H. P. Langtangen, S. Linge, A. E. Løvgren and K. Valen-Sendstad

CSF Flow Modelling

Invited talk at CSR Flow Research Conference at University of Wisconsin, Nov 9

K. Valen-Sendstad, K. Mardal and A. Logg

Simulation Methodology for Bioflows

Talk : Advisory commitee meeting FFI project P1112 Aerosols: Dispersion, Transport and Consequences, May 05

K. Mardal, S. Hentschel, A. Logg and K. Valen-Sendstad

Patient-Specific Hemodynamics in FEniCS

Invited talk at the minisymposium on Computational Vascular and Cardiovascular Mechanics at USNCCM 2009

K. Mardal, A. Logg, S. Hentschel, O. C. Myklebust and K. Valen-Sendstad

Patient-Specific Hemodynamics in FEniCS

Presentation at the FEniCS 09 Workshop

S. Linge, A. E. Løvgren, K. Mardal, V. Haughton and H. P. Langtangen

Cerebrospinal Fluid Flow Investigations With Modelling and Simulation

invited talk at The Chiari Institute, 14th of January, New York, U.S.A.

S. Linge, A. E. Løvgren, K. Mardal, V. Haughton and H. P. Langtangen

Simulating Normal and Abnormal CSF Flow With Idealized Geometries

talk, seminar on cerebrospinal fluid flow, 16th of January, University of Wisconsin, U.S.A.

K. Valen-Sendstad, M. Mortensen, H. P. Langtangen, B. A. P. Reif and K. Mardal

Implementing a K-E Turbulence Model in the FEniCS Finite Element Programming Environment

Talk at MekIT'09: Fifth National Conference on Computational Mechanics, Trondheim, May 26-27

S. Linge, A. E. Løvgren, K. Mardal, V. Haughton and H. P. Langtangen

Tonsilar Herniation - How Is the CSF Flow Influenced?

Invited talk at Rikshospitalet University Hospital, Oslo, Norway, 5th of June

K. Mardal, A. Helgeland, S. Hentschel, H. P. Langtangen, A. Logg, S. Linge, A. E. Løvgren and K. Valen-Sendstad

Some Biomedical Applications at Simula

Talk at the CBC Workshop on Computational Biology with UMB

B. F. Nielsen and K. Mardal

An Operator Theoretical Approach to Preconditioning Optimality Systems

Presented at the Applied Inverse Problems conference, Vienna, Austria

#### Proceedings, refereed

K. Valen-Sendstad, M. Mortensen, H. P. Langtangen, B. A. P. Reif and K. Mardal

Implementing a K-E Turbulence Model in the FEniCS Finite Element Programming Environment

MekIT'09. Fifth national conference on Computational Mechanics

S. Linge, A. E. Løvgren, K. Mardal, V. Haughton and H. P. Langtangen

Effect of Tonsilar Position on Cerebrospinal Fluid Flow in the Spinal Subarachnoid Space Studied With Computational Fluid Dynamics

ASNR - 47th Annual Meeting of the American Society of Neuroradiology

### 2008

#### Proceedings, non-refereed

A. E. Løvgren, S. Linge, K. Mardal, V. Haughton and H. P. Langtangen

CFD Analysis of Cerebrospinal Fluid Flow in the Cranio-Cervical Region

21st Nordic Seminar on Computational Mechanics

O. C. Myklebust, S. Hentschel and K. Mardal

Patient-Specific Computational Fluid Dynamic Simulations in the Circle of Willis

21st Nordic Seminar on Computational Mechanics

#### Journal Articles

J. Isaksen, K. Valen-Sendstad, K. Mardal and T. Ingebrigtsen

Simulation of Hemodynamics in the Aneurysm Neck After Coiling

Neuroradiology

#### Talks, contributed

A. E. Løvgren, S. Linge, K. Mardal, V. Haughton and H. P. Langtangen

CFD Analysis of Cerebrospinal Fluid Flow in the Cranio-Cervical Region

Invited talk at the 21st Nordic Seminar on Computational Mechanics, Trondheim, October 16-17

O. C. Myklebust, S. Hentschel and K. Mardal

Patient-Specific Computational Fluid Dynamic Simulations in the Circle of Willis

Invited talk at the 21st Nordic Seminar on Computational Mechanics, Trondheim, October 16-17

S. Linge, A. E. Løvgren, K. Mardal, V. Haughton and H. P. Langtangen

Chiari Malformation - the Problem and a Mathematical Approach

Invited talk, Vindern Medical Center, 8th of December, Oslo, Norway

K. Mardal, K. Valen-Sendstad, O. C. Myklebust and S. Hentschel

Scientific Computing at Simula

Invited Talk at Workshop on Cerebral Aneurysms and Subarachnoidal Hemorrhage, Tromsø Jan 24-26

K. Mardal, B. F. Nielsen and M. S. Alnæs

Two Steps Towards Automating Efficient Solution of Inverse Problems

Invited Talk at the FEniCS 08 Workshop, March 5-7,Baton Rouge, Louisiana

K. Mardal, K. Valen-Sendstad, O. C. Myklebust and S. Hentschel

Blood Flow Computations at Simula

Invited talk at Medical Physics, University of Wisconsin, March 11.

S. Linge, A. E. Løvgren, K. Mardal, V. Haughton and H. P. Langtangen

Cerebrospinal Fluid Flow in Normal and Chiari Subjects

talk, Seminar at CBC (Simula Research Laboratory), 16th of December, Oslo, Norway

S. Linge, A. E. Løvgren, K. Mardal, V. Haughton and H. P. Langtangen

Cerebrospinal Fluid Flow Simulations - Normal Subjects and Patients With Chiari I Malformation

talk, Seminar at CBC (Simula Research Laboratory), 31st of October, Oslo, Norway)

S. Linge, A. E. Løvgren, K. Mardal and H. P. Langtangen

Simulating the Cerebral Fluid Flow Associated With Chiari I Malformation in Idealized Geometries

talk, Seminar at CBC (Simula Research Laboratory), 25th of June, Oslo, Norway.

S. Linge, A. E. Løvgren, K. Mardal and H. P. Langtangen

Simulating the Cerebral Fluid Flow Associated With Chiari I Malformation in Idealized Geometries

talk, Seminar at CBC (Simula Research Laboratory), 20th of May, Oslo, Norway.

K. Valen-Sendstad, A. Logg and K. Mardal

Developing Flow Solver Methodology for Patientspecific Simulation of Hemodynamics

Talk at Workshop on Finite Element Methods for Fluids and Fluid-Structure Interaction, June 5

M. S. Alnæs and K. Mardal

SFC - the SyFi Form Compiler

Talk at the FEniCS 08 Workshop, March 5-7,Baton Rouge, Louisiana

#### Talks, invited

K. Mardal

Hemodynamics in the Circle of Willis

Invited talk at Institute for Computational and Applied Mathematics, Muenster, Germany, November 18

### 2007

#### Book Chapters

A. Logg, K. Mardal, M. S. Alnæs, H. P. Langtangen and O. Skavhaug

A Hybrid Approach to Efficient Finite Element Code Development

Petascale Computing - Algorithms and Applications

#### Journal Articles

M. S. Alnæs, J. G. Isaksen, K. Mardal, B. Romner, M. K. Morgan and T. Ingebrigtsen

Computation of Hemodynamics in the Circle of Willis

Stroke

K. Mardal, B. F. Nielsen, X. Cai and A. Tveito

An Order Optimal Solver for the Discretized Bidomain Equations

Numerical Linear Algebra with Applications

K. Mardal, T. K. Nilssen and G. A. Staff

Order Optimal Preconditioners for Implicit Runge-Kutta Schemes Applied to Parabolic PDE's

SIAM Journal on Scientific Computing

K. Mardal, O. Skavhaug, G. T. Lines, G. A. Staff and Å. Ødegård

Using Python to Solve Partial Differential Equations

Computing in Science & Engineering

#### Manuals

M. S. Alnæs, A. Logg, K. Mardal, O. Skavhaug and H. P. Langtangen

UFC Specification and User Manual 1.0

#### Talks, contributed

K. Mardal

Computation of Hemodynamics in the Circle of Willis

Talk at Workshop: Modelling and Computation of Biomedical Processes - June 7-14, 2007

K. Mardal

Finite Elements With Symbolic Computations and Code Generation

Talk at Software Issues in Computational Science and Engineering (SCSE 2007), Uppsala, 2007-08-11

M. S. Alnæs, K. Mardal and J. Sundnes

Application of Symbolic Finite Element Tools to Nonlinear Hyperelasticity

Talk at MekIT'07: Fourth National Conference on Computational Mechanics

J. Sundnes, M. S. Alnæs and K. Mardal

A Finite Element Model of Cardiac Electrophysiology and Mechanics

VII International conference on computational plasticity

#### Proceedings, refereed

M. S. Alnæs, K. Mardal and J. Sundnes

Application of Symbolic Finite Element Tools to Nonlinear Hyperelasticity

Fourth national conference on Computational Mechanics (MekIT'07)

### 2006

#### Books

J. Sundnes, G. T. Lines, X. Cai, B. F. Nielsen, K. Mardal and A. Tveito

Computing the Electrical Activity in the Heart

#### Proceedings, non-refereed

C. Tarrou, O. M. Lysaker, X. Cai, K. Mardal, C. Tarrou, T. S. Ruud, M. C. MacLachlan and A. Tveito

Identifying Ischemic Heart Disease in Terms of ECG Recordings and an Inverse Problem for the Bidomain Equations; Modeling and Experiments

The Third International Conference "Inverse Problems: Modeling and Simulation"

#### Journal Articles

K. Mardal and R. Winther

An Observation on Korn's Inequality for Nonconforming Finite Element Methods

Math. Comp.

G. A. Staff, K. Mardal and T. K. Nilssen

Preconditioning of Fully Implicit Runge-Kutta Schemes for Parabolic PDEs

Model. Identif. Control

J. Sundnes, B. F. Nielsen, K. Mardal, X. Cai, G. T. Lines and A. Tveito

On the Computational Complexity of the Bidomain and the Monodomain Models of Electrophysiology

Annals of Biomedical Engineering

K. Mardal and T. K. Nilssen

Reuse of Standard Preconditioners for Higher-Order Time Discretizations of Parabolic PDEs

Journal of Numerical Mathematics

#### Manuals

M. S. Alnæs and K. Mardal

SyFi User Manual

#### Talks, contributed

H. P. Langtangen and K. Mardal

Mathematical Modeling of Blood Flow

Lecture at Svalbard summer school

K. Mardal

SyFi - a Package for Symbolic Finite Element Computations

Presented at the Fenics06 workshop in Delft, Netherlands, 2006.

B. F. Nielsen, O. M. Lysaker, X. Cai, K. Mardal, C. Tarrou, M. C. MacLachlan, J. Sundnes, G. T. Lines and A. Tveito

Computational Issues in Heart Modeling

Presented at the Johann Radon Institute for Computational and Applied Mathematics, Linz, Austria

M. S. Alnæs, A. M. Bruaset, X. Cai, H. P. Langtangen, K. Mardal, H. Moe, O. Skavhaug and Å. Ødegård

Python in High Performance Computing

Tutorial presented at the Para06 Workshop

B. F. Nielsen, O. M. Lysaker, C. Tarrou, J. Sundnes, X. Cai and K. Mardal

On the Use of the Bidomain Equations for Computing the Transmembrane Potential Throughout the Heart Wall: an Inverse Problem

Presented at the Computers in Cardiology conference in Valencia, Spain

K. Mardal

SyFi - an Element Matrix Factory, With Emphasis on the Incompressible Navier-Stokes Equations

Presentation held at the Para06 workshop

#### Proceedings, refereed

B. F. Nielsen, O. M. Lysaker, C. Tarrou, J. Sundnes, X. Cai and K. Mardal

On the Use of the Bidomain Equations for Computing the Transmembrane Potential Throughout the Heart Wall: an Inverse Problem

Computers in Cardiology 2006

G. A. Staff, K. Mardal and T. K. Nilssen

Block Preconditioners for Fully Implicit Runge-Kutta Schemes Applied to the Bidomain Equations

ECCOMAS CFD 06

K. Mardal

SyFi - an Element Matrix Factory, With Emphasis on the Incompressible Navier-Stokes Equations

Para'06

### 2005

#### Talks, contributed

K. Mardal, B. F. Nielsen and A. Tveito

Preconditioners for Elliptic Problems With Variable Coefficients

Presented at the SIAM Conference on Mathematical and Computational Issues in the Geosciences, Avignon, France

A. M. Bruaset, M. S. Alnæs, H. P. Langtangen, K. Mardal, H. Moe, O. Skavhaug and Å. Ødegård

Scientific Computing in Python

Tutorial ASIM 2005

#### Proceedings, refereed

G. A. Staff and K. Mardal

The Accuracy of the Velocity Approximation With Respect to the Pressure Approximation for Incompressible Fluid Flow

Third National Conference on Computational Mechanics (MekIT 05)

G. A. Staff, K. Mardal and T. K. Nilssen

Preconditioning of Fully Implicit Runge-Kutta Schemes for Parabolic PDEs

SIMS05. 46th Conference on Simulation and Modeling, Trondheim, October 13-14

#### Technical reports

O. Skavhaug, K. Mardal and H. P. Langtangen

A Python Framework for Verifying Codes for Numerical Solutions of Partial Differential Equations

K. Mardal, B. F. Nielsen, X. Cai and A. Tveito

An Order Optimal Solver for the Discretized Bidomain Equations

### 2004

#### Journal Articles

K. Mardal and R. Winther

Uniform Preconditioners for the Time Dependent Stokes Problem

Numerische Mathematik

#### Talks, contributed

K. Mardal and A. Tveito

Block Preconditioners for PDEs Arising From the Bi-Domain Model of the Electrical Activity in the Heart

Talk at the Copper Mountain Conference, Colorado, USA

M. Westlie, K. Mardal and H. P. Langtangen

Making a Python Interface to the C++ Library Diffpack

Talk at the EuroPython 2004 Conference, Gothenburg, Sweden

Å. Ødegård, K. Mardal, P. Miller, H. Moe, O. Skavhaug, A. M. Bruaset and H. P. Langtangen

High Performance Computing in Python

Tutorial, SC2004

T. K. Nilssen and K. Mardal

Reuse of Standard Preconditioners for Higher-Order Time Discretizations of Parabolic PDEs

Talk at the Eigth Copper Mountain Conference on Iterative Methods, Copper Mountain, CO, USA

#### Technical reports

P. Böhm, A. M. Bruaset, H. P. Langtangen, K. Mardal and G. Wachutka

Diffpack Implementation of Edge-Based Non-Standard Finite Element Methods

### 2003

#### Book Chapters

H. P. Langtangen and K. Mardal

Using Diffpack From Python Scripts

Advanced Topics in Computational Partial Differential Equations - Numerical Methods and Diffpack Programming

K. Mardal, G. Zumbusch and H. P. Langtangen

Multigrid Methods in Diffpack

Advanced Topics in Computational Partial Differential Equations - Numerical Methods and Diffpack Programming

K. Mardal and H. P. Langtangen

Mixed Elements in Diffpack

Advanced Topics in Computational Partial Differential Equations - Numerical Methods and Diffpack Programming

K. Mardal, J. Sundnes, H. P. Langtangen and A. Tveito

Block Preconditioning and Systems of PDEs

#### Talks, contributed

G. T. Lines, B. F. Nielsen, A. Tveito, J. Sundnes, P. Grøttum, X. Cai and K. Mardal

Computing the Electrical Activity in the Human Heart

Presented at the Centre of Mathematics for Applications, Oslo

A. Tveito, G. T. Lines, J. Sundnes, B. F. Nielsen, P. Grøttum, X. Cai and K. Mardal

Computing the Electrical Activity in the Human Heart

Presented at the European Conference on Numerical Mathematics and Advanced Applications, Prague, Czech Republic

A. Tveito, G. T. Lines, B. F. Nielsen, J. Sundnes, P. Grøttum, X. Cai and K. Mardal

Computing the Heart

Presented at the 21st CAD-FEM users' meeting 2003 - International congress on FEM technology, Potsdam, Germany

K. Mardal, A. Huerta, H. P. Langtangen and D. Harry

Numerical Modeling of Crust and Mantle Movement

Talk presented at SIAM Conference on Mathematical and Computational Issues in the Geosciences (GS0 3), March 17-20, 2003, Austin, Texas.

#### Proceedings, refereed

A. Kristoffersen and K. Mardal

Solving Heat Distribution in Room Using Mixed Finite Element for Coupling the Navier-Stokes Equations and the Heat Equation

Proceedings of the Second National Conference on Computational Mechanics (MekIT'03)

K. Mardal, H. P. Langtangen and R. Winter

Error Estimates for the Linear Navier-Stokes Equations

Proceedings of the Second National Conference on Computational Mechanics (MekIT'03)

#### PhD Thesis

K. Mardal

Software and Numerical Methods for the Incompressible Navier-Stokes Equations

### 2002

#### Journal Articles

H. P. Langtangen, K. Mardal and R. Winther

Numerical Methods for Incompressible Viscous Flow

Advances in Water Resources

K. Mardal, X. Tai and R. Winther

A Robust Finite Element Method for Darcy-Stokes Flow

SIAM Journal on Numerical Analysis

J. Sundnes, G. T. Lines, K. Mardal and A. Tveito

Multigrid Block Preconditioning for a Coupled System of Partial Differential Equations Modeling the Electrical Activity in the Heart

Computer Methods in Biomechanics and Biomedical Engineering

#### Talks, contributed

G. T. Lines, J. Sundnes, A. Tveito, X. Cai, K. Mardal and A. M. Bruaset

Diffpack Simulation of the Electrical Activity in the Heart

Invited minisymposium talk at the 20th CAD-FEM User's Meeting, Friedrichshafen, Germany

#### Proceedings, refereed

H. P. Langtangen and K. Mardal

A Software Framework for Mixed Finite Element Programming

Proceedings of the 2nd International Conference on Computational Science

#### Technical reports

K. Mardal, E. Acklam and D. Calhoun

How to Use MATLAB in C++ Programs

### 2001

#### Talks, contributed

J. Sundnes, G. T. Lines, K. Mardal and A. Tveito

On Numerical Techniques for the Bidomain Model

Presented at the SIAM Annual meeting, San Diego, California

#### Proceedings, refereed

K. Mardal, H. P. Langtangen and R. Winter

An Optimal Iterative Method for the Time-Dependent Stokes Problem

Tenth Conference Virtual Proceedings, Copper Mountain Conference on Multigrid Methods

K. Mardal and H. P. Langtangen

An Efficient Parallel Iterative Approach to a Fully Implicit Mixed Finite Element Formulation for the Navier-Stokes Equations

ECCOMAS CFD 2001, Computational Fluid Dynamics Conference Proceedings

### 2000

#### Proceedings, refereed

K. Mardal and H. P. Langtangen

An Effective Iterative Approach to a Fully Implicit Mixed Finite Element Formulation for the Navier-Stokes Equations

13th Nordic Seminar on Computational Mechanics (NSCM-13)