Kent-Andre Mardal

• Erhardt, André Henrik; Mardal, Kent-Andre & Schreiner, Jakob Emil (2020). Dynamics of a neuron-glia system: the occurrence of seizures and the influence of electroconvulsive stimuli. Journal of Computational Neuroscience.  ISSN 0929-5313.
• Landet, Tormod; Mardal, Kent-Andre & Mortensen, Mikael (2020). Slope limiting the velocity field in a discontinuous Galerkin divergence-free two-phase flow solver. Computers & Fluids.  ISSN 0045-7930.  196 . doi: 10.1016/j.compfluid.2019.104322
• Buccino, Alessio Paolo; Kuchta, Miroslav; Jæger, Karoline Horgmo; Ness, Torbjørn V; Berthet, Pierre; Mardal, Kent-Andre; Cauwenberghs, Gert & Tveito, Aslak (2019). How does the presence of neural probes affect extracellular potentials?. Journal of Neural Engineering.  ISSN 1741-2560.  16(2) . doi: 10.1088/1741-2552/ab03a1 Full text in Research Archive.
• Bærland, Trygve; Kuchta, Miroslav & Mardal, Kent-Andre (2019). Multigrid Methods for Discrete Fractional Sobolev Spaces. SIAM Journal on Scientific Computing.  ISSN 1064-8275.  41(2), s 948- 972 . doi: 10.1137/18M1191488
• Eide, Per Kristian; Valnes, Lars Magnus; Pripp, Are Hugo; Mardal, Kent-Andre & Ringstad, Geir (2019). Delayed clearance of cerebrospinal fluid tracer from choroid plexus in idiopathic normal pressure hydrocephalus. Journal of Cerebral Blood Flow and Metabolism.  ISSN 0271-678X.  s 1- 10 . doi: 10.1177/0271678X19874790
• Funke, Simon Wolfgang; Nordaas, Magne; Evju, Øyvind; Alnæs, Martin & Mardal, Kent-Andre (2019). Variational data assimilation for transient blood flow simulations - Cerebral aneurysms as an illustrative example. International Journal for Numerical Methods in Biomedical Engineering.  ISSN 2040-7939.  35(1) . doi: 10.1002/cnm.3152 Full text in Research Archive.
• Gergelits, Tomas; Mardal, Kent-Andre; Nielsen, Bjørn Fredrik & Strakos, Zdenek (2019). Laplacian preconditioning of elliptic PDEs: Localization of the eigenvalues of the discretized operator. SIAM Journal on Numerical Analysis.  ISSN 0036-1429.  57(3), s 1369- 1394 . doi: 10.1137/18M1212458
• Holter, Karl Erik; Kuchta, Miroslav & Mardal, Kent-Andre (2019). Sub-voxel Perfusion Modeling in Terms of Coupled 3d-1d Problem, In Florin Adrian Radu; Kundan Kumar; Inga Berre; Jan Martin Nordbotten & Iuliu Sorin Pop (ed.),  Numerical Mathematics and Advanced Applications ENUMATH 2017.  Springer Berlin/Heidelberg.  ISBN 978-3-319-96415-7.  Kapittel.  s 35 - 47
• Kuchta, Miroslav; Mardal, Kent-Andre & Mortensen, Mikael (2019). On the singular Neumann problem in linear elasticity. Numerical Linear Algebra with Applications.  ISSN 1070-5325.  26(1) . doi: 10.1002/nla.2212 Full text in Research Archive.
• Kuchta, Miroslav; Mardal, Kent-Andre & Mortensen, Mikael (2019). Preconditioning trace coupled 3d-1d systems using fractional Laplacian. Numerical Methods for Partial Differential Equations.  ISSN 0749-159X.  35(1), s 375- 393 . doi: 10.1002/num.22304
• Lee, Jeonghun J.; Piersanti, Eleonora; Mardal, Kent-Andre & Rognes, Marie Elisabeth (2019). A mixed finite element method for nearly incompressible multiple-network poroelasticity. SIAM Journal on Scientific Computing.  ISSN 1064-8275.  41(2), s 722- 747 . doi: 10.1137/18M1182395 Full text in Research Archive.
• Seljebotn, Dag Sverre; Bærland, Trygve; Eriksen, Hans Kristian Kamfjord; Mardal, Kent-Andre & Wehus, Ingunn Kathrine (2019). Multi-resolution Bayesian CMB component separation through Wiener filtering with a pseudo-inverse preconditioner. Astronomy and Astrophysics.  ISSN 0004-6361.  627 . doi: 10.1051/0004-6361/201732037
• Vinje, Vegard; Ringstad, Geir; Lindstrøm, Erika Kristina; Valnes, Lars Magnus; Rognes, Marie Elisabeth; Eide, Per Kristian & Mardal, Kent-Andre (2019). Respiratory influence on cerebrospinal fluid flow – a computational study based on long-term intracranial pressure measurements. Scientific Reports.  ISSN 2045-2322.  9, s 1- 13 . doi: 10.1038/s41598-019-46055-5
• Lindstrøm, Erika Kristina; Ringstad, Geir; Mardal, Kent-Andre & Eide, Per Kristian (2018). Cerebrospinal fluid volumetric net flow rate and direction in idiopathic normal pressure hydrocephalus. NeuroImage: Clinical.  ISSN 2213-1582.  20, s 731- 741 . doi: 10.1016/j.nicl.2018.09.006 Full text in Research Archive.
• Lindstrøm, Erika Kristina; Ringstad, Geir; Sorteberg, Angelika; Sorteberg, Wilhelm; Mardal, Kent-Andre & Eide, Per Kristian (2018). Magnitude and direction of aqueductal cerebrospinal fluid flow: large variations in patients with intracranial aneurysms with or without a previous subarachnoid hemorrhage. Acta Neurochirurgica.  ISSN 0001-6268.  s 1- 10 . doi: 10.1007/s00701-018-3730-6 Show summary

  Background Net cerebrospinal fluid (CSF) flow within the cerebral aqueduct is usually considered to be antegrade, i.e., from the third to the fourth ventricle with volumes ranging between 500 and 600 ml over 24 h. Knowledge of individual CSF flow dynamics, however, is hitherto scarcely investigated. In order to explore individual CSF flow rate and direction, we assessed net aqueductal CSF flow in individuals with intracranial aneurysms with or without a previous subarachnoid hemorrhage (SAH). Methods A prospective observational study was performed utilizing phase-contrast magnetic resonance imaging (PCMRI) to determine the magnitude and direction of aqueductal CSF flow with an in-depth, pixel-by-pixel approach. Estimation of net flow was used to calculate CSF flow volumes over 24 h. PC-MRI provides positive values when flow is retrograde. Results The study included eight patients with intracranial aneurysms. Four were examined within days after their SAH; three were studied in the chronic stage after SAH while one patient had an unruptured intracranial aneurysm. There was a vast variation in magnitude and direction of aqueductal CSF flow between individuals. Net aqueductal CSF flow was retrograde, i.e., directed towards the third ventricle in 5/8 individuals. For the entire patient cohort, the estimated net aqueductal CSF volumetric flow rate (independent of direction) was median 898 ml/24 h (ranges 69 ml/24 h to 12.9 l/ 24 h). One of the two individuals who had a very high estimated net aqueductal CSF volumetric flow rate, 8.7 l/24 h retrograde, later needed a permanent CSF shunt. Conclusions The magnitude and direction of net aqueductal CSF flow vary extensively in patients with intracranial aneurysms. Following SAH, PC-MRI may offer the possibility to perform individualized assessments of the CSF circulation.

• Lindstrøm, Erika Kristina; Schreiner, Jakob Emil; Ringstad, Geir; Haughton, Victor; Eide, Per Kristian & Mardal, Kent-Andre (2018). Comparison of phase-contrast MR and flow simulations for the study of CSF Dynamics in the cervical spine. The Neuroradiology Journal.  ISSN 1971-4009.  31(3), s 292- 298 . doi: 10.1177/1971400918759812
• Ringstad, Geir; Valnes, Lars Magnus; Dale, Anders; Pripp, Are Hugo; Vatnehol, Svein Are Sirirud; Emblem, Kyrre Eeg; Mardal, Kent-Andre & Eide, Per Kristian (2018). Brain-wide glymphatic enhancement and clearance in humans assessed with MRI. Journal of Clinical Investigation.  ISSN 0021-9738.  3(13) . doi: 10.1172/jci.insight.121537 Full text in Research Archive.
• Valen-Sendstad, Kristian; Bergersen, Aslak Wigdahl; Shimogonya, Yuji; Goubergrits, Leonid; Bruening, Jan; Pallares, Jordi; Cito, Salvatore; Piskin, Senol; Pekkan, Kerem; Geers, Arjan J.; Larrabide, Ignacio; Rapaka, Saikiran; Mihalef, Viorel; Fu, Wenyu; Qiao, Aike; Jain, Kartik; Roller, Sabine; Mardal, Kent-Andre; Kamakoti, Ramji; Spirka, Thomas; Ashton, Neil; Revell, Alistair; Aristokleous, Nicolas; Houston, J. Graeme; Tsuji, Masanori; Ishida, Fujimaro; Menon, Prahlad G.; Browne, Leonard D.; Broderick, Stephen; Shojima, Masaaki; Koizumi, Satoshi; Barbour, Michael; Aliseda, Alberto; Morales, Hernan G.; Lefèvre, Thierry; Hodis, Simona; Al-Smadi, Yahia M.; Tran, Justin S.; Marsden, Alison L.; Vaippummadhom, Sreeja; Einstein, G. Albert; Brown, Alistair G.; Debus, Kristian; Niizuma, Kuniyasu; Rashad, Sherif; Sugiyama, Shin-ichiro; Khan, M. Owais; Updegrove, Adam R.; Shadden, Shawn C.; Cornelissen, Bart M.W.; Majoie, Charles B.L.M.; Berg, Philipp; Saalfield, Sylvia; Kono, Kenichi & Steinman, David A. (2018). Real-world variability in the prediction of intracranial aneurysm wall shear stress: The 2015 international aneurysm CFD challenge. Cardiovascular Engineering and Technology.  ISSN 1869-408X.  9(4), s 544- 564 . doi: 10.1007/s13239-018-00374-2
• Vinje, Vegard; Brucker, Justin; Rognes, Marie Elisabeth; Mardal, Kent-Andre & Haughton, Victor (2018). Fluid dynamics in syringomyelia cavities: Effects of heart rate, CSF velocity, CSF velocity waveform and craniovertebral decompression. The Neuroradiology Journal.  ISSN 1971-4009.  31(5), s 482- 489 . doi: 10.1177/1971400918795482
• Bærland, Trygve; Lee, Jeonghun J.; Mardal, Kent-Andre & Winther, Ragnar (2017). Weakly Imposed Symmetry and Robust Preconditioners for Biot’s Consolidation Model. Computational Methods in Applied Mathematics.  ISSN 1609-4840.  17(3), s 377- 396 . doi: 10.1515/cmam-2017-0016 Full text in Research Archive.
• Evju, Øyvind; Pozo, Jose M.; Frangi, Alejandro F. & Mardal, Kent-Andre (2017). Robustness of common hemodynamic indicators with respect to numerical resolution in 38 middle cerebral artery aneurysms. PLOS ONE.  ISSN 1932-6203.  12(6) . doi: 10.1371/journal.pone.0177566 Full text in Research Archive.
• Haga, Per Thomas; Pizzichelli, Giulia; Mortensen, Mikael; Kuchta, Miroslav; Pahlavian, Soroush Heidari; Sinibaldi, Edoardo; Martin, Bryn A. & Mardal, Kent-Andre (2017). A numerical investigation of intrathecal isobaric drug dispersion within the cervical subarachnoid space. PLOS ONE.  ISSN 1932-6203.  12(3) . doi: 10.1371/journal.pone.0173680 Full text in Research Archive.
• Holter, Karl Erik; Kehlet, Benjamin Dam; Devor, Anna; Sejnowski, Terrence J.; Dale, Anders M.; Omholt, Stig William; Ottersen, Ole Petter; Nagelhus, Erlend Arnulf; Mardal, Kent-Andre & Pettersen, Klas (2017). Interstitial solute transport in 3D reconstructed neuropil occurs by diffusion rather than bulk flow. Proceedings of the National Academy of Sciences of the United States of America.  ISSN 0027-8424.  114(37), s 9894- 9899 . doi: 10.1073/pnas.1706942114 Full text in Research Archive.
• Jain, Kartik; Ringstad, Geir; Eide, Per Kristian & Mardal, Kent-Andre (2017). Direct numerical simulation of transitional hydrodynamcis of the cerebrospinal fluid in Chiari I malformation: The role of cranio-vertebral junction. International Journal for Numerical Methods in Biomedical Engineering.  ISSN 2040-7939.  33(9) . doi: 10.1002/cnm.2853
• Lee, Jeonghun; Mardal, Kent-Andre & Winther, Ragnar (2017). Parameter-robust discretization and preconditioning of Biot's consolidation model. SIAM Journal on Scientific Computing.  ISSN 1064-8275.  39(1), s A1- A24 . doi: 10.1137/15M1029473 Full text in Research Archive.
• Pizzichelli, Giulia; Kehlet, Benjamin Dam; Evju, Øyvind; Martin, Bryn A.; Rognes, Marie Elisabeth; Mardal, Kent-Andre & Sinibaldi, Edoardo (2017). Numerical study of intrathecal drug delivery to a permeable spinal cord: effect of catheter position and angle. Computer Methods in Biomechanics and Biomedical Engineering.  ISSN 1025-5842.  20(15), s 1599- 1608 . doi: 10.1080/10255842.2017.1393805
• Ringstad, Geir; Lindstrøm, Erika Kristina; Vatnehol, Svein Are Sirirud; Mardal, Kent-Andre; Emblem, Kyrre Eeg & Eide, Per Kristian (2017). Non-invasive assessment of pulsatile intracranial pressure with phase-contrast magnetic resonance imaging. PLOS ONE.  ISSN 1932-6203.  12(11), s 1- 17 . doi: 10.1371/journal.pone.0188896 Full text in Research Archive.
• Tveito, Aslak; Jæger, Karoline Horgmo; Kuchta, Miroslav; Mardal, Kent-Andre & Rognes, Marie Elisabeth (2017). A cell-based framework for numerical modeling of electrical conduction in cardiac tissue. Frontiers in Physics.  ISSN 2296-424X.  5 . doi: 10.3389/fphy.2017.00048 Full text in Research Archive.
• Fric, Radek; Lindstrøm, Erika Kristina; Ringstad, Geir; Mardal, Kent-Andre & Eide, Per Kristian (2016). The association between the pulse pressure gradient at the cranio-cervical junction derived from phase-contrast magnetic resonance imaging and invasively measured pulsatile intracranial pressure in symptomatic patients with Chiari malformation type 1. Acta Neurochirurgica.  ISSN 0001-6268.  158(12), s 2295- 2304 . doi: 10.1007/s00701-016-2979-x
• Jain, Kartik; Jiang, Jingfeng; Strother, Charles M & Mardal, Kent-Andre (2016). Transitional hemodynamics in intracranial aneurysms - Comparative velocity investigations with high resolution Lattice Boltzmann simulations, normal resolution ANSYS simulations and MR imaging. Medical Physics (Lancaster).  ISSN 0094-2405.  43(11), s 6186- 6198 . doi: 10.1118/1.4964793
• Jain, Kartik; Roller, Sabine & Mardal, Kent-Andre (2016). Transitional flow in intracranial aneurysms - A space and time refinement study below the Kolmogorov scales using Lattice Boltzmann Method. Computers & Fluids.  ISSN 0045-7930.  127, s 36- 46 . doi: 10.1016/j.compfluid.2015.12.011
• Kuchta, Miroslav; Nordaas, Magne; Verschaeve, Joris C. G.; Mortensen, Mikael & Mardal, Kent-Andre (2016). Preconditioners for saddle point systems with trace constraints coupling 2D and 1D domains. SIAM Journal on Scientific Computing.  ISSN 1064-8275.  38(6), s B962- B987 . doi: 10.1137/15M1052822
• Mardal, Kent-Andre; Nielsen, Bjørn Fredrik & Nordaas, Magne (2016). Robust preconditioners for PDE-constrained optimization with limited observations. BIT Numerical Mathematics.  ISSN 0006-3835.  57(2), s 405- 431 . doi: 10.1007/s10543-016-0635-8
• Støverud, Karen-Helene; Alnæs, Martin Sandve; Langtangen, Hans Petter; Haughton, Victor & Mardal, Kent-Andre (2016). 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.  ISSN 1025-5842.  19(6), s 686- 698 . doi: 10.1080/10255842.2015.1058927
• Støverud, Karen-Helene; Langtangen, Hans Petter; Ringstad, Geir; Eide, Per Kristian & Mardal, Kent-Andre (2016). Computational investigation of cerebrospinal fluid dynamics in the posterior cranial fossa and cervical subarachnoid space in patients with Chiari I malformation. PLOS ONE.  ISSN 1932-6203.  11(10) . doi: 10.1371/journal.pone.0162938
• Alnæs, Martin Sandve; Mardal, Kent-Andre; Bakke, Søren Jacob & Sorteberg, Angelika (2015). Computational fluid dynamics evaluation of flow reversal treatment of giant basilar tip aneurysm. Interventional Neuroradiology.  ISSN 1591-0199.  21(5), s 586- 591 . doi: 10.1177/1591019915597415
• Evju, Øyvind & Mardal, Kent-Andre (2015). On the Assumption of Laminar Flow in Physiological Flows: Cerebral Aneurysms As an Illustrative Example, In Alfio Quarterioni (ed.),  Modeling the Heart and the Circulatory System.  Springer.  ISBN 3319052292.  7.  s 177 - 195
• Jain, Kartik & Mardal, Kent-Andre (2015). Exploring The Critical Reynolds Number For Transition In Intracranial Aneurysms–highly Resolved Simulations Below Kolmogorov Scales, In  CMBE15 4th International Conference on Computational & Mathematical Biomedical Engineering.  CMBE.  ISBN 978-0-9562914-3-1.  MS-D5.
• Kuchta, Miroslav; Mardal, Kent-Andre & Mortensen, Mikael (2015). Characterization of the space of rigid motions in arbitrary domains, In Bjørn Helge Skallerud & Helge Ingolf Andersson (ed.),  Proceedings of MekIT'15 Eighth National Conference on Computational Mechanics.  International Center for Numerical Methods in Engineering (CIMNE).  ISBN 97884944244-96.  kapittel 16.  s 259 - 274
• Mortensen, Mikael; Kuchta, Miroslav; Mardal, Kent-Andre & Verschaeve, Joris C. G. (2015). BEND|P|Y: Python framework for computing bending of complex plate-beam systems, In Bjørn Helge Skallerud & Helge Ingolf Andersson (ed.),  Proceedings of MekIT'15 Eighth National Conference on Computational Mechanics.  International Center for Numerical Methods in Engineering (CIMNE).  ISBN 97884944244-96.  kapittel 19.  s 307 - 320
• Helgeland, Anders; Mardal, Kent-Andre; Haughton, Victor & Reif, Bjørn Anders Pettersson (2014). Numerical simulations of the pulsating flow of cerebrospinal fluid flow in the cervical spinal canal of a Chiari patient. Journal of Biomechanics.  ISSN 0021-9290.  47(5), s 1082- 1090 . doi: 10.1016/j.jbiomech.2013.12.023
• Linge, Svein; Mardal, Kent-Andre; Helgeland, Anders; Heiss, John D. & Haughton, Victor (2014). Effect of craniovertebral decompression on CSF dynamics in Chiari malformation Type I studied with computational fluid dynamics. Journal of Neurosurgery : Spine.  ISSN 1547-5654.  21(4), s 559- 564 . doi: 10.3171/2014.6.SPINE13950
• Seljebotn, Dag Sverre; Mardal, Kent-Andre; Jewell, J. B.; Eriksen, Hans Kristian Kamfjord & Bull, Philip James (2014). A MULTI-LEVEL SOLVER FOR GAUSSIAN CONSTRAINED COSMIC MICROWAVE BACKGROUND REALIZATIONS. Astrophysical Journal Supplement Series.  ISSN 0067-0049.  210(2) . doi: 10.1088/0067-0049/210/2/24 Full text in Research Archive.
• Victor, Haughton & Mardal, Kent-Andre (2014). Spinal Fluid Biomechanics and Imaging: An Update for Neuroradiologists. American Journal of Neuroradiology.  ISSN 0195-6108.  35, s 1864- 1869 . doi: 10.3174/ajnr.A4023
• Drøsdal, Ida Nordehaug; Mardal, Kent-Andre; Støverud, Karen-Helene & Haughton, Victor (2013). Effect of the Central Canal in the Spinal Cord on Fluid Movement within the Cord. The Neuroradiology Journal.  ISSN 1971-4009.  26(5), s 585- 590
• Evju, Øyvind; Valen-Senstad, Kristian & Mardal, Kent-Andre (2013). A study of wall shear stress in 12 aneurysms with respect to different viscosity models and flow conditions. Journal of Biomechanics.  ISSN 0021-9290.  46(16), s 2802- 2808 . doi: 10.1016/j.jbiomech.2013.09.004
• Linge, Svein; Mardal, Kent-Andre; Haughton, Victor & Helgeland, Anders (2013). Simulating CSF flow dynamics in the normal and chiari I subarachnoid space during rest and exertion. American Journal of Neuroradiology.  ISSN 0195-6108.  34(1), s 41- 45 . doi: 10.3174/ajnr.A3282
• Mardal, Kent-Andre; Rutkowska, G.; Linge, Svein & Haughton, Victor (2013). Estimation of CSF flow resistance in the upper cervical spine. The Neuroradiology Journal.  ISSN 1971-4009.  26(1), s 106- 110
• Mardal, Kent-Andre; Schoberl, Joachim & Winther, Ragnar (2013). A uniformly stable Fortin operator for the Taylor-Hood element. Numerische Mathematik.  ISSN 0029-599X.  123(3), s 537- 551 . doi: 10.1007/s00211-012-0492-6
• Mortensen, Mikael; Mardal, Kent-Andre; Martin, B & Pahlavian, S. (2013). Preliminary study of the impact of spinal cord nerve roots and denticulate ligaments on drug movement in the cervical spinal subarachnoid space, In Kent-Andre Mardal; Anders Bernhard Logg & Andre Massing (ed.),  Proceedings of the 26th Nordic Seminar on Computational Mechanics.  Simula Research Laboratory.  ISBN 978-82-92593-12-7.  Kapittel.  s 213 - 216
• Nielsen, Bjørn Fredrik & Mardal, Kent-Andre (2013). Analysis of the Minimal Residual Method Applied to Ill Posed Optimality Systems. SIAM Journal on Scientific Computing.  ISSN 1064-8275.  35(2), s A785- A814 . doi: 10.1137/120871547
• Støverud, Karen-Helene; Langtangen, Hans Petter; Haughton, Victor & Mardal, Kent-Andre (2013). CSF pressure and velocity in obstructions of the subarachnoid spaces. The Neuroradiology Journal.  ISSN 1971-4009.  26(2)
• Støverud, Karen-Helene; Mardal, Kent-Andre; Langtangen, Hans Petter & Haughton, Victor (2013). Effect of oscillatory cerebrospinal fluid pressure on fluid movement in the spinal cord, In Bjørn Helge Skallerud & Helge Andersson (ed.),  MekIT'13 Seventh National Conference on Computational Mechanics, Trondheim 13-14 May 2013.  Akademika forlag.  ISBN 978-82-321-0266-2.  Kapittel.
• Valen-Sendstad, Kristian; Mardal, Kent-Andre & Steinman, D. A. (2013). High-resolution computational fluid dynamics detects high-frequency velocity fluctuations in bifurcation, but not sidewall, aneurysms of the middle cerebral artery. Journal of Biomechanics.  ISSN 0021-9290.  46(2), s 402- 407 . doi: 10.1016/j.jbiomech.2012.10.042
• Alnæs, Martin Sandve; Logg, Anders Bernhard & Mardal, Kent-Andre (2012). UFC: a finite element code generation interface, In Anders Logg; Kent-Andre Mardal & Garth N. Wells (ed.),  Automated Solution of Differential Equations by the Finite Element Method.  Springer.  ISBN 9783642230981.  Kapittel 16.  s 283 - 302
• Alnæs, Martin Sandve & Mardal, Kent-Andre (2012). SyFi and SFC: symbolic finite elements and form compilation, In Anders Logg; Kent-Andre Mardal & Garth N. Wells (ed.),  Automated Solution of Differential Equations by the Finite Element Method.  Springer.  ISBN 9783642230981.  Kapittel 15.  s 273 - 282
• Hake, Johan Elon & Mardal, Kent-Andre (2012). Lessons learned in mixed language programming, In Anders Logg; Kent-Andre Mardal & Garth N. Wells (ed.),  Automated Solution of Differential Equations by the Finite Element Method.  Springer.  ISBN 9783642230981.  Kapittel 19.  s 363 - 381
• Kirby, R.C. & Mardal, Kent-Andre (2012). Constructing general reference finite elements, In Anders Logg; Kent-Andre Mardal & Garth N. Wells (ed.),  Automated Solution of Differential Equations by the Finite Element Method.  Springer.  ISBN 9783642230981.  Kapittel 4.  s 121 - 132
• Logg, Anders Bernhard; Mardal, Kent-Andre & Wells, Garth N. (2012). Finite element assembly, In Anders Logg; Kent-Andre Mardal & Garth N. Wells (ed.),  Automated Solution of Differential Equations by the Finite Element Method.  Springer.  ISBN 9783642230981.  Kapittel 6.  s 141 - 146
• Mardal, Kent-Andre & Haga, Joachim Berdal (2012). Block preconditioning of systems of PDEs, In Anders Logg; Kent-Andre Mardal & Garth N. Wells (ed.),  Automated Solution of Differential Equations by the Finite Element Method.  Springer.  ISBN 9783642230981.  Kapittel 35.  s 643 - 655
• Mortensen, Mikael; Mardal, Kent-Andre & Langtangen, Hans Petter (2012). Simulation of transitional flows, In Anders Logg; Kent-Andre Mardal & Garth N. Wells (ed.),  Automated Solution of Differential Equations by the Finite Element Method.  Springer.  ISBN 9783642230981.  Kapittel 22.  s 421 - 440
• Støle-Hentschel, Susanne; Linge, Svein; Løvgren, Alf Emil & Mardal, Kent-Andre (2012). Cerebrospinal fluid flow, In Anders Logg; Kent-Andre Mardal & Garth N. Wells (ed.),  Automated Solution of Differential Equations by the Finite Element Method.  Springer.  ISBN 9783642230981.  Applications.  s 455 - 471
• Valen-Senstad, Kristian; Logg, Anders Bernhard; Mardal, Kent-Andre; Narayanan, Harish & Mortensen, Mikael (2012). A comparison of finite element schemes for the incompressible Navier–Stokes equations, In Anders Logg; Kent-Andre Mardal & Garth N. Wells (ed.),  Automated Solution of Differential Equations by the Finite Element Method.  Springer.  ISBN 9783642230981.  Kapittel 21.  s 399 - 420
• Valen-Senstad, Kristian; Mardal, Kent-Andre & Logg, Anders Bernhard (2012). Computational hemodynamics, In Anders Logg; Kent-Andre Mardal & Garth N. Wells (ed.),  Automated Solution of Differential Equations by the Finite Element Method.  Springer.  ISBN 9783642230981.  Kapittel 23.  s 441 - 454
• Wilbers, Ilmar Michaael; Mardal, Kent-Andre & Alnæs, Martin Sandve (2012). Instant: just-in-time compilation of C/C++ in Python, In Anders Logg; Kent-Andre Mardal & Garth N. Wells (ed.),  Automated Solution of Differential Equations by the Finite Element Method.  Springer.  ISBN 9783642230981.  Kapittel 14.  s 257 - 272
• Jiang, Jingfeng; Johnson, Kevin; Wieben, Oliver; Valen-Senstad, Kristian; Mardal, Kent-Andre & Strother, Charles M (2011). Flow characteristics in a canine aneurysm model: A comparison of 4D accelerated phase-contrast MR measurements and computational fluid dynamics simulations. Medical Physics (Lancaster).  ISSN 0094-2405.  38(11), s 6300- 6312 . doi: 10.1118/1.3652917
• Linge, Svein; Haughton, Victor; Løvgren, Alf Emil; Mardal, Kent-Andre; Helgeland, Anders & Langtangen, Hans Petter (2011). Effect of Tonsillar Herniation on Cyclic CSF Flow Studied with Computational Flow Analysis. American Journal of Neuroradiology.  ISSN 0195-6108.  32, s 1474- 1481 . doi: 10.3174/ajnr.A2496 Full text in Research Archive.
• Mardal, Kent-Andre & Winther, Ragnar (2011). Preconditioning discretizations of systems of partial differential equations. Numerical Linear Algebra with Applications.  ISSN 1070-5325.  18(1), s 1- 40 . doi: 10.1002/nla.716
• Nilssen, Trygve Kastberg; Staff, Gunnar Andreas & Mardal, Kent-Andre (2011). Order Optimal Preconditioners for Fully Implicit Runge-Kutta Schemes Applied to the Bidomain Equations. Numerical Methods for Partial Differential Equations.  ISSN 0749-159X.  27(5), s 1290- 1312 . doi: 10.1002/num.20582 Show summary

  The partial differential equation part of the bidomain equations is discretized in time with fully implicit Runge–Kutta methods, and the resulting block systems are preconditioned with a block diagonal preconditioner. By studying the time-stepping operator in the proper Sobolev spaces, we show that the preconditioned systems have bounded condition numbers given that the Runge–Kutta scheme is A-stable and irreducible with an invertible coefficient matrix. A new proof of order optimality of the preconditioners for the one-leg discretization in time of the bidomain equations is also presented. The theoretical results are verified by numerical experiments. Additionally, the concept of weakly positive-definite matrices is introduced and analyzed.

• Støverud, Karen-Helene; Mardal, Kent-Andre; Langtangen, Hans Petter & Haughton, Victor (2011). The effect of varying cross-sectional areas on cerebrospinal fluid flow and pressure in the cervical spine, In Bjørn Helge Skallerud & Helge Ingolf Andersson (ed.),  MekIT'11: Sixth National Conference on Computational Mechanics, Trondheim 23-24 May 2011.  Tapir Akademisk Forlag.  ISBN 978-82-519-2798-7.  Kapittel. Show summary

  The aim of this study was to determine CSF pressure and velocities in idealized geometries representing the stenosed spinal canal found in Chiari patients.We applied the Navier-Stokes equation to simulate the cyclic CSF flow during one cardiac cycle. Hereby, we have illuminated a well–established medical hypothesis for the relation between the Chiari I malformation and syringomyelia: namely that spinal cord cysts are caused by the so-called Venturi effect (predicted by Bernoulli’s law) appearing in fluids that flow through obstructed areas. The results showed that the pressure gradient in geometries with obstructions comparable to Chiari patients may be 10 times as high as under normal flow conditions. The results also showed that the pressure gradients at the level of an obstruction may be twice as large as that predicted from steady flow or Bernoulli’s law.

• Støverud, Karen-Helene; Støverud, Karen-Helene; Mardal, Kent-Andre; Haughton, Victor; Langtangen, Hans Petter & Langtangen, Hans Petter (2011). CSF Flow in Chiari I and Syringomyelia from the Perspective of Computational Fluid Dynamics. The Neuroradiology Journal.  ISSN 1971-4009.  24(1), s 20- 23
• Valen-Senstad, Kristian; Mardal, Kent-Andre; Mortensen, Mikael; Reif, Bjørn Anders Pettersson & Langtangen, Hans Petter (2011). Direct numerical simulation of transitional flow in a patient-specific intracranial aneurysm. Journal of Biomechanics.  ISSN 0021-9290.  44(16), s 2826- 2832 . doi: 10.1016/j.jbiomech.2011.08.015
• Valen-Senstad, Kristian; Mardal, Kent-Andre; Mortensen, Mikael; Reif, Bjørn Anders Pettersson & Langtangen, Hans Petter (2011). On The Complexity of Stationary Flow in Patient–Specific Aneurysms, In Bjørn Helge Skallerud & Helge Ingolf Andersson (ed.),  MekIT'11: Sixth National Conference on Computational Mechanics, Trondheim 23-24 May 2011.  Tapir Akademisk Forlag.  ISBN 978-82-519-2798-7.  Kapittel. Show summary

  Summary Sound or bruits in the vasculatory system at the range of 1Hz-1kHz is known to occur, and frequency peaks at high frequencies are associated with sick blood vessels. The exact reason for these sounds are not known, but the sound may be generated by turbulence. Turbulence generated sound is typically associated with high frequencies but also with low energy levels. Unfortunately, most blood flow simulations are performed with space and time resolutions where rapid fluctuations typ- ically associated with non-laminar flow cannot be captured. Complex non-laminar flow and the subsequent oscillatory wall stresses can po- tentially be of importance in understanding aneurysm rupture through the local arterial wall response. To investigate the possible presence of complex non-laminar blood flow in intracranial aneurysms, we per- formed high resolution computational fluid dynamics (CFD) simulations for patient specific middle cerebral artery (MCA) aneurysms with sta- tionary inflow conditions. The current study confirms, through high resolution simulations, that complex oscillatory flow may occur in in- tracranial aneurysms. CFD practitioners should therefore be aware of the potentially strong demands to space-time computational resolution in blood flow simulations.

• Winther, Ragnar & Mardal, Kent-Andre (2011). Construction of preconditioners by mapping properties for systems of partial differential equations, In Owe Axelsson & Janos Karatson (ed.),  Efficient Preconditioned Solution Methods for Elliptic Partial Differential Equations.  Bentham eBooks.  ISBN 978-1-60805-291-2.  Chapter 4.  s 65 - 83
• Alnæs, Martin Sandve & Mardal, Kent-Andre (2010). On the Efficiency of Symbolic Computations Combined with Code Generation for Finite Element Methods. ACM Transactions on Mathematical Software.  ISSN 0098-3500.  37(1) . doi: 10.1145/1644001.1644007
• Burger, Martin; Mardal, Kent-Andre & Nielsen, Bjørn Fredrik (2010). Stability analysis of the inverse transmembrane potential problem in electrocardiography. Inverse Problems.  ISSN 0266-5611.  26(10) . doi: 10.1088/0266-5611/26/10/105012

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• Langtangen, Hans Petter & Mardal, Kent-Andre (2019). Introduction to Numerical Methods for Variational Problems. Springer Nature.  ISBN 978-3-030-23787-5.  395 s.
• Mardal, Kent-Andre; Logg, Anders Bernhard & Massing, Andre (ed.) (2013). Proceedings of the 26th Nordic Seminar on Computational Mechanics. Simula Research Laboratory.  ISBN 978-82-92593-12-7.  243 s.
• Logg, Anders; Mardal, Kent-Andre & Wells, Garth N. (ed.) (2012). Automated Solution of Differential Equations by the Finite Element Method. Springer.  ISBN 9783642230981.  720 s.

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• Eide, Per Kristian; Sorteberg, Angelika; Sorteberg, Wilhelm; Lindstrøm, Erika Kristina; Mardal, Kent-Andre & Ringstad, Geir (2018). "Bucket" cerebrospinal fluid bulk flow: when the terrain disagrees with the map. Acta Neurochirurgica.  ISSN 0001-6268.  161(2), s 259- 261 . doi: 10.1007/s00701-018-3775-6
• Mardal, Kent-Andre (2017). Computational modeling of the glymphatic system: how is waste cleared from the brain?.
• Mardal, Kent-Andre (2017). The operator preconditioning framework with various applications to interstitial fluid flow and the aging human brain.
• Mardal, Kent-Andre; Lindstrøm, Erika Kristina & Haughton, Victor (2017). Physics of oscillatory CSF Flow.
• Pettersen, Klas; Holter, Karl Erik; Kehlet, Benjamin; Devor, Anna; Sejnowski, Terrence J.; Dale, Anders; Omholt, Stig William; Ottersen, Ole Petter; Mardal, Kent-Andre & Nagelhus, Erlend Arnulf (2017). Interstitial solute transport in 3D reconstructed neuropil: Diffusion predominates.
• Bradley, William G.; Haughton, Victor & Mardal, Kent-Andre (2016). Cerebrospinal fluid flow in adults, In Joseph C Masdeu & R Gilberto Gonzalez (ed.),  Handbook of clinical neurology Neuroimaging, part I.  Elsevier.  ISBN 978-0-444-53485-9.  chapter 28.  s 591 - 603
• Kylstad, Nina Kristine; Mardal, Kent-Andre; Haughton, Victor & Rognes, Marie Elisabeth (2015). Effect of Spinal Cord Viscoelasticity on Its Response to CSF Pressure Waves: a Computational Study.
• Mardal, Kent-Andre (2015). 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.
• Mardal, Kent-Andre & Haughton, Victor (2015). Role of CSF flow in the pathogenesis of Syringomyelia.
• Mardal, Kent-Andre; Jain, Kartik; Støverud, Karen Helene; Ringstad, Geir & Eide, Per Kristian (2015). On the complexity of the Cerebrospinal fluid flow in the upper spinal column – is the assumption of laminar flow appropriate?.
• Mardal, Kent-Andre (2014). On the modeling of the central nervous system in Chiari patients - transitional flow, poroelasticity and porous-viscus flow couplings.
• Mardal, Kent-Andre; Helgeland, Anders; Haugthon, Victor; Reif, Anders & Støverud, Karen-Helene (2014). On the assumption of laminar flow of CSF in Chiari patients.
• Mardal, Kent-Andre; Khan, Owasis; Valen-Sendstad, Kristian; Steinman, David & Jain, Kartik (2014). On numerical methods for transitional flow – application to blood flow in aneurysms.
• Mardal, Kent-Andre; Langtangen, Hans Petter; Røtnes, Pål & Seland, Torbjørn (2014). Er zombier en trussel mot menneskeheten?.
• Mardal, Kent-Andre; Støverud, Karen-Helene; Mortensen, Mikael; Jain, Kartik; Martin, Bryn & Pahlavian, Soroush (2014). Cerebrospinal fluid flow in association with the central nervous system -- Chiari and drug delivery.
• Elvetun, Ole Løseth; Nielsen, Bjørn Fredrik & Mardal, Kent-Andre (2012). Early detection of heart attacks using PDE-constrained optimization.
• Nielsen, Bjørn Fredrik & Mardal, Kent-Andre (2012). The Minimal Residual Method applied to ill-posed optimality systems; eigenvalues and convergence properties.
• Linge, Svein; Haughton, P.D.W.; Løvgren, Alf Emil; Mardal, Kent-Andre; Helgeland, A; Langtangen, Hans Petter & Støverud, Karen-Helene (2011). Cyclic Cerebrospinal Fluid Flow (1): Towards the Understanding of Cerebrospinal Fluid Flow Dynamics in Chiari I Malformation.
• Linge, Svein; Mardal, Kent-Andre; Haughton, Victor & Helgeland, Anders (2011). Cerebrospinal fluid flow characteristics at double heart rate.
• Mardal, Kent-Andre & Nielsen, Bjørn Fredrik (2011). Efficient preconditioning of optimality systems.
• Støverud, Karen-Helene; Mardal, Kent-Andre; Haughton, Victor; Langtangen, Hans Petter & Linge, Svein (2011). Cyclic Cerebrospinal Fluid Flow (II): The role of Cerebrospinal Fluid Pressure in the Pathogenesis of Syringomyelia.

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