Biomedical flows#
I have been working from 2012-2016 as an adjunct research scientist at Simula Research Laboratory. Here I had the great honor to be working with the late Prof. Hans Petter Langtangen [Mortensen and Langtangen, 2016, Mortensen et al., 2011, Mortensen et al., 2012, Valen-Sendstad et al., 2011], at the Center for Biomedical Computing.
I have contributed quite a bit to the FEniCS project, and the incompressible Navier-Stokes solver Oasis has been developed within the FEniCS framework. The solver has been developed for efficiency, with MPI, and it is written entirely in Python. The Oasis solver is documented in the Computer Physics Communications paper [Mortensen and Valen-Sendstad, 2015], where we show that it may run as fast and accurate as the low-level finite volume C++ solvers OpenFOAM and CDP (Stanford).
The Oasis solver has been used in a range of master theses (see Teaching). For one of my master students, Per Thomas Haga, the thesis led to a journal paper on injecting drugs in the Cerebrospinal fluid (CSF) [Haga et al., 2017]. The animation on the right shows how an injected drug moves up and down inside the CSF channel. It can also be seen that, due to the very low diffusivity of the scalar drug, we modelled the scalar transport using Lagrangian particle tracking.
I have been working quite a bit together with Kristian Valen-Sendstad at Simula, on different aspects of biomedical flows. Our simulations on intracranial aneurysms [Valen-Sendstad et al., 2011], actually reached the headlines of Norway’s larges newspaper VG, when we found a correlation between transition to turbulence and the risk of aneurysm rupture (more famously known as stroke). For this work I performed most of the simulations when still at FFI.
More recently we have been studying transition and mesh sensitivity in the FDA nozzle benchmark. In [Bergersen et al., 2019] we use both regular CFD and linear stability analysis to show that care must be taken when designing a CFD benchmark. Transition to turbulence can only come from a seed, or perturbation, and an ideal case like the FDA benchmark should not transtition at all unless some noise is added to the system. Figure is showing an unstable eigenmode in the FDA bechmark, showing that transition should in deed occur at the Reynolds number=3500. Here I have conducted the stability simulations using the dog linear stability analysis software package.
Linear stability analysis of the FDA benchmark. Showing the most unstable eigenmode.
References#
Aslak W. Bergersen, Mikael Mortensen, and Kristian Valen-Sendstad. The fda nozzle benchmark: “in theory there is no difference between theory and practice, but in practice there is”. International Journal for Numerical Methods in Biomedical Engineering, 35(1):e3150, 2019. e3150 cnm.3150. doi:10.1002/cnm.3150.
Per Thomas Haga, Giulia Pizzichelli, Mikael Mortensen, Miroslav Kuchta, Soroush Heidari Pahlavian, Edoardo Sinibaldi, Bryn A. Martin, and Kent-Andre Mardal. A numerical investigation of intrathecal isobaric drug dispersion within the cervical subarachnoid space. PLOS ONE, 12(3):1–21, 03 2017. doi:10.1371/journal.pone.0173680.
M. Mortensen and H. P. Langtangen. High performance Python for direct numerical simulations of turbulent flows. Computer Physics Communications, 203:53–65, 2016. doi:10.1016/j.cpc.2016.02.005.
Mikael Mortensen, Hans Petter Langtangen, and Garth N. Wells. A fenics-based programming framework for modeling turbulent flow by the reynolds-averaged Navier-Stokes equations. Advances in Water Resources, 34(9):1082–1101, 2011. doi:10.1016/j.advwatres.2011.02.013.
Mikael Mortensen, Kent-Andre Mardal, and Hans Petter Langtangen. Simulation of Transitional Flows, pages 421–440. Springer, Berlin, Heidelberg, 2012. doi:10.1007/978-3-642-23099-8_22.
Mikael Mortensen and Kristian Valen-Sendstad. Oasis: a high-level/high-performance open source Navier-Stokes solver. Computer Physics Communications, 188:177–188, 2015. doi:10.1016/j.cpc.2014.10.026.
Kristian Valen-Sendstad, Kent-André Mardal, Mikael Mortensen, Bjørn Anders Pettersson Reif, and Hans Petter Langtangen. Direct numerical simulation of transitional flow in a patient-specific intracranial aneurysm. Journal of Biomechanics, 44(16):2826–2832, 2011. doi:10.1016/j.jbiomech.2011.08.015.