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Portable simulation framework for diffusion MRI
KTH, School of Electrical Engineering and Computer Science (EECS), Computational Science and Technology (CST).ORCID iD: 0000-0002-3213-0040
KTH, School of Electrical Engineering and Computer Science (EECS), Computational Science and Technology (CST).
KTH, School of Electrical Engineering and Computer Science (EECS), Computational Science and Technology (CST).
KTH, School of Electrical Engineering and Computer Science (EECS), Computational Science and Technology (CST).ORCID iD: 0000-0002-1695-8809
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2019 (English)In: Journal of magnetic resonance, ISSN 1090-7807, E-ISSN 1096-0856, Vol. 309, article id 106611Article in journal (Refereed) Published
Abstract [en]

The numerical simulation of the diffusion MRI signal arising from complex tissue micro-structures is helpful for understanding and interpreting imaging data as well as for designing and optimizing MRI sequences. The discretization of the Bloch-Torrey equation by finite elements is a more recently developed approach for this purpose, in contrast to random walk simulations, which has a longer history. While finite elements discretization is more difficult to implement than random walk simulations, the approach benefits from a long history of theoretical and numerical developments by the mathematical and engineering communities. In particular, software packages for the automated solutions of partial differential equations using finite elements discretization, such as FEniCS, are undergoing active support and development. However, because diffusion MRI simulation is a relatively new application area, there is still a gap between the simulation needs of the MRI community and the available tools provided by finite elements software packages. In this paper, we address two potential difficulties in using FEniCS for diffusion MRI simulation. First, we simplified software installation by the use of FEniCS containers that are completely portable across multiple platforms. Second, we provide a portable simulation framework based on Python and whose code is open source. This simulation framework can be seamlessly integrated with cloud computing resources such as Google Colaboratory notebooks working on a web browser or with Google Cloud Platform with MPI parallelization. We show examples illustrating the accuracy, the computational times, and parallel computing capabilities. The framework contributes to reproducible science and open-source software in computational diffusion MRI with the hope that it will help to speed up method developments and stimulate research collaborations.

Place, publisher, year, edition, pages
Academic Press, 2019. Vol. 309, article id 106611
Keywords [en]
Cloud computing, diffusion MRI, Bloch-Torrey equation, interface conditions, pseudo-periodic conditions, FEniCS.
National Category
Mathematics
Research subject
Applied and Computational Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-256328DOI: 10.1016/j.jmr.2019.106611PubMedID: 31574354Scopus ID: 2-s2.0-85072714990OAI: oai:DiVA.org:kth-256328DiVA, id: diva2:1344749
Note

QC 20190822

Available from: 2019-08-21 Created: 2019-08-21 Last updated: 2019-11-06Bibliographically approved
In thesis
1. High Performance Finite Element Methods with Application to Simulation of Vertical Axis Wind Turbines and Diffusion MRI
Open this publication in new window or tab >>High Performance Finite Element Methods with Application to Simulation of Vertical Axis Wind Turbines and Diffusion MRI
2019 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Finite element methods have been developed over decades, and together with the growth of computer power, they become more and more important in dealing with large-scale simulations in science and industry.The objective of this thesis is to develop high-performance finite element methods, with two concrete applications: computational fluid dynamics (CFD) with simulation of turbulent flow past a vertical axis wind turbine (VAWT), and computational diffusion magnetic resonance imaging (CDMRI). The thesis presents contributions in the form of both new numerical methods for high-performance computing frameworks and efficient, tested software, published open source as part of the FEniCS/FEniCS-HPC platform. More specifically, we have four main contributions through the thesis work.

First, we develop a DFS-ALE method which combines the Direct finite element simulation method (DFS) with the Arbitrary Lagrangian-Eulerian method (ALE) to solve the Navier-Stokes equations for a rotating turbine. This method is enhanced with dual-based a posteriori error control and automated mesh adaptation. Turbulent boundary layers are modeled by a slip boundary condition to avoid a full resolution which is impossible even with the most powerful computers available today. The method is validated against experimental data with a good agreement.

Second, we propose a partition of unity finite element method to tackle interface problems. In CFD, it allows for imposing slip velocity boundary conditions on conforming internal interfaces for a fluid-structure interaction model. In CDMRI, it helps to overcome the difficulties that the standard approaches have when imposing the microscopic heterogeneity of the biological tissues and allows for efficient solutions of the Bloch-Torrey equation in heterogeneous domains. The method facilitates a straightforward implementation on the FEniCS/ FEniCS-HPC platform. The method is validated against reference solutions, and the implementation shows a strong parallel scalability.

Third, we propose a finite element discretization on manifolds in order to efficiently simulate the diffusion MRI signal in domains that have a thin layer or a thin tube geometrical structure. The method helps to significantly reduce the required simulation time, computer memory, and difficulties associated with mesh generation, while maintaining the accuracy. Thus, it opens the possibility to simulate complicated structures at a low cost, for a better understanding of diffusion MRI in the brain.

Finally, we propose an efficient portable simulation framework that integrates recent advanced techniques in both mathematics and computer science to enable the users to perform simulations with the Cloud computing technology. The simulation framework consists of Python, IPython and C++ solvers working either on a web browser with Google Colaboratory notebooks or on the Google Cloud Platform with MPI parallelization.

Abstract [sv]

Finita elementmetoder har utvecklats under årtionden, och har, till- sammans med tillväxten i datorkraft, blivit allt viktigare för att utföra storskaliga simuleringar inom både akademin och industrin. Målet med denna avhandling är att utveckla finita elementmetoder med högprestanda, med särskilt fokus på två konkreta applikationer; beräknings- strömningsdynamik (eng. Computational Fluid Dynamics (CFD)) för simulering av turbulent flöde runt en vindturbin, och beräkningar inom diffusionsmagnetresonanstomografi (eng. Computational diffusion magnetic resonance imaging (CDMRI)). Denna avhandling innehåller bidrag till ovanstående områden i form av såväl nya numeriska metoder för högprestandaberäkningsramverk och testad effektiv programvara vilken publicerats som öppen källkod som del av plattformen FEniCS/FEniCS-HPC. Mer specifikt presenterar vi fyra huvudbidrag i detta avhandlingsarbete.

Först utvecklar vi en DFS-ALE-metod som kombinerar Direkt Fini- ta Elementsimulering (DFS) med den Arbiträra Lagrange-Eulermetoden (ALE) för att lösa Navier-Stokes ekvationer för en roterande turbin. Vår metod är en förbättrad variant med dualbaserad a posteriori felkontroll och automatiserad adaptering av beräkningsnätet. Turbulenta gränsskikt modelleras med ett sliprandvillkor för att undvika full upplösning av problemet, vilket är omöjligt även med de mest kraftfulla datorer som finns att tillgå idag. Metoden valideras mot experimentell data, med god överensstämmelse.

Därnäst föreslår vi en enhetspartitions finita element metod för att tackla interfaceproblem. Inom CFD möjliggör detta att påtvinga ett sliprandvillkor på konforma inre interface för en fluidstrukturinter-kationsmodell. Inom CDMRI bidrar det med att överkomma svårigheterna med att påtvinga mikroskopisk heterogenitet av den biologiska vävnaden, och möjliggör effektiv lösning av Bloch-Torrey ekvationen i heterogena domäner. Metoden gör det enklare att göra en rättfram implementering i FEniCS/FEniCS-HPC. Metoden valideras mot referenslösnignar, och implementationen visar på stark parallel skalning (eng. strong parallel scaling).

Sedan föreslår vi en finita elementdisktretisering på mångfalder för att effektivt kunna simulera diffusions-MRI-signaler i områden med en tunn geometrisk struktur. Metoden bidrar med att signifikant reducera simuleringstiden, minnesåtgång och svårigheter associerade med genereringen av beräkningsnät, utan att påverka precisionen i beräkningarna. Detta öppnar för möjligheter att simulera komplicerade strukturer till låg kostnad, för att bättre förstå diffusionsmagnettomografi i hjärnan.

Tilll sist föreslår vi ett effektivt portabelt simuleringsramverk som integrear nya avancerade tekniker inom både matematik och datave- tenskap för att möjliggöra för användaren att utföra simuleringar med datormolnberäkningsteknologin. Simuleringsramverket består av Python, IPython och C++-lösare som används tillsammans antingen i en webbläsare med Google Colaboration notebooks eller på Google Cloud-plattformen med MPI-parallellisering.

Place, publisher, year, edition, pages
KTH Royal Institute of Technology, 2019. p. 53
Series
TRITA-EECS-AVL ; 2019:76
Keywords
High performance finite element method, computational diffusion MRI, turbulent flow, vertical axis wind turbine, Cloud computing., högprestanda finita elementmetod, beräkningsdiffusionsmagnetresonanstomografi, turbulent flöde, vertikalaxlad vindturbin, datormolnberäkning
National Category
Natural Sciences Medical and Health Sciences
Research subject
Applied and Computational Mathematics; Biological Physics; Computer Science; Engineering Mechanics; Mathematics; Physics, Biological and Biomedical Physics
Identifiers
urn:nbn:se:kth:diva-263200 (URN)978-91-7873-337-8 (ISBN)
Public defence
2019-12-04, F3, Lindstedtsvägen 26, Stockholm, 10:15 (English)
Opponent
Supervisors
Note

QC 20191105

Available from: 2019-11-05 Created: 2019-11-01 Last updated: 2019-11-11Bibliographically approved

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Dancheva, TamaraJansson, JohanHoffman, Johan

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