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Kronborg, J. & Hoffman, J. (2023). The triple decomposition of the velocity gradient tensor as a standardized real Schur form. Physics of fluids, 35(3), Article ID 031703.
Open this publication in new window or tab >>The triple decomposition of the velocity gradient tensor as a standardized real Schur form
2023 (English)In: Physics of fluids, ISSN 1070-6631, E-ISSN 1089-7666, Vol. 35, no 3, article id 031703Article in journal (Refereed) Published
Abstract [en]

The triple decomposition of a velocity gradient tensor provides an analysis tool in fluid mechanics by which the flow can be split into a sum of irrotational straining flow, shear flow, and rigid body rotational flow. In 2007, Kolar formulated an optimization problem to compute the triple decomposition [V. Kolar, "Vortex identification: New requirements and limitations, " Int. J. Heat Fluid Flow 28, 638-652 (2007)], and more recently, the triple decomposition has been connected to the Schur form of the associated matrix. We show that the standardized real Schur form, which can be computed by state of the art linear algebra routines, is a solution to the optimization problem posed by Kolar. We also demonstrate why using the standardized variant of the real Schur form makes computation of the triple decomposition more efficient. Furthermore, we illustrate why different structures of the real Schur form correspond to different alignments of the coordinate system with the fluid flow and may, therefore, lead to differences in the resulting triple decomposition. Based on these results, we propose a new, simplified algorithm for computing the triple decomposition, which guarantees consistent results.

Place, publisher, year, edition, pages
AIP Publishing, 2023
National Category
Computer Sciences
Identifiers
urn:nbn:se:kth:diva-325216 (URN)10.1063/5.0138180 (DOI)000944031400005 ()2-s2.0-85149821952 (Scopus ID)
Note

QC 20230403

Available from: 2023-04-03 Created: 2023-04-03 Last updated: 2023-04-03Bibliographically approved
Balmus, M., Hoffman, J., Massing, A. & Nordsletten, D. A. (2022). A stabilized multidomain partition of unity approach to solving incompressible viscous flow. Computer Methods in Applied Mechanics and Engineering, 392, Article ID 114656.
Open this publication in new window or tab >>A stabilized multidomain partition of unity approach to solving incompressible viscous flow
2022 (English)In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 392, article id 114656Article in journal (Refereed) Published
Abstract [en]

In this work we propose a new stabilized approach for solving the incompressible Navier-Stokes equations on fixed overlapping grids. This new approach is based on the partition of unity finite element method, which defines the solution fields as weighted sums of local fields, supported by the different grids. Here, the discrete weak formulation of the problem is re-set in cG(1)cG(1) stabilized form, which has the dual benefit of lowering grid resolution requirements for convection dominated flows and allowing for the use of velocity and pressure discretizations which do not satisfy the inf-sup condition. Additionally, we provide an outline of our implementation within an existing distributed parallel application and identify four key options to improve the code efficiency namely: the use of cache to store mapped quadrature points and basis function gradients, the intersection volume splitting algorithm, the use of lower order quadrature schemes, and tuning the partition weight associated with the interface elements. The new method is shown to have comparable accuracy to the single mesh boundary-fitted version of the same stabilized solver based on three transient flow tests including both 2D and 3D settings, as well as low and moderate Reynolds number flow conditions. Moreover, we demonstrate how the four implementation options have a synergistic effect lowering the residual assembly time by an order of magnitude compared to a naive implementation, and showing good load balancing properties.

Place, publisher, year, edition, pages
Elsevier BV, 2022
Keywords
Finite element methods, Fluid-structure interaction, Overlapping domains, Partition of unity, Stabilized flow
National Category
Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-312227 (URN)10.1016/j.cma.2022.114656 (DOI)000783077800001 ()2-s2.0-85124597609 (Scopus ID)
Note

QC 20220516

Available from: 2022-05-16 Created: 2022-05-16 Last updated: 2022-06-25Bibliographically approved
Kronborg, J., Svelander, F., Eriksson Lidbrink, S., Lindström, L., Homs Pons, C., Lucor, D. & Hoffman, J. (2022). Computational Analysis of Flow Structures in Turbulent Ventricular Blood Flow Associated With Mitral Valve Intervention. Frontiers in Physiology, 13, Article ID 806534.
Open this publication in new window or tab >>Computational Analysis of Flow Structures in Turbulent Ventricular Blood Flow Associated With Mitral Valve Intervention
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2022 (English)In: Frontiers in Physiology, E-ISSN 1664-042X, Vol. 13, article id 806534Article in journal (Refereed) Published
Abstract [en]

Cardiac disease and clinical intervention may both lead to an increased risk for thrombosis events due to a modified blood flow in the heart, and thereby a change in the mechanical stimuli of blood cells passing through the chambers of the heart. Specifically, the degree of platelet activation is influenced by the level and type of mechanical stresses in the blood flow. In this article we analyze the blood flow in the left ventricle of the heart through a computational model constructed from patient-specific data. The blood flow in the ventricle is modelled by the Navier-Stokes equations, and the flow through the mitral valve by a parameterized model which represents the projected opening of the valve. A finite element method is used to solve the equations, from which a simulation of the velocity and pressure of the blood flow is constructed. The intraventricular blood flow is complex, in particular in diastole when the inflow jet from the atrium breaks down into turbulent flow on a range of scales. A triple decomposition of the velocity gradient tensor is then used to distinguish between rigid body rotational flow, irrotational straining flow, and shear flow. The triple decomposition enables the separation of three fundamentally different flow structures, that each generates a distinct type of mechanical stimulus on the blood cells in the flow. We compare the results in a simulation where a mitral valve clip intervention is modelled, which leads to a significant modification of the intraventricular flow. Further, we perform a sensitivity study of the results with respect to the positioning of the clip. It was found that the shear in the simulation cases treated with clips increased more compared to the untreated case than the rotation and strain did. A decrease in valve opening area of 64% in one of the cases led to a 90% increase in rotation and strain, but a 150% increase in shear. The computational analysis opens up for improvements in models of shear-induced platelet activation, by offering an algorithm to distinguish shear from other modalities in intraventricular blood flow.

Place, publisher, year, edition, pages
Frontiers Media SA, 2022
Keywords
patient-specific heart modelling, left ventricle, mitral valve clip, finite element method, FEM, turbulent blood flow, triple decomposition of velocity gradient tensor
National Category
Cardiac and Cardiovascular Systems Computer Sciences
Identifiers
urn:nbn:se:kth:diva-315889 (URN)10.3389/fphys.2022.806534 (DOI)000826442700001 ()35846019 (PubMedID)2-s2.0-85134248956 (Scopus ID)
Note

QC 20220728

Available from: 2022-07-28 Created: 2022-07-28 Last updated: 2024-01-17Bibliographically approved
Koivumäki, J. T., Hoffman, J., Maleckar, M. M., Einevoll, G. T. & Sundnes, J. (2022). Computational cardiac physiology for new modelers: Origins, foundations, and future. Acta Physiologica, 236(2), Article ID e13865.
Open this publication in new window or tab >>Computational cardiac physiology for new modelers: Origins, foundations, and future
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2022 (English)In: Acta Physiologica, ISSN 1748-1708, E-ISSN 1748-1716, Vol. 236, no 2, article id e13865Article, review/survey (Refereed) Published
Abstract [en]

Mathematical models of the cardiovascular system have come a long way since they were first introduced in the early 19th century. Driven by a rapid development of experimental techniques, numerical methods, and computer hardware, detailed models that describe physical scales from the molecular level up to organs and organ systems have been derived and used for physiological research. Mathematical and computational models can be seen as condensed and quantitative formulations of extensive physiological knowledge and are used for formulating and testing hypotheses, interpreting and directing experimental research, and have contributed substantially to our understanding of cardiovascular physiology. However, in spite of the strengths of mathematics to precisely describe complex relationships and the obvious need for the mathematical and computational models to be informed by experimental data, there still exist considerable barriers between experimental and computational physiological research. In this review, we present a historical overview of the development of mathematical and computational models in cardiovascular physiology, including the current state of the art. We further argue why a tighter integration is needed between experimental and computational scientists in physiology, and point out important obstacles and challenges that must be overcome in order to fully realize the synergy of experimental and computational physiological research.

Place, publisher, year, edition, pages
Wiley, 2022
Keywords
cardiovascular physiology, computer models, mathematical modeling
National Category
Other Mathematics Cardiac and Cardiovascular Systems
Identifiers
urn:nbn:se:kth:diva-329157 (URN)10.1111/apha.13865 (DOI)000844163200001 ()35959512 (PubMedID)2-s2.0-85136556268 (Scopus ID)
Note

QC 20230614

Available from: 2023-06-15 Created: 2023-06-15 Last updated: 2023-06-15Bibliographically approved
Spühler, J. & Hoffman, J. (2021). An interface-tracking unified continuum model for fluid-structure interaction with topology change and full-friction contact with application to aortic valves. International Journal for Numerical Methods in Engineering, 122(19), 5258-5278
Open this publication in new window or tab >>An interface-tracking unified continuum model for fluid-structure interaction with topology change and full-friction contact with application to aortic valves
2021 (English)In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 122, no 19, p. 5258-5278Article in journal (Refereed) Published
Abstract [en]

An interface tracking finite element methodology is presented for 3D turbulent flow fluid-structure interaction, including full-friction contact and topology changes, with specific focus on heart valve simulations. The methodology is based on a unified continuum fluid-structure interaction model, which is a monolithic approach, where the fundamental conservation laws are formulated for the combined fluid-structure continuum. Contact is modeled by local phase changes in the unified continuum, and computational results show the promise of the approach. The core algorithms are all based on the solution of partial differential equations with standard finite element methods, and hence any general purpose finite element library which can leverage state of the art hardware platforms can be used for the implementation of the methodology.

Place, publisher, year, edition, pages
Wiley-Blackwell, 2021
Keywords
fluid-structure interaction, heart simulation, finite element method
National Category
Computational Mathematics
Research subject
Applied and Computational Mathematics, Numerical Analysis
Identifiers
urn:nbn:se:kth:diva-299804 (URN)10.1002/nme.6384 (DOI)000532596700001 ()2-s2.0-85084591989 (Scopus ID)
Funder
Swedish Research Council, 2018-04854
Note

QC 20210820

Available from: 2021-08-17 Created: 2021-08-17 Last updated: 2023-10-09Bibliographically approved
Hoffman, J. (2021). Energy stability analysis of turbulent incompressible flow based on the triple decomposition of the velocity gradient tensor [Letter to the editor]. Physics of fluids, 33(8), Article ID 081707.
Open this publication in new window or tab >>Energy stability analysis of turbulent incompressible flow based on the triple decomposition of the velocity gradient tensor
2021 (English)In: Physics of fluids, ISSN 1070-6631, E-ISSN 1089-7666, Vol. 33, no 8, article id 081707Article in journal, Letter (Refereed) Published
Abstract [en]

In the context of flow visualization, a triple decomposition of the velocity gradient into irrotational straining flow, shear flow, and rigid body rotational flow was proposed by Kolar in 2007 [V. Kolar, "Vortex identification: New requirements and limitations," Int. J. Heat Fluid Flow, 28, 638-652 (2007)], which has recently received renewed interest. The triple decomposition opens for a refined energy stability analysis of the Navier-Stokes equations, with implications for the mathematical analysis of the structure, computability, and regularity of turbulent flow. We here perform an energy stability analysis of turbulent incompressible flow, which suggests a scenario where at macroscopic scales, any exponentially unstable irrotational straining flow structures rapidly evolve toward linearly unstable shear flow and stable rigid body rotational flow. This scenario does not rule out irrotational straining flow close to the Kolmogorov microscales, since there viscous dissipation stabilizes the unstable flow structures. In contrast to worst case energy stability estimates, this refined stability analysis reflects the existence of stable flow structures in turbulence over extended time.

Place, publisher, year, edition, pages
AIP Publishing, 2021
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-300857 (URN)10.1063/5.0060584 (DOI)000685767200008 ()2-s2.0-85113709519 (Scopus ID)
Note

QC 20210923

Available from: 2021-09-23 Created: 2021-09-23 Last updated: 2022-06-25Bibliographically approved
Spühler, J. H., Jansson, J., Jansson, N. & Hoffman, J. (2020). A High Performance Computing Framework for Finite Element Simulation of Blood Flow in the Left Ventricle of the Human Heart. In: Lecture Notes in Computational Science and Engineering: . Paper presented at Numerical Methods for Flows, 5 April 2017 through 7 April 2017 (pp. 155-164). Springer
Open this publication in new window or tab >>A High Performance Computing Framework for Finite Element Simulation of Blood Flow in the Left Ventricle of the Human Heart
2020 (English)In: Lecture Notes in Computational Science and Engineering, Springer , 2020, p. 155-164Conference paper, Published paper (Refereed)
Abstract [en]

We present a high performance computing framework for finite element simulation of blood flow in the left ventricle of the human heart. The mathematical model is described together with the discretization method and the parallel implementation in Unicorn which is part of the open source software framework FEniCS-HPC. We show results based on patient-specific data that capture essential features observed with other computational models and imaging techniques, and thus indicate that our framework possesses the potential to provide relevant clinical information for diagnosis and medical treatment. Several other studies have been conducted to simulate the three dimensional blood flow in the left ventricle of the human heart with prescribed wall movement. Our contribution to the field of cardiac research lies in establishing an open source framework modular both in modelling and numerical algorithms.

Place, publisher, year, edition, pages
Springer, 2020
Keywords
Arbitrary Lagrangian–Eulerian method, Blood flow, Finite element method, Left ventricle, Parallel algorithm, Patient-specific heart model, Blood, Computer programming, Diagnosis, Discrete event simulation, Heart, Hemodynamics, Medical imaging, Numerical methods, Open source software, Open systems, Parallel algorithms, Patient treatment, Eulerian method, Finite element simulations, Heart model, High performance computing, Left ventricles, Open source frameworks, Parallel implementations
National Category
Computational Mathematics Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-274260 (URN)10.1007/978-3-030-30705-9_14 (DOI)2-s2.0-85081752309 (Scopus ID)
Conference
Numerical Methods for Flows, 5 April 2017 through 7 April 2017
Note

QC 20200713

Available from: 2020-07-13 Created: 2020-07-13 Last updated: 2024-01-10Bibliographically approved
Balmus, M., Massing, A., Hoffman, J., Razavi, R. & Nordsletten, D. A. (2020). A partition of unity approach to fluid mechanics and fluid-structure interaction. Computer Methods in Applied Mechanics and Engineering, 362, Article ID 112842.
Open this publication in new window or tab >>A partition of unity approach to fluid mechanics and fluid-structure interaction
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2020 (English)In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 362, article id 112842Article in journal (Refereed) Published
Abstract [en]

For problems involving large deformations of thin structures, simulating fluid-structure interaction (FSI) remains a computationally expensive endeavour which continues to drive interest in the development of novel approaches. Overlapping domain techniques have been introduced as a way to combine the fluid-solid mesh conformity, seen in moving-mesh methods, without the need for mesh smoothing or re-meshing, which is a core characteristic of fixed mesh approaches. In this work, we introduce a novel overlapping domain method based on a partition of unity approach. Unified function spaces are defined as a weighted sum of fields given on two overlapping meshes. The method is shown to achieve optimal convergence rates and to be stable for steady-state Stokes, Navier-Stokes, and ALE Navier-Stokes problems. Finally, we present results for FSI in the case of 2D flow past an elastic beam simulation. These initial results point to the potential applicability of the method to a wide range of FSI applications, enabling boundary layer refinement and large deformations without the need for re-meshing or user-defined stabilization.

Place, publisher, year, edition, pages
ELSEVIER SCIENCE SA, 2020
Keywords
Finite element methods, Fluid-structure interaction, Overlapping domains, Partition of unity
National Category
Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-271266 (URN)10.1016/j.cma.2020.112842 (DOI)000515542500012 ()34093912 (PubMedID)2-s2.0-85078801140 (Scopus ID)
Note

QC 20200401

Available from: 2020-04-01 Created: 2020-04-01 Last updated: 2022-06-26Bibliographically approved
Hoffman, J. (2020). High shear stress amplitude in combination with prolonged stimulus duration determine induction of osteoclast formation by hematopoietic progenitor cells. The FASEB Journal, 34(2), 3755-3772
Open this publication in new window or tab >>High shear stress amplitude in combination with prolonged stimulus duration determine induction of osteoclast formation by hematopoietic progenitor cells
2020 (English)In: The FASEB Journal, ISSN 0892-6638, E-ISSN 1530-6860, Vol. 34, no 2, p. 3755-3772Article in journal (Refereed) Published
Place, publisher, year, edition, pages
Wiley-Blackwell, 2020
National Category
Cell Biology
Research subject
SRA - Molecular Bioscience
Identifiers
urn:nbn:se:kth:diva-299805 (URN)10.1096/fj.201901458R (DOI)000508136200001 ()31957079 (PubMedID)2-s2.0-85078669440 (Scopus ID)
Funder
Swedish Research Council, 2018-04854
Note

QC 20210820

Available from: 2021-08-17 Created: 2021-08-17 Last updated: 2022-06-25Bibliographically approved
Nguyen, V. D., Jansson, J., Tran, H. T., Hoffman, J. & Li, J.-R. (2019). Diffusion MRI simulation in thin-layer and thin-tube media using a discretization on manifolds. Journal of magnetic resonance, 299, 176-187
Open this publication in new window or tab >>Diffusion MRI simulation in thin-layer and thin-tube media using a discretization on manifolds
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2019 (English)In: Journal of magnetic resonance, ISSN 1090-7807, E-ISSN 1096-0856, Vol. 299, p. 176-187Article in journal (Refereed) Published
Abstract [en]

The Bloch-Torrey partial differential equation can be used to describe the evolution of the transverse magnetization of the imaged sample under the influence of diffusion-encoding magnetic field gradients inside the MRI scanner. The integral of the magnetization inside a voxel gives the simulated diffusion MRI signal. This paper proposes 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 variable thickness of the three-dimensional domains is included in the weak formulation established on the manifolds. We conducted a numerical study of the proposed approach by simulating the diffusion MRI signals from the extracellular space (a thin layer medium) and from neurons (a thin tube medium), comparing the results with the reference signals obtained using a standard three-dimensional finite element discretization. We show good agreements between the simulated signals using our proposed method and the reference signals for a wide range of diffusion MRI parameters. The approximation becomes better as the diffusion time increases. The method helps to significantly reduce the required simulation time, computational memory, and difficulties associated with mesh generation, thus opening the possibilities to simulating complicated structures at low cost for a better understanding of diffusion MRI in the brain.

Place, publisher, year, edition, pages
Academic Press, 2019
Keywords
Diffusion MRI; finite element method; Bloch-Torrey equation; FEniCS; thin layer; thin tube.
National Category
Medical and Health Sciences
Research subject
Applied and Computational Mathematics; Computer Science
Identifiers
urn:nbn:se:kth:diva-235070 (URN)10.1016/j.jmr.2019.01.002 (DOI)000460655200018 ()30641268 (PubMedID)2-s2.0-85059768594 (Scopus ID)
Funder
Swedish Energy Agency, P40435-1
Note

QC 20180919

Available from: 2018-09-14 Created: 2018-09-14 Last updated: 2024-03-18Bibliographically approved
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ORCID iD: ORCID iD iconorcid.org/0000-0003-4256-0463

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