@misc{FrauenrathdeGeyerd'OrthNiendorf2011, author = {Frauenrath, Tobias and de Geyer d'Orth, Thibaut and Niendorf, Thoralf}, title = {Assessment of Accuracy \& Reproducibility of ECG, Pulse Oximetry \& Phonocardiogram Gating of Cardiac MRI at 7T}, series = {2011 ISMRM Annual Meeting Proceedings}, journal = {2011 ISMRM Annual Meeting Proceedings}, issn = {1545-4428}, year = {2011}, abstract = {At (ultra)high magnetic fields the artifact sensitivity of ECG recordings increases. This bears the risk of R-wave mis-registration which has been consistently reported for ECG triggered CMR at 7.0T. Realizing the constraints of conventional ECG, acoustic cardiac triggering (ACT) has been proposed. The clinical ACT has not been carefully examined yet. For this reason, this work scrutinizes the suitability, accuracy and reproducibility of ACT for CMR at 7.0T. For this purpose, the trigger reliability and trigger detection variance are examined together with an qualitative and quantitative assessment of image quality of the heart at 7.0T.}, language = {en} } @misc{MartinFrauenrathZerdemetal.2011, author = {Martin, Conrad Steven and Frauenrath, Tobias and Zerdem, Celal and Renz, Wolfgang and Niendorf, Thoralf}, title = {Evaluation of Magneto Alert Sensor (MALSE) to Improve MR Safety by Decreasing the Incidence of Ferromagnetic Projectile Accidents}, series = {2011 ISMRM Annual Meeting Proceedings}, journal = {2011 ISMRM Annual Meeting Proceedings}, issn = {1545-4428}, year = {2011}, abstract = {The magnetic forces of fringe magnetic fields of MR systems on ferromagnetic components can impose a severe patient, occupational health and safety hazard. MRI accidents are listed as number 9 of the top 10 risks in modern medicine. With the advent of ultrahigh field MR systems including passively shielded magnet versions, this risk, commonly known as the missile or projectile effect is even more pronounced. A strategy employing magnetic field sensors which can be attached to ferromagnetic objects that are commonly used in a clinical environment is conceptually appealing for the pursuit of reducing the risk of ferromagnetic projectile accidents.}, language = {en} } @misc{FrauenrathRenzRiegeretal.2010, author = {Frauenrath, Tobias and Renz, Wolfgang and Rieger, Jan and G{\"o}mmel, Andreas and Butenweg, Christoph and Niendorf, Thoralf}, title = {High Spatial Resolution 3D MRI of the Larynx Using a Dedicated TX/RX Phased Array Coil at 7.0T}, series = {2010 ISMRM-ESMRMB joint annual meeting}, journal = {2010 ISMRM-ESMRMB joint annual meeting}, issn = {1545-4428}, year = {2010}, abstract = {MRI holds great potential for elucidating laryngeal and vocal fold anatomy together with the assessment of physiological processes associated in human phonation. However, MRI of human phonation remains very challenging due to the small size of the targeted structures, interfering signal from fat, air between the vocal folds and surrounding muscles and physiological motion. These anatomical/physiological constraints translate into stringent technical requirements in balancing, scan time, image contrast, immunity to physiological motion, temporal resolution and spatial resolution. Motivated by these challenges and limitations this study is aiming at translating the sensitivity gain at ultra-high magnetic fields for enhanced high spatial resolution 3D imaging of the larynx and vocal tract. To approach this goal a dedicated two channel TX/RX larynx coil is being proposed.}, language = {en} } @misc{HezelFrauenrathRenzetal.2010, author = {Hezel, Fabian and Frauenrath, Tobias and Renz, Wolfgang and Schulz-Menger, Jeanette and Niendorf, Thoralf}, title = {Feasibility of CINE Myocardial T2* Mapping Using Susceptibility Weighted Gradient-Echo Imaging at 7.0 T}, series = {2010 ISMRM-ESMRMB joint annual meeting}, journal = {2010 ISMRM-ESMRMB joint annual meeting}, issn = {1545-4428}, year = {2010}, abstract = {This study is designed to demonstrate the promise of susceptibility weighted 2D CINE FLASH and T2* Mapping of the heart at 7T.}, language = {en} } @misc{FrauenrathBeckerHezeletal.2010, author = {Frauenrath, Tobias and Becker, Meike and Hezel, Fabian and Krombach, Gabriele A. and Kremer, Ute and Schulz-Menger, Jeanette and Niendorf, Thoralf}, title = {Comparison of Left Function Assessment Using Phonocardiogram and Electrocardiogram Triggered 2D SSFP CINE MR Imaging at 1.5 T and 3.0 T}, series = {2010 ISMRM-ESMRMB joint annual meeting}, journal = {2010 ISMRM-ESMRMB joint annual meeting}, issn = {1545-4428}, year = {2010}, abstract = {As high-field cardiac MRI (CMR) becomes more widespread the propensity of ECG to distortions and mistriggering increases and with it the motivation for a cardiac triggering alternative. Hence, this study explores the suitability of acoustic cardiac triggering (ACT) for left ventricular (LV) function assessment in healthy subjects at 1.5T and 3.0T.}, language = {en} } @misc{DieringerRenzLindeletal.2010, author = {Dieringer, Matthias A. and Renz, Wolfgang and Lindel, Tomasz and Seifert, Frank and Frauenrath, Tobias and Waiczies, Helmar and von Knobelsdorff-Brenkhoff, Florian and Santoro, Davide and Hoffmann, Werner and Ittermann, Bernd and Schulz-Menger, Jeanette and Niendorf, Thoralf}, title = {4CH TX/RX Surface Coil for 7T: Design, Optimization and Application for Cardiac Function Imaging}, series = {2010 ISMRM-ESMRMB joint annual meeting}, journal = {2010 ISMRM-ESMRMB joint annual meeting}, issn = {1545-4428}, year = {2010}, abstract = {Practical impediments of ultra high field cardiovascular MR (CVMR) can be catalogued in exacerbated magnetic field and radio frequency (RF) inhomogeneities, susceptibility and off-resonance effects, conductive and dielectric effects in tissue, and RF power deposition constraints, which all bear the potential to spoil the benefit of CVMR at 7T. Therefore, a four element cardiac transceive surface coil array was developed. Cardiac imaging provided clinically acceptable signal homogeneity with an excellent blood myocardium contrast. Subtle anatomic structures, such as pericardium, mitral and tricuspid valves and their apparatus, papillary muscles, and trabecles were accurately delineated.}, language = {en} } @article{FiedlerOrzadaFloeseretal.2021, author = {Fiedler, Thomas M. and Orzada, Stephan and Fl{\"o}ser, Martina and Rietsch, Stefan H. G. and Quick, Harald H. and Ladd, Mark E. and Bitz, Andreas}, title = {Performance analysis of integrated RF microstrip transmit antenna arrays with high channel count for body imaging at 7 T}, series = {NMR in Biomedicine}, volume = {34}, journal = {NMR in Biomedicine}, number = {7}, publisher = {Wiley}, address = {Weinheim}, issn = {0952-3480 (ISSN)}, doi = {10.1002/nbm.4515}, pages = {18 SeitenWiley}, year = {2021}, abstract = {The aim of the current study was to investigate the performance of integrated RF transmit arrays with high channel count consisting of meander microstrip antennas for body imaging at 7 T and to optimize the position and number of transmit ele- ments. RF simulations using multiring antenna arrays placed behind the bore liner were performed for realistic exposure conditions for body imaging. Simulations were performed for arrays with as few as eight elements and for arrays with high channel counts of up to 48 elements. The B1+ field was evaluated regarding the degrees of freedom for RF shimming in the abdomen. Worst-case specific absorption rate (SARwc ), SAR overestimation in the matrix compression, the number of virtual obser- vation points (VOPs) and SAR efficiency were evaluated. Constrained RF shimming was performed in differently oriented regions of interest in the body, and the devia- tion from a target B1+ field was evaluated. Results show that integrated multiring arrays are able to generate homogeneous B1+ field distributions for large FOVs, espe- cially for coronal/sagittal slices, and thus enable body imaging at 7 T with a clinical workflow; however, a low duty cycle or a high SAR is required to achieve homoge- neous B1+ distributions and to exploit the full potential. In conclusion, integrated arrays allow for high element counts that have high degrees of freedom for the pulse optimization but also produce high SARwc , which reduces the SAR accuracy in the VOP compression for low-SAR protocols, leading to a potential reduction in array performance. Smaller SAR overestimations can increase SAR accuracy, but lead to a high number of VOPs, which increases the computational cost for VOP evaluation and makes online SAR monitoring or pulse optimization challenging. Arrays with interleaved rings showed the best results in the study.}, language = {en} } @article{HarrisKleefeld2018, author = {Harris, Isaac and Kleefeld, Andreas}, title = {The inverse scattering problem for a conductive boundary condition and transmission eigenvalues}, series = {Applicable Analysis}, volume = {99}, journal = {Applicable Analysis}, number = {3}, publisher = {Taylor \& Francis}, address = {London}, issn = {1563-504X}, doi = {10.1080/00036811.2018.1504028}, pages = {508 -- 529}, year = {2018}, abstract = {In this paper, we consider the inverse scattering problem associated with an inhomogeneous media with a conductive boundary. In particular, we are interested in two problems that arise from this inverse problem: the inverse conductivity problem and the corresponding interior transmission eigenvalue problem. The inverse conductivity problem is to recover the conductive boundary parameter from the measured scattering data. We prove that the measured scatted data uniquely determine the conductivity parameter as well as describe a direct algorithm to recover the conductivity. The interior transmission eigenvalue problem is an eigenvalue problem associated with the inverse scattering of such materials. We investigate the convergence of the eigenvalues as the conductivity parameter tends to zero as well as prove existence and discreteness for the case of an absorbing media. Lastly, several numerical and analytical results support the theory and we show that the inside-outside duality method can be used to reconstruct the interior conductive eigenvalues.}, language = {en} } @article{KleefeldPieronek2020, author = {Kleefeld, Andreas and Pieronek, J.}, title = {Elastic transmission eigenvalues and their computation via the method of fundamental solutions}, series = {Applicable Analysis}, volume = {100}, journal = {Applicable Analysis}, number = {16}, publisher = {Taylore \& Francis}, address = {London}, issn = {1563-504X}, doi = {10.1080/00036811.2020.1721473}, pages = {3445 -- 3462}, year = {2020}, abstract = {A stabilized version of the fundamental solution method to catch ill-conditioning effects is investigated with focus on the computation of complex-valued elastic interior transmission eigenvalues in two dimensions for homogeneous and isotropic media. Its algorithm can be implemented very shortly and adopts to many similar partial differential equation-based eigenproblems as long as the underlying fundamental solution function can be easily generated. We develop a corroborative approximation analysis which also implicates new basic results for transmission eigenfunctions and present some numerical examples which together prove successful feasibility of our eigenvalue recovery approach.}, language = {en} } @article{BreussKleefeld2020, author = {Breuß, Michael and Kleefeld, Andreas}, title = {Implicit monotone difference methods for scalar conservation laws with source terms}, series = {Acta Mathematica Vietnamica}, volume = {45}, journal = {Acta Mathematica Vietnamica}, publisher = {Springer Singapore}, address = {Singapore}, issn = {2315-4144}, doi = {10.1007/s40306-019-00354-1}, pages = {709 -- 738}, year = {2020}, abstract = {In this article, a concept of implicit methods for scalar conservation laws in one or more spatial dimensions allowing also for source terms of various types is presented. This material is a significant extension of previous work of the first author (Breuß SIAM J. Numer. Anal. 43(3), 970-986 2005). Implicit notions are developed that are centered around a monotonicity criterion. We demonstrate a connection between a numerical scheme and a discrete entropy inequality, which is based on a classical approach by Crandall and Majda. Additionally, three implicit methods are investigated using the developed notions. Next, we conduct a convergence proof which is not based on a classical compactness argument. Finally, the theoretical results are confirmed by various numerical tests.}, language = {en} } @article{AsanteAsamaniKleefeldWade2020, author = {Asante-Asamani, E.O. and Kleefeld, Andreas and Wade, B.A.}, title = {A second-order exponential time differencing scheme for non-linear reaction-diffusion systems with dimensional splitting}, series = {Journal of Computational Physics}, volume = {415}, journal = {Journal of Computational Physics}, publisher = {Elsevier}, address = {Amsterdam}, issn = {0021-9991}, doi = {10.1016/j.jcp.2020.109490}, year = {2020}, abstract = {A second-order L-stable exponential time-differencing (ETD) method is developed by combining an ETD scheme with approximating the matrix exponentials by rational functions having real distinct poles (RDP), together with a dimensional splitting integrating factor technique. A variety of non-linear reaction-diffusion equations in two and three dimensions with either Dirichlet, Neumann, or periodic boundary conditions are solved with this scheme and shown to outperform a variety of other second-order implicit-explicit schemes. An additional performance boost is gained through further use of basic parallelization techniques.}, language = {en} } @incollection{Kleefeld2020, author = {Kleefeld, Andreas}, title = {Numerical calculation of interior transmission eigenvalues with mixed boundary conditions}, series = {Computational and Analytic Methods in Science and Engineering}, booktitle = {Computational and Analytic Methods in Science and Engineering}, editor = {Constanda, Christian}, publisher = {Birkh{\"a}user}, address = {Cham}, isbn = {978-3-030-48185-8 (Hardcover)}, doi = {10.1007/978-3-030-48186-5_9}, pages = {173 -- 195}, year = {2020}, abstract = {Interior transmission eigenvalue problems for the Helmholtz equation play an important role in inverse wave scattering. Some distribution properties of those eigenvalues in the complex plane are reviewed. Further, a new scattering model for the interior transmission eigenvalue problem with mixed boundary conditions is described and an efficient algorithm for computing the interior transmission eigenvalues is proposed. Finally, extensive numerical results for a variety of two-dimensional scatterers are presented to show the validity of the proposed scheme.}, language = {en} } @article{MartinVaqueroKleefeld2020, author = {Mart{\´i}n-Vaquero, J. and Kleefeld, Andreas}, title = {Solving nonlinear parabolic PDEs in several dimensions: Parallelized ESERK codes}, series = {Journal of Computational Physics}, journal = {Journal of Computational Physics}, number = {423}, publisher = {Elsevier}, address = {Amsterdam}, issn = {0021-9991}, doi = {10.1016/j.jcp.2020.109771}, year = {2020}, abstract = {There is a very large number of very important situations which can be modeled with nonlinear parabolic partial differential equations (PDEs) in several dimensions. In general, these PDEs can be solved by discretizing in the spatial variables and transforming them into huge systems of ordinary differential equations (ODEs), which are very stiff. Therefore, standard explicit methods require a large number of iterations to solve stiff problems. But implicit schemes are computationally very expensive when solving huge systems of nonlinear ODEs. Several families of Extrapolated Stabilized Explicit Runge-Kutta schemes (ESERK) with different order of accuracy (3 to 6) are derived and analyzed in this work. They are explicit methods, with stability regions extended, along the negative real semi-axis, quadratically with respect to the number of stages s, hence they can be considered to solve stiff problems much faster than traditional explicit schemes. Additionally, they allow the adaptation of the step length easily with a very small cost. Two new families of ESERK schemes (ESERK3 and ESERK6) are derived, and analyzed, in this work. Each family has more than 50 new schemes, with up to 84.000 stages in the case of ESERK6. For the first time, we also parallelized all these new variable step length and variable number of stages algorithms (ESERK3, ESERK4, ESERK5, and ESERK6). These parallelized strategies allow to decrease times significantly, as it is discussed and also shown numerically in two problems. Thus, the new codes provide very good results compared to other well-known ODE solvers. Finally, a new strategy is proposed to increase the efficiency of these schemes, and it is discussed the idea of combining ESERK families in one code, because typically, stiff problems have different zones and according to them and the requested tolerance the optimum order of convergence is different.}, language = {en} } @article{Kleefeld2021, author = {Kleefeld, Andreas}, title = {The hot spots conjecture can be false: some numerical examples}, series = {Advances in Computational Mathematics}, volume = {47}, journal = {Advances in Computational Mathematics}, publisher = {Springer}, address = {Dordrecht}, issn = {1019-7168}, doi = {10.1007/s10444-021-09911-5}, year = {2021}, abstract = {The hot spots conjecture is only known to be true for special geometries. This paper shows numerically that the hot spots conjecture can fail to be true for easy to construct bounded domains with one hole. The underlying eigenvalue problem for the Laplace equation with Neumann boundary condition is solved with boundary integral equations yielding a non-linear eigenvalue problem. Its discretization via the boundary element collocation method in combination with the algorithm by Beyn yields highly accurate results both for the first non-zero eigenvalue and its corresponding eigenfunction which is due to superconvergence. Additionally, it can be shown numerically that the ratio between the maximal/minimal value inside the domain and its maximal/minimal value on the boundary can be larger than 1 + 10- 3. Finally, numerical examples for easy to construct domains with up to five holes are provided which fail the hot spots conjecture as well.}, language = {en} } @misc{BurgethKleefeldNaegeletal.2020, author = {Burgeth, Bernhard and Kleefeld, Andreas and Naegel, Beno{\^i}t and Perret, Benjamin}, title = {Editorial — Special Issue: ISMM 2019}, series = {Mathematical Morphology - Theory and Applications}, volume = {4}, journal = {Mathematical Morphology - Theory and Applications}, number = {1}, publisher = {De Gruyter}, address = {Warschau}, issn = {2353-3390}, doi = {10.1515/mathm-2020-0200}, pages = {159 -- 161}, year = {2020}, abstract = {This editorial presents the Special Issue dedicated to the conference ISMM 2019 and summarizes the articles published in this Special Issue.}, language = {en} } @article{KleefeldZimmermann2022, author = {Kleefeld, Andreas and Zimmermann, M.}, title = {Computing Elastic Interior Transmission Eigenvalues}, series = {Integral Methods in Science and Engineering}, journal = {Integral Methods in Science and Engineering}, editor = {Constanda, Christian and Bodmann, Bardo E.J. and Harris, Paul J.}, publisher = {Birkh{\"a}user}, address = {Cham}, isbn = {978-3-031-07171-3}, doi = {10.1007/978-3-031-07171-3_10}, pages = {139 -- 155}, year = {2022}, abstract = {An alternative method is presented to numerically compute interior elastic transmission eigenvalues for various domains in two dimensions. This is achieved by discretizing the resulting system of boundary integral equations in combination with a nonlinear eigenvalue solver. Numerical results are given to show that this new approach can provide better results than the finite element method when dealing with general domains.}, language = {en} } @inproceedings{BurgethKleefeldZhangetal.2022, author = {Burgeth, Bernhard and Kleefeld, Andreas and Zhang, Eugene and Zhang, Yue}, title = {Towards Topological Analysis of Non-symmetric Tensor Fields via Complexification}, series = {Discrete Geometry and Mathematical Morphology}, booktitle = {Discrete Geometry and Mathematical Morphology}, editor = {Baudrier, {\´E}tienne and Naegel, Beno{\^i}t and Kr{\"a}henb{\"u}hl, Adrien and Tajine, Mohamed}, publisher = {Springer}, address = {Cham}, isbn = {978-3-031-19897-7}, doi = {10.1007/978-3-031-19897-7_5}, pages = {48 -- 59}, year = {2022}, abstract = {Fields of asymmetric tensors play an important role in many applications such as medical imaging (diffusion tensor magnetic resonance imaging), physics, and civil engineering (for example Cauchy-Green-deformation tensor, strain tensor with local rotations, etc.). However, such asymmetric tensors are usually symmetrized and then further processed. Using this procedure results in a loss of information. A new method for the processing of asymmetric tensor fields is proposed restricting our attention to tensors of second-order given by a 2x2 array or matrix with real entries. This is achieved by a transformation resulting in Hermitian matrices that have an eigendecomposition similar to symmetric matrices. With this new idea numerical results for real-world data arising from a deformation of an object by external forces are given. It is shown that the asymmetric part indeed contains valuable information.}, language = {en} } @article{ChwallekNawrathKrastinaetal.2024, author = {Chwallek, Constanze and Nawrath, Lara and Krastina, Anzelika and Bruksle, Ieva}, title = {Supportive research on sustainable entrepreneurship and business practices}, series = {SECA Sustainable Entrepreneurship for Climate Action}, journal = {SECA Sustainable Entrepreneurship for Climate Action}, number = {3}, publisher = {Lapland University of Applied Sciences Ltd}, address = {Rovaniemi}, isbn = {978-952-316-514-4 (pdf)}, issn = {2954-1654 (on-line publication)}, pages = {67 Seiten}, year = {2024}, language = {en} } @article{HarrisKleefeld2022, author = {Harris, Isaac and Kleefeld, Andreas}, title = {Analysis and computation of the transmission eigenvalues with a conductive boundary condition}, series = {Applicable Analysis}, volume = {101}, journal = {Applicable Analysis}, number = {6}, publisher = {Taylor \& Francis}, address = {London}, issn = {1563-504X}, doi = {10.1080/00036811.2020.1789598}, pages = {1880 -- 1895}, year = {2022}, abstract = {We provide a new analytical and computational study of the transmission eigenvalues with a conductive boundary condition. These eigenvalues are derived from the scalar inverse scattering problem for an inhomogeneous material with a conductive boundary condition. The goal is to study how these eigenvalues depend on the material parameters in order to estimate the refractive index. The analytical questions we study are: deriving Faber-Krahn type lower bounds, the discreteness and limiting behavior of the transmission eigenvalues as the conductivity tends to infinity for a sign changing contrast. We also provide a numerical study of a new boundary integral equation for computing the eigenvalues. Lastly, using the limiting behavior we will numerically estimate the refractive index from the eigenvalues provided the conductivity is sufficiently large but unknown.}, language = {en} } @article{ClausnitzerKleefeld2024, author = {Clausnitzer, Julian and Kleefeld, Andreas}, title = {A spectral Galerkin exponential Euler time-stepping scheme for parabolic SPDEs on two-dimensional domains with a C² boundary}, series = {Discrete and Continuous Dynamical Systems - Series B}, volume = {29}, journal = {Discrete and Continuous Dynamical Systems - Series B}, number = {4}, publisher = {AIMS}, address = {Springfield}, issn = {1531-3492}, doi = {10.3934/dcdsb.2023148}, pages = {1624 -- 1651}, year = {2024}, abstract = {We consider the numerical approximation of second-order semi-linear parabolic stochastic partial differential equations interpreted in the mild sense which we solve on general two-dimensional domains with a C² boundary with homogeneous Dirichlet boundary conditions. The equations are driven by Gaussian additive noise, and several Lipschitz-like conditions are imposed on the nonlinear function. We discretize in space with a spectral Galerkin method and in time using an explicit Euler-like scheme. For irregular shapes, the necessary Dirichlet eigenvalues and eigenfunctions are obtained from a boundary integral equation method. This yields a nonlinear eigenvalue problem, which is discretized using a boundary element collocation method and is solved with the Beyn contour integral algorithm. We present an error analysis as well as numerical results on an exemplary asymmetric shape, and point out limitations of the approach.}, language = {en} }