@article{KurzKampfBuschleetal.2016,
  author    = {Kurz, Felix T. and Kampf, Thomas and Buschle, Lukas R. and Schlemmer, Heinz-Peter and Bendszus, Martin and Heiland, Sabine and Ziener, Christian H.},
  title     = {Generalized moment analysis of magnetic field correlations for accumulations of spherical and cylindrical magnetic perturbers},
  series = {Frontiers in Physics},
  volume    = {4},
  journal   = {Frontiers in Physics},
  issn      = {2296-424X},
  doi       = {10.3389/fphy.2016.00046},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-190604},
  year      = {2016},
  abstract  = {In biological tissue, an accumulation of similarly shaped objects with a susceptibility difference to the surrounding tissue generates a local distortion of the external magnetic field in magnetic resonance imaging. It induces stochastic field fluctuations that characteristically influence proton spin dephasing in the vicinity of these magnetic perturbers. The magnetic field correlation that is associated with such local magnetic field inhomogeneities can be expressed in the form of a dynamic frequency autocorrelation function that is related to the time evolution of the measured magnetization. Here, an eigenfunction expansion for two simple magnetic perturber shapes, that of spheres and cylinders, is considered for restricted spin diffusion in a simple model geometry. Then, the concept of generalized moment analysis, an approximation technique that is applied in the study of (non-)reactive processes that involve Brownian motion, allows deriving analytical expressions of the correlation function for different exponential decay forms. Results for the biexponential decay for both spherical and cylindrical magnetized objects are derived and compared with the frequently used (less accurate) monoexponential decay forms. They are in asymptotic agreement with the numerically exact value of the correlation function for long and short times.},
  language  = {en}
}
@article{KurzKampfBuschleetal.2015,
  author    = {Kurz, Felix T. and Kampf, Thomas and Buschle, Lukas R. and Schlemmer, Heinz-Peter and Heiland, Sabine and Bendszus, Martin and Ziener, Christian H.},
  title     = {Microstructural Analysis of Peripheral Lung Tissue through CPMG Inter-Echo Time R2 Dispersion},
  series = {PLoS One},
  volume    = {10},
  journal   = {PLoS One},
  number    = {11},
  doi       = {10.1371/journal.pone.0141894},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-138345},
  pages     = {e0141894},
  year      = {2015},
  abstract  = {Since changes in lung microstructure are important indicators for (early stage) lung pathology, there is a need for quantifiable information of diagnostically challenging cases in a clinical setting, e.g. to evaluate early emphysematous changes in peripheral lung tissue. Considering alveoli as spherical air-spaces surrounded by a thin film of lung tissue allows deriving an expression for Carr-Purcell-Meiboom-Gill transverse relaxation rates R-2 with a dependence on inter-echo time, local air-tissue volume fraction, diffusion coefficient and alveolar diameter, within a weak field approximation. The model relaxation rate exhibits the same hyperbolic tangent dependency as seen in the Luz-Meiboom model and limiting cases agree with Brooks et al. and Jensen et al. In addition, the model is tested against experimental data for passively deflated rat lungs: the resulting mean alveolar radius of RA = 31.46 \(\pm\) 13.15 \(\mu\)m is very close to the literature value (similar to 34 \(\mu\)m). Also, modeled radii obtained from relaxometer measurements of ageing hydrogel foam (that mimics peripheral lung tissue) are in good agreement with those obtained from mu CT images of the same foam (mean relative error: 0.06 \(\pm\) 0.01). The model's ability to determine the alveolar radius and/or air volume fraction will be useful in quantifying peripheral lung microstructure.},
  language  = {en}
}
@article{ZienerKurzBuschleetal.2015,
  author    = {Ziener, Christian H. and Kurz, Felix T. and Buschle, Lukas R. and Kampf, Thomas},
  title     = {Orthogonality, Lommel integrals and cross product zeros of linear combinations of Bessel functions},
  series = {SpringerPlus},
  volume    = {4},
  journal   = {SpringerPlus},
  number    = {390},
  doi       = {10.1186/s40064-015-1142-0},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-151432},
  year      = {2015},
  abstract  = {The cylindrical Bessel differential equation and the spherical Bessel differential equation in the interval R\(\leq\)r\(\leq\)\(\gamma\)R with Neumann boundary conditions are considered. The eigenfunctions are linear combinations of the Bessel function \(\Phi\)\(_{n,ν}\)(r) = Y'\(_{ν}\) (\(\lambda\)\(_{n,ν}\))J\(_{ν}\)(\(\lambda\)\(_{n,ν}\) r/R) - J'\(_{ν}\)(\(\lambda\)\(_{n,ν}\))Y\(_{ν}\)(\(\lambda\)\(_{n,ν}\)r/R) or linear combinations of the spherical Bessel functions \(\psi\)\(_{m,ν}\)(r) = y'\(_{ν}\)(\(\lambda\)\(_{m,ν}\))j\(_{ν}\)(\(\lambda\)\(_{m,ν}\)r/R) - j'\(_{ν}\)(\(\lambda\)\(_{m,ν}\))y\(_{ν}\)(\(\lambda\)\(_{m,ν}\)r/R). The orthogonality relations with analytical expressions for the normalization constant are given. Explicit expressions for the Lommel integrals in terms of Lommel functions are derived. The cross product zeros Y'\(_{ν}\)\(\lambda\)\(_{n,ν}\))J'\(_{ν}\)(\(\gamma\)\(\lambda\)\(_{n,ν}\))- J'\(_{ν}\)(\(\lambda\)\(_{n,ν}\))Y'\(_{ν}\)(\(\gamma\)\(\lambda\)\(_{n,ν}\)) = 0 and y'\(_{ν}\)(\(\lambda\)\(_{m,ν}\))j'\(_{ν}\)(\(\gamma\)\(\lambda\)\(_{m,ν}\)) - j'\(_{ν}\)(\(\lambda\)\(_{m,ν}\))y'\(_{ν}\)(\(\gamma\)\(\lambda\)\(_{m,ν}\)) = 0 are considered in the complex plane for real as well as complex values of the index ν and approximations for the exceptional zero \(\lambda\)\(_{1,ν}\) are obtained. A numerical scheme based on the discretization of the twodimensional and three-dimensional Laplace operator with Neumann boundary conditions is presented. Explicit representations of the radial part of the Laplace operator in form of a tridiagonal matrix allow the simple computation of the cross product zeros.},
  language  = {en}
}