@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} } @article{WinterAndelovicKampfetal.2021, author = {Winter, Patrick M. and Andelovic, Kristina and Kampf, Thomas and Hansmann, Jan and Jakob, Peter Michael and Bauer, Wolfgang Rudolf and Zernecke, Alma and Herold, Volker}, title = {Simultaneous measurements of 3D wall shear stress and pulse wave velocity in the murine aortic arch}, series = {Journal of Cardiovascular Magnetic Resonance}, volume = {23}, journal = {Journal of Cardiovascular Magnetic Resonance}, number = {1}, doi = {10.1186/s12968-021-00725-4}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-259152}, pages = {34}, year = {2021}, abstract = {Purpose Wall shear stress (WSS) and pulse wave velocity (PWV) are important parameters to characterize blood flow in the vessel wall. Their quantification with flow-sensitive phase-contrast (PC) cardiovascular magnetic resonance (CMR), however, is time-consuming. Furthermore, the measurement of WSS requires high spatial resolution, whereas high temporal resolution is necessary for PWV measurements. For these reasons, PWV and WSS are challenging to measure in one CMR session, making it difficult to directly compare these parameters. By using a retrospective approach with a flexible reconstruction framework, we here aimed to simultaneously assess both PWV and WSS in the murine aortic arch from the same 4D flow measurement. Methods Flow was measured in the aortic arch of 18-week-old wildtype (n = 5) and ApoE\(^{-/-}\) mice (n = 5) with a self-navigated radial 4D-PC-CMR sequence. Retrospective data analysis was used to reconstruct the same dataset either at low spatial and high temporal resolution (PWV analysis) or high spatial and low temporal resolution (WSS analysis). To assess WSS, the aortic lumen was labeled by semi-automatically segmenting the reconstruction with high spatial resolution. WSS was determined from the spatial velocity gradients at the lumen surface. For calculation of the PWV, segmentation data was interpolated along the temporal dimension. Subsequently, PWV was quantified from the through-plane flow data using the multiple-points transit-time method. Reconstructions with varying frame rates and spatial resolutions were performed to investigate the influence of spatiotemporal resolution on the PWV and WSS quantification. Results 4D flow measurements were conducted in an acquisition time of only 35 min. Increased peak flow and peak WSS values and lower errors in PWV estimation were observed in the reconstructions with high temporal resolution. Aortic PWV was significantly increased in ApoE\(^{-/-}\) mice compared to the control group (1.7 ± 0.2 versus 2.6 ± 0.2 m/s, p < 0.001). Mean WSS magnitude values averaged over the aortic arch were (1.17 ± 0.07) N/m\(^2\) in wildtype mice and (1.27 ± 0.10) N/m\(^2\) in ApoE\(^{-/-}\) mice. Conclusion The post processing algorithm using the flexible reconstruction framework developed in this study permitted quantification of global PWV and 3D-WSS in a single acquisition. The possibility to assess both parameters in only 35 min will markedly improve the analyses and information content of in vivo measurements.}, language = {en} } @article{WinterKampfHelluyetal.2013, author = {Winter, Patrick and Kampf, Thomas and Helluy, Xavier and Gutjahr, Fabian T. and Meyer, Cord B. and Rommel, Eberhard and Bauer, Wolfgang R. and Jakob, Peter M. and Herold, Volker}, title = {Fast retrospectively triggered local pulse-wave velocity measurements in mice with CMR-microscopy using a radial trajectory}, series = {Journal of Cardiovascular Magnetic Resonance}, journal = {Journal of Cardiovascular Magnetic Resonance}, doi = {10.1186/1532-429X-15-88}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-96602}, year = {2013}, abstract = {Background The aortic pulse-wave velocity (PWV) is an important indicator of cardiovascular risk. In recent studies MRI methods have been developed to measure this parameter noninvasively in mice. Present techniques require additional hardware for cardiac and respiratory gating. In this work a robust self-gated measurement of the local PWV in mice without the need of triggering probes is proposed. Methods The local PWV of 6-months-old wild-type C57BL/6J mice (n=6) was measured in the abdominal aorta with a retrospectively triggered radial Phase Contrast (PC) MR sequence using the flow-area (QA) method. A navigator signal was extracted from the CMR data of highly asymmetric radial projections with short repetition time (TR=3 ms) and post-processed with high-pass and low-pass filters for retrospective cardiac and respiratory gating. The self-gating signal was used for a reconstruction of high-resolution Cine frames of the aortic motion. To assess the local PWV the volume flow Q and the cross-sectional area A of the aorta were determined. The results were compared with the values measured with a triggered Cartesian and an undersampled triggered radial PC-Cine sequence. Results In all examined animals a self-gating signal could be extracted and used for retrospective breath-gating and PC-Cine reconstruction. With the non-triggered measurement PWV values of 2.3±0.2 m/s were determined. These values are in agreement with those measured with the triggered Cartesian (2.4±0.2 m/s) and the triggered radial (2.3±0.2 m/s) measurement. Due to the strong robustness of the radial trajectory against undersampling an acceleration of more than two relative to the prospectively triggered Cartesian sampling could be achieved with the retrospective method. Conclusion With the radial flow-encoding sequence the extraction of a self-gating signal is feasible. The retrospective method enables a robust and fast measurement of the local PWV without the need of additional trigger hardware.}, language = {en} } @article{WinterAndelovicKampfetal.2019, author = {Winter, Patrick and Andelovic, Kristina and Kampf, Thomas and Gutjahr, Fabian Tobias and Heidenreich, Julius and Zernecke, Alma and Bauer, Wolfgang Rudolf and Jakob, Peter Michael and Herold, Volker}, title = {Fast self-navigated wall shear stress measurements in the murine aortic archusing radial 4D-phase contrast cardiovascular magnetic resonance at 17.6 T}, series = {Journal of Cardiovascular Magnetic Resonance}, volume = {21}, journal = {Journal of Cardiovascular Magnetic Resonance}, doi = {10.1186/s12968-019-0566-z}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-201120}, pages = {64}, year = {2019}, abstract = {Purpose 4D flow cardiovascular magnetic resonance (CMR) and the assessment of wall shear stress (WSS) are non-invasive tools to study cardiovascular risks in vivo. Major limitations of conventional triggered methods are the long measurement times needed for high-resolution data sets and the necessity of stable electrocardiographic (ECG) triggering. In this work an ECG-free retrospectively synchronized method is presented that enables accelerated high-resolution measurements of 4D flow and WSS in the aortic arch of mice. Methods 4D flow and WSS were measured in the aortic arch of 12-week-old wildtype C57BL/6 J mice (n = 7) with a radial 4D-phase-contrast (PC)-CMR sequence, which was validated in a flow phantom. Cardiac and respiratory motion signals were extracted from the radial CMR signal and were used for the reconstruction of 4D-flow data. Rigid motion correction and a first order B0 correction was used to improve the robustness of magnitude and velocity data. The aortic lumen was segmented semi-automatically. Temporally averaged and time-resolved WSS and oscillatory shear index (OSI) were calculated from the spatial velocity gradients at the lumen surface at 14 locations along the aortic arch. Reproducibility was tested in 3 animals and the influence of subsampling was investigated. Results Volume flow, cross-sectional areas, WSS and the OSI were determined in a measurement time of only 32 min. Longitudinal and circumferential WSS and radial stress were assessed at 14 analysis planes along the aortic arch. The average longitudinal, circumferential and radial stress values were 1.52 ± 0.29 N/m2, 0.28 ± 0.24 N/m2 and - 0.21 ± 0.19 N/m2, respectively. Good reproducibility of WSS values was observed. Conclusion This work presents a robust measurement of 4D flow and WSS in mice without the need of ECG trigger signals. The retrospective approach provides fast flow quantification within 35 min and a flexible reconstruction framework.}, language = {en} } @article{WeiseBasseLuesebrinkKleinschnitzetal.2011, author = {Weise, Gesa and Basse-L{\"u}sebrink, Thomas C. and Kleinschnitz, Christoph and Kampf, Thomas and Jakob, Peter M. and Stoll, Guido}, title = {In Vivo Imaging of Stepwise Vessel Occlusion in Cerebral Photothrombosis of Mice by \(^{19}\)F MRI}, series = {PLoS One}, volume = {6}, journal = {PLoS One}, number = {12}, doi = {10.1371/journal.pone.0028143}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-137792}, pages = {e28143}, year = {2011}, abstract = {Background \(^{19}\)F magnetic resonance imaging (MRI) was recently introduced as a promising technique for in vivo cell tracking. In the present study we compared \(^{19}\)F MRI with iron-enhanced MRI in mice with photothrombosis (PT) at 7 Tesla. PT represents a model of focal cerebral ischemia exhibiting acute vessel occlusion and delayed neuroinflammation. Methods/Principal Findings Perfluorocarbons (PFC) or superparamagnetic iron oxide particles (SPIO) were injected intravenously at different time points after photothrombotic infarction. While administration of PFC directly after PT induction led to a strong \(^{19}\)F signal throughout the entire lesion, two hours delayed application resulted in a rim-like \(^{19}\)F signal at the outer edge of the lesion. These findings closely resembled the distribution of signal loss on T2-weighted MRI seen after SPIO injection reflecting intravascular accumulation of iron particles trapped in vessel thrombi as confirmed histologically. By sequential administration of two chemically shifted PFC compounds 0 and 2 hours after illumination the different spatial distribution of the \(^{19}\)F markers (infarct core/rim) could be visualized in the same animal. When PFC were applied at day 6 the fluorine marker was only detected after long acquisition times ex vivo. SPIO-enhanced MRI showed slight signal loss in vivo which was much more prominent ex vivo indicative for neuroinflammation at this late lesion stage. Conclusion Our study shows that vessel occlusion can be followed in vivo by \(^{19}\)F and SPIO-enhanced high-field MRI while in vivo imaging of neuroinflammation remains challenging. The timing of contrast agent application was the major determinant of the underlying processes depicted by both imaging techniques. Importantly, sequential application of different PFC compounds allowed depiction of ongoing vessel occlusion from the core to the margin of the ischemic lesions in a single MRI measurement.}, language = {en} } @article{WeibelBasseLuesebrinkHessetal.2013, author = {Weibel, Stephanie and Basse-Luesebrink, Thomas Christian and Hess, Michael and Hofmann, Elisabeth and Seubert, Carolin and Langbein-Laugwitz, Johanna and Gentschev, Ivaylo and Sturm, Volker J{\"o}rg Friedrich and Ye, Yuxiang and Kampf, Thomas and Jakob, Peter Michael and Szalay, Aladar A.}, title = {Imaging of Intratumoral Inflammation during Oncolytic Virotherapy of Tumors by \(^{19}\)F-Magnetic Resonance Imaging (MRI)}, series = {PLoS ONE}, volume = {8}, journal = {PLoS ONE}, number = {3}, doi = {10.1371/journal.pone.0056317}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-130311}, pages = {e56317}, year = {2013}, abstract = {Background Oncolytic virotherapy of tumors is an up-coming, promising therapeutic modality of cancer therapy. Unfortunately, non-invasive techniques to evaluate the inflammatory host response to treatment are rare. Here, we evaluate \(^{19}\)F magnetic resonance imaging (MRI) which enables the non-invasive visualization of inflammatory processes in pathological conditions by the use of perfluorocarbon nanoemulsions (PFC) for monitoring of oncolytic virotherapy. Methodology/Principal Findings The Vaccinia virus strain GLV-1h68 was used as an oncolytic agent for the treatment of different tumor models. Systemic application of PFC emulsions followed by \(^1H\)/\(^{19}\)F MRI of mock-infected and GLV-1h68-infected tumor-bearing mice revealed a significant accumulation of the \(^{19}\)F signal in the tumor rim of virus-treated mice. Histological examination of tumors confirmed a similar spatial distribution of the \(^{19}\)F signal hot spots and \(CD68^+\)-macrophages. Thereby, the \(CD68^+\)-macrophages encapsulate the GFP-positive viral infection foci. In multiple tumor models, we specifically visualized early inflammatory cell recruitment in Vaccinia virus colonized tumors. Furthermore, we documented that the \(^{19}\)F signal correlated with the extent of viral spreading within tumors. Conclusions/Significance These results suggest \(^{19}\)F MRI as a non-invasive methodology to document the tumor-associated host immune response as well as the extent of intratumoral viral replication. Thus, \(^{19}\)F MRI represents a new platform to non-invasively investigate the role of the host immune response for therapeutic outcome of oncolytic virotherapy and individual patient response.}, language = {en} } @article{VogelRueckertFriedrichetal.2022, author = {Vogel, Patrick and R{\"u}ckert, Martin Andreas and Friedrich, Bernhard and Tietze, Rainer and Lyer, Stefan and Kampf, Thomas and Hennig, Thomas and D{\"o}lken, Lars and Alexiou, Christoph and Behr, Volker Christian}, title = {Critical Offset Magnetic PArticle SpectroScopy for rapid and highly sensitive medical point-of-care diagnostics}, series = {Nature Communications}, volume = {13}, journal = {Nature Communications}, doi = {10.1038/s41467-022-34941-y}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-300893}, year = {2022}, abstract = {Magnetic nanoparticles (MNPs) have been adapted for many applications, e.g., bioassays for the detection of biomarkers such as antibodies, by controlled engineering of specific surface properties. Specific measurement of such binding states is of high interest but currently limited to highly sensitive techniques such as ELISA or flow cytometry, which are relatively inflexible, difficult to handle, expensive and time-consuming. Here we report a method named COMPASS (Critical-Offset-Magnetic-Particle-SpectroScopy), which is based on a critical offset magnetic field, enabling sensitive detection to minimal changes in mobility of MNP ensembles, e.g., resulting from SARS-CoV-2 antibodies binding to the S antigen on the surface of functionalized MNPs. With a sensitivity of 0.33 fmole/50 µl (≙7 pM) for SARS-CoV-2-S1 antibodies, measured with a low-cost portable COMPASS device, the proposed technique is competitive with respect to sensitivity while providing flexibility, robustness, and a measurement time of seconds per sample. In addition, initial results with blood serum demonstrate high specificity.}, language = {en} } @article{RiedlKampfHeroldetal.2020, author = {Riedl, Katharina A. and Kampf, Thomas and Herold, Volker and Behr, Volker C. and Bauer, Wolfgang R.}, title = {Wall shear stress analysis using 17.6 Tesla MRI: A longitudinal study in ApoE\(^{-/-}\)mice with histological analysis}, series = {PLoS One}, volume = {15}, journal = {PLoS One}, number = {8}, doi = {10.1371/journal.pone.0238112}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-229318}, year = {2020}, abstract = {This longitudinal study was performed to evaluate the feasibility of detecting the interaction between wall shear stress (WSS) and plaque development. 20 ApoE\(^{-/-}\)mice were separated in 12 mice with Western Diet and 8 mice with Chow Diet. Magnetic resonance (MR) scans at 17.6 Tesla and histological analysis were performed after one week, eight and twelve weeks. Allin vivoMR measurements were acquired using a flow sensitive phase contrast method for determining vectorial flow. Histological sections were stained with Hematoxylin and Eosin, Elastica van Gieson and CD68 staining. Data analysis was performed using Ensight and a Matlab-based "Flow Tool". The body weight of ApoE\(^{-/-}\)mice increased significantly over 12 weeks. WSS values increased in the Western Diet group over the time period; in contrast, in the Chow Diet group the values decreased from the first to the second measurement point. Western Diet mice showed small plaque formations with elastin fragmentations after 8 weeks and big plaque formations after 12 weeks; Chow Diet mice showed a few elastin fragmentations after 8 weeks and small plaque formations after 12 weeks. Favored by high-fat diet, plaque formation results in higher values of WSS. With wall shear stress being a known predictor for atherosclerotic plaque development, ultra highfield MRI can serve as a tool for studying the causes and beginnings of atherosclerosis.}, 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{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} }