TY - JOUR A1 - Wormell, Caroline L. A1 - Reich, Sebastian T1 - Spectral convergence of diffusion maps BT - Improved error bounds and an alternative normalization JF - SIAM journal on numerical analysis / Society for Industrial and Applied Mathematics N2 - Diffusion maps is a manifold learning algorithm widely used for dimensionality reduction. Using a sample from a distribution, it approximates the eigenvalues and eigenfunctions of associated Laplace-Beltrami operators. Theoretical bounds on the approximation error are, however, generally much weaker than the rates that are seen in practice. This paper uses new approaches to improve the error bounds in the model case where the distribution is supported on a hypertorus. For the data sampling (variance) component of the error we make spatially localized compact embedding estimates on certain Hardy spaces; we study the deterministic (bias) component as a perturbation of the Laplace-Beltrami operator's associated PDE and apply relevant spectral stability results. Using these approaches, we match long-standing pointwise error bounds for both the spectral data and the norm convergence of the operator discretization. We also introduce an alternative normalization for diffusion maps based on Sinkhorn weights. This normalization approximates a Langevin diffusion on the sample and yields a symmetric operator approximation. We prove that it has better convergence compared with the standard normalization on flat domains, and we present a highly efficient rigorous algorithm to compute the Sinkhorn weights. KW - diffusion maps KW - graph Laplacian KW - Sinkhorn problem KW - kernel methods Y1 - 2021 U6 - https://doi.org/10.1137/20M1344093 SN - 0036-1429 SN - 1095-7170 VL - 59 IS - 3 SP - 1687 EP - 1734 PB - Society for Industrial and Applied Mathematics CY - Philadelphia ER - TY - JOUR A1 - Keller, Matthias A1 - Liu, Shiping A1 - Peyerimhoff, Norbert T1 - A note on eigenvalue bounds for non-compact manifolds JF - Mathematische Nachrichten N2 - In this article we prove upper bounds for the Laplace eigenvalues lambda(k) below the essential spectrum for strictly negatively curved Cartan-Hadamard manifolds. Our bound is given in terms of k(2) and specific geometric data of the manifold. This applies also to the particular case of non-compact manifolds whose sectional curvature tends to -infinity, where no essential spectrum is present due to a theorem of Donnelly/Li. The result stands in clear contrast to Laplacians on graphs where such a bound fails to be true in general. KW - Cheeger inequality KW - eigenvalues KW - Laplacian KW - negative curvature KW - Riemannian manifold Y1 - 2021 U6 - https://doi.org/10.1002/mana.201900209 SN - 0025-584X SN - 1522-2616 VL - 294 IS - 6 SP - 1134 EP - 1139 PB - Wiley-VCH CY - Weinheim ER - TY - JOUR A1 - Peng, Junhao A1 - Sandev, Trifce A1 - Kocarev, Ljupco T1 - First encounters on Bethe lattices and Cayley trees JF - Communications in nonlinear science & numerical simulation N2 - In this work we consider the first encounter problems between a fixed and/or mobile target A and a moving trap B on Bethe lattices and Cayley trees. The survival probabilities (SPs) of the target A on the both kinds of structures are considered analytically and compared. On Bethe lattices, the results show that the fixed target will still prolong its survival time, whereas, on Cayley trees, there are some initial positions where the target should move to prolong its survival time. The mean first encounter time (MFET) for mobile target A is evaluated numerically and compared with the mean first passage time (MFPT) for the fixed target A. Different initial settings are addressed and clear boundaries are obtained. These findings are helpful for optimizing the strategy to prolong the survival time of the target or to speed up the search process on Cayley trees, in relation to the target's movement and the initial position configuration of the two walkers. We also present a new method, which uses a small amount of memory, for simulating random walks on Cayley trees. (C) 2020 Elsevier B.V. All rights reserved. KW - Random walks KW - Survival probability KW - Mean first encounter time KW - Bethe KW - lattices KW - Cayley trees Y1 - 2021 U6 - https://doi.org/10.1016/j.cnsns.2020.105594 SN - 1007-5704 SN - 1878-7274 VL - 95 PB - Elsevier CY - Amsterdam ER - TY - JOUR A1 - Andjelkovic, Marko A1 - Simevski, Aleksandar A1 - Chen, Junchao A1 - Schrape, Oliver A1 - Stamenkovic, Zoran A1 - Krstić, Miloš A1 - Ilic, Stefan A1 - Ristic, Goran A1 - Jaksic, Aleksandar A1 - Vasovic, Nikola A1 - Duane, Russell A1 - Palma, Alberto J. A1 - Lallena, Antonio M. A1 - Carvajal, Miguel A. T1 - A design concept for radiation hardened RADFET readout system for space applications JF - Microprocessors and microsystems N2 - Instruments for measuring the absorbed dose and dose rate under radiation exposure, known as radiation dosimeters, are indispensable in space missions. They are composed of radiation sensors that generate current or voltage response when exposed to ionizing radiation, and processing electronics for computing the absorbed dose and dose rate. Among a wide range of existing radiation sensors, the Radiation Sensitive Field Effect Transistors (RADFETs) have unique advantages for absorbed dose measurement, and a proven record of successful exploitation in space missions. It has been shown that the RADFETs may be also used for the dose rate monitoring. In that regard, we propose a unique design concept that supports the simultaneous operation of a single RADFET as absorbed dose and dose rate monitor. This enables to reduce the cost of implementation, since the need for other types of radiation sensors can be minimized or eliminated. For processing the RADFET's response we propose a readout system composed of analog signal conditioner (ASC) and a self-adaptive multiprocessing system-on-chip (MPSoC). The soft error rate of MPSoC is monitored in real time with embedded sensors, allowing the autonomous switching between three operating modes (high-performance, de-stress and fault-tolerant), according to the application requirements and radiation conditions. KW - RADFET KW - Radiation hardness KW - Absorbed dose KW - Dose rate KW - Self-adaptive MPSoC Y1 - 2022 U6 - https://doi.org/10.1016/j.micpro.2022.104486 SN - 0141-9331 SN - 1872-9436 VL - 90 PB - Elsevier CY - Amsterdam ER - TY - JOUR A1 - Chang, Der-Chen A1 - Schulze, Bert-Wolfgang T1 - Corner spaces and Mellin quantization JF - Journal of nonlinear and convex analysis : an international journal N2 - Manifolds with corners in the present investigation are non-smooth configurations - specific stratified spaces - with an incomplete metric such as cones, manifolds with edges, or corners of piecewise smooth domains in Euclidean space. We focus here on operators on such "corner manifolds" of singularity order <= 2, acting in weighted corner Sobolev spaces. The corresponding corner degenerate pseudo-differential operators are formulated via Mellin quantizations, and they also make sense on infinite singular cones. KW - Mellin quantizations KW - operator-valued symbols KW - weighted edge and corner spaces Y1 - 2018 SN - 1345-4773 SN - 1880-5221 VL - 19 IS - 2 SP - 179 EP - 195 PB - Yokohama Publishers CY - Yokohama ER - TY - JOUR A1 - Chang, Der-Chen A1 - Schulze, Bert-Wolfgang T1 - Ellipticity on spaces with higher singularities JF - Science China Mathematics N2 - We study corner-degenerate pseudo-differential operators of any singularity order and develop ellipticity based on the principal symbolic hierarchy, associated with the stratification of the underlying space. We construct parametrices within the calculus and discuss the aspect of additional trace and potential conditions along lower-dimensional strata. KW - pseudo-differential operators KW - operator-valued symbols KW - Fourier and Mellin transforms Y1 - 2017 U6 - https://doi.org/10.1007/s11425-016-0519-9 SN - 1674-7283 SN - 1869-1862 VL - 60 IS - 11 SP - 2053 EP - 2076 PB - Science China Press CY - Beijing ER - TY - JOUR A1 - Khalil, Sara A1 - Schulze, Bert-Wolfgang T1 - Boundary problems on a manifold with edge JF - Asian-European Journal of Mathematics N2 - We establish a calculus of boundary value problems (BVPs) on a manifold N with boundary and edge, based on Boutet de Monvel’s theory of BVPs in the case of a smooth boundary and on the edge calculus, where in the present case the model cone has a base which is a compact manifold with boundary. The corresponding calculus with boundary and edge is a unification of both structures and controls different operator-valued symbolic structures, in order to obtain ellipticity and parametrices. KW - manifolds with edge and boundary KW - distribution with asymptotics KW - ellipticity KW - Fredholm property Y1 - 2017 U6 - https://doi.org/10.1142/S1793557117500875 SN - 1793-5571 SN - 1793-7183 VL - 10 IS - 2 PB - World Scientific CY - Singapore ER - TY - JOUR A1 - Chang, Der-Chen A1 - Hedayat Mahmoudi, Mahdi A1 - Schulze, Bert-Wolfgang T1 - Singular degenerate operators JF - Applicable analysis : an international journal N2 - We outline some simplified and more general method for constructing parametrices on higher singular spaces. We also outline basic ideas on operators on manifolds with conical or edge singularities. KW - Operators on singular cones KW - Mellin symbols with values in the edge calculus KW - parametrices of elliptic operators Y1 - 2017 U6 - https://doi.org/10.1080/00036811.2017.1336546 SN - 0003-6811 SN - 1563-504X VL - 96 IS - 14 SP - 2434 EP - 2456 PB - Routledge, Taylor & Francis Group CY - Abingdon ER - TY - JOUR A1 - Harutyunyan, Gohar A1 - Schulze, Bert-Wolfgang T1 - The Zaremba problem with singular interfaces as a corner boundary value problem JF - Potential analysis : an international journal devoted to the interactions between potential theory, probability theory, geometry and functional analysis N2 - We study mixed boundary value problems for an elliptic operator A on a manifold X with boundary Y, i.e., Au = f in int X, T (+/-) u = g(+/-) on int Y+/-, where Y is subdivided into subsets Y+/- with an interface Z and boundary conditions T+/- on Y+/- that are Shapiro-Lopatinskij elliptic up to Z from the respective sides. We assume that Z subset of Y is a manifold with conical singularity v. As an example we consider the Zaremba problem, where A is the Laplacian and T- Dirichlet, T+ Neumann conditions. The problem is treated as a corner boundary value problem near v which is the new point and the main difficulty in this paper. Outside v the problem belongs to the edge calculus as is shown in Bull. Sci. Math. ( to appear). With a mixed problem we associate Fredholm operators in weighted corner Sobolev spaces with double weights, under suitable edge conditions along Z {v} of trace and potential type. We construct parametrices within the calculus and establish the regularity of solutions. KW - Zaremba problem KW - corner Sobolev spaces with double weights KW - pseudo-differential boundary value problems Y1 - 2006 U6 - https://doi.org/10.1007/s11118-006-9020-6 SN - 0926-2601 VL - 25 SP - 327 EP - 369 PB - Springer CY - Dordrecht ER - TY - JOUR A1 - Hedayat Mahmoudi, Mahdi A1 - Schulze, Bert-Wolfgang T1 - A new approach to the second order edge calculus JF - Journal of pseudo-differential operators and applications N2 - We establish essential steps of an iterative approach to operator algebras, ellipticity and Fredholm property on stratified spaces with singularities of second order. We cover, in particular, corner-degenerate differential operators. Our constructions are focused on the case where no additional conditions of trace and potential type are posed, but this case works well and will be considered in a forthcoming paper as a conclusion of the present calculus. KW - Operators on singular manifolds KW - Mellin transform KW - Stratified spaces KW - Ellipticity and parametrices Y1 - 2018 U6 - https://doi.org/10.1007/s11868-017-0191-2 SN - 1662-9981 SN - 1662-999X VL - 9 IS - 2 SP - 265 EP - 300 PB - Springer CY - Basel ER - TY - JOUR A1 - Khalil, Sara A1 - Schulze, Bert-Wolfgang T1 - Calculus on a Manifold with Edge and Boundary JF - Complex analysis and operator theory N2 - We study elements of the calculus of boundary value problems in a variant of Boutet de Monvel’s algebra (Acta Math 126:11–51, 1971) on a manifold N with edge and boundary. If the boundary is empty then the approach corresponds to Schulze (Symposium on partial differential equations (Holzhau, 1988), BSB Teubner, Leipzig, 1989) and other papers from the subsequent development. For non-trivial boundary we study Mellin-edge quantizations and compositions within the structure in terms a new Mellin-edge quantization, compared with a more traditional technique. Similar structures in the closed case have been studied in Gil et al. KW - algebra KW - Mellin quantization Y1 - 2019 U6 - https://doi.org/10.1007/s11785-018-0800-y SN - 1661-8254 SN - 1661-8262 VL - 13 IS - 6 SP - 2627 EP - 2670 PB - Springer CY - Basel ER - TY - JOUR A1 - Schulze, Bert-Wolfgang A1 - Seiler, Jörg T1 - Elliptic complexes on manifolds with boundary JF - The journal of geometric analysis N2 - We show that elliptic complexes of (pseudo) differential operators on smooth compact manifolds with boundary can always be complemented to a Fredholm problem by boundary conditions involving global pseudodifferential projections on the boundary (similarly as the spectral boundary conditions of Atiyah, Patodi, and Singer for a single operator). We prove that boundary conditions without projections can be chosen if, and only if, the topological Atiyah-Bott obstruction vanishes. These results make use of a Fredholm theory for complexes of operators in algebras of generalized pseudodifferential operators of Toeplitz type which we also develop in the present paper. KW - Elliptic complexes KW - Manifolds with boundary KW - Atiyah-Bott obstruction KW - Toeplitz-type pseudodifferential operators Y1 - 2018 U6 - https://doi.org/10.1007/s12220-018-0014-6 SN - 1050-6926 SN - 1559-002X VL - 29 IS - 1 SP - 656 EP - 706 PB - Springer CY - New York ER - TY - JOUR A1 - Zöller, Gert A1 - Hainzl, Sebastian A1 - Tilmann, Frederik A1 - Woith, Heiko A1 - Dahm, Torsten T1 - Comment on: Wikelski, Martin; Müller, Uschi; Scocco, Paola; Catorci, Andrea; Desinov, Lev V.; Belyaev, Mikhail Y.; Keim, Daniel A.; Pohlmeier, Winfried; Fechteler, Gerhard; Mai, Martin P. : Potential short-term earthquake forecasting by farm animal monitoring. - Ethology. - 126 (2020), 9. - S. 931 - 941. -ISSN 0179-1613. - eISSN 1439-0310. - doi 10.1111/eth.13078 JF - Ethology N2 - Based on an analysis of continuous monitoring of farm animal behavior in the region of the 2016 M6.6 Norcia earthquake in Italy, Wikelski et al., 2020; (Seismol Res Lett, 89, 2020, 1238) conclude that animal activity can be anticipated with subsequent seismic activity and that this finding might help to design a "short-term earthquake forecasting method." We show that this result is based on an incomplete analysis and misleading interpretations. Applying state-of-the-art methods of statistics, we demonstrate that the proposed anticipatory patterns cannot be distinguished from random patterns, and consequently, the observed anomalies in animal activity do not have any forecasting power. KW - animal behavior KW - earthquake precursor KW - error diagram KW - prediction KW - randomness KW - statistics Y1 - 2020 U6 - https://doi.org/10.1111/eth.13105 SN - 0179-1613 SN - 1439-0310 VL - 127 IS - 3 SP - 302 EP - 306 PB - Wiley CY - Hoboken ER - TY - JOUR A1 - Pohle, Jennifer A1 - Adam, Timo A1 - Beumer, Larissa T1 - Flexible estimation of the state dwell-time distribution in hidden semi-Markov models JF - Computational statistics & data analysis N2 - Hidden semi-Markov models generalise hidden Markov models by explicitly modelling the time spent in a given state, the so-called dwell time, using some distribution defined on the natural numbers. While the (shifted) Poisson and negative binomial distribution provide natural choices for such distributions, in practice, parametric distributions can lack the flexibility to adequately model the dwell times. To overcome this problem, a penalised maximum likelihood approach is proposed that allows for a flexible and data-driven estimation of the dwell-time distributions without the need to make any distributional assumption. This approach is suitable for direct modelling purposes or as an exploratory tool to investigate the latent state dynamics. The feasibility and potential of the suggested approach is illustrated in a simulation study and by modelling muskox movements in northeast Greenland using GPS tracking data. The proposed method is implemented in the R-package PHSMM which is available on CRAN. KW - Penalized likelihood KW - Smoothing KW - Time series KW - Animal movement modeling Y1 - 2022 U6 - https://doi.org/10.1016/j.csda.2022.107479 SN - 0167-9473 SN - 1872-7352 VL - 172 PB - Elsevier CY - Amsterdam ER - TY - JOUR A1 - Biskaborn, Boris A1 - Smith, Sharon L. A1 - Noetzli, Jeannette A1 - Matthes, Heidrun A1 - Vieira, Goncalo A1 - Streletskiy, Dmitry A. A1 - Schoeneich, Philippe A1 - Romanovsky, Vladimir E. A1 - Lewkowicz, Antoni G. A1 - Abramov, Andrey A1 - Allard, Michel A1 - Boike, Julia A1 - Cable, William L. A1 - Christiansen, Hanne H. A1 - Delaloye, Reynald A1 - Diekmann, Bernhard A1 - Drozdov, Dmitry A1 - Etzelmueller, Bernd A1 - Grosse, Guido A1 - Guglielmin, Mauro A1 - Ingeman-Nielsen, Thomas A1 - Isaksen, Ketil A1 - Ishikawa, Mamoru A1 - Johansson, Margareta A1 - Johannsson, Halldor A1 - Joo, Anseok A1 - Kaverin, Dmitry A1 - Kholodov, Alexander A1 - Konstantinov, Pavel A1 - Kroeger, Tim A1 - Lambiel, Christophe A1 - Lanckman, Jean-Pierre A1 - Luo, Dongliang A1 - Malkova, Galina A1 - Meiklejohn, Ian A1 - Moskalenko, Natalia A1 - Oliva, Marc A1 - Phillips, Marcia A1 - Ramos, Miguel A1 - Sannel, A. Britta K. A1 - Sergeev, Dmitrii A1 - Seybold, Cathy A1 - Skryabin, Pavel A1 - Vasiliev, Alexander A1 - Wu, Qingbai A1 - Yoshikawa, Kenji A1 - Zheleznyak, Mikhail A1 - Lantuit, Hugues T1 - Permafrost is warming at a global scale JF - Nature Communications N2 - Permafrost warming has the potential to amplify global climate change, because when frozen sediments thaw it unlocks soil organic carbon. Yet to date, no globally consistent assessment of permafrost temperature change has been compiled. Here we use a global data set of permafrost temperature time series from the Global Terrestrial Network for Permafrost to evaluate temperature change across permafrost regions for the period since the International Polar Year (2007-2009). During the reference decade between 2007 and 2016, ground temperature near the depth of zero annual amplitude in the continuous permafrost zone increased by 0.39 +/- 0.15 degrees C. Over the same period, discontinuous permafrost warmed by 0.20 +/- 0.10 degrees C. Permafrost in mountains warmed by 0.19 +/- 0.05 degrees C and in Antarctica by 0.37 +/- 0.10 degrees C. Globally, permafrost temperature increased by 0.29 +/- 0.12 degrees C. The observed trend follows the Arctic amplification of air temperature increase in the Northern Hemisphere. In the discontinuous zone, however, ground warming occurred due to increased snow thickness while air temperature remained statistically unchanged. Y1 - 2019 U6 - https://doi.org/10.1038/s41467-018-08240-4 SN - 2041-1723 VL - 10 PB - Nature Publ. Group CY - London ER - TY - BOOK ED - Kuzle, Ana ED - Rott, Benjamin ED - Gebel, Inga T1 - Implementation research on problem solving in school settings BT - Proceedings of the 2018 Joint Conference of ProMath and the GDM Working Group on Problem Solving T3 - Ars inveniendi et dejudicandi ; 13 Y1 - 2019 SN - 978-3-95987-116-7 SN - 978-3-95987-115-0 PB - WTM-Verlag CY - Münster ER - TY - GEN A1 - Krause, Andreas A1 - Kloft, Charlotte A1 - Huisinga, Wilhelm A1 - Karlsson, Mats A1 - Pinheiro, José A1 - Bies, Robert A1 - Rogers, James A1 - Mentré, France A1 - Musser, Bret J. T1 - Comment on Jaki et al., A proposal for a new PhD level curriculum on quantitative methods for drug development T2 - Pharmaceutical statistics : the journal of applied statistics in the pharmaceutical industry Y1 - 2019 SN - 1539-1604 SN - 1539-1612 VL - 18 IS - 3 SP - 278 EP - 281 PB - Wiley CY - Hoboken ER - TY - THES A1 - Seuring, Markus T1 - Output space compaction for testing and concurrent checking N2 - In der Dissertation werden neue Entwurfsmethoden für Kompaktoren für die Ausgänge von digitalen Schaltungen beschrieben, die die Anzahl der zu testenden Ausgänge drastisch verkleinern und dabei die Testbarkeit der Schaltungen nur wenig oder gar nicht verschlechtern. Der erste Teil der Arbeit behandelt für kombinatorische Schaltungen Methoden, die die Struktur der Schaltungen beim Entwurf der Kompaktoren berücksichtigen. Verschiedene Algorithmen zur Analyse von Schaltungsstrukturen werden zum ersten Mal vorgestellt und untersucht. Die Komplexität der vorgestellten Verfahren zur Erzeugung von Kompaktoren ist linear bezüglich der Anzahl der Gatter in der Schaltung und ist damit auf sehr große Schaltungen anwendbar. Im zweiten Teil wird erstmals ein solches Verfahren für sequentielle Schaltkreise beschrieben. Dieses Verfahren baut im wesentlichen auf das erste auf. Der dritte Teil beschreibt eine Entwurfsmethode, die keine Informationen über die interne Struktur der Schaltung oder über das zugrundeliegende Fehlermodell benötigt. Der Entwurf basiert alleine auf einem vorgegebenen Satz von Testvektoren und die dazugehörenden Testantworten der fehlerfreien Schaltung. Ein nach diesem Verfahren erzeugter Kompaktor maskiert keinen der Fehler, die durch das Testen mit den vorgegebenen Vektoren an den Ausgängen der Schaltung beobachtbar sind. N2 - The objective of this thesis is to provide new space compaction techniques for testing or concurrent checking of digital circuits. In particular, the work focuses on the design of space compactors that achieve high compaction ratio and minimal loss of testability of the circuits. In the first part, the compactors are designed for combinational circuits based on the knowledge of the circuit structure. Several algorithms for analyzing circuit structures are introduced and discussed for the first time. The complexity of each design procedure is linear with respect to the number of gates of the circuit. Thus, the procedures are applicable to large circuits. In the second part, the first structural approach for output compaction for sequential circuits is introduced. Essentially, it enhances the first part. For the approach introduced in the third part it is assumed that the structure of the circuit and the underlying fault model are unknown. The space compaction approach requires only the knowledge of the fault-free test responses for a precomputed test set. The proposed compactor design guarantees zero-aliasing with respect to the precomputed test set. KW - digital circuit KW - output space compaction KW - zero-aliasing KW - test KW - concurrent checking KW - propagation probability KW - IP core Y1 - 2000 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-0000165 ER - TY - JOUR A1 - Mueller-Schoell, Anna A1 - Groenland, Stefanie L. A1 - Scherf-Clavel, Oliver A1 - van Dyk, Madele A1 - Huisinga, Wilhelm A1 - Michelet, Robin A1 - Jaehde, Ulrich A1 - Steeghs, Neeltje A1 - Huitema, Alwin D. R. A1 - Kloft, Charlotte T1 - Therapeutic drug monitoring of oral targeted antineoplastic drugs JF - European journal of clinical pharmacology N2 - Purpose This review provides an overview of the current challenges in oral targeted antineoplastic drug (OAD) dosing and outlines the unexploited value of therapeutic drug monitoring (TDM). Factors influencing the pharmacokinetic exposure in OAD therapy are depicted together with an overview of different TDM approaches. Finally, current evidence for TDM for all approved OADs is reviewed. Methods A comprehensive literature search (covering literature published until April 2020), including primary and secondary scientific literature on pharmacokinetics and dose individualisation strategies for OADs, together with US FDA Clinical Pharmacology and Biopharmaceutics Reviews and the Committee for Medicinal Products for Human Use European Public Assessment Reports was conducted. Results OADs are highly potent drugs, which have substantially changed treatment options for cancer patients. Nevertheless, high pharmacokinetic variability and low treatment adherence are risk factors for treatment failure. TDM is a powerful tool to individualise drug dosing, ensure drug concentrations within the therapeutic window and increase treatment success rates. After reviewing the literature for 71 approved OADs, we show that exposure-response and/or exposure-toxicity relationships have been established for the majority. Moreover, TDM has been proven to be feasible for individualised dosing of abiraterone, everolimus, imatinib, pazopanib, sunitinib and tamoxifen in prospective studies. There is a lack of experience in how to best implement TDM as part of clinical routine in OAD cancer therapy. Conclusion Sub-therapeutic concentrations and severe adverse events are current challenges in OAD treatment, which can both be addressed by the application of TDM-guided dosing, ensuring concentrations within the therapeutic window. KW - targeted antineoplastic drugs KW - tyrosine kinase inhibitors KW - therapeutic KW - drug monitoring KW - oral anticancer drugs KW - personalised medicine Y1 - 2020 U6 - https://doi.org/10.1007/s00228-020-03014-8 SN - 0031-6970 SN - 1432-1041 VL - 77 IS - 4 SP - 441 EP - 464 PB - Springer CY - Heidelberg ER - TY - JOUR A1 - Grisic, Ana-Marija A1 - Eser, Alexander A1 - Huisinga, Wilhelm A1 - Reinisch, Walter A1 - Kloft, Charlotte T1 - Quantitative relationship between infliximab exposure and inhibition of C-reactive protein synthesis to support inflammatory bowel disease management JF - British journal of clinical pharmacology N2 - Aim Quantitative and kinetic insights into the drug exposure-disease response relationship might enhance our knowledge on loss of response and support more effective monitoring of inflammatory activity by biomarkers in patients with inflammatory bowel disease (IBD) treated with infliximab (IFX). This study aimed to derive recommendations for dose adjustment and treatment optimisation based on mechanistic characterisation of the relationship between IFX serum concentration and C-reactive protein (CRP) concentration.
Methods Data from an investigator-initiated trial included 121 patients with IBD during IFX maintenance treatment. Serum concentrations of IFX, antidrug antibodies (ADA), CRP, and disease-related covariates were determined at the mid-term and end of a dosing interval. Data were analysed using a pharmacometric nonlinear mixed-effects modelling approach. An IFX exposure-CRP model was generated and applied to evaluate dosing regimens to achieve CRP remission.
Results The generated quantitative model showed that IFX has the potential to inhibit up to 72% (9% relative standard error [RSE]) of CRP synthesis in a patient. IFX concentration leading to 90% of the maximum CRP synthesis inhibition was 18.4 mu g/mL (43% RSE). Presence of ADA was the most influential factor on IFX exposure. With standard dosing strategy, >= 55% of ADA+ patients experienced CRP nonremission. Shortening the dosing interval and co-therapy with immunomodulators were found to be the most beneficial strategies to maintain CRP remission.
Conclusions With the generated model we could for the first time establish a robust relationship between IFX exposure and CRP synthesis inhibition, which could be utilised for treatment optimisation in IBD patients. KW - C‐ reactive protein remission KW - inflammatory bowel disease KW - infliximab dosing Y1 - 2020 U6 - https://doi.org/10.1111/bcp.14648 SN - 0306-5251 SN - 1365-2125 VL - 87 IS - 5 SP - 2374 EP - 2384 PB - Wiley CY - Hoboken ER - TY - JOUR A1 - Kluwe, Franziska A1 - Michelet, Robin A1 - Müller-Schöll, Anna A1 - Maier, Corinna A1 - Klopp-Schulze, Lena A1 - van Dyk, Madele A1 - Mikus, Gerd A1 - Huisinga, Wilhelm A1 - Kloft, Charlotte T1 - Perspectives on model-informed precision dosing in the digital health era BT - challenges, opportunities, and recommendations JF - Clinical pharmacology & therapeutics Y1 - 2020 U6 - https://doi.org/10.1002/cpt.2049 SN - 0009-9236 SN - 1532-6535 VL - 109 IS - 1 SP - 29 EP - 36 PB - Wiley CY - Hoboken ER - TY - JOUR A1 - Nassar, Yomna M. A1 - Hohmann, Nicolas A1 - Michelet, Robin A1 - Gottwalt, Katharina A1 - Meid, Andreas D. A1 - Burhenne, Jürgen A1 - Huisinga, Wilhelm A1 - Haefeli, Walter E. A1 - Mikus, Gerd A1 - Kloft, Charlotte T1 - Quantification of the Time Course of CYP3A Inhibition, Activation, and Induction Using a Population Pharmacokinetic Model of Microdosed Midazolam Continuous Infusion JF - Clinical Pharmacokinetics N2 - Background Cytochrome P450 (CYP) 3A contributes to the metabolism of many approved drugs. CYP3A perpetrator drugs can profoundly alter the exposure of CYP3A substrates. However, effects of such drug-drug interactions are usually reported as maximum effects rather than studied as time-dependent processes. Identification of the time course of CYP3A modulation can provide insight into when significant changes to CYP3A activity occurs, help better design drug-drug interaction studies, and manage drug-drug interactions in clinical practice. Objective We aimed to quantify the time course and extent of the in vivo modulation of different CYP3A perpetrator drugs on hepatic CYP3A activity and distinguish different modulatory mechanisms by their time of onset, using pharmacologically inactive intravenous microgram doses of the CYP3A-specific substrate midazolam, as a marker of CYP3A activity. Methods Twenty-four healthy individuals received an intravenous midazolam bolus followed by a continuous infusion for 10 or 36 h. Individuals were randomized into four arms: within each arm, two individuals served as a placebo control and, 2 h after start of the midazolam infusion, four individuals received the CYP3A perpetrator drug: voriconazole (inhibitor, orally or intravenously), rifampicin (inducer, orally), or efavirenz (activator, orally). After midazolam bolus administration, blood samples were taken every hour (rifampicin arm) or every 15 min (remaining study arms) until the end of midazolam infusion. A total of 1858 concentrations were equally divided between midazolam and its metabolite, 1'-hydroxymidazolam. A nonlinear mixed-effects population pharmacokinetic model of both compounds was developed using NONMEM (R). CYP3A activity modulation was quantified over time, as the relative change of midazolam clearance encountered by the perpetrator drug, compared to the corresponding clearance value in the placebo arm. Results Time course of CYP3A modulation and magnitude of maximum effect were identified for each perpetrator drug. While efavirenz CYP3A activation was relatively fast and short, reaching a maximum after approximately 2-3 h, the induction effect of rifampicin could only be observed after 22 h, with a maximum after approximately 28-30 h followed by a steep drop to almost baseline within 1-2 h. In contrast, the inhibitory impact of both oral and intravenous voriconazole was prolonged with a steady inhibition of CYP3A activity followed by a gradual increase in the inhibitory effect until the end of sampling at 8 h. Relative maximum clearance changes were +59.1%, +46.7%, -70.6%, and -61.1% for efavirenz, rifampicin, oral voriconazole, and intravenous voriconazole, respectively. Conclusions We could distinguish between different mechanisms of CYP3A modulation by the time of onset. Identification of the time at which clearance significantly changes, per perpetrator drug, can guide the design of an optimal sampling schedule for future drug-drug interaction studies. The impact of a short-term combination of different perpetrator drugs on the paradigm CYP3A substrate midazolam was characterized and can define combination intervals in which no relevant interaction is to be expected. Y1 - 2022 U6 - https://doi.org/10.1007/s40262-022-01175-6 SN - 0312-5963 SN - 1179-1926 VL - 61 IS - 11 SP - 1595 EP - 1607 PB - Springer CY - Northcote ER - TY - GEN A1 - Weisser, Karin A1 - Stübler, Sabine A1 - Matheis, Walter A1 - Huisinga, Wilhelm T1 - Towards toxicokinetic modelling of aluminium exposure from adjuvants in medicinal products T2 - Regulatory toxicology and pharmacology : official journal of the International Society for Regulatory Toxicology and Pharmacology N2 - As a potentially toxic agent on nervous system and bone, the safety of aluminium exposure from adjuvants in vaccines and subcutaneous immune therapy (SCIT) products has to be continuously reevaluated, especially regarding concomitant administrations. For this purpose, knowledge on absorption and disposition of aluminium in plasma and tissues is essential. Pharmacokinetic data after vaccination in humans, however, are not available, and for methodological and ethical reasons difficult to obtain. To overcome these limitations, we discuss the possibility of an in vitro-in silico approach combining a toxicokinetic model for aluminium disposition with biorelevant kinetic absorption parameters from adjuvants. We critically review available kinetic aluminium-26 data for model building and, on the basis of a reparameterized toxicokinetic model (Nolte et al., 2001), we identify main modelling gaps. The potential of in vitro dissolution experiments for the prediction of intramuscular absorption kinetics of aluminium after vaccination is explored. It becomes apparent that there is need for detailed in vitro dissolution and in vivo absorption data to establish an in vitro-in vivo correlation (IVIVC) for aluminium adjuvants. We conclude that a combination of new experimental data and further refinement of the Nolte model has the potential to fill a gap in aluminium risk assessment. (C) 2017 Elsevier Inc. All rights reserved. KW - Aluminium KW - Aluminium adjuvants KW - Absorption kinetics KW - Toxicokinetic modelling KW - In vitro dissolution Y1 - 2017 U6 - https://doi.org/10.1016/j.yrtph.2017.02.018 SN - 0273-2300 SN - 1096-0295 VL - 88 SP - 310 EP - 321 PB - Elsevier CY - San Diego ER - TY - JOUR A1 - Wicha, Sebastian G. A1 - Huisinga, Wilhelm A1 - Kloft, Charlotte T1 - Translational pharmacometric evaluation of typical antibiotic broad-spectrum combination therapies against staphylococcus aureus exploiting in vitro information JF - CPT: pharmacometrics & systems pharmacology N2 - Broad-spectrum antibiotic combination therapy is frequently applied due to increasing resistance development of infective pathogens. The objective of the present study was to evaluate two common empiric broad-spectrum combination therapies consisting of either linezolid (LZD) or vancomycin (VAN) combined with meropenem (MER) against Staphylococcus aureus (S. aureus) as the most frequent causative pathogen of severe infections. A semimechanistic pharmacokinetic-pharmacodynamic (PK-PD) model mimicking a simplified bacterial life-cycle of S. aureus was developed upon time-kill curve data to describe the effects of LZD, VAN, and MER alone and in dual combinations. The PK-PD model was successfully (i) evaluated with external data from two clinical S. aureus isolates and further drug combinations and (ii) challenged to predict common clinical PK-PD indices and breakpoints. Finally, clinical trial simulations were performed that revealed that the combination of VAN-MER might be favorable over LZD-MER due to an unfavorable antagonistic interaction between LZD and MER. Y1 - 2017 U6 - https://doi.org/10.1002/psp4.12197 SN - 2163-8306 VL - 6 SP - 512 EP - 522 PB - Wiley CY - Hoboken ER - TY - JOUR A1 - Edlund, Helena A1 - Grisic, Ana-Marija A1 - Steenholdt, Casper A1 - Ainsworth, Mark Andrew A1 - Brynskov, Torn A1 - Huisinga, Wilhelm A1 - Kloft, Charlotte T1 - Absence of Relationship Between Crohn's Disease Activity Index or C-Reactive Protein and Infliximab Exposure Calls for Objective Crohn's Disease Activity Measures for the Evaluation of Treatment Effects at Treatment Failure JF - Therapeutic drug monitoring : official journal of the International Association of Therapeutic Drug Monitoring and Clinical Toxicology N2 - Background: Circulating infliximab (IFX) concentrations correlate with clinical outcomes, forming the basis of the IFX concentration monitoring in patients with Crohn's disease. This study aims to investigate and refine the exposure-response relationship by linking the disease activity markers "Crohn's disease activity index" (CDAI) and C-reactive protein (CRP) to IFX exposure. In addition, we aim to explore the correlations between different disease markers and exposure metrics. Methods: Data from 47 Crohn's disease patients of a randomized controlled trial were analyzed post hoc. All patients had secondary treatment failure at inclusion and had received intensified IFX of 5 mg/kg every 4 weeks for up to 20 weeks. Graphical analyses were performed to explore exposure-response relationships. Metrics of exposure included area under the concentration-time curve (AUC) and trough concentrations (Cmin). Disease activity was measured by CDAI and CRP values, their change from baseline/last visit, and response/remission outcomes at week 12. Results: Although trends toward lower Cmin and lower AUC in nonresponders were observed, neither CDAI nor CRP showed consistent trends of lower disease activity with higher IFX exposure across the 30 evaluated relationships. As can be expected, Cmin and AUC were strongly correlated with each other. Contrarily, the disease activity markers were only weakly correlated with each other. Conclusions: No significant relationship between disease activity, as evaluated by CDAI or CRP, and IFX exposure was identified. AUC did not add benefit compared with Cmin. These findings support the continued use of Cmin and call for stringent objective disease activity (bio-)markers (eg, endoscopy) to form the basis of personalized IFX therapy for Crohn's disease patients with IFX treatment failure. Y1 - 2019 U6 - https://doi.org/10.1097/FTD.0000000000000590 SN - 0163-4356 SN - 1536-3694 VL - 41 IS - 2 SP - 235 EP - 242 PB - Lippincott Williams & Wilkins CY - Philadelphia ER - TY - JOUR A1 - Knöchel, Jane A1 - Kloft, Charlotte A1 - Huisinga, Wilhelm T1 - Understanding and reducing complex systems pharmacology models based on a novel input-response index JF - Journal of pharmacokinetics and pharmacodynamics N2 - A growing understanding of complex processes in biology has led to large-scale mechanistic models of pharmacologically relevant processes. These models are increasingly used to study the response of the system to a given input or stimulus, e.g., after drug administration. Understanding the input–response relationship, however, is often a challenging task due to the complexity of the interactions between its constituents as well as the size of the models. An approach that quantifies the importance of the different constituents for a given input–output relationship and allows to reduce the dynamics to its essential features is therefore highly desirable. In this article, we present a novel state- and time-dependent quantity called the input–response index that quantifies the importance of state variables for a given input–response relationship at a particular time. It is based on the concept of time-bounded controllability and observability, and defined with respect to a reference dynamics. In application to the brown snake venom–fibrinogen (Fg) network, the input–response indices give insight into the coordinated action of specific coagulation factors and about those factors that contribute only little to the response. We demonstrate how the indices can be used to reduce large-scale models in a two-step procedure: (i) elimination of states whose dynamics have only minor impact on the input–response relationship, and (ii) proper lumping of the remaining (lower order) model. In application to the brown snake venom–fibrinogen network, this resulted in a reduction from 62 to 8 state variables in the first step, and a further reduction to 5 state variables in the second step. We further illustrate that the sequence, in which a recursive algorithm eliminates and/or lumps state variables, has an impact on the final reduced model. The input–response indices are particularly suited to determine an informed sequence, since they are based on the dynamics of the original system. In summary, the novel measure of importance provides a powerful tool for analysing the complex dynamics of large-scale systems and a means for very efficient model order reduction of nonlinear systems. KW - Control theory KW - Model order reduction KW - Blood coagulation network KW - Nonlinear systems Y1 - 2017 U6 - https://doi.org/10.1007/s10928-017-9561-x SN - 1567-567X SN - 1573-8744 VL - 45 IS - 1 SP - 139 EP - 157 PB - Springer Science + Business Media B.V. CY - New York ER - TY - THES A1 - Knöchel, Jane T1 - Model reduction of mechanism-based pharmacodynamic models and its link to classical drug effect models T1 - Modellreduktion von mechanistischen pharmacodynamischen Modellen und deren Verbindung zu klassischen Wirkstoff-Effekt-Modellen N2 - Continuous insight into biological processes has led to the development of large-scale, mechanistic systems biology models of pharmacologically relevant networks. While these models are typically designed to study the impact of diverse stimuli or perturbations on multiple system variables, the focus in pharmacological research is often on a specific input, e.g., the dose of a drug, and a specific output related to the drug effect or response in terms of some surrogate marker. To study a chosen input-output pair, the complexity of the interactions as well as the size of the models hinders easy access and understanding of the details of the input-output relationship. The objective of this thesis is the development of a mathematical approach, in specific a model reduction technique, that allows (i) to quantify the importance of the different state variables for a given input-output relationship, and (ii) to reduce the dynamics to its essential features -- allowing for a physiological interpretation of state variables as well as parameter estimation in the statistical analysis of clinical data. We develop a model reduction technique using a control theoretic setting by first defining a novel type of time-limited controllability and observability gramians for nonlinear systems. We then show the superiority of the time-limited generalised gramians for nonlinear systems in the context of balanced truncation for a benchmark system from control theory. The concept of time-limited controllability and observability gramians is subsequently used to introduce a state and time-dependent quantity called the input-response (ir) index that quantifies the importance of state variables for a given input-response relationship at a particular time. We subsequently link our approach to sensitivity analysis, thus, enabling for the first time the use of sensitivity coefficients for state space reduction. The sensitivity based ir-indices are given as a product of two sensitivity coefficients. This allows not only for a computational more efficient calculation but also for a clear distinction of the extent to which the input impacts a state variable and the extent to which a state variable impacts the output. The ir-indices give insight into the coordinated action of specific state variables for a chosen input-response relationship. Our developed model reduction technique results in reduced models that still allow for a mechanistic interpretation in terms of the quantities/state variables of the original system, which is a key requirement in the field of systems pharmacology and systems biology and distinguished the reduced models from so-called empirical drug effect models. The ir-indices are explicitly defined with respect to a reference trajectory and thereby dependent on the initial state (this is an important feature of the measure). This is demonstrated for an example from the field of systems pharmacology, showing that the reduced models are very informative in their ability to detect (genetic) deficiencies in certain physiological entities. Comparing our novel model reduction technique to the already existing techniques shows its superiority. The novel input-response index as a measure of the importance of state variables provides a powerful tool for understanding the complex dynamics of large-scale systems in the context of a specific drug-response relationship. Furthermore, the indices provide a means for a very efficient model order reduction and, thus, an important step towards translating insight from biological processes incorporated in detailed systems pharmacology models into the population analysis of clinical data. N2 - Die kontinuierliche Erforschung von biologischen Prozessen hat zur Entwicklung umfangreicher, mechanistischer systembiologischer Modelle von pharmakologisch relevanten Netzwerken beigetragen. Während diese Modelle in der Regel darauf ausgelegt sind, die Auswirkung von Stimuli oder Störungen auf die Systemdynamik zu untersuchen, liegt der Fokus in der pharmakologis- chen Forschung häufig auf einer bestimmten Kontrolle, z.B. der Dosis eines Wirkstoffes, und einer bestimmten Ausgangsgröße, welche in Bezug steht zu dem Wirkstoff-Effekt oder das Ansprechen auf einen Wirkstoff über einen Surrogatmarker. Die Untersuchung und ein einfaches Verständnis einer spezifischen Eingabe-Ausgabe-Beziehung wird durch die Komplexität der Interaktionen sowie der Größe des Modells erschwert. Das Ziel dieser vorliegenden Arbeit ist die Entwicklung eines mathematischen Ansatzes, insbesondere eines Modellreduktionsverfahrens, der es ermöglicht, (i) die Bedeutung der verschiedenen Zustandsvariablen für eine gegebene Eingabe-Ausgabe-Beziehung zu quantifizieren, und (ii) die Dynamik des Systems auf seine wesentlichen Merkmale zu reduzieren, während gleichzeitig die physiologische Interpretierbarkeit von Zustandsvariablen sowie eine Parameterschätzung im Rahmen von einer statistischen Analyse klinischer Daten ermöglicht wird. Unter Verwendung eines kontrolltheoretischen Settings entwickeln wir eine Modellreduktionstechnik, indem wir vorerst einen neuartigen Typ von zeitlich begrenzten Kontrolllierbarkeits- und Beobachtbarkeitsgramian für nichtlineare Systeme definieren. Anschließend zeigen wir die Überlegenkeit der zeitlich begrenzten verallgemeinerten Gramian für nichtlineare Systeme im Kontext von Balanced Truncation am Beispiel eines Benchmark-Systems aus der Kontrolltheorie. Wir nutzten das Konzept der zeitlich begrenzten Kontrolllierbarkeits- und Beobachtbarkeitsgramian, um eine neue Zustands- und zeitabhängige Größe, die als Input-Response (IR-) Index bezeichnet wird, einzuführen. Dieser Index quantifiziert die Bedeutung von Zustandsvariablen zu einem bestimmten Zeitpunkt für eine bestimmte Eingabe-Ausgabe-Beziehung. Schließlich verknüpfen wir unseren Ansatz mit der Sensitivitätsanalyse und ermöglichen so erstmals die Verwendung von Sensitivitätskoeffizienten im Rahmen der Reduktion des Zustandsraumes. Wir erhalten die sensitivitätsbasierten IR-Indizes als Produkt zweier Sensitivitätskoeffizienten. Dies ermöglicht nicht nur eine effizientere Berechnung, sondern auch eine klare Unterscheidung, inwieweit die Eingabe eine Zustandsvariable beeinflusst und inwieweit eine Zustandsvariable die Ausgabe beeinflusst. Mit Hilfe der IR-Indizes erhalten wir einen Einblick in den koordinierten Ablauf der Aktivierung von spezifischen Zustandsvariablen für eine ausgewählte Eingabe-Ausgabe-Beziehung. Unser entwickeltes Modellreduktionsverfahren resultiert in reduzierten Modelle, welche eine mechanistische Interpretation hinsichtlich der Originalgrößen und Zustandsvariablen des Ursprungssystems zulassen. Dies war eine wichtige Anforderung an das Verfahren von Seiten der Systempharmakologie und -biologie. Die reduzierten Modelle unterscheiden sich damit wesentlich von den so genannten empirischen Wirkstoff-Effekt-Modellen. Die IR-Indizes sind explizit in Bezug auf eine Referenzlösung definiert und damit vom Anfangszustand abhängig (dies ist ein wichtiges Merkmal der Indizes). Wir zeigen anhand eines Beispiels aus dem Bereich der Systempharmakologie, dass die reduzierten Modelle sehr aussagekräftig sind, um (genetische) Mängel in bestimmten physiologischen Einheiten festzustellen. Der Vergleich unseres neuartigen Modellreduktionsverfahrens mit den bereits vorhandenen Verfahren zeigt dessen Überlegenheit. Der neuartige IR-Index als Maß für die Wichtigkeit von Zustandsvariablen bietet ein leistungsfähiges mathematisches Werkzeug zum Verständnis und der Analyse der komplexen Dynamik von großen Systemen im Kontext einer bestimmten Wirkstoff-Effekt-Beziehung. Darüber hinaus sind die Indizes eine wichtige Grundlage für das eingeführte und sehr effiziente Modellreduktionsverfahren. Insgesamt stellt dies einen wichtigen Schritt zur Nutzung von Erkenntnissen über biologische Prozesse in Form von detaillierten systempharmakologischen Modellen in der Populationsanalyse klinischer Daten dar. KW - model order reduction KW - control theory KW - large-scale mechanistic systems KW - systems pharmacology KW - Modellreduktion KW - Kontrolltheorie KW - komplexe mechanistische Systeme KW - Systempharmakologie Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-440598 ER - TY - THES A1 - Solms, Alexander Maximilian T1 - Integrating nonlinear mixed effects and physiologically–based modeling approaches for the analysis of repeated measurement studies T1 - Integration nicht-linearer gemischter Modelle und physiologie-basierte Modellierung Ansätze in die Auswertung longitudinaler Studien BT - with applications in quantitative pharmacology and quantitative psycholinguistics N2 - During the drug discovery & development process, several phases encompassing a number of preclinical and clinical studies have to be successfully passed to demonstrate safety and efficacy of a new drug candidate. As part of these studies, the characterization of the drug's pharmacokinetics (PK) is an important aspect, since the PK is assumed to strongly impact safety and efficacy. To this end, drug concentrations are measured repeatedly over time in a study population. The objectives of such studies are to describe the typical PK time-course and the associated variability between subjects. Furthermore, underlying sources significantly contributing to this variability, e.g. the use of comedication, should be identified. The most commonly used statistical framework to analyse repeated measurement data is the nonlinear mixed effect (NLME) approach. At the same time, ample knowledge about the drug's properties already exists and has been accumulating during the discovery & development process: Before any drug is tested in humans, detailed knowledge about the PK in different animal species has to be collected. This drug-specific knowledge and general knowledge about the species' physiology is exploited in mechanistic physiological based PK (PBPK) modeling approaches -it is, however, ignored in the classical NLME modeling approach. Mechanistic physiological based models aim to incorporate relevant and known physiological processes which contribute to the overlying process of interest. In comparison to data--driven models they are usually more complex from a mathematical perspective. For example, in many situations, the number of model parameters outrange the number of measurements and thus reliable parameter estimation becomes more complex and partly impossible. As a consequence, the integration of powerful mathematical estimation approaches like the NLME modeling approach -which is widely used in data-driven modeling -and the mechanistic modeling approach is not well established; the observed data is rather used as a confirming instead of a model informing and building input. Another aggravating circumstance of an integrated approach is the inaccessibility to the details of the NLME methodology so that these approaches can be adapted to the specifics and needs of mechanistic modeling. Despite the fact that the NLME modeling approach exists for several decades, details of the mathematical methodology is scattered around a wide range of literature and a comprehensive, rigorous derivation is lacking. Available literature usually only covers selected parts of the mathematical methodology. Sometimes, important steps are not described or are only heuristically motivated, e.g. the iterative algorithm to finally determine the parameter estimates. Thus, in the present thesis the mathematical methodology of NLME modeling is systemically described and complemented to a comprehensive description, comprising the common theme from ideas and motivation to the final parameter estimation. Therein, new insights for the interpretation of different approximation methods used in the context of the NLME modeling approach are given and illustrated; furthermore, similarities and differences between them are outlined. Based on these findings, an expectation-maximization (EM) algorithm to determine estimates of a NLME model is described. Using the EM algorithm and the lumping methodology by Pilari2010, a new approach on how PBPK and NLME modeling can be combined is presented and exemplified for the antibiotic levofloxacin. Therein, the lumping identifies which processes are informed by the available data and the respective model reduction improves the robustness in parameter estimation. Furthermore, it is shown how apriori known factors influencing the variability and apriori known unexplained variability is incorporated to further mechanistically drive the model development. Concludingly, correlation between parameters and between covariates is automatically accounted for due to the mechanistic derivation of the lumping and the covariate relationships. A useful feature of PBPK models compared to classical data-driven PK models is in the possibility to predict drug concentration within all organs and tissue in the body. Thus, the resulting PBPK model for levofloxacin is used to predict drug concentrations and their variability within soft tissues which are the site of action for levofloxacin. These predictions are compared with data of muscle and adipose tissue obtained by microdialysis, which is an invasive technique to measure a proportion of drug in the tissue, allowing to approximate the concentrations in the interstitial fluid of tissues. Because, so far, comparing human in vivo tissue PK and PBPK predictions are not established, a new conceptual framework is derived. The comparison of PBPK model predictions and microdialysis measurements shows an adequate agreement and reveals further strengths of the presented new approach. We demonstrated how mechanistic PBPK models, which are usually developed in the early stage of drug development, can be used as basis for model building in the analysis of later stages, i.e. in clinical studies. As a consequence, the extensively collected and accumulated knowledge about species and drug are utilized and updated with specific volunteer or patient data. The NLME approach combined with mechanistic modeling reveals new insights for the mechanistic model, for example identification and quantification of variability in mechanistic processes. This represents a further contribution to the learn & confirm paradigm across different stages of drug development. Finally, the applicability of mechanism--driven model development is demonstrated on an example from the field of Quantitative Psycholinguistics to analyse repeated eye movement data. Our approach gives new insight into the interpretation of these experiments and the processes behind. N2 - Für die Erforschung und Entwicklung eines neuen Arzneistoffes wird die sichere und wirksame Anwendung in präklinischen und klinischen Studien systematisch untersucht. Ein wichtiger Bestandteil dieser Studien ist die Bestimmung der Pharmakokinetik (PK), da über diese das Wirkungs- und Nebenwirkungsprofil maßgeblich mitbestimmt wird. Um die PK zu bestimmen wird in der Studienpopulation die Wirkstoffkonzentration im Blut wiederholt über die Zeit gemessen. Damit kann sowohl der Konzentrations-Zeit-Verlauf als auch die dazugehörige Variabilität in der Studienpopulation bestimmt werden. Darüber hinaus ist ein weiteres Ziel, die Ursachen dieser Variabilität zu identifizieren. Fär die Auswertung der Daten werden nichtlineare, gemischte Effektmodelle (NLME) eingesetzt. Im Vorfeld der klinischen Studien sind bereits viele Eigenschaften des Wirkstoffes bekannt, da der Wirkstoff-Testung am Menschen die Bestimmung der PK an verschiedenen Tierspezies voraus geht. Auf Basis dieser wirkstoffspezifischen Daten und des Wissens um die spezifische humane Physiologie können mittels mechanistisch physiologiebasierter Modelle Vorhersagen für die humane PK getroffen werden. Bei der Analyse von PK Daten mittels NLME Modellen wird dieses vorhandene Wissen jedoch nicht verwertet. In physiologiebasierten Modellen werden physiologische Prozesse, die die PK bestimmen und beeinflussen können, ber+cksichtigt. Aus mathematischer Sicht sind solche mechanistischen Modelle im Allgemeinen deutlich komplexer als empirisch motivierte Modelle. In der Anwendung kommt es deswegen häufig zu Situationen, in denen die Anzahl der Modellparameter die Anzahl der zugrunde liegenden Beobachtungen übertrifft. Daraus folgt unter anderem, dass die Parameterschätzung, wie sie in empirisch motivierten Modellen genutzt wird, in der Regel unzuverlässig bzw. nicht möglich ist. In Folge dessen werden klinische Daten in der mechanistischen Modellierung meist nur zur Modellqualifizierung genutzt und nicht in die Modell(weiter)entwicklung integriert. Ein weiterer erschwerender Umstand, NLME und PBPK Modelle in der Anwendung zu kombinieren, beruht auch auf der Komplexität des NLME Ansatzes. Obwohl diese Methode seit Jahrzehnten existiert, sind in der Literatur nur ausgewählte Teilstücke der zugrunde liegenden Mathematik beschrieben und hergeleitet; eine lückenlose Beschreibung fehlt. Aus diesem Grund werden in der vorliegenden Arbeit systematisch die Methodik und mathematischen Zusammenhänge des NLME Ansatzes, von der ursprüngliche Idee und Motivation bis zur Parameterschätzung beschrieben. In diesem Kontext werden neue Interpretationen der unterschiedlichen Methoden, die im Rahmen der NLME Modellierung verwendet werden, vorgestellt; zudem werden Gemeinsamkeiten und Unterschiede zwischen diesen herausgearbeitet. Mittels dieser Erkenntnisse wird ein Expectation-Maximization (EM) Algorithmus zur Parameterschätzung in einer NLME Analyse beschrieben. Mittels des neuen EM Algorithmus, kombiniert mit dem Lumping-Ansatz von Pilari und Huisinga (S. Pilari, W. Huisinga, JPKPD Vol. 37(4), 2010.) wird anhand des Antibiotikums Levofloxacin ein neuer konzeptioneller Ansatz entwickelt, der PBPK- und NLME-Modellierung zur Datenanalyse integriert. Die Lumping-Methode definiert hierbei, welche Prozesse von den verfügbaren Daten informiert werden, sie verbessert somit die Robustheit der Parameterschätzung. Weiterhin wird gezeigt, wie a-priori Wissen über Variabilität und Faktoren, die diese beeinflussen, sowie unerklärte Variabilität in das Modell integriert werden können. Ein elementarer Vorteil von PBPK Modellen gegenüber empirisch motivieren PK Modellen besteht in der Möglichkeit, Wirkstoffkonzentrationen innerhalb von Organen und Gewebe im Körper vorherzusagen. So kann das PBPK-Modell für Levofloxacin genutzt werden, um Wirkstoffkonzentrationen innerhalb der Gewebe vorherzusagen, in denen typischerweise Infektionen auftreten. Für Muskel- und Fettgewebe werden die PBPK-Vorhersagen mit Mikrodialyse Gewebemessungen verglichen. Die gute übereinstimmung von PBPK-Modell und Mikrodialyse stellt eine noch nicht vorhanden Validierung des PBPK-Gewebemodells im Menschen dar. In dieser Dissertation wird gezeigt, wie mechanistische PBPK Modelle, die in der Regel in der frühen Phase der Arzneimittelentwicklung entwickelt werden, erfolgreich zur Analyse von klinischen Studien eingesetzt werden können. Das bestehende Wissen über den neuen Wirkstoff wird somit gezielt genutzt und mit klinischen Daten von Probanden oder Patienten aktualisiert. Im Fall von Levofloxacin konnte Variabilität in mechanistischen Prozessen identifiziert und quantifiziert werden. Dieses Vorgehen liefert einen weiteren Beitrag zum learn & confirm Paradigma im Forschungs- und Entwicklungsprozess eines neuen Wirkstoffes. Abschließend wird anhand eines weiteren real world-Beispieles aus dem Bereich der quantitativen Psycholinguistik die Anwendbarkeit und der Nutzen des vorgestellten integrierten Ansatz aus mechanistischer und NLME Modellierung in der Analyse von Blickbewegungsdaten gezeigt. Mittels eines mechanistisch motivierten Modells wird die Komplexität des Experimentes und der Daten abgebildet, wodurch sich neue Interpretationsmöglichkeiten ergeben. KW - NLME KW - PBPK KW - EM KW - lumping KW - popPBPK KW - mechanistic modeling KW - population analysis KW - popPK KW - microdialysis KW - nicht-lineare gemischte Modelle (NLME) KW - physiologie-basierte Pharmacokinetic (PBPK) KW - EM KW - Lumping KW - popPBPK KW - popPK KW - mechanistische Modellierung KW - Populations Analyse KW - Microdialyse Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-397070 ER - TY - THES A1 - Gopalakrishnan, Sathej T1 - Mathematical modelling of host-disease-drug interactions in HIV disease T1 - Mathematische Modellierung von Pathogen-Wirkstoff-Wirt-Interaktionen im Kontext der HIV Erkrankung N2 - The human immunodeficiency virus (HIV) has resisted nearly three decades of efforts targeting a cure. Sustained suppression of the virus has remained a challenge, mainly due to the remarkable evolutionary adaptation that the virus exhibits by the accumulation of drug-resistant mutations in its genome. Current therapeutic strategies aim at achieving and maintaining a low viral burden and typically involve multiple drugs. The choice of optimal combinations of these drugs is crucial, particularly in the background of treatment failure having occurred previously with certain other drugs. An understanding of the dynamics of viral mutant genotypes aids in the assessment of treatment failure with a certain drug combination, and exploring potential salvage treatment regimens. Mathematical models of viral dynamics have proved invaluable in understanding the viral life cycle and the impact of antiretroviral drugs. However, such models typically use simplified and coarse-grained mutation schemes, that curbs the extent of their application to drug-specific clinical mutation data, in order to assess potential next-line therapies. Statistical models of mutation accumulation have served well in dissecting mechanisms of resistance evolution by reconstructing mutation pathways under different drug-environments. While these models perform well in predicting treatment outcomes by statistical learning, they do not incorporate drug effect mechanistically. Additionally, due to an inherent lack of temporal features in such models, they are less informative on aspects such as predicting mutational abundance at treatment failure. This limits their application in analyzing the pharmacology of antiretroviral drugs, in particular, time-dependent characteristics of HIV therapy such as pharmacokinetics and pharmacodynamics, and also in understanding the impact of drug efficacy on mutation dynamics. In this thesis, we develop an integrated model of in vivo viral dynamics incorporating drug-specific mutation schemes learned from clinical data. Our combined modelling approach enables us to study the dynamics of different mutant genotypes and assess mutational abundance at virological failure. As an application of our model, we estimate in vivo fitness characteristics of viral mutants under different drug environments. Our approach also extends naturally to multiple-drug therapies. Further, we demonstrate the versatility of our model by showing how it can be modified to incorporate recently elucidated mechanisms of drug action including molecules that target host factors. Additionally, we address another important aspect in the clinical management of HIV disease, namely drug pharmacokinetics. It is clear that time-dependent changes in in vivo drug concentration could have an impact on the antiviral effect, and also influence decisions on dosing intervals. We present a framework that provides an integrated understanding of key characteristics of multiple-dosing regimens including drug accumulation ratios and half-lifes, and then explore the impact of drug pharmacokinetics on viral suppression. Finally, parameter identifiability in such nonlinear models of viral dynamics is always a concern, and we investigate techniques that alleviate this issue in our setting. N2 - Das Humane Immundefiecienz-Virus (HIV) widerstanden hat fast drei Jahrzehnten eff Orts targeting eine Heilung. Eine anhaltende Unterdrückung des Virus hat noch eine Herausforderung, vor allem aufgrund der bemerkenswerten evolutionären Anpassung, dass das Virus Exponate durch die Ansammlung von Medikamenten-resistenten Mutationen in seinem Genom. Aktuelle therapeutische Strategien zielen auf das Erreichen und die Erhaltung einer niedrigen virale Belastung und umfassen in der Regel mehrere Medikamente. Die Wahl der optimalen Kombinationen dieser Medikamente ist von entscheidender Bedeutung, besonders im Hintergrund der Behandlung Fehler eingetreten, die zuvor mit bestimmten anderen Medikamenten. Ein Verständnis für die Dynamik der viralen mutierten Genotypen Aids in die Bewertung der Behandlung Fehler mit einer bestimmten Kombination und der Erkundung potenzieller Bergung Behandlungsschemata. Mathematische Modelle für virale Dynamik haben sich als unschätzbar erwiesen hat im Verständnis der viralen Lebenszyklus und die Auswirkungen von antiretroviralen Medikamenten. Allerdings sind solche Modelle verwenden in der Regel simplified und grobkörnigen Mutation Regelungen, dass Aufkantungen den Umfang ihrer Anwendung auf Arzneimittel-ganz speziellec Mutation klinische Daten, um zu beurteilen, mögliche nächste-line Therapien. Statistische Modelle der Mutation Anhäufung gedient haben gut in präparieren Mechanismen der Resistenz Evolution durch Mutation Rekonstruktion Pathways unter verschiedenen Medikamenten-Umgebungen. Während diese Modelle führen gut in der Vorhersage der Ergebnisse der Behandlung durch statistische lernen, sie enthalten keine Droge E ffect mechanistisch. Darüber hinaus aufgrund einer innewohnenden Mangel an zeitlichen Funktionen in solchen Modellen, sie sind weniger informativ auf Aspekte wie die Vorhersage mutational Fülle an Versagen der Behandlung. Dies schränkt die Anwendung in der Analyse der Pharmakologie von antiretroviralen Medikamenten, insbesondere, Zeit-abhängige Merkmale der HIV-Therapie wie Pharmakokinetik und Pharmakodynamik, und auch in dem Verständnis der Auswirkungen von Drogen e fficacy auf Mutation Dynamik. In dieser Arbeit, die wir bei der Entwicklung eines integrierten Modells von In-vivo-virale Dynamik Einbeziehung drug-ganz speziellec Mutation Systeme gelernt aus den klinischen Daten. Unsere kombinierten Modellansatz ermöglicht uns die Untersuchung der Dynamik von diff schiedene mutierten Genotypen und bewerten mutational Fülle an virologischem Versagen. Als Anwendung unseres Modells schätzen wir In-vivo-fitness Merkmale der viralen Mutanten unter di fferent drug Umgebungen. Unser Ansatz erstreckt sich auch natürlich auf mehrere-Therapien. Weitere zeigen wir die Vielseitigkeit unseres Modells zeigen, wie es können Modified zu integrieren kürzlich aufgeklärt Mechanismen der Drug Action einschließlich Molekülen, dass target host Faktoren. Zusätzlich haben wir Adresse ein weiterer wichtiger Aspekt in der klinischen Management der HIV-Erkrankung, das heißt Drogen Pharmakokinetik. Es ist klar, dass die Zeit-abhängige Änderungen in In-vivo-Wirkstoffkonzentration könnten die Auswirkungen auf die antivirale E ffect und haben auch Einfluss auf die Entscheidungen über Dosierungsintervalle. Wir präsentieren ein Framework, bietet ein integriertes Verständnis der wichtigsten Merkmale von mehreren Dosierungsschemata einschließlich Kumulation Übersetzungen und Halbwertszeiten, und untersuchen Sie die Auswirkungen von Drogen auf die Pharmakokinetik Virussuppression. Schließlich, Parameter identifiFähigkeit in solchen nichtlineare Modelle der virale Dynamik ist immer ein Anliegen, und wir untersuchen Methoden, um dieses Problem in unserer Einstellung. KW - HIV KW - mathematical modelling KW - viral fitness KW - pharmacokinetics KW - parameter estimation KW - HIV Erkrankung KW - Pharmakokinetik KW - Fitness KW - mathematische Modellierung KW - Kombinationstherapie Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-100100 ER - TY - JOUR A1 - Stachanow, Viktoria A1 - Neumann, Uta A1 - Blankenstein, Oliver A1 - Bindellini, Davide A1 - Melin, Johanna A1 - Ross, Richard A1 - Whitaker, Martin J. J. A1 - Huisinga, Wilhelm A1 - Michelet, Robin A1 - Kloft, Charlotte T1 - Exploring dried blood spot cortisol concentrations as an alternative for monitoring pediatric adrenal insufficiency patients BT - a model-based analysis JF - Frontiers in pharmacology N2 - Congenital adrenal hyperplasia (CAH) is the most common form of adrenal insufficiency in childhood; it requires cortisol replacement therapy with hydrocortisone (HC, synthetic cortisol) from birth and therapy monitoring for successful treatment. In children, the less invasive dried blood spot (DBS) sampling with whole blood including red blood cells (RBCs) provides an advantageous alternative to plasma sampling. Potential differences in binding/association processes between plasma and DBS however need to be considered to correctly interpret DBS measurements for therapy monitoring. While capillary DBS samples would be used in clinical practice, venous cortisol DBS samples from children with adrenal insufficiency were analyzed due to data availability and to directly compare and thus understand potential differences between venous DBS and plasma. A previously published HC plasma pharmacokinetic (PK) model was extended by leveraging these DBS concentrations. In addition to previously characterized binding of cortisol to albumin (linear process) and corticosteroid-binding globulin (CBG; saturable process), DBS data enabled the characterization of a linear cortisol association with RBCs, and thereby providing a quantitative link between DBS and plasma cortisol concentrations. The ratio between the observed cortisol plasma and DBS concentrations varies highly from 2 to 8. Deterministic simulations of the different cortisol binding/association fractions demonstrated that with higher blood cortisol concentrations, saturation of cortisol binding to CBG was observed, leading to an increase in all other cortisol binding fractions. In conclusion, a mathematical PK model was developed which links DBS measurements to plasma exposure and thus allows for quantitative interpretation of measurements of DBS samples. KW - adrenal insufficiency KW - cortisol KW - dried blood spots KW - pediatrics KW - pharmacokinetics KW - binding KW - association KW - red blood cells Y1 - 2022 U6 - https://doi.org/10.3389/fphar.2022.819590 SN - 1663-9812 VL - 13 PB - Frontiers Media CY - Lausanne ER - TY - THES A1 - Schindler, Daniel T1 - Mathematical modeling and simulation of protrusion-driven cell dynamics T1 - Mathematische Modellierung und Simulation von amöboiden Zelldynamiken N2 - Amoeboid cell motility takes place in a variety of biomedical processes such as cancer metastasis, embryonic morphogenesis, and wound healing. In contrast to other forms of cell motility, it is mainly driven by substantial cell shape changes. Based on the interplay of explorative membrane protrusions at the front and a slower-acting membrane retraction at the rear, the cell moves in a crawling kind of way. Underlying these protrusions and retractions are multiple physiological processes resulting in changes of the cytoskeleton, a meshwork of different multi-functional proteins. The complexity and versatility of amoeboid cell motility raise the need for novel computational models based on a profound theoretical framework to analyze and simulate the dynamics of the cell shape. The objective of this thesis is the development of (i) a mathematical framework to describe contour dynamics in time and space, (ii) a computational model to infer expansion and retraction characteristics of individual cell tracks and to produce realistic contour dynamics, (iii) and a complementing Open Science approach to make the above methods fully accessible and easy to use. In this work, we mainly used single-cell recordings of the model organism Dictyostelium discoideum. Based on stacks of segmented microscopy images, we apply a Bayesian approach to obtain smooth representations of the cell membrane, so-called cell contours. We introduce a one-parameter family of regularized contour flows to track reference points on the contour (virtual markers) in time and space. This way, we define a coordinate system to visualize local geometric and dynamic quantities of individual contour dynamics in so-called kymograph plots. In particular, we introduce the local marker dispersion as a measure to identify membrane protrusions and retractions in a fully automated way. This mathematical framework is the basis of a novel contour dynamics model, which consists of three biophysiologically motivated components: one stochastic term, accounting for membrane protrusions, and two deterministic terms to control the shape and area of the contour, which account for membrane retractions. Our model provides a fully automated approach to infer protrusion and retraction characteristics from experimental cell tracks while being also capable of simulating realistic and qualitatively different contour dynamics. Furthermore, the model is used to classify two different locomotion types: the amoeboid and a so-called fan-shaped type. With the complementing Open Science approach, we ensure a high standard regarding the usability of our methods and the reproducibility of our research. In this context, we introduce our software publication named AmoePy, an open-source Python package to segment, analyze, and simulate amoeboid cell motility. Furthermore, we describe measures to improve its usability and extensibility, e.g., by detailed run instructions and an automatically generated source code documentation, and to ensure its functionality and stability, e.g., by automatic software tests, data validation, and a hierarchical package structure. The mathematical approaches of this work provide substantial improvements regarding the modeling and analysis of amoeboid cell motility. We deem the above methods, due to their generalized nature, to be of greater value for other scientific applications, e.g., varying organisms and experimental setups or the transition from unicellular to multicellular movement. Furthermore, we enable other researchers from different fields, i.e., mathematics, biophysics, and medicine, to apply our mathematical methods. By following Open Science standards, this work is of greater value for the cell migration community and a potential role model for other Open Science contributions. N2 - Amöboide Zellmotilität findet bei einer Vielzahl biomedizinischer Prozesse wie Krebsmetastasierung, embryonaler Morphogenese und Wundheilung statt. Im Gegensatz zu anderen Formen der Zellmotilität wird sie hauptsächlich durch erhebliche Formveränderungen der Zelle angetrieben. Sie beruht auf dem Zusammenspiel von explorativen Membranausstülpungen an der Vorderseite und einem langsamer wirkenden Membraneinzug an der Rückseite. Die Komplexität amöboider Zellmotilität machen neue Berechnungsmodelle erforderlich, um die Dynamik der Zellform mathematisch fundiert zu analysieren und zu simulieren. Ziel dieser Arbeit ist die Entwicklung (i) eines mathematischen Frameworks zur Beschreibung der Konturendynamik in Zeit und Raum, (ii) eines Computermodells, um Eigenschaften der Membranveränderungen von einzelnen Zellen zu inferieren und gleichzeitig realistische Konturdynamiken zu simulieren, (iii) und eines ergänzenden Open-Science-Ansatzes, um die oben genannten Methoden vollständig zugänglich und leicht anwendbar zu machen. Auf der Grundlage von aufeinander folgenden Mikroskopiebildern vom Modellorganismus Dictyostelium discoideum, wenden wir einen Bayesschen Ansatz an, um glatte Darstellungen der Zellmembran, sogenannte Zellkonturen, zu erhalten. Wir führen eine einparametrige Familie von regularisierten Konturflüssen ein, um Referenzpunkte auf der Kontur (virtuelle Marker) in Zeit und Raum zu verfolgen. Auf diese Weise definieren wir ein Koordinatensystem zur Visualisierung lokaler geometrischer und dynamischer Größen der individuellen Konturdynamiken in sogenannten Kymographen-Plots. Insbesondere führen wir die lokale Marker-Dispersion ein, mit der signifikante Membranveränderungen identifiziert werden können. Dieses mathematische Framework bildet die Grundlage für unser neues Modell zur Beschreibung von Konturendynamiken. Es besteht aus drei biophysiologisch motivierten Komponenten: einem stochastischen Term, der die Membranausstülpungen steuert, und zwei deterministischen Termen, die das Membraneinziehen, unter Berücksichtigung der Konturform und -fläche, steuern. Unser Modell bietet einen vollautomatisierten Ansatz zur Inferrenz der Charakteristiken von Membranveränderungen für experimentelle Zelldaten. Außerdem ermöglicht es die Simulation von realistischen und qualitativ unterschiedlichen Konturendynamiken. Mit dem ergänzenden Open-Science-Ansatz setzen wir einen hohen Standard hinsichtlich der Nutzbarkeit unserer Methoden und der Reproduzierbarkeit unserer Forschung. In diesem Kontext stellen wir die Softwarepublikation AmoePy vor, ein Open-Source-Pythonpaket zur Segmentierung, Analyse und Simulation von amöboider Zellmotilität. Darüber hinaus beschreiben wir Maßnahmen zur Verbesserung der Benutzerfreundlichkeit und Erweiterbarkeit, z. B. durch detaillierte Ausführanweisungen und eine automatisch generierte Quellcodedokumentation, und zur Gewährleistung der Funktionalität und Stabilität, z. B. durch automatische Softwaretests, Datenvalidierung und eine hierarchische Paketstruktur. Die mathematischen Methoden dieser Arbeit stellen wesentliche Verbesserungen in der Modellierung und Analyse der amöboiden Zellmotilität dar. Wir sind der Ansicht, dass die oben genannten Methoden aufgrund ihrer Verallgemeinerbarkeit von größerem Wert für andere wissenschaftliche Anwendungen sind und potentiell einsetzbar in verschiedenen Wissenschaftsfeldern sind, u. a. Mathematik, Biophysik und Medizin. Durch die Einhaltung von Open-Science-Standards ist diese Arbeit von größerem Wert und ein potenzielles Vorbild für andere Open-Science-Beiträge. KW - amöboide Bewegung KW - Zellmotilität KW - mathematische Modellierung KW - offene Wissenschaft KW - amoeboid motion KW - cell motility KW - mathematical modeling KW - open science Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-613275 ER - TY - JOUR A1 - Hijazi, Saddam A1 - Freitag, Melina A. A1 - Landwehr, Niels T1 - POD-Galerkin reduced order models and physics-informed neural networks for solving inverse problems for the Navier-Stokes equations JF - Advanced modeling and simulation in engineering sciences : AMSES N2 - We present a Reduced Order Model (ROM) which exploits recent developments in Physics Informed Neural Networks (PINNs) for solving inverse problems for the Navier-Stokes equations (NSE). In the proposed approach, the presence of simulated data for the fluid dynamics fields is assumed. A POD-Galerkin ROM is then constructed by applying POD on the snapshots matrices of the fluid fields and performing a Galerkin projection of the NSE (or the modified equations in case of turbulence modeling) onto the POD reduced basis. A POD-Galerkin PINN ROM is then derived by introducing deep neural networks which approximate the reduced outputs with the input being time and/or parameters of the model. The neural networks incorporate the physical equations (the POD-Galerkin reduced equations) into their structure as part of the loss function. Using this approach, the reduced model is able to approximate unknown parameters such as physical constants or the boundary conditions. A demonstration of the applicability of the proposed ROM is illustrated by three cases which are the steady flow around a backward step, the flow around a circular cylinder and the unsteady turbulent flow around a surface mounted cubic obstacle. KW - Proper orthogonal decomposition KW - Inverse problems KW - Physics-based machine learning KW - Navier-Stokes equations Y1 - 2023 U6 - https://doi.org/10.1186/s40323-023-00242-2 SN - 2213-7467 VL - 10 IS - 1 PB - SpringerOpen CY - Berlin ER - TY - JOUR A1 - Molkenthin, Christian A1 - Donner, Christian A1 - Reich, Sebastian A1 - Zöller, Gert A1 - Hainzl, Sebastian A1 - Holschneider, Matthias A1 - Opper, Manfred T1 - GP-ETAS: semiparametric Bayesian inference for the spatio-temporal epidemic type aftershock sequence model JF - Statistics and Computing N2 - The spatio-temporal epidemic type aftershock sequence (ETAS) model is widely used to describe the self-exciting nature of earthquake occurrences. While traditional inference methods provide only point estimates of the model parameters, we aim at a fully Bayesian treatment of model inference, allowing naturally to incorporate prior knowledge and uncertainty quantification of the resulting estimates. Therefore, we introduce a highly flexible, non-parametric representation for the spatially varying ETAS background intensity through a Gaussian process (GP) prior. Combined with classical triggering functions this results in a new model formulation, namely the GP-ETAS model. We enable tractable and efficient Gibbs sampling by deriving an augmented form of the GP-ETAS inference problem. This novel sampling approach allows us to assess the posterior model variables conditioned on observed earthquake catalogues, i.e., the spatial background intensity and the parameters of the triggering function. Empirical results on two synthetic data sets indicate that GP-ETAS outperforms standard models and thus demonstrate the predictive power for observed earthquake catalogues including uncertainty quantification for the estimated parameters. Finally, a case study for the l'Aquila region, Italy, with the devastating event on 6 April 2009, is presented. KW - Self-exciting point process KW - Hawkes process KW - Spatio-temporal ETAS model KW - Bayesian inference KW - Sampling KW - Earthquake modeling KW - Gaussian process KW - Data augmentation Y1 - 2022 U6 - https://doi.org/10.1007/s11222-022-10085-3 SN - 0960-3174 SN - 1573-1375 VL - 32 IS - 2 PB - Springer CY - Dordrecht ER - TY - JOUR A1 - Kucharski, Maciej A1 - Ergintav, Arzu A1 - Ahmad, Wael Abdullah A1 - Krstić, Miloš A1 - Ng, Herman Jalli A1 - Kissinger, Dietmar T1 - A Scalable 79-GHz Radar Platform Based on Single-Channel Transceivers JF - IEEE Transactions on Microwave Theory and Techniques N2 - This paper presents a scalable E-band radar platform based on single-channel fully integrated transceivers (TRX) manufactured using 130-nm silicon-germanium (SiGe) BiCMOS technology. The TRX is suitable for flexible radar systems exploiting massive multiple-input-multipleoutput (MIMO) techniques for multidimensional sensing. A fully integrated fractional-N phase-locked loop (PLL) comprising a 39.5-GHz voltage-controlled oscillator is used to generate wideband frequency-modulated continuous-wave (FMCW) chirp for E-band radar front ends. The TRX is equipped with a vector modulator (VM) for high-speed carrier modulation and beam-forming techniques. A single TRX achieves 19.2-dBm maximum output power and 27.5-dB total conversion gain with input-referred 1-dB compression point of -10 dBm. It consumes 220 mA from 3.3-V supply and occupies 3.96 mm(2) silicon area. A two-channel radar platform based on full-custom TRXs and PLL was fabricated to demonstrate high-precision and high-resolution FMCW sensing. The radar enables up to 10-GHz frequency ramp generation in 74-84-GHz range, which results in 1.5-cm spatial resolution. Due to high output power, thus high signal-to-noise ratio (SNR), a ranging precision of 7.5 mu m for a target at 2 m was achieved. The proposed architecture supports scalable multichannel applications for automotive FMCW using a single local oscillator (LO). KW - Automotive KW - E-band KW - frequency-modulated continuous-wave (FMCW) KW - patch antenna KW - phase-locked loop (PLL) KW - power amplifier (PA) KW - radar KW - scalable KW - transceiver (TRX) Y1 - 2019 U6 - https://doi.org/10.1109/TMTT.2019.2914104 SN - 0018-9480 SN - 1557-9670 VL - 67 IS - 9 SP - 3882 EP - 3896 PB - Inst. of Electr. and Electronics Engineers CY - Piscataway ER - TY - JOUR A1 - Sharma, Shubham A1 - Hainzl, Sebastian A1 - Zöller, Gert A1 - Holschneider, Matthias T1 - Is Coulomb stress the best choice for aftershock forecasting? JF - Journal of geophysical research : Solid earth N2 - The Coulomb failure stress (CFS) criterion is the most commonly used method for predicting spatial distributions of aftershocks following large earthquakes. However, large uncertainties are always associated with the calculation of Coulomb stress change. The uncertainties mainly arise due to nonunique slip inversions and unknown receiver faults; especially for the latter, results are highly dependent on the choice of the assumed receiver mechanism. Based on binary tests (aftershocks yes/no), recent studies suggest that alternative stress quantities, a distance-slip probabilistic model as well as deep neural network (DNN) approaches, all are superior to CFS with predefined receiver mechanism. To challenge this conclusion, which might have large implications, we use 289 slip inversions from SRCMOD database to calculate more realistic CFS values for a layered half-space and variable receiver mechanisms. We also analyze the effect of the magnitude cutoff, grid size variation, and aftershock duration to verify the use of receiver operating characteristic (ROC) analysis for the ranking of stress metrics. The observations suggest that introducing a layered half-space does not improve the stress maps and ROC curves. However, results significantly improve for larger aftershocks and shorter time periods but without changing the ranking. We also go beyond binary testing and apply alternative statistics to test the ability to estimate aftershock numbers, which confirm that simple stress metrics perform better than the classic Coulomb failure stress calculations and are also better than the distance-slip probabilistic model. Y1 - 2020 U6 - https://doi.org/10.1029/2020JB019553 SN - 2169-9313 SN - 2169-9356 VL - 125 IS - 9 PB - American Geophysical Union CY - Washington ER - TY - JOUR A1 - Engbert, Ralf A1 - Rabe, Maximilian Michael A1 - Kliegl, Reinhold A1 - Reich, Sebastian T1 - Sequential data assimilation of the stochastic SEIR epidemic model for regional COVID-19 dynamics JF - Bulletin of mathematical biology : official journal of the Society for Mathematical Biology N2 - Newly emerging pandemics like COVID-19 call for predictive models to implement precisely tuned responses to limit their deep impact on society. Standard epidemic models provide a theoretically well-founded dynamical description of disease incidence. For COVID-19 with infectiousness peaking before and at symptom onset, the SEIR model explains the hidden build-up of exposed individuals which creates challenges for containment strategies. However, spatial heterogeneity raises questions about the adequacy of modeling epidemic outbreaks on the level of a whole country. Here, we show that by applying sequential data assimilation to the stochastic SEIR epidemic model, we can capture the dynamic behavior of outbreaks on a regional level. Regional modeling, with relatively low numbers of infected and demographic noise, accounts for both spatial heterogeneity and stochasticity. Based on adapted models, short-term predictions can be achieved. Thus, with the help of these sequential data assimilation methods, more realistic epidemic models are within reach. KW - Stochastic epidemic model KW - Sequential data assimilation KW - Ensemble Kalman KW - filter KW - COVID-19 Y1 - 2020 U6 - https://doi.org/10.1007/s11538-020-00834-8 SN - 0092-8240 SN - 1522-9602 VL - 83 IS - 1 PB - Springer CY - New York ER -