TY - JOUR A1 - Saynisch-Wagner, Jan A1 - Bärenzung, Julien A1 - Hornschild, Aaron A1 - Irrgang, Christopher A1 - Thomas, Maik T1 - Tide-induced magnetic signals and their errors derived from CHAMP and Swarm satellite magnetometer observations JF - Earth, planets and space : EPS N2 - Satellite-measured tidal magnetic signals are of growing importance. These fields are mainly used to infer Earth's mantle conductivity, but also to derive changes in the oceanic heat content. We present a new Kalman filter-based method to derive tidal magnetic fields from satellite magnetometers: KALMAG. The method's advantage is that it allows to study a precisely estimated posterior error covariance matrix. We present the results of a simultaneous estimation of the magnetic signals of 8 major tides from 17 years of Swarm and CHAMP data. For the first time, robustly derived posterior error distributions are reported along with the reported tidal magnetic fields. The results are compared to other estimates that are either based on numerical forward models or on satellite inversions of the same data. For all comparisons, maximal differences and the corresponding globally averaged RMSE are reported. We found that the inter-product differences are comparable with the KALMAG-based errors only in a global mean sense. Here, all approaches give values of the same order, e.g., 0.09 nT-0.14 nT for M2. Locally, the KALMAG posterior errors are up to one order smaller than the inter-product differences, e.g., 0.12 nT vs. 0.96 nT for M2. KW - Tides KW - Electromagnetic induction KW - Error covariance KW - Satellite magnetometer observations Y1 - 2021 U6 - https://doi.org/10.1186/s40623-021-01557-3 SN - 1880-5981 VL - 73 IS - 1 PB - Springer CY - Heidelberg ER - TY - JOUR A1 - Rodríguez Zuluaga, Juan A1 - Stolle, Claudia A1 - Yamazaki, Yosuke A1 - Xiong, Chao A1 - England, Scott L. T1 - A synoptic-scale wavelike structure in the nighttime equatorial ionization anomaly JF - Earth and Space Science : ESS N2 - Both ground- and satellite-based airglow imaging have significantly contributed to understanding the low-latitude ionosphere, especially the morphology and dynamics of the equatorial ionization anomaly (EIA). The NASA Global-scale Observations of the Limb and Disk (GOLD) mission focuses on far-ultraviolet airglow images from a geostationary orbit at 47.5 degrees W. This region is of particular interest at low magnetic latitudes because of the high magnetic declination (i.e., about -20 degrees) and proximity of the South Atlantic magnetic anomaly. In this study, we characterize an exciting feature of the nighttime EIA using GOLD observations from October 5, 2018 to June 30, 2020. It consists of a wavelike structure of a few thousand kilometers seen as poleward and equatorward displacements of the EIA-crests. Initial analyses show that the synoptic-scale structure is symmetric about the dip equator and appears nearly stationary with time over the night. In quasi-dipole coordinates, maxima poleward displacements of the EIA-crests are seen at about +/- 12 degrees latitude and around 20 and 60 degrees longitude (i.e., in geographic longitude at the dip equator, about 53 degrees W and 14 degrees W). The wavelike structure presents typical zonal wavelengths of about 6.7 x 10(3) km and 3.3 x 10(3) km. The structure's occurrence and wavelength are highly variable on a day-to-day basis with no apparent dependence on geomagnetic activity. In addition, a cluster or quasi-periodic wave train of equatorial plasma depletions (EPDs) is often detected within the synoptic-scale structure. We further outline the difference in observing these EPDs from FUV images and in situ measurements during a GOLD and Swarm mission conjunction. KW - equatorial ionization anomaly KW - equatorial ionosphere KW - equatorial plasma bubbles KW - wave structure KW - forcing from below Y1 - 2021 U6 - https://doi.org/10.1029/2020EA001529 SN - 2333-5084 VL - 8 IS - 2 PB - American Geophysical Union CY - Malden, Mass. ER - TY - JOUR A1 - Schindler, Daniel A1 - Moldenhawer, Ted A1 - Stange, Maike A1 - Lepro, Valentino A1 - Beta, Carsten A1 - Holschneider, Matthias A1 - Huisinga, Wilhelm T1 - Analysis of protrusion dynamics in amoeboid cell motility by means of regularized contour flows JF - PLoS Computational Biology : a new community journal N2 - Amoeboid cell motility is essential for a wide range of biological processes including wound healing, embryonic morphogenesis, and cancer metastasis. It relies on complex dynamical patterns of cell shape changes that pose long-standing challenges to mathematical modeling and raise a need for automated and reproducible approaches to extract quantitative morphological features from image sequences. Here, we introduce a theoretical framework and a computational method for obtaining smooth representations of the spatiotemporal contour dynamics from stacks of segmented microscopy images. Based on a Gaussian process regression we propose a one-parameter family of regularized contour flows that allows us to continuously track reference points (virtual markers) between successive cell contours. We use this approach to define a coordinate system on the moving cell boundary and to represent different local geometric quantities in this frame of reference. In particular, we introduce the local marker dispersion as a measure to identify localized membrane expansions and provide a fully automated way to extract the properties of such expansions, including their area and growth time. The methods are available as an open-source software package called AmoePy, a Python-based toolbox for analyzing amoeboid cell motility (based on time-lapse microscopy data), including a graphical user interface and detailed documentation. Due to the mathematical rigor of our framework, we envision it to be of use for the development of novel cell motility models. We mainly use experimental data of the social amoeba Dictyostelium discoideum to illustrate and validate our approach.
Author summary Amoeboid motion is a crawling-like cell migration that plays an important key role in multiple biological processes such as wound healing and cancer metastasis. This type of cell motility results from expanding and simultaneously contracting parts of the cell membrane. From fluorescence images, we obtain a sequence of points, representing the cell membrane, for each time step. By using regression analysis on these sequences, we derive smooth representations, so-called contours, of the membrane. Since the number of measurements is discrete and often limited, the question is raised of how to link consecutive contours with each other. In this work, we present a novel mathematical framework in which these links are described by regularized flows allowing a certain degree of concentration or stretching of neighboring reference points on the same contour. This stretching rate, the so-called local dispersion, is used to identify expansions and contractions of the cell membrane providing a fully automated way of extracting properties of these cell shape changes. We applied our methods to time-lapse microscopy data of the social amoeba Dictyostelium discoideum. Y1 - 2021 U6 - https://doi.org/10.1371/journal.pcbi.1009268 SN - 1553-734X SN - 1553-7358 VL - 17 IS - 8 PB - PLoS CY - San Fransisco ER - TY - JOUR A1 - Hartung, Niklas A1 - Wahl, Martin A1 - Rastogi, Abhishake A1 - Huisinga, Wilhelm T1 - Nonparametric goodness-of-fit testing for parametric covariate models in pharmacometric analyses JF - CPT: pharmacometrics & systems pharmacology N2 - The characterization of covariate effects on model parameters is a crucial step during pharmacokinetic/pharmacodynamic analyses. Although covariate selection criteria have been studied extensively, the choice of the functional relationship between covariates and parameters, however, has received much less attention. Often, a simple particular class of covariate-to-parameter relationships (linear, exponential, etc.) is chosen ad hoc or based on domain knowledge, and a statistical evaluation is limited to the comparison of a small number of such classes. Goodness-of-fit testing against a nonparametric alternative provides a more rigorous approach to covariate model evaluation, but no such test has been proposed so far. In this manuscript, we derive and evaluate nonparametric goodness-of-fit tests for parametric covariate models, the null hypothesis, against a kernelized Tikhonov regularized alternative, transferring concepts from statistical learning to the pharmacological setting. The approach is evaluated in a simulation study on the estimation of the age-dependent maturation effect on the clearance of a monoclonal antibody. Scenarios of varying data sparsity and residual error are considered. The goodness-of-fit test correctly identified misspecified parametric models with high power for relevant scenarios. The case study provides proof-of-concept of the feasibility of the proposed approach, which is envisioned to be beneficial for applications that lack well-founded covariate models. Y1 - 2021 U6 - https://doi.org/10.1002/psp4.12614 SN - 2163-8306 VL - 10 IS - 6 SP - 564 EP - 576 PB - Nature Publ. Group CY - London ER - TY - JOUR A1 - Hethey, Christoph Philipp A1 - Hartung, Niklas A1 - Wangorsch, Gaby A1 - Weisser, Karin A1 - Huisinga, Wilhelm T1 - Physiology-based toxicokinetic modelling of aluminium in rat and man JF - Archives of toxicology : official journal of EUROTOX N2 - A sufficient quantitative understanding of aluminium (Al) toxicokinetics (TK) in man is still lacking, although highly desirable for risk assessment of Al exposure. Baseline exposure and the risk of contamination severely limit the feasibility of TK studies administering the naturally occurring isotope Al-27, both in animals and man. These limitations are absent in studies with Al-26 as a tracer, but tissue data are limited to animal studies. A TK model capable of inter-species translation to make valid predictions of Al levels in humans-especially in toxicological relevant tissues like bone and brain-is urgently needed. Here, we present: (i) a curated dataset which comprises all eligible studies with single doses of Al-26 tracer administered as citrate or chloride salts orally and/or intravenously to rats and humans, including ultra-long-term kinetic profiles for plasma, blood, liver, spleen, muscle, bone, brain, kidney, and urine up to 150 weeks; and (ii) the development of a physiology-based (PB) model for Al TK after intravenous and oral administration of aqueous Al citrate and Al chloride solutions in rats and humans. Based on the comprehensive curated Al-26 dataset, we estimated substance-dependent parameters within a non-linear mixed-effect modelling context. The model fitted the heterogeneous Al-26 data very well and was successfully validated against datasets in rats and humans. The presented PBTK model for Al, based on the most extensive and diverse dataset of Al exposure to date, constitutes a major advancement in the field, thereby paving the way towards a more quantitative risk assessment in humans. KW - PBTK KW - Toxicokinetics KW - Al-26 KW - Aluminium Y1 - 2021 U6 - https://doi.org/10.1007/s00204-021-03107-y SN - 0340-5761 SN - 1432-0738 VL - 95 IS - 9 SP - 2977 EP - 3000 PB - Springer CY - Berlin ; Heidelberg ER - TY - THES A1 - Perera, Upeksha T1 - Solutions of direct and inverse Sturm–Liouville problems T1 - Lösungen von direkten und inversen Sturm-Liouville-Problemen N2 - Lie group method in combination with Magnus expansion is utilized to develop a universal method applicable to solving a Sturm–Liouville Problem (SLP) of any order with arbitrary boundary conditions. It is shown that the method has ability to solve direct regular and some singular SLPs of even orders (tested up to order eight), with a mix of boundary conditions (including non-separable and finite singular endpoints), accurately and efficiently. The present technique is successfully applied to overcome the difficulties in finding suitable sets of eigenvalues so that the inverse SLP problem can be effectively solved. Next, a concrete implementation to the inverse Sturm–Liouville problem algorithm proposed by Barcilon (1974) is provided. Furthermore, computational feasibility and applicability of this algorithm to solve inverse Sturm–Liouville problems of order n=2,4 is verified successfully. It is observed that the method is successful even in the presence of significant noise, provided that the assumptions of the algorithm are satisfied. In conclusion, this work provides methods that can be adapted successfully for solving a direct (regular/singular) or inverse SLP of an arbitrary order with arbitrary boundary conditions. N2 - Die Lie-Gruppen-Methode in Kombination mit der Magnus-Expansion wird verwendet, um eine universelle Methode zu entwickeln, die zur Lösung eines Sturm-Liouville-Problems (SLP) beliebiger Ordnung mit beliebigen Randbedingungen anwendbar ist. Es wird gezeigt, dass die Methode in der Lage ist, direkte reguläre und einige singuläre SLPs gerader Ordnung (getestet bis zur 8. Ordnung) mit einer Mischung von Randbedingungen (einschließlich nicht trennbarer und endlicher singulärer Endpunkte) genau und effizient zu lösen. Die vorliegende Technik wird erfolgreich angewendet, um die Schwierigkeiten beim Finden geeigneter Sätze von Eigenwerten zu überwinden, so dass das inverse SLP-Problem effektiv gelöst werden kann. Als nächstes wird eine konkrete Implementierung des von Barcilon (1974) vorgeschlagenen inversen Sturm-Liouville-Problemalgorithmus bereitgestellt. Weiterhin wird die rechnerische Durchführbarkeit und Anwendbarkeit dieses Algorithmus zur Lösung inverser Sturm-Liouville-Probleme der Ordnung n=2,4 erfolgreich verifiziert. Es wird beobachtet, dass das Verfahren selbst bei Vorhandensein von signifikantem Rauschen erfolgreich ist, vorausgesetzt, dass die Annahmen des Algorithmus erfüllt sind. Zusammenfassend stellt diese Arbeit Methoden zur Verfügung, die erfolgreich zur Lösung eines direkten (regulär/singulären) oder inversen SLP beliebiger Ordnung mit beliebigen Randbedingungen angepasst werden können. KW - Sturm-Liouville problem KW - Inverse Sturm-Liouville problem KW - Higher-order Sturm-Liouville problem KW - Sturm-Liouville-Problem höherer Ordnung KW - Inverses Sturm-Liouville-Problem KW - Sturm-Liouville-Problem Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-530064 ER - TY - THES A1 - Maier, Corinna T1 - Bayesian data assimilation and reinforcement learning for model-informed precision dosing in oncology T1 - Bayes’sche Datenassimilation und Reinforcement Learning für die modellinformierte Präzisionsdosierung in der Onkologie N2 - While patients are known to respond differently to drug therapies, current clinical practice often still follows a standardized dosage regimen for all patients. For drugs with a narrow range of both effective and safe concentrations, this approach may lead to a high incidence of adverse events or subtherapeutic dosing in the presence of high patient variability. Model-informedprecision dosing (MIPD) is a quantitative approach towards dose individualization based on mathematical modeling of dose-response relationships integrating therapeutic drug/biomarker monitoring (TDM) data. MIPD may considerably improve the efficacy and safety of many drug therapies. Current MIPD approaches, however, rely either on pre-calculated dosing tables or on simple point predictions of the therapy outcome. These approaches lack a quantification of uncertainties and the ability to account for effects that are delayed. In addition, the underlying models are not improved while applied to patient data. Therefore, current approaches are not well suited for informed clinical decision-making based on a differentiated understanding of the individually predicted therapy outcome. The objective of this thesis is to develop mathematical approaches for MIPD, which (i) provide efficient fully Bayesian forecasting of the individual therapy outcome including associated uncertainties, (ii) integrate Markov decision processes via reinforcement learning (RL) for a comprehensive decision framework for dose individualization, (iii) allow for continuous learning across patients and hospitals. Cytotoxic anticancer chemotherapy with its major dose-limiting toxicity, neutropenia, serves as a therapeutically relevant application example. For more comprehensive therapy forecasting, we apply Bayesian data assimilation (DA) approaches, integrating patient-specific TDM data into mathematical models of chemotherapy-induced neutropenia that build on prior population analyses. The value of uncertainty quantification is demonstrated as it allows reliable computation of the patient-specific probabilities of relevant clinical quantities, e.g., the neutropenia grade. In view of novel home monitoring devices that increase the amount of TDM data available, the data processing of sequential DA methods proves to be more efficient and facilitates handling of the variability between dosing events. By transferring concepts from DA and RL we develop novel approaches for MIPD. While DA-guided dosing integrates individualized uncertainties into dose selection, RL-guided dosing provides a framework to consider delayed effects of dose selections. The combined DA-RL approach takes into account both aspects simultaneously and thus represents a holistic approach towards MIPD. Additionally, we show that RL can be used to gain insights into important patient characteristics for dose selection. The novel dosing strategies substantially reduce the occurrence of both subtherapeutic and life-threatening neutropenia grades in a simulation study based on a recent clinical study (CEPAC-TDM trial) compared to currently used MIPD approaches. If MIPD is to be implemented in routine clinical practice, a certain model bias with respect to the underlying model is inevitable, as the models are typically based on data from comparably small clinical trials that reflect only to a limited extent the diversity in real-world patient populations. We propose a sequential hierarchical Bayesian inference framework that enables continuous cross-patient learning to learn the underlying model parameters of the target patient population. It is important to note that the approach only requires summary information of the individual patient data to update the model. This separation of the individual inference from population inference enables implementation across different centers of care. The proposed approaches substantially improve current MIPD approaches, taking into account new trends in health care and aspects of practical applicability. They enable progress towards more informed clinical decision-making, ultimately increasing patient benefits beyond the current practice. N2 - Obwohl Patienten sehr unterschiedlich auf medikamentöse Therapien ansprechen, werden in der klinischen Praxis häufig noch standardisierte Dosierungsschemata angewendet. Bei Arzneimitteln mit engen therapeutischen Fenstern zwischen minimal wirksamen und toxischen Konzentrationen kann dieser Ansatz bei hoher interindividueller Variabilität zu häufigem Auftreten von Toxizitäten oder subtherapeutischen Konzentrationen führen. Die modellinformierte Präzisionsdosierung (MIPD) ist ein quantitativer Ansatz zur Dosisindividualisierung, der auf der mathematischen Modellierung von Dosis-Wirkungs-Beziehungen beruht und Daten aus dem therapeutischen Drug/Biomarker-Monitoring (TDM) einbezieht. Die derzeitigen MIPD-Ansätze verwenden entweder Dosierungstabellen oder einfache Punkt-Vorhersagen des Therapieverlaufs. Diesen Ansätzen fehlt eine Quantifizierung der Unsicherheiten, verzögerte Effekte werden nicht berücksichtigt und die zugrunde liegenden Modelle werden im Laufe der Anwendung nicht verbessert. Daher sind die derzeitigen Ansätze nicht ideal für eine fundierte klinische Entscheidungsfindung auf Grundlage eines differenzierten Verständnisses des individuell vorhergesagten Therapieverlaufs. Das Ziel dieser Arbeit ist es, mathematische Ansätze für das MIPD zu entwickeln, die (i) eine effiziente, vollständig Bayes’sche Vorhersage des individuellen Therapieverlaufs einschließlich der damit verbundenen Unsicherheiten ermöglichen, (ii) Markov-Entscheidungsprozesse mittels Reinforcement Learning (RL) in einen umfassenden Entscheidungsrahmen zur Dosisindividualisierung integrieren, und (iii) ein kontinuierliches Lernen zwischen Patienten erlauben. Die antineoplastische Chemotherapie mit ihrer wichtigen dosislimitierenden Toxizität, der Neutropenie, dient als therapeutisch relevantes Anwendungsbeispiel. Für eine umfassendere Therapievorhersage wenden wir Bayes’sche Datenassimilationsansätze (DA) an, um TDM-Daten in mathematische Modelle der Chemotherapie-induzierten Neutropenie zu integrieren. Wir zeigen, dass die Quantifizierung von Unsicherheiten einen großen Mehrwert bietet, da sie eine zuverlässige Berechnung der Wahrscheinlichkeiten relevanter klinischer Größen, z.B. des Neutropeniegrades, ermöglicht. Im Hinblick auf neue Home-Monitoring-Geräte, die die Anzahl der verfügbaren TDM-Daten erhöhen, erweisen sich sequenzielle DA-Methoden als effizienter und erleichtern den Umgang mit der Unsicherheit zwischen Dosierungsereignissen. Basierend auf Konzepten aus DA und RL, entwickeln wir neue Ansätze für MIPD. Während die DA-geleitete Dosierung individualisierte Unsicherheiten in die Dosisauswahl integriert, berücksichtigt die RL-geleitete Dosierung verzögerte Effekte der Dosisauswahl. Der kombinierte DA-RL-Ansatz vereint beide Aspekte und stellt somit einen ganzheitlichen Ansatz für MIPD dar. Zusätzlich zeigen wir, dass RL Informationen über die für die Dosisauswahl relevanten Patientencharakteristika liefert. Der Vergleich zu derzeit verwendeten MIPD Ansätzen in einer auf einer klinischen Studie (CEPAC-TDM-Studie) basierenden Simulationsstudie zeigt, dass die entwickelten Dosierungsstrategien das Auftreten subtherapeutischer Konzentrationen sowie lebensbedrohlicher Neutropenien drastisch reduzieren. Wird MIPD in der klinischen Routine eingesetzt, ist eine gewisse Modellverzerrung unvermeidlich. Die Modelle basieren in der Regel auf Daten aus vergleichsweise kleinen klinischen Studien, die die Heterogenität realer Patientenpopulationen nur begrenzt widerspiegeln. Wir schlagen einen sequenziellen hierarchischen Bayes’schen Inferenzrahmen vor, der ein kontinuierliches patientenübergreifendes Lernen ermöglicht, um die zugrunde liegenden Modellparameter der Ziel-Patientenpopulation zu erlernen. Zur Aktualisierung des Modells erfordert dieser Ansatz lediglich zusammenfassende Informationen der individuellen Patientendaten, was eine Umsetzung über verschiedene Versorgungszentren hinweg erlaubt. Die vorgeschlagenen Ansätze verbessern die derzeitigen MIPD-Ansätze erheblich, wobei neue Trends in der Gesundheitsversorgung und Aspekte der praktischen Anwendbarkeit berücksichtigt werden. Damit stellen sie einen Fortschritt in Richtung einer fundierteren klinischen Entscheidungsfindung dar. KW - data assimilation KW - Datenassimilation KW - reinforcement learning KW - model-informed precision dosing KW - pharmacometrics KW - oncology KW - modellinformierte Präzisionsdosierung KW - Onkologie KW - Pharmakometrie KW - Reinforcement Learning Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-515870 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 -