TY - GEN A1 - Ehrig, Rainald A1 - Nowak, Ulrich T1 - Algorithmen- und Softwareoptimierung für die Satellitenbahn- und Schwerefeldmodellierung N2 - Dieser Report enthält die Ergebnisse der Untersuchungen, die gemäss dem Forschungs-- und Entwicklungsvertrag Gravity zwischen dem GeoForschungsZentrum Potsdam und dem Konrad--Zuse--Zentrum Berlin vorgenommen wurden. Die damit vereinbarte wissenschaftliche Kooperation hat die folgenden Ziele: \item{die am GFZ vorhandenen Algorithmen und Softwaremodule auf ihre Effizienz hisichtlich Nutzung der Rechnerresourcen zu untersuchen und Lösungen für einen schnelleren Datendurchsatz zu entwickeln und zu implementieren,} \item{Methoden zur Regularisierung und Lösung schlecht konditionierter Normalgleichungssysteme (für Schwerefeldkoeffizienten) kritisch zu untersuchen und eine mathematisch objektive Strategie der Regularisierung zu entwickeln, und} \item{insbesondere im Hinblick auf die Anforderungen bei GRACE, verschiedene Bahnintegrationsverfahren hinsichtlich ihrer numerischen Genauigkeit und Einsatzmöglichkeiten zu untersuchen.} T3 - ZIB-Report - 00-01 KW - geodesy KW - gravity field models KW - regularization KW - ill-posed systems KW - orbit integration Y1 - 2000 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-5694 ER - TY - GEN A1 - Schlegel, Martin A1 - Marquardt, Wolfgang A1 - Ehrig, Rainald A1 - Nowak, Ulrich T1 - Sensitivity analysis of linearly-implicit differential-algebraic systems by one-step extrapolation N2 - In this work we present an approach for the sensitivity analysis of linearly-implicit differential-algebraic equation systems. Solutions for both, states and sensitivities are obtained by applying an extrapolated linearly implicit Euler discretization scheme. This approach is compared to the widely used sensitivity extensions of multi-step BDF methods by means of case studies. Especially, we point out the benefit of this method in the context of dynamic optimization using the sequential approach. T3 - ZIB-Report - 02-38 KW - sensitivity evaluation KW - differential-algebraic systems KW - extrapolation methods KW - dynamic optimization KW - optimal control Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7052 ER - TY - GEN A1 - Ehrig, Rainald A1 - Ofenloch, Oliver A1 - Schaber, Karlheinz A1 - Deuflhard, Peter T1 - Modelling and Simulation of Aerosol Formation by Heterogeneous Nucleation in Gas-Liquid Contact Devices N2 - This paper describes a new simulation tool for the prediction of aerosol formation and behavior in gas--liquid contact devices such as absorbers, scrubbers, quench coolers, and condensers as well as multistage gas cleaning processes, respectively. Aerosol formation can impact severely the separation efficiency of gas cleaning processes. Aerosol or fog formation can arise by spontaneous condensation or desublimation in supersaturated gas phases. The rigorous description of the mass and energy transfer between the gas phase, the liquid phase, and the growing aerosol droplets leads to a system of partial differential and algebraic equations. For the solution of these systems we have developed the plant simulation tool AerCoDe. This program bases upon the linearly--implicit Euler discretisation, which in combination with extrapolation permits an adaptive step size and order control. Typical simulation results of a multistage industrial flue gas scrubbing process are presented. It is shown, that experimental data can be confirmed if the number concentration of condensation nuclei as an input parameter is roughly known. T3 - ZIB-Report - 01-15 KW - aerosols KW - heterogeneous nucleation KW - two-phase flow KW - balance equations KW - extrapolation methods Y1 - 2001 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-6416 ER - TY - GEN A1 - Ehrig, Rainald A1 - Nowak, Ulrich A1 - Deuflhard, Peter T1 - Highly scalable parallel linearly-implicit extrapolation algorithms N2 - We present parallel formulations of the well established extrapolation algorithms EULSIM and LIMEX and its implementation on a distributed memory architecture. The discretization of partial differential equations by the method of lines yields large banded systems, which can be efficiently solved in parallel only by iterative methods. Polynomial preconditioning with a Neumann series expansion combined with an overlapping domain decomposition appears as a very efficient, robust and highly scalable preconditioner for different iterative solvers. A further advantage of this preconditioner is that all computation can be restricted to the overlap region as long as the subdomain problems are solved exactly. With this approach the iterative algorithms operate on very short vectors, the length of the vectors depends only on the number of gridpoints in the overlap region and the number of processors, but not on the size of the linear system. As the most reliable and fast iterative methods based on this preconditioning scheme appeared GMRES or FOM and BICGSTAB. To further reduce the number of iterations in GMRES or FOM we can reuse the Krylov-spaces constructed in preceeding extrapolation steps. The implementation of the method within the program LIMEX results in a highly parallel and scalable program for solving differential algebraic problems getting an almost linear speedup up to 64 processors even for medium size problems. Results are presented for a difficult application from chemical engineering simulating the formation of aerosols in industrial gas exhaust purification. T3 - ZIB-Report - TR-96-11 Y1 - 1996 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-5405 ER - TY - GEN A1 - Ehrig, Rainald A1 - Nowak, Ulrich A1 - Deuflhard, Peter T1 - Massively Parallel Linearly-Implicit Extrapolation Algorithms as a Powerful Tool in Process Simulation. N2 - We study the parallelization of linearly--implicit extrapolation codes for the solution of large scale PDE systems and differential algebraic equations on distributed memory machines. The main advantage of these algorithms is that they enable adapativity both in time and space. Additive Krylov--Schwarz methods yield high parallel perfomance for such extrapolation methods. Our approach combines a slightly overlapping domain decomposition together with a polynomial block Neumann preconditioner and a reduced system technique. Furthermore we get important advantages through the explicit computation of the matrix--products of the preconditioner and the matrix of the linear system. The parallel algorithms exhibit scalability up to 64 processors already for medium--sized test problems. We show that the codes are really efficient in large application systems for chemical engineering problems. T3 - ZIB-Report - SC-97-43 Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-3127 ER - TY - GEN A1 - Ehrig, Rainald A1 - Deuflhard, Peter T1 - GMERR - an Error Minimizing Variant of GMRES N2 - The paper analyzes a recently proposed iterative error minimizing method for the solution of linear systems. Sufficient and necessary conditions for convergence are studied, which show that the method essentially requires normal matrices. An efficient implementation similar to GMRES has been worked out in detail. Numerical tests on general non--normal matrices, of course, indicate that this approach is not competitive with GMRES. Summarizing, if error minimizing is important, one should rather choose CGNE. A computational niche for GMERR might be problems, where normal but non--symmetric matrices occur, like dissipative quantum mechanics. T3 - ZIB-Report - SC-97-63 Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-3323 ER - TY - GEN A1 - Nowak, Ulrich A1 - Ehrig, Rainald A1 - Oeverdieck, Lars T1 - Parallel Extrapolation Methods and Their Application in Chemical Engineering N2 - We study the parallelization of linearly--implicit extrapolation methods for the solution of large scale systems of differential algebraic equations arising in a method of lines (MOL ) treatment of partial differential equations. In our approach we combine a slightly overlapping domain decomposi tion together with a polynomial block Neumann preconditioner. Through the explicit computation of the matrix products of the pre conditioner and the system matrix a significant gain in overall efficiency is achieved for medium--sized problems. The parallel algorithm exhibits a good scalability up to 32 proces sors on a Cray T3E. Preliminary results for computations on a workstation cluster are reported. T3 - ZIB-Report - SC-97-69 Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-3387 ER - TY - JOUR A1 - Bergmann, G. A1 - Graichen, F. A1 - Rohlmann, A. A1 - Bender, Alwina A1 - Ehrig, Rainald A1 - Westerhoff, P. A1 - Heinlein, B. T1 - Design and calibration of load sensing orthopaedic implants JF - Journal Biomech. Eng. Y1 - 2008 SP - 02109 EP - 1–02109–9 ER - TY - JOUR A1 - Schaber, Karlheinz A1 - Koerber, Jens A1 - Ofenloch, O. A1 - Ehrig, Rainald A1 - Deuflhard, Peter T1 - Aerosol Formation in Gas-Liquid Contact Devices- Nucleation, Growth and Particle Dynamics JF - Chem.Eng.Sci. Y1 - 2002 VL - 57 SP - 4345 EP - 4356 ER - TY - CHAP A1 - Nowak, Ulrich A1 - Ehrig, Rainald A1 - Oeverdieck, Lars ED - Sloot, P. ED - Bubak, Marian ED - Hertzberger, B. T1 - Parallel Extrapolation Methods and Their Application in Chemical Engineering T2 - High-Performance Computing and Networking Y1 - 1998 VL - 1401 SP - 419 EP - 428 PB - Springer ER - TY - JOUR A1 - Schlegel, Martin A1 - Marquardt, Wolfgang A1 - Ehrig, Rainald A1 - Nowak, Ulrich T1 - Sensitivity analysis of linearly-implicit differential-algebraic systems by one-step extrapolation JF - Applied Numerical Mathematics Y1 - 2004 IS - 48 SP - 83 EP - 102 ER - TY - JOUR A1 - Ehrig, Rainald A1 - Taylor, William R. A1 - Duda, G. A1 - Heller, Markus O. T1 - A Survey for Formal Methods for Determining the Centre of Ball Joints JF - Journal of Biomechanics Y1 - 2006 IS - 39 SP - 2798 EP - 2809 ER - TY - CHAP A1 - Ehrig, Rainald A1 - Taylor, William R. A1 - Duda, G. A1 - Heller, Markus O. T1 - A New Approach for the Determination of Joint Axes T2 - Proceedings of the 52th Annual Meeting of the Orthopedic Society Y1 - 2006 CY - Chicago ER - TY - CHAP A1 - Ehrig, Rainald A1 - Nowak, Ulrich A1 - Deuflhard, Peter ED - Khoroshevsky, V. T1 - Massively Parallel Simulation in Chemical Engineering by Extrapolation Algorithms T2 - Procs. 16th International Workshop on Distributed Data Processing, Novosibirsk, Russia Y1 - 1998 SP - 1 EP - 6 ER - TY - CHAP A1 - Ehrig, Rainald A1 - Nowak, Ulrich A1 - Oeverdieck, Lars A1 - Deuflhard, Peter ED - H.-J. Bungartz, F. T1 - Advanced Extrapolation Methods for Large Scale Differential Algebraic Problems T2 - High Performance Scientific and Engineering Computing Y1 - 1999 VL - 8 SP - 233 EP - 244 PB - Springer Verlag ER - TY - JOUR A1 - Ehrig, Rainald A1 - Ofenloch, O. A1 - Schaber, Karlheinz A1 - Deuflhard, Peter T1 - Modelling and Simulation of Aerosol Formation by Heterogeneous Nucleation in Gas-Liquid Contact Devices JF - Chem.Eng.Sci. Y1 - 2002 VL - 57 IS - 7 SP - 1151 EP - 1163 ER - TY - JOUR A1 - Heller, Markus O. A1 - Duda, Georg A1 - Ehrig, Rainald A1 - Schell, H. A1 - Seebeck, P. A1 - Taylor, William R. T1 - Muskuloskeletale Belastungen im Schafshinterlauf JF - Materialwissenschaft und Werkstofftechnik Y1 - 2005 IS - 36 SP - 775 EP - 780 ER - TY - CHAP A1 - Heller, Markus O. A1 - Duda, G. A1 - König, Christian A1 - Taylor, William R. A1 - Ehrig, Rainald A1 - Hinterwimmer, S. A1 - Graichen, H. T1 - Validation of a New Model of Human Knee Kinematics against in Vivo Data under Physiologic Neuromuscular Activation Patterns T2 - Proceedings of the 51th Annual Meeting of the Orthopedic Society Y1 - 2005 CY - Washington ER - TY - JOUR A1 - Heller, Markus O. A1 - König, Christian A1 - Graichen, F. A1 - Hinterwimmer, S. A1 - Ehrig, Rainald A1 - Duda, G. A1 - Taylor, William R. T1 - A new model to predict in vivo human knee kinematics under physiological-like muscle activation JF - Journal of Biomechanics Y1 - 2007 SP - 45 EP - 53 ER - TY - JOUR A1 - Koerber, Jens A1 - Schaber, Karlheinz A1 - Ehrig, Rainald A1 - Deuflhard, Peter T1 - Modelling and simulation of aerosol formation in absorption processes JF - J. Aerosol Sci Y1 - 1998 VL - 29 SP - 579 EP - 580 ER - TY - CHAP A1 - Kratzenstein, Stefan A1 - Taylor, William R. A1 - Ehrig, Rainald A1 - Heller, Markus O. T1 - Reduction of the influence of skin marker artefacts using the optimal common shape technique T2 - Annual meeting of the ESMAC 2009 Y1 - 2009 CY - London ER - TY - CHAP A1 - Kassi, J.-P. A1 - Taylor, William R. A1 - Schwarzkopf, J. A1 - Schell, H. A1 - Duda, G. A1 - Ehrig, Rainald T1 - Wie sind Osteosynthesesysteme und Defektzonen in vivo belastet? T2 - 68. Jahrestagung der Deutschen Gesellschaft für Unfallchirurgie in Verbindung mit dem Deutschen Orthopädenkongress Y1 - 2004 CY - Berlin ER - TY - JOUR A1 - Kratzenstein, Stefan A1 - Kornaropoulos, Evgenios I. A1 - Ehrig, Rainald A1 - Heller, Markus O. A1 - Pöpplau, Berry M. A1 - Taylor, William R. T1 - Effective marker placement for functional identification of the centre of rotation at the hip JF - Gait & Posture Y1 - 2012 U6 - https://doi.org/http://dx.doi.org/10.1016/j.gaitpost.2012.04.011 VL - 36 IS - 3 SP - 482 EP - 486 ER - TY - JOUR A1 - Stötzel, Claudia A1 - Ehrig, Rainald A1 - Boer, H. Marike T. A1 - Plöntzke, Julia A1 - Röblitz, Susanna T1 - Exploration of different wave patterns in a model of the bovine estrous cycle by Fourier analysis JF - BIOMAT - Proceedings of the 14th International Symposium on Mathematical and Computational Biology, Bedlewo, Poland N2 - Cows typically have different numbers of follicular waves during their hormonal cycle. Understanding the underlying regulations leads to insights into the reasons for declined fertility, a phenomenon that has been observed during the last decades. We present a systematic approach based on Fourier analysis to examine how parameter changes in a model of the bovine estrous cycle lead to different wave patterns. Even without any biological considerations, this allows to detect the responsible model parameters that control the type of periodicity of the solution, thus supporting experimental planning of animal scientists. Y1 - 2014 ER - TY - JOUR A1 - Moualeu-Ngangue, Dany Pascal A1 - Weiser, Martin A1 - Ehrig, Rainald A1 - Deuflhard, Peter T1 - Optimal control for a tuberculosis model with undetected cases in Cameroon JF - Communications in Nonlinear Science and Numerical Simulation N2 - This paper considers the optimal control of tuberculosis through education, diagnosis campaign and chemoprophylaxis of latently infected. A mathematical model which includes important components such as undiagnosed infectious, diagnosed infectious, latently infected and lost-sight infectious is formulated. The model combines a frequency dependent and a density dependent force of infection for TB transmission. Through optimal control theory and numerical simulations, a cost-effective balance of two different intervention methods is obtained. Seeking to minimize the amount of money the government spends when tuberculosis remain endemic in the Cameroonian population, Pontryagin's maximum principle is used to characterize the optimal control. The optimality system is derived and solved numerically using the forward-backward sweep method (FBSM). Results provide a framework for designing cost-effective strategies for diseases with multiple intervention methods. It comes out that combining chemoprophylaxis and education, the burden of TB can be reduced by 80 % in 10 years. Y1 - 2015 U6 - https://doi.org/10.1016/j.cnsns.2014.06.037 VL - 20 IS - 3 SP - 986 EP - 1003 ER - TY - JOUR A1 - Hengartner, Michael A1 - Krüger, Tillmann H. C. A1 - Geraedts, Kirsten A1 - Tronci, Enrico A1 - Mancini, Toni A1 - Ille, Fabian A1 - Egli, Marcel A1 - Röblitz, Susanna A1 - Ehrig, Rainald A1 - Saleh, Lanja A1 - Spanaus, Katharina A1 - Schippert, Cordula A1 - Zhang, Yuanyuan A1 - Leeners, Brigitte T1 - Negative affect is unrelated to fluctuations in hormone levels across the menstrual cycle: evidence from a multisite observational study across two successive cycles JF - Journal of Psychosomatic Research Y1 - 2017 U6 - https://doi.org/10.1016/j.jpsychores.2017.05.018 VL - 99 SP - 21 EP - 27 ER - TY - JOUR A1 - Moewis, Philippe A1 - Boeth, Heide A1 - Heller, Markus O. A1 - Yntema, Caroline A1 - Jung, Tobias A1 - Doyscher, Ralf A1 - Ehrig, Rainald A1 - Zhong, Yanlin A1 - Taylor, William R. T1 - Towards understanding knee joint laxity: Errors in non-invasive assessment of joint rotation can be corrected JF - Medical Engineering and Physics Y1 - 2014 U6 - https://doi.org/doi.org/10.1016/j.medengphy.2014.03.017 VL - 36 IS - 7 SP - 889 EP - 895 ER - TY - JOUR A1 - Ehrig, Rainald A1 - Heller, Markus O. T1 - On intrinsic equivalences of the finite helical axis, the instantaneous helical axis, and the SARA approach. A mathematical perspective. JF - Journal of Biomechanics Y1 - 2019 U6 - https://doi.org/10.1016/j.jbiomech.2018.12.034 VL - 84 SP - 4 EP - 10 ER - TY - JOUR A1 - Lang, Annemarie A1 - Volkamer, Andrea A1 - Behm, Laura A1 - Röblitz, Susanna A1 - Ehrig, Rainald A1 - Schneider, Marlon A1 - Geris, Lisbet A1 - Wichard, Joerg A1 - Buttgereit, Frank T1 - In silico Methods - Computational Alternatives to Animal Testing JF - ALTEX N2 - A seminar and interactive workshop on “In silico Methods – Computational Alternatives to Animal Testing” was held in Berlin, Germany, organized by Annemarie Lang, Frank Butt- gereit and Andrea Volkamer at the Charité-Universitätsmedizin Berlin, on August 17-18, 2017. During the half-day seminar, the variety and applications of in silico methods as alternatives to animal testing were presented with room for scientific discus- sions with experts from academia, industry and the German fed- eral ministry (Fig. 1). Talks on computational systems biology were followed by detailed information on predictive toxicology in order to display the diversity of in silico methods and the potential to embrace them in current approaches (Hartung and Hoffmann, 2009; Luechtefeld and Hartung, 2017). The follow- ing interactive one-day Design Thinking Workshop was aimed at experts, interested researchers and PhD-students interested in the use of in silico as alternative methods to promote the 3Rs (Fig. 2). Forty participants took part in the seminar while the workshop was restricted to sixteen participants. Y1 - 2018 U6 - https://doi.org/10.14573/altex.1712031 VL - 35 IS - 1 SP - 126 EP - 128 ER - TY - CHAP A1 - Taylor, William R. A1 - Kratzenstein, Stefan A1 - Kornaropoulos, Evgenios I. A1 - Ehrig, Rainald A1 - Moewis, Philippe A1 - Heller, Markus O. T1 - Non-invasive Assessment of Skeletal Kinematics T2 - Measurement and Sensing in Medicine and Health Y1 - 2009 CY - London ER - TY - CHAP A1 - Taylor, William R. A1 - Kornaropoulos, Evgenios I. A1 - Kratzenstein, Stefan A1 - Ehrig, Rainald A1 - Plank, F. A1 - Heller, Markus O. T1 - Targeted Marker Placement for the Functional Identification of the Hip Joint Centre T2 - Transactions Vol. 36, 2011 Annual Meeting of the Orthopedic Society Y1 - 2011 CY - Long Beach ER - TY - CHAP A1 - Taylor, William R. A1 - König, Christian A1 - Speirs, A. A1 - Ehrig, Rainald A1 - Duda, G. A1 - Heller, Markus O. T1 - The medio-lateral force distribution in the sheep knee during walking T2 - 5. World Congress of Biomechanics, Munich, Journal of Biomechanics Y1 - 2006 IS - 39, Suppl. 1 SP - S491 ER - TY - CHAP A1 - Taylor, William R. A1 - König, Christian A1 - Speirs, A. A1 - Ehrig, Rainald A1 - Duda, G. A1 - Heller, Markus O. T1 - Die medio-laterale Kraftverteilung im Schafsknie T2 - Deutscher Kongress für Orthpädie und Unfallchirurgie, Berlin Y1 - 2006 ER - TY - CHAP A1 - Taylor, William R. A1 - Kassi, J.-P. A1 - Schwarzkopf, J. A1 - Ehrig, Rainald A1 - Schell, H. A1 - Duda, G. T1 - The Profile of Mechanical Loading is Independent of Fracture Fixation Principle T2 - Proceedings of the 51th Annual Meeting of the Orthopedic Society Y1 - 2005 CY - Washington ER - TY - JOUR A1 - Schaber, Karlheinz A1 - Ofenloch, Oliver A1 - Ehrig, Rainald A1 - Deuflhard, Peter T1 - Aerosolbildung in Gas/Flüssigkeits-Kontaktapparaten - Modellierungsstrategien und Simulation JF - Chemie Ingenieur Technik Y1 - 2004 VL - 76 IS - 9 SP - 1358 EP - 1359 ER - TY - CHAP A1 - Taylor, William R. A1 - Ehrig, Rainald A1 - Duda, G. A1 - Heller, Markus O. T1 - The determination of joint axes T2 - 5. World Congress of Biomechanics, Munich, Journal of Biomechanics Y1 - 2006 IS - 39, Suppl. 1 SP - S571 EP - S572 ER - TY - CHAP A1 - Taylor, William R. A1 - Ehrig, Rainald A1 - Duda, G. A1 - Heller, Markus O. T1 - The Symmetrical Axis of Rotation Approach (SARA) for Determination of Joint Axes in Clinical Gait Analysis T2 - 1st Joint ESMAC-GCMAS Meeting, Amsterdam Y1 - 2006 ER - TY - CHAP A1 - Taylor, William R. A1 - Ehrig, Rainald A1 - Heller, Markus O. A1 - Schell, H. A1 - Duda, G. T1 - Can Skin Markers Determine the Kinematics of Underlying Bones? T2 - Proceedings of the 50th Annual Meeting of the Orthopedic Society Y1 - 2004 CY - San Francisco ER - TY - JOUR A1 - Taylor, William R. A1 - Ehrig, Rainald A1 - Heller, Markus O. A1 - Schell, H. A1 - Klein, P. A1 - Duda, G. T1 - On the Influence of Soft Tissue Coverage in the Determination of Bone Kinematics using Bone Markers JF - Journal of Orthopedic Research Y1 - 2005 IS - 23 SP - 726 EP - 734 ER - TY - CHAP A1 - Taylor, William R. A1 - Ehrig, Rainald A1 - Heller, Markus O. A1 - Schell, H. A1 - Seebeck, P. A1 - Duda, G. T1 - Animal Models for Knee Injury Frequently Underestimate the Mechanical Conditions of the Clinical Situation T2 - Proceedings of the 51th Annual Meeting of the Orthopedic Society Y1 - 2005 CY - Washington ER - TY - JOUR A1 - Taylor, William R. A1 - Ehrig, Rainald A1 - Heller, Markus O. A1 - Schell, H. A1 - Seebeck, P. A1 - Duda, G. T1 - Tibio-femoral Joint Contact Forces in Sheep JF - Journal of Biomechanics Y1 - 2006 IS - 39 SP - 791 EP - 798 ER - TY - JOUR A1 - Wix, A. A1 - Schaber, Karlheinz A1 - Ofenloch, O. A1 - Ehrig, Rainald A1 - Deuflhard, Peter T1 - Simulation of Aerosol Formation in Gas-Liquid Contact Devices JF - Chem. Eng. Comm. Y1 - 2007 VL - 194 SP - 565 EP - 577 ER - TY - GEN A1 - Stötzel, Claudia A1 - Ehrig, Rainald A1 - Boer, H. Marike T. A1 - Plöntzke, Julia A1 - Röblitz, Susanna T1 - Exploration of different wave patterns in a model of the bovine estrous cycle by Fourier analysis N2 - Cows typically have different numbers of follicular waves during their hormonal cycle. Understanding the underlying regulations leads to insights into the reasons for declined fertility, a phenomenon that has been observed during the last decades. We present a systematic approach based on Fourier analysis to examine how parameter changes in a model of the bovine estrous cycle lead to different wave patterns. Even without any biological considerations, this allows to detect the responsible model parameters that control the type of periodicity of the solution, thus supporting experimental planning of animal scientists. T3 - ZIB-Report - 16-02 Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-57039 SN - 1438-0064 ER - TY - CHAP A1 - Hajizadeh, Maryam A1 - Schütz, Pascal A1 - List, Renate A1 - Boeth, Heide A1 - Ehrig, Rainald A1 - Postolka, Barbara A1 - Freeman, Michael A. R. A1 - Taylor, William R. T1 - Interpretation of tibio-femoral kinematics critically depends upon the kinematic analysis approach T2 - ISB 2015, 25th congress of the International Society of Biomechanics, Glasgow Y1 - 2015 ER - TY - GEN A1 - Moualeu-Ngangue, Dany Pascal A1 - Röblitz, Susanna A1 - Ehrig, Rainald A1 - Deuflhard, Peter T1 - Parameter Identification for a Tuberculosis Model in Cameroon N2 - A deterministic model of tuberculosis in sub-Saharan Africa in general and Cameroon in particular including lack of access to the treatment and weak diagnose capacity is designed and analyzed with respect to its transmission dynamics. The model includes both frequency- and density-dependent transmissions. It is shown that the model is mathematically well-posed and epidemiologically reasonable. Solutions are non-negative and bounded whenever the initial values are non-negative. A sensitivity analysis of model parameters is performed and most sensitive parameters of the model are identified using a state-of-the-art Gauss-Newton Method. In particular, parameters representing the proportion of individuals having access to medical facilities have a large impact on the dynamics of the disease. It has been shown that an increase of these parameter values over the time can significantly reduce the disease burden in the population within the next 15 years. T3 - ZIB-Report - 13-72 KW - Tuberculosis, parameter identification, sensitivity analysis, Gauss-Newton method, Nonlinear dynamical systems. Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-43087 SN - 1438-0064 ER - TY - GEN A1 - Moualeu-Ngangue, Dany Pascal A1 - Weiser, Martin A1 - Ehrig, Rainald A1 - Deuflhard, Peter T1 - Optimal control for a tuberculosis model with undetected cases in Cameroon N2 - This paper considers the optimal control of tuberculosis through education, diagnosis campaign and chemoprophylaxis of latently infected. A mathematical model which includes important components such as undiagnosed infectious, diagnosed infectious, latently infected and lost-sight infectious is formulated. The model combines a frequency dependent and a density dependent force of infection for TB transmission. Through optimal control theory and numerical simulations, a cost-effective balance of two different intervention methods is obtained. Seeking to minimize the amount of money the government spends when tuberculosis remain endemic in the Cameroonian population, Pontryagin's maximum principle is used to characterize the optimal control. The optimality system is derived and solved numerically using the forward-backward sweep method (FBSM). Results provide a framework for designing cost-effective strategies for diseases with multiple intervention methods. It comes out that combining chemoprophylaxis and education, the burden of TB can be reduced by 80 % in 10 years T3 - ZIB-Report - 13-73 KW - Tuberculosis KW - Optimal control KW - Nonlinear dynamical systems Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-43142 SN - 1438-0064 ER - TY - JOUR A1 - Moualeu-Ngangue, Dany Pascal A1 - Röblitz, Susanna A1 - Ehrig, Rainald A1 - Deuflhard, Peter T1 - Parameter Identification in a Tuberculosis Model for Cameroon JF - PLOS ONE N2 - A deterministic model of tuberculosis in Cameroon is designed and analyzed with respect to its transmission dynamics. The model includes lack of access to treatment and weak diagnosis capacity as well as both frequency- and density-dependent transmissions. It is shown that the model is mathematically well-posed and epidemiologically reasonable. Solutions are non-negative and bounded whenever the initial values are non-negative. A sensitivity analysis of model parameters is performed and the most sensitive ones are identified by means of a state-of-the-art Gauss-Newton method. In particular, parameters representing the proportion of individuals having access to medical facilities are seen to have a large impact on the dynamics of the disease. The model predicts that a gradual increase of these parameters could significantly reduce the disease burden on the population within the next 15 years. Y1 - 2015 U6 - https://doi.org/10.1371/journal.pone.0120607 ER - TY - JOUR A1 - Weber, Marie-Christin A1 - Fischer, Lisa A1 - Damerau, Alexandra A1 - Ponomarev, Igor A1 - Pfeiffenberger, Moritz A1 - Gaber, Timo A1 - Götschel, Sebastian A1 - Lang, Jens A1 - Röblitz, Susanna A1 - Buttgereit, Frank A1 - Ehrig, Rainald A1 - Lang, Annemarie T1 - In vitro and in silico modeling of cellular and matrix-related changes during the early phase of osteoarthritis JF - BioRxiv N2 - Understanding the pathophysiological processes of osteoarthritis (OA) require adequate model systems. Although different in vitro or in vivo models have been described, further comprehensive approaches are needed to study specific parts of the disease. This study aimed to combine in vitro and in silico modeling to describe cellular and matrix-related changes during the early phase of OA. We developed an in vitro OA model based on scaffold-free cartilage-like constructs (SFCCs), which was mathematically modeled using a partial differential equation (PDE) system to resemble the processes during the onset of OA. SFCCs were produced from mesenchymal stromal cells and analyzed weekly by histology and qPCR to characterize the cellular and matrix-related composition. To simulate the early phase of OA, SFCCs were treated with interleukin-1β (IL-1β), tumor necrosis factor α (TNFα) and examined after 3 weeks or cultivated another 3 weeks without inflammatory cytokines to validate the regeneration potential. Mathematical modeling was performed in parallel to the in vitro experiments. SFCCs expressed cartilage-specific markers, and after stimulation an increased expression of inflammatory markers, matrix degrading enzymes, a loss of collagen II (Col-2) and a reduced cell density was observed which could be partially reversed by retraction of stimulation. Based on the PDEs, the distribution processes within the SFCCs, including those of IL-1β, Col-2 degradation and cell number reduction was simulated. By combining in vitro and in silico methods, we aimed to develop a valid, efficient alternative approach to examine and predict disease progression and new therapeutic strategies. Y1 - 2019 U6 - https://doi.org/10.1101/725317 ER - TY - JOUR A1 - Lang, Annemarie A1 - Fischer, Lisa A1 - Weber, Marie-Christin A1 - Gaber, Timo A1 - Ehrig, Rainald A1 - Röblitz, Susanna A1 - Buttgereit, Frank T1 - Combining in vitro simulation and in silico modelling towards a sophisticated human osteoarthritis model JF - Osteoarthritis and Cartilage N2 - Our project aimed at building an in silico model based on our recently developed in vitro osteoarthritis (OA) model seeking for refinement of the model to enhance validity and translatability towards the more sophisticated simulation of OA. In detail, the previously 3D in vitro model is based on 3D chondrogenic constructs generated solely from human bone marrow derived mesenchymal stromal cells (hMSCs). Besides studying the normal state of the model over 3 weeks, the in vitro model was treated with interleukin-1β (IL-1β) and tumor necrosis factor alpha (TNFα) to mimic an OA-like environment. Y1 - 2019 U6 - https://doi.org/10.1016/j.joca.2019.02.277 VL - 27 SP - S183 ER - TY - JOUR A1 - Weber, Marie-Christin A1 - Fischer, Lisa A1 - Damerau, Alexandra A1 - Ponomarev, Igor A1 - Pfeiffenberger, Moritz A1 - Gaber, Timo A1 - Götschel, Sebastian A1 - Lang, Jens A1 - Röblitz, Susanna A1 - Buttgereit, Frank A1 - Ehrig, Rainald A1 - Lang, Annemarie T1 - Macroscale mesenchymal condensation to study cytokine-driven cellular and matrix-related changes during cartilage degradation JF - Biofabrication N2 - Understanding the pathophysiological processes of cartilage degradation requires adequate model systems to develop therapeutic strategies towards osteoarthritis (OA). Although different in vitro or in vivo models have been described, further comprehensive approaches are needed to study specific disease aspects. This study aimed to combine in vitro and in silico modeling based on a tissue-engineering approach using mesenchymal condensation to mimic cytokine-induced cellular and matrix-related changes during cartilage degradation. Thus, scaffold-free cartilage-like constructs (SFCCs) were produced based on self-organization of mesenchymal stromal cells (mesenchymal condensation) and i) characterized regarding their cellular and matrix composition or secondly ii) treated with interleukin-1β (IL-1β) and tumor necrosis factor α (TNFα) for 3 weeks to simulate OA-related matrix degradation. In addition, an existing mathematical model based on partial differential equations was optimized and transferred to the underlying settings to simulate distribution of IL-1β, type II collagen degradation and cell number reduction. By combining in vitro and in silico methods, we aim to develop a valid, efficient alternative approach to examine and predict disease progression and effects of new therapeutics. Y1 - 2020 U6 - https://doi.org/10.1088/1758-5090/aba08f VL - 12 IS - 4 ER -