Running projects

Financed by ECMath

  • CH1

    Reduced basis methods in orthopedic hip surgery planning

    Prof. Dr. Ralf Kornhuber / Dr.-Ing. Stefan Zachow

    Project heads: Prof. Dr. Ralf Kornhuber / Dr.-Ing. Stefan Zachow
    Project members: Dr. Jonathan Youett
    Duration: -
    Status: running
    Located at: Freie Universität Berlin

    Description

    This project aims at the development, analysis and implementation of algorithms for computer-assisted planning in hip surgery and hip joint replacement by fast virtual test. Fast forward simulations of patient-specific motion of hip joints and implants in 3D shall be enabled by exploiting suitable a priori information. To this end, we will derive, analyze, and implement reduced basis methods for heterogeneous joint models (reduced approximation).

    http://www.mi.fu-berlin.de/en/math/groups/ag-numerik/projects/A-CH1/index.html
  • CH2

    Sparse compressed sensing based classifiers for -omics mass-data

    Prof. Dr. Tim Conrad / Prof. Dr. Gitta Kutyniok / Prof. Dr. Christof Schütte

    Project heads: Prof. Dr. Tim Conrad / Prof. Dr. Gitta Kutyniok / Prof. Dr. Christof Schütte
    Project members: Nada Cvetkovic / Martin Genzel
    Duration: -
    Status: running
    Located at: Freie Universität Berlin / Technische Universität Berlin

    Description

    Tumor diseases rank among the most frequent causes of death in Western countries coinciding with an incomplete understanding of the underlying pathogenic mechanisms and a lack of individual treatment options. Hence, early diagnosis of the disease and early relapse monitoring are currently the best available options to improve patient survival. In this project, we aim for the identification of disease specific sets of biological signals that reliably indicate a disease outbreak (or status) in an individual. Such biological signals (e.g. proteomics or genomics data) are typically very large (millions of dimensions), which significantly increases the complexity of algorithms for analyzing the parameter space or makes them even infeasible. However, these types of data usually exhibit a very particular structure, and at the same time, the set of disease specific features is very small compared to the ambient dimension. Such a high-dimensional setting naturally calls for the application of the concept of sparse classifiers, which has been extensively studied in the fields of compressed sensing and statistical learning during the last decade. Our research focuses on both algorithmic improvements of available methods as well as theoretical results such as recovery guarantees for general data models.

    http://medicalbioinformatics.de/research/projects/ecmath-ch2
  • CH3

    Multiview geometry for ophthalmic surgery simulation

    Prof. Dr. Michael Joswig

    Project heads: Prof. Dr. Michael Joswig
    Project members: André Wagner
    Duration: -
    Status: running
    Located at: Technische Universität Berlin

    Description

    A fundamental problem in machine vision asks to generate geometric information about a scene in 3-space from several camera images. This is relevant, e.g., in the context of augmented reality frameworks for eye surgery simulation. It is the goal of this project to apply techniques from geometric combinatorics and algebraic geometry for analyzing the picture space to allow for a profound computational preprocessing.

    http://page.math.tu-berlin.de/~wagner/CH3.htm
  • CH4

    Optimal control of chemical reaction systems and application to drug resistance mitigating therapy

    Prof. Dr. Carsten Hartmann / Dr. Max von Kleist / PD Dr. Marcus Weber

    Project heads: Prof. Dr. Carsten Hartmann / Dr. Max von Kleist / PD Dr. Marcus Weber
    Project members: Wei Zhang
    Duration: -
    Status: running
    Located at: Freie Universität Berlin

    Description

    Development and spread of drug resistant microorganisms is a major health issue which, accompanied by an attrition in drug development, is expected to worsen in the near future. The source of drug resistance development is the inadequate use of antimicrobials: Inadequate therapies insufficiently suppress susceptible strains, which may give rise to a drug resistant type. At the same time, inadequate therapy exerts enough selective pressure to provide the newly emerged resistant strain with a selective advantage that allows it to become fixed in the population. In recent years, we have elaborated the idea, that an optimal switching between existing antimicrobial drugs may mitigate drug resistance development in the individual. Drug resistance development is an intrinsically stochastic process. This process can be accurately described by the chemical master equation (CME). A major mathematical drawback is the fact that the CME cannot be solved directly due to its numerical complexity. Therefore, computation of an optimal control/therapy based on a direct numerical solution of the CME is usually not feasible. The aim of the proposed project is to mathematically characterize and develop optimal control policies derived from approximations of the CME, and to use the developed methods to suggest drug mitigating therapies to clinical partners in the field of HIV-1 and antibiotic resistance.

    http://systems-pharmacology.de/?page_id=621
  • CH5

    Model classification under uncertainties for cellular signaling networks

    Prof. Dr. Alexander Bockmayr / Prof. Dr. Susanna Röblitz / Prof. Dr. Heike Siebert

    Project heads: Prof. Dr. Alexander Bockmayr / Prof. Dr. Susanna Röblitz / Prof. Dr. Heike Siebert
    Project members: Stefanie Kasielke / Adam Streck
    Duration: -
    Status: running
    Located at: Freie Universität Berlin / Konrad-Zuse-Zentrum für Informationstechnik Berlin

    Description

    Mathematical modelling in biological and medical applications is almost always faced with the problem of incomplete and noisy data. Rather than adding unsupported assumptions to obtain a unique model, a different approach generates a pool of models in agreement with all available observations. Analysis and classification of such models allow linking the constraints imposed by the data to essential model characteristics and showcase different implementations of key mechanisms. Within the project, we aim at combining the advantages of logical and continuous modeling to arrive at a comprehensive system analysis under data uncertainty. Model classification will integrate qualitative aspects such as characteristics of the network topology with more quantitative information extracted from clustering of joint parameter distributions derived from Bayesian approaches. The theory development is accompanied by and tested in application to oncogenic signaling networks.

    http://www.mi.fu-berlin.de/en/math/groups/dibimath/projects/A-CH5/index.html
  • CH6

    Uncertainty quantification for Bayesian inverse problems with applications to systems biology

    Prof. Dr. Susanna Röblitz / Prof. Dr. Christof Schütte

    Project heads: Prof. Dr. Susanna Röblitz / Prof. Dr. Christof Schütte
    Project members: Dr Ilja Klebanov
    Duration: -
    Status: running
    Located at: Konrad-Zuse-Zentrum für Informationstechnik Berlin

    Description

    In biotechnology, systems biology, or reaction engineering one is faced with large systems of ordinary differential equations (ODE) that are used to describe the kinetics of the reaction network of interest. These ODE models contain a large number of mostly unknown kinetic parameters that one needs to infer from usually sparse and noisy experimental data. Typically, inverse problems like classical parameter identification are associated with ill-posed behaviour. However, Bayesian approaches can be used to recover joint parameter distributions and allow for the quantification of uncertainty and risk in a way demanded by the applications. In this project, we want to overcome the computational limitations of classical Markov-chain Monte-Carlo methods by developing new algorithmic approaches to Bayesian inverse problems using, e.g., sparse approximation results or empirical Bayes methods. The methods will directly be applied to large-scale networks in systems biology.

    http://www.zib.de/projects/UQ-systems-biology
  • CH7

    Network-of-Network based -omics data integration

    Prof. Dr. Tim Conrad / Prof. Dr. Christof Schütte

    Project heads: Prof. Dr. Tim Conrad / Prof. Dr. Christof Schütte
    Project members: -
    Duration: -
    Status: running
    Located at: Freie Universität Berlin

    Description

    Project Background

    Pancreatic cancer is the fifth leading cause of cancer death in Germany (see DKFZ Report, 2010). It is estimated that in 2030 it will be the second leading cause of cancer death incurring a cost of about 15,8 Billion US-Dollar worldwide to the public health systems.

    Cancer is a systems disease

    "Cancer is no more a disease of cells than a traffic jam is a disease of cars. A lifetime of study of the internal-combustion engine would not help anyone to understand our traffic problems.'" (Smithers1962). It is accepted that gene mutations are part of the process of cancer, but mutations alone are not enough. Cancer involves an interaction between neoplastic cells and surrounding tissue on many different levels, e.g. interaction of RNA molecules, proteins, and metabolites. But most available models are limited to only one or very few levels of interactions and describe a rather static view.

    From single to multi source: data integration on a systems level

    Current high-throughput -omics technologies have dramatically eased the production of part lists for a variety of organisms. What is still missing are the dynamic interactions among an organism's molecular parts, and the interactions between different biological levels, such as transcriptomics and proteomics. This is pivotal to better understanding of an organism's biology, and - in our case - to understand pancreas cancer.

    Therefore, the aim of this project is two-fold: (1) use data acquired in our earlier projects to create a holistic integration of the aforementioned sources and levels for modeling pancreas cancer, which we call Network-of-Networks or short: NoN (in our context networks of different -omics levels, such as genomics, transcriptomics, proteomics and metabolomics. (2) A NoN is a very large and complex object and its structure differs significantly from other biological networks. Thus, new methods for complexity reduction and analyzing NoNs will be developed in this project.

    http://medicalbioinformatics.de/research/projects/ecmath-ch7
  • CH8

    X-ray based anatomy reconstruction with low radiation exposure

    Hon Prof. Hans-Christian Hege / Dr. Martin Weiser / Dr.-Ing. Stefan Zachow

    Project heads: Hon Prof. Hans-Christian Hege / Dr. Martin Weiser / Dr.-Ing. Stefan Zachow
    Project members: Dennis Jentsch
    Duration: -
    Status: running
    Located at: Konrad-Zuse-Zentrum für Informationstechnik Berlin

    Description

    Medical imaging is essential in diagnostics and surgery planning. For representation of bony structures different imaging modalities are used; the leading methods are X-ray projection (projectional radiography) and CT. Disadvantage of these imaging techniques is the ionization caused by X-rays, particularly in CT, where the dose is 250-500 times higher than in classic X-ray projection. From the clinical perspective therefore one would like to replace CT acquisitions by a few possible X-ray projections. The project deals with the ill-posed inverse problem of 3D reconstruction of bony structures from 2D radiographs. Virtual radiographs are generated from virtual bone structure models; these are compared with clinical patient images and incrementally changed until a sufficiently accurate bone model is found whose virtual projections fit to the measured data. By using a statistical shape model as prior knowledge it is possible to formulate a well-posed optimization problem in a Bayesian setting. Using gradient methods and multilevel/multiresolution methods for both the reconstruction parameters and image data, good computational performance is achieved. Uncertainty quantification techniques can be applied to describe the spatially varying accuracy of the reconstructed model. Finding best X-ray projections (recording directions) minimizing both uncertainty and radiation exposure leads to a design of experiments problem. Two flavors of this design optimization are considered: An all-at-once approach finding the best image acquisition setup before any X-ray projections are performed, and a sequential approach determining the best next projection direction based on the accumulated knowledge gained from the previously taken images.

    http://www.zib.de/projects/x-ray-based-anatomy-reconstruction-low-radiation-exposure
  • CH9

    Adaptive algorithms for optimization of hip implant positioning

    Dr. Martin Weiser / Dr.-Ing. Stefan Zachow

    Project heads: Dr. Martin Weiser / Dr.-Ing. Stefan Zachow
    Project members: Marian Moldenhauer
    Duration: -
    Status: running
    Located at: Konrad-Zuse-Zentrum für Informationstechnik Berlin

    Description

    This project aims at a software environment supporting computer-assisted planning for total hip joint replacement by suggesting implant positions optimized for longevity of bone implants. The aim is to pre-operatively assess stress distribution in bone and to determine an optimal implant position with respect to natural function and stress distribution to prevent loosening, early migration, stress shielding, undesired bone remodeling, and fracture. Increasing the longevity of implants will help to enhance quality of life and reduce the cost of health care in aging societies. Focus of the research is the development of efficient optimization algorithms by adaptive quadrature of the high-dimensional space of daily motions and appropriate choice of tolerances for the underlying dynamic contact solver.

    http://www.zib.de/projects/adaptive-algorithms-optimization-hip-implant-positioning
  • CH10

    Analysis and numerics of the chemical master equation

    Prof. Dr. Harry Yserentant

    Project heads: Prof. Dr. Harry Yserentant
    Project members: Janina Oertel
    Duration: 01.06.2014 - 31.05.2017
    Status: running
    Located at: Technische Universität Berlin

    Description

    The chemical master equation is a fundamental equation in chemical kinetics. It underlies the classical reaction-rate equations and takes the stochastic effects into account that cannot be neglected in the case of small population numbers.

    There is an ongoing effort to tackle the chemical master equation numerically. The major challenge is its high dimensionality: for a system of d interacting species the chemical master equation is a differential equation with state space N_0^d, N_0 the set of nonnegative integers.

    The main goal of project A-CH10 is build a sound mathematical basis for the numerical approximation of the chemical master equation and to put numerical methods for this equation on a firm mathematical ground.

    http://www.tu-berlin.de/?id=168383




Financed by others

  • CH-TU25

    Weak convergence of numerical methods for stochastic partial differential equations with applications to neurosciences

    Dr. Raphael Kruse

    Project heads: Dr. Raphael Kruse
    Project members: -
    Duration: 01.05.2014 - 31.05.2017
    Status: running
    Located at: Technische Universität Berlin

    Description

    In this project we develop and investigate novel numerical methods for the discretization of stochastic partial differential equations arising, for instance, in neuroscience. Our numerical methods are based on the Galerkin finite element method combined with suitable time stepping schemes such as the backward Euler method or backward difference formulas.

    http://www.math.tu-berlin.de/fachgebiete_ag_modnumdiff/diffeqs/v_menue/fg_differentialgleichungen/nwg_uq0/v_menue/research_projects/weak_convergence_of_numerical_methods_for_spdes_with_applications_to_neurosciences/
  • CH-AP2

    Genealogies and inference for populations with highly skewed offspring distributions under further evolutionary forces

    Prof. Dr. Jochen Blath

    Project heads: Prof. Dr. Jochen Blath
    Project members: -
    Duration: 01.10.2012 - 30.06.2018
    Status: running
    Located at: Technische Universität Berlin

    Description

    Multiple merger coalescent modeling and analysis has up to now been mainly focused on neutral, haploid, single-locus set-ups. The central aim of this project is to develop the stochastic models, theoretical results and inference methods required to effectively describe and analyse the observed patterns of genetic variation in sequence data in real populations with skewed offspring distributions under the influence of further evolutionary forces, especially recombination, selection and population structure; in other words, the systematic development of the basics of a `mathematical population genetics for highly variableoffspring distributions'. Given recent progress in DNA sequencing technology, and insight in the limitations of inference methods based single locus set-ups, particular emphasis will be put on realistic diploid multi-locus models and the corresponding statistical machinery for data analysis.

    http://www.dfg-spp1590.de/abstracts.php#5
  • CH-AP7

    Efficient calculation of slow and stationary scales in molecular dynamics

    Prof. Dr. Frank Noé

    Project heads: Prof. Dr. Frank Noé
    Project members: -
    Duration: 01.10.2014 - 30.06.2018
    Status: running
    Located at: Freie Universität Berlin

    Description



  • CH-AP8

    Probing scales in equilibrated systems by optimal nonequilibrium forcing

    Prof. Dr. Carsten Hartmann / Prof. Dr. Christof Schütte / PD Dr. Marcus Weber

    Project heads: Prof. Dr. Carsten Hartmann / Prof. Dr. Christof Schütte / PD Dr. Marcus Weber
    Project members: -
    Duration: 01.10.2014 - 30.06.2018
    Status: running
    Located at: Freie Universität Berlin

    Description



  • CH-AP9

    Origin of the scaling cascades in protein dynamics

    Prof. Dr. Carsten Hartmann

    Project heads: Prof. Dr. Carsten Hartmann
    Project members: -
    Duration: 01.10.2014 - 30.06.2018
    Status: running
    Located at: Freie Universität Berlin

    Description

    The molecular dynamics of proteins and peptides is a hierarchical process which in­volves characteristic time scales ranging from 10-12 seconds to 100 seconds. Although the physical models of the local intramolecular interactions are relatively well devel­oped, and molecular dynamics simulations have proven successful in recovering the dynamics of large-scale biomolecular systems, a mathematical understanding of how local interactions in the molecular root model give rise to a cascade of processes on different time scales is still lacking.
    In this project we will investigate how these scaling cascades arise from the physical models of molecular dynamics and develop mathematical tools for their analysis. Our root model is a diffusion in a high-dimensional potential energy landscape that mod­els the local interactions between atoms or groups of atoms. The local interactions in the molecular force .eld (i.e., the gradient of the potential energy) then induce long-range effects and may give rise to the observed long time scales on the order of seconds. Yet the predictability of molecular dynamics with respect to variations in the physical parameters (e.g., force .eld parameters) or boundary conditions (e.g., temperature) is re­markably poor, the reason being the nonlinearity, the large dimensionality of the models and noise present in the systems, which altogether promote large-scale effects induced by small noise or slow collective motions of atoms or groups of atoms.
    For molecular systems with reversible dynamics, the relevant so-called implied time scales are related to the dominant eigenvalues of the underlying Markov generator. These eigenvalues can be estimated from molecular dynamics simulations and serve as approximations of experimentally measurable quantities. In molecular dynamics simu­lations it is possible to selectively tune the strength of a speci.c physical interaction (e.g., strength of long-range forces between different amino acids) or boundary conditions (e.g., temperature or pH), rendering them an ideal tool for analyzing the connection between root model and observed time scales. To investigate how the cascades of time scales arise in molecular dynamics we will extend numerical continuation methods for dynamical systems to stochastic molecular systems in order to study the changes in the implied time scales under variation of force .eld parameters or boundary conditions. We will compare analytical results to results from numerical simulations (classical and ab-initio molecular dynamics) and to results from infrared (IR) spectroscopy. Despite its popularity in the protein folding community, implied time scales are only one possible way to quantify molecular dynamics time scales. For instance, the exponen­tial convergence rate towards the thermodynamic equilibrium state is closely linked to experimentally measurable quantities. A second focus of the project is therefore to com­pare quantities which represent these relaxation time scales. To this end we will extend the numerical continuation approach to other observables, such as entropy production rates that, in certain cases, can be related to the shape of the molecular potential or Han­kel singular values that characterize the response of the system to the environmental noise and can be related to the typical residence time of a conformation.
    The understanding how scaling cascades in protein dynamics originate from the known hierarchy of physical interactions will be crucial for the development of multi-scale models, which consistently capture time scales on any desired level of coarseness. Moreover it will yield insight into biological phenomena such as allosteric regulation mechanisms or pathological misfolding events caused by single-point mutations.

    http://sfb1114.imp.fu-berlin.de/research/index.php?option=com_projectlog&view=project&id=9
  • CH-AP10

    Multiscale modeling and simulation for spatiotemporal master equations

    Prof. Dr. Frank Noé / Prof. Dr. Christof Schütte

    Project heads: Prof. Dr. Frank Noé / Prof. Dr. Christof Schütte
    Project members: -
    Duration: 01.10.2014 - 30.06.2018
    Status: running
    Located at: Freie Universität Berlin

    Description

    Accurate modeling of reaction kinetics is important for understanding the functionality of biological cells and the design of chemical reactors. Depending on the particle con­centrations and on the relation between particle mobility and reaction rate constants, different mathematical models are appropriate. In the limit of slow diffusion and small concentrations, both discrete particle numbers and spatial inhomogeneities must be taken into account. The most detailed root model consists of particle-based reaction-diffusion dynamics (PBRD), where all individual par­ticles are explicitly resolved in time and space, and particle positions are propagated by some equation of motion, and reaction events may occur only when reactive species are adjacent.
    For rapid diffusion or large concentrations, the model may be coarse-grained in dif­ferent ways. Rapid diffusion leads to mixing and implies that spatial resolution is not needed below a certain lengthscale. This permits the system to be modeled via a spa­tiotemporal chemical Master equation (STCME), i.e. a coupled set of chemical Master equations acting on spatial subvolumes. The STCME becomes a chemical Master equa­tion (CME) when diffusion is so fast that the entire system is well-mixed. When particle concentrations are large, populations may be described by concentrations rather than by discrete numbers, leading to a PDE or ODE formulation.

    Many biological processes call for detailed models (PBRD, ST-CME or CME), but these models are extremely costly to solve. Ef.cient mathematical and computational methods are needed in order to approximate the solutions of these models with some guaranteed accuracy level. An approach to optimal or ef.cient switching between different models is, as yet, missing.
    In this project, we will set out to develop a multiscale theory for reaction kinetics processes, starting from a consistent and well-de.ned formulation of PBRD models, and including spatial scaling (PBRD <-> ST-CME <-> CME) coupled to population scaling (CME <-> ODE). In particular, we aim at providing solutions for the problematic cases of having particles at diverse copy numbers (CME . ODE) and at least some slowly diffusing particles (PBRD <-> CME <-> STCME). The cascades of scales in these scenarios and efficient approximation strategies will be explored.

    http://sfb1114.imp.fu-berlin.de/research/index.php?option=com_projectlog&view=project&id=12
  • CH-AP12

    pcCells - physicochemical principles of cellular information processing

    Prof. Dr. Frank Noé

    Project heads: Prof. Dr. Frank Noé
    Project members: -
    Duration: 01.01.2013 - 31.12.2017
    Status: running
    Located at: Freie Universität Berlin

    Description

    Biological cells are able to perform complex signal transduction tasks quickly, energy-efficiently and yet in a robust and noise-tolerant manner. These signal transduction tasks rely on intracellular information processing mechanisms in which chemical signals are sent, transmitted and received and the state of the overall machinery is stored in chemical or conformational switches. The physicochemical principles of information processing in cells is still not well understood, owing to fundamental restrictions in resolution in experiments and in sampling of molecular dynamics simulations. Here, we will develop new simulation methods based on adaptive molecular dynamics and Markov models. These methods, together with new statistical mechanical theories and single-molecule experimental analyses will be employed to investigate the molecular basis of intracellular signal processing mechanisms. Central to our proposal is the hypothesis that intracellular signal processing relies on spatiotemporal order of molecules arising from dynamical sorting. This hypothesis will be tested using examples of protein-ligand and protein-protein sorting in neuronal signalling. The proposed project is highly multidisciplinary, involving physical chemistry, computer science, mathematics and biology.

    http://compmolbio.biocomputing-berlin.de/index.php/projects/80-erc
  • CH-AP14

    Conformational dynamics of biomolecules: Reconciling simulation and experimental data

    Prof. Dr. Frank Noé

    Project heads: Prof. Dr. Frank Noé
    Project members: -
    Duration: 01.01.2012 - 31.12.2018
    Status: running
    Located at: Freie Universität Berlin

    Description

    We develop methods for constructing kinetic models of biomolecular conformation dynamics from single-molecule experimental data, or by reconciling kinetic experimental data and molecular dynamics simulation data. In the present funding period we aim at developing an approach to directly compute MSMs from single-molecule experiments, with the following main objectives:
    1. Estimate conformation dynamics (eigenvalues, eigenvectors of the underlying Markovian dynamics) directly from single-molecule trajectories.
    2. Quantify the estimation errors of 1.
    3. Applications to optical tweezer data (collaboration with Susan Marqusee).
    4. Use 1. to compute improved Markov state models; Applications to simulation data.
    5. Provide publicly available software implementation.


    http://compmolbio.biocomputing-berlin.de/index.php/projects/91-dfg825-2-2
  • CH-AP16

    Projection theory of transfer operators

    Prof. Dr. Christof Schütte / PD Dr. Marcus Weber

    Project heads: Prof. Dr. Christof Schütte / PD Dr. Marcus Weber
    Project members: -
    Duration: 01.01.2014 - 31.12.2017
    Status: running
    Located at: Konrad-Zuse-Zentrum für Informationstechnik Berlin

    Description

    The main object is analysing sufficent ways to compute a galerkin approximation of the transfer operator. This includes to study the theoretical properties of a galerkin approximation of specific systems and to development algorithms which guarantee those properties for the numerical approximation. Furthermore, one is interested in making this computation as cheap as possible.

    http://www.zib.de/projects/projection-theory-transfer-operators
  • CH-AP19

    Meth4SysPharm: Modeling methods for systems pharmacology and application to HIV-1

    Dr. Max von Kleist

    Project heads: Dr. Max von Kleist
    Project members: -
    Duration: 01.03.2014 - 01.03.2019
    Status: running
    Located at: Freie Universität Berlin

    Description

    'Systems pharmacology' denotes the application of systems biology approaches to research questions arising in pharmacology. The aim is to understand the interaction of drugs with com- plex biological networks and to use this knowledge to develop- and improve medical therapy. Within the proposed project we will address unsolved mathematical challenges arising from this novel, interdisciplinary approach. We will integrate knowledge and data from three subtopics in order to study the mechanisms of drug resistance development in HIV-1, as a model system. In close cooperation with experts from the respective fields, the systems' response to drug interference, in terms of 'evolutionary dynamics' will be assessed alongside with the temporal resolution of drug interference ('drug action and pharmacokinetics') and their implications for the 'optimal use of therapy'. The proposed research program is expected to provide methodologi- cal advance that allows projecting these interrelations into measurable clinical outcomes, while addressing a relevant medical problem at the same time.

    http://page.mi.fu-berlin.de/vkleist/CurrentProjects.htm
  • CH-AP20

    Integrative mathematical modeling of physiological- and molecular factors of osteoarthritis of the knee

    Dr. Max von Kleist

    Project heads: Dr. Max von Kleist
    Project members: -
    Duration: 01.03.2014 - 01.03.2018
    Status: running
    Located at: Freie Universität Berlin

    Description

    Osteoarthritis of the knee (OAK) is a complex multi-factorial condition that is characterised by a lack of hyaline cartilage self repair 1, inflammation & pain 2. As for many other multi-factorial conditions, computational models may be useful tools of direct clinical relevance that allow studying the interaction of putative factors. Within this subproject, we want to develop a comprehensive computational model of cartilage homeostasis that will help us to understand and to evaluate the onset and progression of OAK. While the underlying mechanisms of OAK remain unknown, several factors have been previously associated with osteoarthritis and studied in isolation, such as cell density-dependent extracellular matrix (EM) generation 3,4, EM metabolism 5, the effect of nutrient gradients 5,6 and the influence of (mechano-) growth factors 7.

    Our research group has a broad expertise in interdisciplinary research in biomedicine 8,11 with a particular focus on mechanistic mathematical modelling 8,9 including in vitro to in vivo extrapolation, as well as the analysis of complex clinical samples 10. Within this consortium, we aspire to combine biochemical data from PrevOP subprojects SP1-3 (inflammation, cartilage self-repair & pain) and OVERLOAD projects SP5, 7-8 (fluid transport, mechano-sensitive signalling, cartilage self-repair), to successively develop mathematical models of cartilage homeostasis. Particularly, integration of results from OVERLOAD SP5 may allow to couple image-derived clinical data to metabolic events in the cartilage. The developed comprehensive model of OAK will further our understanding of the disease and the interplay of the mentioned factors, provide insights into disease mechanisms and strategies for its prevention (like, e.g. physical training). The aim of the project is thus to provide a translational framework between in vitro bio-molecular studies, ex vivo analysis, animal models and human patients with OAK (clinical projects in PrevOP/OVERLOAD).

    http://overload-prevop.charite.de/verbund/m_v_kleist_cschuette/
  • CH-AP24

    Free Boundary Problems and Level Set Methods

    Prof. Dr. Michael Hintermüller

    Project heads: Prof. Dr. Michael Hintermüller
    Project members: -
    Duration: 01.05.2011 - 31.03.2018
    Status: running
    Located at: Humboldt Universität Berlin

    Description

    Project part FREELEVEL will focus on two research streams: (i) shape and topological sensitivity-based solvers in tomography and (ii) the extension of spatially adapted regularization to more general image restoration problems, e.g., involving blind deconvolution, and non-convex regularization. Concerning tomography problems, a level-set-based algorithm relying on shape and extended topological sensitivities will be realized for FDOT and MIT, respectively. For MIT, first a reduced model leading to an elliptic PDE-system will be studied and, in a next step, the full Maxwell system will be taken into account. For numerical efficiency purposes, a shape-aware adaptive finite element method will be intertwined with the level-set solver (partly with FEMBEM). In the area of image restoration, we are motivated by optical diffusion tomography problems for detecting objects located behind turbid media and by convolution identification in dual-MR techniques (MRI). We formulate these problems in terms of blind deconvolution, preferably with non-convex regularization with respect to the image. The resulting problems will be studied and solved numerically. With respect to the latter - split Bregman - iteratively re-weighted total variation and semismooth Newton solvers will be investigated. Further, motivated by sparse magnetic resonance imaging, problems in compressed sensing with convex (OPTIM) and non-convex relaxation (MRI) of the 0-norm will be treated. The latter is interesting as there is evidence that non-convex regularization goes along with a possible reduction in acquired data. Further, FREELEVEL will focus on topics supporting other projects, such as piecewise polynomial Mumford-Shah based image segmentation using topological sensitivities (INVERSE).

    Within the SFB, FREELEVEL acts as a center of expertise for shape and topological sensitivity-based level-set solvers for tomography problems. Moreover, FREELEVEL contributes expertise and software in image restoration to the SFB through various cooperations with practitioners (MRI) as well as the applied mathematics group within the SFB (OPTIM, INVERSE).

    http://math.uni-graz.at/mobis/freelevel.html