Clinical Research and Health Care

The health care system has experienced a proliferation of innovations aimed at enhancing life expectancy, quality of life, diagnostic and treatment options, as well as efficiency and cost effectiveness. The general trends into patient-specific treatment, optimal therapy planning, and molecular medicine require continuous innovations in our ability to understand bio-medical processes in detail. Predictive models for complex bio-medical processes and digital precision medicine more and more complement the traditional lab-based approaches to answer these needs.

Simultaneously, recent years have seen a revolution regarding experimental techniques in basic biomedical research. New techniques in microscopy, sequencing, and many other fields provide unprecedented resolution in observing cellular processes in vivo simultaneously on many temporal and spatial scales. The thus obtained data alone cannot uncover the hidden laws. But, in combination with new models and massive simulation, it promises deeper insights into the complex processes of life.

Mathematics is essential for more realistic modelling, simulation and visualization of life processes from the molecular up to the organ-level in combination with large-scale analysis of biomedical and medical imaging data. For example, there are many success stories regarding modelling, simulation and optimization based on partial differential equations in application to patient-specific surgery planning, joint movement, or in medical imaging. In addition, younger areas like stochastic optimal control of infection kinetics, metastability analysis of stochastic processes in application to molecular dynamics in drug design or particle-based reaction diffusion models for cellular processes have entered the focus of this application field.



Topics

  • reliable patient-specific joint simulations
  • PDE-constrained optimal control in biomechanics
  • seamless integration of molecular and cellular dynamics
  • stochastic optimal control of pharmacological interventions
  • data-driven multiscale modelling of cellular reaction networks
  • inverse problems in medical imaging
  • shape statistics and shape trajectories in anatomy reconstruction
  • multiscale modelling of ligand-target association in drug design


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: 01.06.2014 - 31.05.2017
    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
  • 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
  • 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: 01.06.2014 - 31.05.2017
    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

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Financed by others

  • 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

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